Add files using upload-large-folder tool

.gitattributes

@@ -353,3 +353,7 @@ llava_next/lib/python3.10/site-packages/scipy/cluster/__pycache__/hierarchy.cpyt
 llava_next/lib/python3.10/site-packages/scipy/optimize/_moduleTNC.cpython-310-x86_64-linux-gnu.so filter=lfs diff=lfs merge=lfs -text
 parrot/lib/python3.10/site-packages/gradio_client/__pycache__/media_data.cpython-310.pyc filter=lfs diff=lfs merge=lfs -text
 parrot/lib/python3.10/site-packages/torchvision.libs/libjpeg.ceea7512.so.62 filter=lfs diff=lfs merge=lfs -text
+llava_next/lib/python3.10/site-packages/scipy/optimize/_lbfgsb.cpython-310-x86_64-linux-gnu.so filter=lfs diff=lfs merge=lfs -text
+llava_next/lib/python3.10/site-packages/scipy/optimize/_pava_pybind.cpython-310-x86_64-linux-gnu.so filter=lfs diff=lfs merge=lfs -text
+llava_next/lib/python3.10/site-packages/scipy/signal/__pycache__/_filter_design.cpython-310.pyc filter=lfs diff=lfs merge=lfs -text
+llava_next/lib/python3.10/site-packages/scipy/optimize/_cobyla.cpython-310-x86_64-linux-gnu.so filter=lfs diff=lfs merge=lfs -text

llava_next/lib/python3.10/site-packages/scipy/optimize/_basinhopping.py

@@ -0,0 +1,753 @@
+"""
+basinhopping: The basinhopping global optimization algorithm
+"""
+import numpy as np
+import math
+import inspect
+import scipy.optimize
+from scipy._lib._util import check_random_state
+
+__all__ = ['basinhopping']
+
+
+_params = (inspect.Parameter('res_new', kind=inspect.Parameter.KEYWORD_ONLY),
+           inspect.Parameter('res_old', kind=inspect.Parameter.KEYWORD_ONLY))
+_new_accept_test_signature = inspect.Signature(parameters=_params)
+
+
+class Storage:
+    """
+    Class used to store the lowest energy structure
+    """
+    def __init__(self, minres):
+        self._add(minres)
+
+    def _add(self, minres):
+        self.minres = minres
+        self.minres.x = np.copy(minres.x)
+
+    def update(self, minres):
+        if minres.success and (minres.fun < self.minres.fun
+                               or not self.minres.success):
+            self._add(minres)
+            return True
+        else:
+            return False
+
+    def get_lowest(self):
+        return self.minres
+
+
+class BasinHoppingRunner:
+    """This class implements the core of the basinhopping algorithm.
+
+    x0 : ndarray
+        The starting coordinates.
+    minimizer : callable
+        The local minimizer, with signature ``result = minimizer(x)``.
+        The return value is an `optimize.OptimizeResult` object.
+    step_taking : callable
+        This function displaces the coordinates randomly. Signature should
+        be ``x_new = step_taking(x)``. Note that `x` may be modified in-place.
+    accept_tests : list of callables
+        Each test is passed the kwargs `f_new`, `x_new`, `f_old` and
+        `x_old`. These tests will be used to judge whether or not to accept
+        the step. The acceptable return values are True, False, or ``"force
+        accept"``. If any of the tests return False then the step is rejected.
+        If ``"force accept"``, then this will override any other tests in
+        order to accept the step. This can be used, for example, to forcefully
+        escape from a local minimum that ``basinhopping`` is trapped in.
+    disp : bool, optional
+        Display status messages.
+
+    """
+    def __init__(self, x0, minimizer, step_taking, accept_tests, disp=False):
+        self.x = np.copy(x0)
+        self.minimizer = minimizer
+        self.step_taking = step_taking
+        self.accept_tests = accept_tests
+        self.disp = disp
+
+        self.nstep = 0
+
+        # initialize return object
+        self.res = scipy.optimize.OptimizeResult()
+        self.res.minimization_failures = 0
+
+        # do initial minimization
+        minres = minimizer(self.x)
+        if not minres.success:
+            self.res.minimization_failures += 1
+            if self.disp:
+                print("warning: basinhopping: local minimization failure")
+        self.x = np.copy(minres.x)
+        self.energy = minres.fun
+        self.incumbent_minres = minres  # best minimize result found so far
+        if self.disp:
+            print("basinhopping step %d: f %g" % (self.nstep, self.energy))
+
+        # initialize storage class
+        self.storage = Storage(minres)
+
+        if hasattr(minres, "nfev"):
+            self.res.nfev = minres.nfev
+        if hasattr(minres, "njev"):
+            self.res.njev = minres.njev
+        if hasattr(minres, "nhev"):
+            self.res.nhev = minres.nhev
+
+    def _monte_carlo_step(self):
+        """Do one Monte Carlo iteration
+
+        Randomly displace the coordinates, minimize, and decide whether
+        or not to accept the new coordinates.
+        """
+        # Take a random step.  Make a copy of x because the step_taking
+        # algorithm might change x in place
+        x_after_step = np.copy(self.x)
+        x_after_step = self.step_taking(x_after_step)
+
+        # do a local minimization
+        minres = self.minimizer(x_after_step)
+        x_after_quench = minres.x
+        energy_after_quench = minres.fun
+        if not minres.success:
+            self.res.minimization_failures += 1
+            if self.disp:
+                print("warning: basinhopping: local minimization failure")
+        if hasattr(minres, "nfev"):
+            self.res.nfev += minres.nfev
+        if hasattr(minres, "njev"):
+            self.res.njev += minres.njev
+        if hasattr(minres, "nhev"):
+            self.res.nhev += minres.nhev
+
+        # accept the move based on self.accept_tests. If any test is False,
+        # then reject the step.  If any test returns the special string
+        # 'force accept', then accept the step regardless. This can be used
+        # to forcefully escape from a local minimum if normal basin hopping
+        # steps are not sufficient.
+        accept = True
+        for test in self.accept_tests:
+            if inspect.signature(test) == _new_accept_test_signature:
+                testres = test(res_new=minres, res_old=self.incumbent_minres)
+            else:
+                testres = test(f_new=energy_after_quench, x_new=x_after_quench,
+                               f_old=self.energy, x_old=self.x)
+
+            if testres == 'force accept':
+                accept = True
+                break
+            elif testres is None:
+                raise ValueError("accept_tests must return True, False, or "
+                                 "'force accept'")
+            elif not testres:
+                accept = False
+
+        # Report the result of the acceptance test to the take step class.
+        # This is for adaptive step taking
+        if hasattr(self.step_taking, "report"):
+            self.step_taking.report(accept, f_new=energy_after_quench,
+                                    x_new=x_after_quench, f_old=self.energy,
+                                    x_old=self.x)
+
+        return accept, minres
+
+    def one_cycle(self):
+        """Do one cycle of the basinhopping algorithm
+        """
+        self.nstep += 1
+        new_global_min = False
+
+        accept, minres = self._monte_carlo_step()
+
+        if accept:
+            self.energy = minres.fun
+            self.x = np.copy(minres.x)
+            self.incumbent_minres = minres  # best minimize result found so far
+            new_global_min = self.storage.update(minres)
+
+        # print some information
+        if self.disp:
+            self.print_report(minres.fun, accept)
+            if new_global_min:
+                print("found new global minimum on step %d with function"
+                      " value %g" % (self.nstep, self.energy))
+
+        # save some variables as BasinHoppingRunner attributes
+        self.xtrial = minres.x
+        self.energy_trial = minres.fun
+        self.accept = accept
+
+        return new_global_min
+
+    def print_report(self, energy_trial, accept):
+        """print a status update"""
+        minres = self.storage.get_lowest()
+        print("basinhopping step %d: f %g trial_f %g accepted %d "
+              " lowest_f %g" % (self.nstep, self.energy, energy_trial,
+                                accept, minres.fun))
+
+
+class AdaptiveStepsize:
+    """
+    Class to implement adaptive stepsize.
+
+    This class wraps the step taking class and modifies the stepsize to
+    ensure the true acceptance rate is as close as possible to the target.
+
+    Parameters
+    ----------
+    takestep : callable
+        The step taking routine.  Must contain modifiable attribute
+        takestep.stepsize
+    accept_rate : float, optional
+        The target step acceptance rate
+    interval : int, optional
+        Interval for how often to update the stepsize
+    factor : float, optional
+        The step size is multiplied or divided by this factor upon each
+        update.
+    verbose : bool, optional
+        Print information about each update
+
+    """
+    def __init__(self, takestep, accept_rate=0.5, interval=50, factor=0.9,
+                 verbose=True):
+        self.takestep = takestep
+        self.target_accept_rate = accept_rate
+        self.interval = interval
+        self.factor = factor
+        self.verbose = verbose
+
+        self.nstep = 0
+        self.nstep_tot = 0
+        self.naccept = 0
+
+    def __call__(self, x):
+        return self.take_step(x)
+
+    def _adjust_step_size(self):
+        old_stepsize = self.takestep.stepsize
+        accept_rate = float(self.naccept) / self.nstep
+        if accept_rate > self.target_accept_rate:
+            # We're accepting too many steps. This generally means we're
+            # trapped in a basin. Take bigger steps.
+            self.takestep.stepsize /= self.factor
+        else:
+            # We're not accepting enough steps. Take smaller steps.
+            self.takestep.stepsize *= self.factor
+        if self.verbose:
+            print(f"adaptive stepsize: acceptance rate {accept_rate:f} target "
+                  f"{self.target_accept_rate:f} new stepsize "
+                  f"{self.takestep.stepsize:g} old stepsize {old_stepsize:g}")
+
+    def take_step(self, x):
+        self.nstep += 1
+        self.nstep_tot += 1
+        if self.nstep % self.interval == 0:
+            self._adjust_step_size()
+        return self.takestep(x)
+
+    def report(self, accept, **kwargs):
+        "called by basinhopping to report the result of the step"
+        if accept:
+            self.naccept += 1
+
+
+class RandomDisplacement:
+    """Add a random displacement of maximum size `stepsize` to each coordinate.
+
+    Calling this updates `x` in-place.
+
+    Parameters
+    ----------
+    stepsize : float, optional
+        Maximum stepsize in any dimension
+    random_gen : {None, int, `numpy.random.Generator`,
+                  `numpy.random.RandomState`}, optional
+
+        If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+        singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used,
+        seeded with `seed`.
+        If `seed` is already a ``Generator`` or ``RandomState`` instance then
+        that instance is used.
+
+    """
+
+    def __init__(self, stepsize=0.5, random_gen=None):
+        self.stepsize = stepsize
+        self.random_gen = check_random_state(random_gen)
+
+    def __call__(self, x):
+        x += self.random_gen.uniform(-self.stepsize, self.stepsize,
+                                     np.shape(x))
+        return x
+
+
+class MinimizerWrapper:
+    """
+    wrap a minimizer function as a minimizer class
+    """
+    def __init__(self, minimizer, func=None, **kwargs):
+        self.minimizer = minimizer
+        self.func = func
+        self.kwargs = kwargs
+
+    def __call__(self, x0):
+        if self.func is None:
+            return self.minimizer(x0, **self.kwargs)
+        else:
+            return self.minimizer(self.func, x0, **self.kwargs)
+
+
+class Metropolis:
+    """Metropolis acceptance criterion.
+
+    Parameters
+    ----------
+    T : float
+        The "temperature" parameter for the accept or reject criterion.
+    random_gen : {None, int, `numpy.random.Generator`,
+                  `numpy.random.RandomState`}, optional
+
+        If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+        singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used,
+        seeded with `seed`.
+        If `seed` is already a ``Generator`` or ``RandomState`` instance then
+        that instance is used.
+        Random number generator used for acceptance test.
+
+    """
+
+    def __init__(self, T, random_gen=None):
+        # Avoid ZeroDivisionError since "MBH can be regarded as a special case
+        # of the BH framework with the Metropolis criterion, where temperature
+        # T = 0." (Reject all steps that increase energy.)
+        self.beta = 1.0 / T if T != 0 else float('inf')
+        self.random_gen = check_random_state(random_gen)
+
+    def accept_reject(self, res_new, res_old):
+        """
+        Assuming the local search underlying res_new was successful:
+        If new energy is lower than old, it will always be accepted.
+        If new is higher than old, there is a chance it will be accepted,
+        less likely for larger differences.
+        """
+        with np.errstate(invalid='ignore'):
+            # The energy values being fed to Metropolis are 1-length arrays, and if
+            # they are equal, their difference is 0, which gets multiplied by beta,
+            # which is inf, and array([0]) * float('inf') causes
+            #
+            # RuntimeWarning: invalid value encountered in multiply
+            #
+            # Ignore this warning so when the algorithm is on a flat plane, it always
+            # accepts the step, to try to move off the plane.
+            prod = -(res_new.fun - res_old.fun) * self.beta
+            w = math.exp(min(0, prod))
+
+        rand = self.random_gen.uniform()
+        return w >= rand and (res_new.success or not res_old.success)
+
+    def __call__(self, *, res_new, res_old):
+        """
+        f_new and f_old are mandatory in kwargs
+        """
+        return bool(self.accept_reject(res_new, res_old))
+
+
+def basinhopping(func, x0, niter=100, T=1.0, stepsize=0.5,
+                 minimizer_kwargs=None, take_step=None, accept_test=None,
+                 callback=None, interval=50, disp=False, niter_success=None,
+                 seed=None, *, target_accept_rate=0.5, stepwise_factor=0.9):
+    """Find the global minimum of a function using the basin-hopping algorithm.
+
+    Basin-hopping is a two-phase method that combines a global stepping
+    algorithm with local minimization at each step. Designed to mimic
+    the natural process of energy minimization of clusters of atoms, it works
+    well for similar problems with "funnel-like, but rugged" energy landscapes
+    [5]_.
+
+    As the step-taking, step acceptance, and minimization methods are all
+    customizable, this function can also be used to implement other two-phase
+    methods.
+
+    Parameters
+    ----------
+    func : callable ``f(x, *args)``
+        Function to be optimized.  ``args`` can be passed as an optional item
+        in the dict `minimizer_kwargs`
+    x0 : array_like
+        Initial guess.
+    niter : integer, optional
+        The number of basin-hopping iterations. There will be a total of
+        ``niter + 1`` runs of the local minimizer.
+    T : float, optional
+        The "temperature" parameter for the acceptance or rejection criterion.
+        Higher "temperatures" mean that larger jumps in function value will be
+        accepted.  For best results `T` should be comparable to the
+        separation (in function value) between local minima.
+    stepsize : float, optional
+        Maximum step size for use in the random displacement.
+    minimizer_kwargs : dict, optional
+        Extra keyword arguments to be passed to the local minimizer
+        `scipy.optimize.minimize` Some important options could be:
+
+            method : str
+                The minimization method (e.g. ``"L-BFGS-B"``)
+            args : tuple
+                Extra arguments passed to the objective function (`func`) and
+                its derivatives (Jacobian, Hessian).
+
+    take_step : callable ``take_step(x)``, optional
+        Replace the default step-taking routine with this routine. The default
+        step-taking routine is a random displacement of the coordinates, but
+        other step-taking algorithms may be better for some systems.
+        `take_step` can optionally have the attribute ``take_step.stepsize``.
+        If this attribute exists, then `basinhopping` will adjust
+        ``take_step.stepsize`` in order to try to optimize the global minimum
+        search.
+    accept_test : callable, ``accept_test(f_new=f_new, x_new=x_new, f_old=fold, x_old=x_old)``, optional
+        Define a test which will be used to judge whether to accept the
+        step. This will be used in addition to the Metropolis test based on
+        "temperature" `T`. The acceptable return values are True,
+        False, or ``"force accept"``. If any of the tests return False
+        then the step is rejected. If the latter, then this will override any
+        other tests in order to accept the step. This can be used, for example,
+        to forcefully escape from a local minimum that `basinhopping` is
+        trapped in.
+    callback : callable, ``callback(x, f, accept)``, optional
+        A callback function which will be called for all minima found. ``x``
+        and ``f`` are the coordinates and function value of the trial minimum,
+        and ``accept`` is whether that minimum was accepted. This can
+        be used, for example, to save the lowest N minima found. Also,
+        `callback` can be used to specify a user defined stop criterion by
+        optionally returning True to stop the `basinhopping` routine.
+    interval : integer, optional
+        interval for how often to update the `stepsize`
+    disp : bool, optional
+        Set to True to print status messages
+    niter_success : integer, optional
+        Stop the run if the global minimum candidate remains the same for this
+        number of iterations.
+    seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional
+
+        If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+        singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used,
+        seeded with `seed`.
+        If `seed` is already a ``Generator`` or ``RandomState`` instance then
+        that instance is used.
+        Specify `seed` for repeatable minimizations. The random numbers
+        generated with this seed only affect the default Metropolis
+        `accept_test` and the default `take_step`. If you supply your own
+        `take_step` and `accept_test`, and these functions use random
+        number generation, then those functions are responsible for the state
+        of their random number generator.
+    target_accept_rate : float, optional
+        The target acceptance rate that is used to adjust the `stepsize`.
+        If the current acceptance rate is greater than the target,
+        then the `stepsize` is increased. Otherwise, it is decreased.
+        Range is (0, 1). Default is 0.5.
+
+        .. versionadded:: 1.8.0
+
+    stepwise_factor : float, optional
+        The `stepsize` is multiplied or divided by this stepwise factor upon
+        each update. Range is (0, 1). Default is 0.9.
+
+        .. versionadded:: 1.8.0
+
+    Returns
+    -------
+    res : OptimizeResult
+        The optimization result represented as a `OptimizeResult` object.
+        Important attributes are: ``x`` the solution array, ``fun`` the value
+        of the function at the solution, and ``message`` which describes the
+        cause of the termination. The ``OptimizeResult`` object returned by the
+        selected minimizer at the lowest minimum is also contained within this
+        object and can be accessed through the ``lowest_optimization_result``
+        attribute.  See `OptimizeResult` for a description of other attributes.
+
+    See Also
+    --------
+    minimize :
+        The local minimization function called once for each basinhopping step.
+        `minimizer_kwargs` is passed to this routine.
+
+    Notes
+    -----
+    Basin-hopping is a stochastic algorithm which attempts to find the global
+    minimum of a smooth scalar function of one or more variables [1]_ [2]_ [3]_
+    [4]_. The algorithm in its current form was described by David Wales and
+    Jonathan Doye [2]_ http://www-wales.ch.cam.ac.uk/.
+
+    The algorithm is iterative with each cycle composed of the following
+    features
+
+    1) random perturbation of the coordinates
+
+    2) local minimization
+
+    3) accept or reject the new coordinates based on the minimized function
+       value
+
+    The acceptance test used here is the Metropolis criterion of standard Monte
+    Carlo algorithms, although there are many other possibilities [3]_.
+
+    This global minimization method has been shown to be extremely efficient
+    for a wide variety of problems in physics and chemistry. It is
+    particularly useful when the function has many minima separated by large
+    barriers. See the `Cambridge Cluster Database
+    <https://www-wales.ch.cam.ac.uk/CCD.html>`_ for databases of molecular
+    systems that have been optimized primarily using basin-hopping. This
+    database includes minimization problems exceeding 300 degrees of freedom.
+
+    See the free software program `GMIN <https://www-wales.ch.cam.ac.uk/GMIN>`_
+    for a Fortran implementation of basin-hopping. This implementation has many
+    variations of the procedure described above, including more
+    advanced step taking algorithms and alternate acceptance criterion.
+
+    For stochastic global optimization there is no way to determine if the true
+    global minimum has actually been found. Instead, as a consistency check,
+    the algorithm can be run from a number of different random starting points
+    to ensure the lowest minimum found in each example has converged to the
+    global minimum. For this reason, `basinhopping` will by default simply
+    run for the number of iterations `niter` and return the lowest minimum
+    found. It is left to the user to ensure that this is in fact the global
+    minimum.
+
+    Choosing `stepsize`:  This is a crucial parameter in `basinhopping` and
+    depends on the problem being solved. The step is chosen uniformly in the
+    region from x0-stepsize to x0+stepsize, in each dimension. Ideally, it
+    should be comparable to the typical separation (in argument values) between
+    local minima of the function being optimized. `basinhopping` will, by
+    default, adjust `stepsize` to find an optimal value, but this may take
+    many iterations. You will get quicker results if you set a sensible
+    initial value for ``stepsize``.
+
+    Choosing `T`: The parameter `T` is the "temperature" used in the
+    Metropolis criterion. Basinhopping steps are always accepted if
+    ``func(xnew) < func(xold)``. Otherwise, they are accepted with
+    probability::
+
+        exp( -(func(xnew) - func(xold)) / T )
+
+    So, for best results, `T` should to be comparable to the typical
+    difference (in function values) between local minima. (The height of
+    "walls" between local minima is irrelevant.)
+
+    If `T` is 0, the algorithm becomes Monotonic Basin-Hopping, in which all
+    steps that increase energy are rejected.
+
+    .. versionadded:: 0.12.0
+
+    References
+    ----------
+    .. [1] Wales, David J. 2003, Energy Landscapes, Cambridge University Press,
+        Cambridge, UK.
+    .. [2] Wales, D J, and Doye J P K, Global Optimization by Basin-Hopping and
+        the Lowest Energy Structures of Lennard-Jones Clusters Containing up to
+        110 Atoms.  Journal of Physical Chemistry A, 1997, 101, 5111.
+    .. [3] Li, Z. and Scheraga, H. A., Monte Carlo-minimization approach to the
+        multiple-minima problem in protein folding, Proc. Natl. Acad. Sci. USA,
+        1987, 84, 6611.
+    .. [4] Wales, D. J. and Scheraga, H. A., Global optimization of clusters,
+        crystals, and biomolecules, Science, 1999, 285, 1368.
+    .. [5] Olson, B., Hashmi, I., Molloy, K., and Shehu1, A., Basin Hopping as
+        a General and Versatile Optimization Framework for the Characterization
+        of Biological Macromolecules, Advances in Artificial Intelligence,
+        Volume 2012 (2012), Article ID 674832, :doi:`10.1155/2012/674832`
+
+    Examples
+    --------
+    The following example is a 1-D minimization problem, with many
+    local minima superimposed on a parabola.
+
+    >>> import numpy as np
+    >>> from scipy.optimize import basinhopping
+    >>> func = lambda x: np.cos(14.5 * x - 0.3) + (x + 0.2) * x
+    >>> x0 = [1.]
+
+    Basinhopping, internally, uses a local minimization algorithm. We will use
+    the parameter `minimizer_kwargs` to tell basinhopping which algorithm to
+    use and how to set up that minimizer. This parameter will be passed to
+    `scipy.optimize.minimize`.
+
+    >>> minimizer_kwargs = {"method": "BFGS"}
+    >>> ret = basinhopping(func, x0, minimizer_kwargs=minimizer_kwargs,
+    ...                    niter=200)
+    >>> # the global minimum is:
+    >>> ret.x, ret.fun
+    -0.1951, -1.0009
+
+    Next consider a 2-D minimization problem. Also, this time, we
+    will use gradient information to significantly speed up the search.
+
+    >>> def func2d(x):
+    ...     f = np.cos(14.5 * x[0] - 0.3) + (x[1] + 0.2) * x[1] + (x[0] +
+    ...                                                            0.2) * x[0]
+    ...     df = np.zeros(2)
+    ...     df[0] = -14.5 * np.sin(14.5 * x[0] - 0.3) + 2. * x[0] + 0.2
+    ...     df[1] = 2. * x[1] + 0.2
+    ...     return f, df
+
+    We'll also use a different local minimization algorithm. Also, we must tell
+    the minimizer that our function returns both energy and gradient (Jacobian).
+
+    >>> minimizer_kwargs = {"method":"L-BFGS-B", "jac":True}
+    >>> x0 = [1.0, 1.0]
+    >>> ret = basinhopping(func2d, x0, minimizer_kwargs=minimizer_kwargs,
+    ...                    niter=200)
+    >>> print("global minimum: x = [%.4f, %.4f], f(x) = %.4f" % (ret.x[0],
+    ...                                                           ret.x[1],
+    ...                                                           ret.fun))
+    global minimum: x = [-0.1951, -0.1000], f(x) = -1.0109
+
+    Here is an example using a custom step-taking routine. Imagine you want
+    the first coordinate to take larger steps than the rest of the coordinates.
+    This can be implemented like so:
+
+    >>> class MyTakeStep:
+    ...    def __init__(self, stepsize=0.5):
+    ...        self.stepsize = stepsize
+    ...        self.rng = np.random.default_rng()
+    ...    def __call__(self, x):
+    ...        s = self.stepsize
+    ...        x[0] += self.rng.uniform(-2.*s, 2.*s)
+    ...        x[1:] += self.rng.uniform(-s, s, x[1:].shape)
+    ...        return x
+
+    Since ``MyTakeStep.stepsize`` exists basinhopping will adjust the magnitude
+    of `stepsize` to optimize the search. We'll use the same 2-D function as
+    before
+
+    >>> mytakestep = MyTakeStep()
+    >>> ret = basinhopping(func2d, x0, minimizer_kwargs=minimizer_kwargs,
+    ...                    niter=200, take_step=mytakestep)
+    >>> print("global minimum: x = [%.4f, %.4f], f(x) = %.4f" % (ret.x[0],
+    ...                                                           ret.x[1],
+    ...                                                           ret.fun))
+    global minimum: x = [-0.1951, -0.1000], f(x) = -1.0109
+
+    Now, let's do an example using a custom callback function which prints the
+    value of every minimum found
+
+    >>> def print_fun(x, f, accepted):
+    ...         print("at minimum %.4f accepted %d" % (f, int(accepted)))
+
+    We'll run it for only 10 basinhopping steps this time.
+
+    >>> rng = np.random.default_rng()
+    >>> ret = basinhopping(func2d, x0, minimizer_kwargs=minimizer_kwargs,
+    ...                    niter=10, callback=print_fun, seed=rng)
+    at minimum 0.4159 accepted 1
+    at minimum -0.4317 accepted 1
+    at minimum -1.0109 accepted 1
+    at minimum -0.9073 accepted 1
+    at minimum -0.4317 accepted 0
+    at minimum -0.1021 accepted 1
+    at minimum -0.7425 accepted 1
+    at minimum -0.9073 accepted 1
+    at minimum -0.4317 accepted 0
+    at minimum -0.7425 accepted 1
+    at minimum -0.9073 accepted 1
+
+    The minimum at -1.0109 is actually the global minimum, found already on the
+    8th iteration.
+
+    """ # numpy/numpydoc#87  # noqa: E501
+    if target_accept_rate <= 0. or target_accept_rate >= 1.:
+        raise ValueError('target_accept_rate has to be in range (0, 1)')
+    if stepwise_factor <= 0. or stepwise_factor >= 1.:
+        raise ValueError('stepwise_factor has to be in range (0, 1)')
+
+    x0 = np.array(x0)
+
+    # set up the np.random generator
+    rng = check_random_state(seed)
+
+    # set up minimizer
+    if minimizer_kwargs is None:
+        minimizer_kwargs = dict()
+    wrapped_minimizer = MinimizerWrapper(scipy.optimize.minimize, func,
+                                         **minimizer_kwargs)
+
+    # set up step-taking algorithm
+    if take_step is not None:
+        if not callable(take_step):
+            raise TypeError("take_step must be callable")
+        # if take_step.stepsize exists then use AdaptiveStepsize to control
+        # take_step.stepsize
+        if hasattr(take_step, "stepsize"):
+            take_step_wrapped = AdaptiveStepsize(
+                take_step, interval=interval,
+                accept_rate=target_accept_rate,
+                factor=stepwise_factor,
+                verbose=disp)
+        else:
+            take_step_wrapped = take_step
+    else:
+        # use default
+        displace = RandomDisplacement(stepsize=stepsize, random_gen=rng)
+        take_step_wrapped = AdaptiveStepsize(displace, interval=interval,
+                                             accept_rate=target_accept_rate,
+                                             factor=stepwise_factor,
+                                             verbose=disp)
+
+    # set up accept tests
+    accept_tests = []
+    if accept_test is not None:
+        if not callable(accept_test):
+            raise TypeError("accept_test must be callable")
+        accept_tests = [accept_test]
+
+    # use default
+    metropolis = Metropolis(T, random_gen=rng)
+    accept_tests.append(metropolis)
+
+    if niter_success is None:
+        niter_success = niter + 2
+
+    bh = BasinHoppingRunner(x0, wrapped_minimizer, take_step_wrapped,
+                            accept_tests, disp=disp)
+
+    # The wrapped minimizer is called once during construction of
+    # BasinHoppingRunner, so run the callback
+    if callable(callback):
+        callback(bh.storage.minres.x, bh.storage.minres.fun, True)
+
+    # start main iteration loop
+    count, i = 0, 0
+    message = ["requested number of basinhopping iterations completed"
+               " successfully"]
+    for i in range(niter):
+        new_global_min = bh.one_cycle()
+
+        if callable(callback):
+            # should we pass a copy of x?
+            val = callback(bh.xtrial, bh.energy_trial, bh.accept)
+            if val is not None:
+                if val:
+                    message = ["callback function requested stop early by"
+                               "returning True"]
+                    break
+
+        count += 1
+        if new_global_min:
+            count = 0
+        elif count > niter_success:
+            message = ["success condition satisfied"]
+            break
+
+    # prepare return object
+    res = bh.res
+    res.lowest_optimization_result = bh.storage.get_lowest()
+    res.x = np.copy(res.lowest_optimization_result.x)
+    res.fun = res.lowest_optimization_result.fun
+    res.message = message
+    res.nit = i + 1
+    res.success = res.lowest_optimization_result.success
+    return res

llava_next/lib/python3.10/site-packages/scipy/optimize/_cobyla.cpython-310-x86_64-linux-gnu.so

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:416e378eb1a89181832672ab92b32ec9d9c9c4da4eec9cfdfc7551ab8e7ee113
+size 100545

llava_next/lib/python3.10/site-packages/scipy/optimize/_cobyqa_py.py

@@ -0,0 +1,62 @@
+import numpy as np
+
+from ._optimize import _check_unknown_options
+
+
+def _minimize_cobyqa(fun, x0, args=(), bounds=None, constraints=(),
+                     callback=None, disp=False, maxfev=None, maxiter=None,
+                     f_target=-np.inf, feasibility_tol=1e-8,
+                     initial_tr_radius=1.0, final_tr_radius=1e-6, scale=False,
+                     **unknown_options):
+    """
+    Minimize a scalar function of one or more variables using the
+    Constrained Optimization BY Quadratic Approximations (COBYQA) algorithm [1]_.
+
+    .. versionadded:: 1.14.0
+
+    Options
+    -------
+    disp : bool
+        Set to True to print information about the optimization procedure.
+    maxfev : int
+        Maximum number of function evaluations.
+    maxiter : int
+        Maximum number of iterations.
+    f_target : float
+        Target value for the objective function. The optimization procedure is
+        terminated when the objective function value of a feasible point (see
+        `feasibility_tol` below) is less than or equal to this target.
+    feasibility_tol : float
+        Absolute tolerance for the constraint violation.
+    initial_tr_radius : float
+        Initial trust-region radius. Typically, this value should be in the
+        order of one tenth of the greatest expected change to the variables.
+    final_tr_radius : float
+        Final trust-region radius. It should indicate the accuracy required in
+        the final values of the variables. If provided, this option overrides
+        the value of `tol` in the `minimize` function.
+    scale : bool
+        Set to True to scale the variables according to the bounds. If True and
+        if all the lower and upper bounds are finite, the variables are scaled
+        to be within the range :math:`[-1, 1]`. If any of the lower or upper
+        bounds is infinite, the variables are not scaled.
+
+    References
+    ----------
+    .. [1] COBYQA
+           https://www.cobyqa.com/stable/
+    """
+    from .._lib.cobyqa import minimize  # import here to avoid circular imports
+
+    _check_unknown_options(unknown_options)
+    options = {
+        'disp': bool(disp),
+        'maxfev': int(maxfev) if maxfev is not None else 500 * len(x0),
+        'maxiter': int(maxiter) if maxiter is not None else 1000 * len(x0),
+        'target': float(f_target),
+        'feasibility_tol': float(feasibility_tol),
+        'radius_init': float(initial_tr_radius),
+        'radius_final': float(final_tr_radius),
+        'scale': bool(scale),
+    }
+    return minimize(fun, x0, args, bounds, constraints, callback, options)

llava_next/lib/python3.10/site-packages/scipy/optimize/_direct_py.py

@@ -0,0 +1,278 @@
+from __future__ import annotations
+from typing import (  # noqa: UP035
+    Any, Callable, Iterable, TYPE_CHECKING
+)
+
+import numpy as np
+from scipy.optimize import OptimizeResult
+from ._constraints import old_bound_to_new, Bounds
+from ._direct import direct as _direct  # type: ignore
+
+if TYPE_CHECKING:
+    import numpy.typing as npt
+
+__all__ = ['direct']
+
+ERROR_MESSAGES = (
+    "Number of function evaluations done is larger than maxfun={}",
+    "Number of iterations is larger than maxiter={}",
+    "u[i] < l[i] for some i",
+    "maxfun is too large",
+    "Initialization failed",
+    "There was an error in the creation of the sample points",
+    "An error occurred while the function was sampled",
+    "Maximum number of levels has been reached.",
+    "Forced stop",
+    "Invalid arguments",
+    "Out of memory",
+)
+
+SUCCESS_MESSAGES = (
+    ("The best function value found is within a relative error={} "
+     "of the (known) global optimum f_min"),
+    ("The volume of the hyperrectangle containing the lowest function value "
+     "found is below vol_tol={}"),
+    ("The side length measure of the hyperrectangle containing the lowest "
+     "function value found is below len_tol={}"),
+)
+
+
+def direct(
+    func: Callable[[npt.ArrayLike, tuple[Any]], float],
+    bounds: Iterable | Bounds,
+    *,
+    args: tuple = (),
+    eps: float = 1e-4,
+    maxfun: int | None = None,
+    maxiter: int = 1000,
+    locally_biased: bool = True,
+    f_min: float = -np.inf,
+    f_min_rtol: float = 1e-4,
+    vol_tol: float = 1e-16,
+    len_tol: float = 1e-6,
+    callback: Callable[[npt.ArrayLike], None] | None = None
+) -> OptimizeResult:
+    """
+    Finds the global minimum of a function using the
+    DIRECT algorithm.
+
+    Parameters
+    ----------
+    func : callable
+        The objective function to be minimized.
+        ``func(x, *args) -> float``
+        where ``x`` is an 1-D array with shape (n,) and ``args`` is a tuple of
+        the fixed parameters needed to completely specify the function.
+    bounds : sequence or `Bounds`
+        Bounds for variables. There are two ways to specify the bounds:
+
+        1. Instance of `Bounds` class.
+        2. ``(min, max)`` pairs for each element in ``x``.
+
+    args : tuple, optional
+        Any additional fixed parameters needed to
+        completely specify the objective function.
+    eps : float, optional
+        Minimal required difference of the objective function values
+        between the current best hyperrectangle and the next potentially
+        optimal hyperrectangle to be divided. In consequence, `eps` serves as a
+        tradeoff between local and global search: the smaller, the more local
+        the search becomes. Default is 1e-4.
+    maxfun : int or None, optional
+        Approximate upper bound on objective function evaluations.
+        If `None`, will be automatically set to ``1000 * N`` where ``N``
+        represents the number of dimensions. Will be capped if necessary to
+        limit DIRECT's RAM usage to app. 1GiB. This will only occur for very
+        high dimensional problems and excessive `max_fun`. Default is `None`.
+    maxiter : int, optional
+        Maximum number of iterations. Default is 1000.
+    locally_biased : bool, optional
+        If `True` (default), use the locally biased variant of the
+        algorithm known as DIRECT_L. If `False`, use the original unbiased
+        DIRECT algorithm. For hard problems with many local minima,
+        `False` is recommended.
+    f_min : float, optional
+        Function value of the global optimum. Set this value only if the
+        global optimum is known. Default is ``-np.inf``, so that this
+        termination criterion is deactivated.
+    f_min_rtol : float, optional
+        Terminate the optimization once the relative error between the
+        current best minimum `f` and the supplied global minimum `f_min`
+        is smaller than `f_min_rtol`. This parameter is only used if
+        `f_min` is also set. Must lie between 0 and 1. Default is 1e-4.
+    vol_tol : float, optional
+        Terminate the optimization once the volume of the hyperrectangle
+        containing the lowest function value is smaller than `vol_tol`
+        of the complete search space. Must lie between 0 and 1.
+        Default is 1e-16.
+    len_tol : float, optional
+        If `locally_biased=True`, terminate the optimization once half of
+        the normalized maximal side length of the hyperrectangle containing
+        the lowest function value is smaller than `len_tol`.
+        If `locally_biased=False`, terminate the optimization once half of
+        the normalized diagonal of the hyperrectangle containing the lowest
+        function value is smaller than `len_tol`. Must lie between 0 and 1.
+        Default is 1e-6.
+    callback : callable, optional
+        A callback function with signature ``callback(xk)`` where ``xk``
+        represents the best function value found so far.
+
+    Returns
+    -------
+    res : OptimizeResult
+        The optimization result represented as a ``OptimizeResult`` object.
+        Important attributes are: ``x`` the solution array, ``success`` a
+        Boolean flag indicating if the optimizer exited successfully and
+        ``message`` which describes the cause of the termination. See
+        `OptimizeResult` for a description of other attributes.
+
+    Notes
+    -----
+    DIviding RECTangles (DIRECT) is a deterministic global
+    optimization algorithm capable of minimizing a black box function with
+    its variables subject to lower and upper bound constraints by sampling
+    potential solutions in the search space [1]_. The algorithm starts by
+    normalising the search space to an n-dimensional unit hypercube.
+    It samples the function at the center of this hypercube and at 2n
+    (n is the number of variables) more points, 2 in each coordinate
+    direction. Using these function values, DIRECT then divides the
+    domain into hyperrectangles, each having exactly one of the sampling
+    points as its center. In each iteration, DIRECT chooses, using the `eps`
+    parameter which defaults to 1e-4, some of the existing hyperrectangles
+    to be further divided. This division process continues until either the
+    maximum number of iterations or maximum function evaluations allowed
+    are exceeded, or the hyperrectangle containing the minimal value found
+    so far becomes small enough. If `f_min` is specified, the optimization
+    will stop once this function value is reached within a relative tolerance.
+    The locally biased variant of DIRECT (originally called DIRECT_L) [2]_ is
+    used by default. It makes the search more locally biased and more
+    efficient for cases with only a few local minima.
+
+    A note about termination criteria: `vol_tol` refers to the volume of the
+    hyperrectangle containing the lowest function value found so far. This
+    volume decreases exponentially with increasing dimensionality of the
+    problem. Therefore `vol_tol` should be decreased to avoid premature
+    termination of the algorithm for higher dimensions. This does not hold
+    for `len_tol`: it refers either to half of the maximal side length
+    (for ``locally_biased=True``) or half of the diagonal of the
+    hyperrectangle (for ``locally_biased=False``).
+
+    This code is based on the DIRECT 2.0.4 Fortran code by Gablonsky et al. at
+    https://ctk.math.ncsu.edu/SOFTWARE/DIRECTv204.tar.gz .
+    This original version was initially converted via f2c and then cleaned up
+    and reorganized by Steven G. Johnson, August 2007, for the NLopt project.
+    The `direct` function wraps the C implementation.
+
+    .. versionadded:: 1.9.0
+
+    References
+    ----------
+    .. [1] Jones, D.R., Perttunen, C.D. & Stuckman, B.E. Lipschitzian
+        optimization without the Lipschitz constant. J Optim Theory Appl
+        79, 157-181 (1993).
+    .. [2] Gablonsky, J., Kelley, C. A Locally-Biased form of the DIRECT
+        Algorithm. Journal of Global Optimization 21, 27-37 (2001).
+
+    Examples
+    --------
+    The following example is a 2-D problem with four local minima: minimizing
+    the Styblinski-Tang function
+    (https://en.wikipedia.org/wiki/Test_functions_for_optimization).
+
+    >>> from scipy.optimize import direct, Bounds
+    >>> def styblinski_tang(pos):
+    ...     x, y = pos
+    ...     return 0.5 * (x**4 - 16*x**2 + 5*x + y**4 - 16*y**2 + 5*y)
+    >>> bounds = Bounds([-4., -4.], [4., 4.])
+    >>> result = direct(styblinski_tang, bounds)
+    >>> result.x, result.fun, result.nfev
+    array([-2.90321597, -2.90321597]), -78.3323279095383, 2011
+
+    The correct global minimum was found but with a huge number of function
+    evaluations (2011). Loosening the termination tolerances `vol_tol` and
+    `len_tol` can be used to stop DIRECT earlier.
+
+    >>> result = direct(styblinski_tang, bounds, len_tol=1e-3)
+    >>> result.x, result.fun, result.nfev
+    array([-2.9044353, -2.9044353]), -78.33230330754142, 207
+
+    """
+    # convert bounds to new Bounds class if necessary
+    if not isinstance(bounds, Bounds):
+        if isinstance(bounds, list) or isinstance(bounds, tuple):
+            lb, ub = old_bound_to_new(bounds)
+            bounds = Bounds(lb, ub)
+        else:
+            message = ("bounds must be a sequence or "
+                       "instance of Bounds class")
+            raise ValueError(message)
+
+    lb = np.ascontiguousarray(bounds.lb, dtype=np.float64)
+    ub = np.ascontiguousarray(bounds.ub, dtype=np.float64)
+
+    # validate bounds
+    # check that lower bounds are smaller than upper bounds
+    if not np.all(lb < ub):
+        raise ValueError('Bounds are not consistent min < max')
+    # check for infs
+    if (np.any(np.isinf(lb)) or np.any(np.isinf(ub))):
+        raise ValueError("Bounds must not be inf.")
+
+    # validate tolerances
+    if (vol_tol < 0 or vol_tol > 1):
+        raise ValueError("vol_tol must be between 0 and 1.")
+    if (len_tol < 0 or len_tol > 1):
+        raise ValueError("len_tol must be between 0 and 1.")
+    if (f_min_rtol < 0 or f_min_rtol > 1):
+        raise ValueError("f_min_rtol must be between 0 and 1.")
+
+    # validate maxfun and maxiter
+    if maxfun is None:
+        maxfun = 1000 * lb.shape[0]
+    if not isinstance(maxfun, int):
+        raise ValueError("maxfun must be of type int.")
+    if maxfun < 0:
+        raise ValueError("maxfun must be > 0.")
+    if not isinstance(maxiter, int):
+        raise ValueError("maxiter must be of type int.")
+    if maxiter < 0:
+        raise ValueError("maxiter must be > 0.")
+
+    # validate boolean parameters
+    if not isinstance(locally_biased, bool):
+        raise ValueError("locally_biased must be True or False.")
+
+    def _func_wrap(x, args=None):
+        x = np.asarray(x)
+        if args is None:
+            f = func(x)
+        else:
+            f = func(x, *args)
+        # always return a float
+        return np.asarray(f).item()
+
+    # TODO: fix disp argument
+    x, fun, ret_code, nfev, nit = _direct(
+        _func_wrap,
+        np.asarray(lb), np.asarray(ub),
+        args,
+        False, eps, maxfun, maxiter,
+        locally_biased,
+        f_min, f_min_rtol,
+        vol_tol, len_tol, callback
+    )
+
+    format_val = (maxfun, maxiter, f_min_rtol, vol_tol, len_tol)
+    if ret_code > 2:
+        message = SUCCESS_MESSAGES[ret_code - 3].format(
+                    format_val[ret_code - 1])
+    elif 0 < ret_code <= 2:
+        message = ERROR_MESSAGES[ret_code - 1].format(format_val[ret_code - 1])
+    elif 0 > ret_code > -100:
+        message = ERROR_MESSAGES[abs(ret_code) + 1]
+    else:
+        message = ERROR_MESSAGES[ret_code + 99]
+
+    return OptimizeResult(x=np.asarray(x), fun=fun, status=ret_code,
+                          success=ret_code > 2, message=message,
+                          nfev=nfev, nit=nit)

llava_next/lib/python3.10/site-packages/scipy/optimize/_highs/src/cython/HighsIO.pxd

@@ -0,0 +1,20 @@
+# cython: language_level=3
+
+
+cdef extern from "HighsIO.h" nogil:
+    # workaround for lack of enum class support in Cython < 3.x
+    # cdef enum class HighsLogType(int):
+    #     kInfo "HighsLogType::kInfo" = 1
+    #     kDetailed "HighsLogType::kDetailed"
+    #     kVerbose "HighsLogType::kVerbose"
+    #     kWarning "HighsLogType::kWarning"
+    #     kError "HighsLogType::kError"
+
+    cdef cppclass HighsLogType:
+        pass
+
+    cdef HighsLogType kInfo "HighsLogType::kInfo"
+    cdef HighsLogType kDetailed "HighsLogType::kDetailed"
+    cdef HighsLogType kVerbose "HighsLogType::kVerbose"
+    cdef HighsLogType kWarning "HighsLogType::kWarning"
+    cdef HighsLogType kError "HighsLogType::kError"

llava_next/lib/python3.10/site-packages/scipy/optimize/_highs/src/cython/HighsInfo.pxd

@@ -0,0 +1,22 @@
+# cython: language_level=3
+
+cdef extern from "HighsInfo.h" nogil:
+    # From HiGHS/src/lp_data/HighsInfo.h
+    cdef cppclass HighsInfo:
+        # Inherited from HighsInfoStruct:
+        int mip_node_count
+        int simplex_iteration_count
+        int ipm_iteration_count
+        int crossover_iteration_count
+        int primal_solution_status
+        int dual_solution_status
+        int basis_validity
+        double objective_function_value
+        double mip_dual_bound
+        double mip_gap
+        int num_primal_infeasibilities
+        double max_primal_infeasibility
+        double sum_primal_infeasibilities
+        int num_dual_infeasibilities
+        double max_dual_infeasibility
+        double sum_dual_infeasibilities

llava_next/lib/python3.10/site-packages/scipy/optimize/_highs/src/cython/HighsLp.pxd

@@ -0,0 +1,46 @@
+# cython: language_level=3
+
+from libcpp cimport bool
+from libcpp.string cimport string
+from libcpp.vector cimport vector
+
+from .HConst cimport HighsBasisStatus, ObjSense, HighsVarType
+from .HighsSparseMatrix cimport HighsSparseMatrix
+
+
+cdef extern from "HighsLp.h" nogil:
+    # From HiGHS/src/lp_data/HighsLp.h
+    cdef cppclass HighsLp:
+        int num_col_
+        int num_row_
+
+        vector[double] col_cost_
+        vector[double] col_lower_
+        vector[double] col_upper_
+        vector[double] row_lower_
+        vector[double] row_upper_
+
+        HighsSparseMatrix a_matrix_
+
+        ObjSense sense_
+        double offset_
+
+        string model_name_
+
+        vector[string] row_names_
+        vector[string] col_names_
+
+        vector[HighsVarType] integrality_
+
+        bool isMip() const
+
+    cdef cppclass HighsSolution:
+        vector[double] col_value
+        vector[double] col_dual
+        vector[double] row_value
+        vector[double] row_dual
+
+    cdef cppclass HighsBasis:
+        bool valid_
+        vector[HighsBasisStatus] col_status
+        vector[HighsBasisStatus] row_status

llava_next/lib/python3.10/site-packages/scipy/optimize/_highs/src/cython/HighsModelUtils.pxd

@@ -0,0 +1,10 @@
+# cython: language_level=3
+
+from libcpp.string cimport string
+
+from .HConst cimport HighsModelStatus
+
+cdef extern from "HighsModelUtils.h" nogil:
+    # From HiGHS/src/lp_data/HighsModelUtils.h
+    string utilHighsModelStatusToString(const HighsModelStatus model_status)
+    string utilBasisStatusToString(const int primal_dual_status)

llava_next/lib/python3.10/site-packages/scipy/optimize/_highs/src/cython/HighsOptions.pxd

@@ -0,0 +1,110 @@
+# cython: language_level=3
+
+from libc.stdio cimport FILE
+
+from libcpp cimport bool
+from libcpp.string cimport string
+from libcpp.vector cimport vector
+
+from .HConst cimport HighsOptionType
+
+cdef extern from "HighsOptions.h" nogil:
+
+    cdef cppclass OptionRecord:
+        HighsOptionType type
+        string name
+        string description
+        bool advanced
+
+    cdef cppclass OptionRecordBool(OptionRecord):
+        bool* value
+        bool default_value
+
+    cdef cppclass OptionRecordInt(OptionRecord):
+        int* value
+        int lower_bound
+        int default_value
+        int upper_bound
+
+    cdef cppclass OptionRecordDouble(OptionRecord):
+        double* value
+        double lower_bound
+        double default_value
+        double upper_bound
+
+    cdef cppclass OptionRecordString(OptionRecord):
+        string* value
+        string default_value
+
+    cdef cppclass HighsOptions:
+        # From HighsOptionsStruct:
+
+        # Options read from the command line
+        string model_file
+        string presolve
+        string solver
+        string parallel
+        double time_limit
+        string options_file
+
+        # Options read from the file
+        double infinite_cost
+        double infinite_bound
+        double small_matrix_value
+        double large_matrix_value
+        double primal_feasibility_tolerance
+        double dual_feasibility_tolerance
+        double ipm_optimality_tolerance
+        double dual_objective_value_upper_bound
+        int highs_debug_level
+        int simplex_strategy
+        int simplex_scale_strategy
+        int simplex_crash_strategy
+        int simplex_dual_edge_weight_strategy
+        int simplex_primal_edge_weight_strategy
+        int simplex_iteration_limit
+        int simplex_update_limit
+        int ipm_iteration_limit
+        int highs_min_threads
+        int highs_max_threads
+        int message_level
+        string solution_file
+        bool write_solution_to_file
+        bool write_solution_pretty
+
+        # Advanced options
+        bool run_crossover
+        bool mps_parser_type_free
+        int keep_n_rows
+        int allowed_simplex_matrix_scale_factor
+        int allowed_simplex_cost_scale_factor
+        int simplex_dualise_strategy
+        int simplex_permute_strategy
+        int dual_simplex_cleanup_strategy
+        int simplex_price_strategy
+        int dual_chuzc_sort_strategy
+        bool simplex_initial_condition_check
+        double simplex_initial_condition_tolerance
+        double dual_steepest_edge_weight_log_error_threshhold
+        double dual_simplex_cost_perturbation_multiplier
+        double start_crossover_tolerance
+        bool less_infeasible_DSE_check
+        bool less_infeasible_DSE_choose_row
+        bool use_original_HFactor_logic
+
+        # Options for MIP solver
+        int mip_max_nodes
+        int mip_report_level
+
+        # Switch for MIP solver
+        bool mip
+
+        # Options for HighsPrintMessage and HighsLogMessage
+        FILE* logfile
+        FILE* output
+        int message_level
+        string solution_file
+        bool write_solution_to_file
+        bool write_solution_pretty
+
+        vector[OptionRecord*] records

llava_next/lib/python3.10/site-packages/scipy/optimize/_highs/src/cython/HighsStatus.pxd

@@ -0,0 +1,12 @@
+# cython: language_level=3
+
+from libcpp.string cimport string
+
+cdef extern from "HighsStatus.h" nogil:
+    ctypedef enum HighsStatus:
+        HighsStatusError "HighsStatus::kError" = -1
+        HighsStatusOK "HighsStatus::kOk" = 0
+        HighsStatusWarning "HighsStatus::kWarning" = 1
+
+
+    string highsStatusToString(HighsStatus status)

llava_next/lib/python3.10/site-packages/scipy/optimize/_highs/src/cython/SimplexConst.pxd

