text: # Licensed under a 3-clause BSD style license - see LICENSE.rst
  """Tests for physical functions."""
  # pylint: disable=no-member, invalid-name
  import pytest
  import numpy as np
  
  from astropy.modeling.physical_models import BlackBody, NFW
  from astropy.modeling.fitting import LevMarLSQFitter
  
  from astropy.tests.helper import assert_quantity_allclose
  from astropy import units as u
  from astropy.utils.exceptions import AstropyUserWarning
  from astropy import cosmology
  
  try:
      from scipy import optimize, integrate  # noqa
  
      HAS_SCIPY = True
  except ImportError:
      HAS_SCIPY = False
  
  __doctest_skip__ = ["*"]
  
  
  # BlackBody tests
  
  
  @pytest.mark.parametrize("temperature", (3000 * u.K, 2726.85 * u.deg_C))
  def test_blackbody_evaluate(temperature):
  
      b = BlackBody(temperature=temperature, scale=1.0)
  
      assert_quantity_allclose(b(1.4 * u.micron), 486787299458.15656 * u.MJy / u.sr)
      assert_quantity_allclose(b(214.13747 * u.THz), 486787299458.15656 * u.MJy / u.sr)
  
  
  def test_blackbody_weins_law():
      b = BlackBody(293.0 * u.K)
      assert_quantity_allclose(b.lambda_max, 9.890006672986939 * u.micron)
      assert_quantity_allclose(b.nu_max, 17.22525080856469 * u.THz)
  
  
  def test_blackbody_sefanboltzman_law():
      b = BlackBody(293.0 * u.K)
      assert_quantity_allclose(b.bolometric_flux, 133.02471751812573 * u.W / (u.m * u.m))
  
  
  def test_blackbody_return_units():
      # return of evaluate has no units when temperature has no units
      b = BlackBody(1000.0 * u.K, scale=1.0)
      assert not isinstance(b.evaluate(1.0 * u.micron, 1000.0, 1.0), u.Quantity)
  
      # return has "standard" units when scale has no units
      b = BlackBody(1000.0 * u.K, scale=1.0)
      assert isinstance(b(1.0 * u.micron), u.Quantity)
      assert b(1.0 * u.micron).unit == u.erg / (u.cm ** 2 * u.s * u.Hz * u.sr)
  
      # return has scale units when scale has units
      b = BlackBody(1000.0 * u.K, scale=1.0 * u.MJy / u.sr)
      assert isinstance(b(1.0 * u.micron), u.Quantity)
      assert b(1.0 * u.micron).unit == u.MJy / u.sr
  
  
  @pytest.mark.skipif("not HAS_SCIPY")
  def test_blackbody_fit():
  
      fitter = LevMarLSQFitter()
  
      b = BlackBody(3000 * u.K, scale=5e-17 * u.Jy / u.sr)
  
      wav = np.array([0.5, 5, 10]) * u.micron
      fnu = np.array([1, 10, 5]) * u.Jy / u.sr
  
      b_fit = fitter(b, wav, fnu, maxiter=1000)
  
      assert_quantity_allclose(b_fit.temperature, 2840.7438355865065 * u.K)
      assert_quantity_allclose(b_fit.scale, 5.803783292762381e-17 * u.Jy / u.sr)
  
  
  def test_blackbody_overflow():
      """Test Planck function with overflow."""
      photlam = u.photon / (u.cm ** 2 * u.s * u.AA)
      wave = [0.0, 1000.0, 100000.0, 1e55]  # Angstrom
      temp = 10000.0  # Kelvin
      bb = BlackBody(temperature=temp * u.K, scale=1.0)
      with pytest.warns(
              AstropyUserWarning,
              match=r'Input contains invalid wavelength/frequency value\(s\)'):
          with np.errstate(all="ignore"):
              bb_lam = bb(wave) * u.sr
      flux = bb_lam.to(photlam, u.spectral_density(wave * u.AA)) / u.sr
  
      # First element is NaN, last element is very small, others normal
      assert np.isnan(flux[0])
      with np.errstate(all="ignore"):
          assert np.log10(flux[-1].value) < -134
      np.testing.assert_allclose(
          flux.value[1:-1], [0.00046368, 0.04636773], rtol=1e-3
      )  # 0.1% accuracy in PHOTLAM/sr
      with np.errstate(all="ignore"):
          flux = bb(1.0 * u.AA)
      assert flux.value == 0
  
  
  def test_blackbody_exceptions_and_warnings():
      """Test exceptions."""
  
