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#include <variant> |
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#include <nanobind/nanobind.h> |
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#include <nanobind/stl/pair.h> |
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#include <nanobind/stl/string.h> |
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#include <nanobind/stl/variant.h> |
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#include <nanobind/stl/vector.h> |
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#include "mlx/linalg.h" |
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#include "python/src/small_vector.h" |
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namespace mx = mlx::core; |
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namespace nb = nanobind; |
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using namespace nb::literals; |
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void init_linalg(nb::module_& parent_module) { |
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auto m = parent_module.def_submodule( |
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"linalg", "mlx.core.linalg: linear algebra routines."); |
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m.def( |
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"norm", |
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[](const mx::array& a, |
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const std::variant<std::monostate, int, double, std::string>& ord_, |
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const std::variant<std::monostate, int, std::vector<int>>& axis_, |
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const bool keepdims, |
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const mx::StreamOrDevice stream) { |
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std::optional<std::vector<int>> axis = std::nullopt; |
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if (auto pv = std::get_if<int>(&axis_); pv) { |
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axis = std::vector<int>{*pv}; |
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} else if (auto pv = std::get_if<std::vector<int>>(&axis_); pv) { |
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axis = *pv; |
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} |
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if (std::holds_alternative<std::monostate>(ord_)) { |
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return mx::linalg::norm(a, axis, keepdims, stream); |
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} else { |
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if (auto pv = std::get_if<std::string>(&ord_); pv) { |
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return mx::linalg::norm(a, *pv, axis, keepdims, stream); |
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} |
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double ord; |
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if (auto pv = std::get_if<int>(&ord_); pv) { |
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ord = *pv; |
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} else { |
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ord = std::get<double>(ord_); |
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} |
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return mx::linalg::norm(a, ord, axis, keepdims, stream); |
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} |
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}, |
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nb::arg(), |
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"ord"_a = nb::none(), |
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"axis"_a = nb::none(), |
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"keepdims"_a = false, |
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nb::kw_only(), |
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"stream"_a = nb::none(), |
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nb::sig( |
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"def norm(a: array, /, ord: Union[None, int, float, str] = None, axis: Union[None, int, list[int]] = None, keepdims: bool = False, *, stream: Union[None, Stream, Device] = None) -> array"), |
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R"pbdoc( |
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Matrix or vector norm. |
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This function computes vector or matrix norms depending on the value of |
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the ``ord`` and ``axis`` parameters. |
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Args: |
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a (array): Input array. If ``axis`` is ``None``, ``a`` must be 1-D or 2-D, |
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unless ``ord`` is ``None``. If both ``axis`` and ``ord`` are ``None``, the |
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2-norm of ``a.flatten`` will be returned. |
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ord (int, float or str, optional): Order of the norm (see table under ``Notes``). |
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If ``None``, the 2-norm (or Frobenius norm for matrices) will be computed |
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along the given ``axis``. Default: ``None``. |
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axis (int or list(int), optional): If ``axis`` is an integer, it specifies the |
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axis of ``a`` along which to compute the vector norms. If ``axis`` is a |
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2-tuple, it specifies the axes that hold 2-D matrices, and the matrix |
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norms of these matrices are computed. If `axis` is ``None`` then |
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either a vector norm (when ``a`` is 1-D) or a matrix norm (when ``a`` is |
