# Licensed under a 3-clause BSD style license - see LICENSE.rst import inspect import sys from io import StringIO import pytest import numpy as np from astropy import units as u from astropy.cosmology import core, flrw from astropy.cosmology.funcs import _z_at_scalar_value, z_at_value from astropy.cosmology.realizations import WMAP1, WMAP3, WMAP5, WMAP7, WMAP9, Planck13, Planck15, Planck18 from astropy.units import allclose from astropy.utils.compat.optional_deps import HAS_SCIPY # noqa from astropy.utils.exceptions import AstropyUserWarning @pytest.mark.skipif('not HAS_SCIPY') def test_z_at_value_scalar(): # These are tests of expected values, and hence have less precision # than the roundtrip tests below (test_z_at_value_roundtrip); # here we have to worry about the cosmological calculations # giving slightly different values on different architectures, # there we are checking internal consistency on the same architecture # and so can be more demanding cosmo = Planck13 assert allclose(z_at_value(cosmo.age, 2 * u.Gyr), 3.19812268, rtol=1e-6) assert allclose(z_at_value(cosmo.lookback_time, 7 * u.Gyr), 0.795198375, rtol=1e-6) assert allclose(z_at_value(cosmo.distmod, 46 * u.mag), 1.991389168, rtol=1e-6) assert allclose(z_at_value(cosmo.luminosity_distance, 1e4 * u.Mpc), 1.36857907, rtol=1e-6) assert allclose(z_at_value(cosmo.luminosity_distance, 26.037193804 * u.Gpc, ztol=1e-10), 3, rtol=1e-9) assert allclose(z_at_value(cosmo.angular_diameter_distance, 1500*u.Mpc, zmax=2), 0.681277696, rtol=1e-6) assert allclose(z_at_value(cosmo.angular_diameter_distance, 1500*u.Mpc, zmin=2.5), 3.7914908, rtol=1e-6) # test behavior when the solution is outside z limits (should # raise a CosmologyError) with pytest.raises(core.CosmologyError): with pytest.warns(AstropyUserWarning, match=r'fval is not bracketed'): z_at_value(cosmo.angular_diameter_distance, 1500*u.Mpc, zmax=0.5) with pytest.raises(core.CosmologyError): with pytest.warns(AstropyUserWarning, match=r'fval is not bracketed'): z_at_value(cosmo.angular_diameter_distance, 1500*u.Mpc, zmin=4.) @pytest.mark.skipif('not HAS_SCIPY') class Test_ZatValue: def setup_class(self): self.cosmo = Planck13 def test_broadcast_arguments(self): """Test broadcast of arguments.""" # broadcasting main argument assert allclose( z_at_value(self.cosmo.age, [2, 7] * u.Gyr), [3.1981206134773115, 0.7562044333305182], rtol=1e-6) # basic broadcast of secondary arguments assert allclose( z_at_value(self.cosmo.angular_diameter_distance, 1500 * u.Mpc, zmin=[0, 2.5], zmax=[2, 4]), [0.681277696, 3.7914908], rtol=1e-6) # more interesting broadcast assert allclose( z_at_value(self.cosmo.angular_diameter_distance, 1500 * u.Mpc, zmin=[[0, 2.5]], zmax=[2, 4]), [[0.681277696, 3.7914908]], rtol=1e-6) def test_broadcast_bracket(self): """`bracket` has special requirements.""" # start with an easy one assert allclose( z_at_value(self.cosmo.age, 2 * u.Gyr, bracket=None), 3.1981206134773115, rtol=1e-6) # now actually have a bracket assert allclose( z_at_value(self.cosmo.age, 2 * u.Gyr, bracket=[0, 4]), 3.1981206134773115, rtol=1e-6) # now a bad length with pytest.raises(ValueError, match="sequence"): z_at_value(self.cosmo.age, 2 * u.Gyr, bracket=[0, 4, 4, 5]) # now the wrong dtype : an ndarray, but