testbed/astropy__astropy/astropy/modeling/tests/test_polynomial.py

# Licensed under a 3-clause BSD style license - see LICENSE.rst

"""Tests for polynomial models."""

import os

from itertools import product

import pytest
import numpy as np

from numpy.testing import assert_allclose

from astropy.modeling import fitting
from astropy import wcs
from astropy.io import fits
from astropy.modeling.polynomial import (Chebyshev1D, Hermite1D, Legendre1D, Polynomial1D,
                          Chebyshev2D, Hermite2D, Legendre2D, Polynomial2D, SIP,
                          PolynomialBase, OrthoPolynomialBase)
from astropy.modeling.functional_models import Linear1D
from astropy.modeling.mappings import Identity
from astropy.utils.data import get_pkg_data_filename

try:
    from scipy import optimize  # pylint: disable=W0611
    HAS_SCIPY = True
except ImportError:
    HAS_SCIPY = False


linear1d = {
    Chebyshev1D: {
        'args': (3,),
        'kwargs': {'domain': [1, 10]},
        'parameters': {'c0': 1.2, 'c1': 2, 'c2': 2.3, 'c3': 0.2},
        'constraints': {'fixed': {'c0': 1.2}}
    },
    Hermite1D: {
        'args': (3,),
        'kwargs': {'domain': [1, 10]},
        'parameters': {'c0': 1.2, 'c1': 2, 'c2': 2.3, 'c3': 0.2},
        'constraints': {'fixed': {'c0': 1.2}}
    },
    Legendre1D: {
        'args': (3,),
        'kwargs': {'domain': [1, 10]},
        'parameters': {'c0': 1.2, 'c1': 2, 'c2': 2.3, 'c3': 0.2},
        'constraints': {'fixed': {'c0': 1.2}}
    },
    Polynomial1D: {
        'args': (3,),
        'kwargs': {'domain': [1, 10]},
        'parameters': {'c0': 1.2, 'c1': 2, 'c2': 2.3, 'c3': 0.2},
        'constraints': {'fixed': {'c0': 1.2}}
    },
    Linear1D: {
        'args': (),
        'kwargs': {},
        'parameters': {'intercept': 1.2, 'slope': 23.1},
        'constraints': {'fixed': {'intercept': 1.2}}
    }
}


linear2d = {
    Chebyshev2D: {
        'args': (1, 1),
        'kwargs': {'x_domain': [0, 99], 'y_domain': [0, 82]},
        'parameters': {'c0_0': 1.2, 'c1_0': 2, 'c0_1': 2.3, 'c1_1': 0.2},
        'constraints': {'fixed': {'c0_0': 1.2}}
    },
    Hermite2D: {
        'args': (1, 1),
        'kwargs': {'x_domain': [0, 99], 'y_domain': [0, 82]},
        'parameters': {'c0_0': 1.2, 'c1_0': 2, 'c0_1': 2.3, 'c1_1': 0.2},
        'constraints': {'fixed': {'c0_0': 1.2}}
    },
    Legendre2D: {
        'args': (1, 1),
        'kwargs': {'x_domain': [0, 99], 'y_domain': [0, 82]},
        'parameters': {'c0_0': 1.2, 'c1_0': 2, 'c0_1': 2.3, 'c1_1': 0.2},
        'constraints': {'fixed': {'c0_0': 1.2}}
    },
    Polynomial2D: {
        'args': (1,),
        'kwargs': {},
        'parameters': {'c0_0': 1.2, 'c1_0': 2, 'c0_1': 2.3},
        'constraints': {'fixed': {'c0_0': 1.2}}
    }
}


@pytest.mark.skipif('not HAS_SCIPY')
class TestFitting:
    """Test linear fitter with polynomial models."""

    def setup_class(self):
        self.N = 100
        self.M = 100
        self.x1 = np.linspace(1, 10, 100)
        self.y2, self.x2 = np.mgrid[:100, :83]
        rsn = np.random.RandomState(0)
        self.n1 = rsn.randn(self.x1.size) * .1
        self.n2 = rsn.randn(self.x2.size)
        self.n2.shape = self.x2.shape
        self.linear_fitter = fitting.LinearLSQFitter()
        self.non_linear_fitter = fitting.LevMarLSQFitter()

    # TODO: Most of these test cases have some pretty repetitive setup that we
    # could probably factor out

    @pytest.mark.parametrize(('model_class', 'constraints'),
                             list(product(sorted(linear1d, key=str), (False, True))))
    def test_linear_fitter_1D(self, model_class, constraints):
        """Test fitting with LinearLSQFitter"""

        model_args = linear1d[model_class]
        kwargs = {}
        kwargs.update(model_args['kwargs'])
        kwargs.update(model_args['parameters'])

        if constraints:
            kwargs.update(model_args['constraints'])

        model = model_class(*model_args['args'], **kwargs)

        y1 = model(self.x1)
        model_lin = self.linear_fitter(model, self.x1, y1 + self.n1)

        if constraints:
            # For the constraints tests we're not checking the overall fit,
            # just that the constraint was maintained
            fixed = model_args['constraints'].get('fixed', None)
            if fixed:
                for param, value in fixed.items():
                    expected = model_args['parameters'][param]
                    assert getattr(model_lin, param).value == expected
        else:
            assert_allclose(model_lin.parameters, model.parameters,
                            atol=0.2)