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2-D) is returned. Default: ``None``. |
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keepdims (bool, optional): If ``True``, the axes which are normed over are |
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left in the result as dimensions with size one. Default ``False``. |
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Returns: |
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array: The output containing the norm(s). |
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Notes: |
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For values of ``ord < 1``, the result is, strictly speaking, not a |
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mathematical norm, but it may still be useful for various numerical |
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purposes. |
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The following norms can be calculated: |
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===== ============================ ========================== |
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ord norm for matrices norm for vectors |
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===== ============================ ========================== |
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None Frobenius norm 2-norm |
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'fro' Frobenius norm -- |
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'nuc' nuclear norm -- |
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inf max(sum(abs(x), axis=1)) max(abs(x)) |
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-inf min(sum(abs(x), axis=1)) min(abs(x)) |
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0 -- sum(x != 0) |
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1 max(sum(abs(x), axis=0)) as below |
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-1 min(sum(abs(x), axis=0)) as below |
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2 2-norm (largest sing. value) as below |
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-2 smallest singular value as below |
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other -- sum(abs(x)**ord)**(1./ord) |
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===== ============================ ========================== |
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The Frobenius norm is given by [1]_: |
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:math:`||A||_F = [\sum_{i,j} abs(a_{i,j})^2]^{1/2}` |
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The nuclear norm is the sum of the singular values. |
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Both the Frobenius and nuclear norm orders are only defined for |
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matrices and raise a ``ValueError`` when ``a.ndim != 2``. |
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References: |
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.. [1] G. H. Golub and C. F. Van Loan, *Matrix Computations*, |
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Baltimore, MD, Johns Hopkins University Press, 1985, pg. 15 |
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Examples: |
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>>> import mlx.core as mx |
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>>> from mlx.core import linalg as la |
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>>> a = mx.arange(9) - 4 |
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>>> a |
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array([-4, -3, -2, ..., 2, 3, 4], dtype=int32) |
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>>> b = a.reshape((3,3)) |
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>>> b |
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array([[-4, -3, -2], |
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[-1, 0, 1], |
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[ 2, 3, 4]], dtype=int32) |
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>>> la.norm(a) |
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array(7.74597, dtype=float32) |
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>>> la.norm(b) |
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array(7.74597, dtype=float32) |
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>>> la.norm(b, 'fro') |
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array(7.74597, dtype=float32) |
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>>> la.norm(a, float("inf")) |
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array(4, dtype=float32) |
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>>> la.norm(b, float("inf")) |
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array(9, dtype=float32) |
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>>> la.norm(a, -float("inf")) |
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array(0, dtype=float32) |
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>>> la.norm(b, -float("inf")) |
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array(2, dtype=float32) |
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>>> la.norm(a, 1) |
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array(20, dtype=float32) |
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>>> la.norm(b, 1) |
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array(7, dtype=float32) |
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>>> la.norm(a, -1) |
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array(0, dtype=float32) |
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>>> la.norm(b, -1) |
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array(6, dtype=float32) |
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>>> la.norm(a, 2) |
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array(7.74597, dtype=float32) |
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>>> la.norm(a, 3) |