@@ -0,0 +1,95 @@
+# cython: language_level=3
+
+from libcpp cimport bool
+
+cdef extern from "SimplexConst.h" nogil:
+
+    cdef enum SimplexAlgorithm:
+        PRIMAL "SimplexAlgorithm::kPrimal" = 0
+        DUAL "SimplexAlgorithm::kDual"
+
+    cdef enum SimplexStrategy:
+        SIMPLEX_STRATEGY_MIN "SimplexStrategy::kSimplexStrategyMin" = 0
+        SIMPLEX_STRATEGY_CHOOSE "SimplexStrategy::kSimplexStrategyChoose" = SIMPLEX_STRATEGY_MIN
+        SIMPLEX_STRATEGY_DUAL "SimplexStrategy::kSimplexStrategyDual"
+        SIMPLEX_STRATEGY_DUAL_PLAIN "SimplexStrategy::kSimplexStrategyDualPlain" = SIMPLEX_STRATEGY_DUAL
+        SIMPLEX_STRATEGY_DUAL_TASKS "SimplexStrategy::kSimplexStrategyDualTasks"
+        SIMPLEX_STRATEGY_DUAL_MULTI "SimplexStrategy::kSimplexStrategyDualMulti"
+        SIMPLEX_STRATEGY_PRIMAL "SimplexStrategy::kSimplexStrategyPrimal"
+        SIMPLEX_STRATEGY_MAX "SimplexStrategy::kSimplexStrategyMax" = SIMPLEX_STRATEGY_PRIMAL
+        SIMPLEX_STRATEGY_NUM "SimplexStrategy::kSimplexStrategyNum"
+
+    cdef enum SimplexCrashStrategy:
+        SIMPLEX_CRASH_STRATEGY_MIN "SimplexCrashStrategy::kSimplexCrashStrategyMin" = 0
+        SIMPLEX_CRASH_STRATEGY_OFF "SimplexCrashStrategy::kSimplexCrashStrategyOff" = SIMPLEX_CRASH_STRATEGY_MIN
+        SIMPLEX_CRASH_STRATEGY_LTSSF_K "SimplexCrashStrategy::kSimplexCrashStrategyLtssfK"
+        SIMPLEX_CRASH_STRATEGY_LTSSF "SimplexCrashStrategy::kSimplexCrashStrategyLtssf" = SIMPLEX_CRASH_STRATEGY_LTSSF_K
+        SIMPLEX_CRASH_STRATEGY_BIXBY "SimplexCrashStrategy::kSimplexCrashStrategyBixby"
+        SIMPLEX_CRASH_STRATEGY_LTSSF_PRI "SimplexCrashStrategy::kSimplexCrashStrategyLtssfPri"
+        SIMPLEX_CRASH_STRATEGY_LTSF_K "SimplexCrashStrategy::kSimplexCrashStrategyLtsfK"
+        SIMPLEX_CRASH_STRATEGY_LTSF_PRI "SimplexCrashStrategy::kSimplexCrashStrategyLtsfPri"
+        SIMPLEX_CRASH_STRATEGY_LTSF "SimplexCrashStrategy::kSimplexCrashStrategyLtsf"
+        SIMPLEX_CRASH_STRATEGY_BIXBY_NO_NONZERO_COL_COSTS "SimplexCrashStrategy::kSimplexCrashStrategyBixbyNoNonzeroColCosts"
+        SIMPLEX_CRASH_STRATEGY_BASIC "SimplexCrashStrategy::kSimplexCrashStrategyBasic"
+        SIMPLEX_CRASH_STRATEGY_TEST_SING "SimplexCrashStrategy::kSimplexCrashStrategyTestSing"
+        SIMPLEX_CRASH_STRATEGY_MAX "SimplexCrashStrategy::kSimplexCrashStrategyMax" = SIMPLEX_CRASH_STRATEGY_TEST_SING
+
+    cdef enum SimplexEdgeWeightStrategy:
+        SIMPLEX_EDGE_WEIGHT_STRATEGY_MIN "SimplexEdgeWeightStrategy::kSimplexEdgeWeightStrategyMin" = -1
+        SIMPLEX_EDGE_WEIGHT_STRATEGY_CHOOSE "SimplexEdgeWeightStrategy::kSimplexEdgeWeightStrategyChoose" = SIMPLEX_EDGE_WEIGHT_STRATEGY_MIN
+        SIMPLEX_EDGE_WEIGHT_STRATEGY_DANTZIG "SimplexEdgeWeightStrategy::kSimplexEdgeWeightStrategyDantzig"
+        SIMPLEX_EDGE_WEIGHT_STRATEGY_DEVEX "SimplexEdgeWeightStrategy::kSimplexEdgeWeightStrategyDevex"
+        SIMPLEX_EDGE_WEIGHT_STRATEGY_STEEPEST_EDGE "SimplexEdgeWeightStrategy::kSimplexEdgeWeightStrategySteepestEdge"
+        SIMPLEX_EDGE_WEIGHT_STRATEGY_STEEPEST_EDGE_UNIT_INITIAL "SimplexEdgeWeightStrategy::kSimplexEdgeWeightStrategySteepestEdgeUnitInitial"
+        SIMPLEX_EDGE_WEIGHT_STRATEGY_MAX "SimplexEdgeWeightStrategy::kSimplexEdgeWeightStrategyMax" = SIMPLEX_EDGE_WEIGHT_STRATEGY_STEEPEST_EDGE_UNIT_INITIAL
+
+    cdef enum SimplexPriceStrategy:
+        SIMPLEX_PRICE_STRATEGY_MIN = 0
+        SIMPLEX_PRICE_STRATEGY_COL = SIMPLEX_PRICE_STRATEGY_MIN
+        SIMPLEX_PRICE_STRATEGY_ROW
+        SIMPLEX_PRICE_STRATEGY_ROW_SWITCH
+        SIMPLEX_PRICE_STRATEGY_ROW_SWITCH_COL_SWITCH
+        SIMPLEX_PRICE_STRATEGY_MAX = SIMPLEX_PRICE_STRATEGY_ROW_SWITCH_COL_SWITCH
+
+    cdef enum SimplexDualChuzcStrategy:
+        SIMPLEX_DUAL_CHUZC_STRATEGY_MIN = 0
+        SIMPLEX_DUAL_CHUZC_STRATEGY_CHOOSE = SIMPLEX_DUAL_CHUZC_STRATEGY_MIN
+        SIMPLEX_DUAL_CHUZC_STRATEGY_QUAD
+        SIMPLEX_DUAL_CHUZC_STRATEGY_HEAP
+        SIMPLEX_DUAL_CHUZC_STRATEGY_BOTH
+        SIMPLEX_DUAL_CHUZC_STRATEGY_MAX = SIMPLEX_DUAL_CHUZC_STRATEGY_BOTH
+
+    cdef enum InvertHint:
+        INVERT_HINT_NO = 0
+        INVERT_HINT_UPDATE_LIMIT_REACHED
+        INVERT_HINT_SYNTHETIC_CLOCK_SAYS_INVERT
+        INVERT_HINT_POSSIBLY_OPTIMAL
+        INVERT_HINT_POSSIBLY_PRIMAL_UNBOUNDED
+        INVERT_HINT_POSSIBLY_DUAL_UNBOUNDED
+        INVERT_HINT_POSSIBLY_SINGULAR_BASIS
+        INVERT_HINT_PRIMAL_INFEASIBLE_IN_PRIMAL_SIMPLEX
+        INVERT_HINT_CHOOSE_COLUMN_FAIL
+        INVERT_HINT_Count
+
+    cdef enum DualEdgeWeightMode:
+        DANTZIG "DualEdgeWeightMode::DANTZIG" = 0
+        DEVEX "DualEdgeWeightMode::DEVEX"
+        STEEPEST_EDGE "DualEdgeWeightMode::STEEPEST_EDGE"
+        Count "DualEdgeWeightMode::Count"
+
+    cdef enum PriceMode:
+        ROW "PriceMode::ROW" = 0
+        COL "PriceMode::COL"
+
+    const int PARALLEL_THREADS_DEFAULT
+    const int DUAL_TASKS_MIN_THREADS
+    const int DUAL_MULTI_MIN_THREADS
+
+    const bool invert_if_row_out_negative
+
+    const int NONBASIC_FLAG_TRUE
+    const int NONBASIC_FLAG_FALSE
+
+    const int NONBASIC_MOVE_UP
+    const int NONBASIC_MOVE_DN
+    const int NONBASIC_MOVE_ZE

llava_next/lib/python3.10/site-packages/scipy/optimize/_highs/src/cython/highs_c_api.pxd

@@ -0,0 +1,7 @@
+# cython: language_level=3
+
+cdef extern from "highs_c_api.h" nogil:
+    int Highs_passLp(void* highs, int numcol, int numrow, int numnz,
+                     double* colcost, double* collower, double* colupper,
+                     double* rowlower, double* rowupper,
+                     int* astart, int* aindex,  double* avalue)

llava_next/lib/python3.10/site-packages/scipy/optimize/_lbfgsb.cpython-310-x86_64-linux-gnu.so

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d0e0cc53dba47fe455ac20e0c5588de5dcd553f4c8df5bc5b11a81d84339d015
+size 524785

llava_next/lib/python3.10/site-packages/scipy/optimize/_linprog.py

@@ -0,0 +1,716 @@
+"""
+A top-level linear programming interface.
+
+.. versionadded:: 0.15.0
+
+Functions
+---------
+.. autosummary::
+   :toctree: generated/
+
+    linprog
+    linprog_verbose_callback
+    linprog_terse_callback
+
+"""
+
+import numpy as np
+
+from ._optimize import OptimizeResult, OptimizeWarning
+from warnings import warn
+from ._linprog_highs import _linprog_highs
+from ._linprog_ip import _linprog_ip
+from ._linprog_simplex import _linprog_simplex
+from ._linprog_rs import _linprog_rs
+from ._linprog_doc import (_linprog_highs_doc, _linprog_ip_doc,  # noqa: F401
+                           _linprog_rs_doc, _linprog_simplex_doc,
+                           _linprog_highs_ipm_doc, _linprog_highs_ds_doc)
+from ._linprog_util import (
+    _parse_linprog, _presolve, _get_Abc, _LPProblem, _autoscale,
+    _postsolve, _check_result, _display_summary)
+from copy import deepcopy
+
+__all__ = ['linprog', 'linprog_verbose_callback', 'linprog_terse_callback']
+
+__docformat__ = "restructuredtext en"
+
+LINPROG_METHODS = [
+    'simplex', 'revised simplex', 'interior-point', 'highs', 'highs-ds', 'highs-ipm'
+]
+
+
+def linprog_verbose_callback(res):
+    """
+    A sample callback function demonstrating the linprog callback interface.
+    This callback produces detailed output to sys.stdout before each iteration
+    and after the final iteration of the simplex algorithm.
+
+    Parameters
+    ----------
+    res : A `scipy.optimize.OptimizeResult` consisting of the following fields:
+
+        x : 1-D array
+            The independent variable vector which optimizes the linear
+            programming problem.
+        fun : float
+            Value of the objective function.
+        success : bool
+            True if the algorithm succeeded in finding an optimal solution.
+        slack : 1-D array
+            The values of the slack variables. Each slack variable corresponds
+            to an inequality constraint. If the slack is zero, then the
+            corresponding constraint is active.
+        con : 1-D array
+            The (nominally zero) residuals of the equality constraints, that is,
+            ``b - A_eq @ x``
+        phase : int
+            The phase of the optimization being executed. In phase 1 a basic
+            feasible solution is sought and the T has an additional row
+            representing an alternate objective function.
+        status : int
+            An integer representing the exit status of the optimization::
+
+                 0 : Optimization terminated successfully
+                 1 : Iteration limit reached
+                 2 : Problem appears to be infeasible
+                 3 : Problem appears to be unbounded
+                 4 : Serious numerical difficulties encountered
+
+        nit : int
+            The number of iterations performed.
+        message : str
+            A string descriptor of the exit status of the optimization.
+    """
+    x = res['x']
+    fun = res['fun']
+    phase = res['phase']
+    status = res['status']
+    nit = res['nit']
+    message = res['message']
+    complete = res['complete']
+
+    saved_printoptions = np.get_printoptions()
+    np.set_printoptions(linewidth=500,
+                        formatter={'float': lambda x: f"{x: 12.4f}"})
+    if status:
+        print('--------- Simplex Early Exit -------\n')
+        print(f'The simplex method exited early with status {status:d}')
+        print(message)
+    elif complete:
+        print('--------- Simplex Complete --------\n')
+        print(f'Iterations required: {nit}')
+    else:
+        print(f'--------- Iteration {nit:d}  ---------\n')
+
+    if nit > 0:
+        if phase == 1:
+            print('Current Pseudo-Objective Value:')
+        else:
+            print('Current Objective Value:')
+        print('f = ', fun)
+        print()
+        print('Current Solution Vector:')
+        print('x = ', x)
+        print()
+
+    np.set_printoptions(**saved_printoptions)
+
+
+def linprog_terse_callback(res):
+    """
+    A sample callback function demonstrating the linprog callback interface.
+    This callback produces brief output to sys.stdout before each iteration
+    and after the final iteration of the simplex algorithm.
+
+    Parameters
+    ----------
+    res : A `scipy.optimize.OptimizeResult` consisting of the following fields:
+
+        x : 1-D array
+            The independent variable vector which optimizes the linear
+            programming problem.
+        fun : float
+            Value of the objective function.
+        success : bool
+            True if the algorithm succeeded in finding an optimal solution.
+        slack : 1-D array
+            The values of the slack variables. Each slack variable corresponds
+            to an inequality constraint. If the slack is zero, then the
+            corresponding constraint is active.
+        con : 1-D array
+            The (nominally zero) residuals of the equality constraints, that is,
+            ``b - A_eq @ x``.
+        phase : int
+            The phase of the optimization being executed. In phase 1 a basic
+            feasible solution is sought and the T has an additional row
+            representing an alternate objective function.
+        status : int
+            An integer representing the exit status of the optimization::
+
+                 0 : Optimization terminated successfully
+                 1 : Iteration limit reached
+                 2 : Problem appears to be infeasible
+                 3 : Problem appears to be unbounded
+                 4 : Serious numerical difficulties encountered
+
+        nit : int
+            The number of iterations performed.
+        message : str
+            A string descriptor of the exit status of the optimization.
+    """
+    nit = res['nit']
+    x = res['x']
+
+    if nit == 0:
+        print("Iter:   X:")
+    print(f"{nit: <5d}   ", end="")
+    print(x)
+
+
+def linprog(c, A_ub=None, b_ub=None, A_eq=None, b_eq=None,
+            bounds=(0, None), method='highs', callback=None,
+            options=None, x0=None, integrality=None):
+    r"""
+    Linear programming: minimize a linear objective function subject to linear
+    equality and inequality constraints.
+
+    Linear programming solves problems of the following form:
+
+    .. math::
+
+        \min_x \ & c^T x \\
+        \mbox{such that} \ & A_{ub} x \leq b_{ub},\\
+        & A_{eq} x = b_{eq},\\
+        & l \leq x \leq u ,
+
+    where :math:`x` is a vector of decision variables; :math:`c`,
+    :math:`b_{ub}`, :math:`b_{eq}`, :math:`l`, and :math:`u` are vectors; and
+    :math:`A_{ub}` and :math:`A_{eq}` are matrices.
+
+    Alternatively, that's:
+
+        - minimize ::
+
+            c @ x
+
+        - such that ::
+
+            A_ub @ x <= b_ub
+            A_eq @ x == b_eq
+            lb <= x <= ub
+
+    Note that by default ``lb = 0`` and ``ub = None``. Other bounds can be
+    specified with ``bounds``.
+
+    Parameters
+    ----------
+    c : 1-D array
+        The coefficients of the linear objective function to be minimized.
+    A_ub : 2-D array, optional
+        The inequality constraint matrix. Each row of ``A_ub`` specifies the
+        coefficients of a linear inequality constraint on ``x``.
+    b_ub : 1-D array, optional
+        The inequality constraint vector. Each element represents an
+        upper bound on the corresponding value of ``A_ub @ x``.
+    A_eq : 2-D array, optional
+        The equality constraint matrix. Each row of ``A_eq`` specifies the
+        coefficients of a linear equality constraint on ``x``.
+    b_eq : 1-D array, optional
+        The equality constraint vector. Each element of ``A_eq @ x`` must equal
+        the corresponding element of ``b_eq``.
+    bounds : sequence, optional
+        A sequence of ``(min, max)`` pairs for each element in ``x``, defining
+        the minimum and maximum values of that decision variable.
+        If a single tuple ``(min, max)`` is provided, then ``min`` and ``max``
+        will serve as bounds for all decision variables.
+        Use ``None`` to indicate that there is no bound. For instance, the
+        default bound ``(0, None)`` means that all decision variables are
+        non-negative, and the pair ``(None, None)`` means no bounds at all,
+        i.e. all variables are allowed to be any real.
+    method : str, optional
+        The algorithm used to solve the standard form problem.
+        :ref:`'highs' <optimize.linprog-highs>` (default),
+        :ref:`'highs-ds' <optimize.linprog-highs-ds>`,
+        :ref:`'highs-ipm' <optimize.linprog-highs-ipm>`,
+        :ref:`'interior-point' <optimize.linprog-interior-point>` (legacy),
+        :ref:`'revised simplex' <optimize.linprog-revised_simplex>` (legacy),
+        and
+        :ref:`'simplex' <optimize.linprog-simplex>` (legacy) are supported.
+        The legacy methods are deprecated and will be removed in SciPy 1.11.0.
+    callback : callable, optional
+        If a callback function is provided, it will be called at least once per
+        iteration of the algorithm. The callback function must accept a single
+        `scipy.optimize.OptimizeResult` consisting of the following fields:
+
+        x : 1-D array
+            The current solution vector.
+        fun : float
+            The current value of the objective function ``c @ x``.
+        success : bool
+            ``True`` when the algorithm has completed successfully.
+        slack : 1-D array
+            The (nominally positive) values of the slack,
+            ``b_ub - A_ub @ x``.
+        con : 1-D array
+            The (nominally zero) residuals of the equality constraints,
+            ``b_eq - A_eq @ x``.
+        phase : int
+            The phase of the algorithm being executed.
+        status : int
+            An integer representing the status of the algorithm.
+
+            ``0`` : Optimization proceeding nominally.
+
+            ``1`` : Iteration limit reached.
+
+            ``2`` : Problem appears to be infeasible.
+
+            ``3`` : Problem appears to be unbounded.
+
+            ``4`` : Numerical difficulties encountered.
+
+            nit : int
+                The current iteration number.
+            message : str
+                A string descriptor of the algorithm status.
+
+        Callback functions are not currently supported by the HiGHS methods.
+
+    options : dict, optional
+        A dictionary of solver options. All methods accept the following
+        options:
+
+        maxiter : int
+            Maximum number of iterations to perform.
+            Default: see method-specific documentation.
+        disp : bool
+            Set to ``True`` to print convergence messages.
+            Default: ``False``.
+        presolve : bool
+            Set to ``False`` to disable automatic presolve.
+            Default: ``True``.
+
+        All methods except the HiGHS solvers also accept:
+
+        tol : float
+            A tolerance which determines when a residual is "close enough" to
+            zero to be considered exactly zero.
+        autoscale : bool
+            Set to ``True`` to automatically perform equilibration.
+            Consider using this option if the numerical values in the
+            constraints are separated by several orders of magnitude.
+            Default: ``False``.
+        rr : bool
+            Set to ``False`` to disable automatic redundancy removal.
+            Default: ``True``.
+        rr_method : string
+            Method used to identify and remove redundant rows from the
+            equality constraint matrix after presolve. For problems with
+            dense input, the available methods for redundancy removal are:
+
+            "SVD":
+                Repeatedly performs singular value decomposition on
+                the matrix, detecting redundant rows based on nonzeros
+                in the left singular vectors that correspond with
+                zero singular values. May be fast when the matrix is
+                nearly full rank.
+            "pivot":
+                Uses the algorithm presented in [5]_ to identify
+                redundant rows.
+            "ID":
+                Uses a randomized interpolative decomposition.
+                Identifies columns of the matrix transpose not used in
+                a full-rank interpolative decomposition of the matrix.
+            None:
+                Uses "svd" if the matrix is nearly full rank, that is,
+                the difference between the matrix rank and the number
+                of rows is less than five. If not, uses "pivot". The
+                behavior of this default is subject to change without
+                prior notice.
+
+            Default: None.
+            For problems with sparse input, this option is ignored, and the
+            pivot-based algorithm presented in [5]_ is used.
+
+        For method-specific options, see
+        :func:`show_options('linprog') <show_options>`.
+
+    x0 : 1-D array, optional
+        Guess values of the decision variables, which will be refined by
+        the optimization algorithm. This argument is currently used only by the
+        'revised simplex' method, and can only be used if `x0` represents a
+        basic feasible solution.
+
+    integrality : 1-D array or int, optional
+        Indicates the type of integrality constraint on each decision variable.
+
+        ``0`` : Continuous variable; no integrality constraint.
+
+        ``1`` : Integer variable; decision variable must be an integer
+        within `bounds`.
+
+        ``2`` : Semi-continuous variable; decision variable must be within
+        `bounds` or take value ``0``.
+
+        ``3`` : Semi-integer variable; decision variable must be an integer
+        within `bounds` or take value ``0``.
+
+        By default, all variables are continuous.
+
+        For mixed integrality constraints, supply an array of shape `c.shape`.
+        To infer a constraint on each decision variable from shorter inputs,
+        the argument will be broadcasted to `c.shape` using `np.broadcast_to`.
+
+        This argument is currently used only by the ``'highs'`` method and
+        ignored otherwise.
+
+    Returns
+    -------
+    res : OptimizeResult
+        A :class:`scipy.optimize.OptimizeResult` consisting of the fields
+        below. Note that the return types of the fields may depend on whether
+        the optimization was successful, therefore it is recommended to check
+        `OptimizeResult.status` before relying on the other fields:
+
+        x : 1-D array
+            The values of the decision variables that minimizes the
+            objective function while satisfying the constraints.
+        fun : float
+            The optimal value of the objective function ``c @ x``.
+        slack : 1-D array
+            The (nominally positive) values of the slack variables,
+            ``b_ub - A_ub @ x``.
+        con : 1-D array
+            The (nominally zero) residuals of the equality constraints,
+            ``b_eq - A_eq @ x``.
+        success : bool
+            ``True`` when the algorithm succeeds in finding an optimal
+            solution.
+        status : int
+            An integer representing the exit status of the algorithm.
+
+            ``0`` : Optimization terminated successfully.
+
+            ``1`` : Iteration limit reached.
+
+            ``2`` : Problem appears to be infeasible.
+
+            ``3`` : Problem appears to be unbounded.
+
+            ``4`` : Numerical difficulties encountered.
+
+        nit : int
+            The total number of iterations performed in all phases.
+        message : str
+            A string descriptor of the exit status of the algorithm.
+
+    See Also
+    --------
+    show_options : Additional options accepted by the solvers.
+
+    Notes
+    -----
+    This section describes the available solvers that can be selected by the
+    'method' parameter.
+
+    `'highs-ds'` and
+    `'highs-ipm'` are interfaces to the
+    HiGHS simplex and interior-point method solvers [13]_, respectively.
+    `'highs'` (default) chooses between
+    the two automatically. These are the fastest linear
+    programming solvers in SciPy, especially for large, sparse problems;
+    which of these two is faster is problem-dependent.
+    The other solvers (`'interior-point'`, `'revised simplex'`, and
+    `'simplex'`) are legacy methods and will be removed in SciPy 1.11.0.
+
+    Method *highs-ds* is a wrapper of the C++ high performance dual
+    revised simplex implementation (HSOL) [13]_, [14]_. Method *highs-ipm*
+    is a wrapper of a C++ implementation of an **i**\ nterior-\ **p**\ oint
+    **m**\ ethod [13]_; it features a crossover routine, so it is as accurate
+    as a simplex solver. Method *highs* chooses between the two automatically.
+    For new code involving `linprog`, we recommend explicitly choosing one of
+    these three method values.
+
+    .. versionadded:: 1.6.0
+
+    Method *interior-point* uses the primal-dual path following algorithm
+    as outlined in [4]_. This algorithm supports sparse constraint matrices and
+    is typically faster than the simplex methods, especially for large, sparse
+    problems. Note, however, that the solution returned may be slightly less
+    accurate than those of the simplex methods and will not, in general,
+    correspond with a vertex of the polytope defined by the constraints.
+
+    .. versionadded:: 1.0.0
+
+    Method *revised simplex* uses the revised simplex method as described in
+    [9]_, except that a factorization [11]_ of the basis matrix, rather than
+    its inverse, is efficiently maintained and used to solve the linear systems
+    at each iteration of the algorithm.
+
+    .. versionadded:: 1.3.0
+
+    Method *simplex* uses a traditional, full-tableau implementation of
+    Dantzig's simplex algorithm [1]_, [2]_ (*not* the
+    Nelder-Mead simplex). This algorithm is included for backwards
+    compatibility and educational purposes.
+
+    .. versionadded:: 0.15.0
+
+    Before applying *interior-point*, *revised simplex*, or *simplex*,
+    a presolve procedure based on [8]_ attempts
+    to identify trivial infeasibilities, trivial unboundedness, and potential
+    problem simplifications. Specifically, it checks for:
+
+    - rows of zeros in ``A_eq`` or ``A_ub``, representing trivial constraints;
+    - columns of zeros in ``A_eq`` `and` ``A_ub``, representing unconstrained
+      variables;
+    - column singletons in ``A_eq``, representing fixed variables; and
+    - column singletons in ``A_ub``, representing simple bounds.
+
+    If presolve reveals that the problem is unbounded (e.g. an unconstrained
+    and unbounded variable has negative cost) or infeasible (e.g., a row of
+    zeros in ``A_eq`` corresponds with a nonzero in ``b_eq``), the solver
+    terminates with the appropriate status code. Note that presolve terminates
+    as soon as any sign of unboundedness is detected; consequently, a problem
+    may be reported as unbounded when in reality the problem is infeasible
+    (but infeasibility has not been detected yet). Therefore, if it is
+    important to know whether the problem is actually infeasible, solve the
+    problem again with option ``presolve=False``.
+
+    If neither infeasibility nor unboundedness are detected in a single pass
+    of the presolve, bounds are tightened where possible and fixed
+    variables are removed from the problem. Then, linearly dependent rows
+    of the ``A_eq`` matrix are removed, (unless they represent an
+    infeasibility) to avoid numerical difficulties in the primary solve
+    routine. Note that rows that are nearly linearly dependent (within a
+    prescribed tolerance) may also be removed, which can change the optimal
+    solution in rare cases. If this is a concern, eliminate redundancy from
+    your problem formulation and run with option ``rr=False`` or
+    ``presolve=False``.
+
+    Several potential improvements can be made here: additional presolve
+    checks outlined in [8]_ should be implemented, the presolve routine should
+    be run multiple times (until no further simplifications can be made), and
+    more of the efficiency improvements from [5]_ should be implemented in the
+    redundancy removal routines.
+
+    After presolve, the problem is transformed to standard form by converting
+    the (tightened) simple bounds to upper bound constraints, introducing
+    non-negative slack variables for inequality constraints, and expressing
+    unbounded variables as the difference between two non-negative variables.
+    Optionally, the problem is automatically scaled via equilibration [12]_.
+    The selected algorithm solves the standard form problem, and a
+    postprocessing routine converts the result to a solution to the original
+    problem.
+
+    References
+    ----------
+    .. [1] Dantzig, George B., Linear programming and extensions. Rand
+           Corporation Research Study Princeton Univ. Press, Princeton, NJ,
+           1963
+    .. [2] Hillier, S.H. and Lieberman, G.J. (1995), "Introduction to
+           Mathematical Programming", McGraw-Hill, Chapter 4.
+    .. [3] Bland, Robert G. New finite pivoting rules for the simplex method.
+           Mathematics of Operations Research (2), 1977: pp. 103-107.
+    .. [4] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point
+           optimizer for linear programming: an implementation of the
+           homogeneous algorithm." High performance optimization. Springer US,
+           2000. 197-232.
+    .. [5] Andersen, Erling D. "Finding all linearly dependent rows in
+           large-scale linear programming." Optimization Methods and Software
+           6.3 (1995): 219-227.
+    .. [6] Freund, Robert M. "Primal-Dual Interior-Point Methods for Linear
+           Programming based on Newton's Method." Unpublished Course Notes,
+           March 2004. Available 2/25/2017 at
+           https://ocw.mit.edu/courses/sloan-school-of-management/15-084j-nonlinear-programming-spring-2004/lecture-notes/lec14_int_pt_mthd.pdf
+    .. [7] Fourer, Robert. "Solving Linear Programs by Interior-Point Methods."
+           Unpublished Course Notes, August 26, 2005. Available 2/25/2017 at
+           http://www.4er.org/CourseNotes/Book%20B/B-III.pdf
+    .. [8] Andersen, Erling D., and Knud D. Andersen. "Presolving in linear
+           programming." Mathematical Programming 71.2 (1995): 221-245.
+    .. [9] Bertsimas, Dimitris, and J. Tsitsiklis. "Introduction to linear
+           programming." Athena Scientific 1 (1997): 997.
+    .. [10] Andersen, Erling D., et al. Implementation of interior point
+            methods for large scale linear programming. HEC/Universite de
+            Geneve, 1996.
+    .. [11] Bartels, Richard H. "A stabilization of the simplex method."
+            Journal in  Numerische Mathematik 16.5 (1971): 414-434.
+    .. [12] Tomlin, J. A. "On scaling linear programming problems."
+            Mathematical Programming Study 4 (1975): 146-166.
+    .. [13] Huangfu, Q., Galabova, I., Feldmeier, M., and Hall, J. A. J.
+            "HiGHS - high performance software for linear optimization."
+            https://highs.dev/
+    .. [14] Huangfu, Q. and Hall, J. A. J. "Parallelizing the dual revised
+            simplex method." Mathematical Programming Computation, 10 (1),
+            119-142, 2018. DOI: 10.1007/s12532-017-0130-5
+
+    Examples
+    --------
+    Consider the following problem:
+
+    .. math::
+
+        \min_{x_0, x_1} \ -x_0 + 4x_1 & \\
+        \mbox{such that} \ -3x_0 + x_1 & \leq 6,\\
+        -x_0 - 2x_1 & \geq -4,\\
+        x_1 & \geq -3.
+
+    The problem is not presented in the form accepted by `linprog`. This is
+    easily remedied by converting the "greater than" inequality
+    constraint to a "less than" inequality constraint by
+    multiplying both sides by a factor of :math:`-1`. Note also that the last
+    constraint is really the simple bound :math:`-3 \leq x_1 \leq \infty`.
+    Finally, since there are no bounds on :math:`x_0`, we must explicitly
+    specify the bounds :math:`-\infty \leq x_0 \leq \infty`, as the
+    default is for variables to be non-negative. After collecting coeffecients
+    into arrays and tuples, the input for this problem is:
+
+    >>> from scipy.optimize import linprog
+    >>> c = [-1, 4]
+    >>> A = [[-3, 1], [1, 2]]
+    >>> b = [6, 4]
+    >>> x0_bounds = (None, None)
+    >>> x1_bounds = (-3, None)
+    >>> res = linprog(c, A_ub=A, b_ub=b, bounds=[x0_bounds, x1_bounds])
+    >>> res.fun
+    -22.0
+    >>> res.x
+    array([10., -3.])
+    >>> res.message
+    'Optimization terminated successfully. (HiGHS Status 7: Optimal)'
+
+    The marginals (AKA dual values / shadow prices / Lagrange multipliers)
+    and residuals (slacks) are also available.
+
+    >>> res.ineqlin
+      residual: [ 3.900e+01  0.000e+00]
+     marginals: [-0.000e+00 -1.000e+00]
+
+    For example, because the marginal associated with the second inequality
+    constraint is -1, we expect the optimal value of the objective function
+    to decrease by ``eps`` if we add a small amount ``eps`` to the right hand
+    side of the second inequality constraint:
+
+    >>> eps = 0.05
+    >>> b[1] += eps
+    >>> linprog(c, A_ub=A, b_ub=b, bounds=[x0_bounds, x1_bounds]).fun
+    -22.05
+
+    Also, because the residual on the first inequality constraint is 39, we
+    can decrease the right hand side of the first constraint by 39 without
+    affecting the optimal solution.
+
+    >>> b = [6, 4]  # reset to original values
+    >>> b[0] -= 39
+    >>> linprog(c, A_ub=A, b_ub=b, bounds=[x0_bounds, x1_bounds]).fun
+    -22.0
+
+    """
+
+    meth = method.lower()
+    methods = {"highs", "highs-ds", "highs-ipm",
+               "simplex", "revised simplex", "interior-point"}
+
+    if meth not in methods:
+        raise ValueError(f"Unknown solver '{method}'")
+
+    if x0 is not None and meth != "revised simplex":
+        warning_message = "x0 is used only when method is 'revised simplex'. "
+        warn(warning_message, OptimizeWarning, stacklevel=2)
+
+    if np.any(integrality) and not meth == "highs":
+        integrality = None
+        warning_message = ("Only `method='highs'` supports integer "
+                           "constraints. Ignoring `integrality`.")
+        warn(warning_message, OptimizeWarning, stacklevel=2)
+    elif np.any(integrality):
+        integrality = np.broadcast_to(integrality, np.shape(c))
+    else:
+        integrality = None
+
+    lp = _LPProblem(c, A_ub, b_ub, A_eq, b_eq, bounds, x0, integrality)
+    lp, solver_options = _parse_linprog(lp, options, meth)
+    tol = solver_options.get('tol', 1e-9)
+
+    # Give unmodified problem to HiGHS
+    if meth.startswith('highs'):
+        if callback is not None:
+            raise NotImplementedError("HiGHS solvers do not support the "
+                                      "callback interface.")
+        highs_solvers = {'highs-ipm': 'ipm', 'highs-ds': 'simplex',
+                         'highs': None}
+
+        sol = _linprog_highs(lp, solver=highs_solvers[meth],
+                             **solver_options)
+        sol['status'], sol['message'] = (
+            _check_result(sol['x'], sol['fun'], sol['status'], sol['slack'],
+                          sol['con'], lp.bounds, tol, sol['message'],
+                          integrality))
+        sol['success'] = sol['status'] == 0
+        return OptimizeResult(sol)
+
+    warn(f"`method='{meth}'` is deprecated and will be removed in SciPy "
+         "1.11.0. Please use one of the HiGHS solvers (e.g. "
+         "`method='highs'`) in new code.", DeprecationWarning, stacklevel=2)
+
+    iteration = 0
+    complete = False  # will become True if solved in presolve
+    undo = []
+
+    # Keep the original arrays to calculate slack/residuals for original
+    # problem.
+    lp_o = deepcopy(lp)
+
+    # Solve trivial problem, eliminate variables, tighten bounds, etc.
+    rr_method = solver_options.pop('rr_method', None)  # need to pop these;
+    rr = solver_options.pop('rr', True)  # they're not passed to methods
+    c0 = 0  # we might get a constant term in the objective
+    if solver_options.pop('presolve', True):
+        (lp, c0, x, undo, complete, status, message) = _presolve(lp, rr,
+                                                                 rr_method,
+                                                                 tol)
+
+    C, b_scale = 1, 1  # for trivial unscaling if autoscale is not used
+    postsolve_args = (lp_o._replace(bounds=lp.bounds), undo, C, b_scale)
+
+    if not complete:
+        A, b, c, c0, x0 = _get_Abc(lp, c0)
+        if solver_options.pop('autoscale', False):
+            A, b, c, x0, C, b_scale = _autoscale(A, b, c, x0)
+            postsolve_args = postsolve_args[:-2] + (C, b_scale)
+
+        if meth == 'simplex':
+            x, status, message, iteration = _linprog_simplex(
+                c, c0=c0, A=A, b=b, callback=callback,
+                postsolve_args=postsolve_args, **solver_options)
+        elif meth == 'interior-point':
+            x, status, message, iteration = _linprog_ip(
+                c, c0=c0, A=A, b=b, callback=callback,
+                postsolve_args=postsolve_args, **solver_options)
+        elif meth == 'revised simplex':
+            x, status, message, iteration = _linprog_rs(
+                c, c0=c0, A=A, b=b, x0=x0, callback=callback,
+                postsolve_args=postsolve_args, **solver_options)
+
+    # Eliminate artificial variables, re-introduce presolved variables, etc.
+    disp = solver_options.get('disp', False)
+
+    x, fun, slack, con = _postsolve(x, postsolve_args, complete)
+
+    status, message = _check_result(x, fun, status, slack, con, lp_o.bounds,
+                                    tol, message, integrality)
+
+    if disp:
+        _display_summary(message, status, fun, iteration)
+
+    sol = {
+        'x': x,
+        'fun': fun,
+        'slack': slack,
+        'con': con,
+        'status': status,
+        'message': message,
+        'nit': iteration,
+        'success': status == 0}
+
+    return OptimizeResult(sol)

llava_next/lib/python3.10/site-packages/scipy/optimize/_linprog_highs.py

@@ -0,0 +1,440 @@
+"""HiGHS Linear Optimization Methods
+
+Interface to HiGHS linear optimization software.
+https://highs.dev/
+
+.. versionadded:: 1.5.0
+
+References
+----------
+.. [1] Q. Huangfu and J.A.J. Hall. "Parallelizing the dual revised simplex
+           method." Mathematical Programming Computation, 10 (1), 119-142,
+           2018. DOI: 10.1007/s12532-017-0130-5
+
+"""
+
+import inspect
+import numpy as np
+from ._optimize import OptimizeWarning, OptimizeResult
+from warnings import warn
+from ._highs._highs_wrapper import _highs_wrapper
+from ._highs._highs_constants import (
+    CONST_INF,
+    MESSAGE_LEVEL_NONE,
+    HIGHS_OBJECTIVE_SENSE_MINIMIZE,
+
+    MODEL_STATUS_NOTSET,
+    MODEL_STATUS_LOAD_ERROR,
+    MODEL_STATUS_MODEL_ERROR,
+    MODEL_STATUS_PRESOLVE_ERROR,
+    MODEL_STATUS_SOLVE_ERROR,
+    MODEL_STATUS_POSTSOLVE_ERROR,
+    MODEL_STATUS_MODEL_EMPTY,
+    MODEL_STATUS_OPTIMAL,
+    MODEL_STATUS_INFEASIBLE,
+    MODEL_STATUS_UNBOUNDED_OR_INFEASIBLE,
+    MODEL_STATUS_UNBOUNDED,
+    MODEL_STATUS_REACHED_DUAL_OBJECTIVE_VALUE_UPPER_BOUND
+    as MODEL_STATUS_RDOVUB,
+    MODEL_STATUS_REACHED_OBJECTIVE_TARGET,
+    MODEL_STATUS_REACHED_TIME_LIMIT,
+    MODEL_STATUS_REACHED_ITERATION_LIMIT,
+
+    HIGHS_SIMPLEX_STRATEGY_DUAL,
+
+    HIGHS_SIMPLEX_CRASH_STRATEGY_OFF,
+
+    HIGHS_SIMPLEX_EDGE_WEIGHT_STRATEGY_CHOOSE,
+    HIGHS_SIMPLEX_EDGE_WEIGHT_STRATEGY_DANTZIG,
+    HIGHS_SIMPLEX_EDGE_WEIGHT_STRATEGY_DEVEX,
+    HIGHS_SIMPLEX_EDGE_WEIGHT_STRATEGY_STEEPEST_EDGE,
+)
+from scipy.sparse import csc_matrix, vstack, issparse
+
+
+def _highs_to_scipy_status_message(highs_status, highs_message):
+    """Converts HiGHS status number/message to SciPy status number/message"""
+
+    scipy_statuses_messages = {
+        None: (4, "HiGHS did not provide a status code. "),
+        MODEL_STATUS_NOTSET: (4, ""),
+        MODEL_STATUS_LOAD_ERROR: (4, ""),
+        MODEL_STATUS_MODEL_ERROR: (2, ""),
+        MODEL_STATUS_PRESOLVE_ERROR: (4, ""),
+        MODEL_STATUS_SOLVE_ERROR: (4, ""),
+        MODEL_STATUS_POSTSOLVE_ERROR: (4, ""),
+        MODEL_STATUS_MODEL_EMPTY: (4, ""),
+        MODEL_STATUS_RDOVUB: (4, ""),
+        MODEL_STATUS_REACHED_OBJECTIVE_TARGET: (4, ""),
+        MODEL_STATUS_OPTIMAL: (0, "Optimization terminated successfully. "),
+        MODEL_STATUS_REACHED_TIME_LIMIT: (1, "Time limit reached. "),
+        MODEL_STATUS_REACHED_ITERATION_LIMIT: (1, "Iteration limit reached. "),
+        MODEL_STATUS_INFEASIBLE: (2, "The problem is infeasible. "),
+        MODEL_STATUS_UNBOUNDED: (3, "The problem is unbounded. "),
+        MODEL_STATUS_UNBOUNDED_OR_INFEASIBLE: (4, "The problem is unbounded "
+                                               "or infeasible. ")}
+    unrecognized = (4, "The HiGHS status code was not recognized. ")
+    scipy_status, scipy_message = (
+        scipy_statuses_messages.get(highs_status, unrecognized))
+    scipy_message = (f"{scipy_message}"
+                     f"(HiGHS Status {highs_status}: {highs_message})")
+    return scipy_status, scipy_message
+
+
+def _replace_inf(x):
+    # Replace `np.inf` with CONST_INF
+    infs = np.isinf(x)
+    with np.errstate(invalid="ignore"):
+        x[infs] = np.sign(x[infs])*CONST_INF
+    return x
+
+
+def _convert_to_highs_enum(option, option_str, choices):
+    # If option is in the choices we can look it up, if not use
+    # the default value taken from function signature and warn:
+    try:
+        return choices[option.lower()]
+    except AttributeError:
+        return choices[option]
+    except KeyError:
+        sig = inspect.signature(_linprog_highs)
+        default_str = sig.parameters[option_str].default
+        warn(f"Option {option_str} is {option}, but only values in "
+             f"{set(choices.keys())} are allowed. Using default: "
+             f"{default_str}.",
+             OptimizeWarning, stacklevel=3)
+        return choices[default_str]
+
+
+def _linprog_highs(lp, solver, time_limit=None, presolve=True,
+                   disp=False, maxiter=None,
+                   dual_feasibility_tolerance=None,
+                   primal_feasibility_tolerance=None,
+                   ipm_optimality_tolerance=None,
+                   simplex_dual_edge_weight_strategy=None,
+                   mip_rel_gap=None,
+                   mip_max_nodes=None,
+                   **unknown_options):
+    r"""
+    Solve the following linear programming problem using one of the HiGHS
+    solvers:
+
+    User-facing documentation is in _linprog_doc.py.
+
+    Parameters
+    ----------
+    lp :  _LPProblem
+        A ``scipy.optimize._linprog_util._LPProblem`` ``namedtuple``.
+    solver : "ipm" or "simplex" or None
+        Which HiGHS solver to use.  If ``None``, "simplex" will be used.
+
+    Options
+    -------
+    maxiter : int
+        The maximum number of iterations to perform in either phase. For
+        ``solver='ipm'``, this does not include the number of crossover
+        iterations.  Default is the largest possible value for an ``int``
+        on the platform.
+    disp : bool
+        Set to ``True`` if indicators of optimization status are to be printed
+        to the console each iteration; default ``False``.
+    time_limit : float
+        The maximum time in seconds allotted to solve the problem; default is
+        the largest possible value for a ``double`` on the platform.
+    presolve : bool
+        Presolve attempts to identify trivial infeasibilities,
+        identify trivial unboundedness, and simplify the problem before
+        sending it to the main solver. It is generally recommended
+        to keep the default setting ``True``; set to ``False`` if presolve is
+        to be disabled.
+    dual_feasibility_tolerance : double
+        Dual feasibility tolerance.  Default is 1e-07.
+        The minimum of this and ``primal_feasibility_tolerance``
+        is used for the feasibility tolerance when ``solver='ipm'``.
+    primal_feasibility_tolerance : double
+        Primal feasibility tolerance.  Default is 1e-07.
+        The minimum of this and ``dual_feasibility_tolerance``
+        is used for the feasibility tolerance when ``solver='ipm'``.
+    ipm_optimality_tolerance : double
+        Optimality tolerance for ``solver='ipm'``.  Default is 1e-08.
+        Minimum possible value is 1e-12 and must be smaller than the largest
+        possible value for a ``double`` on the platform.
+    simplex_dual_edge_weight_strategy : str (default: None)
+        Strategy for simplex dual edge weights. The default, ``None``,
+        automatically selects one of the following.
+
+        ``'dantzig'`` uses Dantzig's original strategy of choosing the most
+        negative reduced cost.
+
+        ``'devex'`` uses the strategy described in [15]_.
+
+        ``steepest`` uses the exact steepest edge strategy as described in
+        [16]_.
+
+        ``'steepest-devex'`` begins with the exact steepest edge strategy
+        until the computation is too costly or inexact and then switches to
+        the devex method.
+
+        Currently, using ``None`` always selects ``'steepest-devex'``, but this
+        may change as new options become available.
+
+    mip_max_nodes : int
+        The maximum number of nodes allotted to solve the problem; default is
+        the largest possible value for a ``HighsInt`` on the platform.
+        Ignored if not using the MIP solver.
+    unknown_options : dict
+        Optional arguments not used by this particular solver. If
+        ``unknown_options`` is non-empty, a warning is issued listing all
+        unused options.
+
+    Returns
+    -------
+    sol : dict
+        A dictionary consisting of the fields:
+
+            x : 1D array
+                The values of the decision variables that minimizes the
+                objective function while satisfying the constraints.
+            fun : float
+                The optimal value of the objective function ``c @ x``.
+            slack : 1D array
+                The (nominally positive) values of the slack,
+                ``b_ub - A_ub @ x``.
+            con : 1D array
+                The (nominally zero) residuals of the equality constraints,
+                ``b_eq - A_eq @ x``.
+            success : bool
+                ``True`` when the algorithm succeeds in finding an optimal
+                solution.
+            status : int
+                An integer representing the exit status of the algorithm.
+
+                ``0`` : Optimization terminated successfully.
+
+                ``1`` : Iteration or time limit reached.
+
+                ``2`` : Problem appears to be infeasible.
+
+                ``3`` : Problem appears to be unbounded.
+
+                ``4`` : The HiGHS solver ran into a problem.
+
+            message : str
+                A string descriptor of the exit status of the algorithm.
+            nit : int
+                The total number of iterations performed.
+                For ``solver='simplex'``, this includes iterations in all
+                phases. For ``solver='ipm'``, this does not include
+                crossover iterations.
+            crossover_nit : int
+                The number of primal/dual pushes performed during the
+                crossover routine for ``solver='ipm'``.  This is ``0``
+                for ``solver='simplex'``.
+            ineqlin : OptimizeResult
+                Solution and sensitivity information corresponding to the
+                inequality constraints, `b_ub`. A dictionary consisting of the
+                fields:
+
+                residual : np.ndnarray
+                    The (nominally positive) values of the slack variables,
+                    ``b_ub - A_ub @ x``.  This quantity is also commonly
+                    referred to as "slack".
+
+                marginals : np.ndarray
+                    The sensitivity (partial derivative) of the objective
+                    function with respect to the right-hand side of the
+                    inequality constraints, `b_ub`.
+
+            eqlin : OptimizeResult
+                Solution and sensitivity information corresponding to the
+                equality constraints, `b_eq`.  A dictionary consisting of the
+                fields:
+
+                residual : np.ndarray
+                    The (nominally zero) residuals of the equality constraints,
+                    ``b_eq - A_eq @ x``.
+
+                marginals : np.ndarray
+                    The sensitivity (partial derivative) of the objective
+                    function with respect to the right-hand side of the
+                    equality constraints, `b_eq`.
+
+            lower, upper : OptimizeResult
+                Solution and sensitivity information corresponding to the
+                lower and upper bounds on decision variables, `bounds`.
+
+                residual : np.ndarray
+                    The (nominally positive) values of the quantity
+                    ``x - lb`` (lower) or ``ub - x`` (upper).
+
+                marginals : np.ndarray
+                    The sensitivity (partial derivative) of the objective
+                    function with respect to the lower and upper
+                    `bounds`.
+
+            mip_node_count : int
+                The number of subproblems or "nodes" solved by the MILP
+                solver. Only present when `integrality` is not `None`.
+
+            mip_dual_bound : float
+                The MILP solver's final estimate of the lower bound on the
+                optimal solution. Only present when `integrality` is not
+                `None`.
+
+            mip_gap : float
+                The difference between the final objective function value
+                and the final dual bound, scaled by the final objective
+                function value. Only present when `integrality` is not
+                `None`.
+
+    Notes
+    -----
+    The result fields `ineqlin`, `eqlin`, `lower`, and `upper` all contain
+    `marginals`, or partial derivatives of the objective function with respect
+    to the right-hand side of each constraint. These partial derivatives are
+    also referred to as "Lagrange multipliers", "dual values", and
+    "shadow prices". The sign convention of `marginals` is opposite that
+    of Lagrange multipliers produced by many nonlinear solvers.
+
+    References
+    ----------
+    .. [15] Harris, Paula MJ. "Pivot selection methods of the Devex LP code."
+            Mathematical programming 5.1 (1973): 1-28.
+    .. [16] Goldfarb, Donald, and John Ker Reid. "A practicable steepest-edge
+            simplex algorithm." Mathematical Programming 12.1 (1977): 361-371.
+    """
+    if unknown_options:
+        message = (f"Unrecognized options detected: {unknown_options}. "
+                   "These will be passed to HiGHS verbatim.")
+        warn(message, OptimizeWarning, stacklevel=3)
+
+    # Map options to HiGHS enum values
+    simplex_dual_edge_weight_strategy_enum = _convert_to_highs_enum(
+        simplex_dual_edge_weight_strategy,
+        'simplex_dual_edge_weight_strategy',
+        choices={'dantzig': HIGHS_SIMPLEX_EDGE_WEIGHT_STRATEGY_DANTZIG,
+                 'devex': HIGHS_SIMPLEX_EDGE_WEIGHT_STRATEGY_DEVEX,
+                 'steepest-devex': HIGHS_SIMPLEX_EDGE_WEIGHT_STRATEGY_CHOOSE,
+                 'steepest':
+                 HIGHS_SIMPLEX_EDGE_WEIGHT_STRATEGY_STEEPEST_EDGE,
+                 None: None})
+
+    c, A_ub, b_ub, A_eq, b_eq, bounds, x0, integrality = lp
+
+    lb, ub = bounds.T.copy()  # separate bounds, copy->C-cntgs
+    # highs_wrapper solves LHS <= A*x <= RHS, not equality constraints
+    with np.errstate(invalid="ignore"):
+        lhs_ub = -np.ones_like(b_ub)*np.inf  # LHS of UB constraints is -inf
+    rhs_ub = b_ub  # RHS of UB constraints is b_ub
+    lhs_eq = b_eq  # Equality constraint is inequality
+    rhs_eq = b_eq  # constraint with LHS=RHS
+    lhs = np.concatenate((lhs_ub, lhs_eq))
+    rhs = np.concatenate((rhs_ub, rhs_eq))
+
+    if issparse(A_ub) or issparse(A_eq):
+        A = vstack((A_ub, A_eq))
+    else:
+        A = np.vstack((A_ub, A_eq))
+    A = csc_matrix(A)
+
+    options = {
+        'presolve': presolve,
+        'sense': HIGHS_OBJECTIVE_SENSE_MINIMIZE,
+        'solver': solver,
+        'time_limit': time_limit,
+        'highs_debug_level': MESSAGE_LEVEL_NONE,
+        'dual_feasibility_tolerance': dual_feasibility_tolerance,
+        'ipm_optimality_tolerance': ipm_optimality_tolerance,
+        'log_to_console': disp,
+        'mip_max_nodes': mip_max_nodes,
+        'output_flag': disp,
+        'primal_feasibility_tolerance': primal_feasibility_tolerance,
+        'simplex_dual_edge_weight_strategy':
+            simplex_dual_edge_weight_strategy_enum,
+        'simplex_strategy': HIGHS_SIMPLEX_STRATEGY_DUAL,
+        'simplex_crash_strategy': HIGHS_SIMPLEX_CRASH_STRATEGY_OFF,
+        'ipm_iteration_limit': maxiter,
+        'simplex_iteration_limit': maxiter,
+        'mip_rel_gap': mip_rel_gap,
+    }
+    options.update(unknown_options)
+
+    # np.inf doesn't work; use very large constant
+    rhs = _replace_inf(rhs)
+    lhs = _replace_inf(lhs)
+    lb = _replace_inf(lb)
+    ub = _replace_inf(ub)
+
+    if integrality is None or np.sum(integrality) == 0:
+        integrality = np.empty(0)
+    else:
+        integrality = np.array(integrality)
+
+    res = _highs_wrapper(c, A.indptr, A.indices, A.data, lhs, rhs,
+                         lb, ub, integrality.astype(np.uint8), options)
+
+    # HiGHS represents constraints as lhs/rhs, so
+    # Ax + s = b => Ax = b - s
+    # and we need to split up s by A_ub and A_eq
+    if 'slack' in res:
+        slack = res['slack']
+        con = np.array(slack[len(b_ub):])
+        slack = np.array(slack[:len(b_ub)])
+    else:
+        slack, con = None, None
+
+    # lagrange multipliers for equalities/inequalities and upper/lower bounds
+    if 'lambda' in res:
+        lamda = res['lambda']
+        marg_ineqlin = np.array(lamda[:len(b_ub)])
+        marg_eqlin = np.array(lamda[len(b_ub):])
+        marg_upper = np.array(res['marg_bnds'][1, :])
+        marg_lower = np.array(res['marg_bnds'][0, :])
+    else:
+        marg_ineqlin, marg_eqlin = None, None
+        marg_upper, marg_lower = None, None
+
+    # this needs to be updated if we start choosing the solver intelligently
+
+    # Convert to scipy-style status and message
+    highs_status = res.get('status', None)
+    highs_message = res.get('message', None)
+    status, message = _highs_to_scipy_status_message(highs_status,
+                                                     highs_message)
+
+    x = np.array(res['x']) if 'x' in res else None
+    sol = {'x': x,
+           'slack': slack,
+           'con': con,
+           'ineqlin': OptimizeResult({
+               'residual': slack,
+               'marginals': marg_ineqlin,
+           }),
+           'eqlin': OptimizeResult({
+               'residual': con,
+               'marginals': marg_eqlin,
+           }),
+           'lower': OptimizeResult({
+               'residual': None if x is None else x - lb,
+               'marginals': marg_lower,
+           }),
+           'upper': OptimizeResult({
+               'residual': None if x is None else ub - x,
+               'marginals': marg_upper
+            }),
+           'fun': res.get('fun'),
+           'status': status,
+           'success': res['status'] == MODEL_STATUS_OPTIMAL,
+           'message': message,
+           'nit': res.get('simplex_nit', 0) or res.get('ipm_nit', 0),
+           'crossover_nit': res.get('crossover_nit'),
+           }
+
+    if np.any(x) and integrality is not None:
+        sol.update({
+            'mip_node_count': res.get('mip_node_count', 0),
+            'mip_dual_bound': res.get('mip_dual_bound', 0.0),
+            'mip_gap': res.get('mip_gap', 0.0),
+        })
+
+    return sol