      # Negative temperature
      with pytest.raises(ValueError) as exc:
          bb = BlackBody(-100 * u.K)
          bb(1.0 * u.micron)
      assert exc.value.args[0] == "Temperature should be positive: [-100.] K"
  
      bb = BlackBody(5000 * u.K)
  
      # Zero wavelength given for conversion to Hz
      with pytest.warns(AstropyUserWarning, match='invalid') as w:
          bb(0 * u.AA)
      assert len(w) == 3  # 2 of these are RuntimeWarning from zero divide
  
      # Negative wavelength given for conversion to Hz
      with pytest.warns(AstropyUserWarning, match='invalid') as w:
          bb(-1.0 * u.AA)
      assert len(w) == 1
  
      # Test that a non surface brightness converatable scale unit
      with pytest.raises(ValueError) as exc:
          bb = BlackBody(5000 * u.K, scale=1.0 * u.Jy)
          bb(1.0 * u.micron)
      assert exc.value.args[0] == "scale units not surface brightness: Jy"
  
  
  def test_blackbody_array_temperature():
      """Regression test to make sure that the temperature can be an array."""
      multibb = BlackBody([100, 200, 300] * u.K)
      flux = multibb(1.2 * u.mm)
      np.testing.assert_allclose(
          flux.value, [1.804908e-12, 3.721328e-12, 5.638513e-12], rtol=1e-5
      )
  
      flux = multibb([2, 4, 6] * u.mm)
      np.testing.assert_allclose(
          flux.value, [6.657915e-13, 3.420677e-13, 2.291897e-13], rtol=1e-5
      )
  
      multibb = BlackBody(np.ones(4) * u.K)
      flux = multibb(np.ones((3, 4)) * u.mm)
      assert flux.shape == (3, 4)
  
  
  @pytest.mark.parametrize("mass", (2.0000000000000E15 * u.M_sun, 3.976819741e+45 * u.kg))
  def test_NFW_evaluate(mass):
      """Evalution, density, and radii validation of NFW model."""
      # Test parameters
      concentration = 8.5
      redshift = 0.63
      cosmo = cosmology.Planck15
  
      # Parsec tests
      # 200c Overdensity
      massfactor = ("critical", 200)
  
      n200c = NFW(mass=mass, concentration=concentration, redshift=redshift, cosmo=cosmo,
                  massfactor=massfactor)
      assert_quantity_allclose(n200c(3.0 * u.Mpc), (3.709693508e+12 * (u.solMass / u.Mpc ** 3),
                                                    7.376391187e+42 * (u.kg / u.Mpc ** 3)))
      assert_quantity_allclose(n200c.rho_scale, (7800150779863018.0 * (u.solMass / u.Mpc ** 3)))
      assert_quantity_allclose(n200c.r_s, (0.24684627641195428 * u.Mpc))
      assert_quantity_allclose(n200c.r_virial, (2.0981933495016114 * u.Mpc))
  
      # 200m Overdensity
      massfactor = ("mean", 200)
  
      n200m = NFW(mass=mass, concentration=concentration, redshift=redshift, cosmo=cosmo,
                  massfactor=massfactor)
      assert_quantity_allclose(n200m(3.0 * u.Mpc), (3.626093406e+12 * (u.solMass / u.Mpc**3),
                                                    7.210159921e+42 * (u.kg / u.Mpc**3)))
      assert_quantity_allclose(n200m.rho_scale, (5118547639858115.0 * (u.solMass / u.Mpc ** 3)))
      assert_quantity_allclose(n200m.r_s, (0.2840612517326848 * u.Mpc))
      assert_quantity_allclose(n200m.r_virial, (2.414520639727821 * u.Mpc))
  
