Fixed database typo and removed unnecessary class identifier.

venv/Lib/site-packages/scipy/special/tests/data/README

@@ -0,0 +1,578 @@
+This directory contains numerical data for testing special functions.
+The data is in version control as text files.
+
+The data is automatically packed into npz files by setup.py.
+The npz files should not be checked in version control.
+
+The data in gsl is computed using the GNU scientific library, the data
+in local is computed using mpmath, and the data in boost is a copy of
+data distributed with the boost library and comes with the following
+license:
+
+Boost Software License - Version 1.0 - August 17th, 2003
+
+Permission is hereby granted, free of charge, to any person or organization
+obtaining a copy of the software and accompanying documentation covered by
+this license (the "Software") to use, reproduce, display, distribute,
+execute, and transmit the Software, and to prepare derivative works of the
+Software, and to permit third-parties to whom the Software is furnished to
+do so, all subject to the following:
+
+The copyright notices in the Software and this entire statement, including
+the above license grant, this restriction and the following disclaimer,
+must be included in all copies of the Software, in whole or in part, and
+all derivative works of the Software, unless such copies or derivative
+works are solely in the form of machine-executable object code generated by
+a source language processor.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
+SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
+FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
+ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
+DEALINGS IN THE SOFTWARE.
+
+=========
+
+Copyright holders of each file are listed here:
+
+Jamfile.v2:# Copyright Daryle Walker, Hubert Holin, John Maddock 2006 - 2007
+acosh_data.ipp:// Copyright John Maddock 2008.
+acosh_test.hpp://  (C) Copyright Hubert Holin 2003.
+almost_equal.ipp:// Copyright (c) 2006 Johan Rade
+asinh_data.ipp:// Copyright John Maddock 2008.
+asinh_test.hpp://  (C) Copyright Hubert Holin 2003.
+assoc_legendre_p.ipp://  (C) Copyright John Maddock 2006-7.
+atanh_data.ipp:// Copyright John Maddock 2008.
+atanh_test.hpp://  (C) Copyright Hubert Holin 2003.
+bessel_i_data.ipp://  Copyright (c) 2007 John Maddock
+bessel_i_int_data.ipp://  Copyright (c) 2007 John Maddock
+bessel_j_data.ipp://  Copyright (c) 2007 John Maddock
+bessel_j_int_data.ipp://  Copyright (c) 2007 John Maddock
+bessel_j_large_data.ipp://  Copyright (c) 2007 John Maddock
+bessel_k_data.ipp://  Copyright (c) 2007 John Maddock
+bessel_k_int_data.ipp://  Copyright (c) 2007 John Maddock
+bessel_y01_data.ipp://  Copyright (c) 2007 John Maddock
+bessel_yn_data.ipp://  Copyright (c) 2007 John Maddock
+bessel_yv_data.ipp://  Copyright (c) 2007 John Maddock
+beta_exp_data.ipp://  (C) Copyright John Maddock 2006.
+beta_med_data.ipp://  (C) Copyright John Maddock 2006.
+beta_small_data.ipp://  (C) Copyright John Maddock 2006.
+binomial_data.ipp://  (C) Copyright John Maddock 2006-7.
+binomial_large_data.ipp://  (C) Copyright John Maddock 2006-7.
+binomial_quantile.ipp://  (C) Copyright John Maddock 2006-7.
+cbrt_data.ipp://  (C) Copyright John Maddock 2006-7.
+common_factor_test.cpp://  (C) Copyright Daryle Walker 2001, 2006.
+compile_test/tools_rational_inc_test.cpp://  Copyright John Maddock 2006.
+compile_test/tools_real_cast_inc_test.cpp://  Copyright John Maddock 2006.
+compile_test/tools_remez_inc_test.cpp://  Copyright John Maddock 2006.
+compile_test/dist_chi_squared_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/dist_complement_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/sf_sign_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/sf_digamma_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/sf_trunc_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/constants_incl_test.cpp://  Copyright John Maddock 2012.
+compile_test/sf_sinc_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/sf_binomial_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/dist_binomial_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/tools_test_inc_test.cpp://  Copyright John Maddock 2006.
+compile_test/dist_normal_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/sf_sinhc_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/sf_ellint_rc_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/sf_sin_pi_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/sf_sph_harm_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/dist_poisson_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/test_traits.cpp://  Copyright John Maddock 2007.
+compile_test/dist_gamma_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/sf_cos_pi_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/dist_logistic_incl_test.cpp://  Copyright John Maddock 2008.
+compile_test/sf_fpclassify_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/compl_atanh_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/tools_precision_inc_test.cpp://  Copyright John Maddock 2006.
+compile_test/sf_hankel_incl_test.cpp://  Copyright John Maddock 2012.
+compile_test/sf_cbrt_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/dist_nc_beta_incl_test.cpp://  Copyright John Maddock 2008.
+compile_test/sf_legendre_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/tools_stats_inc_test.cpp://  Copyright John Maddock 2006.
+compile_test/tools_polynomial_inc_test.cpp://  Copyright John Maddock 2006.
+compile_test/tools_config_inc_test.cpp://  Copyright John Maddock 2006.
+compile_test/dist_exponential_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/dist_students_t_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/dist_inv_gamma_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/compl_acosh_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/dist_beta_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/dist_fisher_f_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/dist_triangular_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/instantiate.hpp://  Copyright John Maddock 2006.
+compile_test/instantiate.hpp://  Copyright Paul A. Bristow 2007, 2010.
+compile_test/tools_solve_inc_test.cpp://  Copyright John Maddock 2006.
+compile_test/sf_next_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/generate.sh://  Copyright John Maddock 2006.
+compile_test/generate.sh://  Copyright John Maddock 2006.
+compile_test/generate.sh://  Copyright John Maddock 2006.
+compile_test/distribution_concept_check.cpp://  Copyright John Maddock 2006.
+compile_test/sf_laguerre_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/tr1_incl_test.cpp://  Copyright John Maddock 2008.
+compile_test/sf_ellint_rj_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/dist_nc_chi_squ_incl_test.cpp://  Copyright John Maddock 2008.
+compile_test/dist_skew_norm_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/sf_modf_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/dist_find_location_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/compl_acos_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/sf_ellint_rd_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/tools_roots_inc_test.cpp://  Copyright John Maddock 2006.
+compile_test/tools_test_data_inc_test.cpp://  Copyright John Maddock 2006.
+compile_test/compl_abs_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/dist_nc_t_incl_test.cpp://  Copyright John Maddock 2008.
+compile_test/sf_factorials_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/sf_gamma_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/compl_atan_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/sf_powm1_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/sf_hypot_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/dist_pareto_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/sf_round_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/dist_weibull_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/std_real_concept_check.cpp://  Copyright John Maddock 2006.
+compile_test/dist_hypergeo_incl_test.cpp://  Copyright John Maddock 2008.
+compile_test/dist_inv_chi_sq_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/sf_sqrt1pm1_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/sf_log1p_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/sf_jacobi_incl_test.cpp://  Copyright John Maddock 2012.
+compile_test/dist_neg_binom_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/dist_nc_f_incl_test.cpp://  Copyright John Maddock 2008.
+compile_test/dist_find_scale_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/sf_bessel_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/tools_minima_inc_test.cpp://  Copyright John Maddock 2006.
+compile_test/compl_asin_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/dist_extreme_val_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/sf_lanczos_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/dist_uniform_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/test_compile_result.hpp://  Copyright John Maddock 2007.
+compile_test/tools_series_inc_test.cpp://  Copyright John Maddock 2006.
+compile_test/sf_ellint_3_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/sf_ellint_rf_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/sf_ellint_2_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/sf_hermite_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/poison.hpp://  Copyright John Maddock 2013.
+compile_test/sf_zeta_incl_test.cpp://  Copyright John Maddock 2007.
+compile_test/dist_laplace_incl_test.cpp://  Copyright John Maddock 2008.
+compile_test/sf_expint_incl_test.cpp://  Copyright John Maddock 2007.
+compile_test/sf_expm1_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/dist_bernoulli_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/compl_asinh_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/sf_beta_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/tools_fraction_inc_test.cpp://  Copyright John Maddock 2006.
+compile_test/sf_owens_t_incl_test.cpp://  Copyright John Maddock 2012.
+compile_test/tools_toms748_inc_test.cpp://  Copyright John Maddock 2006.
+compile_test/sf_ellint_1_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/sf_erf_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/main.cpp://  Copyright John Maddock 2009.
+compile_test/sf_math_fwd_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/sf_airy_incl_test.cpp://  Copyright John Maddock 2012.
+compile_test/dist_lognormal_incl_test.cpp://  Copyright John Maddock 2006.
+compile_test/dist_cauchy_incl_test.cpp://  Copyright John Maddock 2006.
+complex_test.cpp://  (C) Copyright John Maddock 2005.
+digamma_data.ipp://  (C) Copyright John Maddock 2006-7.
+digamma_neg_data.ipp://  (C) Copyright John Maddock 2006-7.
+digamma_root_data.ipp://  (C) Copyright John Maddock 2006-7.
+digamma_small_data.ipp://  (C) Copyright John Maddock 2006-7.
+e_float_concept_check.cpp://  Copyright John Maddock 2011.
+ellint_e2_data.ipp://  Copyright (c) 2006 John Maddock
+ellint_e_data.ipp://  Copyright (c) 2006 John Maddock
+ellint_f_data.ipp://  Copyright (c) 2006 John Maddock
+ellint_k_data.ipp://  (C) Copyright John Maddock 2006-7.
+ellint_pi2_data.ipp://  Copyright (c) 2006 John Maddock
+ellint_pi3_data.ipp://  Copyright (c) 2006 John Maddock
+ellint_pi3_large_data.ipp://  Copyright (c) 2006 John Maddock
+ellint_rc_data.ipp://  Copyright (c) 2006 John Maddock
+ellint_rd_data.ipp://  Copyright (c) 2006 John Maddock
+ellint_rf_data.ipp://  Copyright (c) 2006 John Maddock
+ellint_rj_data.ipp://  Copyright (c) 2006 John Maddock
+erf_data.ipp://  (C) Copyright John Maddock 2006-7.
+erf_inv_data.ipp://  (C) Copyright John Maddock 2006-7.
+erf_large_data.ipp://  (C) Copyright John Maddock 2006-7.
+erf_small_data.ipp://  (C) Copyright John Maddock 2006.
+erfc_inv_big_data.ipp://  (C) Copyright John Maddock 2006-7.
+erfc_inv_data.ipp://  (C) Copyright John Maddock 2006-7.
+expint_1_data.ipp://  Copyright John Maddock 2008.
+expint_data.ipp://  Copyright John Maddock 2008.
+expint_small_data.ipp://  Copyright John Maddock 2008.
+expinti_data.ipp://  Copyright John Maddock 2008.
+expinti_data_double.ipp://  Copyright John Maddock 2008.
+expinti_data_long.ipp://  Copyright John Maddock 2008.
+functor.hpp://  (C) Copyright John Maddock 2007.
+gamma_inv_big_data.ipp://  (C) Copyright John Maddock 2006-7.
+gamma_inv_data.ipp://  (C) Copyright John Maddock 2006-7.
+gamma_inv_small_data.ipp://  (C) Copyright John Maddock 2006-7.
+handle_test_result.hpp://  (C) Copyright John Maddock 2006-7.
+hermite.ipp://  (C) Copyright John Maddock 2006-7.
+hypergeometric_dist_data2.ipp:// Copyright John Maddock 2008
+hypergeometric_test_data.ipp:// Copyright Gautam Sewani 2008
+hypot_test.cpp://  (C) Copyright John Maddock 2005.
+ibeta_data.ipp://  (C) Copyright John Maddock 2006.
+ibeta_int_data.ipp://  (C) Copyright John Maddock 2006-7.
+ibeta_inv_data.ipp://  (C) Copyright John Maddock 2006-7.
+ibeta_inva_data.ipp://  (C) Copyright John Maddock 2006-7.
+ibeta_large_data.ipp://  (C) Copyright John Maddock 2006.
+ibeta_small_data.ipp://  (C) Copyright John Maddock 2006.
+igamma_big_data.ipp://  (C) Copyright John Maddock 2006.
+igamma_int_data.ipp://  (C) Copyright John Maddock 2006-7.
+igamma_inva_data.ipp://  (C) Copyright John Maddock 2006-7.
+igamma_med_data.ipp://  (C) Copyright John Maddock 2006.
+igamma_small_data.ipp://  (C) Copyright John Maddock 2006.
+jacobi_elliptic.ipp:// Copyright John Maddock 2012.
+jacobi_elliptic_small.ipp:// Copyright John Maddock 2012.
+jacobi_large_phi.ipp:// Copyright John Maddock 2012.
+jacobi_near_1.ipp:// Copyright John Maddock 2012.
+laguerre2.ipp://  (C) Copyright John Maddock 2006-7.
+laguerre3.ipp://  (C) Copyright John Maddock 2006-7.
+legendre_p.ipp://  (C) Copyright John Maddock 2006-7.
+legendre_p_large.ipp://  (C) Copyright John Maddock 2006-7.
+log1p_expm1_data.ipp://  (C) Copyright John Maddock 2006-7.
+log1p_expm1_test.cpp://  Copyright John Maddock 2005.