llava_next/lib/python3.10/site-packages/scipy/optimize/_linprog_util.py

@@ -0,0 +1,1522 @@
+"""
+Method agnostic utility functions for linear programming
+"""
+
+import numpy as np
+import scipy.sparse as sps
+from warnings import warn
+from ._optimize import OptimizeWarning
+from scipy.optimize._remove_redundancy import (
+    _remove_redundancy_svd, _remove_redundancy_pivot_sparse,
+    _remove_redundancy_pivot_dense, _remove_redundancy_id
+    )
+from collections import namedtuple
+
+_LPProblem = namedtuple('_LPProblem',
+                        'c A_ub b_ub A_eq b_eq bounds x0 integrality')
+_LPProblem.__new__.__defaults__ = (None,) * 7  # make c the only required arg
+_LPProblem.__doc__ = \
+    """ Represents a linear-programming problem.
+
+    Attributes
+    ----------
+    c : 1D array
+        The coefficients of the linear objective function to be minimized.
+    A_ub : 2D array, optional
+        The inequality constraint matrix. Each row of ``A_ub`` specifies the
+        coefficients of a linear inequality constraint on ``x``.
+    b_ub : 1D array, optional
+        The inequality constraint vector. Each element represents an
+        upper bound on the corresponding value of ``A_ub @ x``.
+    A_eq : 2D array, optional
+        The equality constraint matrix. Each row of ``A_eq`` specifies the
+        coefficients of a linear equality constraint on ``x``.
+    b_eq : 1D array, optional
+        The equality constraint vector. Each element of ``A_eq @ x`` must equal
+        the corresponding element of ``b_eq``.
+    bounds : various valid formats, optional
+        The bounds of ``x``, as ``min`` and ``max`` pairs.
+        If bounds are specified for all N variables separately, valid formats
+        are:
+        * a 2D array (N x 2);
+        * a sequence of N sequences, each with 2 values.
+        If all variables have the same bounds, the bounds can be specified as
+        a 1-D or 2-D array or sequence with 2 scalar values.
+        If all variables have a lower bound of 0 and no upper bound, the bounds
+        parameter can be omitted (or given as None).
+        Absent lower and/or upper bounds can be specified as -numpy.inf (no
+        lower bound), numpy.inf (no upper bound) or None (both).
+    x0 : 1D array, optional
+        Guess values of the decision variables, which will be refined by
+        the optimization algorithm. This argument is currently used only by the
+        'revised simplex' method, and can only be used if `x0` represents a
+        basic feasible solution.
+    integrality : 1-D array or int, optional
+        Indicates the type of integrality constraint on each decision variable.
+
+        ``0`` : Continuous variable; no integrality constraint.
+
+        ``1`` : Integer variable; decision variable must be an integer
+        within `bounds`.
+
+        ``2`` : Semi-continuous variable; decision variable must be within
+        `bounds` or take value ``0``.
+
+        ``3`` : Semi-integer variable; decision variable must be an integer
+        within `bounds` or take value ``0``.
+
+        By default, all variables are continuous.
+
+        For mixed integrality constraints, supply an array of shape `c.shape`.
+        To infer a constraint on each decision variable from shorter inputs,
+        the argument will be broadcasted to `c.shape` using `np.broadcast_to`.
+
+        This argument is currently used only by the ``'highs'`` method and
+        ignored otherwise.
+
+    Notes
+    -----
+    This namedtuple supports 2 ways of initialization:
+    >>> lp1 = _LPProblem(c=[-1, 4], A_ub=[[-3, 1], [1, 2]], b_ub=[6, 4])
+    >>> lp2 = _LPProblem([-1, 4], [[-3, 1], [1, 2]], [6, 4])
+
+    Note that only ``c`` is a required argument here, whereas all other arguments
+    ``A_ub``, ``b_ub``, ``A_eq``, ``b_eq``, ``bounds``, ``x0`` are optional with
+    default values of None.
+    For example, ``A_eq`` and ``b_eq`` can be set without ``A_ub`` or ``b_ub``:
+    >>> lp3 = _LPProblem(c=[-1, 4], A_eq=[[2, 1]], b_eq=[10])
+    """
+
+
+def _check_sparse_inputs(options, meth, A_ub, A_eq):
+    """
+    Check the provided ``A_ub`` and ``A_eq`` matrices conform to the specified
+    optional sparsity variables.
+
+    Parameters
+    ----------
+    A_ub : 2-D array, optional
+        2-D array such that ``A_ub @ x`` gives the values of the upper-bound
+        inequality constraints at ``x``.
+    A_eq : 2-D array, optional
+        2-D array such that ``A_eq @ x`` gives the values of the equality
+        constraints at ``x``.
+    options : dict
+        A dictionary of solver options. All methods accept the following
+        generic options:
+
+            maxiter : int
+                Maximum number of iterations to perform.
+            disp : bool
+                Set to True to print convergence messages.
+
+        For method-specific options, see :func:`show_options('linprog')`.
+    method : str, optional
+        The algorithm used to solve the standard form problem.
+
+    Returns
+    -------
+    A_ub : 2-D array, optional
+        2-D array such that ``A_ub @ x`` gives the values of the upper-bound
+        inequality constraints at ``x``.
+    A_eq : 2-D array, optional
+        2-D array such that ``A_eq @ x`` gives the values of the equality
+        constraints at ``x``.
+    options : dict
+        A dictionary of solver options. All methods accept the following
+        generic options:
+
+            maxiter : int
+                Maximum number of iterations to perform.
+            disp : bool
+                Set to True to print convergence messages.
+
+        For method-specific options, see :func:`show_options('linprog')`.
+    """
+    # This is an undocumented option for unit testing sparse presolve
+    _sparse_presolve = options.pop('_sparse_presolve', False)
+    if _sparse_presolve and A_eq is not None:
+        A_eq = sps.coo_matrix(A_eq)
+    if _sparse_presolve and A_ub is not None:
+        A_ub = sps.coo_matrix(A_ub)
+
+    sparse_constraint = sps.issparse(A_eq) or sps.issparse(A_ub)
+
+    preferred_methods = {"highs", "highs-ds", "highs-ipm"}
+    dense_methods = {"simplex", "revised simplex"}
+    if meth in dense_methods and sparse_constraint:
+        raise ValueError(f"Method '{meth}' does not support sparse "
+                         "constraint matrices. Please consider using one of "
+                         f"{preferred_methods}.")
+
+    sparse = options.get('sparse', False)
+    if not sparse and sparse_constraint and meth == 'interior-point':
+        options['sparse'] = True
+        warn("Sparse constraint matrix detected; setting 'sparse':True.",
+             OptimizeWarning, stacklevel=4)
+    return options, A_ub, A_eq
+
+
+def _format_A_constraints(A, n_x, sparse_lhs=False):
+    """Format the left hand side of the constraints to a 2-D array
+
+    Parameters
+    ----------
+    A : 2-D array
+        2-D array such that ``A @ x`` gives the values of the upper-bound
+        (in)equality constraints at ``x``.
+    n_x : int
+        The number of variables in the linear programming problem.
+    sparse_lhs : bool
+        Whether either of `A_ub` or `A_eq` are sparse. If true return a
+        coo_matrix instead of a numpy array.
+
+    Returns
+    -------
+    np.ndarray or sparse.coo_matrix
+        2-D array such that ``A @ x`` gives the values of the upper-bound
+        (in)equality constraints at ``x``.
+
+    """
+    if sparse_lhs:
+        return sps.coo_matrix(
+            (0, n_x) if A is None else A, dtype=float, copy=True
+        )
+    elif A is None:
+        return np.zeros((0, n_x), dtype=float)
+    else:
+        return np.array(A, dtype=float, copy=True)
+
+
+def _format_b_constraints(b):
+    """Format the upper bounds of the constraints to a 1-D array
+
+    Parameters
+    ----------
+    b : 1-D array
+        1-D array of values representing the upper-bound of each (in)equality
+        constraint (row) in ``A``.
+
+    Returns
+    -------
+    1-D np.array
+        1-D array of values representing the upper-bound of each (in)equality
+        constraint (row) in ``A``.
+
+    """
+    if b is None:
+        return np.array([], dtype=float)
+    b = np.array(b, dtype=float, copy=True).squeeze()
+    return b if b.size != 1 else b.reshape(-1)
+
+
+def _clean_inputs(lp):
+    """
+    Given user inputs for a linear programming problem, return the
+    objective vector, upper bound constraints, equality constraints,
+    and simple bounds in a preferred format.
+
+    Parameters
+    ----------
+    lp : A `scipy.optimize._linprog_util._LPProblem` consisting of the following fields:
+
+        c : 1D array
+            The coefficients of the linear objective function to be minimized.
+        A_ub : 2D array, optional
+            The inequality constraint matrix. Each row of ``A_ub`` specifies the
+            coefficients of a linear inequality constraint on ``x``.
+        b_ub : 1D array, optional
+            The inequality constraint vector. Each element represents an
+            upper bound on the corresponding value of ``A_ub @ x``.
+        A_eq : 2D array, optional
+            The equality constraint matrix. Each row of ``A_eq`` specifies the
+            coefficients of a linear equality constraint on ``x``.
+        b_eq : 1D array, optional
+            The equality constraint vector. Each element of ``A_eq @ x`` must equal
+            the corresponding element of ``b_eq``.
+        bounds : various valid formats, optional
+            The bounds of ``x``, as ``min`` and ``max`` pairs.
+            If bounds are specified for all N variables separately, valid formats are:
+            * a 2D array (2 x N or N x 2);
+            * a sequence of N sequences, each with 2 values.
+            If all variables have the same bounds, a single pair of values can
+            be specified. Valid formats are:
+            * a sequence with 2 scalar values;
+            * a sequence with a single element containing 2 scalar values.
+            If all variables have a lower bound of 0 and no upper bound, the bounds
+            parameter can be omitted (or given as None).
+        x0 : 1D array, optional
+            Guess values of the decision variables, which will be refined by
+            the optimization algorithm. This argument is currently used only by the
+            'revised simplex' method, and can only be used if `x0` represents a
+            basic feasible solution.
+
+    Returns
+    -------
+    lp : A `scipy.optimize._linprog_util._LPProblem` consisting of the following fields:
+
+        c : 1D array
+            The coefficients of the linear objective function to be minimized.
+        A_ub : 2D array, optional
+            The inequality constraint matrix. Each row of ``A_ub`` specifies the
+            coefficients of a linear inequality constraint on ``x``.
+        b_ub : 1D array, optional
+            The inequality constraint vector. Each element represents an
+            upper bound on the corresponding value of ``A_ub @ x``.
+        A_eq : 2D array, optional
+            The equality constraint matrix. Each row of ``A_eq`` specifies the
+            coefficients of a linear equality constraint on ``x``.
+        b_eq : 1D array, optional
+            The equality constraint vector. Each element of ``A_eq @ x`` must equal
+            the corresponding element of ``b_eq``.
+        bounds : 2D array
+            The bounds of ``x``, as ``min`` and ``max`` pairs, one for each of the N
+            elements of ``x``. The N x 2 array contains lower bounds in the first
+            column and upper bounds in the 2nd. Unbounded variables have lower
+            bound -np.inf and/or upper bound np.inf.
+        x0 : 1D array, optional
+            Guess values of the decision variables, which will be refined by
+            the optimization algorithm. This argument is currently used only by the
+            'revised simplex' method, and can only be used if `x0` represents a
+            basic feasible solution.
+
+    """
+    c, A_ub, b_ub, A_eq, b_eq, bounds, x0, integrality = lp
+
+    if c is None:
+        raise TypeError
+
+    try:
+        c = np.array(c, dtype=np.float64, copy=True).squeeze()
+    except ValueError as e:
+        raise TypeError(
+            "Invalid input for linprog: c must be a 1-D array of numerical "
+            "coefficients") from e
+    else:
+        # If c is a single value, convert it to a 1-D array.
+        if c.size == 1:
+            c = c.reshape(-1)
+
+        n_x = len(c)
+        if n_x == 0 or len(c.shape) != 1:
+            raise ValueError(
+                "Invalid input for linprog: c must be a 1-D array and must "
+                "not have more than one non-singleton dimension")
+        if not np.isfinite(c).all():
+            raise ValueError(
+                "Invalid input for linprog: c must not contain values "
+                "inf, nan, or None")
+
+    sparse_lhs = sps.issparse(A_eq) or sps.issparse(A_ub)
+    try:
+        A_ub = _format_A_constraints(A_ub, n_x, sparse_lhs=sparse_lhs)
+    except ValueError as e:
+        raise TypeError(
+            "Invalid input for linprog: A_ub must be a 2-D array "
+            "of numerical values") from e
+    else:
+        n_ub = A_ub.shape[0]
+        if len(A_ub.shape) != 2 or A_ub.shape[1] != n_x:
+            raise ValueError(
+                "Invalid input for linprog: A_ub must have exactly two "
+                "dimensions, and the number of columns in A_ub must be "
+                "equal to the size of c")
+        if (sps.issparse(A_ub) and not np.isfinite(A_ub.data).all()
+                or not sps.issparse(A_ub) and not np.isfinite(A_ub).all()):
+            raise ValueError(
+                "Invalid input for linprog: A_ub must not contain values "
+                "inf, nan, or None")
+
+    try:
+        b_ub = _format_b_constraints(b_ub)
+    except ValueError as e:
+        raise TypeError(
+            "Invalid input for linprog: b_ub must be a 1-D array of "
+            "numerical values, each representing the upper bound of an "
+            "inequality constraint (row) in A_ub") from e
+    else:
+        if b_ub.shape != (n_ub,):
+            raise ValueError(
+                "Invalid input for linprog: b_ub must be a 1-D array; b_ub "
+                "must not have more than one non-singleton dimension and "
+                "the number of rows in A_ub must equal the number of values "
+                "in b_ub")
+        if not np.isfinite(b_ub).all():
+            raise ValueError(
+                "Invalid input for linprog: b_ub must not contain values "
+                "inf, nan, or None")
+
+    try:
+        A_eq = _format_A_constraints(A_eq, n_x, sparse_lhs=sparse_lhs)
+    except ValueError as e:
+        raise TypeError(
+            "Invalid input for linprog: A_eq must be a 2-D array "
+            "of numerical values") from e
+    else:
+        n_eq = A_eq.shape[0]
+        if len(A_eq.shape) != 2 or A_eq.shape[1] != n_x:
+            raise ValueError(
+                "Invalid input for linprog: A_eq must have exactly two "
+                "dimensions, and the number of columns in A_eq must be "
+                "equal to the size of c")
+
+        if (sps.issparse(A_eq) and not np.isfinite(A_eq.data).all()
+                or not sps.issparse(A_eq) and not np.isfinite(A_eq).all()):
+            raise ValueError(
+                "Invalid input for linprog: A_eq must not contain values "
+                "inf, nan, or None")
+
+    try:
+        b_eq = _format_b_constraints(b_eq)
+    except ValueError as e:
+        raise TypeError(
+            "Invalid input for linprog: b_eq must be a dense, 1-D array of "
+            "numerical values, each representing the right hand side of an "
+            "equality constraint (row) in A_eq") from e
+    else:
+        if b_eq.shape != (n_eq,):
+            raise ValueError(
+                "Invalid input for linprog: b_eq must be a 1-D array; b_eq "
+                "must not have more than one non-singleton dimension and "
+                "the number of rows in A_eq must equal the number of values "
+                "in b_eq")
+        if not np.isfinite(b_eq).all():
+            raise ValueError(
+                "Invalid input for linprog: b_eq must not contain values "
+                "inf, nan, or None")
+
+    # x0 gives a (optional) starting solution to the solver. If x0 is None,
+    # skip the checks. Initial solution will be generated automatically.
+    if x0 is not None:
+        try:
+            x0 = np.array(x0, dtype=float, copy=True).squeeze()
+        except ValueError as e:
+            raise TypeError(
+                "Invalid input for linprog: x0 must be a 1-D array of "
+                "numerical coefficients") from e
+        if x0.ndim == 0:
+            x0 = x0.reshape(-1)
+        if len(x0) == 0 or x0.ndim != 1:
+            raise ValueError(
+                "Invalid input for linprog: x0 should be a 1-D array; it "
+                "must not have more than one non-singleton dimension")
+        if not x0.size == c.size:
+            raise ValueError(
+                "Invalid input for linprog: x0 and c should contain the "
+                "same number of elements")
+        if not np.isfinite(x0).all():
+            raise ValueError(
+                "Invalid input for linprog: x0 must not contain values "
+                "inf, nan, or None")
+
+    # Bounds can be one of these formats:
+    # (1) a 2-D array or sequence, with shape N x 2
+    # (2) a 1-D or 2-D sequence or array with 2 scalars
+    # (3) None (or an empty sequence or array)
+    # Unspecified bounds can be represented by None or (-)np.inf.
+    # All formats are converted into a N x 2 np.array with (-)np.inf where
+    # bounds are unspecified.
+
+    # Prepare clean bounds array
+    bounds_clean = np.zeros((n_x, 2), dtype=float)
+
+    # Convert to a numpy array.
+    # np.array(..,dtype=float) raises an error if dimensions are inconsistent
+    # or if there are invalid data types in bounds. Just add a linprog prefix
+    # to the error and re-raise.
+    # Creating at least a 2-D array simplifies the cases to distinguish below.
+    if bounds is None or np.array_equal(bounds, []) or np.array_equal(bounds, [[]]):
+        bounds = (0, np.inf)
+    try:
+        bounds_conv = np.atleast_2d(np.array(bounds, dtype=float))
+    except ValueError as e:
+        raise ValueError(
+            "Invalid input for linprog: unable to interpret bounds, "
+            "check values and dimensions: " + e.args[0]) from e
+    except TypeError as e:
+        raise TypeError(
+            "Invalid input for linprog: unable to interpret bounds, "
+            "check values and dimensions: " + e.args[0]) from e
+
+    # Check bounds options
+    bsh = bounds_conv.shape
+    if len(bsh) > 2:
+        # Do not try to handle multidimensional bounds input
+        raise ValueError(
+            "Invalid input for linprog: provide a 2-D array for bounds, "
+            f"not a {len(bsh):d}-D array.")
+    elif np.all(bsh == (n_x, 2)):
+        # Regular N x 2 array
+        bounds_clean = bounds_conv
+    elif (np.all(bsh == (2, 1)) or np.all(bsh == (1, 2))):
+        # 2 values: interpret as overall lower and upper bound
+        bounds_flat = bounds_conv.flatten()
+        bounds_clean[:, 0] = bounds_flat[0]
+        bounds_clean[:, 1] = bounds_flat[1]
+    elif np.all(bsh == (2, n_x)):
+        # Reject a 2 x N array
+        raise ValueError(
+            f"Invalid input for linprog: provide a {n_x:d} x 2 array for bounds, "
+            f"not a 2 x {n_x:d} array.")
+    else:
+        raise ValueError(
+            "Invalid input for linprog: unable to interpret bounds with this "
+            f"dimension tuple: {bsh}.")
+
+    # The process above creates nan-s where the input specified None
+    # Convert the nan-s in the 1st column to -np.inf and in the 2nd column
+    # to np.inf
+    i_none = np.isnan(bounds_clean[:, 0])
+    bounds_clean[i_none, 0] = -np.inf
+    i_none = np.isnan(bounds_clean[:, 1])
+    bounds_clean[i_none, 1] = np.inf
+
+    return _LPProblem(c, A_ub, b_ub, A_eq, b_eq, bounds_clean, x0, integrality)
+
+
+def _presolve(lp, rr, rr_method, tol=1e-9):
+    """
+    Given inputs for a linear programming problem in preferred format,
+    presolve the problem: identify trivial infeasibilities, redundancies,
+    and unboundedness, tighten bounds where possible, and eliminate fixed
+    variables.
+
+    Parameters
+    ----------
+    lp : A `scipy.optimize._linprog_util._LPProblem` consisting of the following fields:
+
+        c : 1D array
+            The coefficients of the linear objective function to be minimized.
+        A_ub : 2D array, optional
+            The inequality constraint matrix. Each row of ``A_ub`` specifies the
+            coefficients of a linear inequality constraint on ``x``.
+        b_ub : 1D array, optional
+            The inequality constraint vector. Each element represents an
+            upper bound on the corresponding value of ``A_ub @ x``.
+        A_eq : 2D array, optional
+            The equality constraint matrix. Each row of ``A_eq`` specifies the
+            coefficients of a linear equality constraint on ``x``.
+        b_eq : 1D array, optional
+            The equality constraint vector. Each element of ``A_eq @ x`` must equal
+            the corresponding element of ``b_eq``.
+        bounds : 2D array
+            The bounds of ``x``, as ``min`` and ``max`` pairs, one for each of the N
+            elements of ``x``. The N x 2 array contains lower bounds in the first
+            column and upper bounds in the 2nd. Unbounded variables have lower
+            bound -np.inf and/or upper bound np.inf.
+        x0 : 1D array, optional
+            Guess values of the decision variables, which will be refined by
+            the optimization algorithm. This argument is currently used only by the
+            'revised simplex' method, and can only be used if `x0` represents a
+            basic feasible solution.
+
+    rr : bool
+        If ``True`` attempts to eliminate any redundant rows in ``A_eq``.
+        Set False if ``A_eq`` is known to be of full row rank, or if you are
+        looking for a potential speedup (at the expense of reliability).
+    rr_method : string
+        Method used to identify and remove redundant rows from the
+        equality constraint matrix after presolve.
+    tol : float
+        The tolerance which determines when a solution is "close enough" to
+        zero in Phase 1 to be considered a basic feasible solution or close
+        enough to positive to serve as an optimal solution.
+
+    Returns
+    -------
+    lp : A `scipy.optimize._linprog_util._LPProblem` consisting of the following fields:
+
+        c : 1D array
+            The coefficients of the linear objective function to be minimized.
+        A_ub : 2D array, optional
+            The inequality constraint matrix. Each row of ``A_ub`` specifies the
+            coefficients of a linear inequality constraint on ``x``.
+        b_ub : 1D array, optional
+            The inequality constraint vector. Each element represents an
+            upper bound on the corresponding value of ``A_ub @ x``.
+        A_eq : 2D array, optional
+            The equality constraint matrix. Each row of ``A_eq`` specifies the
+            coefficients of a linear equality constraint on ``x``.
+        b_eq : 1D array, optional
+            The equality constraint vector. Each element of ``A_eq @ x`` must equal
+            the corresponding element of ``b_eq``.
+        bounds : 2D array
+            The bounds of ``x``, as ``min`` and ``max`` pairs, possibly tightened.
+        x0 : 1D array, optional
+            Guess values of the decision variables, which will be refined by
+            the optimization algorithm. This argument is currently used only by the
+            'revised simplex' method, and can only be used if `x0` represents a
+            basic feasible solution.
+
+    c0 : 1D array
+        Constant term in objective function due to fixed (and eliminated)
+        variables.
+    x : 1D array
+        Solution vector (when the solution is trivial and can be determined
+        in presolve)
+    revstack: list of functions
+        the functions in the list reverse the operations of _presolve()
+        the function signature is x_org = f(x_mod), where x_mod is the result
+        of a presolve step and x_org the value at the start of the step
+        (currently, the revstack contains only one function)
+    complete: bool
+        Whether the solution is complete (solved or determined to be infeasible
+        or unbounded in presolve)
+    status : int
+        An integer representing the exit status of the optimization::
+
+         0 : Optimization terminated successfully
+         1 : Iteration limit reached
+         2 : Problem appears to be infeasible
+         3 : Problem appears to be unbounded
+         4 : Serious numerical difficulties encountered
+
+    message : str
+        A string descriptor of the exit status of the optimization.
+
+    References
+    ----------
+    .. [5] Andersen, Erling D. "Finding all linearly dependent rows in
+           large-scale linear programming." Optimization Methods and Software
+           6.3 (1995): 219-227.
+    .. [8] Andersen, Erling D., and Knud D. Andersen. "Presolving in linear
+           programming." Mathematical Programming 71.2 (1995): 221-245.
+
+    """
+    # ideas from Reference [5] by Andersen and Andersen
+    # however, unlike the reference, this is performed before converting
+    # problem to standard form
+    # There are a few advantages:
+    #  * artificial variables have not been added, so matrices are smaller
+    #  * bounds have not been converted to constraints yet. (It is better to
+    #    do that after presolve because presolve may adjust the simple bounds.)
+    # There are many improvements that can be made, namely:
+    #  * implement remaining checks from [5]
+    #  * loop presolve until no additional changes are made
+    #  * implement additional efficiency improvements in redundancy removal [2]
+
+    c, A_ub, b_ub, A_eq, b_eq, bounds, x0, _ = lp
+
+    revstack = []               # record of variables eliminated from problem
+    # constant term in cost function may be added if variables are eliminated
+    c0 = 0
+    complete = False        # complete is True if detected infeasible/unbounded
+    x = np.zeros(c.shape)   # this is solution vector if completed in presolve
+
+    status = 0              # all OK unless determined otherwise
+    message = ""
+
+    # Lower and upper bounds. Copy to prevent feedback.
+    lb = bounds[:, 0].copy()
+    ub = bounds[:, 1].copy()
+
+    m_eq, n = A_eq.shape
+    m_ub, n = A_ub.shape
+
+    if (rr_method is not None
+            and rr_method.lower() not in {"svd", "pivot", "id"}):
+        message = ("'" + str(rr_method) + "' is not a valid option "
+                   "for redundancy removal. Valid options are 'SVD', "
+                   "'pivot', and 'ID'.")
+        raise ValueError(message)
+
+    if sps.issparse(A_eq):
+        A_eq = A_eq.tocsr()
+        A_ub = A_ub.tocsr()
+
+        def where(A):
+            return A.nonzero()
+
+        vstack = sps.vstack
+    else:
+        where = np.where
+        vstack = np.vstack
+
+    # upper bounds > lower bounds
+    if np.any(ub < lb) or np.any(lb == np.inf) or np.any(ub == -np.inf):
+        status = 2
+        message = ("The problem is (trivially) infeasible since one "
+                   "or more upper bounds are smaller than the corresponding "
+                   "lower bounds, a lower bound is np.inf or an upper bound "
+                   "is -np.inf.")
+        complete = True
+        return (_LPProblem(c, A_ub, b_ub, A_eq, b_eq, bounds, x0),
+                c0, x, revstack, complete, status, message)
+
+    # zero row in equality constraints
+    zero_row = np.array(np.sum(A_eq != 0, axis=1) == 0).flatten()
+    if np.any(zero_row):
+        if np.any(
+            np.logical_and(
+                zero_row,
+                np.abs(b_eq) > tol)):  # test_zero_row_1
+            # infeasible if RHS is not zero
+            status = 2
+            message = ("The problem is (trivially) infeasible due to a row "
+                       "of zeros in the equality constraint matrix with a "
+                       "nonzero corresponding constraint value.")
+            complete = True
+            return (_LPProblem(c, A_ub, b_ub, A_eq, b_eq, bounds, x0),
+                    c0, x, revstack, complete, status, message)
+        else:  # test_zero_row_2
+            # if RHS is zero, we can eliminate this equation entirely
+            A_eq = A_eq[np.logical_not(zero_row), :]
+            b_eq = b_eq[np.logical_not(zero_row)]
+
+    # zero row in inequality constraints
+    zero_row = np.array(np.sum(A_ub != 0, axis=1) == 0).flatten()
+    if np.any(zero_row):
+        if np.any(np.logical_and(zero_row, b_ub < -tol)):  # test_zero_row_1
+            # infeasible if RHS is less than zero (because LHS is zero)
+            status = 2
+            message = ("The problem is (trivially) infeasible due to a row "
+                       "of zeros in the equality constraint matrix with a "
+                       "nonzero corresponding  constraint value.")
+            complete = True
+            return (_LPProblem(c, A_ub, b_ub, A_eq, b_eq, bounds, x0),
+                    c0, x, revstack, complete, status, message)
+        else:  # test_zero_row_2
+            # if LHS is >= 0, we can eliminate this constraint entirely
+            A_ub = A_ub[np.logical_not(zero_row), :]
+            b_ub = b_ub[np.logical_not(zero_row)]
+
+    # zero column in (both) constraints
+    # this indicates that a variable isn't constrained and can be removed
+    A = vstack((A_eq, A_ub))
+    if A.shape[0] > 0:
+        zero_col = np.array(np.sum(A != 0, axis=0) == 0).flatten()
+        # variable will be at upper or lower bound, depending on objective
+        x[np.logical_and(zero_col, c < 0)] = ub[
+            np.logical_and(zero_col, c < 0)]
+        x[np.logical_and(zero_col, c > 0)] = lb[
+            np.logical_and(zero_col, c > 0)]
+        if np.any(np.isinf(x)):  # if an unconstrained variable has no bound
+            status = 3
+            message = ("If feasible, the problem is (trivially) unbounded "
+                       "due  to a zero column in the constraint matrices. If "
+                       "you wish to check whether the problem is infeasible, "
+                       "turn presolve off.")
+            complete = True
+            return (_LPProblem(c, A_ub, b_ub, A_eq, b_eq, bounds, x0),
+                    c0, x, revstack, complete, status, message)
+        # variables will equal upper/lower bounds will be removed later
+        lb[np.logical_and(zero_col, c < 0)] = ub[
+            np.logical_and(zero_col, c < 0)]
+        ub[np.logical_and(zero_col, c > 0)] = lb[
+            np.logical_and(zero_col, c > 0)]
+
+    # row singleton in equality constraints
+    # this fixes a variable and removes the constraint
+    singleton_row = np.array(np.sum(A_eq != 0, axis=1) == 1).flatten()
+    rows = where(singleton_row)[0]
+    cols = where(A_eq[rows, :])[1]
+    if len(rows) > 0:
+        for row, col in zip(rows, cols):
+            val = b_eq[row] / A_eq[row, col]
+            if not lb[col] - tol <= val <= ub[col] + tol:
+                # infeasible if fixed value is not within bounds
+                status = 2
+                message = ("The problem is (trivially) infeasible because a "
+                           "singleton row in the equality constraints is "
+                           "inconsistent with the bounds.")
+                complete = True
+                return (_LPProblem(c, A_ub, b_ub, A_eq, b_eq, bounds, x0),
+                        c0, x, revstack, complete, status, message)
+            else:
+                # sets upper and lower bounds at that fixed value - variable
+                # will be removed later
+                lb[col] = val
+                ub[col] = val
+        A_eq = A_eq[np.logical_not(singleton_row), :]
+        b_eq = b_eq[np.logical_not(singleton_row)]
+
+    # row singleton in inequality constraints
+    # this indicates a simple bound and the constraint can be removed
+    # simple bounds may be adjusted here
+    # After all of the simple bound information is combined here, get_Abc will
+    # turn the simple bounds into constraints
+    singleton_row = np.array(np.sum(A_ub != 0, axis=1) == 1).flatten()
+    cols = where(A_ub[singleton_row, :])[1]
+    rows = where(singleton_row)[0]
+    if len(rows) > 0:
+        for row, col in zip(rows, cols):
+            val = b_ub[row] / A_ub[row, col]
+            if A_ub[row, col] > 0:  # upper bound
+                if val < lb[col] - tol:  # infeasible
+                    complete = True
+                elif val < ub[col]:  # new upper bound
+                    ub[col] = val
+            else:  # lower bound
+                if val > ub[col] + tol:  # infeasible
+                    complete = True
+                elif val > lb[col]:  # new lower bound
+                    lb[col] = val
+            if complete:
+                status = 2
+                message = ("The problem is (trivially) infeasible because a "
+                           "singleton row in the upper bound constraints is "
+                           "inconsistent with the bounds.")
+                return (_LPProblem(c, A_ub, b_ub, A_eq, b_eq, bounds, x0),
+                        c0, x, revstack, complete, status, message)
+        A_ub = A_ub[np.logical_not(singleton_row), :]
+        b_ub = b_ub[np.logical_not(singleton_row)]
+
+    # identical bounds indicate that variable can be removed
+    i_f = np.abs(lb - ub) < tol   # indices of "fixed" variables
+    i_nf = np.logical_not(i_f)  # indices of "not fixed" variables
+
+    # test_bounds_equal_but_infeasible
+    if np.all(i_f):  # if bounds define solution, check for consistency
+        residual = b_eq - A_eq.dot(lb)
+        slack = b_ub - A_ub.dot(lb)
+        if ((A_ub.size > 0 and np.any(slack < 0)) or
+                (A_eq.size > 0 and not np.allclose(residual, 0))):
+            status = 2
+            message = ("The problem is (trivially) infeasible because the "
+                       "bounds fix all variables to values inconsistent with "
+                       "the constraints")
+            complete = True
+            return (_LPProblem(c, A_ub, b_ub, A_eq, b_eq, bounds, x0),
+                    c0, x, revstack, complete, status, message)
+
+    ub_mod = ub
+    lb_mod = lb
+    if np.any(i_f):
+        c0 += c[i_f].dot(lb[i_f])
+        b_eq = b_eq - A_eq[:, i_f].dot(lb[i_f])
+        b_ub = b_ub - A_ub[:, i_f].dot(lb[i_f])
+        c = c[i_nf]
+        x_undo = lb[i_f]  # not x[i_f], x is just zeroes
+        x = x[i_nf]
+        # user guess x0 stays separate from presolve solution x
+        if x0 is not None:
+            x0 = x0[i_nf]
+        A_eq = A_eq[:, i_nf]
+        A_ub = A_ub[:, i_nf]
+        # modify bounds
+        lb_mod = lb[i_nf]
+        ub_mod = ub[i_nf]
+
+        def rev(x_mod):
+            # Function to restore x: insert x_undo into x_mod.
+            # When elements have been removed at positions k1, k2, k3, ...
+            # then these must be replaced at (after) positions k1-1, k2-2,
+            # k3-3, ... in the modified array to recreate the original
+            i = np.flatnonzero(i_f)
+            # Number of variables to restore
+            N = len(i)
+            index_offset = np.arange(N)
+            # Create insert indices
+            insert_indices = i - index_offset
+            x_rev = np.insert(x_mod.astype(float), insert_indices, x_undo)
+            return x_rev
+
+        # Use revstack as a list of functions, currently just this one.
+        revstack.append(rev)
+
+    # no constraints indicates that problem is trivial
+    if A_eq.size == 0 and A_ub.size == 0:
+        b_eq = np.array([])
+        b_ub = np.array([])
+        # test_empty_constraint_1
+        if c.size == 0:
+            status = 0
+            message = ("The solution was determined in presolve as there are "
+                       "no non-trivial constraints.")
+        elif (np.any(np.logical_and(c < 0, ub_mod == np.inf)) or
+              np.any(np.logical_and(c > 0, lb_mod == -np.inf))):
+            # test_no_constraints()
+            # test_unbounded_no_nontrivial_constraints_1
+            # test_unbounded_no_nontrivial_constraints_2
+            status = 3
+            message = ("The problem is (trivially) unbounded "
+                       "because there are no non-trivial constraints and "
+                       "a) at least one decision variable is unbounded "
+                       "above and its corresponding cost is negative, or "
+                       "b) at least one decision variable is unbounded below "
+                       "and its corresponding cost is positive. ")
+        else:  # test_empty_constraint_2
+            status = 0
+            message = ("The solution was determined in presolve as there are "
+                       "no non-trivial constraints.")
+        complete = True
+        x[c < 0] = ub_mod[c < 0]
+        x[c > 0] = lb_mod[c > 0]
+        # where c is zero, set x to a finite bound or zero
+        x_zero_c = ub_mod[c == 0]
+        x_zero_c[np.isinf(x_zero_c)] = ub_mod[c == 0][np.isinf(x_zero_c)]
+        x_zero_c[np.isinf(x_zero_c)] = 0
+        x[c == 0] = x_zero_c
+        # if this is not the last step of presolve, should convert bounds back
+        # to array and return here
+
+    # Convert modified lb and ub back into N x 2 bounds
+    bounds = np.hstack((lb_mod[:, np.newaxis], ub_mod[:, np.newaxis]))
+
+    # remove redundant (linearly dependent) rows from equality constraints
+    n_rows_A = A_eq.shape[0]
+    redundancy_warning = ("A_eq does not appear to be of full row rank. To "
+                          "improve performance, check the problem formulation "
+                          "for redundant equality constraints.")
+    if (sps.issparse(A_eq)):
+        if rr and A_eq.size > 0:  # TODO: Fast sparse rank check?
+            rr_res = _remove_redundancy_pivot_sparse(A_eq, b_eq)
+            A_eq, b_eq, status, message = rr_res
+            if A_eq.shape[0] < n_rows_A:
+                warn(redundancy_warning, OptimizeWarning, stacklevel=1)
+            if status != 0:
+                complete = True
+        return (_LPProblem(c, A_ub, b_ub, A_eq, b_eq, bounds, x0),
+                c0, x, revstack, complete, status, message)
+
+    # This is a wild guess for which redundancy removal algorithm will be
+    # faster. More testing would be good.
+    small_nullspace = 5
+    if rr and A_eq.size > 0:
+        try:  # TODO: use results of first SVD in _remove_redundancy_svd
+            rank = np.linalg.matrix_rank(A_eq)
+        # oh well, we'll have to go with _remove_redundancy_pivot_dense
+        except Exception:
+            rank = 0
+    if rr and A_eq.size > 0 and rank < A_eq.shape[0]:
+        warn(redundancy_warning, OptimizeWarning, stacklevel=3)
+        dim_row_nullspace = A_eq.shape[0]-rank
+        if rr_method is None:
+            if dim_row_nullspace <= small_nullspace:
+                rr_res = _remove_redundancy_svd(A_eq, b_eq)
+                A_eq, b_eq, status, message = rr_res
+            if dim_row_nullspace > small_nullspace or status == 4:
+                rr_res = _remove_redundancy_pivot_dense(A_eq, b_eq)
+                A_eq, b_eq, status, message = rr_res
+
+        else:
+            rr_method = rr_method.lower()
+            if rr_method == "svd":
+                rr_res = _remove_redundancy_svd(A_eq, b_eq)
+                A_eq, b_eq, status, message = rr_res
+            elif rr_method == "pivot":
+                rr_res = _remove_redundancy_pivot_dense(A_eq, b_eq)
+                A_eq, b_eq, status, message = rr_res
+            elif rr_method == "id":
+                rr_res = _remove_redundancy_id(A_eq, b_eq, rank)
+                A_eq, b_eq, status, message = rr_res
+            else:  # shouldn't get here; option validity checked above
+                pass
+        if A_eq.shape[0] < rank:
+            message = ("Due to numerical issues, redundant equality "
+                       "constraints could not be removed automatically. "
+                       "Try providing your constraint matrices as sparse "
+                       "matrices to activate sparse presolve, try turning "
+                       "off redundancy removal, or try turning off presolve "
+                       "altogether.")
+            status = 4
+        if status != 0:
+            complete = True
+    return (_LPProblem(c, A_ub, b_ub, A_eq, b_eq, bounds, x0),
+            c0, x, revstack, complete, status, message)
+
+
+def _parse_linprog(lp, options, meth):
+    """
+    Parse the provided linear programming problem
+
+    ``_parse_linprog`` employs two main steps ``_check_sparse_inputs`` and
+    ``_clean_inputs``. ``_check_sparse_inputs`` checks for sparsity in the
+    provided constraints (``A_ub`` and ``A_eq) and if these match the provided
+    sparsity optional values.
+
+    ``_clean inputs`` checks of the provided inputs. If no violations are
+    identified the objective vector, upper bound constraints, equality
+    constraints, and simple bounds are returned in the expected format.
+
+    Parameters
+    ----------
+    lp : A `scipy.optimize._linprog_util._LPProblem` consisting of the following fields:
+
+        c : 1D array
+            The coefficients of the linear objective function to be minimized.
+        A_ub : 2D array, optional
+            The inequality constraint matrix. Each row of ``A_ub`` specifies the
+            coefficients of a linear inequality constraint on ``x``.
+        b_ub : 1D array, optional
+            The inequality constraint vector. Each element represents an
+            upper bound on the corresponding value of ``A_ub @ x``.
+        A_eq : 2D array, optional
+            The equality constraint matrix. Each row of ``A_eq`` specifies the
+            coefficients of a linear equality constraint on ``x``.
+        b_eq : 1D array, optional
+            The equality constraint vector. Each element of ``A_eq @ x`` must equal
+            the corresponding element of ``b_eq``.
+        bounds : various valid formats, optional
+            The bounds of ``x``, as ``min`` and ``max`` pairs.
+            If bounds are specified for all N variables separately, valid formats are:
+            * a 2D array (2 x N or N x 2);
+            * a sequence of N sequences, each with 2 values.
+            If all variables have the same bounds, a single pair of values can
+            be specified. Valid formats are:
+            * a sequence with 2 scalar values;
+            * a sequence with a single element containing 2 scalar values.
+            If all variables have a lower bound of 0 and no upper bound, the bounds
+            parameter can be omitted (or given as None).
+        x0 : 1D array, optional
+            Guess values of the decision variables, which will be refined by
+            the optimization algorithm. This argument is currently used only by the
+            'revised simplex' method, and can only be used if `x0` represents a
+            basic feasible solution.
+
+    options : dict
+        A dictionary of solver options. All methods accept the following
+        generic options:
+
+            maxiter : int
+                Maximum number of iterations to perform.
+            disp : bool
+                Set to True to print convergence messages.
+
+        For method-specific options, see :func:`show_options('linprog')`.
+
+    Returns
+    -------
+    lp : A `scipy.optimize._linprog_util._LPProblem` consisting of the following fields:
+
+        c : 1D array
+            The coefficients of the linear objective function to be minimized.
+        A_ub : 2D array, optional
+            The inequality constraint matrix. Each row of ``A_ub`` specifies the
+            coefficients of a linear inequality constraint on ``x``.
+        b_ub : 1D array, optional
+            The inequality constraint vector. Each element represents an
+            upper bound on the corresponding value of ``A_ub @ x``.
+        A_eq : 2D array, optional
+            The equality constraint matrix. Each row of ``A_eq`` specifies the
+            coefficients of a linear equality constraint on ``x``.
+        b_eq : 1D array, optional
+            The equality constraint vector. Each element of ``A_eq @ x`` must equal
+            the corresponding element of ``b_eq``.
+        bounds : 2D array
+            The bounds of ``x``, as ``min`` and ``max`` pairs, one for each of the N
+            elements of ``x``. The N x 2 array contains lower bounds in the first
+            column and upper bounds in the 2nd. Unbounded variables have lower
+            bound -np.inf and/or upper bound np.inf.
+        x0 : 1D array, optional
+            Guess values of the decision variables, which will be refined by
+            the optimization algorithm. This argument is currently used only by the
+            'revised simplex' method, and can only be used if `x0` represents a
+            basic feasible solution.
+
+    options : dict, optional
+        A dictionary of solver options. All methods accept the following
+        generic options:
+
+            maxiter : int
+                Maximum number of iterations to perform.
+            disp : bool
+                Set to True to print convergence messages.
+
+        For method-specific options, see :func:`show_options('linprog')`.
+
+    """
+    if options is None:
+        options = {}
+
+    solver_options = {k: v for k, v in options.items()}
+    solver_options, A_ub, A_eq = _check_sparse_inputs(solver_options, meth,
+                                                      lp.A_ub, lp.A_eq)
+    # Convert lists to numpy arrays, etc...
+    lp = _clean_inputs(lp._replace(A_ub=A_ub, A_eq=A_eq))
+    return lp, solver_options
+
+
+def _get_Abc(lp, c0):
+    """
+    Given a linear programming problem of the form:
+
+    Minimize::
+
+        c @ x
+
+    Subject to::
+
+        A_ub @ x <= b_ub
+        A_eq @ x == b_eq
+         lb <= x <= ub
+
+    where ``lb = 0`` and ``ub = None`` unless set in ``bounds``.
+
+    Return the problem in standard form:
+
+    Minimize::
+
+        c @ x
+
+    Subject to::
+
+        A @ x == b
+            x >= 0
+
+    by adding slack variables and making variable substitutions as necessary.
+
+    Parameters
+    ----------
+    lp : A `scipy.optimize._linprog_util._LPProblem` consisting of the following fields:
+
+        c : 1D array
+            The coefficients of the linear objective function to be minimized.
+        A_ub : 2D array, optional
+            The inequality constraint matrix. Each row of ``A_ub`` specifies the
+            coefficients of a linear inequality constraint on ``x``.
+        b_ub : 1D array, optional
+            The inequality constraint vector. Each element represents an
+            upper bound on the corresponding value of ``A_ub @ x``.
+        A_eq : 2D array, optional
+            The equality constraint matrix. Each row of ``A_eq`` specifies the
+            coefficients of a linear equality constraint on ``x``.
+        b_eq : 1D array, optional
+            The equality constraint vector. Each element of ``A_eq @ x`` must equal
+            the corresponding element of ``b_eq``.
+        bounds : 2D array
+            The bounds of ``x``, lower bounds in the 1st column, upper
+            bounds in the 2nd column. The bounds are possibly tightened
+            by the presolve procedure.
+        x0 : 1D array, optional
+            Guess values of the decision variables, which will be refined by
+            the optimization algorithm. This argument is currently used only by the
+            'revised simplex' method, and can only be used if `x0` represents a
+            basic feasible solution.
+
+    c0 : float
+        Constant term in objective function due to fixed (and eliminated)
+        variables.
+
+    Returns
+    -------
+    A : 2-D array
+        2-D array such that ``A`` @ ``x``, gives the values of the equality
+        constraints at ``x``.
+    b : 1-D array
+        1-D array of values representing the RHS of each equality constraint
+        (row) in A (for standard form problem).
+    c : 1-D array
+        Coefficients of the linear objective function to be minimized (for
+        standard form problem).
+    c0 : float
+        Constant term in objective function due to fixed (and eliminated)
+        variables.
+    x0 : 1-D array
+        Starting values of the independent variables, which will be refined by
+        the optimization algorithm
+
+    References
+    ----------
+    .. [9] Bertsimas, Dimitris, and J. Tsitsiklis. "Introduction to linear
+           programming." Athena Scientific 1 (1997): 997.
+
+    """
+    c, A_ub, b_ub, A_eq, b_eq, bounds, x0, integrality = lp
+
+    if sps.issparse(A_eq):
+        sparse = True
+        A_eq = sps.csr_matrix(A_eq)
+        A_ub = sps.csr_matrix(A_ub)
+
+        def hstack(blocks):
+            return sps.hstack(blocks, format="csr")
+
+        def vstack(blocks):
+            return sps.vstack(blocks, format="csr")
+
+        zeros = sps.csr_matrix
+        eye = sps.eye
+    else:
+        sparse = False
+        hstack = np.hstack
+        vstack = np.vstack
+        zeros = np.zeros
+        eye = np.eye
+
+    # Variables lbs and ubs (see below) may be changed, which feeds back into
+    # bounds, so copy.
+    bounds = np.array(bounds, copy=True)
+
+    # modify problem such that all variables have only non-negativity bounds
+    lbs = bounds[:, 0]
+    ubs = bounds[:, 1]
+    m_ub, n_ub = A_ub.shape
+
+    lb_none = np.equal(lbs, -np.inf)
+    ub_none = np.equal(ubs, np.inf)
+    lb_some = np.logical_not(lb_none)
+    ub_some = np.logical_not(ub_none)
+
+    # unbounded below: substitute xi = -xi' (unbounded above)
+    # if -inf <= xi <= ub, then -ub <= -xi <= inf, so swap and invert bounds
+    l_nolb_someub = np.logical_and(lb_none, ub_some)
+    i_nolb = np.nonzero(l_nolb_someub)[0]
+    lbs[l_nolb_someub], ubs[l_nolb_someub] = (
+        -ubs[l_nolb_someub], -lbs[l_nolb_someub])
+    lb_none = np.equal(lbs, -np.inf)
+    ub_none = np.equal(ubs, np.inf)
+    lb_some = np.logical_not(lb_none)
+    ub_some = np.logical_not(ub_none)
+    c[i_nolb] *= -1
+    if x0 is not None:
+        x0[i_nolb] *= -1
+    if len(i_nolb) > 0:
+        if A_ub.shape[0] > 0:  # sometimes needed for sparse arrays... weird
+            A_ub[:, i_nolb] *= -1
+        if A_eq.shape[0] > 0:
+            A_eq[:, i_nolb] *= -1
+
+    # upper bound: add inequality constraint
+    i_newub, = ub_some.nonzero()
+    ub_newub = ubs[ub_some]
+    n_bounds = len(i_newub)
+    if n_bounds > 0:
+        shape = (n_bounds, A_ub.shape[1])
+        if sparse:
+            idxs = (np.arange(n_bounds), i_newub)
+            A_ub = vstack((A_ub, sps.csr_matrix((np.ones(n_bounds), idxs),
+                                                shape=shape)))
+        else:
+            A_ub = vstack((A_ub, np.zeros(shape)))
+            A_ub[np.arange(m_ub, A_ub.shape[0]), i_newub] = 1
+        b_ub = np.concatenate((b_ub, np.zeros(n_bounds)))
+        b_ub[m_ub:] = ub_newub
+
+    A1 = vstack((A_ub, A_eq))
+    b = np.concatenate((b_ub, b_eq))
+    c = np.concatenate((c, np.zeros((A_ub.shape[0],))))
+    if x0 is not None:
+        x0 = np.concatenate((x0, np.zeros((A_ub.shape[0],))))
+    # unbounded: substitute xi = xi+ + xi-
+    l_free = np.logical_and(lb_none, ub_none)
+    i_free = np.nonzero(l_free)[0]
+    n_free = len(i_free)
+    c = np.concatenate((c, np.zeros(n_free)))
+    if x0 is not None:
+        x0 = np.concatenate((x0, np.zeros(n_free)))
+    A1 = hstack((A1[:, :n_ub], -A1[:, i_free]))
+    c[n_ub:n_ub+n_free] = -c[i_free]
+    if x0 is not None:
+        i_free_neg = x0[i_free] < 0
+        x0[np.arange(n_ub, A1.shape[1])[i_free_neg]] = -x0[i_free[i_free_neg]]
+        x0[i_free[i_free_neg]] = 0
+
+    # add slack variables
+    A2 = vstack([eye(A_ub.shape[0]), zeros((A_eq.shape[0], A_ub.shape[0]))])
+
+    A = hstack([A1, A2])
+
+    # lower bound: substitute xi = xi' + lb
+    # now there is a constant term in objective
+    i_shift = np.nonzero(lb_some)[0]
+    lb_shift = lbs[lb_some].astype(float)
+    c0 += np.sum(lb_shift * c[i_shift])
+    if sparse:
+        b = b.reshape(-1, 1)
+        A = A.tocsc()
+        b -= (A[:, i_shift] * sps.diags(lb_shift)).sum(axis=1)
+        b = b.ravel()
+    else:
+        b -= (A[:, i_shift] * lb_shift).sum(axis=1)
+    if x0 is not None:
+        x0[i_shift] -= lb_shift
+
+    return A, b, c, c0, x0
+
+
+def _round_to_power_of_two(x):
+    """
+    Round elements of the array to the nearest power of two.
+    """
+    return 2**np.around(np.log2(x))
+
+
+def _autoscale(A, b, c, x0):
+    """
+    Scales the problem according to equilibration from [12].
+    Also normalizes the right hand side vector by its maximum element.
+    """
+    m, n = A.shape
+
+    C = 1
+    R = 1
+
+    if A.size > 0:
+
+        R = np.max(np.abs(A), axis=1)
+        if sps.issparse(A):
+            R = R.toarray().flatten()
+        R[R == 0] = 1
+        R = 1/_round_to_power_of_two(R)
+        A = sps.diags(R)*A if sps.issparse(A) else A*R.reshape(m, 1)
+        b = b*R
+
+        C = np.max(np.abs(A), axis=0)
+        if sps.issparse(A):
+            C = C.toarray().flatten()
+        C[C == 0] = 1
+        C = 1/_round_to_power_of_two(C)
+        A = A*sps.diags(C) if sps.issparse(A) else A*C
+        c = c*C
+
+    b_scale = np.max(np.abs(b)) if b.size > 0 else 1
+    if b_scale == 0:
+        b_scale = 1.
+    b = b/b_scale
+
+    if x0 is not None:
+        x0 = x0/b_scale*(1/C)
+    return A, b, c, x0, C, b_scale
+
+
+def _unscale(x, C, b_scale):
+    """
+    Converts solution to _autoscale problem -> solution to original problem.
+    """
+
+    try:
+        n = len(C)
+        # fails if sparse or scalar; that's OK.
+        # this is only needed for original simplex (never sparse)
+    except TypeError:
+        n = len(x)
+
+    return x[:n]*b_scale*C
+
+
+def _display_summary(message, status, fun, iteration):
+    """
+    Print the termination summary of the linear program
+
+    Parameters
+    ----------
+    message : str
+            A string descriptor of the exit status of the optimization.
+    status : int
+        An integer representing the exit status of the optimization::
+
+                0 : Optimization terminated successfully
+                1 : Iteration limit reached
+                2 : Problem appears to be infeasible
+                3 : Problem appears to be unbounded
+                4 : Serious numerical difficulties encountered
+
+    fun : float
+        Value of the objective function.
+    iteration : iteration
+        The number of iterations performed.
+    """
+    print(message)
+    if status in (0, 1):
+        print(f"         Current function value: {fun: <12.6f}")
+    print(f"         Iterations: {iteration:d}")
+
+
+def _postsolve(x, postsolve_args, complete=False):
+    """
+    Given solution x to presolved, standard form linear program x, add
+    fixed variables back into the problem and undo the variable substitutions
+    to get solution to original linear program. Also, calculate the objective
+    function value, slack in original upper bound constraints, and residuals
+    in original equality constraints.
+
+    Parameters
+    ----------
+    x : 1-D array
+        Solution vector to the standard-form problem.
+    postsolve_args : tuple
+        Data needed by _postsolve to convert the solution to the standard-form
+        problem into the solution to the original problem, including:
+
+    lp : A `scipy.optimize._linprog_util._LPProblem` consisting of the following fields:
+
+        c : 1D array
+            The coefficients of the linear objective function to be minimized.
+        A_ub : 2D array, optional
+            The inequality constraint matrix. Each row of ``A_ub`` specifies the
+            coefficients of a linear inequality constraint on ``x``.
+        b_ub : 1D array, optional
+            The inequality constraint vector. Each element represents an
+            upper bound on the corresponding value of ``A_ub @ x``.
+        A_eq : 2D array, optional
+            The equality constraint matrix. Each row of ``A_eq`` specifies the
+            coefficients of a linear equality constraint on ``x``.
+        b_eq : 1D array, optional
+            The equality constraint vector. Each element of ``A_eq @ x`` must equal
+            the corresponding element of ``b_eq``.
+        bounds : 2D array
+            The bounds of ``x``, lower bounds in the 1st column, upper
+            bounds in the 2nd column. The bounds are possibly tightened
+            by the presolve procedure.
+        x0 : 1D array, optional
+            Guess values of the decision variables, which will be refined by
+            the optimization algorithm. This argument is currently used only by the
+            'revised simplex' method, and can only be used if `x0` represents a
+            basic feasible solution.
+
+    revstack: list of functions
+        the functions in the list reverse the operations of _presolve()
+        the function signature is x_org = f(x_mod), where x_mod is the result
+        of a presolve step and x_org the value at the start of the step
+    complete : bool
+        Whether the solution is was determined in presolve (``True`` if so)
+
+    Returns
+    -------
+    x : 1-D array
+        Solution vector to original linear programming problem
+    fun: float
+        optimal objective value for original problem
+    slack : 1-D array
+        The (non-negative) slack in the upper bound constraints, that is,
+        ``b_ub - A_ub @ x``
+    con : 1-D array
+        The (nominally zero) residuals of the equality constraints, that is,
+        ``b - A_eq @ x``
+    """
+    # note that all the inputs are the ORIGINAL, unmodified versions
+    # no rows, columns have been removed
+
+    c, A_ub, b_ub, A_eq, b_eq, bounds, x0, integrality = postsolve_args[0]
+    revstack, C, b_scale = postsolve_args[1:]
+
+    x = _unscale(x, C, b_scale)
+
+    # Undo variable substitutions of _get_Abc()
+    # if "complete", problem was solved in presolve; don't do anything here
+    n_x = bounds.shape[0]
+    if not complete and bounds is not None:  # bounds are never none, probably
+        n_unbounded = 0
+        for i, bi in enumerate(bounds):
+            lbi = bi[0]
+            ubi = bi[1]
+            if lbi == -np.inf and ubi == np.inf:
+                n_unbounded += 1
+                x[i] = x[i] - x[n_x + n_unbounded - 1]
+            else:
+                if lbi == -np.inf:
+                    x[i] = ubi - x[i]
+                else:
+                    x[i] += lbi
+    # all the rest of the variables were artificial
+    x = x[:n_x]
+
+    # If there were variables removed from the problem, add them back into the
+    # solution vector
+    # Apply the functions in revstack (reverse direction)
+    for rev in reversed(revstack):
+        x = rev(x)
+
+    fun = x.dot(c)
+    slack = b_ub - A_ub.dot(x)  # report slack for ORIGINAL UB constraints
+    # report residuals of ORIGINAL EQ constraints
+    con = b_eq - A_eq.dot(x)
+
+    return x, fun, slack, con
+
+
+def _check_result(x, fun, status, slack, con, bounds, tol, message,
+                  integrality):
+    """
+    Check the validity of the provided solution.
+
+    A valid (optimal) solution satisfies all bounds, all slack variables are
+    negative and all equality constraint residuals are strictly non-zero.
+    Further, the lower-bounds, upper-bounds, slack and residuals contain
+    no nan values.
+
+    Parameters
+    ----------
+    x : 1-D array
+        Solution vector to original linear programming problem
+    fun: float
+        optimal objective value for original problem
+    status : int
+        An integer representing the exit status of the optimization::
+
+             0 : Optimization terminated successfully
+             1 : Iteration limit reached
+             2 : Problem appears to be infeasible
+             3 : Problem appears to be unbounded
+             4 : Serious numerical difficulties encountered
+
+    slack : 1-D array
+        The (non-negative) slack in the upper bound constraints, that is,
+        ``b_ub - A_ub @ x``
+    con : 1-D array
+        The (nominally zero) residuals of the equality constraints, that is,
+        ``b - A_eq @ x``
+    bounds : 2D array
+        The bounds on the original variables ``x``
+    message : str
+        A string descriptor of the exit status of the optimization.
+    tol : float
+        Termination tolerance; see [1]_ Section 4.5.
+
+    Returns
+    -------
+    status : int
+        An integer representing the exit status of the optimization::
+
+             0 : Optimization terminated successfully
+             1 : Iteration limit reached
+             2 : Problem appears to be infeasible
+             3 : Problem appears to be unbounded
+             4 : Serious numerical difficulties encountered
+
+    message : str
+        A string descriptor of the exit status of the optimization.
+    """
+    # Somewhat arbitrary
+    tol = np.sqrt(tol) * 10
+
+    if x is None:
+        # HiGHS does not provide x if infeasible/unbounded
+        if status == 0:  # Observed with HiGHS Simplex Primal
+            status = 4
+            message = ("The solver did not provide a solution nor did it "
+                       "report a failure. Please submit a bug report.")
+        return status, message
+
+    contains_nans = (
+        np.isnan(x).any()
+        or np.isnan(fun)
+        or np.isnan(slack).any()
+        or np.isnan(con).any()
+    )
+
+    if contains_nans:
+        is_feasible = False
+    else:
+        if integrality is None:
+            integrality = 0
+        valid_bounds = (x >= bounds[:, 0] - tol) & (x <= bounds[:, 1] + tol)
+        # When integrality is 2 or 3, x must be within bounds OR take value 0
+        valid_bounds |= (integrality > 1) & np.isclose(x, 0, atol=tol)
+        invalid_bounds = not np.all(valid_bounds)
+
+        invalid_slack = status != 3 and (slack < -tol).any()
+        invalid_con = status != 3 and (np.abs(con) > tol).any()
+        is_feasible = not (invalid_bounds or invalid_slack or invalid_con)
+
+    if status == 0 and not is_feasible:
+        status = 4
+        message = ("The solution does not satisfy the constraints within the "
+                   "required tolerance of " + f"{tol:.2E}" + ", yet "
+                   "no errors were raised and there is no certificate of "
+                   "infeasibility or unboundedness. Check whether "
+                   "the slack and constraint residuals are acceptable; "
+                   "if not, consider enabling presolve, adjusting the "
+                   "tolerance option(s), and/or using a different method. "
+                   "Please consider submitting a bug report.")
+    elif status == 2 and is_feasible:
+        # Occurs if the simplex method exits after phase one with a very
+        # nearly basic feasible solution. Postsolving can make the solution
+        # basic, however, this solution is NOT optimal
+        status = 4
+        message = ("The solution is feasible, but the solver did not report "
+                   "that the solution was optimal. Please try a different "
+                   "method.")
+
+    return status, message