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array(5.84804, dtype=float32) |
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>>> la.norm(a, -3) |
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array(0, dtype=float32) |
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>>> c = mx.array([[ 1, 2, 3], |
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... [-1, 1, 4]]) |
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>>> la.norm(c, axis=0) |
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array([1.41421, 2.23607, 5], dtype=float32) |
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>>> la.norm(c, axis=1) |
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array([3.74166, 4.24264], dtype=float32) |
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>>> la.norm(c, ord=1, axis=1) |
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array([6, 6], dtype=float32) |
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>>> m = mx.arange(8).reshape(2,2,2) |
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>>> la.norm(m, axis=(1,2)) |
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array([3.74166, 11.225], dtype=float32) |
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>>> la.norm(m[0, :, :]), LA.norm(m[1, :, :]) |
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(array(3.74166, dtype=float32), array(11.225, dtype=float32)) |
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)pbdoc"); |
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m.def( |
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"qr", |
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&mx::linalg::qr, |
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"a"_a, |
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nb::kw_only(), |
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"stream"_a = nb::none(), |
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nb::sig( |
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"def qr(a: array, *, stream: Union[None, Stream, Device] = None) -> Tuple[array, array]"), |
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R"pbdoc( |
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The QR factorization of the input matrix. |
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This function supports arrays with at least 2 dimensions. The matrices |
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which are factorized are assumed to be in the last two dimensions of |
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the input. |
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Args: |
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a (array): Input array. |
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stream (Stream, optional): Stream or device. Defaults to ``None`` |
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in which case the default stream of the default device is used. |
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Returns: |
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tuple(array, array): ``Q`` and ``R`` matrices such that ``Q @ R = a``. |
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Example: |
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>>> A = mx.array([[2., 3.], [1., 2.]]) |
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>>> Q, R = mx.linalg.qr(A, stream=mx.cpu) |
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>>> Q |
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array([[-0.894427, -0.447214], |
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[-0.447214, 0.894427]], dtype=float32) |
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>>> R |
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array([[-2.23607, -3.57771], |
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[0, 0.447214]], dtype=float32) |
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)pbdoc"); |
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m.def( |
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"svd", |
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[](const mx::array& a, |
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bool compute_uv , |
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mx::StreamOrDevice s ) -> nb::object { |
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const auto result = mx::linalg::svd(a, compute_uv, s); |
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if (result.size() == 1) { |
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return nb::cast(result.at(0)); |
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} else { |
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return nb::make_tuple(result.at(0), result.at(1), result.at(2)); |
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} |
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}, |
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"a"_a, |
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"compute_uv"_a = true, |
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nb::kw_only(), |
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"stream"_a = nb::none(), |
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nb::sig( |
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"def svd(a: array, compute_uv: bool = True, *, stream: Union[None, Stream, Device] = None) -> Tuple[array, array, array]"), |
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R"pbdoc( |
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The Singular Value Decomposition (SVD) of the input matrix. |
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This function supports arrays with at least 2 dimensions. When the input |
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has more than two dimensions, the function iterates over all indices of the first |
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a.ndim - 2 dimensions and for each combination SVD is applied to the last two indices. |
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Args: |
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a (array): Input array. |