    @pytest.mark.parametrize(('model_class', 'constraints'),
                             list(product(sorted(linear1d, key=str), (False, True))))
    def test_non_linear_fitter_1D(self, model_class, constraints):
        """Test fitting with non-linear LevMarLSQFitter"""

        model_args = linear1d[model_class]
        kwargs = {}
        kwargs.update(model_args['kwargs'])
        kwargs.update(model_args['parameters'])

        if constraints:
            kwargs.update(model_args['constraints'])

        model = model_class(*model_args['args'], **kwargs)

        y1 = model(self.x1)
        model_nlin = self.non_linear_fitter(model, self.x1, y1 + self.n1)

        if constraints:
            fixed = model_args['constraints'].get('fixed', None)
            if fixed:
                for param, value in fixed.items():
                    expected = model_args['parameters'][param]
                    assert getattr(model_nlin, param).value == expected
        else:
            assert_allclose(model_nlin.parameters, model.parameters,
                            atol=0.2)

    @pytest.mark.parametrize(('model_class', 'constraints'),
                             list(product(sorted(linear2d, key=str), (False, True))))
    def test_linear_fitter_2D(self, model_class, constraints):
        """Test fitting with LinearLSQFitter"""

        model_args = linear2d[model_class]
        kwargs = {}
        kwargs.update(model_args['kwargs'])
        kwargs.update(model_args['parameters'])

        if constraints:
            kwargs.update(model_args['constraints'])

        model = model_class(*model_args['args'], **kwargs)

        z = model(self.x2, self.y2)
        model_lin = self.linear_fitter(model, self.x2, self.y2, z + self.n2)

        if constraints:
            fixed = model_args['constraints'].get('fixed', None)
            if fixed:
                for param, value in fixed.items():
                    expected = model_args['parameters'][param]
                    assert getattr(model_lin, param).value == expected
        else:
            assert_allclose(model_lin.parameters, model.parameters,
                            atol=0.2)

    @pytest.mark.parametrize(('model_class', 'constraints'),
                             list(product(sorted(linear2d, key=str), (False, True))))
    def test_non_linear_fitter_2D(self, model_class, constraints):
        """Test fitting with non-linear LevMarLSQFitter"""

        model_args = linear2d[model_class]
        kwargs = {}
        kwargs.update(model_args['kwargs'])
        kwargs.update(model_args['parameters'])

        if constraints:
            kwargs.update(model_args['constraints'])

        model = model_class(*model_args['args'], **kwargs)

        z = model(self.x2, self.y2)
        model_nlin = self.non_linear_fitter(model, self.x2, self.y2,
                                            z + self.n2)

        if constraints:
            fixed = model_args['constraints'].get('fixed', None)
            if fixed:
                for param, value in fixed.items():
                    expected = model_args['parameters'][param]
                    assert getattr(model_nlin, param).value == expected
        else:
            assert_allclose(model_nlin.parameters, model.parameters,
                            atol=0.2)


@pytest.mark.parametrize('model_class',
                         [cls for cls in list(linear1d) + list(linear2d)
                          if isinstance(cls, PolynomialBase)])
def test_polynomial_init_with_constraints(model_class):
    """
    Test that polynomial models can be instantiated with constraints, but no
    parameters specified.

    Regression test for https://github.com/astropy/astropy/issues/3606
    """

    # Just determine which parameter to place a constraint on; it doesn't
    # matter which parameter it is to exhibit the problem so long as it's a
    # valid parameter for the model
    if '1D' in model_class.__name__:
        param = 'c0'
    else:
        param = 'c0_0'

    if issubclass(model_class, OrthoPolynomialBase):
        degree = (2, 2)
    else:
        degree = (2,)

    m = model_class(*degree, fixed={param: True})

    assert m.fixed[param] is True
    assert getattr(m, param).fixed is True


def test_sip_hst():
    """Test SIP against astropy.wcs"""

    test_file = get_pkg_data_filename(os.path.join('data', 'hst_sip.hdr'))
    hdr = fits.Header.fromtextfile(test_file)
    crpix1 = hdr['CRPIX1']
    crpix2 = hdr['CRPIX2']
    wobj = wcs.WCS(hdr)
    a_pars = dict(**hdr['A_*'])
    b_pars = dict(**hdr['B_*'])
    a_order = a_pars.pop('A_ORDER')
    b_order = b_pars.pop('B_ORDER')
    sip = SIP([crpix1, crpix2], a_order, b_order, a_pars, b_pars)
    coords = [1, 1]
    rel_coords = [1 - crpix1, 1 - crpix2]
    astwcs_result = wobj.sip_pix2foc([coords], 1)[0] - rel_coords
    assert_allclose(sip(1, 1), astwcs_result)