llava_next/lib/python3.10/site-packages/scipy/optimize/_lsq/__init__.py

@@ -0,0 +1,5 @@
+"""This module contains least-squares algorithms."""
+from .least_squares import least_squares
+from .lsq_linear import lsq_linear
+
+__all__ = ['least_squares', 'lsq_linear']

llava_next/lib/python3.10/site-packages/scipy/optimize/_lsq/bvls.py

@@ -0,0 +1,183 @@
+"""Bounded-variable least-squares algorithm."""
+import numpy as np
+from numpy.linalg import norm, lstsq
+from scipy.optimize import OptimizeResult
+
+from .common import print_header_linear, print_iteration_linear
+
+
+def compute_kkt_optimality(g, on_bound):
+    """Compute the maximum violation of KKT conditions."""
+    g_kkt = g * on_bound
+    free_set = on_bound == 0
+    g_kkt[free_set] = np.abs(g[free_set])
+    return np.max(g_kkt)
+
+
+def bvls(A, b, x_lsq, lb, ub, tol, max_iter, verbose, rcond=None):
+    m, n = A.shape
+
+    x = x_lsq.copy()
+    on_bound = np.zeros(n)
+
+    mask = x <= lb
+    x[mask] = lb[mask]
+    on_bound[mask] = -1
+
+    mask = x >= ub
+    x[mask] = ub[mask]
+    on_bound[mask] = 1
+
+    free_set = on_bound == 0
+    active_set = ~free_set
+    free_set, = np.nonzero(free_set)
+
+    r = A.dot(x) - b
+    cost = 0.5 * np.dot(r, r)
+    initial_cost = cost
+    g = A.T.dot(r)
+
+    cost_change = None
+    step_norm = None
+    iteration = 0
+
+    if verbose == 2:
+        print_header_linear()
+
+    # This is the initialization loop. The requirement is that the
+    # least-squares solution on free variables is feasible before BVLS starts.
+    # One possible initialization is to set all variables to lower or upper
+    # bounds, but many iterations may be required from this state later on.
+    # The implemented ad-hoc procedure which intuitively should give a better
+    # initial state: find the least-squares solution on current free variables,
+    # if its feasible then stop, otherwise, set violating variables to
+    # corresponding bounds and continue on the reduced set of free variables.
+
+    while free_set.size > 0:
+        if verbose == 2:
+            optimality = compute_kkt_optimality(g, on_bound)
+            print_iteration_linear(iteration, cost, cost_change, step_norm,
+                                   optimality)
+
+        iteration += 1
+        x_free_old = x[free_set].copy()
+
+        A_free = A[:, free_set]
+        b_free = b - A.dot(x * active_set)
+        z = lstsq(A_free, b_free, rcond=rcond)[0]
+
+        lbv = z < lb[free_set]
+        ubv = z > ub[free_set]
+        v = lbv | ubv
+
+        if np.any(lbv):
+            ind = free_set[lbv]
+            x[ind] = lb[ind]
+            active_set[ind] = True
+            on_bound[ind] = -1
+
+        if np.any(ubv):
+            ind = free_set[ubv]
+            x[ind] = ub[ind]
+            active_set[ind] = True
+            on_bound[ind] = 1
+
+        ind = free_set[~v]
+        x[ind] = z[~v]
+
+        r = A.dot(x) - b
+        cost_new = 0.5 * np.dot(r, r)
+        cost_change = cost - cost_new
+        cost = cost_new
+        g = A.T.dot(r)
+        step_norm = norm(x[free_set] - x_free_old)
+
+        if np.any(v):
+            free_set = free_set[~v]
+        else:
+            break
+
+    if max_iter is None:
+        max_iter = n
+    max_iter += iteration
+
+    termination_status = None
+
+    # Main BVLS loop.
+
+    optimality = compute_kkt_optimality(g, on_bound)
+    for iteration in range(iteration, max_iter):  # BVLS Loop A
+        if verbose == 2:
+            print_iteration_linear(iteration, cost, cost_change,
+                                   step_norm, optimality)
+
+        if optimality < tol:
+            termination_status = 1
+
+        if termination_status is not None:
+            break
+
+        move_to_free = np.argmax(g * on_bound)
+        on_bound[move_to_free] = 0
+        
+        while True:   # BVLS Loop B
+
+            free_set = on_bound == 0
+            active_set = ~free_set
+            free_set, = np.nonzero(free_set)
+    
+            x_free = x[free_set]
+            x_free_old = x_free.copy()
+            lb_free = lb[free_set]
+            ub_free = ub[free_set]
+
+            A_free = A[:, free_set]
+            b_free = b - A.dot(x * active_set)
+            z = lstsq(A_free, b_free, rcond=rcond)[0]
+
+            lbv, = np.nonzero(z < lb_free)
+            ubv, = np.nonzero(z > ub_free)
+            v = np.hstack((lbv, ubv))
+
+            if v.size > 0:
+                alphas = np.hstack((
+                    lb_free[lbv] - x_free[lbv],
+                    ub_free[ubv] - x_free[ubv])) / (z[v] - x_free[v])
+
+                i = np.argmin(alphas)
+                i_free = v[i]
+                alpha = alphas[i]
+
+                x_free *= 1 - alpha
+                x_free += alpha * z
+                x[free_set] = x_free
+
+                if i < lbv.size:
+                    on_bound[free_set[i_free]] = -1
+                else:
+                    on_bound[free_set[i_free]] = 1
+            else:
+                x_free = z
+                x[free_set] = x_free
+                break
+
+        step_norm = norm(x_free - x_free_old)
+
+        r = A.dot(x) - b
+        cost_new = 0.5 * np.dot(r, r)
+        cost_change = cost - cost_new
+
+        if cost_change < tol * cost:
+            termination_status = 2
+        cost = cost_new
+
+        g = A.T.dot(r)
+        optimality = compute_kkt_optimality(g, on_bound)
+
+    if termination_status is None:
+        termination_status = 0
+
+    return OptimizeResult(
+        x=x, fun=r, cost=cost, optimality=optimality, active_mask=on_bound,
+        nit=iteration + 1, status=termination_status,
+        initial_cost=initial_cost)

llava_next/lib/python3.10/site-packages/scipy/optimize/_lsq/common.py

@@ -0,0 +1,733 @@
+"""Functions used by least-squares algorithms."""
+from math import copysign
+
+import numpy as np
+from numpy.linalg import norm
+
+from scipy.linalg import cho_factor, cho_solve, LinAlgError
+from scipy.sparse import issparse
+from scipy.sparse.linalg import LinearOperator, aslinearoperator
+
+
+EPS = np.finfo(float).eps
+
+
+# Functions related to a trust-region problem.
+
+
+def intersect_trust_region(x, s, Delta):
+    """Find the intersection of a line with the boundary of a trust region.
+
+    This function solves the quadratic equation with respect to t
+    ||(x + s*t)||**2 = Delta**2.
+
+    Returns
+    -------
+    t_neg, t_pos : tuple of float
+        Negative and positive roots.
+
+    Raises
+    ------
+    ValueError
+        If `s` is zero or `x` is not within the trust region.
+    """
+    a = np.dot(s, s)
+    if a == 0:
+        raise ValueError("`s` is zero.")
+
+    b = np.dot(x, s)
+
+    c = np.dot(x, x) - Delta**2
+    if c > 0:
+        raise ValueError("`x` is not within the trust region.")
+
+    d = np.sqrt(b*b - a*c)  # Root from one fourth of the discriminant.
+
+    # Computations below avoid loss of significance, see "Numerical Recipes".
+    q = -(b + copysign(d, b))
+    t1 = q / a
+    t2 = c / q
+
+    if t1 < t2:
+        return t1, t2
+    else:
+        return t2, t1
+
+
+def solve_lsq_trust_region(n, m, uf, s, V, Delta, initial_alpha=None,
+                           rtol=0.01, max_iter=10):
+    """Solve a trust-region problem arising in least-squares minimization.
+
+    This function implements a method described by J. J. More [1]_ and used
+    in MINPACK, but it relies on a single SVD of Jacobian instead of series
+    of Cholesky decompositions. Before running this function, compute:
+    ``U, s, VT = svd(J, full_matrices=False)``.
+
+    Parameters
+    ----------
+    n : int
+        Number of variables.
+    m : int
+        Number of residuals.
+    uf : ndarray
+        Computed as U.T.dot(f).
+    s : ndarray
+        Singular values of J.
+    V : ndarray
+        Transpose of VT.
+    Delta : float
+        Radius of a trust region.
+    initial_alpha : float, optional
+        Initial guess for alpha, which might be available from a previous
+        iteration. If None, determined automatically.
+    rtol : float, optional
+        Stopping tolerance for the root-finding procedure. Namely, the
+        solution ``p`` will satisfy ``abs(norm(p) - Delta) < rtol * Delta``.
+    max_iter : int, optional
+        Maximum allowed number of iterations for the root-finding procedure.
+
+    Returns
+    -------
+    p : ndarray, shape (n,)
+        Found solution of a trust-region problem.
+    alpha : float
+        Positive value such that (J.T*J + alpha*I)*p = -J.T*f.
+        Sometimes called Levenberg-Marquardt parameter.
+    n_iter : int
+        Number of iterations made by root-finding procedure. Zero means
+        that Gauss-Newton step was selected as the solution.
+
+    References
+    ----------
+    .. [1] More, J. J., "The Levenberg-Marquardt Algorithm: Implementation
+           and Theory," Numerical Analysis, ed. G. A. Watson, Lecture Notes
+           in Mathematics 630, Springer Verlag, pp. 105-116, 1977.
+    """
+    def phi_and_derivative(alpha, suf, s, Delta):
+        """Function of which to find zero.
+
+        It is defined as "norm of regularized (by alpha) least-squares
+        solution minus `Delta`". Refer to [1]_.
+        """
+        denom = s**2 + alpha
+        p_norm = norm(suf / denom)
+        phi = p_norm - Delta
+        phi_prime = -np.sum(suf ** 2 / denom**3) / p_norm
+        return phi, phi_prime
+
+    suf = s * uf
+
+    # Check if J has full rank and try Gauss-Newton step.
+    if m >= n:
+        threshold = EPS * m * s[0]
+        full_rank = s[-1] > threshold
+    else:
+        full_rank = False
+
+    if full_rank:
+        p = -V.dot(uf / s)
+        if norm(p) <= Delta:
+            return p, 0.0, 0
+
+    alpha_upper = norm(suf) / Delta
+
+    if full_rank:
+        phi, phi_prime = phi_and_derivative(0.0, suf, s, Delta)
+        alpha_lower = -phi / phi_prime
+    else:
+        alpha_lower = 0.0
+
+    if initial_alpha is None or not full_rank and initial_alpha == 0:
+        alpha = max(0.001 * alpha_upper, (alpha_lower * alpha_upper)**0.5)
+    else:
+        alpha = initial_alpha
+
+    for it in range(max_iter):
+        if alpha < alpha_lower or alpha > alpha_upper:
+            alpha = max(0.001 * alpha_upper, (alpha_lower * alpha_upper)**0.5)
+
+        phi, phi_prime = phi_and_derivative(alpha, suf, s, Delta)
+
+        if phi < 0:
+            alpha_upper = alpha
+
+        ratio = phi / phi_prime
+        alpha_lower = max(alpha_lower, alpha - ratio)
+        alpha -= (phi + Delta) * ratio / Delta
+
+        if np.abs(phi) < rtol * Delta:
+            break
+
+    p = -V.dot(suf / (s**2 + alpha))
+
+    # Make the norm of p equal to Delta, p is changed only slightly during
+    # this. It is done to prevent p lie outside the trust region (which can
+    # cause problems later).
+    p *= Delta / norm(p)
+
+    return p, alpha, it + 1
+
+
+def solve_trust_region_2d(B, g, Delta):
+    """Solve a general trust-region problem in 2 dimensions.
+
+    The problem is reformulated as a 4th order algebraic equation,
+    the solution of which is found by numpy.roots.
+
+    Parameters
+    ----------
+    B : ndarray, shape (2, 2)
+        Symmetric matrix, defines a quadratic term of the function.
+    g : ndarray, shape (2,)
+        Defines a linear term of the function.
+    Delta : float
+        Radius of a trust region.
+
+    Returns
+    -------
+    p : ndarray, shape (2,)
+        Found solution.
+    newton_step : bool
+        Whether the returned solution is the Newton step which lies within
+        the trust region.
+    """
+    try:
+        R, lower = cho_factor(B)
+        p = -cho_solve((R, lower), g)
+        if np.dot(p, p) <= Delta**2:
+            return p, True
+    except LinAlgError:
+        pass
+
+    a = B[0, 0] * Delta**2
+    b = B[0, 1] * Delta**2
+    c = B[1, 1] * Delta**2
+
+    d = g[0] * Delta
+    f = g[1] * Delta
+
+    coeffs = np.array(
+        [-b + d, 2 * (a - c + f), 6 * b, 2 * (-a + c + f), -b - d])
+    t = np.roots(coeffs)  # Can handle leading zeros.
+    t = np.real(t[np.isreal(t)])
+
+    p = Delta * np.vstack((2 * t / (1 + t**2), (1 - t**2) / (1 + t**2)))
+    value = 0.5 * np.sum(p * B.dot(p), axis=0) + np.dot(g, p)
+    i = np.argmin(value)
+    p = p[:, i]
+
+    return p, False
+
+
+def update_tr_radius(Delta, actual_reduction, predicted_reduction,
+                     step_norm, bound_hit):
+    """Update the radius of a trust region based on the cost reduction.
+
+    Returns
+    -------
+    Delta : float
+        New radius.
+    ratio : float
+        Ratio between actual and predicted reductions.
+    """
+    if predicted_reduction > 0:
+        ratio = actual_reduction / predicted_reduction
+    elif predicted_reduction == actual_reduction == 0:
+        ratio = 1
+    else:
+        ratio = 0
+
+    if ratio < 0.25:
+        Delta = 0.25 * step_norm
+    elif ratio > 0.75 and bound_hit:
+        Delta *= 2.0
+
+    return Delta, ratio
+
+
+# Construction and minimization of quadratic functions.
+
+
+def build_quadratic_1d(J, g, s, diag=None, s0=None):
+    """Parameterize a multivariate quadratic function along a line.
+
+    The resulting univariate quadratic function is given as follows::
+
+        f(t) = 0.5 * (s0 + s*t).T * (J.T*J + diag) * (s0 + s*t) +
+               g.T * (s0 + s*t)
+
+    Parameters
+    ----------
+    J : ndarray, sparse matrix or LinearOperator shape (m, n)
+        Jacobian matrix, affects the quadratic term.
+    g : ndarray, shape (n,)
+        Gradient, defines the linear term.
+    s : ndarray, shape (n,)
+        Direction vector of a line.
+    diag : None or ndarray with shape (n,), optional
+        Addition diagonal part, affects the quadratic term.
+        If None, assumed to be 0.
+    s0 : None or ndarray with shape (n,), optional
+        Initial point. If None, assumed to be 0.
+
+    Returns
+    -------
+    a : float
+        Coefficient for t**2.
+    b : float
+        Coefficient for t.
+    c : float
+        Free term. Returned only if `s0` is provided.
+    """
+    v = J.dot(s)
+    a = np.dot(v, v)
+    if diag is not None:
+        a += np.dot(s * diag, s)
+    a *= 0.5
+
+    b = np.dot(g, s)
+
+    if s0 is not None:
+        u = J.dot(s0)
+        b += np.dot(u, v)
+        c = 0.5 * np.dot(u, u) + np.dot(g, s0)
+        if diag is not None:
+            b += np.dot(s0 * diag, s)
+            c += 0.5 * np.dot(s0 * diag, s0)
+        return a, b, c
+    else:
+        return a, b
+
+
+def minimize_quadratic_1d(a, b, lb, ub, c=0):
+    """Minimize a 1-D quadratic function subject to bounds.
+
+    The free term `c` is 0 by default. Bounds must be finite.
+
+    Returns
+    -------
+    t : float
+        Minimum point.
+    y : float
+        Minimum value.
+    """
+    t = [lb, ub]
+    if a != 0:
+        extremum = -0.5 * b / a
+        if lb < extremum < ub:
+            t.append(extremum)
+    t = np.asarray(t)
+    y = t * (a * t + b) + c
+    min_index = np.argmin(y)
+    return t[min_index], y[min_index]
+
+
+def evaluate_quadratic(J, g, s, diag=None):
+    """Compute values of a quadratic function arising in least squares.
+
+    The function is 0.5 * s.T * (J.T * J + diag) * s + g.T * s.
+
+    Parameters
+    ----------
+    J : ndarray, sparse matrix or LinearOperator, shape (m, n)
+        Jacobian matrix, affects the quadratic term.
+    g : ndarray, shape (n,)
+        Gradient, defines the linear term.
+    s : ndarray, shape (k, n) or (n,)
+        Array containing steps as rows.
+    diag : ndarray, shape (n,), optional
+        Addition diagonal part, affects the quadratic term.
+        If None, assumed to be 0.
+
+    Returns
+    -------
+    values : ndarray with shape (k,) or float
+        Values of the function. If `s` was 2-D, then ndarray is
+        returned, otherwise, float is returned.
+    """
+    if s.ndim == 1:
+        Js = J.dot(s)
+        q = np.dot(Js, Js)
+        if diag is not None:
+            q += np.dot(s * diag, s)
+    else:
+        Js = J.dot(s.T)
+        q = np.sum(Js**2, axis=0)
+        if diag is not None:
+            q += np.sum(diag * s**2, axis=1)
+
+    l = np.dot(s, g)
+
+    return 0.5 * q + l
+
+
+# Utility functions to work with bound constraints.
+
+
+def in_bounds(x, lb, ub):
+    """Check if a point lies within bounds."""
+    return np.all((x >= lb) & (x <= ub))
+
+
+def step_size_to_bound(x, s, lb, ub):
+    """Compute a min_step size required to reach a bound.
+
+    The function computes a positive scalar t, such that x + s * t is on
+    the bound.
+
+    Returns
+    -------
+    step : float
+        Computed step. Non-negative value.
+    hits : ndarray of int with shape of x
+        Each element indicates whether a corresponding variable reaches the
+        bound:
+
+             *  0 - the bound was not hit.
+             * -1 - the lower bound was hit.
+             *  1 - the upper bound was hit.
+    """
+    non_zero = np.nonzero(s)
+    s_non_zero = s[non_zero]
+    steps = np.empty_like(x)
+    steps.fill(np.inf)
+    with np.errstate(over='ignore'):
+        steps[non_zero] = np.maximum((lb - x)[non_zero] / s_non_zero,
+                                     (ub - x)[non_zero] / s_non_zero)
+    min_step = np.min(steps)
+    return min_step, np.equal(steps, min_step) * np.sign(s).astype(int)
+
+
+def find_active_constraints(x, lb, ub, rtol=1e-10):
+    """Determine which constraints are active in a given point.
+
+    The threshold is computed using `rtol` and the absolute value of the
+    closest bound.
+
+    Returns
+    -------
+    active : ndarray of int with shape of x
+        Each component shows whether the corresponding constraint is active:
+
+             *  0 - a constraint is not active.
+             * -1 - a lower bound is active.
+             *  1 - a upper bound is active.
+    """
+    active = np.zeros_like(x, dtype=int)
+
+    if rtol == 0:
+        active[x <= lb] = -1
+        active[x >= ub] = 1
+        return active
+
+    lower_dist = x - lb
+    upper_dist = ub - x
+
+    lower_threshold = rtol * np.maximum(1, np.abs(lb))
+    upper_threshold = rtol * np.maximum(1, np.abs(ub))
+
+    lower_active = (np.isfinite(lb) &
+                    (lower_dist <= np.minimum(upper_dist, lower_threshold)))
+    active[lower_active] = -1
+
+    upper_active = (np.isfinite(ub) &
+                    (upper_dist <= np.minimum(lower_dist, upper_threshold)))
+    active[upper_active] = 1
+
+    return active
+
+
+def make_strictly_feasible(x, lb, ub, rstep=1e-10):
+    """Shift a point to the interior of a feasible region.
+
+    Each element of the returned vector is at least at a relative distance
+    `rstep` from the closest bound. If ``rstep=0`` then `np.nextafter` is used.
+    """
+    x_new = x.copy()
+
+    active = find_active_constraints(x, lb, ub, rstep)
+    lower_mask = np.equal(active, -1)
+    upper_mask = np.equal(active, 1)
+
+    if rstep == 0:
+        x_new[lower_mask] = np.nextafter(lb[lower_mask], ub[lower_mask])
+        x_new[upper_mask] = np.nextafter(ub[upper_mask], lb[upper_mask])
+    else:
+        x_new[lower_mask] = (lb[lower_mask] +
+                             rstep * np.maximum(1, np.abs(lb[lower_mask])))
+        x_new[upper_mask] = (ub[upper_mask] -
+                             rstep * np.maximum(1, np.abs(ub[upper_mask])))
+
+    tight_bounds = (x_new < lb) | (x_new > ub)
+    x_new[tight_bounds] = 0.5 * (lb[tight_bounds] + ub[tight_bounds])
+
+    return x_new
+
+
+def CL_scaling_vector(x, g, lb, ub):
+    """Compute Coleman-Li scaling vector and its derivatives.
+
+    Components of a vector v are defined as follows::
+
+               | ub[i] - x[i], if g[i] < 0 and ub[i] < np.inf
+        v[i] = | x[i] - lb[i], if g[i] > 0 and lb[i] > -np.inf
+               | 1,           otherwise
+
+    According to this definition v[i] >= 0 for all i. It differs from the
+    definition in paper [1]_ (eq. (2.2)), where the absolute value of v is
+    used. Both definitions are equivalent down the line.
+    Derivatives of v with respect to x take value 1, -1 or 0 depending on a
+    case.
+
+    Returns
+    -------
+    v : ndarray with shape of x
+        Scaling vector.
+    dv : ndarray with shape of x
+        Derivatives of v[i] with respect to x[i], diagonal elements of v's
+        Jacobian.
+
+    References
+    ----------
+    .. [1] M.A. Branch, T.F. Coleman, and Y. Li, "A Subspace, Interior,
+           and Conjugate Gradient Method for Large-Scale Bound-Constrained
+           Minimization Problems," SIAM Journal on Scientific Computing,
+           Vol. 21, Number 1, pp 1-23, 1999.
+    """
+    v = np.ones_like(x)
+    dv = np.zeros_like(x)
+
+    mask = (g < 0) & np.isfinite(ub)
+    v[mask] = ub[mask] - x[mask]
+    dv[mask] = -1
+
+    mask = (g > 0) & np.isfinite(lb)
+    v[mask] = x[mask] - lb[mask]
+    dv[mask] = 1
+
+    return v, dv
+
+
+def reflective_transformation(y, lb, ub):
+    """Compute reflective transformation and its gradient."""
+    if in_bounds(y, lb, ub):
+        return y, np.ones_like(y)
+
+    lb_finite = np.isfinite(lb)
+    ub_finite = np.isfinite(ub)
+
+    x = y.copy()
+    g_negative = np.zeros_like(y, dtype=bool)
+
+    mask = lb_finite & ~ub_finite
+    x[mask] = np.maximum(y[mask], 2 * lb[mask] - y[mask])
+    g_negative[mask] = y[mask] < lb[mask]
+
+    mask = ~lb_finite & ub_finite
+    x[mask] = np.minimum(y[mask], 2 * ub[mask] - y[mask])
+    g_negative[mask] = y[mask] > ub[mask]
+
+    mask = lb_finite & ub_finite
+    d = ub - lb
+    t = np.remainder(y[mask] - lb[mask], 2 * d[mask])
+    x[mask] = lb[mask] + np.minimum(t, 2 * d[mask] - t)
+    g_negative[mask] = t > d[mask]
+
+    g = np.ones_like(y)
+    g[g_negative] = -1
+
+    return x, g
+
+
+# Functions to display algorithm's progress.
+
+
+def print_header_nonlinear():
+    print("{:^15}{:^15}{:^15}{:^15}{:^15}{:^15}"
+          .format("Iteration", "Total nfev", "Cost", "Cost reduction",
+                  "Step norm", "Optimality"))
+
+
+def print_iteration_nonlinear(iteration, nfev, cost, cost_reduction,
+                              step_norm, optimality):
+    if cost_reduction is None:
+        cost_reduction = " " * 15
+    else:
+        cost_reduction = f"{cost_reduction:^15.2e}"
+
+    if step_norm is None:
+        step_norm = " " * 15
+    else:
+        step_norm = f"{step_norm:^15.2e}"
+
+    print("{:^15}{:^15}{:^15.4e}{}{}{:^15.2e}"
+          .format(iteration, nfev, cost, cost_reduction,
+                  step_norm, optimality))
+
+
+def print_header_linear():
+    print("{:^15}{:^15}{:^15}{:^15}{:^15}"
+          .format("Iteration", "Cost", "Cost reduction", "Step norm",
+                  "Optimality"))
+
+
+def print_iteration_linear(iteration, cost, cost_reduction, step_norm,
+                           optimality):
+    if cost_reduction is None:
+        cost_reduction = " " * 15
+    else:
+        cost_reduction = f"{cost_reduction:^15.2e}"
+
+    if step_norm is None:
+        step_norm = " " * 15
+    else:
+        step_norm = f"{step_norm:^15.2e}"
+
+    print(f"{iteration:^15}{cost:^15.4e}{cost_reduction}{step_norm}{optimality:^15.2e}")
+
+
+# Simple helper functions.
+
+
+def compute_grad(J, f):
+    """Compute gradient of the least-squares cost function."""
+    if isinstance(J, LinearOperator):
+        return J.rmatvec(f)
+    else:
+        return J.T.dot(f)
+
+
+def compute_jac_scale(J, scale_inv_old=None):
+    """Compute variables scale based on the Jacobian matrix."""
+    if issparse(J):
+        scale_inv = np.asarray(J.power(2).sum(axis=0)).ravel()**0.5
+    else:
+        scale_inv = np.sum(J**2, axis=0)**0.5
+
+    if scale_inv_old is None:
+        scale_inv[scale_inv == 0] = 1
+    else:
+        scale_inv = np.maximum(scale_inv, scale_inv_old)
+
+    return 1 / scale_inv, scale_inv
+
+
+def left_multiplied_operator(J, d):
+    """Return diag(d) J as LinearOperator."""
+    J = aslinearoperator(J)
+
+    def matvec(x):
+        return d * J.matvec(x)
+
+    def matmat(X):
+        return d[:, np.newaxis] * J.matmat(X)
+
+    def rmatvec(x):
+        return J.rmatvec(x.ravel() * d)
+
+    return LinearOperator(J.shape, matvec=matvec, matmat=matmat,
+                          rmatvec=rmatvec)
+
+
+def right_multiplied_operator(J, d):
+    """Return J diag(d) as LinearOperator."""
+    J = aslinearoperator(J)
+
+    def matvec(x):
+        return J.matvec(np.ravel(x) * d)
+
+    def matmat(X):
+        return J.matmat(X * d[:, np.newaxis])
+
+    def rmatvec(x):
+        return d * J.rmatvec(x)
+
+    return LinearOperator(J.shape, matvec=matvec, matmat=matmat,
+                          rmatvec=rmatvec)
+
+
+def regularized_lsq_operator(J, diag):
+    """Return a matrix arising in regularized least squares as LinearOperator.
+
+    The matrix is
+        [ J ]
+        [ D ]
+    where D is diagonal matrix with elements from `diag`.
+    """
+    J = aslinearoperator(J)
+    m, n = J.shape
+
+    def matvec(x):
+        return np.hstack((J.matvec(x), diag * x))
+
+    def rmatvec(x):
+        x1 = x[:m]
+        x2 = x[m:]
+        return J.rmatvec(x1) + diag * x2
+
+    return LinearOperator((m + n, n), matvec=matvec, rmatvec=rmatvec)
+
+
+def right_multiply(J, d, copy=True):
+    """Compute J diag(d).
+
+    If `copy` is False, `J` is modified in place (unless being LinearOperator).
+    """
+    if copy and not isinstance(J, LinearOperator):
+        J = J.copy()
+
+    if issparse(J):
+        J.data *= d.take(J.indices, mode='clip')  # scikit-learn recipe.
+    elif isinstance(J, LinearOperator):
+        J = right_multiplied_operator(J, d)
+    else:
+        J *= d
+
+    return J
+
+
+def left_multiply(J, d, copy=True):
+    """Compute diag(d) J.
+
+    If `copy` is False, `J` is modified in place (unless being LinearOperator).
+    """
+    if copy and not isinstance(J, LinearOperator):
+        J = J.copy()
+
+    if issparse(J):
+        J.data *= np.repeat(d, np.diff(J.indptr))  # scikit-learn recipe.
+    elif isinstance(J, LinearOperator):
+        J = left_multiplied_operator(J, d)
+    else:
+        J *= d[:, np.newaxis]
+
+    return J
+
+
+def check_termination(dF, F, dx_norm, x_norm, ratio, ftol, xtol):
+    """Check termination condition for nonlinear least squares."""
+    ftol_satisfied = dF < ftol * F and ratio > 0.25
+    xtol_satisfied = dx_norm < xtol * (xtol + x_norm)
+
+    if ftol_satisfied and xtol_satisfied:
+        return 4
+    elif ftol_satisfied:
+        return 2
+    elif xtol_satisfied:
+        return 3
+    else:
+        return None
+
+
+def scale_for_robust_loss_function(J, f, rho):
+    """Scale Jacobian and residuals for a robust loss function.
+
+    Arrays are modified in place.
+    """
+    J_scale = rho[1] + 2 * rho[2] * f**2
+    J_scale[J_scale < EPS] = EPS
+    J_scale **= 0.5
+
+    f *= rho[1] / J_scale
+
+    return left_multiply(J, J_scale, copy=False), f

llava_next/lib/python3.10/site-packages/scipy/optimize/_lsq/dogbox.py

@@ -0,0 +1,331 @@
+"""
+Dogleg algorithm with rectangular trust regions for least-squares minimization.
+
+The description of the algorithm can be found in [Voglis]_. The algorithm does
+trust-region iterations, but the shape of trust regions is rectangular as
+opposed to conventional elliptical. The intersection of a trust region and
+an initial feasible region is again some rectangle. Thus, on each iteration a
+bound-constrained quadratic optimization problem is solved.
+
+A quadratic problem is solved by well-known dogleg approach, where the
+function is minimized along piecewise-linear "dogleg" path [NumOpt]_,
+Chapter 4. If Jacobian is not rank-deficient then the function is decreasing
+along this path, and optimization amounts to simply following along this
+path as long as a point stays within the bounds. A constrained Cauchy step
+(along the anti-gradient) is considered for safety in rank deficient cases,
+in this situations the convergence might be slow.
+
+If during iterations some variable hit the initial bound and the component
+of anti-gradient points outside the feasible region, then a next dogleg step
+won't make any progress. At this state such variables satisfy first-order
+optimality conditions and they are excluded before computing a next dogleg
+step.
+
+Gauss-Newton step can be computed exactly by `numpy.linalg.lstsq` (for dense
+Jacobian matrices) or by iterative procedure `scipy.sparse.linalg.lsmr` (for
+dense and sparse matrices, or Jacobian being LinearOperator). The second
+option allows to solve very large problems (up to couple of millions of
+residuals on a regular PC), provided the Jacobian matrix is sufficiently
+sparse. But note that dogbox is not very good for solving problems with
+large number of constraints, because of variables exclusion-inclusion on each
+iteration (a required number of function evaluations might be high or accuracy
+of a solution will be poor), thus its large-scale usage is probably limited
+to unconstrained problems.
+
+References
+----------
+.. [Voglis] C. Voglis and I. E. Lagaris, "A Rectangular Trust Region Dogleg
+            Approach for Unconstrained and Bound Constrained Nonlinear
+            Optimization", WSEAS International Conference on Applied
+            Mathematics, Corfu, Greece, 2004.
+.. [NumOpt] J. Nocedal and S. J. Wright, "Numerical optimization, 2nd edition".
+"""
+import numpy as np
+from numpy.linalg import lstsq, norm
+
+from scipy.sparse.linalg import LinearOperator, aslinearoperator, lsmr
+from scipy.optimize import OptimizeResult
+
+from .common import (
+    step_size_to_bound, in_bounds, update_tr_radius, evaluate_quadratic,
+    build_quadratic_1d, minimize_quadratic_1d, compute_grad,
+    compute_jac_scale, check_termination, scale_for_robust_loss_function,
+    print_header_nonlinear, print_iteration_nonlinear)
+
+
+def lsmr_operator(Jop, d, active_set):
+    """Compute LinearOperator to use in LSMR by dogbox algorithm.
+
+    `active_set` mask is used to excluded active variables from computations
+    of matrix-vector products.
+    """
+    m, n = Jop.shape
+
+    def matvec(x):
+        x_free = x.ravel().copy()
+        x_free[active_set] = 0
+        return Jop.matvec(x * d)
+
+    def rmatvec(x):
+        r = d * Jop.rmatvec(x)
+        r[active_set] = 0
+        return r
+
+    return LinearOperator((m, n), matvec=matvec, rmatvec=rmatvec, dtype=float)
+
+
+def find_intersection(x, tr_bounds, lb, ub):
+    """Find intersection of trust-region bounds and initial bounds.
+
+    Returns
+    -------
+    lb_total, ub_total : ndarray with shape of x
+        Lower and upper bounds of the intersection region.
+    orig_l, orig_u : ndarray of bool with shape of x
+        True means that an original bound is taken as a corresponding bound
+        in the intersection region.
+    tr_l, tr_u : ndarray of bool with shape of x
+        True means that a trust-region bound is taken as a corresponding bound
+        in the intersection region.
+    """
+    lb_centered = lb - x
+    ub_centered = ub - x
+
+    lb_total = np.maximum(lb_centered, -tr_bounds)
+    ub_total = np.minimum(ub_centered, tr_bounds)
+
+    orig_l = np.equal(lb_total, lb_centered)
+    orig_u = np.equal(ub_total, ub_centered)
+
+    tr_l = np.equal(lb_total, -tr_bounds)
+    tr_u = np.equal(ub_total, tr_bounds)
+
+    return lb_total, ub_total, orig_l, orig_u, tr_l, tr_u
+
+
+def dogleg_step(x, newton_step, g, a, b, tr_bounds, lb, ub):
+    """Find dogleg step in a rectangular region.
+
+    Returns
+    -------
+    step : ndarray, shape (n,)
+        Computed dogleg step.
+    bound_hits : ndarray of int, shape (n,)
+        Each component shows whether a corresponding variable hits the
+        initial bound after the step is taken:
+            *  0 - a variable doesn't hit the bound.
+            * -1 - lower bound is hit.
+            *  1 - upper bound is hit.
+    tr_hit : bool
+        Whether the step hit the boundary of the trust-region.
+    """
+    lb_total, ub_total, orig_l, orig_u, tr_l, tr_u = find_intersection(
+        x, tr_bounds, lb, ub
+    )
+    bound_hits = np.zeros_like(x, dtype=int)
+
+    if in_bounds(newton_step, lb_total, ub_total):
+        return newton_step, bound_hits, False
+
+    to_bounds, _ = step_size_to_bound(np.zeros_like(x), -g, lb_total, ub_total)
+
+    # The classical dogleg algorithm would check if Cauchy step fits into
+    # the bounds, and just return it constrained version if not. But in a
+    # rectangular trust region it makes sense to try to improve constrained
+    # Cauchy step too. Thus, we don't distinguish these two cases.
+
+    cauchy_step = -minimize_quadratic_1d(a, b, 0, to_bounds)[0] * g
+
+    step_diff = newton_step - cauchy_step
+    step_size, hits = step_size_to_bound(cauchy_step, step_diff,
+                                         lb_total, ub_total)
+    bound_hits[(hits < 0) & orig_l] = -1
+    bound_hits[(hits > 0) & orig_u] = 1
+    tr_hit = np.any((hits < 0) & tr_l | (hits > 0) & tr_u)
+
+    return cauchy_step + step_size * step_diff, bound_hits, tr_hit
+
+
+def dogbox(fun, jac, x0, f0, J0, lb, ub, ftol, xtol, gtol, max_nfev, x_scale,
+           loss_function, tr_solver, tr_options, verbose):
+    f = f0
+    f_true = f.copy()
+    nfev = 1
+
+    J = J0
+    njev = 1
+
+    if loss_function is not None:
+        rho = loss_function(f)
+        cost = 0.5 * np.sum(rho[0])
+        J, f = scale_for_robust_loss_function(J, f, rho)
+    else:
+        cost = 0.5 * np.dot(f, f)
+
+    g = compute_grad(J, f)
+
+    jac_scale = isinstance(x_scale, str) and x_scale == 'jac'
+    if jac_scale:
+        scale, scale_inv = compute_jac_scale(J)
+    else:
+        scale, scale_inv = x_scale, 1 / x_scale
+
+    Delta = norm(x0 * scale_inv, ord=np.inf)
+    if Delta == 0:
+        Delta = 1.0
+
+    on_bound = np.zeros_like(x0, dtype=int)
+    on_bound[np.equal(x0, lb)] = -1
+    on_bound[np.equal(x0, ub)] = 1
+
+    x = x0
+    step = np.empty_like(x0)
+
+    if max_nfev is None:
+        max_nfev = x0.size * 100
+
+    termination_status = None
+    iteration = 0
+    step_norm = None
+    actual_reduction = None
+
+    if verbose == 2:
+        print_header_nonlinear()
+
+    while True:
+        active_set = on_bound * g < 0
+        free_set = ~active_set
+
+        g_free = g[free_set]
+        g_full = g.copy()
+        g[active_set] = 0
+
+        g_norm = norm(g, ord=np.inf)
+        if g_norm < gtol:
+            termination_status = 1
+
+        if verbose == 2:
+            print_iteration_nonlinear(iteration, nfev, cost, actual_reduction,
+                                      step_norm, g_norm)
+
+        if termination_status is not None or nfev == max_nfev:
+            break
+
+        x_free = x[free_set]
+        lb_free = lb[free_set]
+        ub_free = ub[free_set]
+        scale_free = scale[free_set]
+
+        # Compute (Gauss-)Newton and build quadratic model for Cauchy step.
+        if tr_solver == 'exact':
+            J_free = J[:, free_set]
+            newton_step = lstsq(J_free, -f, rcond=-1)[0]
+
+            # Coefficients for the quadratic model along the anti-gradient.
+            a, b = build_quadratic_1d(J_free, g_free, -g_free)
+        elif tr_solver == 'lsmr':
+            Jop = aslinearoperator(J)
+
+            # We compute lsmr step in scaled variables and then
+            # transform back to normal variables, if lsmr would give exact lsq
+            # solution, this would be equivalent to not doing any
+            # transformations, but from experience it's better this way.
+
+            # We pass active_set to make computations as if we selected
+            # the free subset of J columns, but without actually doing any
+            # slicing, which is expensive for sparse matrices and impossible
+            # for LinearOperator.
+
+            lsmr_op = lsmr_operator(Jop, scale, active_set)
+            newton_step = -lsmr(lsmr_op, f, **tr_options)[0][free_set]
+            newton_step *= scale_free
+
+            # Components of g for active variables were zeroed, so this call
+            # is correct and equivalent to using J_free and g_free.
+            a, b = build_quadratic_1d(Jop, g, -g)
+
+        actual_reduction = -1.0
+        while actual_reduction <= 0 and nfev < max_nfev:
+            tr_bounds = Delta * scale_free
+
+            step_free, on_bound_free, tr_hit = dogleg_step(
+                x_free, newton_step, g_free, a, b, tr_bounds, lb_free, ub_free)
+
+            step.fill(0.0)
+            step[free_set] = step_free
+
+            if tr_solver == 'exact':
+                predicted_reduction = -evaluate_quadratic(J_free, g_free,
+                                                          step_free)
+            elif tr_solver == 'lsmr':
+                predicted_reduction = -evaluate_quadratic(Jop, g, step)
+
+            # gh11403 ensure that solution is fully within bounds.
+            x_new = np.clip(x + step, lb, ub)
+
+            f_new = fun(x_new)
+            nfev += 1
+
+            step_h_norm = norm(step * scale_inv, ord=np.inf)
+
+            if not np.all(np.isfinite(f_new)):
+                Delta = 0.25 * step_h_norm
+                continue
+
+            # Usual trust-region step quality estimation.
+            if loss_function is not None:
+                cost_new = loss_function(f_new, cost_only=True)
+            else:
+                cost_new = 0.5 * np.dot(f_new, f_new)
+            actual_reduction = cost - cost_new
+
+            Delta, ratio = update_tr_radius(
+                Delta, actual_reduction, predicted_reduction,
+                step_h_norm, tr_hit
+            )
+
+            step_norm = norm(step)
+            termination_status = check_termination(
+                actual_reduction, cost, step_norm, norm(x), ratio, ftol, xtol)
+
+            if termination_status is not None:
+                break
+
+        if actual_reduction > 0:
+            on_bound[free_set] = on_bound_free
+
+            x = x_new
+            # Set variables exactly at the boundary.
+            mask = on_bound == -1
+            x[mask] = lb[mask]
+            mask = on_bound == 1
+            x[mask] = ub[mask]
+
+            f = f_new
+            f_true = f.copy()
+
+            cost = cost_new
+
+            J = jac(x, f)
+            njev += 1
+
+            if loss_function is not None:
+                rho = loss_function(f)
+                J, f = scale_for_robust_loss_function(J, f, rho)
+
+            g = compute_grad(J, f)
+
+            if jac_scale:
+                scale, scale_inv = compute_jac_scale(J, scale_inv)
+        else:
+            step_norm = 0
+            actual_reduction = 0
+
+        iteration += 1
+
+    if termination_status is None:
+        termination_status = 0
+
+    return OptimizeResult(
+        x=x, cost=cost, fun=f_true, jac=J, grad=g_full, optimality=g_norm,
+        active_mask=on_bound, nfev=nfev, njev=njev, status=termination_status)