+log1p_expm1_test.cpp://  Copyright Paul A. Bristow 2010
+log1p_expm1_test.hpp://  Copyright John Maddock 2005.
+log1p_expm1_test.hpp://  Copyright Paul A. Bristow 2010
+mpfr_concept_check.cpp://  Copyright John Maddock 2007-8.
+mpreal_concept_check.cpp://  Copyright John Maddock 2007-8.
+multiprc_concept_check_1.cpp://  Copyright John Maddock 2013.
+multiprc_concept_check_2.cpp://  Copyright John Maddock 2013.
+multiprc_concept_check_3.cpp://  Copyright John Maddock 2013.
+multiprc_concept_check_4.cpp://  Copyright John Maddock 2013.
+ncbeta.ipp://  Copyright John Maddock 2008.
+ncbeta_big.ipp://  Copyright John Maddock 2008.
+nccs.ipp://  Copyright John Maddock 2008.
+nccs_big.ipp:// Copyright John Maddock 2008.
+nct.ipp:// Copyright John Maddock 2008.
+nct_asym.ipp:// Copyright John Maddock 2012.
+nct_small_delta.ipp:// Copyright John Maddock 2012.
+negative_binomial_quantile.ipp://  (C) Copyright John Maddock 2006-7.
+ntl_concept_check.cpp://  Copyright John Maddock 2007-8.
+ntl_concept_check.cpp://  Copyright Paul A. Bristow 2009, 2011
+owens_t.ipp://  Copyright John Maddock 2012.
+owens_t_T7.hpp:// Copyright (C) Benjamin Sobotta 2012
+owens_t_large_data.ipp://  Copyright John Maddock 2012.
+pch.hpp://  Copyright John Maddock 2008.
+pch_light.hpp://  Copyright John Maddock 2008.
+poisson_quantile.ipp://  (C) Copyright John Maddock 2006-7.
+pow_test.cpp://  (C) Copyright Bruno Lalande 2008.
+powm1_sqrtp1m1_test.cpp://  (C) Copyright John Maddock 2006.
+powm1_sqrtp1m1_test.hpp://  Copyright John Maddock 2006.
+s_.ipp:// Copyright (c) 2006 Johan Rade
+s_.ipp:// Copyright (c) 2012 Paul A. Bristow
+sinc_test.hpp://  (C) Copyright Hubert Holin 2003.
+sinhc_test.hpp://  (C) Copyright Hubert Holin 2003.
+special_functions_test.cpp://  (C) Copyright Hubert Holin 2003.
+special_functions_test.cpp:    BOOST_TEST_MESSAGE("(C) Copyright Hubert Holin 2003-2005.");
+sph_bessel_data.ipp://  Copyright (c) 2007 John Maddock
+sph_neumann_data.ipp://  Copyright (c) 2007 John Maddock
+spherical_harmonic.ipp://  (C) Copyright John Maddock 2006-7.
+std_real_concept_check.cpp://  Copyright John Maddock 2006.
+table_type.hpp:// Copyright John Maddock 2012.
+test_airy.cpp://  Copyright John Maddock 2012
+test_archive.cpp:// Copyright (c) 2006 Johan Rade
+test_archive.cpp:// Copyright (c) 2011 Paul A. Bristow - filename changes for boost-trunk.
+test_basic_nonfinite.cpp:// Copyright (c) 2006 Johan Rade
+test_basic_nonfinite.cpp:// Copyright (c) 2011 Paul A. Bristow comments
+test_basic_nonfinite.cpp:// Copyright (c) 2011 John Maddock
+test_bernoulli.cpp:// Copyright John Maddock 2006.
+test_bernoulli.cpp:// Copyright  Paul A. Bristow 2007, 2012.
+test_bessel_airy_zeros.cpp://  Copyright John Maddock 2013
+test_bessel_airy_zeros.cpp://  Copyright Christopher Kormanyos 2013.
+test_bessel_airy_zeros.cpp://  Copyright Paul A. Bristow 2013.
+test_bessel_hooks.hpp://  (C) Copyright John Maddock 2007.
+test_bessel_i.cpp://  (C) Copyright John Maddock 2007.
+test_bessel_i.hpp://  (C) Copyright John Maddock 2007.
+test_bessel_j.cpp://  (C) Copyright John Maddock 2007.
+test_bessel_j.hpp://  (C) Copyright John Maddock 2007.
+test_bessel_k.cpp://  Copyright John Maddock 2006, 2007
+test_bessel_k.cpp://  Copyright Paul A. Bristow 2007
+test_bessel_k.hpp://  (C) Copyright John Maddock 2007.
+test_bessel_y.cpp://  (C) Copyright John Maddock 2007.
+test_bessel_y.hpp://  (C) Copyright John Maddock 2007.
+test_beta.cpp:// Copyright John Maddock 2006.
+test_beta.cpp:// Copyright Paul A. Bristow 2007, 2009
+test_beta.hpp:// Copyright John Maddock 2006.
+test_beta.hpp:// Copyright Paul A. Bristow 2007, 2009
+test_beta_dist.cpp:// Copyright John Maddock 2006.
+test_beta_dist.cpp:// Copyright  Paul A. Bristow 2007, 2009, 2010, 2012.
+test_beta_hooks.hpp://  (C) Copyright John Maddock 2006.
+test_binomial.cpp:// Copyright John Maddock 2006.
+test_binomial.cpp:// Copyright  Paul A. Bristow 2007.
+test_binomial_coeff.cpp://  (C) Copyright John Maddock 2006.
+test_binomial_coeff.hpp:// Copyright John Maddock 2006.
+test_binomial_coeff.hpp:// Copyright Paul A. Bristow 2007, 2009
+test_carlson.cpp://  Copyright 2006 John Maddock
+test_carlson.cpp:// Copyright Paul A. Bristow 2007.
+test_carlson.hpp:// Copyright John Maddock 2006.
+test_carlson.hpp:// Copyright Paul A. Bristow 2007, 2009
+test_cauchy.cpp:// Copyright John Maddock 2006, 2007.
+test_cauchy.cpp:// Copyright Paul A. Bristow 2007
+test_cbrt.cpp://  Copyright John Maddock 2006.
+test_cbrt.cpp://  Copyright Paul A. Bristow 2010
+test_cbrt.hpp:// Copyright John Maddock 2006.
+test_cbrt.hpp:// Copyright Paul A. Bristow 2007, 2009
+test_chi_squared.cpp:// Copyright Paul A. Bristow 2006.
+test_chi_squared.cpp:// Copyright John Maddock 2007.
+test_classify.cpp://  Copyright John Maddock 2006.
+test_classify.cpp://  Copyright Paul A. Bristow 2007
+test_common_factor_gmpxx.cpp://  (C) Copyright John Maddock 2010.
+test_constant_generate.cpp:// Copyright John Maddock 2010.
+test_constants.cpp:// Copyright Paul Bristow 2007, 2011.
+test_constants.cpp:// Copyright John Maddock 2006, 2011.
+test_digamma.cpp://  (C) Copyright John Maddock 2006.
+test_digamma.hpp:// Copyright John Maddock 2006.
+test_digamma.hpp:// Copyright Paul A. Bristow 2007, 2009
+test_dist_overloads.cpp:// Copyright John Maddock 2006.
+test_dist_overloads.cpp:// Copyright Paul A. Bristow 2007.
+test_ellint_1.cpp://  Copyright Xiaogang Zhang 2006
+test_ellint_1.cpp://  Copyright John Maddock 2006, 2007
+test_ellint_1.cpp://  Copyright Paul A. Bristow 2007
+test_ellint_1.hpp:// Copyright John Maddock 2006.
+test_ellint_1.hpp:// Copyright Paul A. Bristow 2007, 2009
+test_ellint_2.cpp://  Copyright Xiaogang Zhang 2006
+test_ellint_2.cpp://  Copyright John Maddock 2006, 2007
+test_ellint_2.cpp://  Copyright Paul A. Bristow 2007
+test_ellint_2.hpp:// Copyright John Maddock 2006.
+test_ellint_2.hpp:// Copyright Paul A. Bristow 2007, 2009
+test_ellint_3.cpp://  Copyright Xiaogang Zhang 2006
+test_ellint_3.cpp://  Copyright John Maddock 2006, 2007
+test_ellint_3.cpp://  Copyright Paul A. Bristow 2007
+test_ellint_3.hpp:// Copyright John Maddock 2006.
+test_ellint_3.hpp:// Copyright Paul A. Bristow 2007, 2009
+test_erf.cpp://  Copyright John Maddock 2006.
+test_erf.cpp://  Copyright Paul A. Bristow 2007
+test_erf.hpp:// Copyright John Maddock 2006.
+test_erf.hpp:// Copyright Paul A. Bristow 2007, 2009
+test_erf_hooks.hpp://  (C) Copyright John Maddock 2006.
+test_error_handling.cpp:// Copyright Paul A. Bristow 2006-7.
+test_error_handling.cpp:// Copyright John Maddock 2006-7.
+test_expint.cpp://  (C) Copyright John Maddock 2007.
+test_expint.hpp:// Copyright John Maddock 2006.
+test_expint.hpp:// Copyright Paul A. Bristow 2007, 2009
+test_expint_hooks.hpp://  (C) Copyright John Maddock 2006.
+test_exponential_dist.cpp:// Copyright John Maddock 2006.
+test_exponential_dist.cpp:// Copyright Paul A. Bristow 2007.
+test_extreme_value.cpp:// Copyright John Maddock 2006.
+test_factorials.cpp://  Copyright John Maddock 2006.
+test_find_location.cpp:// Copyright John Maddock 2007.
+test_find_location.cpp:// Copyright Paul A. Bristow 2007.
+test_find_scale.cpp:// Copyright John Maddock 2007.
+test_find_scale.cpp:// Copyright Paul A. Bristow 2007.
+test_fisher_f.cpp:// Copyright Paul A. Bristow 2006.
+test_fisher_f.cpp:// Copyright John Maddock 2007.
+test_fisher_f.cpp:   // Distcalc version 1.2 Copyright 2002 H Lohninger, TU Wein
+test_gamma.cpp://  (C) Copyright John Maddock 2006.
+test_gamma.hpp:// Copyright John Maddock 2006.
+test_gamma.hpp:// Copyright Paul A. Bristow 2007, 2009
+test_gamma_data.ipp://  (C) Copyright John Maddock 2006.
+test_gamma_dist.cpp:// Copyright John Maddock 2006.
+test_gamma_dist.cpp:// Copyright Paul A. Bristow 2007, 2010.
+test_gamma_hooks.hpp://  (C) Copyright John Maddock 2006.
+test_geometric.cpp:// Copyright Paul A. Bristow 2010.
+test_geometric.cpp:// Copyright John Maddock 2010.
+test_hankel.cpp://  Copyright John Maddock 2012
+test_hermite.cpp://  Copyright John Maddock 2006, 2007
+test_hermite.cpp://  Copyright Paul A. Bristow 2007
+test_hermite.hpp:// Copyright John Maddock 2006.
+test_hermite.hpp:// Copyright Paul A. Bristow 2007, 2009
+test_hypergeometric_dist.cpp:// Copyright John Maddock 2008
+test_hypergeometric_dist.cpp:// Copyright Paul A. Bristow 
+test_hypergeometric_dist.cpp:// Copyright Gautam Sewani
+test_ibeta.cpp://  (C) Copyright John Maddock 2006.
+test_ibeta.hpp:// Copyright John Maddock 2006.
+test_ibeta.hpp:// Copyright Paul A. Bristow 2007, 2009
+test_ibeta_inv.cpp://  (C) Copyright John Maddock 2006.
+test_ibeta_inv.hpp:// Copyright John Maddock 2006.
+test_ibeta_inv.hpp:// Copyright Paul A. Bristow 2007, 2009
+test_ibeta_inv_ab.cpp://  (C) Copyright John Maddock 2006.
+test_ibeta_inv_ab.hpp:// Copyright John Maddock 2006.
+test_ibeta_inv_ab.hpp:// Copyright Paul A. Bristow 2007, 2009
+test_igamma.cpp://  (C) Copyright John Maddock 2006.
+test_igamma.hpp:// Copyright John Maddock 2006.
+test_igamma.hpp:// Copyright Paul A. Bristow 2007, 2009
+test_igamma_inv.cpp://  (C) Copyright John Maddock 2006.
+test_igamma_inv.hpp:// Copyright John Maddock 2006.
+test_igamma_inv.hpp:// Copyright Paul A. Bristow 2007, 2009
+test_igamma_inva.cpp://  (C) Copyright John Maddock 2006.
+test_igamma_inva.hpp:// Copyright John Maddock 2006.
+test_igamma_inva.hpp:// Copyright Paul A. Bristow 2007, 2009
+test_instances/double_test_instances_4.cpp:// Copyright John Maddock 2011.
+test_instances/ldouble_test_instances_4.cpp:// Copyright John Maddock 2011.
+test_instances/float_test_instances_8.cpp:// Copyright John Maddock 2011.
+test_instances/double_test_instances_9.cpp:// Copyright John Maddock 2011.
+test_instances/Jamfile.v2:# Copyright ohn Maddock 2012
+test_instances/real_concept_test_instances_5.cpp:// Copyright John Maddock 2011.