      # Virial mass
      massfactor = ("virial")
  
      nvir = NFW(mass=mass, concentration=concentration, redshift=redshift, cosmo=cosmo,
                 massfactor=massfactor)
      assert_quantity_allclose(nvir(3.0 * u.Mpc), (3.646475546e+12 * (u.solMass / u.Mpc**3),
                                                   7.250687967e+42 * (u.kg / u.Mpc**3)))
      assert_quantity_allclose(nvir.rho_scale, (5649367524651067.0 * (u.solMass / u.Mpc ** 3)))
      assert_quantity_allclose(nvir.r_s, (0.2748701862303786 * u.Mpc))
      assert_quantity_allclose(nvir.r_virial, (2.3363965829582183 * u.Mpc))
  
      # kpc tests
      # 200c Overdensity
      massfactor = ("critical", 200)
  
      n200c = NFW(mass=mass, concentration=concentration, redshift=redshift, cosmo=cosmo,
                  massfactor=massfactor)
      assert_quantity_allclose(n200c(3141 * u.kpc), (3254.373619264334 * (u.solMass / u.kpc ** 3),
                                                     6.471028627484543e+33 * (u.kg / u.kpc ** 3)))
      assert_quantity_allclose(n200c.rho_scale, (7800150.779863021 * (u.solMass / u.kpc ** 3)))
      assert_quantity_allclose(n200c.r_s, (246.84627641195425 * u.kpc))
      assert_quantity_allclose(n200c.r_virial, (2098.193349501611 * u.kpc))
  
      # 200m Overdensity
      massfactor = ("mean", 200)
  
      n200m = NFW(mass=mass, concentration=concentration, redshift=redshift, cosmo=cosmo,
                  massfactor=massfactor)
      assert_quantity_allclose(n200m(3141 * u.kpc), (3184.0370866188623 * (u.solMass / u.kpc**3),
                                                     6.33117077170161e+33 * (u.kg / u.kpc**3)))
      assert_quantity_allclose(n200m.rho_scale, (5118547.639858116 * (u.solMass / u.kpc ** 3)))
      assert_quantity_allclose(n200m.r_s, (284.0612517326848 * u.kpc))
      assert_quantity_allclose(n200m.r_virial, (2414.5206397278207 * u.kpc))
  
      # Virial mass
      massfactor = ("virial")
  
      nvir = NFW(mass=mass, concentration=concentration, redshift=redshift, cosmo=cosmo,
                 massfactor=massfactor)
      assert_quantity_allclose(nvir(3141 * u.kpc), (3201.1946851294997 * (u.solMass / u.kpc**3),
                                                    6.365287109937637e+33 * (u.kg / u.kpc**3)))
      assert_quantity_allclose(nvir.rho_scale, (5649367.5246510655 * (u.solMass / u.kpc ** 3)))
      assert_quantity_allclose(nvir.r_s, (274.87018623037864 * u.kpc))
      assert_quantity_allclose(nvir.r_virial, (2336.3965829582185 * u.kpc))
  
      # Meter tests
      # 200c Overdensity
      massfactor = ("critical", 200)
  
      n200c = NFW(mass=mass, concentration=concentration, redshift=redshift, cosmo=cosmo,
                  massfactor=massfactor)
      assert_quantity_allclose(n200c(4.2e+23 * u.m), (1.527649658673012e-57 * (u.solMass / u.m ** 3),
                                                      3.0375936602739256e-27 * (u.kg / u.m ** 3)))
      assert_quantity_allclose(n200c.rho_scale, (2.654919529637763e-52 * (u.solMass / u.m ** 3)))
      assert_quantity_allclose(n200c.r_s, (7.616880211930209e+21 * u.m))
      assert_quantity_allclose(n200c.r_virial, (6.474348180140678e+22 * u.m))
  