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compute_uv (bool, optional): If ``True``, return the ``U``, ``S``, and ``Vt`` components. |
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If ``False``, return only the ``S`` array. Default: ``True``. |
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stream (Stream, optional): Stream or device. Defaults to ``None`` |
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in which case the default stream of the default device is used. |
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Returns: |
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Union[tuple(array, ...), array]: |
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If compute_uv is ``True`` returns the ``U``, ``S``, and ``Vt`` matrices, such that |
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``A = U @ diag(S) @ Vt``. If compute_uv is ``False`` returns singular values array ``S``. |
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)pbdoc"); |
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m.def( |
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"inv", |
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&mx::linalg::inv, |
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"a"_a, |
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nb::kw_only(), |
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"stream"_a = nb::none(), |
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nb::sig( |
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"def inv(a: array, *, stream: Union[None, Stream, Device] = None) -> array"), |
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R"pbdoc( |
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Compute the inverse of a square matrix. |
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This function supports arrays with at least 2 dimensions. When the input |
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has more than two dimensions, the inverse is computed for each matrix |
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in the last two dimensions of ``a``. |
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Args: |
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a (array): Input array. |
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stream (Stream, optional): Stream or device. Defaults to ``None`` |
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in which case the default stream of the default device is used. |
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Returns: |
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array: ``ainv`` such that ``dot(a, ainv) = dot(ainv, a) = eye(a.shape[0])`` |
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)pbdoc"); |
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m.def( |
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"tri_inv", |
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&mx::linalg::tri_inv, |
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"a"_a, |
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"upper"_a = false, |
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nb::kw_only(), |
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"stream"_a = nb::none(), |
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nb::sig( |
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"def tri_inv(a: array, upper: bool = False, *, stream: Union[None, Stream, Device] = None) -> array"), |
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R"pbdoc( |
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Compute the inverse of a triangular square matrix. |
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This function supports arrays with at least 2 dimensions. When the input |
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has more than two dimensions, the inverse is computed for each matrix |
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in the last two dimensions of ``a``. |
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Args: |
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a (array): Input array. |
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upper (bool, optional): Whether the array is upper or lower triangular. Defaults to ``False``. |
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stream (Stream, optional): Stream or device. Defaults to ``None`` |
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in which case the default stream of the default device is used. |
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Returns: |
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array: ``ainv`` such that ``dot(a, ainv) = dot(ainv, a) = eye(a.shape[0])`` |
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)pbdoc"); |
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m.def( |
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"cholesky", |
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&mx::linalg::cholesky, |
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"a"_a, |
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"upper"_a = false, |
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nb::kw_only(), |
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"stream"_a = nb::none(), |
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nb::sig( |
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"def cholesky(a: array, upper: bool = False, *, stream: Union[None, Stream, Device] = None) -> array"), |
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R"pbdoc( |
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Compute the Cholesky decomposition of a real symmetric positive semi-definite matrix. |
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This function supports arrays with at least 2 dimensions. When the input |
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has more than two dimensions, the Cholesky decomposition is computed for each matrix |
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in the last two dimensions of ``a``. |