+test_instances/ldouble_test_instances_6.cpp:// Copyright John Maddock 2011.
+test_instances/real_concept_test_instances_4.cpp:// Copyright John Maddock 2011.
+test_instances/double_test_instances_7.cpp:// Copyright John Maddock 2011.
+test_instances/real_concept_test_instances_2.cpp:// Copyright John Maddock 2011.
+test_instances/double_test_instances_5.cpp:// Copyright John Maddock 2011.
+test_instances/ldouble_test_instances_9.cpp:// Copyright John Maddock 2011.
+test_instances/real_concept_test_instances_1.cpp:// Copyright John Maddock 2011.
+test_instances/float_test_instances_6.cpp:// Copyright John Maddock 2011.
+test_instances/real_concept_test_instances_6.cpp:// Copyright John Maddock 2011.
+test_instances/ldouble_test_instances_7.cpp:// Copyright John Maddock 2011.
+test_instances/real_concept_test_instances_7.cpp:// Copyright John Maddock 2011.
+test_instances/float_test_instances_3.cpp:// Copyright John Maddock 2011.
+test_instances/double_test_instances_6.cpp:// Copyright John Maddock 2011.
+test_instances/real_concept_test_instances_9.cpp:// Copyright John Maddock 2011.
+test_instances/double_test_instances_2.cpp:// Copyright John Maddock 2011.
+test_instances/pch.hpp://  Copyright John Maddock 2012.
+test_instances/ldouble_test_instances_2.cpp:// Copyright John Maddock 2011.
+test_instances/long_double_test_instances_1.cpp:// Copyright John Maddock 2011.
+test_instances/float_test_instances_7.cpp:// Copyright John Maddock 2011.
+test_instances/test_instances.hpp:// Copyright John Maddock 2011.
+test_instances/double_test_instances_10.cpp:// Copyright John Maddock 2011.
+test_instances/double_test_instances_3.cpp:// Copyright John Maddock 2011.
+test_instances/ldouble_test_instances_3.cpp:// Copyright John Maddock 2011.
+test_instances/real_concept_test_instances_10.cpp:// Copyright John Maddock 2011.
+test_instances/float_test_instances_5.cpp:// Copyright John Maddock 2011.
+test_instances/real_concept_test_instances_8.cpp:// Copyright John Maddock 2011.
+test_instances/ldouble_test_instances_8.cpp:// Copyright John Maddock 2011.
+test_instances/double_test_instances_1.cpp:// Copyright John Maddock 2011.
+test_instances/float_test_instances_10.cpp:// Copyright John Maddock 2011.
+test_instances/ldouble_test_instances_10.cpp:// Copyright John Maddock 2011.
+test_instances/float_test_instances_9.cpp:// Copyright John Maddock 2011.
+test_instances/float_test_instances_4.cpp:// Copyright John Maddock 2011.
+test_instances/real_concept_test_instances_3.cpp:// Copyright John Maddock 2011.
+test_instances/float_test_instances_2.cpp:// Copyright John Maddock 2011.
+test_instances/float_test_instances_1.cpp:// Copyright John Maddock 2011.
+test_instances/double_test_instances_8.cpp:// Copyright John Maddock 2011.
+test_instances/ldouble_test_instances_5.cpp:// Copyright John Maddock 2011.
+test_instantiate1.cpp://  Copyright John Maddock 2006.
+test_instantiate2.cpp://  Copyright John Maddock 2006.
+test_inv_hyp.cpp://  (C) Copyright John Maddock 2006.
+test_inverse_chi_squared.cpp:// Copyright Paul A. Bristow 2010.
+test_inverse_chi_squared.cpp:// Copyright John Maddock 2010.
+test_inverse_chi_squared_distribution.cpp:// Copyright Paul A. Bristow 2010.
+test_inverse_chi_squared_distribution.cpp:// Copyright John Maddock 2010.
+test_inverse_gamma_distribution.cpp:// Copyright Paul A. Bristow 2010.
+test_inverse_gamma_distribution.cpp:// Copyright John Maddock 2010.
+test_inverse_gaussian.cpp:// Copyright Paul A. Bristow 2010.
+test_inverse_gaussian.cpp:// Copyright John Maddock 2010.
+test_jacobi.cpp://  Copyright John Maddock 2012
+test_jacobi.hpp:// Copyright John Maddock 2006.
+test_jacobi.hpp:// Copyright Paul A. Bristow 2007, 2009
+test_laguerre.cpp://  (C) Copyright John Maddock 2006.
+test_laguerre.hpp:// Copyright John Maddock 2006.
+test_laguerre.hpp:// Copyright Paul A. Bristow 2007, 2009
+test_laplace.cpp://  Copyright Thijs van den Berg, 2008.
+test_laplace.cpp://  Copyright John Maddock 2008.
+test_laplace.cpp://  Copyright Paul A. Bristow 2008, 2009.
+test_ldouble_simple.cpp:// Copyright John Maddock 2013.
+test_legacy_nonfinite.cpp:// Copyright (c) 2006 Johan Rade
+test_legacy_nonfinite.cpp:// Copyright (c) 2011 Paul A. Bristow comments
+test_legendre.cpp://  (C) Copyright John Maddock 2006.
+test_legendre.hpp:// Copyright John Maddock 2006.
+test_legendre.hpp:// Copyright Paul A. Bristow 2007, 2009
+test_legendre_hooks.hpp://  (C) Copyright John Maddock 2006.
+test_lexical_cast.cpp:// Copyright (c) 2006 Johan Rade
+test_lexical_cast.cpp:// Copyright (c) 2011 Paul A. Bristow incorporated Boost.Math
+test_logistic_dist.cpp:// Copyright 2008 Gautam Sewani
+test_lognormal.cpp:// Copyright John Maddock 2006.
+test_lognormal.cpp:// Copyright Paul A. Bristow 2007
+test_long_double_support.cpp:// Copyright John Maddock 2009
+test_math_fwd.cpp://  Copyright John Maddock 2010.
+test_math_fwd.cpp://  Copyright Paul A. Bristow 2010.
+test_minima.cpp://  Copyright John Maddock 2006.
+test_minima.cpp://  Copyright Paul A. Bristow 2007.
+test_nc_beta.cpp:// Copyright John Maddock 2008.
+test_nc_chi_squared.cpp:// Copyright John Maddock 2008.
+test_nc_f.cpp:// Copyright John Maddock 2008.
+test_nc_t.cpp:// Copyright John Maddock 2008, 2012.
+test_nc_t.cpp:// Copyright Paul A. Bristow 2012.
+test_ncbeta_hooks.hpp://  (C) Copyright John Maddock 2008.
+test_nccs_hooks.hpp://  (C) Copyright John Maddock 2008.
+test_negative_binomial.cpp:// Copyright Paul A. Bristow 2007.
+test_negative_binomial.cpp:// Copyright John Maddock 2006.
+test_next.cpp://  (C) Copyright John Maddock 2008.
+test_nonfinite_io.cpp:// Copyright 2011 Paul A. Bristow 
+test_nonfinite_trap.cpp:// Copyright (c) 2006 Johan Rade
+test_nonfinite_trap.cpp:// Copyright (c) 2011 Paul A. Bristow To incorporate into Boost.Math
+test_normal.cpp:// Copyright Paul A. Bristow 2010.
+test_normal.cpp:// Copyright John Maddock 2007.
+test_out_of_range.hpp:// Copyright John Maddock 2012.
+test_owens_t.cpp:// Copyright Paul A. Bristow 2012.
+test_owens_t.cpp:// Copyright Benjamin Sobotta 2012.
+test_pareto.cpp:// Copyright Paul A. Bristow 2007, 2009.
+test_pareto.cpp:// Copyright John Maddock 2006.
+test_poisson.cpp:// Copyright Paul A. Bristow 2007.
+test_poisson.cpp:// Copyright John Maddock 2006.
+test_policy.cpp:// Copyright John Maddock 2007.
+test_policy_2.cpp:// Copyright John Maddock 2007.
+test_policy_3.cpp:// Copyright John Maddock 2007.
+test_policy_4.cpp:// Copyright John Maddock 2007.
+test_policy_5.cpp:// Copyright John Maddock 2007.
+test_policy_6.cpp:// Copyright John Maddock 2007.
+test_policy_7.cpp:// Copyright John Maddock 2007.
+test_policy_8.cpp:// Copyright John Maddock 2007.
+test_policy_sf.cpp://  (C) Copyright John Maddock 2007.
+test_print_info_on_type.cpp:// Copyright John Maddock 2010.
+test_rational_instances/test_rational_ldouble2.cpp://  (C) Copyright John Maddock 2006-7.
+test_rational_instances/test_rational_float2.cpp://  (C) Copyright John Maddock 2006-7.
+test_rational_instances/test_rational_double2.cpp://  (C) Copyright John Maddock 2006-7.
+test_rational_instances/test_rational_double3.cpp://  (C) Copyright John Maddock 2006-7.
+test_rational_instances/test_rational_ldouble1.cpp://  (C) Copyright John Maddock 2006-7.
+test_rational_instances/test_rational_float4.cpp://  (C) Copyright John Maddock 2006-7.
+test_rational_instances/test_rational_double5.cpp://  (C) Copyright John Maddock 2006-7.
+test_rational_instances/test_rational_double4.cpp://  (C) Copyright John Maddock 2006-7.
+test_rational_instances/test_rational_real_concept1.cpp://  (C) Copyright John Maddock 2006-7.
+test_rational_instances/test_rational_real_concept3.cpp://  (C) Copyright John Maddock 2006-7.
+test_rational_instances/test_rational.hpp://  (C) Copyright John Maddock 2006-7.
+test_rational_instances/test_rational_ldouble3.cpp://  (C) Copyright John Maddock 2006-7.
+test_rational_instances/test_rational_float3.cpp://  (C) Copyright John Maddock 2006-7.
+test_rational_instances/test_rational_real_concept5.cpp://  (C) Copyright John Maddock 2006-7.
+test_rational_instances/test_rational_ldouble5.cpp://  (C) Copyright John Maddock 2006-7.
+test_rational_instances/test_rational_ldouble4.cpp://  (C) Copyright John Maddock 2006-7.
+test_rational_instances/test_rational_double1.cpp://  (C) Copyright John Maddock 2006-7.
+test_rational_instances/test_rational_real_concept4.cpp://  (C) Copyright John Maddock 2006-7.
+test_rational_instances/test_rational_real_concept2.cpp://  (C) Copyright John Maddock 2006-7.
+test_rational_instances/test_rational_float1.cpp://  (C) Copyright John Maddock 2006-7.
+test_rationals.cpp://  (C) Copyright John Maddock 2006.
+test_rayleigh.cpp:// Copyright John Maddock 2006.
+test_real_concept.cpp:// Copyright John Maddock 2010
+test_real_concept_neg_bin.cpp:// Copyright Paul A. Bristow 2010.
+test_real_concept_neg_bin.cpp:// Copyright John Maddock 2010.
+test_remez.cpp://  Copyright John Maddock 2006
+test_remez.cpp://  Copyright Paul A. Bristow 2007
+test_roots.cpp://  (C) Copyright John Maddock 2006.
+test_round.cpp://  (C) Copyright John Maddock 2007.
+test_sign.cpp:#define BOOST_TEST_MAIN// Copyright John Maddock 2008
+test_sign.cpp://  (C) Copyright Paul A. Bristow 2011 (added tests for changesign)
+test_signed_zero.cpp:// Copyright 2006 Johan Rade
+test_signed_zero.cpp:// Copyright 2011 Paul A. Bristow  To incorporate into Boost.Math
+test_signed_zero.cpp:// Copyright 2012 Paul A. Bristow with new tests.
+test_skew_normal.cpp:// Copyright Paul A. Bristow 2012.
+test_skew_normal.cpp:// Copyright John Maddock 2012.
+test_skew_normal.cpp:// Copyright Benjamin Sobotta 2012
+test_spherical_harmonic.cpp://  (C) Copyright John Maddock 2006.
+test_students_t.cpp:// Copyright Paul A. Bristow 2006.
+test_students_t.cpp:// Copyright John Maddock 2006.
+test_tgamma_ratio.cpp://  (C) Copyright John Maddock 2006.
+test_tgamma_ratio.hpp:// Copyright John Maddock 2006.
+test_tgamma_ratio.hpp:// Copyright Paul A. Bristow 2007, 2009
+test_toms748_solve.cpp://  (C) Copyright John Maddock 2006.
+test_tr1.c:/*  (C) Copyright John Maddock 2008.
+test_tr1.cpp://  (C) Copyright John Maddock 2008.
+test_triangular.cpp:// Copyright Paul Bristow 2006, 2007.
+test_triangular.cpp:// Copyright John Maddock 2006, 2007.
+test_uniform.cpp:// Copyright Paul Bristow 2007.
+test_uniform.cpp:// Copyright John Maddock 2006.
+test_weibull.cpp:// Copyright John Maddock 2006, 2012.
+test_weibull.cpp:// Copyright Paul A. Bristow 2007, 2012.
+test_zeta.cpp://  (C) Copyright John Maddock 2006.
+test_zeta.hpp:// Copyright John Maddock 2006.
+test_zeta.hpp:// Copyright Paul A. Bristow 2007, 2009
+test_zeta_hooks.hpp://  (C) Copyright John Maddock 2006.