not an object array with pytest.raises(TypeError, match="dtype"): z_at_value(self.cosmo.age, 2 * u.Gyr, bracket=np.array([0, 4])) # now an object array of brackets bracket=np.array([[0, 4], [0, 3, 4]], dtype=object) assert allclose( z_at_value(self.cosmo.age, 2 * u.Gyr, bracket=bracket), [3.1981206134773115, 3.1981206134773115], rtol=1e-6) def test_bad_broadcast(self): """Shapes mismatch as expected""" with pytest.raises(ValueError, match="broadcast"): z_at_value(self.cosmo.angular_diameter_distance, 1500 * u.Mpc, zmin=[0, 2.5, 0.1], zmax=[2, 4]) def test_scalar_input_to_output(self): """Test scalar input returns a scalar.""" z = z_at_value(self.cosmo.angular_diameter_distance, 1500 * u.Mpc, zmin=0, zmax=2) assert isinstance(z, u.Quantity) assert z.dtype == np.float64 assert z.shape == () @pytest.mark.skipif('not HAS_SCIPY') def test_z_at_value_numpyvectorize(): """Test that numpy vectorize fails on Quantities. If this test starts failing then numpy vectorize can be used instead of the home-brewed vectorization. Please submit a PR making the change. """ z_at_value = np.vectorize(_z_at_scalar_value, excluded=["func", "method", "verbose"]) with pytest.raises(u.UnitConversionError, match="dimensionless quantities"): z_at_value(Planck15.age, 10*u.Gyr) @pytest.mark.skipif('not HAS_SCIPY') def test_z_at_value_verbose(monkeypatch): cosmo = Planck13 # Test the "verbose" flag. Since this uses "print", need to mod stdout mock_stdout = StringIO() monkeypatch.setattr(sys, 'stdout', mock_stdout) resx = z_at_value(cosmo.age, 2 * u.Gyr, verbose=True) assert str(resx.value) in mock_stdout.getvalue() # test "verbose" prints res @pytest.mark.skipif('not HAS_SCIPY') @pytest.mark.parametrize('method', ['Brent', 'Golden', 'Bounded']) def test_z_at_value_bracketed(method): """ Test 2 solutions for angular diameter distance by not constraining zmin, zmax, but setting `bracket` on the appropriate side of the turning point z. Setting zmin / zmax should override `bracket`. """ cosmo = Planck13 if method == 'Bounded': with pytest.warns(AstropyUserWarning, match=r'fval is not bracketed'): z = z_at_value(cosmo.angular_diameter_distance, 1500*u.Mpc, method=method) if z > 1.6: z = 3.7914908 bracket = (0.9, 1.5) else: z = 0.6812777 bracket = (1.6, 2.0) with pytest.warns(UserWarning, match=r"Option 'bracket' is ignored"): assert allclose(z_at_value(cosmo.angular_diameter_distance, 1500*u.Mpc, method=method, bracket=bracket), z, rtol=1e-6) else: assert allclose(z_at_value(cosmo.angular_diameter_distance, 1500*u.Mpc, method=method, bracket=(0.3, 1.0)), 0.6812777, rtol=1e-6) assert allclose(z_at_value(cosmo.angular_diameter_distance, 1500*u.Mpc, method=method, bracket=(2.0, 4.0)), 3.7914908, rtol=1e-6) assert allclose(z_at_value(cosmo.angular_diameter_distance, 1500*u.Mpc, method=method, bracket=(0.1, 1.5)), 0.6812777, rtol=1e-6) assert allclose(z_at_value(cosmo.angular_diameter_distance, 1500*u.Mpc, method=method, bracket=(0.1, 1.0, 2.0)), 0.6812777, rtol=1e-6) with pytest.warns(AstropyUserWarning, match=r'fval is not bracketed'): assert allclose(z_at_value(cosmo.angular_diameter_distance, 1500*u.Mpc, method=method, bracket=(0.9, 1.5)), 0.6812777, rtol=1e-6) assert allclose(z_at_value(cosmo.angular_diameter_distance, 