llava_next/lib/python3.10/site-packages/scipy/optimize/_lsq/least_squares.py

@@ -0,0 +1,967 @@
+"""Generic interface for least-squares minimization."""
+from warnings import warn
+
+import numpy as np
+from numpy.linalg import norm
+
+from scipy.sparse import issparse
+from scipy.sparse.linalg import LinearOperator
+from scipy.optimize import _minpack, OptimizeResult
+from scipy.optimize._numdiff import approx_derivative, group_columns
+from scipy.optimize._minimize import Bounds
+
+from .trf import trf
+from .dogbox import dogbox
+from .common import EPS, in_bounds, make_strictly_feasible
+
+
+TERMINATION_MESSAGES = {
+    -1: "Improper input parameters status returned from `leastsq`",
+    0: "The maximum number of function evaluations is exceeded.",
+    1: "`gtol` termination condition is satisfied.",
+    2: "`ftol` termination condition is satisfied.",
+    3: "`xtol` termination condition is satisfied.",
+    4: "Both `ftol` and `xtol` termination conditions are satisfied."
+}
+
+
+FROM_MINPACK_TO_COMMON = {
+    0: -1,  # Improper input parameters from MINPACK.
+    1: 2,
+    2: 3,
+    3: 4,
+    4: 1,
+    5: 0
+    # There are 6, 7, 8 for too small tolerance parameters,
+    # but we guard against it by checking ftol, xtol, gtol beforehand.
+}
+
+
+def call_minpack(fun, x0, jac, ftol, xtol, gtol, max_nfev, x_scale, diff_step):
+    n = x0.size
+
+    if diff_step is None:
+        epsfcn = EPS
+    else:
+        epsfcn = diff_step**2
+
+    # Compute MINPACK's `diag`, which is inverse of our `x_scale` and
+    # ``x_scale='jac'`` corresponds to ``diag=None``.
+    if isinstance(x_scale, str) and x_scale == 'jac':
+        diag = None
+    else:
+        diag = 1 / x_scale
+
+    full_output = True
+    col_deriv = False
+    factor = 100.0
+
+    if jac is None:
+        if max_nfev is None:
+            # n squared to account for Jacobian evaluations.
+            max_nfev = 100 * n * (n + 1)
+        x, info, status = _minpack._lmdif(
+            fun, x0, (), full_output, ftol, xtol, gtol,
+            max_nfev, epsfcn, factor, diag)
+    else:
+        if max_nfev is None:
+            max_nfev = 100 * n
+        x, info, status = _minpack._lmder(
+            fun, jac, x0, (), full_output, col_deriv,
+            ftol, xtol, gtol, max_nfev, factor, diag)
+
+    f = info['fvec']
+
+    if callable(jac):
+        J = jac(x)
+    else:
+        J = np.atleast_2d(approx_derivative(fun, x))
+
+    cost = 0.5 * np.dot(f, f)
+    g = J.T.dot(f)
+    g_norm = norm(g, ord=np.inf)
+
+    nfev = info['nfev']
+    njev = info.get('njev', None)
+
+    status = FROM_MINPACK_TO_COMMON[status]
+    active_mask = np.zeros_like(x0, dtype=int)
+
+    return OptimizeResult(
+        x=x, cost=cost, fun=f, jac=J, grad=g, optimality=g_norm,
+        active_mask=active_mask, nfev=nfev, njev=njev, status=status)
+
+
+def prepare_bounds(bounds, n):
+    lb, ub = (np.asarray(b, dtype=float) for b in bounds)
+    if lb.ndim == 0:
+        lb = np.resize(lb, n)
+
+    if ub.ndim == 0:
+        ub = np.resize(ub, n)
+
+    return lb, ub
+
+
+def check_tolerance(ftol, xtol, gtol, method):
+    def check(tol, name):
+        if tol is None:
+            tol = 0
+        elif tol < EPS:
+            warn(f"Setting `{name}` below the machine epsilon ({EPS:.2e}) effectively "
+                 f"disables the corresponding termination condition.",
+                 stacklevel=3)
+        return tol
+
+    ftol = check(ftol, "ftol")
+    xtol = check(xtol, "xtol")
+    gtol = check(gtol, "gtol")
+
+    if method == "lm" and (ftol < EPS or xtol < EPS or gtol < EPS):
+        raise ValueError("All tolerances must be higher than machine epsilon "
+                         f"({EPS:.2e}) for method 'lm'.")
+    elif ftol < EPS and xtol < EPS and gtol < EPS:
+        raise ValueError("At least one of the tolerances must be higher than "
+                         f"machine epsilon ({EPS:.2e}).")
+
+    return ftol, xtol, gtol
+
+
+def check_x_scale(x_scale, x0):
+    if isinstance(x_scale, str) and x_scale == 'jac':
+        return x_scale
+
+    try:
+        x_scale = np.asarray(x_scale, dtype=float)
+        valid = np.all(np.isfinite(x_scale)) and np.all(x_scale > 0)
+    except (ValueError, TypeError):
+        valid = False
+
+    if not valid:
+        raise ValueError("`x_scale` must be 'jac' or array_like with "
+                         "positive numbers.")
+
+    if x_scale.ndim == 0:
+        x_scale = np.resize(x_scale, x0.shape)
+
+    if x_scale.shape != x0.shape:
+        raise ValueError("Inconsistent shapes between `x_scale` and `x0`.")
+
+    return x_scale
+
+
+def check_jac_sparsity(jac_sparsity, m, n):
+    if jac_sparsity is None:
+        return None
+
+    if not issparse(jac_sparsity):
+        jac_sparsity = np.atleast_2d(jac_sparsity)
+
+    if jac_sparsity.shape != (m, n):
+        raise ValueError("`jac_sparsity` has wrong shape.")
+
+    return jac_sparsity, group_columns(jac_sparsity)
+
+
+# Loss functions.
+
+
+def huber(z, rho, cost_only):
+    mask = z <= 1
+    rho[0, mask] = z[mask]
+    rho[0, ~mask] = 2 * z[~mask]**0.5 - 1
+    if cost_only:
+        return
+    rho[1, mask] = 1
+    rho[1, ~mask] = z[~mask]**-0.5
+    rho[2, mask] = 0
+    rho[2, ~mask] = -0.5 * z[~mask]**-1.5
+
+
+def soft_l1(z, rho, cost_only):
+    t = 1 + z
+    rho[0] = 2 * (t**0.5 - 1)
+    if cost_only:
+        return
+    rho[1] = t**-0.5
+    rho[2] = -0.5 * t**-1.5
+
+
+def cauchy(z, rho, cost_only):
+    rho[0] = np.log1p(z)
+    if cost_only:
+        return
+    t = 1 + z
+    rho[1] = 1 / t
+    rho[2] = -1 / t**2
+
+
+def arctan(z, rho, cost_only):
+    rho[0] = np.arctan(z)
+    if cost_only:
+        return
+    t = 1 + z**2
+    rho[1] = 1 / t
+    rho[2] = -2 * z / t**2
+
+
+IMPLEMENTED_LOSSES = dict(linear=None, huber=huber, soft_l1=soft_l1,
+                          cauchy=cauchy, arctan=arctan)
+
+
+def construct_loss_function(m, loss, f_scale):
+    if loss == 'linear':
+        return None
+
+    if not callable(loss):
+        loss = IMPLEMENTED_LOSSES[loss]
+        rho = np.empty((3, m))
+
+        def loss_function(f, cost_only=False):
+            z = (f / f_scale) ** 2
+            loss(z, rho, cost_only=cost_only)
+            if cost_only:
+                return 0.5 * f_scale ** 2 * np.sum(rho[0])
+            rho[0] *= f_scale ** 2
+            rho[2] /= f_scale ** 2
+            return rho
+    else:
+        def loss_function(f, cost_only=False):
+            z = (f / f_scale) ** 2
+            rho = loss(z)
+            if cost_only:
+                return 0.5 * f_scale ** 2 * np.sum(rho[0])
+            rho[0] *= f_scale ** 2
+            rho[2] /= f_scale ** 2
+            return rho
+
+    return loss_function
+
+
+def least_squares(
+        fun, x0, jac='2-point', bounds=(-np.inf, np.inf), method='trf',
+        ftol=1e-8, xtol=1e-8, gtol=1e-8, x_scale=1.0, loss='linear',
+        f_scale=1.0, diff_step=None, tr_solver=None, tr_options={},
+        jac_sparsity=None, max_nfev=None, verbose=0, args=(), kwargs={}):
+    """Solve a nonlinear least-squares problem with bounds on the variables.
+
+    Given the residuals f(x) (an m-D real function of n real
+    variables) and the loss function rho(s) (a scalar function), `least_squares`
+    finds a local minimum of the cost function F(x)::
+
+        minimize F(x) = 0.5 * sum(rho(f_i(x)**2), i = 0, ..., m - 1)
+        subject to lb <= x <= ub
+
+    The purpose of the loss function rho(s) is to reduce the influence of
+    outliers on the solution.
+
+    Parameters
+    ----------
+    fun : callable
+        Function which computes the vector of residuals, with the signature
+        ``fun(x, *args, **kwargs)``, i.e., the minimization proceeds with
+        respect to its first argument. The argument ``x`` passed to this
+        function is an ndarray of shape (n,) (never a scalar, even for n=1).
+        It must allocate and return a 1-D array_like of shape (m,) or a scalar.
+        If the argument ``x`` is complex or the function ``fun`` returns
+        complex residuals, it must be wrapped in a real function of real
+        arguments, as shown at the end of the Examples section.
+    x0 : array_like with shape (n,) or float
+        Initial guess on independent variables. If float, it will be treated
+        as a 1-D array with one element. When `method` is 'trf', the initial
+        guess might be slightly adjusted to lie sufficiently within the given
+        `bounds`.
+    jac : {'2-point', '3-point', 'cs', callable}, optional
+        Method of computing the Jacobian matrix (an m-by-n matrix, where
+        element (i, j) is the partial derivative of f[i] with respect to
+        x[j]). The keywords select a finite difference scheme for numerical
+        estimation. The scheme '3-point' is more accurate, but requires
+        twice as many operations as '2-point' (default). The scheme 'cs'
+        uses complex steps, and while potentially the most accurate, it is
+        applicable only when `fun` correctly handles complex inputs and
+        can be analytically continued to the complex plane. Method 'lm'
+        always uses the '2-point' scheme. If callable, it is used as
+        ``jac(x, *args, **kwargs)`` and should return a good approximation
+        (or the exact value) for the Jacobian as an array_like (np.atleast_2d
+        is applied), a sparse matrix (csr_matrix preferred for performance) or
+        a `scipy.sparse.linalg.LinearOperator`.
+    bounds : 2-tuple of array_like or `Bounds`, optional
+        There are two ways to specify bounds:
+
+            1. Instance of `Bounds` class
+            2. Lower and upper bounds on independent variables. Defaults to no
+               bounds. Each array must match the size of `x0` or be a scalar,
+               in the latter case a bound will be the same for all variables.
+               Use ``np.inf`` with an appropriate sign to disable bounds on all
+               or some variables.
+    method : {'trf', 'dogbox', 'lm'}, optional
+        Algorithm to perform minimization.
+
+            * 'trf' : Trust Region Reflective algorithm, particularly suitable
+              for large sparse problems with bounds. Generally robust method.
+            * 'dogbox' : dogleg algorithm with rectangular trust regions,
+              typical use case is small problems with bounds. Not recommended
+              for problems with rank-deficient Jacobian.
+            * 'lm' : Levenberg-Marquardt algorithm as implemented in MINPACK.
+              Doesn't handle bounds and sparse Jacobians. Usually the most
+              efficient method for small unconstrained problems.
+
+        Default is 'trf'. See Notes for more information.
+    ftol : float or None, optional
+        Tolerance for termination by the change of the cost function. Default
+        is 1e-8. The optimization process is stopped when ``dF < ftol * F``,
+        and there was an adequate agreement between a local quadratic model and
+        the true model in the last step.
+
+        If None and 'method' is not 'lm', the termination by this condition is
+        disabled. If 'method' is 'lm', this tolerance must be higher than
+        machine epsilon.
+    xtol : float or None, optional
+        Tolerance for termination by the change of the independent variables.
+        Default is 1e-8. The exact condition depends on the `method` used:
+
+            * For 'trf' and 'dogbox' : ``norm(dx) < xtol * (xtol + norm(x))``.
+            * For 'lm' : ``Delta < xtol * norm(xs)``, where ``Delta`` is
+              a trust-region radius and ``xs`` is the value of ``x``
+              scaled according to `x_scale` parameter (see below).
+
+        If None and 'method' is not 'lm', the termination by this condition is
+        disabled. If 'method' is 'lm', this tolerance must be higher than
+        machine epsilon.
+    gtol : float or None, optional
+        Tolerance for termination by the norm of the gradient. Default is 1e-8.
+        The exact condition depends on a `method` used:
+
+            * For 'trf' : ``norm(g_scaled, ord=np.inf) < gtol``, where
+              ``g_scaled`` is the value of the gradient scaled to account for
+              the presence of the bounds [STIR]_.
+            * For 'dogbox' : ``norm(g_free, ord=np.inf) < gtol``, where
+              ``g_free`` is the gradient with respect to the variables which
+              are not in the optimal state on the boundary.
+            * For 'lm' : the maximum absolute value of the cosine of angles
+              between columns of the Jacobian and the residual vector is less
+              than `gtol`, or the residual vector is zero.
+
+        If None and 'method' is not 'lm', the termination by this condition is
+        disabled. If 'method' is 'lm', this tolerance must be higher than
+        machine epsilon.
+    x_scale : array_like or 'jac', optional
+        Characteristic scale of each variable. Setting `x_scale` is equivalent
+        to reformulating the problem in scaled variables ``xs = x / x_scale``.
+        An alternative view is that the size of a trust region along jth
+        dimension is proportional to ``x_scale[j]``. Improved convergence may
+        be achieved by setting `x_scale` such that a step of a given size
+        along any of the scaled variables has a similar effect on the cost
+        function. If set to 'jac', the scale is iteratively updated using the
+        inverse norms of the columns of the Jacobian matrix (as described in
+        [JJMore]_).
+    loss : str or callable, optional
+        Determines the loss function. The following keyword values are allowed:
+
+            * 'linear' (default) : ``rho(z) = z``. Gives a standard
+              least-squares problem.
+            * 'soft_l1' : ``rho(z) = 2 * ((1 + z)**0.5 - 1)``. The smooth
+              approximation of l1 (absolute value) loss. Usually a good
+              choice for robust least squares.
+            * 'huber' : ``rho(z) = z if z <= 1 else 2*z**0.5 - 1``. Works
+              similarly to 'soft_l1'.
+            * 'cauchy' : ``rho(z) = ln(1 + z)``. Severely weakens outliers
+              influence, but may cause difficulties in optimization process.
+            * 'arctan' : ``rho(z) = arctan(z)``. Limits a maximum loss on
+              a single residual, has properties similar to 'cauchy'.
+
+        If callable, it must take a 1-D ndarray ``z=f**2`` and return an
+        array_like with shape (3, m) where row 0 contains function values,
+        row 1 contains first derivatives and row 2 contains second
+        derivatives. Method 'lm' supports only 'linear' loss.
+    f_scale : float, optional
+        Value of soft margin between inlier and outlier residuals, default
+        is 1.0. The loss function is evaluated as follows
+        ``rho_(f**2) = C**2 * rho(f**2 / C**2)``, where ``C`` is `f_scale`,
+        and ``rho`` is determined by `loss` parameter. This parameter has
+        no effect with ``loss='linear'``, but for other `loss` values it is
+        of crucial importance.
+    max_nfev : None or int, optional
+        Maximum number of function evaluations before the termination.
+        If None (default), the value is chosen automatically:
+
+            * For 'trf' and 'dogbox' : 100 * n.
+            * For 'lm' :  100 * n if `jac` is callable and 100 * n * (n + 1)
+              otherwise (because 'lm' counts function calls in Jacobian
+              estimation).
+
+    diff_step : None or array_like, optional
+        Determines the relative step size for the finite difference
+        approximation of the Jacobian. The actual step is computed as
+        ``x * diff_step``. If None (default), then `diff_step` is taken to be
+        a conventional "optimal" power of machine epsilon for the finite
+        difference scheme used [NR]_.
+    tr_solver : {None, 'exact', 'lsmr'}, optional
+        Method for solving trust-region subproblems, relevant only for 'trf'
+        and 'dogbox' methods.
+
+            * 'exact' is suitable for not very large problems with dense
+              Jacobian matrices. The computational complexity per iteration is
+              comparable to a singular value decomposition of the Jacobian
+              matrix.
+            * 'lsmr' is suitable for problems with sparse and large Jacobian
+              matrices. It uses the iterative procedure
+              `scipy.sparse.linalg.lsmr` for finding a solution of a linear
+              least-squares problem and only requires matrix-vector product
+              evaluations.
+
+        If None (default), the solver is chosen based on the type of Jacobian
+        returned on the first iteration.
+    tr_options : dict, optional
+        Keyword options passed to trust-region solver.
+
+            * ``tr_solver='exact'``: `tr_options` are ignored.
+            * ``tr_solver='lsmr'``: options for `scipy.sparse.linalg.lsmr`.
+              Additionally,  ``method='trf'`` supports  'regularize' option
+              (bool, default is True), which adds a regularization term to the
+              normal equation, which improves convergence if the Jacobian is
+              rank-deficient [Byrd]_ (eq. 3.4).
+
+    jac_sparsity : {None, array_like, sparse matrix}, optional
+        Defines the sparsity structure of the Jacobian matrix for finite
+        difference estimation, its shape must be (m, n). If the Jacobian has
+        only few non-zero elements in *each* row, providing the sparsity
+        structure will greatly speed up the computations [Curtis]_. A zero
+        entry means that a corresponding element in the Jacobian is identically
+        zero. If provided, forces the use of 'lsmr' trust-region solver.
+        If None (default), then dense differencing will be used. Has no effect
+        for 'lm' method.
+    verbose : {0, 1, 2}, optional
+        Level of algorithm's verbosity:
+
+            * 0 (default) : work silently.
+            * 1 : display a termination report.
+            * 2 : display progress during iterations (not supported by 'lm'
+              method).
+
+    args, kwargs : tuple and dict, optional
+        Additional arguments passed to `fun` and `jac`. Both empty by default.
+        The calling signature is ``fun(x, *args, **kwargs)`` and the same for
+        `jac`.
+
+    Returns
+    -------
+    result : OptimizeResult
+        `OptimizeResult` with the following fields defined:
+
+            x : ndarray, shape (n,)
+                Solution found.
+            cost : float
+                Value of the cost function at the solution.
+            fun : ndarray, shape (m,)
+                Vector of residuals at the solution.
+            jac : ndarray, sparse matrix or LinearOperator, shape (m, n)
+                Modified Jacobian matrix at the solution, in the sense that J^T J
+                is a Gauss-Newton approximation of the Hessian of the cost function.
+                The type is the same as the one used by the algorithm.
+            grad : ndarray, shape (m,)
+                Gradient of the cost function at the solution.
+            optimality : float
+                First-order optimality measure. In unconstrained problems, it is
+                always the uniform norm of the gradient. In constrained problems,
+                it is the quantity which was compared with `gtol` during iterations.
+            active_mask : ndarray of int, shape (n,)
+                Each component shows whether a corresponding constraint is active
+                (that is, whether a variable is at the bound):
+
+                    *  0 : a constraint is not active.
+                    * -1 : a lower bound is active.
+                    *  1 : an upper bound is active.
+
+                Might be somewhat arbitrary for 'trf' method as it generates a
+                sequence of strictly feasible iterates and `active_mask` is
+                determined within a tolerance threshold.
+            nfev : int
+                Number of function evaluations done. Methods 'trf' and 'dogbox' do
+                not count function calls for numerical Jacobian approximation, as
+                opposed to 'lm' method.
+            njev : int or None
+                Number of Jacobian evaluations done. If numerical Jacobian
+                approximation is used in 'lm' method, it is set to None.
+            status : int
+                The reason for algorithm termination:
+
+                    * -1 : improper input parameters status returned from MINPACK.
+                    *  0 : the maximum number of function evaluations is exceeded.
+                    *  1 : `gtol` termination condition is satisfied.
+                    *  2 : `ftol` termination condition is satisfied.
+                    *  3 : `xtol` termination condition is satisfied.
+                    *  4 : Both `ftol` and `xtol` termination conditions are satisfied.
+
+            message : str
+                Verbal description of the termination reason.
+            success : bool
+                True if one of the convergence criteria is satisfied (`status` > 0).
+
+    See Also
+    --------
+    leastsq : A legacy wrapper for the MINPACK implementation of the
+              Levenberg-Marquadt algorithm.
+    curve_fit : Least-squares minimization applied to a curve-fitting problem.
+
+    Notes
+    -----
+    Method 'lm' (Levenberg-Marquardt) calls a wrapper over least-squares
+    algorithms implemented in MINPACK (lmder, lmdif). It runs the
+    Levenberg-Marquardt algorithm formulated as a trust-region type algorithm.
+    The implementation is based on paper [JJMore]_, it is very robust and
+    efficient with a lot of smart tricks. It should be your first choice
+    for unconstrained problems. Note that it doesn't support bounds. Also,
+    it doesn't work when m < n.
+
+    Method 'trf' (Trust Region Reflective) is motivated by the process of
+    solving a system of equations, which constitute the first-order optimality
+    condition for a bound-constrained minimization problem as formulated in
+    [STIR]_. The algorithm iteratively solves trust-region subproblems
+    augmented by a special diagonal quadratic term and with trust-region shape
+    determined by the distance from the bounds and the direction of the
+    gradient. This enhancements help to avoid making steps directly into bounds
+    and efficiently explore the whole space of variables. To further improve
+    convergence, the algorithm considers search directions reflected from the
+    bounds. To obey theoretical requirements, the algorithm keeps iterates
+    strictly feasible. With dense Jacobians trust-region subproblems are
+    solved by an exact method very similar to the one described in [JJMore]_
+    (and implemented in MINPACK). The difference from the MINPACK
+    implementation is that a singular value decomposition of a Jacobian
+    matrix is done once per iteration, instead of a QR decomposition and series
+    of Givens rotation eliminations. For large sparse Jacobians a 2-D subspace
+    approach of solving trust-region subproblems is used [STIR]_, [Byrd]_.
+    The subspace is spanned by a scaled gradient and an approximate
+    Gauss-Newton solution delivered by `scipy.sparse.linalg.lsmr`. When no
+    constraints are imposed the algorithm is very similar to MINPACK and has
+    generally comparable performance. The algorithm works quite robust in
+    unbounded and bounded problems, thus it is chosen as a default algorithm.
+
+    Method 'dogbox' operates in a trust-region framework, but considers
+    rectangular trust regions as opposed to conventional ellipsoids [Voglis]_.
+    The intersection of a current trust region and initial bounds is again
+    rectangular, so on each iteration a quadratic minimization problem subject
+    to bound constraints is solved approximately by Powell's dogleg method
+    [NumOpt]_. The required Gauss-Newton step can be computed exactly for
+    dense Jacobians or approximately by `scipy.sparse.linalg.lsmr` for large
+    sparse Jacobians. The algorithm is likely to exhibit slow convergence when
+    the rank of Jacobian is less than the number of variables. The algorithm
+    often outperforms 'trf' in bounded problems with a small number of
+    variables.
+
+    Robust loss functions are implemented as described in [BA]_. The idea
+    is to modify a residual vector and a Jacobian matrix on each iteration
+    such that computed gradient and Gauss-Newton Hessian approximation match
+    the true gradient and Hessian approximation of the cost function. Then
+    the algorithm proceeds in a normal way, i.e., robust loss functions are
+    implemented as a simple wrapper over standard least-squares algorithms.
+
+    .. versionadded:: 0.17.0
+
+    References
+    ----------
+    .. [STIR] M. A. Branch, T. F. Coleman, and Y. Li, "A Subspace, Interior,
+              and Conjugate Gradient Method for Large-Scale Bound-Constrained
+              Minimization Problems," SIAM Journal on Scientific Computing,
+              Vol. 21, Number 1, pp 1-23, 1999.
+    .. [NR] William H. Press et. al., "Numerical Recipes. The Art of Scientific
+            Computing. 3rd edition", Sec. 5.7.
+    .. [Byrd] R. H. Byrd, R. B. Schnabel and G. A. Shultz, "Approximate
+              solution of the trust region problem by minimization over
+              two-dimensional subspaces", Math. Programming, 40, pp. 247-263,
+              1988.
+    .. [Curtis] A. Curtis, M. J. D. Powell, and J. Reid, "On the estimation of
+                sparse Jacobian matrices", Journal of the Institute of
+                Mathematics and its Applications, 13, pp. 117-120, 1974.
+    .. [JJMore] J. J. More, "The Levenberg-Marquardt Algorithm: Implementation
+                and Theory," Numerical Analysis, ed. G. A. Watson, Lecture
+                Notes in Mathematics 630, Springer Verlag, pp. 105-116, 1977.
+    .. [Voglis] C. Voglis and I. E. Lagaris, "A Rectangular Trust Region
+                Dogleg Approach for Unconstrained and Bound Constrained
+                Nonlinear Optimization", WSEAS International Conference on
+                Applied Mathematics, Corfu, Greece, 2004.
+    .. [NumOpt] J. Nocedal and S. J. Wright, "Numerical optimization,
+                2nd edition", Chapter 4.
+    .. [BA] B. Triggs et. al., "Bundle Adjustment - A Modern Synthesis",
+            Proceedings of the International Workshop on Vision Algorithms:
+            Theory and Practice, pp. 298-372, 1999.
+
+    Examples
+    --------
+    In this example we find a minimum of the Rosenbrock function without bounds
+    on independent variables.
+
+    >>> import numpy as np
+    >>> def fun_rosenbrock(x):
+    ...     return np.array([10 * (x[1] - x[0]**2), (1 - x[0])])
+
+    Notice that we only provide the vector of the residuals. The algorithm
+    constructs the cost function as a sum of squares of the residuals, which
+    gives the Rosenbrock function. The exact minimum is at ``x = [1.0, 1.0]``.
+
+    >>> from scipy.optimize import least_squares
+    >>> x0_rosenbrock = np.array([2, 2])
+    >>> res_1 = least_squares(fun_rosenbrock, x0_rosenbrock)
+    >>> res_1.x
+    array([ 1.,  1.])
+    >>> res_1.cost
+    9.8669242910846867e-30
+    >>> res_1.optimality
+    8.8928864934219529e-14
+
+    We now constrain the variables, in such a way that the previous solution
+    becomes infeasible. Specifically, we require that ``x[1] >= 1.5``, and
+    ``x[0]`` left unconstrained. To this end, we specify the `bounds` parameter
+    to `least_squares` in the form ``bounds=([-np.inf, 1.5], np.inf)``.
+
+    We also provide the analytic Jacobian:
+
+    >>> def jac_rosenbrock(x):
+    ...     return np.array([
+    ...         [-20 * x[0], 10],
+    ...         [-1, 0]])
+
+    Putting this all together, we see that the new solution lies on the bound:
+
+    >>> res_2 = least_squares(fun_rosenbrock, x0_rosenbrock, jac_rosenbrock,
+    ...                       bounds=([-np.inf, 1.5], np.inf))
+    >>> res_2.x
+    array([ 1.22437075,  1.5       ])
+    >>> res_2.cost
+    0.025213093946805685
+    >>> res_2.optimality
+    1.5885401433157753e-07
+
+    Now we solve a system of equations (i.e., the cost function should be zero
+    at a minimum) for a Broyden tridiagonal vector-valued function of 100000
+    variables:
+
+    >>> def fun_broyden(x):
+    ...     f = (3 - x) * x + 1
+    ...     f[1:] -= x[:-1]
+    ...     f[:-1] -= 2 * x[1:]
+    ...     return f
+
+    The corresponding Jacobian matrix is sparse. We tell the algorithm to
+    estimate it by finite differences and provide the sparsity structure of
+    Jacobian to significantly speed up this process.
+
+    >>> from scipy.sparse import lil_matrix
+    >>> def sparsity_broyden(n):
+    ...     sparsity = lil_matrix((n, n), dtype=int)
+    ...     i = np.arange(n)
+    ...     sparsity[i, i] = 1
+    ...     i = np.arange(1, n)
+    ...     sparsity[i, i - 1] = 1
+    ...     i = np.arange(n - 1)
+    ...     sparsity[i, i + 1] = 1
+    ...     return sparsity
+    ...
+    >>> n = 100000
+    >>> x0_broyden = -np.ones(n)
+    ...
+    >>> res_3 = least_squares(fun_broyden, x0_broyden,
+    ...                       jac_sparsity=sparsity_broyden(n))
+    >>> res_3.cost
+    4.5687069299604613e-23
+    >>> res_3.optimality
+    1.1650454296851518e-11
+
+    Let's also solve a curve fitting problem using robust loss function to
+    take care of outliers in the data. Define the model function as
+    ``y = a + b * exp(c * t)``, where t is a predictor variable, y is an
+    observation and a, b, c are parameters to estimate.
+
+    First, define the function which generates the data with noise and
+    outliers, define the model parameters, and generate data:
+
+    >>> from numpy.random import default_rng
+    >>> rng = default_rng()
+    >>> def gen_data(t, a, b, c, noise=0., n_outliers=0, seed=None):
+    ...     rng = default_rng(seed)
+    ...
+    ...     y = a + b * np.exp(t * c)
+    ...
+    ...     error = noise * rng.standard_normal(t.size)
+    ...     outliers = rng.integers(0, t.size, n_outliers)
+    ...     error[outliers] *= 10
+    ...
+    ...     return y + error
+    ...
+    >>> a = 0.5
+    >>> b = 2.0
+    >>> c = -1
+    >>> t_min = 0
+    >>> t_max = 10
+    >>> n_points = 15
+    ...
+    >>> t_train = np.linspace(t_min, t_max, n_points)
+    >>> y_train = gen_data(t_train, a, b, c, noise=0.1, n_outliers=3)
+
+    Define function for computing residuals and initial estimate of
+    parameters.
+
+    >>> def fun(x, t, y):
+    ...     return x[0] + x[1] * np.exp(x[2] * t) - y
+    ...
+    >>> x0 = np.array([1.0, 1.0, 0.0])
+
+    Compute a standard least-squares solution:
+
+    >>> res_lsq = least_squares(fun, x0, args=(t_train, y_train))
+
+    Now compute two solutions with two different robust loss functions. The
+    parameter `f_scale` is set to 0.1, meaning that inlier residuals should
+    not significantly exceed 0.1 (the noise level used).
+
+    >>> res_soft_l1 = least_squares(fun, x0, loss='soft_l1', f_scale=0.1,
+    ...                             args=(t_train, y_train))
+    >>> res_log = least_squares(fun, x0, loss='cauchy', f_scale=0.1,
+    ...                         args=(t_train, y_train))
+
+    And, finally, plot all the curves. We see that by selecting an appropriate
+    `loss`  we can get estimates close to optimal even in the presence of
+    strong outliers. But keep in mind that generally it is recommended to try
+    'soft_l1' or 'huber' losses first (if at all necessary) as the other two
+    options may cause difficulties in optimization process.
+
+    >>> t_test = np.linspace(t_min, t_max, n_points * 10)
+    >>> y_true = gen_data(t_test, a, b, c)
+    >>> y_lsq = gen_data(t_test, *res_lsq.x)
+    >>> y_soft_l1 = gen_data(t_test, *res_soft_l1.x)
+    >>> y_log = gen_data(t_test, *res_log.x)
+    ...
+    >>> import matplotlib.pyplot as plt
+    >>> plt.plot(t_train, y_train, 'o')
+    >>> plt.plot(t_test, y_true, 'k', linewidth=2, label='true')
+    >>> plt.plot(t_test, y_lsq, label='linear loss')
+    >>> plt.plot(t_test, y_soft_l1, label='soft_l1 loss')
+    >>> plt.plot(t_test, y_log, label='cauchy loss')
+    >>> plt.xlabel("t")
+    >>> plt.ylabel("y")
+    >>> plt.legend()
+    >>> plt.show()
+
+    In the next example, we show how complex-valued residual functions of
+    complex variables can be optimized with ``least_squares()``. Consider the
+    following function:
+
+    >>> def f(z):
+    ...     return z - (0.5 + 0.5j)
+
+    We wrap it into a function of real variables that returns real residuals
+    by simply handling the real and imaginary parts as independent variables:
+
+    >>> def f_wrap(x):
+    ...     fx = f(x[0] + 1j*x[1])
+    ...     return np.array([fx.real, fx.imag])
+
+    Thus, instead of the original m-D complex function of n complex
+    variables we optimize a 2m-D real function of 2n real variables:
+
+    >>> from scipy.optimize import least_squares
+    >>> res_wrapped = least_squares(f_wrap, (0.1, 0.1), bounds=([0, 0], [1, 1]))
+    >>> z = res_wrapped.x[0] + res_wrapped.x[1]*1j
+    >>> z
+    (0.49999999999925893+0.49999999999925893j)
+
+    """
+    if method not in ['trf', 'dogbox', 'lm']:
+        raise ValueError("`method` must be 'trf', 'dogbox' or 'lm'.")
+
+    if jac not in ['2-point', '3-point', 'cs'] and not callable(jac):
+        raise ValueError("`jac` must be '2-point', '3-point', 'cs' or "
+                         "callable.")
+
+    if tr_solver not in [None, 'exact', 'lsmr']:
+        raise ValueError("`tr_solver` must be None, 'exact' or 'lsmr'.")
+
+    if loss not in IMPLEMENTED_LOSSES and not callable(loss):
+        raise ValueError("`loss` must be one of {} or a callable."
+                         .format(IMPLEMENTED_LOSSES.keys()))
+
+    if method == 'lm' and loss != 'linear':
+        raise ValueError("method='lm' supports only 'linear' loss function.")
+
+    if verbose not in [0, 1, 2]:
+        raise ValueError("`verbose` must be in [0, 1, 2].")
+
+    if max_nfev is not None and max_nfev <= 0:
+        raise ValueError("`max_nfev` must be None or positive integer.")
+
+    if np.iscomplexobj(x0):
+        raise ValueError("`x0` must be real.")
+
+    x0 = np.atleast_1d(x0).astype(float)
+
+    if x0.ndim > 1:
+        raise ValueError("`x0` must have at most 1 dimension.")
+
+    if isinstance(bounds, Bounds):
+        lb, ub = bounds.lb, bounds.ub
+        bounds = (lb, ub)
+    else:
+        if len(bounds) == 2:
+            lb, ub = prepare_bounds(bounds, x0.shape[0])
+        else:
+            raise ValueError("`bounds` must contain 2 elements.")
+
+    if method == 'lm' and not np.all((lb == -np.inf) & (ub == np.inf)):
+        raise ValueError("Method 'lm' doesn't support bounds.")
+
+    if lb.shape != x0.shape or ub.shape != x0.shape:
+        raise ValueError("Inconsistent shapes between bounds and `x0`.")
+
+    if np.any(lb >= ub):
+        raise ValueError("Each lower bound must be strictly less than each "
+                         "upper bound.")
+
+    if not in_bounds(x0, lb, ub):
+        raise ValueError("`x0` is infeasible.")
+
+    x_scale = check_x_scale(x_scale, x0)
+
+    ftol, xtol, gtol = check_tolerance(ftol, xtol, gtol, method)
+
+    if method == 'trf':
+        x0 = make_strictly_feasible(x0, lb, ub)
+
+    def fun_wrapped(x):
+        return np.atleast_1d(fun(x, *args, **kwargs))
+
+    f0 = fun_wrapped(x0)
+
+    if f0.ndim != 1:
+        raise ValueError("`fun` must return at most 1-d array_like. "
+                         f"f0.shape: {f0.shape}")
+
+    if not np.all(np.isfinite(f0)):
+        raise ValueError("Residuals are not finite in the initial point.")
+
+    n = x0.size
+    m = f0.size
+
+    if method == 'lm' and m < n:
+        raise ValueError("Method 'lm' doesn't work when the number of "
+                         "residuals is less than the number of variables.")
+
+    loss_function = construct_loss_function(m, loss, f_scale)
+    if callable(loss):
+        rho = loss_function(f0)
+        if rho.shape != (3, m):
+            raise ValueError("The return value of `loss` callable has wrong "
+                             "shape.")
+        initial_cost = 0.5 * np.sum(rho[0])
+    elif loss_function is not None:
+        initial_cost = loss_function(f0, cost_only=True)
+    else:
+        initial_cost = 0.5 * np.dot(f0, f0)
+
+    if callable(jac):
+        J0 = jac(x0, *args, **kwargs)
+
+        if issparse(J0):
+            J0 = J0.tocsr()
+
+            def jac_wrapped(x, _=None):
+                return jac(x, *args, **kwargs).tocsr()
+
+        elif isinstance(J0, LinearOperator):
+            def jac_wrapped(x, _=None):
+                return jac(x, *args, **kwargs)
+
+        else:
+            J0 = np.atleast_2d(J0)
+
+            def jac_wrapped(x, _=None):
+                return np.atleast_2d(jac(x, *args, **kwargs))
+
+    else:  # Estimate Jacobian by finite differences.
+        if method == 'lm':
+            if jac_sparsity is not None:
+                raise ValueError("method='lm' does not support "
+                                 "`jac_sparsity`.")
+
+            if jac != '2-point':
+                warn(f"jac='{jac}' works equivalently to '2-point' for method='lm'.",
+                     stacklevel=2)
+
+            J0 = jac_wrapped = None
+        else:
+            if jac_sparsity is not None and tr_solver == 'exact':
+                raise ValueError("tr_solver='exact' is incompatible "
+                                 "with `jac_sparsity`.")
+
+            jac_sparsity = check_jac_sparsity(jac_sparsity, m, n)
+
+            def jac_wrapped(x, f):
+                J = approx_derivative(fun, x, rel_step=diff_step, method=jac,
+                                      f0=f, bounds=bounds, args=args,
+                                      kwargs=kwargs, sparsity=jac_sparsity)
+                if J.ndim != 2:  # J is guaranteed not sparse.
+                    J = np.atleast_2d(J)
+
+                return J
+
+            J0 = jac_wrapped(x0, f0)
+
+    if J0 is not None:
+        if J0.shape != (m, n):
+            raise ValueError(
+                f"The return value of `jac` has wrong shape: expected {(m, n)}, "
+                f"actual {J0.shape}."
+            )
+
+        if not isinstance(J0, np.ndarray):
+            if method == 'lm':
+                raise ValueError("method='lm' works only with dense "
+                                 "Jacobian matrices.")
+
+            if tr_solver == 'exact':
+                raise ValueError(
+                    "tr_solver='exact' works only with dense "
+                    "Jacobian matrices.")
+
+        jac_scale = isinstance(x_scale, str) and x_scale == 'jac'
+        if isinstance(J0, LinearOperator) and jac_scale:
+            raise ValueError("x_scale='jac' can't be used when `jac` "
+                             "returns LinearOperator.")
+
+        if tr_solver is None:
+            if isinstance(J0, np.ndarray):
+                tr_solver = 'exact'
+            else:
+                tr_solver = 'lsmr'
+
+    if method == 'lm':
+        result = call_minpack(fun_wrapped, x0, jac_wrapped, ftol, xtol, gtol,
+                              max_nfev, x_scale, diff_step)
+
+    elif method == 'trf':
+        result = trf(fun_wrapped, jac_wrapped, x0, f0, J0, lb, ub, ftol, xtol,
+                     gtol, max_nfev, x_scale, loss_function, tr_solver,
+                     tr_options.copy(), verbose)
+
+    elif method == 'dogbox':
+        if tr_solver == 'lsmr' and 'regularize' in tr_options:
+            warn("The keyword 'regularize' in `tr_options` is not relevant "
+                 "for 'dogbox' method.",
+                 stacklevel=2)
+            tr_options = tr_options.copy()
+            del tr_options['regularize']
+
+        result = dogbox(fun_wrapped, jac_wrapped, x0, f0, J0, lb, ub, ftol,
+                        xtol, gtol, max_nfev, x_scale, loss_function,
+                        tr_solver, tr_options, verbose)
+
+    result.message = TERMINATION_MESSAGES[result.status]
+    result.success = result.status > 0
+
+    if verbose >= 1:
+        print(result.message)
+        print("Function evaluations {}, initial cost {:.4e}, final cost "
+              "{:.4e}, first-order optimality {:.2e}."
+              .format(result.nfev, initial_cost, result.cost,
+                      result.optimality))
+
+    return result

llava_next/lib/python3.10/site-packages/scipy/optimize/_lsq/lsq_linear.py

@@ -0,0 +1,362 @@
+"""Linear least squares with bound constraints on independent variables."""
+import numpy as np
+from numpy.linalg import norm
+from scipy.sparse import issparse, csr_matrix
+from scipy.sparse.linalg import LinearOperator, lsmr
+from scipy.optimize import OptimizeResult
+from scipy.optimize._minimize import Bounds
+
+from .common import in_bounds, compute_grad
+from .trf_linear import trf_linear
+from .bvls import bvls
+
+
+def prepare_bounds(bounds, n):
+    if len(bounds) != 2:
+        raise ValueError("`bounds` must contain 2 elements.")
+    lb, ub = (np.asarray(b, dtype=float) for b in bounds)
+
+    if lb.ndim == 0:
+        lb = np.resize(lb, n)
+
+    if ub.ndim == 0:
+        ub = np.resize(ub, n)
+
+    return lb, ub
+
+
+TERMINATION_MESSAGES = {
+    -1: "The algorithm was not able to make progress on the last iteration.",
+    0: "The maximum number of iterations is exceeded.",
+    1: "The first-order optimality measure is less than `tol`.",
+    2: "The relative change of the cost function is less than `tol`.",
+    3: "The unconstrained solution is optimal."
+}
+
+
+def lsq_linear(A, b, bounds=(-np.inf, np.inf), method='trf', tol=1e-10,
+               lsq_solver=None, lsmr_tol=None, max_iter=None,
+               verbose=0, *, lsmr_maxiter=None,):
+    r"""Solve a linear least-squares problem with bounds on the variables.
+
+    Given a m-by-n design matrix A and a target vector b with m elements,
+    `lsq_linear` solves the following optimization problem::
+
+        minimize 0.5 * ||A x - b||**2
+        subject to lb <= x <= ub
+
+    This optimization problem is convex, hence a found minimum (if iterations
+    have converged) is guaranteed to be global.
+
+    Parameters
+    ----------
+    A : array_like, sparse matrix of LinearOperator, shape (m, n)
+        Design matrix. Can be `scipy.sparse.linalg.LinearOperator`.
+    b : array_like, shape (m,)
+        Target vector.
+    bounds : 2-tuple of array_like or `Bounds`, optional
+        Lower and upper bounds on parameters. Defaults to no bounds.
+        There are two ways to specify the bounds:
+
+            - Instance of `Bounds` class.
+
+            - 2-tuple of array_like: Each element of the tuple must be either
+              an array with the length equal to the number of parameters, or a
+              scalar (in which case the bound is taken to be the same for all
+              parameters). Use ``np.inf`` with an appropriate sign to disable
+              bounds on all or some parameters.
+
+    method : 'trf' or 'bvls', optional
+        Method to perform minimization.
+
+            * 'trf' : Trust Region Reflective algorithm adapted for a linear
+              least-squares problem. This is an interior-point-like method
+              and the required number of iterations is weakly correlated with
+              the number of variables.
+            * 'bvls' : Bounded-variable least-squares algorithm. This is
+              an active set method, which requires the number of iterations
+              comparable to the number of variables. Can't be used when `A` is
+              sparse or LinearOperator.
+
+        Default is 'trf'.
+    tol : float, optional
+        Tolerance parameter. The algorithm terminates if a relative change
+        of the cost function is less than `tol` on the last iteration.
+        Additionally, the first-order optimality measure is considered:
+
+            * ``method='trf'`` terminates if the uniform norm of the gradient,
+              scaled to account for the presence of the bounds, is less than
+              `tol`.
+            * ``method='bvls'`` terminates if Karush-Kuhn-Tucker conditions
+              are satisfied within `tol` tolerance.
+
+    lsq_solver : {None, 'exact', 'lsmr'}, optional
+        Method of solving unbounded least-squares problems throughout
+        iterations:
+
+            * 'exact' : Use dense QR or SVD decomposition approach. Can't be
+              used when `A` is sparse or LinearOperator.
+            * 'lsmr' : Use `scipy.sparse.linalg.lsmr` iterative procedure
+              which requires only matrix-vector product evaluations. Can't
+              be used with ``method='bvls'``.
+
+        If None (default), the solver is chosen based on type of `A`.
+    lsmr_tol : None, float or 'auto', optional
+        Tolerance parameters 'atol' and 'btol' for `scipy.sparse.linalg.lsmr`
+        If None (default), it is set to ``1e-2 * tol``. If 'auto', the
+        tolerance will be adjusted based on the optimality of the current
+        iterate, which can speed up the optimization process, but is not always
+        reliable.
+    max_iter : None or int, optional
+        Maximum number of iterations before termination. If None (default), it
+        is set to 100 for ``method='trf'`` or to the number of variables for
+        ``method='bvls'`` (not counting iterations for 'bvls' initialization).
+    verbose : {0, 1, 2}, optional
+        Level of algorithm's verbosity:
+
+            * 0 : work silently (default).
+            * 1 : display a termination report.
+            * 2 : display progress during iterations.
+    lsmr_maxiter : None or int, optional
+        Maximum number of iterations for the lsmr least squares solver,
+        if it is used (by setting ``lsq_solver='lsmr'``). If None (default), it
+        uses lsmr's default of ``min(m, n)`` where ``m`` and ``n`` are the
+        number of rows and columns of `A`, respectively. Has no effect if
+        ``lsq_solver='exact'``.
+
+    Returns
+    -------
+    OptimizeResult with the following fields defined:
+    x : ndarray, shape (n,)
+        Solution found.
+    cost : float
+        Value of the cost function at the solution.
+    fun : ndarray, shape (m,)
+        Vector of residuals at the solution.
+    optimality : float
+        First-order optimality measure. The exact meaning depends on `method`,
+        refer to the description of `tol` parameter.
+    active_mask : ndarray of int, shape (n,)
+        Each component shows whether a corresponding constraint is active
+        (that is, whether a variable is at the bound):
+
+            *  0 : a constraint is not active.
+            * -1 : a lower bound is active.
+            *  1 : an upper bound is active.
+
+        Might be somewhat arbitrary for the `trf` method as it generates a
+        sequence of strictly feasible iterates and active_mask is determined
+        within a tolerance threshold.
+    unbounded_sol : tuple
+        Unbounded least squares solution tuple returned by the least squares
+        solver (set with `lsq_solver` option). If `lsq_solver` is not set or is
+        set to ``'exact'``, the tuple contains an ndarray of shape (n,) with
+        the unbounded solution, an ndarray with the sum of squared residuals,
+        an int with the rank of `A`, and an ndarray with the singular values
+        of `A` (see NumPy's ``linalg.lstsq`` for more information). If
+        `lsq_solver` is set to ``'lsmr'``, the tuple contains an ndarray of
+        shape (n,) with the unbounded solution, an int with the exit code,
+        an int with the number of iterations, and five floats with
+        various norms and the condition number of `A` (see SciPy's
+        ``sparse.linalg.lsmr`` for more information). This output can be
+        useful for determining the convergence of the least squares solver,
+        particularly the iterative ``'lsmr'`` solver. The unbounded least
+        squares problem is to minimize ``0.5 * ||A x - b||**2``.
+    nit : int
+        Number of iterations. Zero if the unconstrained solution is optimal.
+    status : int
+        Reason for algorithm termination:
+
+            * -1 : the algorithm was not able to make progress on the last
+              iteration.
+            *  0 : the maximum number of iterations is exceeded.
+            *  1 : the first-order optimality measure is less than `tol`.
+            *  2 : the relative change of the cost function is less than `tol`.
+            *  3 : the unconstrained solution is optimal.
+
+    message : str
+        Verbal description of the termination reason.
+    success : bool
+        True if one of the convergence criteria is satisfied (`status` > 0).
+
+    See Also
+    --------
+    nnls : Linear least squares with non-negativity constraint.
+    least_squares : Nonlinear least squares with bounds on the variables.
+
+    Notes
+    -----
+    The algorithm first computes the unconstrained least-squares solution by
+    `numpy.linalg.lstsq` or `scipy.sparse.linalg.lsmr` depending on
+    `lsq_solver`. This solution is returned as optimal if it lies within the
+    bounds.
+
+    Method 'trf' runs the adaptation of the algorithm described in [STIR]_ for
+    a linear least-squares problem. The iterations are essentially the same as
+    in the nonlinear least-squares algorithm, but as the quadratic function
+    model is always accurate, we don't need to track or modify the radius of
+    a trust region. The line search (backtracking) is used as a safety net
+    when a selected step does not decrease the cost function. Read more
+    detailed description of the algorithm in `scipy.optimize.least_squares`.
+
+    Method 'bvls' runs a Python implementation of the algorithm described in
+    [BVLS]_. The algorithm maintains active and free sets of variables, on
+    each iteration chooses a new variable to move from the active set to the
+    free set and then solves the unconstrained least-squares problem on free
+    variables. This algorithm is guaranteed to give an accurate solution
+    eventually, but may require up to n iterations for a problem with n
+    variables. Additionally, an ad-hoc initialization procedure is
+    implemented, that determines which variables to set free or active
+    initially. It takes some number of iterations before actual BVLS starts,
+    but can significantly reduce the number of further iterations.
+
+    References
+    ----------
+    .. [STIR] M. A. Branch, T. F. Coleman, and Y. Li, "A Subspace, Interior,
+              and Conjugate Gradient Method for Large-Scale Bound-Constrained
+              Minimization Problems," SIAM Journal on Scientific Computing,
+              Vol. 21, Number 1, pp 1-23, 1999.
+    .. [BVLS] P. B. Start and R. L. Parker, "Bounded-Variable Least-Squares:
+              an Algorithm and Applications", Computational Statistics, 10,
+              129-141, 1995.
+
+    Examples
+    --------
+    In this example, a problem with a large sparse matrix and bounds on the
+    variables is solved.
+
+    >>> import numpy as np
+    >>> from scipy.sparse import rand
+    >>> from scipy.optimize import lsq_linear
+    >>> rng = np.random.default_rng()
+    ...
+    >>> m = 20000
+    >>> n = 10000
+    ...
+    >>> A = rand(m, n, density=1e-4, random_state=rng)
+    >>> b = rng.standard_normal(m)
+    ...
+    >>> lb = rng.standard_normal(n)
+    >>> ub = lb + 1
+    ...
+    >>> res = lsq_linear(A, b, bounds=(lb, ub), lsmr_tol='auto', verbose=1)
+    # may vary
+    The relative change of the cost function is less than `tol`.
+    Number of iterations 16, initial cost 1.5039e+04, final cost 1.1112e+04,
+    first-order optimality 4.66e-08.
+    """
+    if method not in ['trf', 'bvls']:
+        raise ValueError("`method` must be 'trf' or 'bvls'")
+
+    if lsq_solver not in [None, 'exact', 'lsmr']:
+        raise ValueError("`solver` must be None, 'exact' or 'lsmr'.")
+
+    if verbose not in [0, 1, 2]:
+        raise ValueError("`verbose` must be in [0, 1, 2].")
+
+    if issparse(A):
+        A = csr_matrix(A)
+    elif not isinstance(A, LinearOperator):
+        A = np.atleast_2d(np.asarray(A))
+
+    if method == 'bvls':
+        if lsq_solver == 'lsmr':
+            raise ValueError("method='bvls' can't be used with "
+                             "lsq_solver='lsmr'")
+
+        if not isinstance(A, np.ndarray):
+            raise ValueError("method='bvls' can't be used with `A` being "
+                             "sparse or LinearOperator.")
+
+    if lsq_solver is None:
+        if isinstance(A, np.ndarray):
+            lsq_solver = 'exact'
+        else:
+            lsq_solver = 'lsmr'
+    elif lsq_solver == 'exact' and not isinstance(A, np.ndarray):
+        raise ValueError("`exact` solver can't be used when `A` is "
+                         "sparse or LinearOperator.")
+
+    if len(A.shape) != 2:  # No ndim for LinearOperator.
+        raise ValueError("`A` must have at most 2 dimensions.")
+
+    if max_iter is not None and max_iter <= 0:
+        raise ValueError("`max_iter` must be None or positive integer.")
+
+    m, n = A.shape
+
+    b = np.atleast_1d(b)
+    if b.ndim != 1:
+        raise ValueError("`b` must have at most 1 dimension.")
+
+    if b.size != m:
+        raise ValueError("Inconsistent shapes between `A` and `b`.")
+
+    if isinstance(bounds, Bounds):
+        lb = bounds.lb
+        ub = bounds.ub
+    else:
+        lb, ub = prepare_bounds(bounds, n)
+
+    if lb.shape != (n,) and ub.shape != (n,):
+        raise ValueError("Bounds have wrong shape.")
+
+    if np.any(lb >= ub):
+        raise ValueError("Each lower bound must be strictly less than each "
+                         "upper bound.")
+
+    if lsmr_maxiter is not None and lsmr_maxiter < 1:
+        raise ValueError("`lsmr_maxiter` must be None or positive integer.")
+
+    if not ((isinstance(lsmr_tol, float) and lsmr_tol > 0) or
+            lsmr_tol in ('auto', None)):
+        raise ValueError("`lsmr_tol` must be None, 'auto', or positive float.")
+
+    if lsq_solver == 'exact':
+        unbd_lsq = np.linalg.lstsq(A, b, rcond=-1)
+    elif lsq_solver == 'lsmr':
+        first_lsmr_tol = lsmr_tol  # tol of first call to lsmr
+        if lsmr_tol is None or lsmr_tol == 'auto':
+            first_lsmr_tol = 1e-2 * tol  # default if lsmr_tol not defined
+        unbd_lsq = lsmr(A, b, maxiter=lsmr_maxiter,
+                        atol=first_lsmr_tol, btol=first_lsmr_tol)
+    x_lsq = unbd_lsq[0]  # extract the solution from the least squares solver
+
+    if in_bounds(x_lsq, lb, ub):
+        r = A @ x_lsq - b
+        cost = 0.5 * np.dot(r, r)
+        termination_status = 3
+        termination_message = TERMINATION_MESSAGES[termination_status]
+        g = compute_grad(A, r)
+        g_norm = norm(g, ord=np.inf)
+
+        if verbose > 0:
+            print(termination_message)
+            print(f"Final cost {cost:.4e}, first-order optimality {g_norm:.2e}")
+
+        return OptimizeResult(
+            x=x_lsq, fun=r, cost=cost, optimality=g_norm,
+            active_mask=np.zeros(n), unbounded_sol=unbd_lsq,
+            nit=0, status=termination_status,
+            message=termination_message, success=True)
+
+    if method == 'trf':
+        res = trf_linear(A, b, x_lsq, lb, ub, tol, lsq_solver, lsmr_tol,
+                         max_iter, verbose, lsmr_maxiter=lsmr_maxiter)
+    elif method == 'bvls':
+        res = bvls(A, b, x_lsq, lb, ub, tol, max_iter, verbose)
+
+    res.unbounded_sol = unbd_lsq
+    res.message = TERMINATION_MESSAGES[res.status]
+    res.success = res.status > 0
+
+    if verbose > 0:
+        print(res.message)
+        print(
+            f"Number of iterations {res.nit}, initial cost {res.initial_cost:.4e}, "
+            f"final cost {res.cost:.4e}, first-order optimality {res.optimality:.2e}."
+        )
+
+    del res.initial_cost
+
+    return res