+tgamma_delta_ratio_data.ipp://  (C) Copyright John Maddock 2006-7.
+tgamma_delta_ratio_int.ipp://  (C) Copyright John Maddock 2006-7.
+tgamma_delta_ratio_int2.ipp://  (C) Copyright John Maddock 2006-7.
+tgamma_ratio_data.ipp://  (C) Copyright John Maddock 2006-7.
+zeta_1_below_data.ipp://  Copyright John Maddock 2008.
+zeta_1_up_data.ipp://  Copyright John Maddock 2008.
+zeta_data.ipp://  Copyright John Maddock 2008.
+zeta_neg_data.ipp://  Copyright John Maddock 2008.
+ztest_max_digits10.cpp: // Copyright 2010 Paul A. Bristow
+zztest_max_digits10.cpp:// Copyright 2010 Paul A. Bristow

venv/Lib/site-packages/scipy/special/tests/test_bdtr.py

@@ -0,0 +1,112 @@
+import numpy as np
+import scipy.special as sc
+import pytest
+from numpy.testing import assert_allclose, assert_array_equal, suppress_warnings
+
+
+class TestBdtr(object):
+    def test(self):
+        val = sc.bdtr(0, 1, 0.5)
+        assert_allclose(val, 0.5)
+
+    def test_sum_is_one(self):
+        val = sc.bdtr([0, 1, 2], 2, 0.5)
+        assert_array_equal(val, [0.25, 0.75, 1.0])
+
+    def test_rounding(self):
+        double_val = sc.bdtr([0.1, 1.1, 2.1], 2, 0.5)
+        int_val = sc.bdtr([0, 1, 2], 2, 0.5)
+        assert_array_equal(double_val, int_val)
+
+    @pytest.mark.parametrize('k, n, p', [
+        (np.inf, 2, 0.5),
+        (1.0, np.inf, 0.5),
+        (1.0, 2, np.inf)
+    ])
+    def test_inf(self, k, n, p):
+        with suppress_warnings() as sup:
+            sup.filter(DeprecationWarning)
+            val = sc.bdtr(k, n, p)
+        assert np.isnan(val)
+
+    def test_domain(self):
+        val = sc.bdtr(-1.1, 1, 0.5)
+        assert np.isnan(val)
+
+
+class TestBdtrc(object):
+    def test_value(self):
+        val = sc.bdtrc(0, 1, 0.5)
+        assert_allclose(val, 0.5)
+
+    def test_sum_is_one(self):
+        val = sc.bdtrc([0, 1, 2], 2, 0.5)
+        assert_array_equal(val, [0.75, 0.25, 0.0])
+
+    def test_rounding(self):
+        double_val = sc.bdtrc([0.1, 1.1, 2.1], 2, 0.5)
+        int_val = sc.bdtrc([0, 1, 2], 2, 0.5)
+        assert_array_equal(double_val, int_val)
+
+    @pytest.mark.parametrize('k, n, p', [
+        (np.inf, 2, 0.5),
+        (1.0, np.inf, 0.5),
+        (1.0, 2, np.inf)
+    ])
+    def test_inf(self, k, n, p):
+        with suppress_warnings() as sup:
+            sup.filter(DeprecationWarning)
+            val = sc.bdtrc(k, n, p)
+        assert np.isnan(val)
+
+    def test_domain(self):
+        val = sc.bdtrc(-1.1, 1, 0.5)
+        val2 = sc.bdtrc(2.1, 1, 0.5)
+        assert np.isnan(val2)
+        assert_allclose(val, 1.0)
+
+    def test_bdtr_bdtrc_sum_to_one(self):
+        bdtr_vals = sc.bdtr([0, 1, 2], 2, 0.5)
+        bdtrc_vals = sc.bdtrc([0, 1, 2], 2, 0.5)
+        vals = bdtr_vals + bdtrc_vals
+        assert_allclose(vals, [1.0, 1.0, 1.0])
+
+
+class TestBdtri(object):
+    def test_value(self):
+        val = sc.bdtri(0, 1, 0.5)
+        assert_allclose(val, 0.5)
+
+    def test_sum_is_one(self):
+        val = sc.bdtri([0, 1], 2, 0.5)
+        actual = np.asarray([1 - 1/np.sqrt(2), 1/np.sqrt(2)])
+        assert_allclose(val, actual)
+
+    def test_rounding(self):
+        double_val = sc.bdtri([0.1, 1.1], 2, 0.5)
+        int_val = sc.bdtri([0, 1], 2, 0.5)
+        assert_allclose(double_val, int_val)
+
+    @pytest.mark.parametrize('k, n, p', [
+        (np.inf, 2, 0.5),
+        (1.0, np.inf, 0.5),
+        (1.0, 2, np.inf)
+    ])
+    def test_inf(self, k, n, p):
+        with suppress_warnings() as sup:
+            sup.filter(DeprecationWarning)
+            val = sc.bdtri(k, n, p)
+        assert np.isnan(val)
+
+    @pytest.mark.parametrize('k, n, p', [
+        (-1.1, 1, 0.5),
+        (2.1, 1, 0.5)
+    ])
+    def test_domain(self, k, n, p):
+        val = sc.bdtri(k, n, p)
+        assert np.isnan(val)
+
+    def test_bdtr_bdtri_roundtrip(self):
+        bdtr_vals = sc.bdtr([0, 1, 2], 2, 0.5)
+        roundtrip_vals = sc.bdtri([0, 1, 2], 2, bdtr_vals)
+        assert_allclose(roundtrip_vals, [0.5, 0.5, np.nan])

venv/Lib/site-packages/scipy/special/tests/test_boxcox.py

@@ -0,0 +1,106 @@
+import numpy as np
+from numpy.testing import assert_equal, assert_almost_equal, assert_allclose
+from scipy.special import boxcox, boxcox1p, inv_boxcox, inv_boxcox1p
+
+
+# There are more tests of boxcox and boxcox1p in test_mpmath.py.
+
+def test_boxcox_basic():
+    x = np.array([0.5, 1, 2, 4])
+
+    # lambda = 0  =>  y = log(x)
+    y = boxcox(x, 0)
+    assert_almost_equal(y, np.log(x))
+
+    # lambda = 1  =>  y = x - 1
+    y = boxcox(x, 1)
+    assert_almost_equal(y, x - 1)
+
+    # lambda = 2  =>  y = 0.5*(x**2 - 1)
+    y = boxcox(x, 2)
+    assert_almost_equal(y, 0.5*(x**2 - 1))
+
+    # x = 0 and lambda > 0  =>  y = -1 / lambda
+    lam = np.array([0.5, 1, 2])
+    y = boxcox(0, lam)
+    assert_almost_equal(y, -1.0 / lam)
+
+def test_boxcox_underflow():
+    x = 1 + 1e-15
+    lmbda = 1e-306
+    y = boxcox(x, lmbda)
+    assert_allclose(y, np.log(x), rtol=1e-14)
+
+
+def test_boxcox_nonfinite():
+    # x < 0  =>  y = nan
+    x = np.array([-1, -1, -0.5])
+    y = boxcox(x, [0.5, 2.0, -1.5])
+    assert_equal(y, np.array([np.nan, np.nan, np.nan]))
+
+    # x = 0 and lambda <= 0  =>  y = -inf
+    x = 0
+    y = boxcox(x, [-2.5, 0])
+    assert_equal(y, np.array([-np.inf, -np.inf]))
+
+
+def test_boxcox1p_basic():
+    x = np.array([-0.25, -1e-20, 0, 1e-20, 0.25, 1, 3])
+
+    # lambda = 0  =>  y = log(1+x)
+    y = boxcox1p(x, 0)
+    assert_almost_equal(y, np.log1p(x))
+
+    # lambda = 1  =>  y = x
+    y = boxcox1p(x, 1)
+    assert_almost_equal(y, x)
+
+    # lambda = 2  =>  y = 0.5*((1+x)**2 - 1) = 0.5*x*(2 + x)
+    y = boxcox1p(x, 2)
+    assert_almost_equal(y, 0.5*x*(2 + x))
+
+    # x = -1 and lambda > 0  =>  y = -1 / lambda
+    lam = np.array([0.5, 1, 2])
+    y = boxcox1p(-1, lam)
+    assert_almost_equal(y, -1.0 / lam)
+
+
+def test_boxcox1p_underflow():
+    x = np.array([1e-15, 1e-306])
+    lmbda = np.array([1e-306, 1e-18])
+    y = boxcox1p(x, lmbda)
+    assert_allclose(y, np.log1p(x), rtol=1e-14)
+
+
+def test_boxcox1p_nonfinite():
+    # x < -1  =>  y = nan
+    x = np.array([-2, -2, -1.5])
+    y = boxcox1p(x, [0.5, 2.0, -1.5])
+    assert_equal(y, np.array([np.nan, np.nan, np.nan]))
+
+    # x = -1 and lambda <= 0  =>  y = -inf
+    x = -1
+    y = boxcox1p(x, [-2.5, 0])
+    assert_equal(y, np.array([-np.inf, -np.inf]))
+
+
+def test_inv_boxcox():
+    x = np.array([0., 1., 2.])
+    lam = np.array([0., 1., 2.])
+    y = boxcox(x, lam)
+    x2 = inv_boxcox(y, lam)
+    assert_almost_equal(x, x2)
+
+    x = np.array([0., 1., 2.])
+    lam = np.array([0., 1., 2.])
+    y = boxcox1p(x, lam)
+    x2 = inv_boxcox1p(y, lam)
+    assert_almost_equal(x, x2)
+
+
+def test_inv_boxcox1p_underflow():
+    x = 1e-15
+    lam = 1e-306
+    y = inv_boxcox1p(x, lam)
+    assert_allclose(y, x, rtol=1e-14)
+

venv/Lib/site-packages/scipy/special/tests/test_cdflib.py

@@ -0,0 +1,406 @@
+"""
+Test cdflib functions versus mpmath, if available.
+
+The following functions still need tests:
+
+- ncfdtr
+- ncfdtri
+- ncfdtridfn
+- ncfdtridfd
+- ncfdtrinc
+- nbdtrik
+- nbdtrin
+- nrdtrimn
+- nrdtrisd
+- pdtrik
+- nctdtr
+- nctdtrit
+- nctdtridf
+- nctdtrinc
+
+"""
+import itertools
+
+import numpy as np
+from numpy.testing import assert_equal
+import pytest
+
+import scipy.special as sp
+from scipy.special._testutils import (
+    MissingModule, check_version, FuncData)
+from scipy.special._mptestutils import (
+    Arg, IntArg, get_args, mpf2float, assert_mpmath_equal)
+
+try:
+    import mpmath  # type: ignore[import]
+except ImportError:
+    mpmath = MissingModule('mpmath')
+
+
+class ProbArg(object):
+    """Generate a set of probabilities on [0, 1]."""
+    def __init__(self):
+        # Include the endpoints for compatibility with Arg et. al.
+        self.a = 0
+        self.b = 1
+
+    def values(self, n):
+        """Return an array containing approximatively n numbers."""