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If the input matrix is not symmetric positive semi-definite, behaviour is undefined. |
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Args: |
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a (array): Input array. |
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upper (bool, optional): If ``True``, return the upper triangular Cholesky factor. |
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If ``False``, return the lower triangular Cholesky factor. Default: ``False``. |
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stream (Stream, optional): Stream or device. Defaults to ``None`` |
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in which case the default stream of the default device is used. |
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Returns: |
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array: If ``upper = False``, it returns a lower triangular ``L`` matrix such |
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that ``L @ L.T = a``. If ``upper = True``, it returns an upper triangular |
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``U`` matrix such that ``U.T @ U = a``. |
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)pbdoc"); |
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m.def( |
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"cholesky_inv", |
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&mx::linalg::cholesky_inv, |
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"a"_a, |
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"upper"_a = false, |
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nb::kw_only(), |
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"stream"_a = nb::none(), |
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nb::sig( |
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"def cholesky_inv(L: array, upper: bool = False, *, stream: Union[None, Stream, Device] = None) -> array"), |
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R"pbdoc( |
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Compute the inverse of a real symmetric positive semi-definite matrix using it's Cholesky decomposition. |
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Let :math:`\mathbf{A}` be a real symmetric positive semi-definite matrix and :math:`\mathbf{L}` its Cholesky decomposition such that: |
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.. math:: |
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\begin{aligned} |
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\mathbf{A} = \mathbf{L}\mathbf{L}^T |
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\end{aligned} |
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This function computes :math:`\mathbf{A}^{-1}`. |
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This function supports arrays with at least 2 dimensions. When the input |
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has more than two dimensions, the Cholesky inverse is computed for each matrix |
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in the last two dimensions of :math:`\mathbf{L}`. |
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If the input matrix is not a triangular matrix behaviour is undefined. |
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Args: |
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L (array): Input array. |
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upper (bool, optional): If ``True``, return the upper triangular Cholesky factor. |
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If ``False``, return the lower triangular Cholesky factor. Default: ``False``. |
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stream (Stream, optional): Stream or device. Defaults to ``None`` |
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in which case the default stream of the default device is used. |
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Returns: |
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array: :math:`\mathbf{A^{-1}}` where :math:`\mathbf{A} = \mathbf{L}\mathbf{L}^T`. |
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)pbdoc"); |
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m.def( |
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"pinv", |
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&mx::linalg::pinv, |
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"a"_a, |
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nb::kw_only(), |
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"stream"_a = nb::none(), |
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nb::sig( |
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"def pinv(a: array, *, stream: Union[None, Stream, Device] = None) -> array"), |
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R"pbdoc( |
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Compute the (Moore-Penrose) pseudo-inverse of a matrix. |
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This function calculates a generalized inverse of a matrix using its |
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singular-value decomposition. This function supports arrays with at least 2 dimensions. |
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When the input has more than two dimensions, the inverse is computed for each |
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matrix in the last two dimensions of ``a``. |
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|
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Args: |
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a (array): Input array. |
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stream (Stream, optional): Stream or device. Defaults to ``None`` |
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in which case the default stream of the default device is used. |
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Returns: |
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array: ``aplus`` such that ``a @ aplus @ a = a`` |