      # 200m Overdensity
      massfactor = ("mean", 200)
  
      n200m = NFW(mass=mass, concentration=concentration, redshift=redshift, cosmo=cosmo,
                  massfactor=massfactor)
      assert_quantity_allclose(n200m(4.2e+23 * u.m), (1.5194778058079436e-57 * (u.solMass / u.m ** 3),
                                                      3.0213446673751314e-27 * (u.kg / u.m ** 3)))
      assert_quantity_allclose(n200m.rho_scale, (1.742188385322371e-52 * (u.solMass / u.m ** 3)))
      assert_quantity_allclose(n200m.r_s, (8.76521436235054e+21 * u.m))
      assert_quantity_allclose(n200m.r_virial, (7.450432207997959e+22 * u.m))
  
      # Virial mass
      massfactor = ("virial")
  
      nvir = NFW(mass=mass, concentration=concentration, redshift=redshift, cosmo=cosmo,
                 massfactor=massfactor)
      assert_quantity_allclose(nvir(4.2e+23 * u.m), (1.5214899184117633e-57 * (u.solMass / u.m ** 3),
                                                     3.0253455719375224e-27 * (u.kg / u.m ** 3)))
      assert_quantity_allclose(nvir.rho_scale, (1.922862338766335e-52 * (u.solMass / u.m ** 3)))
      assert_quantity_allclose(nvir.r_s, (8.481607714647913e+21 * u.m))
      assert_quantity_allclose(nvir.r_virial, (7.209366557450727e+22 * u.m))
  
      # Verify string input of overdensity type
      # 200c Overdensity
      massfactor = "200c"
  
      n200c = NFW(mass=mass, concentration=concentration, redshift=redshift, cosmo=cosmo,
                  massfactor=massfactor)
      assert_quantity_allclose(n200c(3.0 * u.Mpc), (3.709693508e+12 * (u.solMass / u.Mpc ** 3),
                                                    7.376391187e+42 * (u.kg / u.Mpc ** 3)))
  
      # 200m Overdensity
      massfactor = "200m"
  
      n200m = NFW(mass=mass, concentration=concentration, redshift=redshift, cosmo=cosmo,
                  massfactor=massfactor)
      assert_quantity_allclose(n200m(3.0 * u.Mpc), (3.626093406e+12 * (u.solMass / u.Mpc**3),
                                                    7.210159921e+42 * (u.kg / u.Mpc**3)))
  
      # Virial mass
      massfactor = "virial"
  
      nvir = NFW(mass=mass, concentration=concentration, redshift=redshift,  cosmo=cosmo,
                 massfactor=massfactor)
      assert_quantity_allclose(nvir(3.0 * u.Mpc), (3.646475546e+12 * (u.solMass / u.Mpc**3),
                                                   7.250687967e+42 * (u.kg / u.Mpc**3)))
  
  
  @pytest.mark.skipif("not HAS_SCIPY")
  def test_NFW_fit():
      """Test linear fitting of NFW model."""
      # Fixed parameters
      redshift = 0.63
      cosmo = cosmology.Planck15
  
      # Radial set
      r = np.array([1.00e+01, 1.00e+02, 2.00e+02, 2.50e+02, 3.00e+02, 4.00e+02, 5.00e+02,
                    7.50e+02, 1.00e+03, 1.50e+03, 2.50e+03, 6.50e+03, 1.15e+04]) * u.kpc
  
      # 200c Overdensity
      massfactor = ("critical", 200)
  
      density_r = np.array([1.77842761e+08, 9.75233623e+06, 2.93789626e+06, 1.90107238e+06,
                            1.30776878e+06, 7.01004140e+05, 4.20678479e+05, 1.57421880e+05,
                            7.54669701e+04, 2.56319769e+04, 6.21976562e+03, 3.96522424e+02,
                            7.39336808e+01]) * (u.solMass / u.kpc ** 3)
  
      fitter = LevMarLSQFitter()
  
      n200c = NFW(mass=1.8E15 * u.M_sun, concentration=7.0, redshift=redshift, cosmo=cosmo,
                  massfactor=massfactor)
      n200c.redshift.fixed = True
  
      n_fit = fitter(n200c, r, density_r, maxiter=1000)
  
      assert_quantity_allclose(n_fit.mass, 2.0000000000000E15 * u.M_sun)
      assert_quantity_allclose(n_fit.concentration, 8.5)
  