+        m = max(1, n//3)
+        v1 = np.logspace(-30, np.log10(0.3), m)
+        v2 = np.linspace(0.3, 0.7, m + 1, endpoint=False)[1:]
+        v3 = 1 - np.logspace(np.log10(0.3), -15, m)
+        v = np.r_[v1, v2, v3]
+        return np.unique(v)
+
+
+class EndpointFilter(object):
+    def __init__(self, a, b, rtol, atol):
+        self.a = a
+        self.b = b
+        self.rtol = rtol
+        self.atol = atol
+
+    def __call__(self, x):
+        mask1 = np.abs(x - self.a) < self.rtol*np.abs(self.a) + self.atol
+        mask2 = np.abs(x - self.b) < self.rtol*np.abs(self.b) + self.atol
+        return np.where(mask1 | mask2, False, True)
+
+
+class _CDFData(object):
+    def __init__(self, spfunc, mpfunc, index, argspec, spfunc_first=True,
+                 dps=20, n=5000, rtol=None, atol=None,
+                 endpt_rtol=None, endpt_atol=None):
+        self.spfunc = spfunc
+        self.mpfunc = mpfunc
+        self.index = index
+        self.argspec = argspec
+        self.spfunc_first = spfunc_first
+        self.dps = dps
+        self.n = n
+        self.rtol = rtol
+        self.atol = atol
+
+        if not isinstance(argspec, list):
+            self.endpt_rtol = None
+            self.endpt_atol = None
+        elif endpt_rtol is not None or endpt_atol is not None:
+            if isinstance(endpt_rtol, list):
+                self.endpt_rtol = endpt_rtol
+            else:
+                self.endpt_rtol = [endpt_rtol]*len(self.argspec)
+            if isinstance(endpt_atol, list):
+                self.endpt_atol = endpt_atol
+            else:
+                self.endpt_atol = [endpt_atol]*len(self.argspec)
+        else:
+            self.endpt_rtol = None
+            self.endpt_atol = None
+
+    def idmap(self, *args):
+        if self.spfunc_first:
+            res = self.spfunc(*args)
+            if np.isnan(res):
+                return np.nan
+            args = list(args)
+            args[self.index] = res
+            with mpmath.workdps(self.dps):
+                res = self.mpfunc(*tuple(args))
+                # Imaginary parts are spurious
+                res = mpf2float(res.real)
+        else:
+            with mpmath.workdps(self.dps):
+                res = self.mpfunc(*args)
+                res = mpf2float(res.real)
+            args = list(args)
+            args[self.index] = res
+            res = self.spfunc(*tuple(args))
+        return res
+
+    def get_param_filter(self):
+        if self.endpt_rtol is None and self.endpt_atol is None:
+            return None
+
+        filters = []
+        for rtol, atol, spec in zip(self.endpt_rtol, self.endpt_atol, self.argspec):
+            if rtol is None and atol is None:
+                filters.append(None)
+                continue
+            elif rtol is None:
+                rtol = 0.0
+            elif atol is None:
+                atol = 0.0
+
+            filters.append(EndpointFilter(spec.a, spec.b, rtol, atol))
+        return filters
+
+    def check(self):
+        # Generate values for the arguments
+        args = get_args(self.argspec, self.n)
+        param_filter = self.get_param_filter()
+        param_columns = tuple(range(args.shape[1]))
+        result_columns = args.shape[1]
+        args = np.hstack((args, args[:,self.index].reshape(args.shape[0], 1)))
+        FuncData(self.idmap, args,
+                 param_columns=param_columns, result_columns=result_columns,
+                 rtol=self.rtol, atol=self.atol, vectorized=False,
+                 param_filter=param_filter).check()
+
+
+def _assert_inverts(*a, **kw):
+    d = _CDFData(*a, **kw)
+    d.check()
+
+
+def _binomial_cdf(k, n, p):
+    k, n, p = mpmath.mpf(k), mpmath.mpf(n), mpmath.mpf(p)
+    if k <= 0:
+        return mpmath.mpf(0)
+    elif k >= n:
+        return mpmath.mpf(1)
+
+    onemp = mpmath.fsub(1, p, exact=True)
+    return mpmath.betainc(n - k, k + 1, x2=onemp, regularized=True)
+
+
+def _f_cdf(dfn, dfd, x):
+    if x < 0:
+        return mpmath.mpf(0)
+    dfn, dfd, x = mpmath.mpf(dfn), mpmath.mpf(dfd), mpmath.mpf(x)
+    ub = dfn*x/(dfn*x + dfd)
+    res = mpmath.betainc(dfn/2, dfd/2, x2=ub, regularized=True)
+    return res
+
+
+def _student_t_cdf(df, t, dps=None):
+    if dps is None:
+        dps = mpmath.mp.dps
+    with mpmath.workdps(dps):
+        df, t = mpmath.mpf(df), mpmath.mpf(t)
+        fac = mpmath.hyp2f1(0.5, 0.5*(df + 1), 1.5, -t**2/df)
+        fac *= t*mpmath.gamma(0.5*(df + 1))
+        fac /= mpmath.sqrt(mpmath.pi*df)*mpmath.gamma(0.5*df)
+        return 0.5 + fac
+
+
+def _noncentral_chi_pdf(t, df, nc):
+    res = mpmath.besseli(df/2 - 1, mpmath.sqrt(nc*t))
+    res *= mpmath.exp(-(t + nc)/2)*(t/nc)**(df/4 - 1/2)/2
+    return res
+
+
+def _noncentral_chi_cdf(x, df, nc, dps=None):
+    if dps is None:
+        dps = mpmath.mp.dps
+    x, df, nc = mpmath.mpf(x), mpmath.mpf(df), mpmath.mpf(nc)
+    with mpmath.workdps(dps):
+        res = mpmath.quad(lambda t: _noncentral_chi_pdf(t, df, nc), [0, x])
+        return res
+
+
+def _tukey_lmbda_quantile(p, lmbda):
+    # For lmbda != 0
+    return (p**lmbda - (1 - p)**lmbda)/lmbda
+
+
+@pytest.mark.slow
+@check_version(mpmath, '0.19')
+class TestCDFlib(object):
+
+    @pytest.mark.xfail(run=False)
+    def test_bdtrik(self):
+        _assert_inverts(
+            sp.bdtrik,
+            _binomial_cdf,
+            0, [ProbArg(), IntArg(1, 1000), ProbArg()],
+            rtol=1e-4)
+
+    def test_bdtrin(self):
+        _assert_inverts(
+            sp.bdtrin,
+            _binomial_cdf,
+            1, [IntArg(1, 1000), ProbArg(), ProbArg()],
+            rtol=1e-4, endpt_atol=[None, None, 1e-6])
+
+    def test_btdtria(self):
+        _assert_inverts(
+            sp.btdtria,
+            lambda a, b, x: mpmath.betainc(a, b, x2=x, regularized=True),
+            0, [ProbArg(), Arg(0, 1e2, inclusive_a=False),
+                Arg(0, 1, inclusive_a=False, inclusive_b=False)],
+            rtol=1e-6)
+
+    def test_btdtrib(self):
+        # Use small values of a or mpmath doesn't converge
+        _assert_inverts(
+            sp.btdtrib,
+            lambda a, b, x: mpmath.betainc(a, b, x2=x, regularized=True),
+            1, [Arg(0, 1e2, inclusive_a=False), ProbArg(),
+             Arg(0, 1, inclusive_a=False, inclusive_b=False)],
+            rtol=1e-7, endpt_atol=[None, 1e-18, 1e-15])
+
+    @pytest.mark.xfail(run=False)
+    def test_fdtridfd(self):
+        _assert_inverts(
+            sp.fdtridfd,
+            _f_cdf,
+            1, [IntArg(1, 100), ProbArg(), Arg(0, 100, inclusive_a=False)],
+            rtol=1e-7)
+
+    def test_gdtria(self):
+        _assert_inverts(
+            sp.gdtria,
+            lambda a, b, x: mpmath.gammainc(b, b=a*x, regularized=True),
+            0, [ProbArg(), Arg(0, 1e3, inclusive_a=False),
+                Arg(0, 1e4, inclusive_a=False)], rtol=1e-7,
+            endpt_atol=[None, 1e-7, 1e-10])
+
+    def test_gdtrib(self):
+        # Use small values of a and x or mpmath doesn't converge
+        _assert_inverts(
+            sp.gdtrib,
+            lambda a, b, x: mpmath.gammainc(b, b=a*x, regularized=True),
+            1, [Arg(0, 1e2, inclusive_a=False), ProbArg(),
+                Arg(0, 1e3, inclusive_a=False)], rtol=1e-5)
+
+    def test_gdtrix(self):
+        _assert_inverts(
+            sp.gdtrix,
+            lambda a, b, x: mpmath.gammainc(b, b=a*x, regularized=True),
+            2, [Arg(0, 1e3, inclusive_a=False), Arg(0, 1e3, inclusive_a=False),
+                ProbArg()], rtol=1e-7,
+            endpt_atol=[None, 1e-7, 1e-10])
+
+    def test_stdtr(self):
+        # Ideally the left endpoint for Arg() should be 0.
+        assert_mpmath_equal(
+            sp.stdtr,
+            _student_t_cdf,
+            [IntArg(1, 100), Arg(1e-10, np.inf)], rtol=1e-7)
+
+    @pytest.mark.xfail(run=False)
+    def test_stdtridf(self):
+        _assert_inverts(
+            sp.stdtridf,
+            _student_t_cdf,
+            0, [ProbArg(), Arg()], rtol=1e-7)
+
+    def test_stdtrit(self):
+        _assert_inverts(
+            sp.stdtrit,
+            _student_t_cdf,
+            1, [IntArg(1, 100), ProbArg()], rtol=1e-7,
+            endpt_atol=[None, 1e-10])
+
+    def test_chdtriv(self):
+        _assert_inverts(
+            sp.chdtriv,
+            lambda v, x: mpmath.gammainc(v/2, b=x/2, regularized=True),
+            0, [ProbArg(), IntArg(1, 100)], rtol=1e-4)
+
+    @pytest.mark.xfail(run=False)
+    def test_chndtridf(self):
+        # Use a larger atol since mpmath is doing numerical integration
+        _assert_inverts(
+            sp.chndtridf,
+            _noncentral_chi_cdf,
+            1, [Arg(0, 100, inclusive_a=False), ProbArg(),
+                Arg(0, 100, inclusive_a=False)],
+            n=1000, rtol=1e-4, atol=1e-15)
+
+    @pytest.mark.xfail(run=False)
+    def test_chndtrinc(self):
+        # Use a larger atol since mpmath is doing numerical integration
+        _assert_inverts(
+            sp.chndtrinc,
+            _noncentral_chi_cdf,
+            2, [Arg(0, 100, inclusive_a=False), IntArg(1, 100), ProbArg()],
+            n=1000, rtol=1e-4, atol=1e-15)
+
+    def test_chndtrix(self):
+        # Use a larger atol since mpmath is doing numerical integration
+        _assert_inverts(
+            sp.chndtrix,
+            _noncentral_chi_cdf,
+            0, [ProbArg(), IntArg(1, 100), Arg(0, 100, inclusive_a=False)],
+            n=1000, rtol=1e-4, atol=1e-15,
+            endpt_atol=[1e-6, None, None])
+
+    def test_tklmbda_zero_shape(self):
+        # When lmbda = 0 the CDF has a simple closed form
+        one = mpmath.mpf(1)
+        assert_mpmath_equal(
+            lambda x: sp.tklmbda(x, 0),
+            lambda x: one/(mpmath.exp(-x) + one),
+            [Arg()], rtol=1e-7)
+
+    def test_tklmbda_neg_shape(self):
+        _assert_inverts(
+            sp.tklmbda,
+            _tukey_lmbda_quantile,
+            0, [ProbArg(), Arg(-25, 0, inclusive_b=False)],
+            spfunc_first=False, rtol=1e-5,
+            endpt_atol=[1e-9, 1e-5])
+
+    @pytest.mark.xfail(run=False)
+    def test_tklmbda_pos_shape(self):
+        _assert_inverts(
+            sp.tklmbda,
+            _tukey_lmbda_quantile,
+            0, [ProbArg(), Arg(0, 100, inclusive_a=False)],
+            spfunc_first=False, rtol=1e-5)
+
+
+def test_nonfinite():
+    funcs = [
+        ("btdtria", 3),
+        ("btdtrib", 3),
+        ("bdtrik", 3),
+        ("bdtrin", 3),
+        ("chdtriv", 2),
+        ("chndtr", 3),
+        ("chndtrix", 3),
+        ("chndtridf", 3),
+        ("chndtrinc", 3),
+        ("fdtridfd", 3),
+        ("ncfdtr", 4),
+        ("ncfdtri", 4),
+        ("ncfdtridfn", 4),
+        ("ncfdtridfd", 4),
+        ("ncfdtrinc", 4),
+        ("gdtrix", 3),
+        ("gdtrib", 3),
+        ("gdtria", 3),
+        ("nbdtrik", 3),
+        ("nbdtrin", 3),
+        ("nrdtrimn", 3),
+        ("nrdtrisd", 3),
+        ("pdtrik", 2),
+        ("stdtr", 2),
+        ("stdtrit", 2),