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)pbdoc"); |
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m.def( |
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"cross", |
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&mx::linalg::cross, |
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"a"_a, |
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"b"_a, |
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"axis"_a = -1, |
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nb::kw_only(), |
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"stream"_a = nb::none(), |
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nb::sig( |
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"def cross(a: array, b: array, axis: int = -1, *, stream: Union[None, Stream, Device] = None) -> array"), |
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R"pbdoc( |
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Compute the cross product of two arrays along a specified axis. |
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The cross product is defined for arrays with size 2 or 3 in the |
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specified axis. If the size is 2 then the third value is assumed |
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to be zero. |
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Args: |
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a (array): Input array. |
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b (array): Input array. |
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axis (int, optional): Axis along which to compute the cross |
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product. Default: ``-1``. |
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stream (Stream, optional): Stream or device. Defaults to ``None`` |
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in which case the default stream of the default device is used. |
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Returns: |
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array: The cross product of ``a`` and ``b`` along the specified axis. |
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)pbdoc"); |
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m.def( |
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"eigvals", |
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&mx::linalg::eigvals, |
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"a"_a, |
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nb::kw_only(), |
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"stream"_a = nb::none(), |
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R"pbdoc( |
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Compute the eigenvalues of a square matrix. |
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This function differs from :func:`numpy.linalg.eigvals` in that the |
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return type is always complex even if the eigenvalues are all real. |
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This function supports arrays with at least 2 dimensions. When the |
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input has more than two dimensions, the eigenvalues are computed for |
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each matrix in the last two dimensions. |
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|
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Args: |
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a (array): The input array. |
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stream (Stream, optional): Stream or device. Defaults to ``None`` |
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in which case the default stream of the default device is used. |
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Returns: |
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array: The eigenvalues (not necessarily in order). |
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Example: |
|
|
>>> A = mx.array([[1., -2.], [-2., 1.]]) |
|
|
>>> eigenvalues = mx.linalg.eigvals(A, stream=mx.cpu) |
|
|
>>> eigenvalues |
|
|
array([3+0j, -1+0j], dtype=complex64) |
|
|
)pbdoc"); |
|
|
m.def( |
|
|
"eig", |
|
|
[](const mx::array& a, mx::StreamOrDevice s) { |
|
|
auto result = mx::linalg::eig(a, s); |
|
|
return nb::make_tuple(result.first, result.second); |
|
|
}, |
|
|
"a"_a, |
|
|
nb::kw_only(), |
|
|
"stream"_a = nb::none(), |
|
|
nb::sig( |
|
|
"def eig(a: array, *, stream: Union[None, Stream, Device] = None) -> Tuple[array, array]"), |
|
|
R"pbdoc( |
|
|
Compute the eigenvalues and eigenvectors of a square matrix. |
|
|
|
|
|
This function differs from :func:`numpy.linalg.eig` in that the |
|
|
return type is always complex even if the eigenvalues are all real. |
|
|
|
|
|
This function supports arrays with at least 2 dimensions. When the input |
|
|
has more than two dimensions, the eigenvalues and eigenvectors are |
|
|
computed for each matrix in the last two dimensions. |
|
|
|
|
|
Args: |
|
|
a (array): The input array. |
|
|
stream (Stream, optional): Stream or device. Defaults to ``None`` |
|
|
in which case the default stream of the default device is used. |
|
|
|
|
|
Returns: |
|
|
Tuple[array, array]: |
|
|
A tuple containing the eigenvalues and the normalized right |
|
|
eigenvectors. The column ``v[:, i]`` is the eigenvector |
|
|
corresponding to the i-th eigenvalue. |
|
|
|
|
|
Example: |
|
|
>>> A = mx.array([[1., -2.], [-2., 1.]]) |
|
|
>>> w, v = mx.linalg.eig(A, stream=mx.cpu) |
|
|
>>> w |
|
|
array([3+0j, -1+0j], dtype=complex64) |
|
|
>>> v |
|
|
array([[0.707107+0j, 0.707107+0j], |
|
|
[-0.707107+0j, 0.707107+0j]], dtype=complex64) |
|
|
)pbdoc"); |
|
|
|
|
|
m.def( |
|
|
"eigvalsh", |
|
|
&mx::linalg::eigvalsh, |
|
|
"a"_a, |
|
|
"UPLO"_a = "L", |
|
|
nb::kw_only(), |
|
|
"stream"_a = nb::none(), |
|
|
R"pbdoc( |
|
|
Compute the eigenvalues of a complex Hermitian or real symmetric matrix. |
|
|
|
|
|
This function supports arrays with at least 2 dimensions. When the |
|
|