def test_sip_irac():
    """Test forward and inverse SIP againts astropy.wcs"""

    test_file = get_pkg_data_filename(os.path.join('data', 'irac_sip.hdr'))
    hdr = fits.Header.fromtextfile(test_file)
    crpix1 = hdr['CRPIX1']
    crpix2 = hdr['CRPIX2']
    wobj = wcs.WCS(hdr)
    a_pars = dict(**hdr['A_*'])
    b_pars = dict(**hdr['B_*'])
    ap_pars = dict(**hdr['AP_*'])
    bp_pars = dict(**hdr['BP_*'])
    a_order = a_pars.pop('A_ORDER')
    b_order = b_pars.pop('B_ORDER')
    ap_order = ap_pars.pop('AP_ORDER')
    bp_order = bp_pars.pop('BP_ORDER')
    del a_pars['A_DMAX']
    del b_pars['B_DMAX']
    pix = [200, 200]
    rel_pix = [200 - crpix1, 200 - crpix2]
    sip = SIP([crpix1, crpix2], a_order, b_order, a_pars, b_pars,
              ap_order=ap_order, ap_coeff=ap_pars, bp_order=bp_order,
              bp_coeff=bp_pars)

    foc = wobj.sip_pix2foc([pix], 1)
    newpix = wobj.sip_foc2pix(foc, 1)[0]
    assert_allclose(sip(*pix), foc[0] - rel_pix)
    assert_allclose(sip.inverse(*foc[0]) +
                    foc[0] - rel_pix, newpix - pix)


def test_sip_no_coeff():
    sip = SIP([10, 12], 2, 2)
    assert_allclose(sip.sip1d_a.parameters, [0., 0., 0])
    assert_allclose(sip.sip1d_b.parameters, [0., 0., 0])
    with pytest.raises(NotImplementedError):
        sip.inverse


@pytest.mark.parametrize('cls', (Polynomial1D, Chebyshev1D, Legendre1D,
                                 Polynomial2D, Chebyshev2D, Legendre2D))
def test_zero_degree_polynomial(cls):
    """
    A few tests that degree=0 polynomials are correctly evaluated and
    fitted.

    Regression test for https://github.com/astropy/astropy/pull/3589
    """

    if cls.n_inputs == 1:  # Test 1D polynomials
        p1 = cls(degree=0, c0=1)
        assert p1(0) == 1
        assert np.all(p1(np.zeros(5)) == np.ones(5))

        x = np.linspace(0, 1, 100)
        # Add a little noise along a straight line
        y = 1 + np.random.uniform(0, 0.1, len(x))

        p1_init = cls(degree=0)
        fitter = fitting.LinearLSQFitter()
        p1_fit = fitter(p1_init, x, y)

        # The fit won't be exact of course, but it should get close to within
        # 1%
        assert_allclose(p1_fit.c0, 1, atol=0.10)
    elif cls.n_inputs == 2:  # Test 2D polynomials
        if issubclass(cls, OrthoPolynomialBase):
            p2 = cls(x_degree=0, y_degree=0, c0_0=1)
        else:
            p2 = cls(degree=0, c0_0=1)
        assert p2(0, 0) == 1
        assert np.all(p2(np.zeros(5), np.zeros(5)) == np.ones(5))

        y, x = np.mgrid[0:1:100j, 0:1:100j]
        z = (1 + np.random.uniform(0, 0.1, x.size)).reshape(100, 100)

        if issubclass(cls, OrthoPolynomialBase):
            p2_init = cls(x_degree=0, y_degree=0)
        else:
            p2_init = cls(degree=0)
        fitter = fitting.LinearLSQFitter()
        p2_fit = fitter(p2_init, x, y, z)

        assert_allclose(p2_fit.c0_0, 1, atol=0.10)


@pytest.mark.skipif('not HAS_SCIPY')
def test_2d_orthopolynomial_in_compound_model():
    """
    Ensure that OrthoPolynomialBase (ie. Chebyshev2D & Legendre2D) models get
    evaluated & fitted correctly when part of a compound model.

    Regression test for https://github.com/astropy/astropy/pull/6085.
    """

    y, x = np.mgrid[0:5, 0:5]
    z = x + y

    fitter = fitting.LevMarLSQFitter()
    simple_model = Chebyshev2D(2, 2)
    simple_fit = fitter(simple_model, x, y, z)

    fitter = fitting.LevMarLSQFitter()  # re-init to compare like with like
    compound_model = Identity(2) | Chebyshev2D(2, 2)
    compound_fit = fitter(compound_model, x, y, z)

    assert_allclose(simple_fit(x, y), compound_fit(x, y), atol=1e-15)