llava_next/lib/python3.10/site-packages/scipy/optimize/_lsq/trf.py

@@ -0,0 +1,560 @@
+"""Trust Region Reflective algorithm for least-squares optimization.
+
+The algorithm is based on ideas from paper [STIR]_. The main idea is to
+account for the presence of the bounds by appropriate scaling of the variables (or,
+equivalently, changing a trust-region shape). Let's introduce a vector v:
+
+           | ub[i] - x[i], if g[i] < 0 and ub[i] < np.inf
+    v[i] = | x[i] - lb[i], if g[i] > 0 and lb[i] > -np.inf
+           | 1,           otherwise
+
+where g is the gradient of a cost function and lb, ub are the bounds. Its
+components are distances to the bounds at which the anti-gradient points (if
+this distance is finite). Define a scaling matrix D = diag(v**0.5).
+First-order optimality conditions can be stated as
+
+    D^2 g(x) = 0.
+
+Meaning that components of the gradient should be zero for strictly interior
+variables, and components must point inside the feasible region for variables
+on the bound.
+
+Now consider this system of equations as a new optimization problem. If the
+point x is strictly interior (not on the bound), then the left-hand side is
+differentiable and the Newton step for it satisfies
+
+    (D^2 H + diag(g) Jv) p = -D^2 g
+
+where H is the Hessian matrix (or its J^T J approximation in least squares),
+Jv is the Jacobian matrix of v with components -1, 1 or 0, such that all
+elements of matrix C = diag(g) Jv are non-negative. Introduce the change
+of the variables x = D x_h (_h would be "hat" in LaTeX). In the new variables,
+we have a Newton step satisfying
+
+    B_h p_h = -g_h,
+
+where B_h = D H D + C, g_h = D g. In least squares B_h = J_h^T J_h, where
+J_h = J D. Note that J_h and g_h are proper Jacobian and gradient with respect
+to "hat" variables. To guarantee global convergence we formulate a
+trust-region problem based on the Newton step in the new variables:
+
+    0.5 * p_h^T B_h p + g_h^T p_h -> min, ||p_h|| <= Delta
+
+In the original space B = H + D^{-1} C D^{-1}, and the equivalent trust-region
+problem is
+
+    0.5 * p^T B p + g^T p -> min, ||D^{-1} p|| <= Delta
+
+Here, the meaning of the matrix D becomes more clear: it alters the shape
+of a trust-region, such that large steps towards the bounds are not allowed.
+In the implementation, the trust-region problem is solved in "hat" space,
+but handling of the bounds is done in the original space (see below and read
+the code).
+
+The introduction of the matrix D doesn't allow to ignore bounds, the algorithm
+must keep iterates strictly feasible (to satisfy aforementioned
+differentiability), the parameter theta controls step back from the boundary
+(see the code for details).
+
+The algorithm does another important trick. If the trust-region solution
+doesn't fit into the bounds, then a reflected (from a firstly encountered
+bound) search direction is considered. For motivation and analysis refer to
+[STIR]_ paper (and other papers of the authors). In practice, it doesn't need
+a lot of justifications, the algorithm simply chooses the best step among
+three: a constrained trust-region step, a reflected step and a constrained
+Cauchy step (a minimizer along -g_h in "hat" space, or -D^2 g in the original
+space).
+
+Another feature is that a trust-region radius control strategy is modified to
+account for appearance of the diagonal C matrix (called diag_h in the code).
+
+Note that all described peculiarities are completely gone as we consider
+problems without bounds (the algorithm becomes a standard trust-region type
+algorithm very similar to ones implemented in MINPACK).
+
+The implementation supports two methods of solving the trust-region problem.
+The first, called 'exact', applies SVD on Jacobian and then solves the problem
+very accurately using the algorithm described in [JJMore]_. It is not
+applicable to large problem. The second, called 'lsmr', uses the 2-D subspace
+approach (sometimes called "indefinite dogleg"), where the problem is solved
+in a subspace spanned by the gradient and the approximate Gauss-Newton step
+found by ``scipy.sparse.linalg.lsmr``. A 2-D trust-region problem is
+reformulated as a 4th order algebraic equation and solved very accurately by
+``numpy.roots``. The subspace approach allows to solve very large problems
+(up to couple of millions of residuals on a regular PC), provided the Jacobian
+matrix is sufficiently sparse.
+
+References
+----------
+.. [STIR] Branch, M.A., T.F. Coleman, and Y. Li, "A Subspace, Interior,
+      and Conjugate Gradient Method for Large-Scale Bound-Constrained
+      Minimization Problems," SIAM Journal on Scientific Computing,
+      Vol. 21, Number 1, pp 1-23, 1999.
+.. [JJMore] More, J. J., "The Levenberg-Marquardt Algorithm: Implementation
+    and Theory," Numerical Analysis, ed. G. A. Watson, Lecture
+"""
+import numpy as np
+from numpy.linalg import norm
+from scipy.linalg import svd, qr
+from scipy.sparse.linalg import lsmr
+from scipy.optimize import OptimizeResult
+
+from .common import (
+    step_size_to_bound, find_active_constraints, in_bounds,
+    make_strictly_feasible, intersect_trust_region, solve_lsq_trust_region,
+    solve_trust_region_2d, minimize_quadratic_1d, build_quadratic_1d,
+    evaluate_quadratic, right_multiplied_operator, regularized_lsq_operator,
+    CL_scaling_vector, compute_grad, compute_jac_scale, check_termination,
+    update_tr_radius, scale_for_robust_loss_function, print_header_nonlinear,
+    print_iteration_nonlinear)
+
+
+def trf(fun, jac, x0, f0, J0, lb, ub, ftol, xtol, gtol, max_nfev, x_scale,
+        loss_function, tr_solver, tr_options, verbose):
+    # For efficiency, it makes sense to run the simplified version of the
+    # algorithm when no bounds are imposed. We decided to write the two
+    # separate functions. It violates the DRY principle, but the individual
+    # functions are kept the most readable.
+    if np.all(lb == -np.inf) and np.all(ub == np.inf):
+        return trf_no_bounds(
+            fun, jac, x0, f0, J0, ftol, xtol, gtol, max_nfev, x_scale,
+            loss_function, tr_solver, tr_options, verbose)
+    else:
+        return trf_bounds(
+            fun, jac, x0, f0, J0, lb, ub, ftol, xtol, gtol, max_nfev, x_scale,
+            loss_function, tr_solver, tr_options, verbose)
+
+
+def select_step(x, J_h, diag_h, g_h, p, p_h, d, Delta, lb, ub, theta):
+    """Select the best step according to Trust Region Reflective algorithm."""
+    if in_bounds(x + p, lb, ub):
+        p_value = evaluate_quadratic(J_h, g_h, p_h, diag=diag_h)
+        return p, p_h, -p_value
+
+    p_stride, hits = step_size_to_bound(x, p, lb, ub)
+
+    # Compute the reflected direction.
+    r_h = np.copy(p_h)
+    r_h[hits.astype(bool)] *= -1
+    r = d * r_h
+
+    # Restrict trust-region step, such that it hits the bound.
+    p *= p_stride
+    p_h *= p_stride
+    x_on_bound = x + p
+
+    # Reflected direction will cross first either feasible region or trust
+    # region boundary.
+    _, to_tr = intersect_trust_region(p_h, r_h, Delta)
+    to_bound, _ = step_size_to_bound(x_on_bound, r, lb, ub)
+
+    # Find lower and upper bounds on a step size along the reflected
+    # direction, considering the strict feasibility requirement. There is no
+    # single correct way to do that, the chosen approach seems to work best
+    # on test problems.
+    r_stride = min(to_bound, to_tr)
+    if r_stride > 0:
+        r_stride_l = (1 - theta) * p_stride / r_stride
+        if r_stride == to_bound:
+            r_stride_u = theta * to_bound
+        else:
+            r_stride_u = to_tr
+    else:
+        r_stride_l = 0
+        r_stride_u = -1
+
+    # Check if reflection step is available.
+    if r_stride_l <= r_stride_u:
+        a, b, c = build_quadratic_1d(J_h, g_h, r_h, s0=p_h, diag=diag_h)
+        r_stride, r_value = minimize_quadratic_1d(
+            a, b, r_stride_l, r_stride_u, c=c)
+        r_h *= r_stride
+        r_h += p_h
+        r = r_h * d
+    else:
+        r_value = np.inf
+
+    # Now correct p_h to make it strictly interior.
+    p *= theta
+    p_h *= theta
+    p_value = evaluate_quadratic(J_h, g_h, p_h, diag=diag_h)
+
+    ag_h = -g_h
+    ag = d * ag_h
+
+    to_tr = Delta / norm(ag_h)
+    to_bound, _ = step_size_to_bound(x, ag, lb, ub)
+    if to_bound < to_tr:
+        ag_stride = theta * to_bound
+    else:
+        ag_stride = to_tr
+
+    a, b = build_quadratic_1d(J_h, g_h, ag_h, diag=diag_h)
+    ag_stride, ag_value = minimize_quadratic_1d(a, b, 0, ag_stride)
+    ag_h *= ag_stride
+    ag *= ag_stride
+
+    if p_value < r_value and p_value < ag_value:
+        return p, p_h, -p_value
+    elif r_value < p_value and r_value < ag_value:
+        return r, r_h, -r_value
+    else:
+        return ag, ag_h, -ag_value
+
+
+def trf_bounds(fun, jac, x0, f0, J0, lb, ub, ftol, xtol, gtol, max_nfev,
+               x_scale, loss_function, tr_solver, tr_options, verbose):
+    x = x0.copy()
+
+    f = f0
+    f_true = f.copy()
+    nfev = 1
+
+    J = J0
+    njev = 1
+    m, n = J.shape
+
+    if loss_function is not None:
+        rho = loss_function(f)
+        cost = 0.5 * np.sum(rho[0])
+        J, f = scale_for_robust_loss_function(J, f, rho)
+    else:
+        cost = 0.5 * np.dot(f, f)
+
+    g = compute_grad(J, f)
+
+    jac_scale = isinstance(x_scale, str) and x_scale == 'jac'
+    if jac_scale:
+        scale, scale_inv = compute_jac_scale(J)
+    else:
+        scale, scale_inv = x_scale, 1 / x_scale
+
+    v, dv = CL_scaling_vector(x, g, lb, ub)
+    v[dv != 0] *= scale_inv[dv != 0]
+    Delta = norm(x0 * scale_inv / v**0.5)
+    if Delta == 0:
+        Delta = 1.0
+
+    g_norm = norm(g * v, ord=np.inf)
+
+    f_augmented = np.zeros(m + n)
+    if tr_solver == 'exact':
+        J_augmented = np.empty((m + n, n))
+    elif tr_solver == 'lsmr':
+        reg_term = 0.0
+        regularize = tr_options.pop('regularize', True)
+
+    if max_nfev is None:
+        max_nfev = x0.size * 100
+
+    alpha = 0.0  # "Levenberg-Marquardt" parameter
+
+    termination_status = None
+    iteration = 0
+    step_norm = None
+    actual_reduction = None
+
+    if verbose == 2:
+        print_header_nonlinear()
+
+    while True:
+        v, dv = CL_scaling_vector(x, g, lb, ub)
+
+        g_norm = norm(g * v, ord=np.inf)
+        if g_norm < gtol:
+            termination_status = 1
+
+        if verbose == 2:
+            print_iteration_nonlinear(iteration, nfev, cost, actual_reduction,
+                                      step_norm, g_norm)
+
+        if termination_status is not None or nfev == max_nfev:
+            break
+
+        # Now compute variables in "hat" space. Here, we also account for
+        # scaling introduced by `x_scale` parameter. This part is a bit tricky,
+        # you have to write down the formulas and see how the trust-region
+        # problem is formulated when the two types of scaling are applied.
+        # The idea is that first we apply `x_scale` and then apply Coleman-Li
+        # approach in the new variables.
+
+        # v is recomputed in the variables after applying `x_scale`, note that
+        # components which were identically 1 not affected.
+        v[dv != 0] *= scale_inv[dv != 0]
+
+        # Here, we apply two types of scaling.
+        d = v**0.5 * scale
+
+        # C = diag(g * scale) Jv
+        diag_h = g * dv * scale
+
+        # After all this has been done, we continue normally.
+
+        # "hat" gradient.
+        g_h = d * g
+
+        f_augmented[:m] = f
+        if tr_solver == 'exact':
+            J_augmented[:m] = J * d
+            J_h = J_augmented[:m]  # Memory view.
+            J_augmented[m:] = np.diag(diag_h**0.5)
+            U, s, V = svd(J_augmented, full_matrices=False)
+            V = V.T
+            uf = U.T.dot(f_augmented)
+        elif tr_solver == 'lsmr':
+            J_h = right_multiplied_operator(J, d)
+
+            if regularize:
+                a, b = build_quadratic_1d(J_h, g_h, -g_h, diag=diag_h)
+                to_tr = Delta / norm(g_h)
+                ag_value = minimize_quadratic_1d(a, b, 0, to_tr)[1]
+                reg_term = -ag_value / Delta**2
+
+            lsmr_op = regularized_lsq_operator(J_h, (diag_h + reg_term)**0.5)
+            gn_h = lsmr(lsmr_op, f_augmented, **tr_options)[0]
+            S = np.vstack((g_h, gn_h)).T
+            S, _ = qr(S, mode='economic')
+            JS = J_h.dot(S)  # LinearOperator does dot too.
+            B_S = np.dot(JS.T, JS) + np.dot(S.T * diag_h, S)
+            g_S = S.T.dot(g_h)
+
+        # theta controls step back step ratio from the bounds.
+        theta = max(0.995, 1 - g_norm)
+
+        actual_reduction = -1
+        while actual_reduction <= 0 and nfev < max_nfev:
+            if tr_solver == 'exact':
+                p_h, alpha, n_iter = solve_lsq_trust_region(
+                    n, m, uf, s, V, Delta, initial_alpha=alpha)
+            elif tr_solver == 'lsmr':
+                p_S, _ = solve_trust_region_2d(B_S, g_S, Delta)
+                p_h = S.dot(p_S)
+
+            p = d * p_h  # Trust-region solution in the original space.
+            step, step_h, predicted_reduction = select_step(
+                x, J_h, diag_h, g_h, p, p_h, d, Delta, lb, ub, theta)
+
+            x_new = make_strictly_feasible(x + step, lb, ub, rstep=0)
+            f_new = fun(x_new)
+            nfev += 1
+
+            step_h_norm = norm(step_h)
+
+            if not np.all(np.isfinite(f_new)):
+                Delta = 0.25 * step_h_norm
+                continue
+
+            # Usual trust-region step quality estimation.
+            if loss_function is not None:
+                cost_new = loss_function(f_new, cost_only=True)
+            else:
+                cost_new = 0.5 * np.dot(f_new, f_new)
+            actual_reduction = cost - cost_new
+            Delta_new, ratio = update_tr_radius(
+                Delta, actual_reduction, predicted_reduction,
+                step_h_norm, step_h_norm > 0.95 * Delta)
+
+            step_norm = norm(step)
+            termination_status = check_termination(
+                actual_reduction, cost, step_norm, norm(x), ratio, ftol, xtol)
+            if termination_status is not None:
+                break
+
+            alpha *= Delta / Delta_new
+            Delta = Delta_new
+
+        if actual_reduction > 0:
+            x = x_new
+
+            f = f_new
+            f_true = f.copy()
+
+            cost = cost_new
+
+            J = jac(x, f)
+            njev += 1
+
+            if loss_function is not None:
+                rho = loss_function(f)
+                J, f = scale_for_robust_loss_function(J, f, rho)
+
+            g = compute_grad(J, f)
+
+            if jac_scale:
+                scale, scale_inv = compute_jac_scale(J, scale_inv)
+        else:
+            step_norm = 0
+            actual_reduction = 0
+
+        iteration += 1
+
+    if termination_status is None:
+        termination_status = 0
+
+    active_mask = find_active_constraints(x, lb, ub, rtol=xtol)
+    return OptimizeResult(
+        x=x, cost=cost, fun=f_true, jac=J, grad=g, optimality=g_norm,
+        active_mask=active_mask, nfev=nfev, njev=njev,
+        status=termination_status)
+
+
+def trf_no_bounds(fun, jac, x0, f0, J0, ftol, xtol, gtol, max_nfev,
+                  x_scale, loss_function, tr_solver, tr_options, verbose):
+    x = x0.copy()
+
+    f = f0
+    f_true = f.copy()
+    nfev = 1
+
+    J = J0
+    njev = 1
+    m, n = J.shape
+
+    if loss_function is not None:
+        rho = loss_function(f)
+        cost = 0.5 * np.sum(rho[0])
+        J, f = scale_for_robust_loss_function(J, f, rho)
+    else:
+        cost = 0.5 * np.dot(f, f)
+
+    g = compute_grad(J, f)
+
+    jac_scale = isinstance(x_scale, str) and x_scale == 'jac'
+    if jac_scale:
+        scale, scale_inv = compute_jac_scale(J)
+    else:
+        scale, scale_inv = x_scale, 1 / x_scale
+
+    Delta = norm(x0 * scale_inv)
+    if Delta == 0:
+        Delta = 1.0
+
+    if tr_solver == 'lsmr':
+        reg_term = 0
+        damp = tr_options.pop('damp', 0.0)
+        regularize = tr_options.pop('regularize', True)
+
+    if max_nfev is None:
+        max_nfev = x0.size * 100
+
+    alpha = 0.0  # "Levenberg-Marquardt" parameter
+
+    termination_status = None
+    iteration = 0
+    step_norm = None
+    actual_reduction = None
+
+    if verbose == 2:
+        print_header_nonlinear()
+
+    while True:
+        g_norm = norm(g, ord=np.inf)
+        if g_norm < gtol:
+            termination_status = 1
+
+        if verbose == 2:
+            print_iteration_nonlinear(iteration, nfev, cost, actual_reduction,
+                                      step_norm, g_norm)
+
+        if termination_status is not None or nfev == max_nfev:
+            break
+
+        d = scale
+        g_h = d * g
+
+        if tr_solver == 'exact':
+            J_h = J * d
+            U, s, V = svd(J_h, full_matrices=False)
+            V = V.T
+            uf = U.T.dot(f)
+        elif tr_solver == 'lsmr':
+            J_h = right_multiplied_operator(J, d)
+
+            if regularize:
+                a, b = build_quadratic_1d(J_h, g_h, -g_h)
+                to_tr = Delta / norm(g_h)
+                ag_value = minimize_quadratic_1d(a, b, 0, to_tr)[1]
+                reg_term = -ag_value / Delta**2
+
+            damp_full = (damp**2 + reg_term)**0.5
+            gn_h = lsmr(J_h, f, damp=damp_full, **tr_options)[0]
+            S = np.vstack((g_h, gn_h)).T
+            S, _ = qr(S, mode='economic')
+            JS = J_h.dot(S)
+            B_S = np.dot(JS.T, JS)
+            g_S = S.T.dot(g_h)
+
+        actual_reduction = -1
+        while actual_reduction <= 0 and nfev < max_nfev:
+            if tr_solver == 'exact':
+                step_h, alpha, n_iter = solve_lsq_trust_region(
+                    n, m, uf, s, V, Delta, initial_alpha=alpha)
+            elif tr_solver == 'lsmr':
+                p_S, _ = solve_trust_region_2d(B_S, g_S, Delta)
+                step_h = S.dot(p_S)
+
+            predicted_reduction = -evaluate_quadratic(J_h, g_h, step_h)
+            step = d * step_h
+            x_new = x + step
+            f_new = fun(x_new)
+            nfev += 1
+
+            step_h_norm = norm(step_h)
+
+            if not np.all(np.isfinite(f_new)):
+                Delta = 0.25 * step_h_norm
+                continue
+
+            # Usual trust-region step quality estimation.
+            if loss_function is not None:
+                cost_new = loss_function(f_new, cost_only=True)
+            else:
+                cost_new = 0.5 * np.dot(f_new, f_new)
+            actual_reduction = cost - cost_new
+
+            Delta_new, ratio = update_tr_radius(
+                Delta, actual_reduction, predicted_reduction,
+                step_h_norm, step_h_norm > 0.95 * Delta)
+
+            step_norm = norm(step)
+            termination_status = check_termination(
+                actual_reduction, cost, step_norm, norm(x), ratio, ftol, xtol)
+            if termination_status is not None:
+                break
+
+            alpha *= Delta / Delta_new
+            Delta = Delta_new
+
+        if actual_reduction > 0:
+            x = x_new
+
+            f = f_new
+            f_true = f.copy()
+
+            cost = cost_new
+
+            J = jac(x, f)
+            njev += 1
+
+            if loss_function is not None:
+                rho = loss_function(f)
+                J, f = scale_for_robust_loss_function(J, f, rho)
+
+            g = compute_grad(J, f)
+
+            if jac_scale:
+                scale, scale_inv = compute_jac_scale(J, scale_inv)
+        else:
+            step_norm = 0
+            actual_reduction = 0
+
+        iteration += 1
+
+    if termination_status is None:
+        termination_status = 0
+
+    active_mask = np.zeros_like(x)
+    return OptimizeResult(
+        x=x, cost=cost, fun=f_true, jac=J, grad=g, optimality=g_norm,
+        active_mask=active_mask, nfev=nfev, njev=njev,
+        status=termination_status)

llava_next/lib/python3.10/site-packages/scipy/optimize/_lsq/trf_linear.py

@@ -0,0 +1,249 @@
+"""The adaptation of Trust Region Reflective algorithm for a linear
+least-squares problem."""
+import numpy as np
+from numpy.linalg import norm
+from scipy.linalg import qr, solve_triangular
+from scipy.sparse.linalg import lsmr
+from scipy.optimize import OptimizeResult
+
+from .givens_elimination import givens_elimination
+from .common import (
+    EPS, step_size_to_bound, find_active_constraints, in_bounds,
+    make_strictly_feasible, build_quadratic_1d, evaluate_quadratic,
+    minimize_quadratic_1d, CL_scaling_vector, reflective_transformation,
+    print_header_linear, print_iteration_linear, compute_grad,
+    regularized_lsq_operator, right_multiplied_operator)
+
+
+def regularized_lsq_with_qr(m, n, R, QTb, perm, diag, copy_R=True):
+    """Solve regularized least squares using information from QR-decomposition.
+
+    The initial problem is to solve the following system in a least-squares
+    sense::
+
+        A x = b
+        D x = 0
+
+    where D is diagonal matrix. The method is based on QR decomposition
+    of the form A P = Q R, where P is a column permutation matrix, Q is an
+    orthogonal matrix and R is an upper triangular matrix.
+
+    Parameters
+    ----------
+    m, n : int
+        Initial shape of A.
+    R : ndarray, shape (n, n)
+        Upper triangular matrix from QR decomposition of A.
+    QTb : ndarray, shape (n,)
+        First n components of Q^T b.
+    perm : ndarray, shape (n,)
+        Array defining column permutation of A, such that ith column of
+        P is perm[i]-th column of identity matrix.
+    diag : ndarray, shape (n,)
+        Array containing diagonal elements of D.
+
+    Returns
+    -------
+    x : ndarray, shape (n,)
+        Found least-squares solution.
+    """
+    if copy_R:
+        R = R.copy()
+    v = QTb.copy()
+
+    givens_elimination(R, v, diag[perm])
+
+    abs_diag_R = np.abs(np.diag(R))
+    threshold = EPS * max(m, n) * np.max(abs_diag_R)
+    nns, = np.nonzero(abs_diag_R > threshold)
+
+    R = R[np.ix_(nns, nns)]
+    v = v[nns]
+
+    x = np.zeros(n)
+    x[perm[nns]] = solve_triangular(R, v)
+
+    return x
+
+
+def backtracking(A, g, x, p, theta, p_dot_g, lb, ub):
+    """Find an appropriate step size using backtracking line search."""
+    alpha = 1
+    while True:
+        x_new, _ = reflective_transformation(x + alpha * p, lb, ub)
+        step = x_new - x
+        cost_change = -evaluate_quadratic(A, g, step)
+        if cost_change > -0.1 * alpha * p_dot_g:
+            break
+        alpha *= 0.5
+
+    active = find_active_constraints(x_new, lb, ub)
+    if np.any(active != 0):
+        x_new, _ = reflective_transformation(x + theta * alpha * p, lb, ub)
+        x_new = make_strictly_feasible(x_new, lb, ub, rstep=0)
+        step = x_new - x
+        cost_change = -evaluate_quadratic(A, g, step)
+
+    return x, step, cost_change
+
+
+def select_step(x, A_h, g_h, c_h, p, p_h, d, lb, ub, theta):
+    """Select the best step according to Trust Region Reflective algorithm."""
+    if in_bounds(x + p, lb, ub):
+        return p
+
+    p_stride, hits = step_size_to_bound(x, p, lb, ub)
+    r_h = np.copy(p_h)
+    r_h[hits.astype(bool)] *= -1
+    r = d * r_h
+
+    # Restrict step, such that it hits the bound.
+    p *= p_stride
+    p_h *= p_stride
+    x_on_bound = x + p
+
+    # Find the step size along reflected direction.
+    r_stride_u, _ = step_size_to_bound(x_on_bound, r, lb, ub)
+
+    # Stay interior.
+    r_stride_l = (1 - theta) * r_stride_u
+    r_stride_u *= theta
+
+    if r_stride_u > 0:
+        a, b, c = build_quadratic_1d(A_h, g_h, r_h, s0=p_h, diag=c_h)
+        r_stride, r_value = minimize_quadratic_1d(
+            a, b, r_stride_l, r_stride_u, c=c)
+        r_h = p_h + r_h * r_stride
+        r = d * r_h
+    else:
+        r_value = np.inf
+
+    # Now correct p_h to make it strictly interior.
+    p_h *= theta
+    p *= theta
+    p_value = evaluate_quadratic(A_h, g_h, p_h, diag=c_h)
+
+    ag_h = -g_h
+    ag = d * ag_h
+    ag_stride_u, _ = step_size_to_bound(x, ag, lb, ub)
+    ag_stride_u *= theta
+    a, b = build_quadratic_1d(A_h, g_h, ag_h, diag=c_h)
+    ag_stride, ag_value = minimize_quadratic_1d(a, b, 0, ag_stride_u)
+    ag *= ag_stride
+
+    if p_value < r_value and p_value < ag_value:
+        return p
+    elif r_value < p_value and r_value < ag_value:
+        return r
+    else:
+        return ag
+
+
+def trf_linear(A, b, x_lsq, lb, ub, tol, lsq_solver, lsmr_tol,
+               max_iter, verbose, *, lsmr_maxiter=None):
+    m, n = A.shape
+    x, _ = reflective_transformation(x_lsq, lb, ub)
+    x = make_strictly_feasible(x, lb, ub, rstep=0.1)
+
+    if lsq_solver == 'exact':
+        QT, R, perm = qr(A, mode='economic', pivoting=True)
+        QT = QT.T
+
+        if m < n:
+            R = np.vstack((R, np.zeros((n - m, n))))
+
+        QTr = np.zeros(n)
+        k = min(m, n)
+    elif lsq_solver == 'lsmr':
+        r_aug = np.zeros(m + n)
+        auto_lsmr_tol = False
+        if lsmr_tol is None:
+            lsmr_tol = 1e-2 * tol
+        elif lsmr_tol == 'auto':
+            auto_lsmr_tol = True
+
+    r = A.dot(x) - b
+    g = compute_grad(A, r)
+    cost = 0.5 * np.dot(r, r)
+    initial_cost = cost
+
+    termination_status = None
+    step_norm = None
+    cost_change = None
+
+    if max_iter is None:
+        max_iter = 100
+
+    if verbose == 2:
+        print_header_linear()
+
+    for iteration in range(max_iter):
+        v, dv = CL_scaling_vector(x, g, lb, ub)
+        g_scaled = g * v
+        g_norm = norm(g_scaled, ord=np.inf)
+        if g_norm < tol:
+            termination_status = 1
+
+        if verbose == 2:
+            print_iteration_linear(iteration, cost, cost_change,
+                                   step_norm, g_norm)
+
+        if termination_status is not None:
+            break
+
+        diag_h = g * dv
+        diag_root_h = diag_h ** 0.5
+        d = v ** 0.5
+        g_h = d * g
+
+        A_h = right_multiplied_operator(A, d)
+        if lsq_solver == 'exact':
+            QTr[:k] = QT.dot(r)
+            p_h = -regularized_lsq_with_qr(m, n, R * d[perm], QTr, perm,
+                                           diag_root_h, copy_R=False)
+        elif lsq_solver == 'lsmr':
+            lsmr_op = regularized_lsq_operator(A_h, diag_root_h)
+            r_aug[:m] = r
+            if auto_lsmr_tol:
+                eta = 1e-2 * min(0.5, g_norm)
+                lsmr_tol = max(EPS, min(0.1, eta * g_norm))
+            p_h = -lsmr(lsmr_op, r_aug, maxiter=lsmr_maxiter,
+                        atol=lsmr_tol, btol=lsmr_tol)[0]
+
+        p = d * p_h
+
+        p_dot_g = np.dot(p, g)
+        if p_dot_g > 0:
+            termination_status = -1
+
+        theta = 1 - min(0.005, g_norm)
+        step = select_step(x, A_h, g_h, diag_h, p, p_h, d, lb, ub, theta)
+        cost_change = -evaluate_quadratic(A, g, step)
+
+        # Perhaps almost never executed, the idea is that `p` is descent
+        # direction thus we must find acceptable cost decrease using simple
+        # "backtracking", otherwise the algorithm's logic would break.
+        if cost_change < 0:
+            x, step, cost_change = backtracking(
+                A, g, x, p, theta, p_dot_g, lb, ub)
+        else:
+            x = make_strictly_feasible(x + step, lb, ub, rstep=0)
+
+        step_norm = norm(step)
+        r = A.dot(x) - b
+        g = compute_grad(A, r)
+
+        if cost_change < tol * cost:
+            termination_status = 2
+
+        cost = 0.5 * np.dot(r, r)
+
+    if termination_status is None:
+        termination_status = 0
+
+    active_mask = find_active_constraints(x, lb, ub, rtol=tol)
+
+    return OptimizeResult(
+        x=x, fun=r, cost=cost, optimality=g_norm, active_mask=active_mask,
+        nit=iteration + 1, status=termination_status,
+        initial_cost=initial_cost)

llava_next/lib/python3.10/site-packages/scipy/optimize/_pava_pybind.cpython-310-x86_64-linux-gnu.so

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:eea00160871368c5807d7825188089b3fdb35c1373133b5b4c504be8a5dc9d2c
+size 223832

llava_next/lib/python3.10/site-packages/scipy/optimize/_shgo_lib/_vertex.py

@@ -0,0 +1,460 @@
+import collections
+from abc import ABC, abstractmethod
+
+import numpy as np
+
+from scipy._lib._util import MapWrapper
+
+
+class VertexBase(ABC):
+    """
+    Base class for a vertex.
+    """
+    def __init__(self, x, nn=None, index=None):
+        """
+        Initiation of a vertex object.
+
+        Parameters
+        ----------
+        x : tuple or vector
+            The geometric location (domain).
+        nn : list, optional
+            Nearest neighbour list.
+        index : int, optional
+            Index of vertex.
+        """
+        self.x = x
+        self.hash = hash(self.x)  # Save precomputed hash
+
+        if nn is not None:
+            self.nn = set(nn)  # can use .indexupdate to add a new list
+        else:
+            self.nn = set()
+
+        self.index = index
+
+    def __hash__(self):
+        return self.hash
+
+    def __getattr__(self, item):
+        if item not in ['x_a']:
+            raise AttributeError(f"{type(self)} object has no attribute "
+                                 f"'{item}'")
+        if item == 'x_a':
+            self.x_a = np.array(self.x)
+            return self.x_a
+
+    @abstractmethod
+    def connect(self, v):
+        raise NotImplementedError("This method is only implemented with an "
+                                  "associated child of the base class.")
+
+    @abstractmethod
+    def disconnect(self, v):
+        raise NotImplementedError("This method is only implemented with an "
+                                  "associated child of the base class.")
+
+    def star(self):
+        """Returns the star domain ``st(v)`` of the vertex.
+
+        Parameters
+        ----------
+        v :
+            The vertex ``v`` in ``st(v)``
+
+        Returns
+        -------
+        st : set
+            A set containing all the vertices in ``st(v)``
+        """
+        self.st = self.nn
+        self.st.add(self)
+        return self.st
+
+
+class VertexScalarField(VertexBase):
+    """
+    Add homology properties of a scalar field f: R^n --> R associated with
+    the geometry built from the VertexBase class
+    """
+
+    def __init__(self, x, field=None, nn=None, index=None, field_args=(),
+                 g_cons=None, g_cons_args=()):
+        """
+        Parameters
+        ----------
+        x : tuple,
+            vector of vertex coordinates
+        field : callable, optional
+            a scalar field f: R^n --> R associated with the geometry
+        nn : list, optional
+            list of nearest neighbours
+        index : int, optional
+            index of the vertex
+        field_args : tuple, optional
+            additional arguments to be passed to field
+        g_cons : callable, optional
+            constraints on the vertex
+        g_cons_args : tuple, optional
+            additional arguments to be passed to g_cons
+
+        """
+        super().__init__(x, nn=nn, index=index)
+
+        # Note Vertex is only initiated once for all x so only
+        # evaluated once
+        # self.feasible = None
+
+        # self.f is externally defined by the cache to allow parallel
+        # processing
+        # None type that will break arithmetic operations unless defined
+        # self.f = None
+
+        self.check_min = True
+        self.check_max = True
+
+    def connect(self, v):
+        """Connects self to another vertex object v.
+
+        Parameters
+        ----------
+        v : VertexBase or VertexScalarField object
+        """
+        if v is not self and v not in self.nn:
+            self.nn.add(v)
+            v.nn.add(self)
+
+            # Flags for checking homology properties:
+            self.check_min = True
+            self.check_max = True
+            v.check_min = True
+            v.check_max = True
+
+    def disconnect(self, v):
+        if v in self.nn:
+            self.nn.remove(v)
+            v.nn.remove(self)
+
+            # Flags for checking homology properties:
+            self.check_min = True
+            self.check_max = True
+            v.check_min = True
+            v.check_max = True
+
+    def minimiser(self):
+        """Check whether this vertex is strictly less than all its
+           neighbours"""
+        if self.check_min:
+            self._min = all(self.f < v.f for v in self.nn)
+            self.check_min = False
+
+        return self._min
+
+    def maximiser(self):
+        """
+        Check whether this vertex is strictly greater than all its
+        neighbours.
+        """
+        if self.check_max:
+            self._max = all(self.f > v.f for v in self.nn)
+            self.check_max = False
+
+        return self._max
+
+
+class VertexVectorField(VertexBase):
+    """
+    Add homology properties of a scalar field f: R^n --> R^m associated with
+    the geometry built from the VertexBase class.
+    """
+
+    def __init__(self, x, sfield=None, vfield=None, field_args=(),
+                 vfield_args=(), g_cons=None,
+                 g_cons_args=(), nn=None, index=None):
+        super().__init__(x, nn=nn, index=index)
+
+        raise NotImplementedError("This class is still a work in progress")
+
+
+class VertexCacheBase:
+    """Base class for a vertex cache for a simplicial complex."""
+    def __init__(self):
+
+        self.cache = collections.OrderedDict()
+        self.nfev = 0  # Feasible points
+        self.index = -1
+
+    def __iter__(self):
+        for v in self.cache:
+            yield self.cache[v]
+        return
+
+    def size(self):
+        """Returns the size of the vertex cache."""
+        return self.index + 1
+
+    def print_out(self):
+        headlen = len(f"Vertex cache of size: {len(self.cache)}:")
+        print('=' * headlen)
+        print(f"Vertex cache of size: {len(self.cache)}:")
+        print('=' * headlen)
+        for v in self.cache:
+            self.cache[v].print_out()
+
+
+class VertexCube(VertexBase):
+    """Vertex class to be used for a pure simplicial complex with no associated
+    differential geometry (single level domain that exists in R^n)"""
+    def __init__(self, x, nn=None, index=None):
+        super().__init__(x, nn=nn, index=index)
+
+    def connect(self, v):
+        if v is not self and v not in self.nn:
+            self.nn.add(v)
+            v.nn.add(self)
+
+    def disconnect(self, v):
+        if v in self.nn:
+            self.nn.remove(v)
+            v.nn.remove(self)
+
+
+class VertexCacheIndex(VertexCacheBase):
+    def __init__(self):
+        """
+        Class for a vertex cache for a simplicial complex without an associated
+        field. Useful only for building and visualising a domain complex.
+
+        Parameters
+        ----------
+        """
+        super().__init__()
+        self.Vertex = VertexCube
+
+    def __getitem__(self, x, nn=None):
+        try:
+            return self.cache[x]
+        except KeyError:
+            self.index += 1
+            xval = self.Vertex(x, index=self.index)
+            # logging.info("New generated vertex at x = {}".format(x))
+            # NOTE: Surprisingly high performance increase if logging
+            # is commented out
+            self.cache[x] = xval
+            return self.cache[x]
+
+
+class VertexCacheField(VertexCacheBase):
+    def __init__(self, field=None, field_args=(), g_cons=None, g_cons_args=(),
+                 workers=1):
+        """
+        Class for a vertex cache for a simplicial complex with an associated
+        field.
+
+        Parameters
+        ----------
+        field : callable
+            Scalar or vector field callable.
+        field_args : tuple, optional
+            Any additional fixed parameters needed to completely specify the
+            field function
+        g_cons : dict or sequence of dict, optional
+            Constraints definition.
+            Function(s) ``R**n`` in the form::
+        g_cons_args : tuple, optional
+            Any additional fixed parameters needed to completely specify the
+            constraint functions
+        workers : int  optional
+            Uses `multiprocessing.Pool <multiprocessing>`) to compute the field
+             functions in parallel.
+
+        """
+        super().__init__()
+        self.index = -1
+        self.Vertex = VertexScalarField
+        self.field = field
+        self.field_args = field_args
+        self.wfield = FieldWrapper(field, field_args)  # if workers is not 1
+
+        self.g_cons = g_cons
+        self.g_cons_args = g_cons_args
+        self.wgcons = ConstraintWrapper(g_cons, g_cons_args)
+        self.gpool = set()  # A set of tuples to process for feasibility
+
+        # Field processing objects
+        self.fpool = set()  # A set of tuples to process for scalar function
+        self.sfc_lock = False  # True if self.fpool is non-Empty
+
+        self.workers = workers
+        self._mapwrapper = MapWrapper(workers)
+
+        if workers == 1:
+            self.process_gpool = self.proc_gpool
+            if g_cons is None:
+                self.process_fpool = self.proc_fpool_nog
+            else:
+                self.process_fpool = self.proc_fpool_g
+        else:
+            self.process_gpool = self.pproc_gpool
+            if g_cons is None:
+                self.process_fpool = self.pproc_fpool_nog
+            else:
+                self.process_fpool = self.pproc_fpool_g
+
+    def __getitem__(self, x, nn=None):
+        try:
+            return self.cache[x]
+        except KeyError:
+            self.index += 1
+            xval = self.Vertex(x, field=self.field, nn=nn, index=self.index,
+                               field_args=self.field_args,
+                               g_cons=self.g_cons,
+                               g_cons_args=self.g_cons_args)
+
+            self.cache[x] = xval  # Define in cache
+            self.gpool.add(xval)  # Add to pool for processing feasibility
+            self.fpool.add(xval)  # Add to pool for processing field values
+            return self.cache[x]
+
+    def __getstate__(self):
+        self_dict = self.__dict__.copy()
+        del self_dict['pool']
+        return self_dict
+
+    def process_pools(self):
+        if self.g_cons is not None:
+            self.process_gpool()
+        self.process_fpool()
+        self.proc_minimisers()
+
+    def feasibility_check(self, v):
+        v.feasible = True
+        for g, args in zip(self.g_cons, self.g_cons_args):
+            # constraint may return more than 1 value.
+            if np.any(g(v.x_a, *args) < 0.0):
+                v.f = np.inf
+                v.feasible = False
+                break
+
+    def compute_sfield(self, v):
+        """Compute the scalar field values of a vertex object `v`.
+
+        Parameters
+        ----------
+        v : VertexBase or VertexScalarField object
+        """
+        try:
+            v.f = self.field(v.x_a, *self.field_args)
+            self.nfev += 1
+        except AttributeError:
+            v.f = np.inf
+            # logging.warning(f"Field function not found at x = {self.x_a}")
+        if np.isnan(v.f):
+            v.f = np.inf
+
+    def proc_gpool(self):
+        """Process all constraints."""
+        if self.g_cons is not None:
+            for v in self.gpool:
+                self.feasibility_check(v)
+        # Clean the pool
+        self.gpool = set()
+
+    def pproc_gpool(self):
+        """Process all constraints in parallel."""
+        gpool_l = []
+        for v in self.gpool:
+            gpool_l.append(v.x_a)
+
+        G = self._mapwrapper(self.wgcons.gcons, gpool_l)
+        for v, g in zip(self.gpool, G):
+            v.feasible = g  # set vertex object attribute v.feasible = g (bool)
+
+    def proc_fpool_g(self):
+        """Process all field functions with constraints supplied."""
+        for v in self.fpool:
+            if v.feasible:
+                self.compute_sfield(v)
+        # Clean the pool
+        self.fpool = set()
+
+    def proc_fpool_nog(self):
+        """Process all field functions with no constraints supplied."""
+        for v in self.fpool:
+            self.compute_sfield(v)
+        # Clean the pool
+        self.fpool = set()
+
+    def pproc_fpool_g(self):
+        """
+        Process all field functions with constraints supplied in parallel.
+        """
+        self.wfield.func
+        fpool_l = []
+        for v in self.fpool:
+            if v.feasible:
+                fpool_l.append(v.x_a)
+            else:
+                v.f = np.inf
+        F = self._mapwrapper(self.wfield.func, fpool_l)
+        for va, f in zip(fpool_l, F):
+            vt = tuple(va)
+            self[vt].f = f  # set vertex object attribute v.f = f
+            self.nfev += 1
+        # Clean the pool
+        self.fpool = set()
+
+    def pproc_fpool_nog(self):
+        """
+        Process all field functions with no constraints supplied in parallel.
+        """
+        self.wfield.func
+        fpool_l = []
+        for v in self.fpool:
+            fpool_l.append(v.x_a)
+        F = self._mapwrapper(self.wfield.func, fpool_l)
+        for va, f in zip(fpool_l, F):
+            vt = tuple(va)
+            self[vt].f = f  # set vertex object attribute v.f = f
+            self.nfev += 1
+        # Clean the pool
+        self.fpool = set()
+
+    def proc_minimisers(self):
+        """Check for minimisers."""
+        for v in self:
+            v.minimiser()
+            v.maximiser()
+
+
+class ConstraintWrapper:
+    """Object to wrap constraints to pass to `multiprocessing.Pool`."""
+    def __init__(self, g_cons, g_cons_args):
+        self.g_cons = g_cons
+        self.g_cons_args = g_cons_args
+
+    def gcons(self, v_x_a):
+        vfeasible = True
+        for g, args in zip(self.g_cons, self.g_cons_args):
+            # constraint may return more than 1 value.
+            if np.any(g(v_x_a, *args) < 0.0):
+                vfeasible = False
+                break
+        return vfeasible
+
+
+class FieldWrapper:
+    """Object to wrap field to pass to `multiprocessing.Pool`."""
+    def __init__(self, field, field_args):
+        self.field = field
+        self.field_args = field_args
+
+    def func(self, v_x_a):
+        try:
+            v_f = self.field(v_x_a, *self.field_args)
+        except Exception:
+            v_f = np.inf
+        if np.isnan(v_f):
+            v_f = np.inf
+
+        return v_f

