text: # 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':
          status, message = 1, 'Maximum number of function calls reached.'
      else:
          status, message = None, 'Unsuccessful'
      diag = rf'Solver returned {status}: {message}'
  
      with pytest.warns(AstropyUserWarning, match=diag):
          z0 = z_at_value(cosmo.angular_diameter_distance, 1*u.Gpc, zmax=2, maxfun=13, method=method)
      with pytest.warns(AstropyUserWarning, match=diag):
          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)
  