+        ("stdtridf", 2),
+        ("nctdtr", 3),
+        ("nctdtrit", 3),
+        ("nctdtridf", 3),
+        ("nctdtrinc", 3),
+        ("tklmbda", 2),
+    ]
+
+    np.random.seed(1)
+
+    for func, numargs in funcs:
+        func = getattr(sp, func)
+
+        args_choices = [(float(x), np.nan, np.inf, -np.inf) for x in
+                        np.random.rand(numargs)]
+
+        for args in itertools.product(*args_choices):
+            res = func(*args)
+
+            if any(np.isnan(x) for x in args):
+                # Nan inputs should result to nan output
+                assert_equal(res, np.nan)
+            else:
+                # All other inputs should return something (but not
+                # raise exceptions or cause hangs)
+                pass

venv/Lib/site-packages/scipy/special/tests/test_cython_special.py

@@ -0,0 +1,340 @@
+import pytest
+from itertools import product
+from numpy.testing import assert_allclose, suppress_warnings
+from scipy import special
+from scipy.special import cython_special
+
+
+bint_points = [True, False]
+int_points = [-10, -1, 1, 10]
+real_points = [-10.0, -1.0, 1.0, 10.0]
+complex_points = [complex(*tup) for tup in product(real_points, repeat=2)]
+
+
+CYTHON_SIGNATURE_MAP = {
+    'b': 'bint',
+    'f': 'float',
+    'd': 'double',
+    'g': 'long double',
+    'F': 'float complex',
+    'D': 'double complex',
+    'G': 'long double complex',
+    'i':'int',
+    'l': 'long'
+}
+
+
+TEST_POINTS = {
+    'b': bint_points,
+    'f': real_points,
+    'd': real_points,
+    'g': real_points,
+    'F': complex_points,
+    'D': complex_points,
+    'G': complex_points,
+    'i': int_points,
+    'l': int_points,
+}
+
+
+PARAMS = [
+    (special.agm, cython_special.agm, ('dd',), None),
+    (special.airy, cython_special._airy_pywrap, ('d', 'D'), None),
+    (special.airye, cython_special._airye_pywrap, ('d', 'D'), None),
+    (special.bdtr, cython_special.bdtr, ('dld', 'ddd'), None),
+    (special.bdtrc, cython_special.bdtrc, ('dld', 'ddd'), None),
+    (special.bdtri, cython_special.bdtri, ('dld', 'ddd'), None),
+    (special.bdtrik, cython_special.bdtrik, ('ddd',), None),
+    (special.bdtrin, cython_special.bdtrin, ('ddd',), None),
+    (special.bei, cython_special.bei, ('d',), None),
+    (special.beip, cython_special.beip, ('d',), None),
+    (special.ber, cython_special.ber, ('d',), None),
+    (special.berp, cython_special.berp, ('d',), None),
+    (special.besselpoly, cython_special.besselpoly, ('ddd',), None),
+    (special.beta, cython_special.beta, ('dd',), None),
+    (special.betainc, cython_special.betainc, ('ddd',), None),
+    (special.betaincinv, cython_special.betaincinv, ('ddd',), None),
+    (special.betaln, cython_special.betaln, ('dd',), None),
+    (special.binom, cython_special.binom, ('dd',), None),
+    (special.boxcox, cython_special.boxcox, ('dd',), None),
+    (special.boxcox1p, cython_special.boxcox1p, ('dd',), None),
+    (special.btdtr, cython_special.btdtr, ('ddd',), None),
+    (special.btdtri, cython_special.btdtri, ('ddd',), None),
+    (special.btdtria, cython_special.btdtria, ('ddd',), None),
+    (special.btdtrib, cython_special.btdtrib, ('ddd',), None),
+    (special.cbrt, cython_special.cbrt, ('d',), None),
+    (special.chdtr, cython_special.chdtr, ('dd',), None),
+    (special.chdtrc, cython_special.chdtrc, ('dd',), None),
+    (special.chdtri, cython_special.chdtri, ('dd',), None),
+    (special.chdtriv, cython_special.chdtriv, ('dd',), None),
+    (special.chndtr, cython_special.chndtr, ('ddd',), None),
+    (special.chndtridf, cython_special.chndtridf, ('ddd',), None),
+    (special.chndtrinc, cython_special.chndtrinc, ('ddd',), None),
+    (special.chndtrix, cython_special.chndtrix, ('ddd',), None),
+    (special.cosdg, cython_special.cosdg, ('d',), None),
+    (special.cosm1, cython_special.cosm1, ('d',), None),
+    (special.cotdg, cython_special.cotdg, ('d',), None),
+    (special.dawsn, cython_special.dawsn, ('d', 'D'), None),
+    (special.ellipe, cython_special.ellipe, ('d',), None),
+    (special.ellipeinc, cython_special.ellipeinc, ('dd',), None),
+    (special.ellipj, cython_special._ellipj_pywrap, ('dd',), None),
+    (special.ellipkinc, cython_special.ellipkinc, ('dd',), None),
+    (special.ellipkm1, cython_special.ellipkm1, ('d',), None),
+    (special.ellipk, cython_special.ellipk, ('d',), None),
+    (special.entr, cython_special.entr, ('d',), None),
+    (special.erf, cython_special.erf, ('d', 'D'), None),
+    (special.erfc, cython_special.erfc, ('d', 'D'), None),
+    (special.erfcx, cython_special.erfcx, ('d', 'D'), None),
+    (special.erfi, cython_special.erfi, ('d', 'D'), None),
+    (special.erfinv, cython_special.erfinv, ('d'), None),
+    (special.erfcinv, cython_special.erfcinv, ('d'), None),
+    (special.eval_chebyc, cython_special.eval_chebyc, ('dd', 'dD', 'ld'), None),
+    (special.eval_chebys, cython_special.eval_chebys, ('dd', 'dD', 'ld'),
+     'd and l differ for negative int'),
+    (special.eval_chebyt, cython_special.eval_chebyt, ('dd', 'dD', 'ld'),
+     'd and l differ for negative int'),
+    (special.eval_chebyu, cython_special.eval_chebyu, ('dd', 'dD', 'ld'),
+     'd and l differ for negative int'),
+    (special.eval_gegenbauer, cython_special.eval_gegenbauer, ('ddd', 'ddD', 'ldd'),
+     'd and l differ for negative int'),
+    (special.eval_genlaguerre, cython_special.eval_genlaguerre, ('ddd', 'ddD', 'ldd'),
+     'd and l differ for negative int'),
+    (special.eval_hermite, cython_special.eval_hermite, ('ld',), None),
+    (special.eval_hermitenorm, cython_special.eval_hermitenorm, ('ld',), None),
+    (special.eval_jacobi, cython_special.eval_jacobi, ('dddd', 'dddD', 'lddd'),
+     'd and l differ for negative int'),
+    (special.eval_laguerre, cython_special.eval_laguerre, ('dd', 'dD', 'ld'),
+     'd and l differ for negative int'),
+    (special.eval_legendre, cython_special.eval_legendre, ('dd', 'dD', 'ld'), None),
+    (special.eval_sh_chebyt, cython_special.eval_sh_chebyt, ('dd', 'dD', 'ld'), None),
+    (special.eval_sh_chebyu, cython_special.eval_sh_chebyu, ('dd', 'dD', 'ld'),
+     'd and l differ for negative int'),
+    (special.eval_sh_jacobi, cython_special.eval_sh_jacobi, ('dddd', 'dddD', 'lddd'),
+     'd and l differ for negative int'),
+    (special.eval_sh_legendre, cython_special.eval_sh_legendre, ('dd', 'dD', 'ld'), None),
+    (special.exp1, cython_special.exp1, ('d', 'D'), None),
+    (special.exp10, cython_special.exp10, ('d',), None),
+    (special.exp2, cython_special.exp2, ('d',), None),
+    (special.expi, cython_special.expi, ('d', 'D'), None),
+    (special.expit, cython_special.expit, ('f', 'd', 'g'), None),
+    (special.expm1, cython_special.expm1, ('d', 'D'), None),
+    (special.expn, cython_special.expn, ('ld', 'dd'), None),
+    (special.exprel, cython_special.exprel, ('d',), None),
+    (special.fdtr, cython_special.fdtr, ('ddd',), None),
+    (special.fdtrc, cython_special.fdtrc, ('ddd',), None),
+    (special.fdtri, cython_special.fdtri, ('ddd',), None),
+    (special.fdtridfd, cython_special.fdtridfd, ('ddd',), None),
+    (special.fresnel, cython_special._fresnel_pywrap, ('d', 'D'), None),
+    (special.gamma, cython_special.gamma, ('d', 'D'), None),
+    (special.gammainc, cython_special.gammainc, ('dd',), None),
+    (special.gammaincc, cython_special.gammaincc, ('dd',), None),
+    (special.gammainccinv, cython_special.gammainccinv, ('dd',), None),
+    (special.gammaincinv, cython_special.gammaincinv, ('dd',), None),
+    (special.gammaln, cython_special.gammaln, ('d',), None),
+    (special.gammasgn, cython_special.gammasgn, ('d',), None),
+    (special.gdtr, cython_special.gdtr, ('ddd',), None),
+    (special.gdtrc, cython_special.gdtrc, ('ddd',), None),
+    (special.gdtria, cython_special.gdtria, ('ddd',), None),
+    (special.gdtrib, cython_special.gdtrib, ('ddd',), None),
+    (special.gdtrix, cython_special.gdtrix, ('ddd',), None),
+    (special.hankel1, cython_special.hankel1, ('dD',), None),
+    (special.hankel1e, cython_special.hankel1e, ('dD',), None),
+    (special.hankel2, cython_special.hankel2, ('dD',), None),
+    (special.hankel2e, cython_special.hankel2e, ('dD',), None),
+    (special.huber, cython_special.huber, ('dd',), None),
+    (special.hyp0f1, cython_special.hyp0f1, ('dd', 'dD'), None),
+    (special.hyp1f1, cython_special.hyp1f1, ('ddd', 'ddD'), None),
+    (special.hyp2f1, cython_special.hyp2f1, ('dddd', 'dddD'), None),
+    (special.hyperu, cython_special.hyperu, ('ddd',), None),
+    (special.i0, cython_special.i0, ('d',), None),
+    (special.i0e, cython_special.i0e, ('d',), None),
+    (special.i1, cython_special.i1, ('d',), None),
+    (special.i1e, cython_special.i1e, ('d',), None),
+    (special.inv_boxcox, cython_special.inv_boxcox, ('dd',), None),
+    (special.inv_boxcox1p, cython_special.inv_boxcox1p, ('dd',), None),
+    (special.it2i0k0, cython_special._it2i0k0_pywrap, ('d',), None),
+    (special.it2j0y0, cython_special._it2j0y0_pywrap, ('d',), None),
+    (special.it2struve0, cython_special.it2struve0, ('d',), None),
+    (special.itairy, cython_special._itairy_pywrap, ('d',), None),
+    (special.iti0k0, cython_special._iti0k0_pywrap, ('d',), None),
+    (special.itj0y0, cython_special._itj0y0_pywrap, ('d',), None),
+    (special.itmodstruve0, cython_special.itmodstruve0, ('d',), None),
+    (special.itstruve0, cython_special.itstruve0, ('d',), None),
+    (special.iv, cython_special.iv, ('dd', 'dD'), None),
+    (special.ive, cython_special.ive, ('dd', 'dD'), None),
+    (special.j0, cython_special.j0, ('d',), None),
+    (special.j1, cython_special.j1, ('d',), None),
+    (special.jv, cython_special.jv, ('dd', 'dD'), None),
+    (special.jve, cython_special.jve, ('dd', 'dD'), None),
+    (special.k0, cython_special.k0, ('d',), None),
+    (special.k0e, cython_special.k0e, ('d',), None),
+    (special.k1, cython_special.k1, ('d',), None),
+    (special.k1e, cython_special.k1e, ('d',), None),
+    (special.kei, cython_special.kei, ('d',), None),
+    (special.keip, cython_special.keip, ('d',), None),
+    (special.kelvin, cython_special._kelvin_pywrap, ('d',), None),
+    (special.ker, cython_special.ker, ('d',), None),
+    (special.kerp, cython_special.kerp, ('d',), None),
+    (special.kl_div, cython_special.kl_div, ('dd',), None),
+    (special.kn, cython_special.kn, ('ld', 'dd'), None),
+    (special.kolmogi, cython_special.kolmogi, ('d',), None),
+    (special.kolmogorov, cython_special.kolmogorov, ('d',), None),
+    (special.kv, cython_special.kv, ('dd', 'dD'), None),
+    (special.kve, cython_special.kve, ('dd', 'dD'), None),
+    (special.log1p, cython_special.log1p, ('d', 'D'), None),
+    (special.log_ndtr, cython_special.log_ndtr, ('d', 'D'), None),
+    (special.loggamma, cython_special.loggamma, ('D',), None),
+    (special.logit, cython_special.logit, ('f', 'd', 'g'), None),
+    (special.lpmv, cython_special.lpmv, ('ddd',), None),
+    (special.mathieu_a, cython_special.mathieu_a, ('dd',), None),