llava_next/lib/python3.10/site-packages/scipy/optimize/_tnc.py

@@ -0,0 +1,430 @@
+# TNC Python interface
+# @(#) $Jeannot: tnc.py,v 1.11 2005/01/28 18:27:31 js Exp $
+
+# Copyright (c) 2004-2005, Jean-Sebastien Roy (js@jeannot.org)
+
+# Permission is hereby granted, free of charge, to any person obtaining a
+# copy of this software and associated documentation files (the
+# "Software"), to deal in the Software without restriction, including
+# without limitation the rights to use, copy, modify, merge, publish,
+# distribute, sublicense, and/or sell copies of the Software, and to
+# permit persons to whom the Software is furnished to do so, subject to
+# the following conditions:
+
+# The above copyright notice and this permission notice shall be included
+# in all copies or substantial portions of the Software.
+
+# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+# MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
+# IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
+# CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
+# TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
+# SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+
+"""
+TNC: A Python interface to the TNC non-linear optimizer
+
+TNC is a non-linear optimizer. To use it, you must provide a function to
+minimize. The function must take one argument: the list of coordinates where to
+evaluate the function; and it must return either a tuple, whose first element is the
+value of the function, and whose second argument is the gradient of the function
+(as a list of values); or None, to abort the minimization.
+"""
+
+from scipy.optimize import _moduleTNC as moduleTNC
+from ._optimize import (MemoizeJac, OptimizeResult, _check_unknown_options,
+                       _prepare_scalar_function)
+from ._constraints import old_bound_to_new
+from scipy._lib._array_api import atleast_nd, array_namespace
+
+from numpy import inf, array, zeros
+
+__all__ = ['fmin_tnc']
+
+
+MSG_NONE = 0  # No messages
+MSG_ITER = 1  # One line per iteration
+MSG_INFO = 2  # Informational messages
+MSG_VERS = 4  # Version info
+MSG_EXIT = 8  # Exit reasons
+MSG_ALL = MSG_ITER + MSG_INFO + MSG_VERS + MSG_EXIT
+
+MSGS = {
+        MSG_NONE: "No messages",
+        MSG_ITER: "One line per iteration",
+        MSG_INFO: "Informational messages",
+        MSG_VERS: "Version info",
+        MSG_EXIT: "Exit reasons",
+        MSG_ALL: "All messages"
+}
+
+INFEASIBLE = -1  # Infeasible (lower bound > upper bound)
+LOCALMINIMUM = 0  # Local minimum reached (|pg| ~= 0)
+FCONVERGED = 1  # Converged (|f_n-f_(n-1)| ~= 0)
+XCONVERGED = 2  # Converged (|x_n-x_(n-1)| ~= 0)
+MAXFUN = 3  # Max. number of function evaluations reached
+LSFAIL = 4  # Linear search failed
+CONSTANT = 5  # All lower bounds are equal to the upper bounds
+NOPROGRESS = 6  # Unable to progress
+USERABORT = 7  # User requested end of minimization
+
+RCSTRINGS = {
+        INFEASIBLE: "Infeasible (lower bound > upper bound)",
+        LOCALMINIMUM: "Local minimum reached (|pg| ~= 0)",
+        FCONVERGED: "Converged (|f_n-f_(n-1)| ~= 0)",
+        XCONVERGED: "Converged (|x_n-x_(n-1)| ~= 0)",
+        MAXFUN: "Max. number of function evaluations reached",
+        LSFAIL: "Linear search failed",
+        CONSTANT: "All lower bounds are equal to the upper bounds",
+        NOPROGRESS: "Unable to progress",
+        USERABORT: "User requested end of minimization"
+}
+
+# Changes to interface made by Travis Oliphant, Apr. 2004 for inclusion in
+#  SciPy
+
+
+def fmin_tnc(func, x0, fprime=None, args=(), approx_grad=0,
+             bounds=None, epsilon=1e-8, scale=None, offset=None,
+             messages=MSG_ALL, maxCGit=-1, maxfun=None, eta=-1,
+             stepmx=0, accuracy=0, fmin=0, ftol=-1, xtol=-1, pgtol=-1,
+             rescale=-1, disp=None, callback=None):
+    """
+    Minimize a function with variables subject to bounds, using
+    gradient information in a truncated Newton algorithm. This
+    method wraps a C implementation of the algorithm.
+
+    Parameters
+    ----------
+    func : callable ``func(x, *args)``
+        Function to minimize.  Must do one of:
+
+        1. Return f and g, where f is the value of the function and g its
+           gradient (a list of floats).
+
+        2. Return the function value but supply gradient function
+           separately as `fprime`.
+
+        3. Return the function value and set ``approx_grad=True``.
+
+        If the function returns None, the minimization
+        is aborted.
+    x0 : array_like
+        Initial estimate of minimum.
+    fprime : callable ``fprime(x, *args)``, optional
+        Gradient of `func`. If None, then either `func` must return the
+        function value and the gradient (``f,g = func(x, *args)``)
+        or `approx_grad` must be True.
+    args : tuple, optional
+        Arguments to pass to function.
+    approx_grad : bool, optional
+        If true, approximate the gradient numerically.
+    bounds : list, optional
+        (min, max) pairs for each element in x0, defining the
+        bounds on that parameter. Use None or +/-inf for one of
+        min or max when there is no bound in that direction.
+    epsilon : float, optional
+        Used if approx_grad is True. The stepsize in a finite
+        difference approximation for fprime.
+    scale : array_like, optional
+        Scaling factors to apply to each variable. If None, the
+        factors are up-low for interval bounded variables and
+        1+|x| for the others. Defaults to None.
+    offset : array_like, optional
+        Value to subtract from each variable. If None, the
+        offsets are (up+low)/2 for interval bounded variables
+        and x for the others.
+    messages : int, optional
+        Bit mask used to select messages display during
+        minimization values defined in the MSGS dict. Defaults to
+        MGS_ALL.
+    disp : int, optional
+        Integer interface to messages. 0 = no message, 5 = all messages
+    maxCGit : int, optional
+        Maximum number of hessian*vector evaluations per main
+        iteration. If maxCGit == 0, the direction chosen is
+        -gradient if maxCGit < 0, maxCGit is set to
+        max(1,min(50,n/2)). Defaults to -1.
+    maxfun : int, optional
+        Maximum number of function evaluation. If None, maxfun is
+        set to max(100, 10*len(x0)). Defaults to None. Note that this function
+        may violate the limit because of evaluating gradients by numerical
+        differentiation.
+    eta : float, optional
+        Severity of the line search. If < 0 or > 1, set to 0.25.
+        Defaults to -1.
+    stepmx : float, optional
+        Maximum step for the line search. May be increased during
+        call. If too small, it will be set to 10.0. Defaults to 0.
+    accuracy : float, optional
+        Relative precision for finite difference calculations. If
+        <= machine_precision, set to sqrt(machine_precision).
+        Defaults to 0.
+    fmin : float, optional
+        Minimum function value estimate. Defaults to 0.
+    ftol : float, optional
+        Precision goal for the value of f in the stopping criterion.
+        If ftol < 0.0, ftol is set to 0.0 defaults to -1.
+    xtol : float, optional
+        Precision goal for the value of x in the stopping
+        criterion (after applying x scaling factors). If xtol <
+        0.0, xtol is set to sqrt(machine_precision). Defaults to
+        -1.
+    pgtol : float, optional
+        Precision goal for the value of the projected gradient in
+        the stopping criterion (after applying x scaling factors).
+        If pgtol < 0.0, pgtol is set to 1e-2 * sqrt(accuracy).
+        Setting it to 0.0 is not recommended. Defaults to -1.
+    rescale : float, optional
+        Scaling factor (in log10) used to trigger f value
+        rescaling. If 0, rescale at each iteration. If a large
+        value, never rescale. If < 0, rescale is set to 1.3.
+    callback : callable, optional
+        Called after each iteration, as callback(xk), where xk is the
+        current parameter vector.
+
+    Returns
+    -------
+    x : ndarray
+        The solution.
+    nfeval : int
+        The number of function evaluations.
+    rc : int
+        Return code, see below
+
+    See also
+    --------
+    minimize: Interface to minimization algorithms for multivariate
+        functions. See the 'TNC' `method` in particular.
+
+    Notes
+    -----
+    The underlying algorithm is truncated Newton, also called
+    Newton Conjugate-Gradient. This method differs from
+    scipy.optimize.fmin_ncg in that
+
+    1. it wraps a C implementation of the algorithm
+    2. it allows each variable to be given an upper and lower bound.
+
+    The algorithm incorporates the bound constraints by determining
+    the descent direction as in an unconstrained truncated Newton,
+    but never taking a step-size large enough to leave the space
+    of feasible x's. The algorithm keeps track of a set of
+    currently active constraints, and ignores them when computing
+    the minimum allowable step size. (The x's associated with the
+    active constraint are kept fixed.) If the maximum allowable
+    step size is zero then a new constraint is added. At the end
+    of each iteration one of the constraints may be deemed no
+    longer active and removed. A constraint is considered
+    no longer active is if it is currently active
+    but the gradient for that variable points inward from the
+    constraint. The specific constraint removed is the one
+    associated with the variable of largest index whose
+    constraint is no longer active.
+
+    Return codes are defined as follows::
+
+        -1 : Infeasible (lower bound > upper bound)
+         0 : Local minimum reached (|pg| ~= 0)
+         1 : Converged (|f_n-f_(n-1)| ~= 0)
+         2 : Converged (|x_n-x_(n-1)| ~= 0)
+         3 : Max. number of function evaluations reached
+         4 : Linear search failed
+         5 : All lower bounds are equal to the upper bounds
+         6 : Unable to progress
+         7 : User requested end of minimization
+
+    References
+    ----------
+    Wright S., Nocedal J. (2006), 'Numerical Optimization'
+
+    Nash S.G. (1984), "Newton-Type Minimization Via the Lanczos Method",
+    SIAM Journal of Numerical Analysis 21, pp. 770-778
+
+    """
+    # handle fprime/approx_grad
+    if approx_grad:
+        fun = func
+        jac = None
+    elif fprime is None:
+        fun = MemoizeJac(func)
+        jac = fun.derivative
+    else:
+        fun = func
+        jac = fprime
+
+    if disp is not None:  # disp takes precedence over messages
+        mesg_num = disp
+    else:
+        mesg_num = {0:MSG_NONE, 1:MSG_ITER, 2:MSG_INFO, 3:MSG_VERS,
+                    4:MSG_EXIT, 5:MSG_ALL}.get(messages, MSG_ALL)
+    # build options
+    opts = {'eps': epsilon,
+            'scale': scale,
+            'offset': offset,
+            'mesg_num': mesg_num,
+            'maxCGit': maxCGit,
+            'maxfun': maxfun,
+            'eta': eta,
+            'stepmx': stepmx,
+            'accuracy': accuracy,
+            'minfev': fmin,
+            'ftol': ftol,
+            'xtol': xtol,
+            'gtol': pgtol,
+            'rescale': rescale,
+            'disp': False}
+
+    res = _minimize_tnc(fun, x0, args, jac, bounds, callback=callback, **opts)
+
+    return res['x'], res['nfev'], res['status']
+
+
+def _minimize_tnc(fun, x0, args=(), jac=None, bounds=None,
+                  eps=1e-8, scale=None, offset=None, mesg_num=None,
+                  maxCGit=-1, eta=-1, stepmx=0, accuracy=0,
+                  minfev=0, ftol=-1, xtol=-1, gtol=-1, rescale=-1, disp=False,
+                  callback=None, finite_diff_rel_step=None, maxfun=None,
+                  **unknown_options):
+    """
+    Minimize a scalar function of one or more variables using a truncated
+    Newton (TNC) algorithm.
+
+    Options
+    -------
+    eps : float or ndarray
+        If `jac is None` the absolute step size used for numerical
+        approximation of the jacobian via forward differences.
+    scale : list of floats
+        Scaling factors to apply to each variable. If None, the
+        factors are up-low for interval bounded variables and
+        1+|x] for the others. Defaults to None.
+    offset : float
+        Value to subtract from each variable. If None, the
+        offsets are (up+low)/2 for interval bounded variables
+        and x for the others.
+    disp : bool
+       Set to True to print convergence messages.
+    maxCGit : int
+        Maximum number of hessian*vector evaluations per main
+        iteration. If maxCGit == 0, the direction chosen is
+        -gradient if maxCGit < 0, maxCGit is set to
+        max(1,min(50,n/2)). Defaults to -1.
+    eta : float
+        Severity of the line search. If < 0 or > 1, set to 0.25.
+        Defaults to -1.
+    stepmx : float
+        Maximum step for the line search. May be increased during
+        call. If too small, it will be set to 10.0. Defaults to 0.
+    accuracy : float
+        Relative precision for finite difference calculations. If
+        <= machine_precision, set to sqrt(machine_precision).
+        Defaults to 0.
+    minfev : float
+        Minimum function value estimate. Defaults to 0.
+    ftol : float
+        Precision goal for the value of f in the stopping criterion.
+        If ftol < 0.0, ftol is set to 0.0 defaults to -1.
+    xtol : float
+        Precision goal for the value of x in the stopping
+        criterion (after applying x scaling factors). If xtol <
+        0.0, xtol is set to sqrt(machine_precision). Defaults to
+        -1.
+    gtol : float
+        Precision goal for the value of the projected gradient in
+        the stopping criterion (after applying x scaling factors).
+        If gtol < 0.0, gtol is set to 1e-2 * sqrt(accuracy).
+        Setting it to 0.0 is not recommended. Defaults to -1.
+    rescale : float
+        Scaling factor (in log10) used to trigger f value
+        rescaling.  If 0, rescale at each iteration.  If a large
+        value, never rescale.  If < 0, rescale is set to 1.3.
+    finite_diff_rel_step : None or array_like, optional
+        If `jac in ['2-point', '3-point', 'cs']` the relative step size to
+        use for numerical approximation of the jacobian. The absolute step
+        size is computed as ``h = rel_step * sign(x) * max(1, abs(x))``,
+        possibly adjusted to fit into the bounds. For ``method='3-point'``
+        the sign of `h` is ignored. If None (default) then step is selected
+        automatically.
+    maxfun : int
+        Maximum number of function evaluations. If None, `maxfun` is
+        set to max(100, 10*len(x0)). Defaults to None.
+    """
+    _check_unknown_options(unknown_options)
+    fmin = minfev
+    pgtol = gtol
+
+    xp = array_namespace(x0)
+    x0 = atleast_nd(x0, ndim=1, xp=xp)
+    dtype = xp.float64
+    if xp.isdtype(x0.dtype, "real floating"):
+        dtype = x0.dtype
+    x0 = xp.reshape(xp.astype(x0, dtype), -1)
+
+    n = len(x0)
+
+    if bounds is None:
+        bounds = [(None,None)] * n
+    if len(bounds) != n:
+        raise ValueError('length of x0 != length of bounds')
+    new_bounds = old_bound_to_new(bounds)
+
+    if mesg_num is not None:
+        messages = {0:MSG_NONE, 1:MSG_ITER, 2:MSG_INFO, 3:MSG_VERS,
+                    4:MSG_EXIT, 5:MSG_ALL}.get(mesg_num, MSG_ALL)
+    elif disp:
+        messages = MSG_ALL
+    else:
+        messages = MSG_NONE
+
+    sf = _prepare_scalar_function(fun, x0, jac=jac, args=args, epsilon=eps,
+                                  finite_diff_rel_step=finite_diff_rel_step,
+                                  bounds=new_bounds)
+    func_and_grad = sf.fun_and_grad
+
+    """
+    low, up   : the bounds (lists of floats)
+                if low is None, the lower bounds are removed.
+                if up is None, the upper bounds are removed.
+                low and up defaults to None
+    """
+    low = zeros(n)
+    up = zeros(n)
+    for i in range(n):
+        if bounds[i] is None:
+            l, u = -inf, inf
+        else:
+            l,u = bounds[i]
+            if l is None:
+                low[i] = -inf
+            else:
+                low[i] = l
+            if u is None:
+                up[i] = inf
+            else:
+                up[i] = u
+
+    if scale is None:
+        scale = array([])
+
+    if offset is None:
+        offset = array([])
+
+    if maxfun is None:
+        maxfun = max(100, 10*len(x0))
+
+    rc, nf, nit, x, funv, jacv = moduleTNC.tnc_minimize(
+        func_and_grad, x0, low, up, scale,
+        offset, messages, maxCGit, maxfun,
+        eta, stepmx, accuracy, fmin, ftol,
+        xtol, pgtol, rescale, callback
+    )
+    # the TNC documentation states: "On output, x, f and g may be very
+    # slightly out of sync because of scaling". Therefore re-evaluate
+    # func_and_grad so they are synced.
+    funv, jacv = func_and_grad(x)
+
+    return OptimizeResult(x=x, fun=funv, jac=jacv, nfev=sf.nfev,
+                          nit=nit, status=rc, message=RCSTRINGS[rc],
+                          success=(-1 < rc < 3))

llava_next/lib/python3.10/site-packages/scipy/optimize/_trustregion_constr/__init__.py

@@ -0,0 +1,6 @@
+"""This module contains the equality constrained SQP solver."""
+
+
+from .minimize_trustregion_constr import _minimize_trustregion_constr
+
+__all__ = ['_minimize_trustregion_constr']

llava_next/lib/python3.10/site-packages/scipy/optimize/_trustregion_constr/canonical_constraint.py

@@ -0,0 +1,390 @@
+import numpy as np
+import scipy.sparse as sps
+
+
+class CanonicalConstraint:
+    """Canonical constraint to use with trust-constr algorithm.
+
+    It represents the set of constraints of the form::
+
+        f_eq(x) = 0
+        f_ineq(x) <= 0
+
+    where ``f_eq`` and ``f_ineq`` are evaluated by a single function, see
+    below.
+
+    The class is supposed to be instantiated by factory methods, which
+    should prepare the parameters listed below.
+
+    Parameters
+    ----------
+    n_eq, n_ineq : int
+        Number of equality and inequality constraints respectively.
+    fun : callable
+        Function defining the constraints. The signature is
+        ``fun(x) -> c_eq, c_ineq``, where ``c_eq`` is ndarray with `n_eq`
+        components and ``c_ineq`` is ndarray with `n_ineq` components.
+    jac : callable
+        Function to evaluate the Jacobian of the constraint. The signature
+        is ``jac(x) -> J_eq, J_ineq``, where ``J_eq`` and ``J_ineq`` are
+        either ndarray of csr_matrix of shapes (n_eq, n) and (n_ineq, n),
+        respectively.
+    hess : callable
+        Function to evaluate the Hessian of the constraints multiplied
+        by Lagrange multipliers, that is
+        ``dot(f_eq, v_eq) + dot(f_ineq, v_ineq)``. The signature is
+        ``hess(x, v_eq, v_ineq) -> H``, where ``H`` has an implied
+        shape (n, n) and provide a matrix-vector product operation
+        ``H.dot(p)``.
+    keep_feasible : ndarray, shape (n_ineq,)
+        Mask indicating which inequality constraints should be kept feasible.
+    """
+    def __init__(self, n_eq, n_ineq, fun, jac, hess, keep_feasible):
+        self.n_eq = n_eq
+        self.n_ineq = n_ineq
+        self.fun = fun
+        self.jac = jac
+        self.hess = hess
+        self.keep_feasible = keep_feasible
+
+    @classmethod
+    def from_PreparedConstraint(cls, constraint):
+        """Create an instance from `PreparedConstrained` object."""
+        lb, ub = constraint.bounds
+        cfun = constraint.fun
+        keep_feasible = constraint.keep_feasible
+
+        if np.all(lb == -np.inf) and np.all(ub == np.inf):
+            return cls.empty(cfun.n)
+
+        if np.all(lb == -np.inf) and np.all(ub == np.inf):
+            return cls.empty(cfun.n)
+        elif np.all(lb == ub):
+            return cls._equal_to_canonical(cfun, lb)
+        elif np.all(lb == -np.inf):
+            return cls._less_to_canonical(cfun, ub, keep_feasible)
+        elif np.all(ub == np.inf):
+            return cls._greater_to_canonical(cfun, lb, keep_feasible)
+        else:
+            return cls._interval_to_canonical(cfun, lb, ub, keep_feasible)
+
+    @classmethod
+    def empty(cls, n):
+        """Create an "empty" instance.
+
+        This "empty" instance is required to allow working with unconstrained
+        problems as if they have some constraints.
+        """
+        empty_fun = np.empty(0)
+        empty_jac = np.empty((0, n))
+        empty_hess = sps.csr_matrix((n, n))
+
+        def fun(x):
+            return empty_fun, empty_fun
+
+        def jac(x):
+            return empty_jac, empty_jac
+
+        def hess(x, v_eq, v_ineq):
+            return empty_hess
+
+        return cls(0, 0, fun, jac, hess, np.empty(0, dtype=np.bool_))
+
+    @classmethod
+    def concatenate(cls, canonical_constraints, sparse_jacobian):
+        """Concatenate multiple `CanonicalConstraint` into one.
+
+        `sparse_jacobian` (bool) determines the Jacobian format of the
+        concatenated constraint. Note that items in `canonical_constraints`
+        must have their Jacobians in the same format.
+        """
+        def fun(x):
+            if canonical_constraints:
+                eq_all, ineq_all = zip(
+                        *[c.fun(x) for c in canonical_constraints])
+            else:
+                eq_all, ineq_all = [], []
+
+            return np.hstack(eq_all), np.hstack(ineq_all)
+
+        if sparse_jacobian:
+            vstack = sps.vstack
+        else:
+            vstack = np.vstack
+
+        def jac(x):
+            if canonical_constraints:
+                eq_all, ineq_all = zip(
+                        *[c.jac(x) for c in canonical_constraints])
+            else:
+                eq_all, ineq_all = [], []
+
+            return vstack(eq_all), vstack(ineq_all)
+
+        def hess(x, v_eq, v_ineq):
+            hess_all = []
+            index_eq = 0
+            index_ineq = 0
+            for c in canonical_constraints:
+                vc_eq = v_eq[index_eq:index_eq + c.n_eq]
+                vc_ineq = v_ineq[index_ineq:index_ineq + c.n_ineq]
+                hess_all.append(c.hess(x, vc_eq, vc_ineq))
+                index_eq += c.n_eq
+                index_ineq += c.n_ineq
+
+            def matvec(p):
+                result = np.zeros_like(p)
+                for h in hess_all:
+                    result += h.dot(p)
+                return result
+
+            n = x.shape[0]
+            return sps.linalg.LinearOperator((n, n), matvec, dtype=float)
+
+        n_eq = sum(c.n_eq for c in canonical_constraints)
+        n_ineq = sum(c.n_ineq for c in canonical_constraints)
+        keep_feasible = np.hstack([c.keep_feasible for c in
+                                   canonical_constraints])
+
+        return cls(n_eq, n_ineq, fun, jac, hess, keep_feasible)
+
+    @classmethod
+    def _equal_to_canonical(cls, cfun, value):
+        empty_fun = np.empty(0)
+        n = cfun.n
+
+        n_eq = value.shape[0]
+        n_ineq = 0
+        keep_feasible = np.empty(0, dtype=bool)
+
+        if cfun.sparse_jacobian:
+            empty_jac = sps.csr_matrix((0, n))
+        else:
+            empty_jac = np.empty((0, n))
+
+        def fun(x):
+            return cfun.fun(x) - value, empty_fun
+
+        def jac(x):
+            return cfun.jac(x), empty_jac
+
+        def hess(x, v_eq, v_ineq):
+            return cfun.hess(x, v_eq)
+
+        empty_fun = np.empty(0)
+        n = cfun.n
+        if cfun.sparse_jacobian:
+            empty_jac = sps.csr_matrix((0, n))
+        else:
+            empty_jac = np.empty((0, n))
+
+        return cls(n_eq, n_ineq, fun, jac, hess, keep_feasible)
+
+    @classmethod
+    def _less_to_canonical(cls, cfun, ub, keep_feasible):
+        empty_fun = np.empty(0)
+        n = cfun.n
+        if cfun.sparse_jacobian:
+            empty_jac = sps.csr_matrix((0, n))
+        else:
+            empty_jac = np.empty((0, n))
+
+        finite_ub = ub < np.inf
+        n_eq = 0
+        n_ineq = np.sum(finite_ub)
+
+        if np.all(finite_ub):
+            def fun(x):
+                return empty_fun, cfun.fun(x) - ub
+
+            def jac(x):
+                return empty_jac, cfun.jac(x)
+
+            def hess(x, v_eq, v_ineq):
+                return cfun.hess(x, v_ineq)
+        else:
+            finite_ub = np.nonzero(finite_ub)[0]
+            keep_feasible = keep_feasible[finite_ub]
+            ub = ub[finite_ub]
+
+            def fun(x):
+                return empty_fun, cfun.fun(x)[finite_ub] - ub
+
+            def jac(x):
+                return empty_jac, cfun.jac(x)[finite_ub]
+
+            def hess(x, v_eq, v_ineq):
+                v = np.zeros(cfun.m)
+                v[finite_ub] = v_ineq
+                return cfun.hess(x, v)
+
+        return cls(n_eq, n_ineq, fun, jac, hess, keep_feasible)
+
+    @classmethod
+    def _greater_to_canonical(cls, cfun, lb, keep_feasible):
+        empty_fun = np.empty(0)
+        n = cfun.n
+        if cfun.sparse_jacobian:
+            empty_jac = sps.csr_matrix((0, n))
+        else:
+            empty_jac = np.empty((0, n))
+
+        finite_lb = lb > -np.inf
+        n_eq = 0
+        n_ineq = np.sum(finite_lb)
+
+        if np.all(finite_lb):
+            def fun(x):
+                return empty_fun, lb - cfun.fun(x)
+
+            def jac(x):
+                return empty_jac, -cfun.jac(x)
+
+            def hess(x, v_eq, v_ineq):
+                return cfun.hess(x, -v_ineq)
+        else:
+            finite_lb = np.nonzero(finite_lb)[0]
+            keep_feasible = keep_feasible[finite_lb]
+            lb = lb[finite_lb]
+
+            def fun(x):
+                return empty_fun, lb - cfun.fun(x)[finite_lb]
+
+            def jac(x):
+                return empty_jac, -cfun.jac(x)[finite_lb]
+
+            def hess(x, v_eq, v_ineq):
+                v = np.zeros(cfun.m)
+                v[finite_lb] = -v_ineq
+                return cfun.hess(x, v)
+
+        return cls(n_eq, n_ineq, fun, jac, hess, keep_feasible)
+
+    @classmethod
+    def _interval_to_canonical(cls, cfun, lb, ub, keep_feasible):
+        lb_inf = lb == -np.inf
+        ub_inf = ub == np.inf
+        equal = lb == ub
+        less = lb_inf & ~ub_inf
+        greater = ub_inf & ~lb_inf
+        interval = ~equal & ~lb_inf & ~ub_inf
+
+        equal = np.nonzero(equal)[0]
+        less = np.nonzero(less)[0]
+        greater = np.nonzero(greater)[0]
+        interval = np.nonzero(interval)[0]
+        n_less = less.shape[0]
+        n_greater = greater.shape[0]
+        n_interval = interval.shape[0]
+        n_ineq = n_less + n_greater + 2 * n_interval
+        n_eq = equal.shape[0]
+
+        keep_feasible = np.hstack((keep_feasible[less],
+                                   keep_feasible[greater],
+                                   keep_feasible[interval],
+                                   keep_feasible[interval]))
+
+        def fun(x):
+            f = cfun.fun(x)
+            eq = f[equal] - lb[equal]
+            le = f[less] - ub[less]
+            ge = lb[greater] - f[greater]
+            il = f[interval] - ub[interval]
+            ig = lb[interval] - f[interval]
+            return eq, np.hstack((le, ge, il, ig))
+
+        def jac(x):
+            J = cfun.jac(x)
+            eq = J[equal]
+            le = J[less]
+            ge = -J[greater]
+            il = J[interval]
+            ig = -il
+            if sps.issparse(J):
+                ineq = sps.vstack((le, ge, il, ig))
+            else:
+                ineq = np.vstack((le, ge, il, ig))
+            return eq, ineq
+
+        def hess(x, v_eq, v_ineq):
+            n_start = 0
+            v_l = v_ineq[n_start:n_start + n_less]
+            n_start += n_less
+            v_g = v_ineq[n_start:n_start + n_greater]
+            n_start += n_greater
+            v_il = v_ineq[n_start:n_start + n_interval]
+            n_start += n_interval
+            v_ig = v_ineq[n_start:n_start + n_interval]
+
+            v = np.zeros_like(lb)
+            v[equal] = v_eq
+            v[less] = v_l
+            v[greater] = -v_g
+            v[interval] = v_il - v_ig
+
+            return cfun.hess(x, v)
+
+        return cls(n_eq, n_ineq, fun, jac, hess, keep_feasible)
+
+
+def initial_constraints_as_canonical(n, prepared_constraints, sparse_jacobian):
+    """Convert initial values of the constraints to the canonical format.
+
+    The purpose to avoid one additional call to the constraints at the initial
+    point. It takes saved values in `PreparedConstraint`, modififies and
+    concatenates them to the canonical constraint format.
+    """
+    c_eq = []
+    c_ineq = []
+    J_eq = []
+    J_ineq = []
+
+    for c in prepared_constraints:
+        f = c.fun.f
+        J = c.fun.J
+        lb, ub = c.bounds
+        if np.all(lb == ub):
+            c_eq.append(f - lb)
+            J_eq.append(J)
+        elif np.all(lb == -np.inf):
+            finite_ub = ub < np.inf
+            c_ineq.append(f[finite_ub] - ub[finite_ub])
+            J_ineq.append(J[finite_ub])
+        elif np.all(ub == np.inf):
+            finite_lb = lb > -np.inf
+            c_ineq.append(lb[finite_lb] - f[finite_lb])
+            J_ineq.append(-J[finite_lb])
+        else:
+            lb_inf = lb == -np.inf
+            ub_inf = ub == np.inf
+            equal = lb == ub
+            less = lb_inf & ~ub_inf
+            greater = ub_inf & ~lb_inf
+            interval = ~equal & ~lb_inf & ~ub_inf
+
+            c_eq.append(f[equal] - lb[equal])
+            c_ineq.append(f[less] - ub[less])
+            c_ineq.append(lb[greater] - f[greater])
+            c_ineq.append(f[interval] - ub[interval])
+            c_ineq.append(lb[interval] - f[interval])
+
+            J_eq.append(J[equal])
+            J_ineq.append(J[less])
+            J_ineq.append(-J[greater])
+            J_ineq.append(J[interval])
+            J_ineq.append(-J[interval])
+
+    c_eq = np.hstack(c_eq) if c_eq else np.empty(0)
+    c_ineq = np.hstack(c_ineq) if c_ineq else np.empty(0)
+
+    if sparse_jacobian:
+        vstack = sps.vstack
+        empty = sps.csr_matrix((0, n))
+    else:
+        vstack = np.vstack
+        empty = np.empty((0, n))
+
+    J_eq = vstack(J_eq) if J_eq else empty
+    J_ineq = vstack(J_ineq) if J_ineq else empty
+
+    return c_eq, c_ineq, J_eq, J_ineq

llava_next/lib/python3.10/site-packages/scipy/optimize/_trustregion_constr/equality_constrained_sqp.py

@@ -0,0 +1,231 @@
+"""Byrd-Omojokun Trust-Region SQP method."""
+
+from scipy.sparse import eye as speye
+from .projections import projections
+from .qp_subproblem import modified_dogleg, projected_cg, box_intersections
+import numpy as np
+from numpy.linalg import norm
+
+__all__ = ['equality_constrained_sqp']
+
+
+def default_scaling(x):
+    n, = np.shape(x)
+    return speye(n)
+
+
+def equality_constrained_sqp(fun_and_constr, grad_and_jac, lagr_hess,
+                             x0, fun0, grad0, constr0,
+                             jac0, stop_criteria,
+                             state,
+                             initial_penalty,
+                             initial_trust_radius,
+                             factorization_method,
+                             trust_lb=None,
+                             trust_ub=None,
+                             scaling=default_scaling):
+    """Solve nonlinear equality-constrained problem using trust-region SQP.
+
+    Solve optimization problem:
+
+        minimize fun(x)
+        subject to: constr(x) = 0
+
+    using Byrd-Omojokun Trust-Region SQP method described in [1]_. Several
+    implementation details are based on [2]_ and [3]_, p. 549.
+
+    References
+    ----------
+    .. [1] Lalee, Marucha, Jorge Nocedal, and Todd Plantenga. "On the
+           implementation of an algorithm for large-scale equality
+           constrained optimization." SIAM Journal on
+           Optimization 8.3 (1998): 682-706.
+    .. [2] Byrd, Richard H., Mary E. Hribar, and Jorge Nocedal.
+           "An interior point algorithm for large-scale nonlinear
+           programming." SIAM Journal on Optimization 9.4 (1999): 877-900.
+    .. [3] Nocedal, Jorge, and Stephen J. Wright. "Numerical optimization"
+           Second Edition (2006).
+    """
+    PENALTY_FACTOR = 0.3  # Rho from formula (3.51), reference [2]_, p.891.
+    LARGE_REDUCTION_RATIO = 0.9
+    INTERMEDIARY_REDUCTION_RATIO = 0.3
+    SUFFICIENT_REDUCTION_RATIO = 1e-8  # Eta from reference [2]_, p.892.
+    TRUST_ENLARGEMENT_FACTOR_L = 7.0
+    TRUST_ENLARGEMENT_FACTOR_S = 2.0
+    MAX_TRUST_REDUCTION = 0.5
+    MIN_TRUST_REDUCTION = 0.1
+    SOC_THRESHOLD = 0.1
+    TR_FACTOR = 0.8  # Zeta from formula (3.21), reference [2]_, p.885.
+    BOX_FACTOR = 0.5
+
+    n, = np.shape(x0)  # Number of parameters
+
+    # Set default lower and upper bounds.
+    if trust_lb is None:
+        trust_lb = np.full(n, -np.inf)
+    if trust_ub is None:
+        trust_ub = np.full(n, np.inf)
+
+    # Initial values
+    x = np.copy(x0)
+    trust_radius = initial_trust_radius
+    penalty = initial_penalty
+    # Compute Values
+    f = fun0
+    c = grad0
+    b = constr0
+    A = jac0
+    S = scaling(x)
+    # Get projections
+    try:
+        Z, LS, Y = projections(A, factorization_method)
+    except ValueError as e:
+        if str(e) == "expected square matrix":
+            # can be the case if there are more equality
+            # constraints than independent variables
+            raise ValueError(
+                "The 'expected square matrix' error can occur if there are"
+                " more equality constraints than independent variables."
+                " Consider how your constraints are set up, or use"
+                " factorization_method='SVDFactorization'."
+            ) from e
+        else:
+            raise e
+
+    # Compute least-square lagrange multipliers
+    v = -LS.dot(c)
+    # Compute Hessian
+    H = lagr_hess(x, v)
+
+    # Update state parameters
+    optimality = norm(c + A.T.dot(v), np.inf)
+    constr_violation = norm(b, np.inf) if len(b) > 0 else 0
+    cg_info = {'niter': 0, 'stop_cond': 0,
+               'hits_boundary': False}
+
+    last_iteration_failed = False
+    while not stop_criteria(state, x, last_iteration_failed,
+                            optimality, constr_violation,
+                            trust_radius, penalty, cg_info):
+        # Normal Step - `dn`
+        # minimize 1/2*||A dn + b||^2
+        # subject to:
+        # ||dn|| <= TR_FACTOR * trust_radius
+        # BOX_FACTOR * lb <= dn <= BOX_FACTOR * ub.
+        dn = modified_dogleg(A, Y, b,
+                             TR_FACTOR*trust_radius,
+                             BOX_FACTOR*trust_lb,
+                             BOX_FACTOR*trust_ub)
+
+        # Tangential Step - `dt`
+        # Solve the QP problem:
+        # minimize 1/2 dt.T H dt + dt.T (H dn + c)
+        # subject to:
+        # A dt = 0
+        # ||dt|| <= sqrt(trust_radius**2 - ||dn||**2)
+        # lb - dn <= dt <= ub - dn
+        c_t = H.dot(dn) + c
+        b_t = np.zeros_like(b)
+        trust_radius_t = np.sqrt(trust_radius**2 - np.linalg.norm(dn)**2)
+        lb_t = trust_lb - dn
+        ub_t = trust_ub - dn
+        dt, cg_info = projected_cg(H, c_t, Z, Y, b_t,
+                                   trust_radius_t,
+                                   lb_t, ub_t)
+
+        # Compute update (normal + tangential steps).
+        d = dn + dt
+
+        # Compute second order model: 1/2 d H d + c.T d + f.
+        quadratic_model = 1/2*(H.dot(d)).dot(d) + c.T.dot(d)
+        # Compute linearized constraint: l = A d + b.
+        linearized_constr = A.dot(d)+b
+        # Compute new penalty parameter according to formula (3.52),
+        # reference [2]_, p.891.
+        vpred = norm(b) - norm(linearized_constr)
+        # Guarantee `vpred` always positive,
+        # regardless of roundoff errors.
+        vpred = max(1e-16, vpred)
+        previous_penalty = penalty
+        if quadratic_model > 0:
+            new_penalty = quadratic_model / ((1-PENALTY_FACTOR)*vpred)
+            penalty = max(penalty, new_penalty)
+        # Compute predicted reduction according to formula (3.52),
+        # reference [2]_, p.891.
+        predicted_reduction = -quadratic_model + penalty*vpred
+
+        # Compute merit function at current point
+        merit_function = f + penalty*norm(b)
+        # Evaluate function and constraints at trial point
+        x_next = x + S.dot(d)
+        f_next, b_next = fun_and_constr(x_next)
+        # Compute merit function at trial point
+        merit_function_next = f_next + penalty*norm(b_next)
+        # Compute actual reduction according to formula (3.54),
+        # reference [2]_, p.892.
+        actual_reduction = merit_function - merit_function_next
+        # Compute reduction ratio
+        reduction_ratio = actual_reduction / predicted_reduction
+
+        # Second order correction (SOC), reference [2]_, p.892.
+        if reduction_ratio < SUFFICIENT_REDUCTION_RATIO and \
+           norm(dn) <= SOC_THRESHOLD * norm(dt):
+            # Compute second order correction
+            y = -Y.dot(b_next)
+            # Make sure increment is inside box constraints
+            _, t, intersect = box_intersections(d, y, trust_lb, trust_ub)
+            # Compute tentative point
+            x_soc = x + S.dot(d + t*y)
+            f_soc, b_soc = fun_and_constr(x_soc)
+            # Recompute actual reduction
+            merit_function_soc = f_soc + penalty*norm(b_soc)
+            actual_reduction_soc = merit_function - merit_function_soc
+            # Recompute reduction ratio
+            reduction_ratio_soc = actual_reduction_soc / predicted_reduction
+            if intersect and reduction_ratio_soc >= SUFFICIENT_REDUCTION_RATIO:
+                x_next = x_soc
+                f_next = f_soc
+                b_next = b_soc
+                reduction_ratio = reduction_ratio_soc
+
+        # Readjust trust region step, formula (3.55), reference [2]_, p.892.
+        if reduction_ratio >= LARGE_REDUCTION_RATIO:
+            trust_radius = max(TRUST_ENLARGEMENT_FACTOR_L * norm(d),
+                               trust_radius)
+        elif reduction_ratio >= INTERMEDIARY_REDUCTION_RATIO:
+            trust_radius = max(TRUST_ENLARGEMENT_FACTOR_S * norm(d),
+                               trust_radius)
+        # Reduce trust region step, according to reference [3]_, p.696.
+        elif reduction_ratio < SUFFICIENT_REDUCTION_RATIO:
+            trust_reduction = ((1-SUFFICIENT_REDUCTION_RATIO) /
+                               (1-reduction_ratio))
+            new_trust_radius = trust_reduction * norm(d)
+            if new_trust_radius >= MAX_TRUST_REDUCTION * trust_radius:
+                trust_radius *= MAX_TRUST_REDUCTION
+            elif new_trust_radius >= MIN_TRUST_REDUCTION * trust_radius:
+                trust_radius = new_trust_radius
+            else:
+                trust_radius *= MIN_TRUST_REDUCTION
+
+        # Update iteration
+        if reduction_ratio >= SUFFICIENT_REDUCTION_RATIO:
+            x = x_next
+            f, b = f_next, b_next
+            c, A = grad_and_jac(x)
+            S = scaling(x)
+            # Get projections
+            Z, LS, Y = projections(A, factorization_method)
+            # Compute least-square lagrange multipliers
+            v = -LS.dot(c)
+            # Compute Hessian
+            H = lagr_hess(x, v)
+            # Set Flag
+            last_iteration_failed = False
+            # Otimality values
+            optimality = norm(c + A.T.dot(v), np.inf)
+            constr_violation = norm(b, np.inf) if len(b) > 0 else 0
+        else:
+            penalty = previous_penalty
+            last_iteration_failed = True
+
+    return x, state

llava_next/lib/python3.10/site-packages/scipy/optimize/_trustregion_constr/minimize_trustregion_constr.py