1500*u.Mpc, method=method, bracket=(1.6, 2.0)), 3.7914908, rtol=1e-6) assert allclose(z_at_value(cosmo.angular_diameter_distance, 1500*u.Mpc, method=method, bracket=(1.6, 2.0), zmax=1.6), 0.6812777, rtol=1e-6) assert allclose(z_at_value(cosmo.angular_diameter_distance, 1500*u.Mpc, method=method, bracket=(0.9, 1.5), zmin=1.5), 3.7914908, rtol=1e-6) with pytest.raises(core.CosmologyError): with pytest.warns(AstropyUserWarning, match=r'fval is not bracketed'): z_at_value(cosmo.angular_diameter_distance, 1500*u.Mpc, method=method, bracket=(3.9, 5.0), zmin=4.) @pytest.mark.skipif('not HAS_SCIPY') @pytest.mark.parametrize('method', ['Brent', 'Golden', 'Bounded']) def test_z_at_value_unconverged(method): """ Test warnings on non-converged solution when setting `maxfun` to too small iteration number - only 'Bounded' returns status value and specific message. """ cosmo = Planck18 ztol = {'Brent': [1e-4, 1e-4], 'Golden': [1e-3, 1e-2], 'Bounded': [1e-3, 1e-1]} if method == 'Bounded': ctx = pytest.warns(AstropyUserWarning, match='Solver returned 1: Maximum number of ' 'function calls reached') else: ctx = pytest.warns(AstropyUserWarning, match='Solver returned None') with ctx: z0 = z_at_value(cosmo.angular_diameter_distance, 1*u.Gpc, zmax=2, maxfun=13, method=method) with ctx: z1 = z_at_value(cosmo.angular_diameter_distance, 1*u.Gpc, zmin=2, maxfun=13, method=method) assert allclose(z0, 0.32442, rtol=ztol[method][0]) assert allclose(z1, 8.18551, rtol=ztol[method][1]) @pytest.mark.skipif('not HAS_SCIPY') @pytest.mark.parametrize('cosmo', [Planck13, Planck15, Planck18, WMAP1, WMAP3, WMAP5, WMAP7, WMAP9, flrw.LambdaCDM, flrw.FlatLambdaCDM, flrw.wpwaCDM, flrw.w0wzCDM, flrw.wCDM, flrw.FlatwCDM, flrw.w0waCDM, flrw.Flatw0waCDM]) def test_z_at_value_roundtrip(cosmo): """ Calculate values from a known redshift, and then check that z_at_value returns the right answer. """ z = 0.5 # Skip Ok, w, de_density_scale because in the Planck cosmologies # they are redshift independent and hence uninvertable, # *_distance_z1z2 methods take multiple arguments, so require # special handling # clone is not a redshift-dependent method # nu_relative_density is not redshift-dependent in the WMAP cosmologies skip = ('Ok', 'angular_diameter_distance_z1z2', 'clone', 'is_equivalent', 'de_density_scale', 'w') if str(cosmo.name).startswith('WMAP'): skip += ('nu_relative_density', ) methods = inspect.getmembers(cosmo, predicate=inspect.ismethod) for name, func in methods: if name.startswith('_') or name in skip: continue fval = func(z) # we need zmax here to pick the right solution for # angular_diameter_distance and related methods. # Be slightly more generous with rtol than the default 1e-8 # used in z_at_value got = z_at_value(func, fval, bracket=[0.3, 1.0], ztol=1e-12) assert allclose(got, z, rtol=2e-11), f'Round-trip testing {name} failed' # Test distance functions between two redshifts; only for realizations if isinstance(cosmo.name, str): z2 = 2.0 func_z1z2 = [ lambda z1: cosmo._comoving_distance_z1z2(z1, z2), lambda z1: cosmo._comoving_transverse_distance_z1z2(z1, z2), lambda z1: cosmo.angular_diameter_distance_z1z2(z1, z2) ] for func in func_z1z2: fval = func(z) assert allclose(z, z_at_value(func, fval, zmax=1.5, ztol=1e-12), rtol=2e-11)