      # 200m Overdensity
      massfactor = ("mean", 200)
  
      density_r = np.array([1.35677282e+08, 7.95392979e+06, 2.50352599e+06, 1.64535870e+06,
                            1.14642248e+06, 6.26805453e+05, 3.81691731e+05, 1.46294819e+05,
                            7.11559560e+04, 2.45737796e+04, 6.05459585e+03, 3.92183991e+02,
                            7.34674416e+01]) * (u.solMass / u.kpc ** 3)
  
      fitter = LevMarLSQFitter()
  
      n200m = NFW(mass=1.8E15 * u.M_sun, concentration=7.0, redshift=redshift, cosmo=cosmo,
                  massfactor=massfactor)
      n200m.redshift.fixed = True
  
      n_fit = fitter(n200m, r, density_r, maxiter=1000)
  
      assert_quantity_allclose(n_fit.mass, 2.0000000000000E15 * u.M_sun)
      assert_quantity_allclose(n_fit.concentration, 8.5)
  
      # Virial mass
      massfactor = ("virial", 200)
  
      density_r = np.array([1.44573515e+08, 8.34873998e+06, 2.60137484e+06, 1.70348738e+06,
                            1.18337370e+06, 6.43994654e+05, 3.90800249e+05, 1.48930537e+05,
                            7.21856397e+04, 2.48289464e+04, 6.09477095e+03, 3.93248818e+02,
                            7.35821787e+01]) * (u.solMass / u.kpc ** 3)
  
      fitter = LevMarLSQFitter()
  
      nvir = NFW(mass=1.8E15 * u.M_sun, concentration=7.0, redshift=redshift, cosmo=cosmo,
                 massfactor=massfactor)
      nvir.redshift.fixed = True
  
      n_fit = fitter(nvir, r, density_r, maxiter=1000)
  
      assert_quantity_allclose(n_fit.mass, 2.0000000000000E15 * u.M_sun)
      assert_quantity_allclose(n_fit.concentration, 8.5)
  
  
  def test_NFW_circular_velocity():
      """Test circular velocity and radial validation of NFW model."""
      # Test parameters
      mass = 2.0000000000000E15 * u.M_sun
      concentration = 8.5
      redshift = 0.63
      cosmo = cosmology.Planck15
  
      r_r = np.array([0.01, 0.1, 0.2, 0.25, 0.3, 0.4, 0.5, 0.75, 1.0, 1.5, 2.5, 6.5, 11.5]) * u.Mpc
  
      # 200c Overdensity tests
      massfactor = ("critical", 200)
  
      n200c = NFW(mass=mass, concentration=concentration, redshift=redshift, cosmo=cosmo,
                  massfactor=massfactor)
      circ_v_200c = np.array([702.45487454, 1812.4138346, 2150.50929296, 2231.5802568, 2283.96950242,
                              2338.45989696, 2355.78876772, 2332.41766543, 2276.89433811,
                              2154.53909153, 1950.07947819, 1512.37442943,
                              1260.94034541]) * (u.km / u.s)
      assert_quantity_allclose(n200c.circular_velocity(r_r), circ_v_200c)
      assert_quantity_allclose(n200c.r_max, (0.5338248204429641 * u.Mpc))
      assert_quantity_allclose(n200c.v_max, (2356.7204380904027 * (u.km / u.s)))
  
      # 200m Overdensity tests
      massfactor = ("mean", 200)
      mass = 1.0e14 * u.M_sun
      concentration = 12.3
      redshift = 1.5
  
      n200m = NFW(mass=mass, concentration=concentration, redshift=redshift, cosmo=cosmo,
                  massfactor=massfactor)
      circ_v_200m = np.array([670.18236647, 1088.9843324, 1046.82334367, 1016.88890732, 987.97273478,
                              936.00207134, 891.80115232, 806.63307977, 744.91002191, 659.33401039,
                              557.82823549, 395.9735786, 318.29863006]) * (u.km / u.s)
      assert_quantity_allclose(n200m.circular_velocity(r_r), circ_v_200m)
      assert_quantity_allclose(n200m.r_max, (0.10196917920081808 * u.Mpc))
      assert_quantity_allclose(n200m.v_max, (1089.0224395818727 * (u.km / u.s)))
  