+    (special.mathieu_b, cython_special.mathieu_b, ('dd',), None),
+    (special.mathieu_cem, cython_special._mathieu_cem_pywrap, ('ddd',), None),
+    (special.mathieu_modcem1, cython_special._mathieu_modcem1_pywrap, ('ddd',), None),
+    (special.mathieu_modcem2, cython_special._mathieu_modcem2_pywrap, ('ddd',), None),
+    (special.mathieu_modsem1, cython_special._mathieu_modsem1_pywrap, ('ddd',), None),
+    (special.mathieu_modsem2, cython_special._mathieu_modsem2_pywrap, ('ddd',), None),
+    (special.mathieu_sem, cython_special._mathieu_sem_pywrap, ('ddd',), None),
+    (special.modfresnelm, cython_special._modfresnelm_pywrap, ('d',), None),
+    (special.modfresnelp, cython_special._modfresnelp_pywrap, ('d',), None),
+    (special.modstruve, cython_special.modstruve, ('dd',), None),
+    (special.nbdtr, cython_special.nbdtr, ('lld', 'ddd'), None),
+    (special.nbdtrc, cython_special.nbdtrc, ('lld', 'ddd'), None),
+    (special.nbdtri, cython_special.nbdtri, ('lld', 'ddd'), None),
+    (special.nbdtrik, cython_special.nbdtrik, ('ddd',), None),
+    (special.nbdtrin, cython_special.nbdtrin, ('ddd',), None),
+    (special.ncfdtr, cython_special.ncfdtr, ('dddd',), None),
+    (special.ncfdtri, cython_special.ncfdtri, ('dddd',), None),
+    (special.ncfdtridfd, cython_special.ncfdtridfd, ('dddd',), None),
+    (special.ncfdtridfn, cython_special.ncfdtridfn, ('dddd',), None),
+    (special.ncfdtrinc, cython_special.ncfdtrinc, ('dddd',), None),
+    (special.nctdtr, cython_special.nctdtr, ('ddd',), None),
+    (special.nctdtridf, cython_special.nctdtridf, ('ddd',), None),
+    (special.nctdtrinc, cython_special.nctdtrinc, ('ddd',), None),
+    (special.nctdtrit, cython_special.nctdtrit, ('ddd',), None),
+    (special.ndtr, cython_special.ndtr, ('d', 'D'), None),
+    (special.ndtri, cython_special.ndtri, ('d',), None),
+    (special.nrdtrimn, cython_special.nrdtrimn, ('ddd',), None),
+    (special.nrdtrisd, cython_special.nrdtrisd, ('ddd',), None),
+    (special.obl_ang1, cython_special._obl_ang1_pywrap, ('dddd',), None),
+    (special.obl_ang1_cv, cython_special._obl_ang1_cv_pywrap, ('ddddd',), None),
+    (special.obl_cv, cython_special.obl_cv, ('ddd',), None),
+    (special.obl_rad1, cython_special._obl_rad1_pywrap, ('dddd',), "see gh-6211"),
+    (special.obl_rad1_cv, cython_special._obl_rad1_cv_pywrap, ('ddddd',), "see gh-6211"),
+    (special.obl_rad2, cython_special._obl_rad2_pywrap, ('dddd',), "see gh-6211"),
+    (special.obl_rad2_cv, cython_special._obl_rad2_cv_pywrap, ('ddddd',), "see gh-6211"),
+    (special.pbdv, cython_special._pbdv_pywrap, ('dd',), None),
+    (special.pbvv, cython_special._pbvv_pywrap, ('dd',), None),
+    (special.pbwa, cython_special._pbwa_pywrap, ('dd',), None),
+    (special.pdtr, cython_special.pdtr, ('dd', 'dd'), None),
+    (special.pdtrc, cython_special.pdtrc, ('dd', 'dd'), None),
+    (special.pdtri, cython_special.pdtri, ('ld', 'dd'), None),
+    (special.pdtrik, cython_special.pdtrik, ('dd',), None),
+    (special.poch, cython_special.poch, ('dd',), None),
+    (special.pro_ang1, cython_special._pro_ang1_pywrap, ('dddd',), None),
+    (special.pro_ang1_cv, cython_special._pro_ang1_cv_pywrap, ('ddddd',), None),
+    (special.pro_cv, cython_special.pro_cv, ('ddd',), None),
+    (special.pro_rad1, cython_special._pro_rad1_pywrap, ('dddd',), "see gh-6211"),
+    (special.pro_rad1_cv, cython_special._pro_rad1_cv_pywrap, ('ddddd',), "see gh-6211"),
+    (special.pro_rad2, cython_special._pro_rad2_pywrap, ('dddd',), "see gh-6211"),
+    (special.pro_rad2_cv, cython_special._pro_rad2_cv_pywrap, ('ddddd',), "see gh-6211"),
+    (special.pseudo_huber, cython_special.pseudo_huber, ('dd',), None),
+    (special.psi, cython_special.psi, ('d', 'D'), None),
+    (special.radian, cython_special.radian, ('ddd',), None),
+    (special.rel_entr, cython_special.rel_entr, ('dd',), None),
+    (special.rgamma, cython_special.rgamma, ('d', 'D'), None),
+    (special.round, cython_special.round, ('d',), None),
+    (special.spherical_jn, cython_special.spherical_jn, ('ld', 'ldb', 'lD', 'lDb'), None),
+    (special.spherical_yn, cython_special.spherical_yn, ('ld', 'ldb', 'lD', 'lDb'), None),
+    (special.spherical_in, cython_special.spherical_in, ('ld', 'ldb', 'lD', 'lDb'), None),
+    (special.spherical_kn, cython_special.spherical_kn, ('ld', 'ldb', 'lD', 'lDb'), None),
+    (special.shichi, cython_special._shichi_pywrap, ('d', 'D'), None),
+    (special.sici, cython_special._sici_pywrap, ('d', 'D'), None),
+    (special.sindg, cython_special.sindg, ('d',), None),
+    (special.smirnov, cython_special.smirnov, ('ld', 'dd'), None),
+    (special.smirnovi, cython_special.smirnovi, ('ld', 'dd'), None),
+    (special.spence, cython_special.spence, ('d', 'D'), None),
+    (special.sph_harm, cython_special.sph_harm, ('lldd', 'dddd'), None),
+    (special.stdtr, cython_special.stdtr, ('dd',), None),
+    (special.stdtridf, cython_special.stdtridf, ('dd',), None),
+    (special.stdtrit, cython_special.stdtrit, ('dd',), None),
+    (special.struve, cython_special.struve, ('dd',), None),
+    (special.tandg, cython_special.tandg, ('d',), None),
+    (special.tklmbda, cython_special.tklmbda, ('dd',), None),
+    (special.voigt_profile, cython_special.voigt_profile, ('ddd',), None),
+    (special.wofz, cython_special.wofz, ('D',), None),
+    (special.wrightomega, cython_special.wrightomega, ('D',), None),
+    (special.xlog1py, cython_special.xlog1py, ('dd', 'DD'), None),
+    (special.xlogy, cython_special.xlogy, ('dd', 'DD'), None),
+    (special.y0, cython_special.y0, ('d',), None),
+    (special.y1, cython_special.y1, ('d',), None),
+    (special.yn, cython_special.yn, ('ld', 'dd'), None),
+    (special.yv, cython_special.yv, ('dd', 'dD'), None),
+    (special.yve, cython_special.yve, ('dd', 'dD'), None),
+    (special.zetac, cython_special.zetac, ('d',), None),
+    (special.owens_t, cython_special.owens_t, ('dd',), None)
+]
+
+
+IDS = [x[0].__name__ for x in PARAMS]
+
+
+def _generate_test_points(typecodes):
+    axes = tuple(map(lambda x: TEST_POINTS[x], typecodes))
+    pts = list(product(*axes))
+    return pts
+
+
+def test_cython_api_completeness():
+    # Check that everything is tested
+    for name in dir(cython_special):
+        func = getattr(cython_special, name)
+        if callable(func) and not name.startswith('_'):
+            for _, cyfun, _, _ in PARAMS:
+                if cyfun is func:
+                    break
+            else:
+                raise RuntimeError("{} missing from tests!".format(name))
+
+
+@pytest.mark.parametrize("param", PARAMS, ids=IDS)
+def test_cython_api(param):
+    pyfunc, cyfunc, specializations, knownfailure = param
+    if knownfailure:
+        pytest.xfail(reason=knownfailure)
+
+    # Check which parameters are expected to be fused types
+    max_params = max(len(spec) for spec in specializations)
+    values = [set() for _ in range(max_params)]
+    for typecodes in specializations:
+        for j, v in enumerate(typecodes):
+            values[j].add(v)
+    seen = set()
+    is_fused_code = [False] * len(values)
+    for j, v in enumerate(values):
+        vv = tuple(sorted(v))
+        if vv in seen:
+            continue
+        is_fused_code[j] = (len(v) > 1)
+        seen.add(vv)
+
+    # Check results
+    for typecodes in specializations:
+        # Pick the correct specialized function
+        signature = [CYTHON_SIGNATURE_MAP[code]
+                     for j, code in enumerate(typecodes)
+                     if is_fused_code[j]]
+
+        if signature:
+            cy_spec_func = cyfunc[tuple(signature)]
+        else:
+            signature = None
+            cy_spec_func = cyfunc
+
+        # Test it
+        pts = _generate_test_points(typecodes)
+        for pt in pts:
+            with suppress_warnings() as sup:
+                sup.filter(DeprecationWarning)
+                pyval = pyfunc(*pt)
+                cyval = cy_spec_func(*pt)
+            assert_allclose(cyval, pyval, err_msg="{} {} {}".format(pt, typecodes, signature))

venv/Lib/site-packages/scipy/special/tests/test_data.py

@@ -0,0 +1,495 @@
+import os
+
+import numpy as np
+from numpy import arccosh, arcsinh, arctanh
+from numpy.testing import suppress_warnings
+import pytest
+
+from scipy.special import (
+    lpn, lpmn, lpmv, lqn, lqmn, sph_harm, eval_legendre, eval_hermite,
+    eval_laguerre, eval_genlaguerre, binom, cbrt, expm1, log1p, zeta,
+    jn, jv, yn, yv, iv, kv, kn,
+    gamma, gammaln, gammainc, gammaincc, gammaincinv, gammainccinv, digamma,
+    beta, betainc, betaincinv, poch,
+    ellipe, ellipeinc, ellipk, ellipkm1, ellipkinc, ellipj,
+    erf, erfc, erfinv, erfcinv, exp1, expi, expn,
+    bdtrik, btdtr, btdtri, btdtria, btdtrib, chndtr, gdtr, gdtrc, gdtrix, gdtrib,
+    nbdtrik, pdtrik, owens_t,
+    mathieu_a, mathieu_b, mathieu_cem, mathieu_sem, mathieu_modcem1,
+    mathieu_modsem1, mathieu_modcem2, mathieu_modsem2,
+    ellip_harm, ellip_harm_2, spherical_jn, spherical_yn,
+)
+from scipy.integrate import IntegrationWarning
+
+from scipy.special._testutils import FuncData
+
+DATASETS_BOOST = np.load(os.path.join(os.path.dirname(__file__),
+                                      "data", "boost.npz"))
+
+DATASETS_GSL = np.load(os.path.join(os.path.dirname(__file__),
+                                    "data", "gsl.npz"))
+
+DATASETS_LOCAL = np.load(os.path.join(os.path.dirname(__file__),
+                                    "data", "local.npz"))
+
+
+def data(func, dataname, *a, **kw):
+    kw.setdefault('dataname', dataname)
+    return FuncData(func, DATASETS_BOOST[dataname], *a, **kw)
+
+
+def data_gsl(func, dataname, *a, **kw):
+    kw.setdefault('dataname', dataname)
+    return FuncData(func, DATASETS_GSL[dataname], *a, **kw)
+
+
+def data_local(func, dataname, *a, **kw):
+    kw.setdefault('dataname', dataname)
+    return FuncData(func, DATASETS_LOCAL[dataname], *a, **kw)
+
+
+def ellipk_(k):
+    return ellipk(k*k)
+
+
+def ellipkinc_(f, k):
+    return ellipkinc(f, k*k)
+
+
+def ellipe_(k):
+    return ellipe(k*k)
+
+
+def ellipeinc_(f, k):
+    return ellipeinc(f, k*k)
+
+
+def ellipj_(k):
+    return ellipj(k*k)
+
+
+def zeta_(x):
+    return zeta(x, 1.)
+
+
+def assoc_legendre_p_boost_(nu, mu, x):
+    # the boost test data is for integer orders only
+    return lpmv(mu, nu.astype(int), x)
+
+def legendre_p_via_assoc_(nu, x):
+    return lpmv(0, nu, x)
+
+def lpn_(n, x):
+    return lpn(n.astype('l'), x)[0][-1]
+
+def lqn_(n, x):
+    return lqn(n.astype('l'), x)[0][-1]
+
+def legendre_p_via_lpmn(n, x):
+    return lpmn(0, n, x)[0][0,-1]
+
+def legendre_q_via_lqmn(n, x):
+    return lqmn(0, n, x)[0][0,-1]
+
+def mathieu_ce_rad(m, q, x):
+    return mathieu_cem(m, q, x*180/np.pi)[0]
+
+
+def mathieu_se_rad(m, q, x):
+    return mathieu_sem(m, q, x*180/np.pi)[0]
+
+
+def mathieu_mc1_scaled(m, q, x):
+    # GSL follows a different normalization.
+    # We follow Abramowitz & Stegun, they apparently something else.