input has more than two dimensions, the eigenvalues are computed for |
|
|
each matrix in the last two dimensions. |
|
|
|
|
|
Args: |
|
|
a (array): Input array. Must be a real symmetric or complex |
|
|
Hermitian matrix. |
|
|
UPLO (str, optional): Whether to use the upper (``"U"``) or |
|
|
lower (``"L"``) triangle of the matrix. Default: ``"L"``. |
|
|
stream (Stream, optional): Stream or device. Defaults to ``None`` |
|
|
in which case the default stream of the default device is used. |
|
|
|
|
|
Returns: |
|
|
array: The eigenvalues in ascending order. |
|
|
|
|
|
Note: |
|
|
The input matrix is assumed to be symmetric (or Hermitian). Only |
|
|
the selected triangle is used. No checks for symmetry are performed. |
|
|
|
|
|
Example: |
|
|
>>> A = mx.array([[1., -2.], [-2., 1.]]) |
|
|
>>> eigenvalues = mx.linalg.eigvalsh(A, stream=mx.cpu) |
|
|
>>> eigenvalues |
|
|
array([-1., 3.], dtype=float32) |
|
|
)pbdoc"); |
|
|
m.def( |
|
|
"eigh", |
|
|
[](const mx::array& a, const std::string& UPLO, mx::StreamOrDevice s) { |
|
|
auto result = mx::linalg::eigh(a, UPLO, s); |
|
|
return nb::make_tuple(result.first, result.second); |
|
|
}, |
|
|
"a"_a, |
|
|
"UPLO"_a = "L", |
|
|
nb::kw_only(), |
|
|
"stream"_a = nb::none(), |
|
|
nb::sig( |
|
|
"def eigh(a: array, UPLO: str = 'L', *, stream: Union[None, Stream, Device] = None) -> Tuple[array, array]"), |
|
|
R"pbdoc( |
|
|
Compute the eigenvalues and eigenvectors of a complex Hermitian or |
|
|
real symmetric matrix. |
|
|
|
|
|
This function supports arrays with at least 2 dimensions. When the input |
|
|
has more than two dimensions, the eigenvalues and eigenvectors are |
|
|
computed for each matrix in the last two dimensions. |
|
|
|
|
|
Args: |
|
|
a (array): Input array. Must be a real symmetric or complex |
|
|
Hermitian matrix. |
|
|
UPLO (str, optional): Whether to use the upper (``"U"``) or |
|
|
lower (``"L"``) triangle of the matrix. Default: ``"L"``. |
|
|
stream (Stream, optional): Stream or device. Defaults to ``None`` |
|
|
in which case the default stream of the default device is used. |
|
|
|
|
|
Returns: |
|
|
Tuple[array, array]: |
|
|
A tuple containing the eigenvalues in ascending order and |
|
|
the normalized eigenvectors. The column ``v[:, i]`` is the |
|
|
eigenvector corresponding to the i-th eigenvalue. |
|
|
|
|
|
Note: |
|
|
The input matrix is assumed to be symmetric (or Hermitian). Only |
|
|
the selected triangle is used. No checks for symmetry are performed. |
|
|
|
|
|
Example: |
|
|
>>> A = mx.array([[1., -2.], [-2., 1.]]) |
|
|
>>> w, v = mx.linalg.eigh(A, stream=mx.cpu) |
|
|
>>> w |
|
|
array([-1., 3.], dtype=float32) |
|
|
>>> v |
|
|
array([[ 0.707107, -0.707107], |
|
|
[ 0.707107, 0.707107]], dtype=float32) |
|
|
)pbdoc"); |
|
|
m.def( |
|
|
"lu", |
|
|
[](const mx::array& a, mx::StreamOrDevice s ) { |
|
|
auto result = mx::linalg::lu(a, s); |
|
|
return nb::make_tuple(result.at(0), result.at(1), result.at(2)); |
|
|
}, |
|
|
"a"_a, |
|
|
nb::kw_only(), |
|
|
"stream"_a = nb::none(), |
|
|
nb::sig( |
|
|
"def lu(a: array, *, stream: Union[None, Stream, Device] = None) -> Tuple[array, array, array]"), |
|
|
R"pbdoc( |
|
|
Compute the LU factorization of the given matrix ``A``. |
|
|
|
|
|
Note, unlike the default behavior of ``scipy.linalg.lu``, the pivots |
|
|
are indices. To reconstruct the input use ``L[P, :] @ U`` for 2 |
|
|
dimensions or ``mx.take_along_axis(L, P[..., None], axis=-2) @ U`` |
|
|
for more than 2 dimensions. |
|
|
|
|
|
To construct the full permuation matrix do: |
|
|
|
|
|
.. code-block:: |
|
|
|
|
|
P = mx.put_along_axis(mx.zeros_like(L), p[..., None], mx.array(1.0), axis=-1) |
|
|
|
|
|
Args: |
|
|
a (array): Input array. |
|
|
stream (Stream, optional): Stream or device. Defaults to ``None`` |
|
|
in which case the default stream of the default device is used. |
|
|
|
|
|
Returns: |
|
|
tuple(array, array, array): |
|
|
The ``p``, ``L``, and ``U`` arrays, such that ``A = L[P, :] @ U`` |
|
|
)pbdoc"); |
|
|
m.def( |
|
|
"lu_factor", |
|
|
&mx::linalg::lu_factor, |
|
|
"a"_a, |
|
|
nb::kw_only(), |
|
|
"stream"_a = nb::none(), |
|
|
nb::sig( |
|
|
"def lu_factor(a: array, *, stream: Union[None, Stream, Device] = None) -> Tuple[array, array]"), |
|
|
R"pbdoc( |
|
|
Computes a compact representation of the LU factorization. |
|
|
|
|
|
Args: |
|
|
a (array): Input array. |
|
|
stream (Stream, optional): Stream or device. Defaults to ``None`` |
|
|
in which case the default stream of the default device is used. |
|
|
|
|
|
Returns: |
|
|
tuple(array, array): The ``LU`` matrix and ``pivots`` array. |
|
|
)pbdoc"); |
|
|
m.def( |
|
|
"solve", |
|
|
&mx::linalg::solve, |
|
|
"a"_a, |
|
|
"b"_a, |
|
|
nb::kw_only(), |
|
|
"stream"_a = nb::none(), |
|
|
nb::sig( |
|
|
"def solve(a: array, b: array, *, stream: Union[None, Stream, Device] = None) -> array"), |
|
|
R"pbdoc( |
|
|
Compute the solution to a system of linear equations ``AX = B``. |
|
|
|
|
|
Args: |
|
|
a (array): Input array. |
|
|
b (array): Input array. |
|
|
stream (Stream, optional): Stream or device. Defaults to ``None`` |
|
|
in which case the default stream of the default device is used. |
|
|
|
|
|
Returns: |
|
|
array: The unique solution to the system ``AX = B``. |
|
|
)pbdoc"); |
|
|
m.def( |
|
|
"solve_triangular", |
|
|
&mx::linalg::solve_triangular, |
|
|
"a"_a, |
|
|
"b"_a, |
|
|
nb::kw_only(), |
|
|
"upper"_a = false, |
|
|
"stream"_a = nb::none(), |
|
|
nb::sig( |
|
|
"def solve_triangular(a: array, b: array, *, upper: bool = False, stream: Union[None, Stream, Device] = None) -> array"), |
|
|
R"pbdoc( |
|
|
Computes the solution of a triangular system of linear equations ``AX = B``. |
|
|
|
|
|
Args: |
|
|
a (array): Input array. |
|
|
b (array): Input array. |
|
|
upper (bool, optional): Whether the array is upper or lower |
|
|
triangular. Default: ``False``. |
|
|
stream (Stream, optional): Stream or device. Defaults to ``None`` |
|
|
in which case the default stream of the default device is used. |
|
|
|
|
|
Returns: |
|
|
array: The unique solution to the system ``AX = B``. |
|
|
)pbdoc"); |
|
|
} |
|
|
|