@@ -0,0 +1,564 @@
+import time
+import numpy as np
+from scipy.sparse.linalg import LinearOperator
+from .._differentiable_functions import VectorFunction
+from .._constraints import (
+    NonlinearConstraint, LinearConstraint, PreparedConstraint, Bounds, strict_bounds)
+from .._hessian_update_strategy import BFGS
+from .._optimize import OptimizeResult
+from .._differentiable_functions import ScalarFunction
+from .equality_constrained_sqp import equality_constrained_sqp
+from .canonical_constraint import (CanonicalConstraint,
+                                   initial_constraints_as_canonical)
+from .tr_interior_point import tr_interior_point
+from .report import BasicReport, SQPReport, IPReport
+
+
+TERMINATION_MESSAGES = {
+    0: "The maximum number of function evaluations is exceeded.",
+    1: "`gtol` termination condition is satisfied.",
+    2: "`xtol` termination condition is satisfied.",
+    3: "`callback` function requested termination."
+}
+
+
+class HessianLinearOperator:
+    """Build LinearOperator from hessp"""
+    def __init__(self, hessp, n):
+        self.hessp = hessp
+        self.n = n
+
+    def __call__(self, x, *args):
+        def matvec(p):
+            return self.hessp(x, p, *args)
+
+        return LinearOperator((self.n, self.n), matvec=matvec)
+
+
+class LagrangianHessian:
+    """The Hessian of the Lagrangian as LinearOperator.
+
+    The Lagrangian is computed as the objective function plus all the
+    constraints multiplied with some numbers (Lagrange multipliers).
+    """
+    def __init__(self, n, objective_hess, constraints_hess):
+        self.n = n
+        self.objective_hess = objective_hess
+        self.constraints_hess = constraints_hess
+
+    def __call__(self, x, v_eq=np.empty(0), v_ineq=np.empty(0)):
+        H_objective = self.objective_hess(x)
+        H_constraints = self.constraints_hess(x, v_eq, v_ineq)
+
+        def matvec(p):
+            return H_objective.dot(p) + H_constraints.dot(p)
+
+        return LinearOperator((self.n, self.n), matvec)
+
+
+def update_state_sqp(state, x, last_iteration_failed, objective, prepared_constraints,
+                     start_time, tr_radius, constr_penalty, cg_info):
+    state.nit += 1
+    state.nfev = objective.nfev
+    state.njev = objective.ngev
+    state.nhev = objective.nhev
+    state.constr_nfev = [c.fun.nfev if isinstance(c.fun, VectorFunction) else 0
+                         for c in prepared_constraints]
+    state.constr_njev = [c.fun.njev if isinstance(c.fun, VectorFunction) else 0
+                         for c in prepared_constraints]
+    state.constr_nhev = [c.fun.nhev if isinstance(c.fun, VectorFunction) else 0
+                         for c in prepared_constraints]
+
+    if not last_iteration_failed:
+        state.x = x
+        state.fun = objective.f
+        state.grad = objective.g
+        state.v = [c.fun.v for c in prepared_constraints]
+        state.constr = [c.fun.f for c in prepared_constraints]
+        state.jac = [c.fun.J for c in prepared_constraints]
+        # Compute Lagrangian Gradient
+        state.lagrangian_grad = np.copy(state.grad)
+        for c in prepared_constraints:
+            state.lagrangian_grad += c.fun.J.T.dot(c.fun.v)
+        state.optimality = np.linalg.norm(state.lagrangian_grad, np.inf)
+        # Compute maximum constraint violation
+        state.constr_violation = 0
+        for i in range(len(prepared_constraints)):
+            lb, ub = prepared_constraints[i].bounds
+            c = state.constr[i]
+            state.constr_violation = np.max([state.constr_violation,
+                                             np.max(lb - c),
+                                             np.max(c - ub)])
+
+    state.execution_time = time.time() - start_time
+    state.tr_radius = tr_radius
+    state.constr_penalty = constr_penalty
+    state.cg_niter += cg_info["niter"]
+    state.cg_stop_cond = cg_info["stop_cond"]
+
+    return state
+
+
+def update_state_ip(state, x, last_iteration_failed, objective,
+                    prepared_constraints, start_time,
+                    tr_radius, constr_penalty, cg_info,
+                    barrier_parameter, barrier_tolerance):
+    state = update_state_sqp(state, x, last_iteration_failed, objective,
+                             prepared_constraints, start_time, tr_radius,
+                             constr_penalty, cg_info)
+    state.barrier_parameter = barrier_parameter
+    state.barrier_tolerance = barrier_tolerance
+    return state
+
+
+def _minimize_trustregion_constr(fun, x0, args, grad,
+                                 hess, hessp, bounds, constraints,
+                                 xtol=1e-8, gtol=1e-8,
+                                 barrier_tol=1e-8,
+                                 sparse_jacobian=None,
+                                 callback=None, maxiter=1000,
+                                 verbose=0, finite_diff_rel_step=None,
+                                 initial_constr_penalty=1.0, initial_tr_radius=1.0,
+                                 initial_barrier_parameter=0.1,
+                                 initial_barrier_tolerance=0.1,
+                                 factorization_method=None,
+                                 disp=False):
+    """Minimize a scalar function subject to constraints.
+
+    Parameters
+    ----------
+    gtol : float, optional
+        Tolerance for termination by the norm of the Lagrangian gradient.
+        The algorithm will terminate when both the infinity norm (i.e., max
+        abs value) of the Lagrangian gradient and the constraint violation
+        are smaller than ``gtol``. Default is 1e-8.
+    xtol : float, optional
+        Tolerance for termination by the change of the independent variable.
+        The algorithm will terminate when ``tr_radius < xtol``, where
+        ``tr_radius`` is the radius of the trust region used in the algorithm.
+        Default is 1e-8.
+    barrier_tol : float, optional
+        Threshold on the barrier parameter for the algorithm termination.
+        When inequality constraints are present, the algorithm will terminate
+        only when the barrier parameter is less than `barrier_tol`.
+        Default is 1e-8.
+    sparse_jacobian : {bool, None}, optional
+        Determines how to represent Jacobians of the constraints. If bool,
+        then Jacobians of all the constraints will be converted to the
+        corresponding format. If None (default), then Jacobians won't be
+        converted, but the algorithm can proceed only if they all have the
+        same format.
+    initial_tr_radius: float, optional
+        Initial trust radius. The trust radius gives the maximum distance
+        between solution points in consecutive iterations. It reflects the
+        trust the algorithm puts in the local approximation of the optimization
+        problem. For an accurate local approximation the trust-region should be
+        large and for an  approximation valid only close to the current point it
+        should be a small one. The trust radius is automatically updated throughout
+        the optimization process, with ``initial_tr_radius`` being its initial value.
+        Default is 1 (recommended in [1]_, p. 19).
+    initial_constr_penalty : float, optional
+        Initial constraints penalty parameter. The penalty parameter is used for
+        balancing the requirements of decreasing the objective function
+        and satisfying the constraints. It is used for defining the merit function:
+        ``merit_function(x) = fun(x) + constr_penalty * constr_norm_l2(x)``,
+        where ``constr_norm_l2(x)`` is the l2 norm of a vector containing all
+        the constraints. The merit function is used for accepting or rejecting
+        trial points and ``constr_penalty`` weights the two conflicting goals
+        of reducing objective function and constraints. The penalty is automatically
+        updated throughout the optimization  process, with
+        ``initial_constr_penalty`` being its  initial value. Default is 1
+        (recommended in [1]_, p 19).
+    initial_barrier_parameter, initial_barrier_tolerance: float, optional
+        Initial barrier parameter and initial tolerance for the barrier subproblem.
+        Both are used only when inequality constraints are present. For dealing with
+        optimization problems ``min_x f(x)`` subject to inequality constraints
+        ``c(x) <= 0`` the algorithm introduces slack variables, solving the problem
+        ``min_(x,s) f(x) + barrier_parameter*sum(ln(s))`` subject to the equality
+        constraints  ``c(x) + s = 0`` instead of the original problem. This subproblem
+        is solved for decreasing values of ``barrier_parameter`` and with decreasing
+        tolerances for the termination, starting with ``initial_barrier_parameter``
+        for the barrier parameter and ``initial_barrier_tolerance`` for the
+        barrier tolerance. Default is 0.1 for both values (recommended in [1]_ p. 19).
+        Also note that ``barrier_parameter`` and ``barrier_tolerance`` are updated
+        with the same prefactor.
+    factorization_method : string or None, optional
+        Method to factorize the Jacobian of the constraints. Use None (default)
+        for the auto selection or one of:
+
+            - 'NormalEquation' (requires scikit-sparse)
+            - 'AugmentedSystem'
+            - 'QRFactorization'
+            - 'SVDFactorization'
+
+        The methods 'NormalEquation' and 'AugmentedSystem' can be used only
+        with sparse constraints. The projections required by the algorithm
+        will be computed using, respectively, the normal equation  and the
+        augmented system approaches explained in [1]_. 'NormalEquation'
+        computes the Cholesky factorization of ``A A.T`` and 'AugmentedSystem'
+        performs the LU factorization of an augmented system. They usually
+        provide similar results. 'AugmentedSystem' is used by default for
+        sparse matrices.
+
+        The methods 'QRFactorization' and 'SVDFactorization' can be used
+        only with dense constraints. They compute the required projections
+        using, respectively, QR and SVD factorizations. The 'SVDFactorization'
+        method can cope with Jacobian matrices with deficient row rank and will
+        be used whenever other factorization methods fail (which may imply the
+        conversion of sparse matrices to a dense format when required).
+        By default, 'QRFactorization' is used for dense matrices.
+    finite_diff_rel_step : None or array_like, optional
+        Relative step size for the finite difference approximation.
+    maxiter : int, optional
+        Maximum number of algorithm iterations. Default is 1000.
+    verbose : {0, 1, 2}, optional
+        Level of algorithm's verbosity:
+
+            * 0 (default) : work silently.
+            * 1 : display a termination report.
+            * 2 : display progress during iterations.
+            * 3 : display progress during iterations (more complete report).
+
+    disp : bool, optional
+        If True (default), then `verbose` will be set to 1 if it was 0.
+
+    Returns
+    -------
+    `OptimizeResult` with the fields documented below. Note the following:
+
+        1. All values corresponding to the constraints are ordered as they
+           were passed to the solver. And values corresponding to `bounds`
+           constraints are put *after* other constraints.
+        2. All numbers of function, Jacobian or Hessian evaluations correspond
+           to numbers of actual Python function calls. It means, for example,
+           that if a Jacobian is estimated by finite differences, then the
+           number of Jacobian evaluations will be zero and the number of
+           function evaluations will be incremented by all calls during the
+           finite difference estimation.
+
+    x : ndarray, shape (n,)
+        Solution found.
+    optimality : float
+        Infinity norm of the Lagrangian gradient at the solution.
+    constr_violation : float
+        Maximum constraint violation at the solution.
+    fun : float
+        Objective function at the solution.
+    grad : ndarray, shape (n,)
+        Gradient of the objective function at the solution.
+    lagrangian_grad : ndarray, shape (n,)
+        Gradient of the Lagrangian function at the solution.
+    nit : int
+        Total number of iterations.
+    nfev : integer
+        Number of the objective function evaluations.
+    njev : integer
+        Number of the objective function gradient evaluations.
+    nhev : integer
+        Number of the objective function Hessian evaluations.
+    cg_niter : int
+        Total number of the conjugate gradient method iterations.
+    method : {'equality_constrained_sqp', 'tr_interior_point'}
+        Optimization method used.
+    constr : list of ndarray
+        List of constraint values at the solution.
+    jac : list of {ndarray, sparse matrix}
+        List of the Jacobian matrices of the constraints at the solution.
+    v : list of ndarray
+        List of the Lagrange multipliers for the constraints at the solution.
+        For an inequality constraint a positive multiplier means that the upper
+        bound is active, a negative multiplier means that the lower bound is
+        active and if a multiplier is zero it means the constraint is not
+        active.
+    constr_nfev : list of int
+        Number of constraint evaluations for each of the constraints.
+    constr_njev : list of int
+        Number of Jacobian matrix evaluations for each of the constraints.
+    constr_nhev : list of int
+        Number of Hessian evaluations for each of the constraints.
+    tr_radius : float
+        Radius of the trust region at the last iteration.
+    constr_penalty : float
+        Penalty parameter at the last iteration, see `initial_constr_penalty`.
+    barrier_tolerance : float
+        Tolerance for the barrier subproblem at the last iteration.
+        Only for problems with inequality constraints.
+    barrier_parameter : float
+        Barrier parameter at the last iteration. Only for problems
+        with inequality constraints.
+    execution_time : float
+        Total execution time.
+    message : str
+        Termination message.
+    status : {0, 1, 2, 3}
+        Termination status:
+
+            * 0 : The maximum number of function evaluations is exceeded.
+            * 1 : `gtol` termination condition is satisfied.
+            * 2 : `xtol` termination condition is satisfied.
+            * 3 : `callback` function requested termination.
+
+    cg_stop_cond : int
+        Reason for CG subproblem termination at the last iteration:
+
+            * 0 : CG subproblem not evaluated.
+            * 1 : Iteration limit was reached.
+            * 2 : Reached the trust-region boundary.
+            * 3 : Negative curvature detected.
+            * 4 : Tolerance was satisfied.
+
+    References
+    ----------
+    .. [1] Conn, A. R., Gould, N. I., & Toint, P. L.
+           Trust region methods. 2000. Siam. pp. 19.
+    """
+    x0 = np.atleast_1d(x0).astype(float)
+    n_vars = np.size(x0)
+    if hess is None:
+        if callable(hessp):
+            hess = HessianLinearOperator(hessp, n_vars)
+        else:
+            hess = BFGS()
+    if disp and verbose == 0:
+        verbose = 1
+
+    if bounds is not None:
+        modified_lb = np.nextafter(bounds.lb, -np.inf, where=bounds.lb > -np.inf)
+        modified_ub = np.nextafter(bounds.ub, np.inf, where=bounds.ub < np.inf)
+        modified_lb = np.where(np.isfinite(bounds.lb), modified_lb, bounds.lb)
+        modified_ub = np.where(np.isfinite(bounds.ub), modified_ub, bounds.ub)
+        bounds = Bounds(modified_lb, modified_ub, keep_feasible=bounds.keep_feasible)
+        finite_diff_bounds = strict_bounds(bounds.lb, bounds.ub,
+                                           bounds.keep_feasible, n_vars)
+    else:
+        finite_diff_bounds = (-np.inf, np.inf)
+
+    # Define Objective Function
+    objective = ScalarFunction(fun, x0, args, grad, hess,
+                               finite_diff_rel_step, finite_diff_bounds)
+
+    # Put constraints in list format when needed.
+    if isinstance(constraints, (NonlinearConstraint, LinearConstraint)):
+        constraints = [constraints]
+
+    # Prepare constraints.
+    prepared_constraints = [
+        PreparedConstraint(c, x0, sparse_jacobian, finite_diff_bounds)
+        for c in constraints]
+
+    # Check that all constraints are either sparse or dense.
+    n_sparse = sum(c.fun.sparse_jacobian for c in prepared_constraints)
+    if 0 < n_sparse < len(prepared_constraints):
+        raise ValueError("All constraints must have the same kind of the "
+                         "Jacobian --- either all sparse or all dense. "
+                         "You can set the sparsity globally by setting "
+                         "`sparse_jacobian` to either True of False.")
+    if prepared_constraints:
+        sparse_jacobian = n_sparse > 0
+
+    if bounds is not None:
+        if sparse_jacobian is None:
+            sparse_jacobian = True
+        prepared_constraints.append(PreparedConstraint(bounds, x0,
+                                                       sparse_jacobian))
+
+    # Concatenate initial constraints to the canonical form.
+    c_eq0, c_ineq0, J_eq0, J_ineq0 = initial_constraints_as_canonical(
+        n_vars, prepared_constraints, sparse_jacobian)
+
+    # Prepare all canonical constraints and concatenate it into one.
+    canonical_all = [CanonicalConstraint.from_PreparedConstraint(c)
+                     for c in prepared_constraints]
+
+    if len(canonical_all) == 0:
+        canonical = CanonicalConstraint.empty(n_vars)
+    elif len(canonical_all) == 1:
+        canonical = canonical_all[0]
+    else:
+        canonical = CanonicalConstraint.concatenate(canonical_all,
+                                                    sparse_jacobian)
+
+    # Generate the Hessian of the Lagrangian.
+    lagrangian_hess = LagrangianHessian(n_vars, objective.hess, canonical.hess)
+
+    # Choose appropriate method
+    if canonical.n_ineq == 0:
+        method = 'equality_constrained_sqp'
+    else:
+        method = 'tr_interior_point'
+
+    # Construct OptimizeResult
+    state = OptimizeResult(
+        nit=0, nfev=0, njev=0, nhev=0,
+        cg_niter=0, cg_stop_cond=0,
+        fun=objective.f, grad=objective.g,
+        lagrangian_grad=np.copy(objective.g),
+        constr=[c.fun.f for c in prepared_constraints],
+        jac=[c.fun.J for c in prepared_constraints],
+        constr_nfev=[0 for c in prepared_constraints],
+        constr_njev=[0 for c in prepared_constraints],
+        constr_nhev=[0 for c in prepared_constraints],
+        v=[c.fun.v for c in prepared_constraints],
+        method=method)
+
+    # Start counting
+    start_time = time.time()
+
+    # Define stop criteria
+    if method == 'equality_constrained_sqp':
+        def stop_criteria(state, x, last_iteration_failed,
+                          optimality, constr_violation,
+                          tr_radius, constr_penalty, cg_info):
+            state = update_state_sqp(state, x, last_iteration_failed,
+                                     objective, prepared_constraints,
+                                     start_time, tr_radius, constr_penalty,
+                                     cg_info)
+            if verbose == 2:
+                BasicReport.print_iteration(state.nit,
+                                            state.nfev,
+                                            state.cg_niter,
+                                            state.fun,
+                                            state.tr_radius,
+                                            state.optimality,
+                                            state.constr_violation)
+            elif verbose > 2:
+                SQPReport.print_iteration(state.nit,
+                                          state.nfev,
+                                          state.cg_niter,
+                                          state.fun,
+                                          state.tr_radius,
+                                          state.optimality,
+                                          state.constr_violation,
+                                          state.constr_penalty,
+                                          state.cg_stop_cond)
+            state.status = None
+            state.niter = state.nit  # Alias for callback (backward-compatibility)
+            if callback is not None:
+                callback_stop = False
+                try:
+                    callback_stop = callback(state)
+                except StopIteration:
+                    callback_stop = True
+                if callback_stop:
+                    state.status = 3
+                    return True
+            if state.optimality < gtol and state.constr_violation < gtol:
+                state.status = 1
+            elif state.tr_radius < xtol:
+                state.status = 2
+            elif state.nit >= maxiter:
+                state.status = 0
+            return state.status in (0, 1, 2, 3)
+    elif method == 'tr_interior_point':
+        def stop_criteria(state, x, last_iteration_failed, tr_radius,
+                          constr_penalty, cg_info, barrier_parameter,
+                          barrier_tolerance):
+            state = update_state_ip(state, x, last_iteration_failed,
+                                    objective, prepared_constraints,
+                                    start_time, tr_radius, constr_penalty,
+                                    cg_info, barrier_parameter, barrier_tolerance)
+            if verbose == 2:
+                BasicReport.print_iteration(state.nit,
+                                            state.nfev,
+                                            state.cg_niter,
+                                            state.fun,
+                                            state.tr_radius,
+                                            state.optimality,
+                                            state.constr_violation)
+            elif verbose > 2:
+                IPReport.print_iteration(state.nit,
+                                         state.nfev,
+                                         state.cg_niter,
+                                         state.fun,
+                                         state.tr_radius,
+                                         state.optimality,
+                                         state.constr_violation,
+                                         state.constr_penalty,
+                                         state.barrier_parameter,
+                                         state.cg_stop_cond)
+            state.status = None
+            state.niter = state.nit  # Alias for callback (backward compatibility)
+            if callback is not None:
+                callback_stop = False
+                try:
+                    callback_stop = callback(state)
+                except StopIteration:
+                    callback_stop = True
+                if callback_stop:
+                    state.status = 3
+                    return True
+            if state.optimality < gtol and state.constr_violation < gtol:
+                state.status = 1
+            elif (state.tr_radius < xtol
+                  and state.barrier_parameter < barrier_tol):
+                state.status = 2
+            elif state.nit >= maxiter:
+                state.status = 0
+            return state.status in (0, 1, 2, 3)
+
+    if verbose == 2:
+        BasicReport.print_header()
+    elif verbose > 2:
+        if method == 'equality_constrained_sqp':
+            SQPReport.print_header()
+        elif method == 'tr_interior_point':
+            IPReport.print_header()
+
+    # Call inferior function to do the optimization
+    if method == 'equality_constrained_sqp':
+        def fun_and_constr(x):
+            f = objective.fun(x)
+            c_eq, _ = canonical.fun(x)
+            return f, c_eq
+
+        def grad_and_jac(x):
+            g = objective.grad(x)
+            J_eq, _ = canonical.jac(x)
+            return g, J_eq
+
+        _, result = equality_constrained_sqp(
+            fun_and_constr, grad_and_jac, lagrangian_hess,
+            x0, objective.f, objective.g,
+            c_eq0, J_eq0,
+            stop_criteria, state,
+            initial_constr_penalty, initial_tr_radius,
+            factorization_method)
+
+    elif method == 'tr_interior_point':
+        _, result = tr_interior_point(
+            objective.fun, objective.grad, lagrangian_hess,
+            n_vars, canonical.n_ineq, canonical.n_eq,
+            canonical.fun, canonical.jac,
+            x0, objective.f, objective.g,
+            c_ineq0, J_ineq0, c_eq0, J_eq0,
+            stop_criteria,
+            canonical.keep_feasible,
+            xtol, state, initial_barrier_parameter,
+            initial_barrier_tolerance,
+            initial_constr_penalty, initial_tr_radius,
+            factorization_method)
+
+    # Status 3 occurs when the callback function requests termination,
+    # this is assumed to not be a success.
+    result.success = True if result.status in (1, 2) else False
+    result.message = TERMINATION_MESSAGES[result.status]
+
+    # Alias (for backward compatibility with 1.1.0)
+    result.niter = result.nit
+
+    if verbose == 2:
+        BasicReport.print_footer()
+    elif verbose > 2:
+        if method == 'equality_constrained_sqp':
+            SQPReport.print_footer()
+        elif method == 'tr_interior_point':
+            IPReport.print_footer()
+    if verbose >= 1:
+        print(result.message)
+        print("Number of iterations: {}, function evaluations: {}, "
+              "CG iterations: {}, optimality: {:.2e}, "
+              "constraint violation: {:.2e}, execution time: {:4.2} s."
+              .format(result.nit, result.nfev, result.cg_niter,
+                      result.optimality, result.constr_violation,
+                      result.execution_time))
+    return result

llava_next/lib/python3.10/site-packages/scipy/optimize/_trustregion_constr/projections.py

@@ -0,0 +1,407 @@
+"""Basic linear factorizations needed by the solver."""
+
+from scipy.sparse import (bmat, csc_matrix, eye, issparse)
+from scipy.sparse.linalg import LinearOperator
+import scipy.linalg
+import scipy.sparse.linalg
+try:
+    from sksparse.cholmod import cholesky_AAt
+    sksparse_available = True
+except ImportError:
+    import warnings
+    sksparse_available = False
+import numpy as np
+from warnings import warn
+
+__all__ = [
+    'orthogonality',
+    'projections',
+]
+
+
+def orthogonality(A, g):
+    """Measure orthogonality between a vector and the null space of a matrix.
+
+    Compute a measure of orthogonality between the null space
+    of the (possibly sparse) matrix ``A`` and a given vector ``g``.
+
+    The formula is a simplified (and cheaper) version of formula (3.13)
+    from [1]_.
+    ``orth =  norm(A g, ord=2)/(norm(A, ord='fro')*norm(g, ord=2))``.
+
+    References
+    ----------
+    .. [1] Gould, Nicholas IM, Mary E. Hribar, and Jorge Nocedal.
+           "On the solution of equality constrained quadratic
+            programming problems arising in optimization."
+            SIAM Journal on Scientific Computing 23.4 (2001): 1376-1395.
+    """
+    # Compute vector norms
+    norm_g = np.linalg.norm(g)
+    # Compute Froebnius norm of the matrix A
+    if issparse(A):
+        norm_A = scipy.sparse.linalg.norm(A, ord='fro')
+    else:
+        norm_A = np.linalg.norm(A, ord='fro')
+
+    # Check if norms are zero
+    if norm_g == 0 or norm_A == 0:
+        return 0
+
+    norm_A_g = np.linalg.norm(A.dot(g))
+    # Orthogonality measure
+    orth = norm_A_g / (norm_A*norm_g)
+    return orth
+
+
+def normal_equation_projections(A, m, n, orth_tol, max_refin, tol):
+    """Return linear operators for matrix A using ``NormalEquation`` approach.
+    """
+    # Cholesky factorization
+    factor = cholesky_AAt(A)
+
+    # z = x - A.T inv(A A.T) A x
+    def null_space(x):
+        v = factor(A.dot(x))
+        z = x - A.T.dot(v)
+
+        # Iterative refinement to improve roundoff
+        # errors described in [2]_, algorithm 5.1.
+        k = 0
+        while orthogonality(A, z) > orth_tol:
+            if k >= max_refin:
+                break
+            # z_next = z - A.T inv(A A.T) A z
+            v = factor(A.dot(z))
+            z = z - A.T.dot(v)
+            k += 1
+
+        return z
+
+    # z = inv(A A.T) A x
+    def least_squares(x):
+        return factor(A.dot(x))
+
+    # z = A.T inv(A A.T) x
+    def row_space(x):
+        return A.T.dot(factor(x))
+
+    return null_space, least_squares, row_space
+
+
+def augmented_system_projections(A, m, n, orth_tol, max_refin, tol):
+    """Return linear operators for matrix A - ``AugmentedSystem``."""
+    # Form augmented system
+    K = csc_matrix(bmat([[eye(n), A.T], [A, None]]))
+    # LU factorization
+    # TODO: Use a symmetric indefinite factorization
+    #       to solve the system twice as fast (because
+    #       of the symmetry).
+    try:
+        solve = scipy.sparse.linalg.factorized(K)
+    except RuntimeError:
+        warn("Singular Jacobian matrix. Using dense SVD decomposition to "
+             "perform the factorizations.",
+             stacklevel=3)
+        return svd_factorization_projections(A.toarray(),
+                                             m, n, orth_tol,
+                                             max_refin, tol)
+
+    # z = x - A.T inv(A A.T) A x
+    # is computed solving the extended system:
+    # [I A.T] * [ z ] = [x]
+    # [A  O ]   [aux]   [0]
+    def null_space(x):
+        # v = [x]
+        #     [0]
+        v = np.hstack([x, np.zeros(m)])
+        # lu_sol = [ z ]
+        #          [aux]
+        lu_sol = solve(v)
+        z = lu_sol[:n]
+
+        # Iterative refinement to improve roundoff
+        # errors described in [2]_, algorithm 5.2.
+        k = 0
+        while orthogonality(A, z) > orth_tol:
+            if k >= max_refin:
+                break
+            # new_v = [x] - [I A.T] * [ z ]
+            #         [0]   [A  O ]   [aux]
+            new_v = v - K.dot(lu_sol)
+            # [I A.T] * [delta  z ] = new_v
+            # [A  O ]   [delta aux]
+            lu_update = solve(new_v)
+            #  [ z ] += [delta  z ]
+            #  [aux]    [delta aux]
+            lu_sol += lu_update
+            z = lu_sol[:n]
+            k += 1
+
+        # return z = x - A.T inv(A A.T) A x
+        return z
+
+    # z = inv(A A.T) A x
+    # is computed solving the extended system:
+    # [I A.T] * [aux] = [x]
+    # [A  O ]   [ z ]   [0]
+    def least_squares(x):
+        # v = [x]
+        #     [0]
+        v = np.hstack([x, np.zeros(m)])
+        # lu_sol = [aux]
+        #          [ z ]
+        lu_sol = solve(v)
+        # return z = inv(A A.T) A x
+        return lu_sol[n:m+n]
+
+    # z = A.T inv(A A.T) x
+    # is computed solving the extended system:
+    # [I A.T] * [ z ] = [0]
+    # [A  O ]   [aux]   [x]
+    def row_space(x):
+        # v = [0]
+        #     [x]
+        v = np.hstack([np.zeros(n), x])
+        # lu_sol = [ z ]
+        #          [aux]
+        lu_sol = solve(v)
+        # return z = A.T inv(A A.T) x
+        return lu_sol[:n]
+
+    return null_space, least_squares, row_space
+
+
+def qr_factorization_projections(A, m, n, orth_tol, max_refin, tol):
+    """Return linear operators for matrix A using ``QRFactorization`` approach.
+    """
+    # QRFactorization
+    Q, R, P = scipy.linalg.qr(A.T, pivoting=True, mode='economic')
+
+    if np.linalg.norm(R[-1, :], np.inf) < tol:
+        warn('Singular Jacobian matrix. Using SVD decomposition to ' +
+             'perform the factorizations.',
+             stacklevel=3)
+        return svd_factorization_projections(A, m, n,
+                                             orth_tol,
+                                             max_refin,
+                                             tol)
+
+    # z = x - A.T inv(A A.T) A x
+    def null_space(x):
+        # v = P inv(R) Q.T x
+        aux1 = Q.T.dot(x)
+        aux2 = scipy.linalg.solve_triangular(R, aux1, lower=False)
+        v = np.zeros(m)
+        v[P] = aux2
+        z = x - A.T.dot(v)
+
+        # Iterative refinement to improve roundoff
+        # errors described in [2]_, algorithm 5.1.
+        k = 0
+        while orthogonality(A, z) > orth_tol:
+            if k >= max_refin:
+                break
+            # v = P inv(R) Q.T x
+            aux1 = Q.T.dot(z)
+            aux2 = scipy.linalg.solve_triangular(R, aux1, lower=False)
+            v[P] = aux2
+            # z_next = z - A.T v
+            z = z - A.T.dot(v)
+            k += 1
+
+        return z
+
+    # z = inv(A A.T) A x
+    def least_squares(x):
+        # z = P inv(R) Q.T x
+        aux1 = Q.T.dot(x)
+        aux2 = scipy.linalg.solve_triangular(R, aux1, lower=False)
+        z = np.zeros(m)
+        z[P] = aux2
+        return z
+
+    # z = A.T inv(A A.T) x
+    def row_space(x):
+        # z = Q inv(R.T) P.T x
+        aux1 = x[P]
+        aux2 = scipy.linalg.solve_triangular(R, aux1,
+                                             lower=False,
+                                             trans='T')
+        z = Q.dot(aux2)
+        return z
+
+    return null_space, least_squares, row_space
+
+
+def svd_factorization_projections(A, m, n, orth_tol, max_refin, tol):
+    """Return linear operators for matrix A using ``SVDFactorization`` approach.
+    """
+    # SVD Factorization
+    U, s, Vt = scipy.linalg.svd(A, full_matrices=False)
+
+    # Remove dimensions related with very small singular values
+    U = U[:, s > tol]
+    Vt = Vt[s > tol, :]
+    s = s[s > tol]
+
+    # z = x - A.T inv(A A.T) A x
+    def null_space(x):
+        # v = U 1/s V.T x = inv(A A.T) A x
+        aux1 = Vt.dot(x)
+        aux2 = 1/s*aux1
+        v = U.dot(aux2)
+        z = x - A.T.dot(v)
+
+        # Iterative refinement to improve roundoff
+        # errors described in [2]_, algorithm 5.1.
+        k = 0
+        while orthogonality(A, z) > orth_tol:
+            if k >= max_refin:
+                break
+            # v = U 1/s V.T x = inv(A A.T) A x
+            aux1 = Vt.dot(z)
+            aux2 = 1/s*aux1
+            v = U.dot(aux2)
+            # z_next = z - A.T v
+            z = z - A.T.dot(v)
+            k += 1
+
+        return z
+
+    # z = inv(A A.T) A x
+    def least_squares(x):
+        # z = U 1/s V.T x = inv(A A.T) A x
+        aux1 = Vt.dot(x)
+        aux2 = 1/s*aux1
+        z = U.dot(aux2)
+        return z
+
+    # z = A.T inv(A A.T) x
+    def row_space(x):
+        # z = V 1/s U.T x
+        aux1 = U.T.dot(x)
+        aux2 = 1/s*aux1
+        z = Vt.T.dot(aux2)
+        return z
+
+    return null_space, least_squares, row_space
+
+
+def projections(A, method=None, orth_tol=1e-12, max_refin=3, tol=1e-15):
+    """Return three linear operators related with a given matrix A.
+
+    Parameters
+    ----------
+    A : sparse matrix (or ndarray), shape (m, n)
+        Matrix ``A`` used in the projection.
+    method : string, optional
+        Method used for compute the given linear
+        operators. Should be one of:
+
+            - 'NormalEquation': The operators
+               will be computed using the
+               so-called normal equation approach
+               explained in [1]_. In order to do
+               so the Cholesky factorization of
+               ``(A A.T)`` is computed. Exclusive
+               for sparse matrices.
+            - 'AugmentedSystem': The operators
+               will be computed using the
+               so-called augmented system approach
+               explained in [1]_. Exclusive
+               for sparse matrices.
+            - 'QRFactorization': Compute projections
+               using QR factorization. Exclusive for
+               dense matrices.
+            - 'SVDFactorization': Compute projections
+               using SVD factorization. Exclusive for
+               dense matrices.
+
+    orth_tol : float, optional
+        Tolerance for iterative refinements.
+    max_refin : int, optional
+        Maximum number of iterative refinements.
+    tol : float, optional
+        Tolerance for singular values.
+
+    Returns
+    -------
+    Z : LinearOperator, shape (n, n)
+        Null-space operator. For a given vector ``x``,
+        the null space operator is equivalent to apply
+        a projection matrix ``P = I - A.T inv(A A.T) A``
+        to the vector. It can be shown that this is
+        equivalent to project ``x`` into the null space
+        of A.
+    LS : LinearOperator, shape (m, n)
+        Least-squares operator. For a given vector ``x``,
+        the least-squares operator is equivalent to apply a
+        pseudoinverse matrix ``pinv(A.T) = inv(A A.T) A``
+        to the vector. It can be shown that this vector
+        ``pinv(A.T) x`` is the least_square solution to
+        ``A.T y = x``.
+    Y : LinearOperator, shape (n, m)
+        Row-space operator. For a given vector ``x``,
+        the row-space operator is equivalent to apply a
+        projection matrix ``Q = A.T inv(A A.T)``
+        to the vector.  It can be shown that this
+        vector ``y = Q x``  the minimum norm solution
+        of ``A y = x``.
+
+    Notes
+    -----
+    Uses iterative refinements described in [1]
+    during the computation of ``Z`` in order to
+    cope with the possibility of large roundoff errors.
+
+    References
+    ----------
+    .. [1] Gould, Nicholas IM, Mary E. Hribar, and Jorge Nocedal.
+        "On the solution of equality constrained quadratic
+        programming problems arising in optimization."
+        SIAM Journal on Scientific Computing 23.4 (2001): 1376-1395.
+    """
+    m, n = np.shape(A)
+
+    # The factorization of an empty matrix
+    # only works for the sparse representation.
+    if m*n == 0:
+        A = csc_matrix(A)
+
+    # Check Argument
+    if issparse(A):
+        if method is None:
+            method = "AugmentedSystem"
+        if method not in ("NormalEquation", "AugmentedSystem"):
+            raise ValueError("Method not allowed for sparse matrix.")
+        if method == "NormalEquation" and not sksparse_available:
+            warnings.warn("Only accepts 'NormalEquation' option when "
+                          "scikit-sparse is available. Using "
+                          "'AugmentedSystem' option instead.",
+                          ImportWarning, stacklevel=3)
+            method = 'AugmentedSystem'
+    else:
+        if method is None:
+            method = "QRFactorization"
+        if method not in ("QRFactorization", "SVDFactorization"):
+            raise ValueError("Method not allowed for dense array.")
+
+    if method == 'NormalEquation':
+        null_space, least_squares, row_space \
+            = normal_equation_projections(A, m, n, orth_tol, max_refin, tol)
+    elif method == 'AugmentedSystem':
+        null_space, least_squares, row_space \
+            = augmented_system_projections(A, m, n, orth_tol, max_refin, tol)
+    elif method == "QRFactorization":
+        null_space, least_squares, row_space \
+            = qr_factorization_projections(A, m, n, orth_tol, max_refin, tol)
+    elif method == "SVDFactorization":
+        null_space, least_squares, row_space \
+            = svd_factorization_projections(A, m, n, orth_tol, max_refin, tol)
+
+    Z = LinearOperator((n, n), null_space)
+    LS = LinearOperator((m, n), least_squares)
+    Y = LinearOperator((n, m), row_space)
+
+    return Z, LS, Y

llava_next/lib/python3.10/site-packages/scipy/optimize/_trustregion_constr/qp_subproblem.py

@@ -0,0 +1,637 @@
+"""Equality-constrained quadratic programming solvers."""
+
+from scipy.sparse import (linalg, bmat, csc_matrix)
+from math import copysign
+import numpy as np
+from numpy.linalg import norm
+
+__all__ = [
+    'eqp_kktfact',
+    'sphere_intersections',
+    'box_intersections',
+    'box_sphere_intersections',
+    'inside_box_boundaries',
+    'modified_dogleg',
+    'projected_cg'
+]
+
+
+# For comparison with the projected CG
+def eqp_kktfact(H, c, A, b):
+    """Solve equality-constrained quadratic programming (EQP) problem.
+
+    Solve ``min 1/2 x.T H x + x.t c`` subject to ``A x + b = 0``
+    using direct factorization of the KKT system.
+
+    Parameters
+    ----------
+    H : sparse matrix, shape (n, n)
+        Hessian matrix of the EQP problem.
+    c : array_like, shape (n,)
+        Gradient of the quadratic objective function.
+    A : sparse matrix
+        Jacobian matrix of the EQP problem.
+    b : array_like, shape (m,)
+        Right-hand side of the constraint equation.
+
+    Returns
+    -------
+    x : array_like, shape (n,)
+        Solution of the KKT problem.
+    lagrange_multipliers : ndarray, shape (m,)
+        Lagrange multipliers of the KKT problem.
+    """
+    n, = np.shape(c)  # Number of parameters
+    m, = np.shape(b)  # Number of constraints
+
+    # Karush-Kuhn-Tucker matrix of coefficients.
+    # Defined as in Nocedal/Wright "Numerical
+    # Optimization" p.452 in Eq. (16.4).
+    kkt_matrix = csc_matrix(bmat([[H, A.T], [A, None]]))
+    # Vector of coefficients.
+    kkt_vec = np.hstack([-c, -b])
+
+    # TODO: Use a symmetric indefinite factorization
+    #       to solve the system twice as fast (because
+    #       of the symmetry).
+    lu = linalg.splu(kkt_matrix)
+    kkt_sol = lu.solve(kkt_vec)
+    x = kkt_sol[:n]
+    lagrange_multipliers = -kkt_sol[n:n+m]
+
+    return x, lagrange_multipliers
+
+
+def sphere_intersections(z, d, trust_radius,
+                         entire_line=False):
+    """Find the intersection between segment (or line) and spherical constraints.
+
+    Find the intersection between the segment (or line) defined by the
+    parametric  equation ``x(t) = z + t*d`` and the ball
+    ``||x|| <= trust_radius``.
+
+    Parameters
+    ----------
+    z : array_like, shape (n,)
+        Initial point.
+    d : array_like, shape (n,)
+        Direction.
+    trust_radius : float
+        Ball radius.
+    entire_line : bool, optional
+        When ``True``, the function returns the intersection between the line
+        ``x(t) = z + t*d`` (``t`` can assume any value) and the ball
+        ``||x|| <= trust_radius``. When ``False``, the function returns the intersection
+        between the segment ``x(t) = z + t*d``, ``0 <= t <= 1``, and the ball.
+
+    Returns
+    -------
+    ta, tb : float
+        The line/segment ``x(t) = z + t*d`` is inside the ball for
+        for ``ta <= t <= tb``.
+    intersect : bool
+        When ``True``, there is a intersection between the line/segment
+        and the sphere. On the other hand, when ``False``, there is no
+        intersection.
+    """
+    # Special case when d=0
+    if norm(d) == 0:
+        return 0, 0, False
+    # Check for inf trust_radius
+    if np.isinf(trust_radius):
+        if entire_line:
+            ta = -np.inf
+            tb = np.inf
+        else:
+            ta = 0
+            tb = 1
+        intersect = True
+        return ta, tb, intersect
+
+    a = np.dot(d, d)
+    b = 2 * np.dot(z, d)
+    c = np.dot(z, z) - trust_radius**2
+    discriminant = b*b - 4*a*c
+    if discriminant < 0:
+        intersect = False
+        return 0, 0, intersect
+    sqrt_discriminant = np.sqrt(discriminant)
+
+    # The following calculation is mathematically
+    # equivalent to:
+    # ta = (-b - sqrt_discriminant) / (2*a)
+    # tb = (-b + sqrt_discriminant) / (2*a)
+    # but produce smaller round off errors.
+    # Look at Matrix Computation p.97
+    # for a better justification.
+    aux = b + copysign(sqrt_discriminant, b)
+    ta = -aux / (2*a)
+    tb = -2*c / aux
+    ta, tb = sorted([ta, tb])
+
+    if entire_line:
+        intersect = True
+    else:
+        # Checks to see if intersection happens
+        # within vectors length.
+        if tb < 0 or ta > 1:
+            intersect = False
+            ta = 0
+            tb = 0
+        else:
+            intersect = True
+            # Restrict intersection interval
+            # between 0 and 1.
+            ta = max(0, ta)
+            tb = min(1, tb)
+
+    return ta, tb, intersect
+
+
+def box_intersections(z, d, lb, ub,
+                      entire_line=False):
+    """Find the intersection between segment (or line) and box constraints.
+
+    Find the intersection between the segment (or line) defined by the
+    parametric  equation ``x(t) = z + t*d`` and the rectangular box
+    ``lb <= x <= ub``.
+
+    Parameters
+    ----------
+    z : array_like, shape (n,)
+        Initial point.
+    d : array_like, shape (n,)
+        Direction.
+    lb : array_like, shape (n,)
+        Lower bounds to each one of the components of ``x``. Used
+        to delimit the rectangular box.
+    ub : array_like, shape (n, )
+        Upper bounds to each one of the components of ``x``. Used
+        to delimit the rectangular box.
+    entire_line : bool, optional
+        When ``True``, the function returns the intersection between the line
+        ``x(t) = z + t*d`` (``t`` can assume any value) and the rectangular
+        box. When ``False``, the function returns the intersection between the segment
+        ``x(t) = z + t*d``, ``0 <= t <= 1``, and the rectangular box.
+
+    Returns
+    -------
+    ta, tb : float
+        The line/segment ``x(t) = z + t*d`` is inside the box for
+        for ``ta <= t <= tb``.
+    intersect : bool
+        When ``True``, there is a intersection between the line (or segment)
+        and the rectangular box. On the other hand, when ``False``, there is no
+        intersection.
+    """
+    # Make sure it is a numpy array
+    z = np.asarray(z)
+    d = np.asarray(d)
+    lb = np.asarray(lb)
+    ub = np.asarray(ub)
+    # Special case when d=0
+    if norm(d) == 0:
+        return 0, 0, False
+
+    # Get values for which d==0
+    zero_d = (d == 0)
+    # If the boundaries are not satisfied for some coordinate
+    # for which "d" is zero, there is no box-line intersection.
+    if (z[zero_d] < lb[zero_d]).any() or (z[zero_d] > ub[zero_d]).any():
+        intersect = False
+        return 0, 0, intersect
+    # Remove values for which d is zero
+    not_zero_d = np.logical_not(zero_d)
+    z = z[not_zero_d]
+    d = d[not_zero_d]
+    lb = lb[not_zero_d]
+    ub = ub[not_zero_d]
+
+    # Find a series of intervals (t_lb[i], t_ub[i]).
+    t_lb = (lb-z) / d
+    t_ub = (ub-z) / d
+    # Get the intersection of all those intervals.
+    ta = max(np.minimum(t_lb, t_ub))
+    tb = min(np.maximum(t_lb, t_ub))
+
+    # Check if intersection is feasible
+    if ta <= tb:
+        intersect = True
+    else:
+        intersect = False
+    # Checks to see if intersection happens within vectors length.
+    if not entire_line:
+        if tb < 0 or ta > 1:
+            intersect = False
+            ta = 0
+            tb = 0
+        else:
+            # Restrict intersection interval between 0 and 1.
+            ta = max(0, ta)
+            tb = min(1, tb)
+
+    return ta, tb, intersect
+
+
+def box_sphere_intersections(z, d, lb, ub, trust_radius,
+                             entire_line=False,
+                             extra_info=False):
+    """Find the intersection between segment (or line) and box/sphere constraints.
+
+    Find the intersection between the segment (or line) defined by the
+    parametric  equation ``x(t) = z + t*d``, the rectangular box
+    ``lb <= x <= ub`` and the ball ``||x|| <= trust_radius``.
+
+    Parameters
+    ----------
+    z : array_like, shape (n,)
+        Initial point.
+    d : array_like, shape (n,)
+        Direction.
+    lb : array_like, shape (n,)
+        Lower bounds to each one of the components of ``x``. Used
+        to delimit the rectangular box.
+    ub : array_like, shape (n, )
+        Upper bounds to each one of the components of ``x``. Used
+        to delimit the rectangular box.
+    trust_radius : float
+        Ball radius.
+    entire_line : bool, optional
+        When ``True``, the function returns the intersection between the line
+        ``x(t) = z + t*d`` (``t`` can assume any value) and the constraints.
+        When ``False``, the function returns the intersection between the segment
+        ``x(t) = z + t*d``, ``0 <= t <= 1`` and the constraints.
+    extra_info : bool, optional
+        When ``True``, the function returns ``intersect_sphere`` and ``intersect_box``.
+
+    Returns
+    -------
+    ta, tb : float
+        The line/segment ``x(t) = z + t*d`` is inside the rectangular box and
+        inside the ball for ``ta <= t <= tb``.
+    intersect : bool
+        When ``True``, there is a intersection between the line (or segment)
+        and both constraints. On the other hand, when ``False``, there is no
+        intersection.
+    sphere_info : dict, optional
+        Dictionary ``{ta, tb, intersect}`` containing the interval ``[ta, tb]``
+        for which the line intercepts the ball. And a boolean value indicating
+        whether the sphere is intersected by the line.
+    box_info : dict, optional
+        Dictionary ``{ta, tb, intersect}`` containing the interval ``[ta, tb]``
+        for which the line intercepts the box. And a boolean value indicating
+        whether the box is intersected by the line.
+    """
+    ta_b, tb_b, intersect_b = box_intersections(z, d, lb, ub,
+                                                entire_line)
+    ta_s, tb_s, intersect_s = sphere_intersections(z, d,
+                                                   trust_radius,
+                                                   entire_line)
+    ta = np.maximum(ta_b, ta_s)
+    tb = np.minimum(tb_b, tb_s)
+    if intersect_b and intersect_s and ta <= tb:
+        intersect = True
+    else:
+        intersect = False
+
+    if extra_info:
+        sphere_info = {'ta': ta_s, 'tb': tb_s, 'intersect': intersect_s}
+        box_info = {'ta': ta_b, 'tb': tb_b, 'intersect': intersect_b}
+        return ta, tb, intersect, sphere_info, box_info
+    else:
+        return ta, tb, intersect
+
+
+def inside_box_boundaries(x, lb, ub):
+    """Check if lb <= x <= ub."""
+    return (lb <= x).all() and (x <= ub).all()
+
+
+def reinforce_box_boundaries(x, lb, ub):
+    """Return clipped value of x"""
+    return np.minimum(np.maximum(x, lb), ub)
+
+
+def modified_dogleg(A, Y, b, trust_radius, lb, ub):
+    """Approximately  minimize ``1/2*|| A x + b ||^2`` inside trust-region.
+
+    Approximately solve the problem of minimizing ``1/2*|| A x + b ||^2``
+    subject to ``||x|| < Delta`` and ``lb <= x <= ub`` using a modification
+    of the classical dogleg approach.
+
+    Parameters
+    ----------
+    A : LinearOperator (or sparse matrix or ndarray), shape (m, n)
+        Matrix ``A`` in the minimization problem. It should have
+        dimension ``(m, n)`` such that ``m < n``.
+    Y : LinearOperator (or sparse matrix or ndarray), shape (n, m)
+        LinearOperator that apply the projection matrix
+        ``Q = A.T inv(A A.T)`` to the vector. The obtained vector
+        ``y = Q x`` being the minimum norm solution of ``A y = x``.
+    b : array_like, shape (m,)
+        Vector ``b``in the minimization problem.
+    trust_radius: float
+        Trust radius to be considered. Delimits a sphere boundary
+        to the problem.
+    lb : array_like, shape (n,)
+        Lower bounds to each one of the components of ``x``.
+        It is expected that ``lb <= 0``, otherwise the algorithm
+        may fail. If ``lb[i] = -Inf``, the lower
+        bound for the ith component is just ignored.
+    ub : array_like, shape (n, )
+        Upper bounds to each one of the components of ``x``.
+        It is expected that ``ub >= 0``, otherwise the algorithm
+        may fail. If ``ub[i] = Inf``, the upper bound for the ith
+        component is just ignored.
+
+    Returns
+    -------
+    x : array_like, shape (n,)
+        Solution to the problem.
+
+    Notes
+    -----
+    Based on implementations described in pp. 885-886 from [1]_.
+
+    References
+    ----------
+    .. [1] Byrd, Richard H., Mary E. Hribar, and Jorge Nocedal.
+           "An interior point algorithm for large-scale nonlinear
+           programming." SIAM Journal on Optimization 9.4 (1999): 877-900.
+    """
+    # Compute minimum norm minimizer of 1/2*|| A x + b ||^2.
+    newton_point = -Y.dot(b)
+    # Check for interior point
+    if inside_box_boundaries(newton_point, lb, ub)  \
+       and norm(newton_point) <= trust_radius:
+        x = newton_point
+        return x
+
+    # Compute gradient vector ``g = A.T b``
+    g = A.T.dot(b)
+    # Compute Cauchy point
+    # `cauchy_point = g.T g / (g.T A.T A g)``.
+    A_g = A.dot(g)
+    cauchy_point = -np.dot(g, g) / np.dot(A_g, A_g) * g
+    # Origin
+    origin_point = np.zeros_like(cauchy_point)
+
+    # Check the segment between cauchy_point and newton_point
+    # for a possible solution.
+    z = cauchy_point
+    p = newton_point - cauchy_point
+    _, alpha, intersect = box_sphere_intersections(z, p, lb, ub,
+                                                   trust_radius)
+    if intersect:
+        x1 = z + alpha*p
+    else:
+        # Check the segment between the origin and cauchy_point
+        # for a possible solution.
+        z = origin_point
+        p = cauchy_point
+        _, alpha, _ = box_sphere_intersections(z, p, lb, ub,
+                                               trust_radius)
+        x1 = z + alpha*p
+
+    # Check the segment between origin and newton_point
+    # for a possible solution.
+    z = origin_point
+    p = newton_point
+    _, alpha, _ = box_sphere_intersections(z, p, lb, ub,
+                                           trust_radius)
+    x2 = z + alpha*p
+
+    # Return the best solution among x1 and x2.
+    if norm(A.dot(x1) + b) < norm(A.dot(x2) + b):
+        return x1
+    else:
+        return x2
+
+
+def projected_cg(H, c, Z, Y, b, trust_radius=np.inf,
+                 lb=None, ub=None, tol=None,
+                 max_iter=None, max_infeasible_iter=None,
+                 return_all=False):
+    """Solve EQP problem with projected CG method.
+
+    Solve equality-constrained quadratic programming problem
+    ``min 1/2 x.T H x + x.t c``  subject to ``A x + b = 0`` and,
+    possibly, to trust region constraints ``||x|| < trust_radius``
+    and box constraints ``lb <= x <= ub``.
+
+    Parameters
+    ----------
+    H : LinearOperator (or sparse matrix or ndarray), shape (n, n)
+        Operator for computing ``H v``.
+    c : array_like, shape (n,)
+        Gradient of the quadratic objective function.
+    Z : LinearOperator (or sparse matrix or ndarray), shape (n, n)
+        Operator for projecting ``x`` into the null space of A.
+    Y : LinearOperator,  sparse matrix, ndarray, shape (n, m)
+        Operator that, for a given a vector ``b``, compute smallest
+        norm solution of ``A x + b = 0``.
+    b : array_like, shape (m,)
+        Right-hand side of the constraint equation.
+    trust_radius : float, optional
+        Trust radius to be considered. By default, uses ``trust_radius=inf``,
+        which means no trust radius at all.
+    lb : array_like, shape (n,), optional
+        Lower bounds to each one of the components of ``x``.
+        If ``lb[i] = -Inf`` the lower bound for the i-th
+        component is just ignored (default).
+    ub : array_like, shape (n, ), optional
+        Upper bounds to each one of the components of ``x``.
+        If ``ub[i] = Inf`` the upper bound for the i-th
+        component is just ignored (default).
+    tol : float, optional
+        Tolerance used to interrupt the algorithm.
+    max_iter : int, optional
+        Maximum algorithm iterations. Where ``max_inter <= n-m``.
+        By default, uses ``max_iter = n-m``.
+    max_infeasible_iter : int, optional
+        Maximum infeasible (regarding box constraints) iterations the
+        algorithm is allowed to take.
+        By default, uses ``max_infeasible_iter = n-m``.
+    return_all : bool, optional
+        When ``true``, return the list of all vectors through the iterations.
+
+    Returns
+    -------
+    x : array_like, shape (n,)
+        Solution of the EQP problem.
+    info : Dict
+        Dictionary containing the following:
+
+            - niter : Number of iterations.
+            - stop_cond : Reason for algorithm termination:
+                1. Iteration limit was reached;
+                2. Reached the trust-region boundary;
+                3. Negative curvature detected;
+                4. Tolerance was satisfied.
+            - allvecs : List containing all intermediary vectors (optional).
+            - hits_boundary : True if the proposed step is on the boundary
+              of the trust region.
+
+    Notes
+    -----
+    Implementation of Algorithm 6.2 on [1]_.
+
+    In the absence of spherical and box constraints, for sufficient
+    iterations, the method returns a truly optimal result.
+    In the presence of those constraints, the value returned is only
+    a inexpensive approximation of the optimal value.
+
+    References
+    ----------
+    .. [1] Gould, Nicholas IM, Mary E. Hribar, and Jorge Nocedal.
+           "On the solution of equality constrained quadratic
+            programming problems arising in optimization."
+            SIAM Journal on Scientific Computing 23.4 (2001): 1376-1395.
+    """
+    CLOSE_TO_ZERO = 1e-25
+
+    n, = np.shape(c)  # Number of parameters
+    m, = np.shape(b)  # Number of constraints
+
+    # Initial Values
+    x = Y.dot(-b)
+    r = Z.dot(H.dot(x) + c)
+    g = Z.dot(r)
+    p = -g
+
+    # Store ``x`` value
+    if return_all:
+        allvecs = [x]
+    # Values for the first iteration
+    H_p = H.dot(p)
+    rt_g = norm(g)**2  # g.T g = r.T Z g = r.T g (ref [1]_ p.1389)
+
+    # If x > trust-region the problem does not have a solution.
+    tr_distance = trust_radius - norm(x)
+    if tr_distance < 0:
+        raise ValueError("Trust region problem does not have a solution.")
+    # If x == trust_radius, then x is the solution
+    # to the optimization problem, since x is the
+    # minimum norm solution to Ax=b.
+    elif tr_distance < CLOSE_TO_ZERO:
+        info = {'niter': 0, 'stop_cond': 2, 'hits_boundary': True}
+        if return_all:
+            allvecs.append(x)
+            info['allvecs'] = allvecs
+        return x, info
+
+    # Set default tolerance
+    if tol is None:
+        tol = max(min(0.01 * np.sqrt(rt_g), 0.1 * rt_g), CLOSE_TO_ZERO)
+    # Set default lower and upper bounds
+    if lb is None:
+        lb = np.full(n, -np.inf)
+    if ub is None:
+        ub = np.full(n, np.inf)
+    # Set maximum iterations
+    if max_iter is None:
+        max_iter = n-m
+    max_iter = min(max_iter, n-m)
+    # Set maximum infeasible iterations
+    if max_infeasible_iter is None:
+        max_infeasible_iter = n-m
+
+    hits_boundary = False
+    stop_cond = 1
+    counter = 0
+    last_feasible_x = np.zeros_like(x)
+    k = 0
+    for i in range(max_iter):
+        # Stop criteria - Tolerance : r.T g < tol
+        if rt_g < tol:
+            stop_cond = 4
+            break
+        k += 1
+        # Compute curvature
+        pt_H_p = H_p.dot(p)
+        # Stop criteria - Negative curvature
+        if pt_H_p <= 0:
+            if np.isinf(trust_radius):
+                raise ValueError("Negative curvature not allowed "
+                                 "for unrestricted problems.")
+            else:
+                # Find intersection with constraints
+                _, alpha, intersect = box_sphere_intersections(
+                    x, p, lb, ub, trust_radius, entire_line=True)
+                # Update solution
+                if intersect:
+                    x = x + alpha*p
+                # Reinforce variables are inside box constraints.
+                # This is only necessary because of roundoff errors.
+                x = reinforce_box_boundaries(x, lb, ub)
+                # Attribute information
+                stop_cond = 3
+                hits_boundary = True
+                break
+
+        # Get next step
+        alpha = rt_g / pt_H_p
+        x_next = x + alpha*p
+
+        # Stop criteria - Hits boundary
+        if np.linalg.norm(x_next) >= trust_radius:
+            # Find intersection with box constraints
+            _, theta, intersect = box_sphere_intersections(x, alpha*p, lb, ub,
+                                                           trust_radius)
+            # Update solution
+            if intersect:
+                x = x + theta*alpha*p
+            # Reinforce variables are inside box constraints.
+            # This is only necessary because of roundoff errors.
+            x = reinforce_box_boundaries(x, lb, ub)
+            # Attribute information
+            stop_cond = 2
+            hits_boundary = True
+            break
+
+        # Check if ``x`` is inside the box and start counter if it is not.
+        if inside_box_boundaries(x_next, lb, ub):
+            counter = 0
+        else:
+            counter += 1
+        # Whenever outside box constraints keep looking for intersections.
+        if counter > 0:
+            _, theta, intersect = box_sphere_intersections(x, alpha*p, lb, ub,
+                                                           trust_radius)
+            if intersect:
+                last_feasible_x = x + theta*alpha*p
+                # Reinforce variables are inside box constraints.
+                # This is only necessary because of roundoff errors.
+                last_feasible_x = reinforce_box_boundaries(last_feasible_x,
+                                                           lb, ub)
+                counter = 0
+        # Stop after too many infeasible (regarding box constraints) iteration.
+        if counter > max_infeasible_iter:
+            break
+        # Store ``x_next`` value
+        if return_all:
+            allvecs.append(x_next)
+
+        # Update residual
+        r_next = r + alpha*H_p
+        # Project residual g+ = Z r+
+        g_next = Z.dot(r_next)
+        # Compute conjugate direction step d
+        rt_g_next = norm(g_next)**2  # g.T g = r.T g (ref [1]_ p.1389)
+        beta = rt_g_next / rt_g
+        p = - g_next + beta*p
+        # Prepare for next iteration
+        x = x_next
+        g = g_next
+        r = g_next
+        rt_g = norm(g)**2  # g.T g = r.T Z g = r.T g (ref [1]_ p.1389)
+        H_p = H.dot(p)
+
+    if not inside_box_boundaries(x, lb, ub):
+        x = last_feasible_x
+        hits_boundary = True
+    info = {'niter': k, 'stop_cond': stop_cond,
+            'hits_boundary': hits_boundary}
+    if return_all:
+        info['allvecs'] = allvecs
+    return x, info

llava_next/lib/python3.10/site-packages/scipy/optimize/_trustregion_constr/report.py

@@ -0,0 +1,51 @@
+"""Progress report printers."""
+
+from __future__ import annotations
+
+class ReportBase:
+    COLUMN_NAMES: list[str] = NotImplemented
+    COLUMN_WIDTHS: list[int] = NotImplemented
+    ITERATION_FORMATS: list[str] = NotImplemented
+
+    @classmethod
+    def print_header(cls):
+        fmt = ("|"
+               + "|".join([f"{{:^{x}}}" for x in cls.COLUMN_WIDTHS])
+               + "|")
+        separators = ['-' * x for x in cls.COLUMN_WIDTHS]
+        print(fmt.format(*cls.COLUMN_NAMES))
+        print(fmt.format(*separators))
+
+    @classmethod
+    def print_iteration(cls, *args):
+        iteration_format = [f"{{:{x}}}" for x in cls.ITERATION_FORMATS]
+        fmt = "|" + "|".join(iteration_format) + "|"
+        print(fmt.format(*args))
+
+    @classmethod
+    def print_footer(cls):
+        print()
+
+
+class BasicReport(ReportBase):
+    COLUMN_NAMES = ["niter", "f evals", "CG iter", "obj func", "tr radius",
+                    "opt", "c viol"]
+    COLUMN_WIDTHS = [7, 7, 7, 13, 10, 10, 10]
+    ITERATION_FORMATS = ["^7", "^7", "^7", "^+13.4e",
+                         "^10.2e", "^10.2e", "^10.2e"]
+
+
+class SQPReport(ReportBase):
+    COLUMN_NAMES = ["niter", "f evals", "CG iter", "obj func", "tr radius",
+                    "opt", "c viol", "penalty", "CG stop"]
+    COLUMN_WIDTHS = [7, 7, 7, 13, 10, 10, 10, 10, 7]
+    ITERATION_FORMATS = ["^7", "^7", "^7", "^+13.4e", "^10.2e", "^10.2e",
+                         "^10.2e", "^10.2e", "^7"]
+
+
+class IPReport(ReportBase):
+    COLUMN_NAMES = ["niter", "f evals", "CG iter", "obj func", "tr radius",
+                    "opt", "c viol", "penalty", "barrier param", "CG stop"]
+    COLUMN_WIDTHS = [7, 7, 7, 13, 10, 10, 10, 10, 13, 7]
+    ITERATION_FORMATS = ["^7", "^7", "^7", "^+13.4e", "^10.2e", "^10.2e",
+                         "^10.2e", "^10.2e", "^13.2e", "^7"]