      # Virial Overdensity tests
      massfactor = ("virial")
      mass = 1.2e+45 * u.kg
      concentration = 2.4
      redshift = 0.34
  
      r_r = np.array([3.08567758e+20, 3.08567758e+21, 6.17135516e+21, 7.71419395e+21,
                      9.25703274e+21, 1.23427103e+22, 1.54283879e+22, 2.31425819e+22,
                      3.08567758e+22, 4.62851637e+22, 7.71419395e+22, 2.00569043e+23,
                      3.54852922e+23]) * u.m
  
      nvir = NFW(mass=mass, concentration=concentration, redshift=redshift, cosmo=cosmo,
                 massfactor=massfactor)
      circ_v_vir = np.array([205.87461783, 604.65091823, 793.9190629, 857.52516521, 908.90280843,
                             986.53582718, 1041.69089845, 1124.19719446, 1164.58270747, 1191.33193561,
                             1174.02934755, 1023.69360527, 895.52206321]) * (u.km / u.s)
      assert_quantity_allclose(nvir.circular_velocity(r_r), circ_v_vir)
      assert_quantity_allclose(nvir.r_max, (1.6484542328623448 * u.Mpc))
      assert_quantity_allclose(nvir.v_max, (1192.3130989914962 * (u.km / u.s)))
  
  
  def test_NFW_exceptions_and_warnings_and_misc():
      """Test NFW exceptions."""
  
      # Arbitrary Test parameters
      mass = 2.0000000000000E15 * u.M_sun
      concentration = 8.5
      redshift = 0.63
      cosmo = cosmology.Planck15
      massfactor = ("critical", 200)
  
      r_r = np.array([1.00e+01, 1.00e+02, 2.00e+02, 2.50e+02, 3.00e+02, 4.00e+02, 5.00e+02,
                      7.50e+02, 1.00e+03, 1.50e+03, 2.50e+03, 6.50e+03, 1.15e+04]) * u.kpc
  
      # Massfactor exception tests
      with pytest.raises(ValueError) as exc:
          NFW(mass=mass, concentration=concentration, redshift=redshift, cosmo=cosmo,
              massfactor=("not", "virial"))
      assert exc.value.args[0] == "Massfactor 'not' not one of 'critical', 'mean', or 'virial'"
      with pytest.raises(ValueError) as exc:
          NFW(mass=mass, concentration=concentration, redshift=redshift, cosmo=cosmo,
              massfactor="not virial")
      assert exc.value.args[0] == "Massfactor not virial string not of the form '#m', '#c', " \
                                  "or 'virial'"
      with pytest.raises(TypeError) as exc:
          NFW(mass=mass, concentration=concentration, redshift=redshift, cosmo=cosmo,
              massfactor=200)
      assert exc.value.args[0] == "Massfactor 200 not a tuple or string"
  
      # Verify unitless mass
      # Density test
      n200c = NFW(mass=mass.value, concentration=concentration, redshift=redshift, cosmo=cosmo,
                  massfactor=massfactor)
      assert_quantity_allclose(n200c(3000.0), (3.709693508e+12 * (u.solMass / u.Mpc ** 3),
                                               7.376391187e+42 * (u.kg / u.Mpc ** 3)))
  
      # Circular velocity test with unitless mass
      circ_v_200c = np.array([702.45487454, 1812.4138346, 2150.50929296, 2231.5802568, 2283.96950242,
                              2338.45989696, 2355.78876772, 2332.41766543, 2276.89433811,
                              2154.53909153, 1950.07947819, 1512.37442943,
                              1260.94034541]) * (u.km / u.s)
      assert_quantity_allclose(n200c.circular_velocity(r_r), circ_v_200c)
  
      # Test Default Cosmology
      ncos = NFW(mass=mass, concentration=concentration, redshift=redshift)
      assert_quantity_allclose(ncos.A_NFW(concentration), 1.356554956501232)
  