+    return mathieu_modcem1(m, q, x)[0] * np.sqrt(np.pi/2)
+
+
+def mathieu_ms1_scaled(m, q, x):
+    return mathieu_modsem1(m, q, x)[0] * np.sqrt(np.pi/2)
+
+
+def mathieu_mc2_scaled(m, q, x):
+    return mathieu_modcem2(m, q, x)[0] * np.sqrt(np.pi/2)
+
+
+def mathieu_ms2_scaled(m, q, x):
+    return mathieu_modsem2(m, q, x)[0] * np.sqrt(np.pi/2)
+
+def eval_legendre_ld(n, x):
+    return eval_legendre(n.astype('l'), x)
+
+def eval_legendre_dd(n, x):
+    return eval_legendre(n.astype('d'), x)
+
+def eval_hermite_ld(n, x):
+    return eval_hermite(n.astype('l'), x)
+
+def eval_laguerre_ld(n, x):
+    return eval_laguerre(n.astype('l'), x)
+
+def eval_laguerre_dd(n, x):
+    return eval_laguerre(n.astype('d'), x)
+
+def eval_genlaguerre_ldd(n, a, x):
+    return eval_genlaguerre(n.astype('l'), a, x)
+
+def eval_genlaguerre_ddd(n, a, x):
+    return eval_genlaguerre(n.astype('d'), a, x)
+
+def bdtrik_comp(y, n, p):
+    return bdtrik(1-y, n, p)
+
+def btdtri_comp(a, b, p):
+    return btdtri(a, b, 1-p)
+
+def btdtria_comp(p, b, x):
+    return btdtria(1-p, b, x)
+
+def btdtrib_comp(a, p, x):
+    return btdtrib(a, 1-p, x)
+
+def gdtr_(p, x):
+    return gdtr(1.0, p, x)
+
+def gdtrc_(p, x):
+    return gdtrc(1.0, p, x)
+
+def gdtrix_(b, p):
+    return gdtrix(1.0, b, p)
+
+def gdtrix_comp(b, p):
+    return gdtrix(1.0, b, 1-p)
+
+def gdtrib_(p, x):
+    return gdtrib(1.0, p, x)
+
+def gdtrib_comp(p, x):
+    return gdtrib(1.0, 1-p, x)
+
+def nbdtrik_comp(y, n, p):
+    return nbdtrik(1-y, n, p)
+
+def pdtrik_comp(p, m):
+    return pdtrik(1-p, m)
+
+def poch_(z, m):
+    return 1.0 / poch(z, m)
+
+def poch_minus(z, m):
+    return 1.0 / poch(z, -m)
+
+def spherical_jn_(n, x):
+    return spherical_jn(n.astype('l'), x)
+
+def spherical_yn_(n, x):
+    return spherical_yn(n.astype('l'), x)
+
+def sph_harm_(m, n, theta, phi):
+    y = sph_harm(m, n, theta, phi)
+    return (y.real, y.imag)
+
+def cexpm1(x, y):
+    z = expm1(x + 1j*y)
+    return z.real, z.imag
+
+def clog1p(x, y):
+    z = log1p(x + 1j*y)
+    return z.real, z.imag
+
+
+BOOST_TESTS = [
+        data(arccosh, 'acosh_data_ipp-acosh_data', 0, 1, rtol=5e-13),
+        data(arccosh, 'acosh_data_ipp-acosh_data', 0j, 1, rtol=5e-13),
+
+        data(arcsinh, 'asinh_data_ipp-asinh_data', 0, 1, rtol=1e-11),
+        data(arcsinh, 'asinh_data_ipp-asinh_data', 0j, 1, rtol=1e-11),
+
+        data(arctanh, 'atanh_data_ipp-atanh_data', 0, 1, rtol=1e-11),
+        data(arctanh, 'atanh_data_ipp-atanh_data', 0j, 1, rtol=1e-11),
+
+        data(assoc_legendre_p_boost_, 'assoc_legendre_p_ipp-assoc_legendre_p', (0,1,2), 3, rtol=1e-11),
+
+        data(legendre_p_via_assoc_, 'legendre_p_ipp-legendre_p', (0,1), 2, rtol=1e-11),
+        data(legendre_p_via_assoc_, 'legendre_p_large_ipp-legendre_p_large', (0,1), 2, rtol=9.6e-14),
+        data(legendre_p_via_lpmn, 'legendre_p_ipp-legendre_p', (0,1), 2, rtol=5e-14, vectorized=False),
+        data(legendre_p_via_lpmn, 'legendre_p_large_ipp-legendre_p_large', (0,1), 2, rtol=9.6e-14, vectorized=False),
+        data(lpn_, 'legendre_p_ipp-legendre_p', (0,1), 2, rtol=5e-14, vectorized=False),
+        data(lpn_, 'legendre_p_large_ipp-legendre_p_large', (0,1), 2, rtol=3e-13, vectorized=False),
+        data(eval_legendre_ld, 'legendre_p_ipp-legendre_p', (0,1), 2, rtol=6e-14),
+        data(eval_legendre_ld, 'legendre_p_large_ipp-legendre_p_large', (0,1), 2, rtol=2e-13),
+        data(eval_legendre_dd, 'legendre_p_ipp-legendre_p', (0,1), 2, rtol=2e-14),
+        data(eval_legendre_dd, 'legendre_p_large_ipp-legendre_p_large', (0,1), 2, rtol=2e-13),
+
+        data(lqn_, 'legendre_p_ipp-legendre_p', (0,1), 3, rtol=2e-14, vectorized=False),
+        data(lqn_, 'legendre_p_large_ipp-legendre_p_large', (0,1), 3, rtol=2e-12, vectorized=False),
+        data(legendre_q_via_lqmn, 'legendre_p_ipp-legendre_p', (0,1), 3, rtol=2e-14, vectorized=False),
+        data(legendre_q_via_lqmn, 'legendre_p_large_ipp-legendre_p_large', (0,1), 3, rtol=2e-12, vectorized=False),
+
+        data(beta, 'beta_exp_data_ipp-beta_exp_data', (0,1), 2, rtol=1e-13),
+        data(beta, 'beta_exp_data_ipp-beta_exp_data', (0,1), 2, rtol=1e-13),
+        data(beta, 'beta_small_data_ipp-beta_small_data', (0,1), 2),
+        data(beta, 'beta_med_data_ipp-beta_med_data', (0,1), 2, rtol=5e-13),
+
+        data(betainc, 'ibeta_small_data_ipp-ibeta_small_data', (0,1,2), 5, rtol=6e-15),
+        data(betainc, 'ibeta_data_ipp-ibeta_data', (0,1,2), 5, rtol=5e-13),
+        data(betainc, 'ibeta_int_data_ipp-ibeta_int_data', (0,1,2), 5, rtol=2e-14),
+        data(betainc, 'ibeta_large_data_ipp-ibeta_large_data', (0,1,2), 5, rtol=4e-10),
+
+        data(betaincinv, 'ibeta_inv_data_ipp-ibeta_inv_data', (0,1,2), 3, rtol=1e-5),
+
+        data(btdtr, 'ibeta_small_data_ipp-ibeta_small_data', (0,1,2), 5, rtol=6e-15),
+        data(btdtr, 'ibeta_data_ipp-ibeta_data', (0,1,2), 5, rtol=4e-13),
+        data(btdtr, 'ibeta_int_data_ipp-ibeta_int_data', (0,1,2), 5, rtol=2e-14),
+        data(btdtr, 'ibeta_large_data_ipp-ibeta_large_data', (0,1,2), 5, rtol=4e-10),
+
+        data(btdtri, 'ibeta_inv_data_ipp-ibeta_inv_data', (0,1,2), 3, rtol=1e-5),
+        data(btdtri_comp, 'ibeta_inv_data_ipp-ibeta_inv_data', (0,1,2), 4, rtol=8e-7),
+
+        data(btdtria, 'ibeta_inva_data_ipp-ibeta_inva_data', (2,0,1), 3, rtol=5e-9),
+        data(btdtria_comp, 'ibeta_inva_data_ipp-ibeta_inva_data', (2,0,1), 4, rtol=5e-9),
+
+        data(btdtrib, 'ibeta_inva_data_ipp-ibeta_inva_data', (0,2,1), 5, rtol=5e-9),
+        data(btdtrib_comp, 'ibeta_inva_data_ipp-ibeta_inva_data', (0,2,1), 6, rtol=5e-9),
+
+        data(binom, 'binomial_data_ipp-binomial_data', (0,1), 2, rtol=1e-13),
+        data(binom, 'binomial_large_data_ipp-binomial_large_data', (0,1), 2, rtol=5e-13),
+
+        data(bdtrik, 'binomial_quantile_ipp-binomial_quantile_data', (2,0,1), 3, rtol=5e-9),
+        data(bdtrik_comp, 'binomial_quantile_ipp-binomial_quantile_data', (2,0,1), 4, rtol=5e-9),
+
+        data(nbdtrik, 'negative_binomial_quantile_ipp-negative_binomial_quantile_data', (2,0,1), 3, rtol=4e-9),
+        data(nbdtrik_comp, 'negative_binomial_quantile_ipp-negative_binomial_quantile_data', (2,0,1), 4, rtol=4e-9),
+
+        data(pdtrik, 'poisson_quantile_ipp-poisson_quantile_data', (1,0), 2, rtol=3e-9),
+        data(pdtrik_comp, 'poisson_quantile_ipp-poisson_quantile_data', (1,0), 3, rtol=4e-9),
+
+        data(cbrt, 'cbrt_data_ipp-cbrt_data', 1, 0),
+
+        data(digamma, 'digamma_data_ipp-digamma_data', 0, 1),
+        data(digamma, 'digamma_data_ipp-digamma_data', 0j, 1),
+        data(digamma, 'digamma_neg_data_ipp-digamma_neg_data', 0, 1, rtol=2e-13),
+        data(digamma, 'digamma_neg_data_ipp-digamma_neg_data', 0j, 1, rtol=1e-13),
+        data(digamma, 'digamma_root_data_ipp-digamma_root_data', 0, 1, rtol=1e-15),
+        data(digamma, 'digamma_root_data_ipp-digamma_root_data', 0j, 1, rtol=1e-15),
+        data(digamma, 'digamma_small_data_ipp-digamma_small_data', 0, 1, rtol=1e-15),
+        data(digamma, 'digamma_small_data_ipp-digamma_small_data', 0j, 1, rtol=1e-14),
+
+        data(ellipk_, 'ellint_k_data_ipp-ellint_k_data', 0, 1),
+        data(ellipkinc_, 'ellint_f_data_ipp-ellint_f_data', (0,1), 2, rtol=1e-14),
+        data(ellipe_, 'ellint_e_data_ipp-ellint_e_data', 0, 1),
+        data(ellipeinc_, 'ellint_e2_data_ipp-ellint_e2_data', (0,1), 2, rtol=1e-14),
+
+        data(erf, 'erf_data_ipp-erf_data', 0, 1),
+        data(erf, 'erf_data_ipp-erf_data', 0j, 1, rtol=1e-13),
+        data(erfc, 'erf_data_ipp-erf_data', 0, 2, rtol=6e-15),
+        data(erf, 'erf_large_data_ipp-erf_large_data', 0, 1),
+        data(erf, 'erf_large_data_ipp-erf_large_data', 0j, 1),
+        data(erfc, 'erf_large_data_ipp-erf_large_data', 0, 2, rtol=4e-14),
+        data(erf, 'erf_small_data_ipp-erf_small_data', 0, 1),
+        data(erf, 'erf_small_data_ipp-erf_small_data', 0j, 1, rtol=1e-13),
+        data(erfc, 'erf_small_data_ipp-erf_small_data', 0, 2),
+
+        data(erfinv, 'erf_inv_data_ipp-erf_inv_data', 0, 1),
+        data(erfcinv, 'erfc_inv_data_ipp-erfc_inv_data', 0, 1),
+        data(erfcinv, 'erfc_inv_big_data_ipp-erfc_inv_big_data2', 0, 1),
+
+        data(exp1, 'expint_1_data_ipp-expint_1_data', 1, 2, rtol=1e-13),
+        data(exp1, 'expint_1_data_ipp-expint_1_data', 1j, 2, rtol=5e-9),
+        data(expi, 'expinti_data_ipp-expinti_data', 0, 1, rtol=1e-13),
+        data(expi, 'expinti_data_double_ipp-expinti_data_double', 0, 1, rtol=1e-13),
+
+        data(expn, 'expint_small_data_ipp-expint_small_data', (0,1), 2),
+        data(expn, 'expint_data_ipp-expint_data', (0,1), 2, rtol=1e-14),
+
+        data(gamma, 'test_gamma_data_ipp-near_0', 0, 1),
+        data(gamma, 'test_gamma_data_ipp-near_1', 0, 1),
+        data(gamma, 'test_gamma_data_ipp-near_2', 0, 1),
+        data(gamma, 'test_gamma_data_ipp-near_m10', 0, 1),
+        data(gamma, 'test_gamma_data_ipp-near_m55', 0, 1, rtol=7e-12),
+        data(gamma, 'test_gamma_data_ipp-factorials', 0, 1, rtol=4e-14),
+        data(gamma, 'test_gamma_data_ipp-near_0', 0j, 1, rtol=2e-9),
+        data(gamma, 'test_gamma_data_ipp-near_1', 0j, 1, rtol=2e-9),
+        data(gamma, 'test_gamma_data_ipp-near_2', 0j, 1, rtol=2e-9),
+        data(gamma, 'test_gamma_data_ipp-near_m10', 0j, 1, rtol=2e-9),
+        data(gamma, 'test_gamma_data_ipp-near_m55', 0j, 1, rtol=2e-9),
+        data(gamma, 'test_gamma_data_ipp-factorials', 0j, 1, rtol=2e-13),
+        data(gammaln, 'test_gamma_data_ipp-near_0', 0, 2, rtol=5e-11),
+        data(gammaln, 'test_gamma_data_ipp-near_1', 0, 2, rtol=5e-11),
+        data(gammaln, 'test_gamma_data_ipp-near_2', 0, 2, rtol=2e-10),
+        data(gammaln, 'test_gamma_data_ipp-near_m10', 0, 2, rtol=5e-11),
+        data(gammaln, 'test_gamma_data_ipp-near_m55', 0, 2, rtol=5e-11),
+        data(gammaln, 'test_gamma_data_ipp-factorials', 0, 2),
+
+        data(gammainc, 'igamma_small_data_ipp-igamma_small_data', (0,1), 5, rtol=5e-15),
+        data(gammainc, 'igamma_med_data_ipp-igamma_med_data', (0,1), 5, rtol=2e-13),
+        data(gammainc, 'igamma_int_data_ipp-igamma_int_data', (0,1), 5, rtol=2e-13),
+        data(gammainc, 'igamma_big_data_ipp-igamma_big_data', (0,1), 5, rtol=1e-12),
+
+        data(gdtr_, 'igamma_small_data_ipp-igamma_small_data', (0,1), 5, rtol=1e-13),
+        data(gdtr_, 'igamma_med_data_ipp-igamma_med_data', (0,1), 5, rtol=2e-13),
+        data(gdtr_, 'igamma_int_data_ipp-igamma_int_data', (0,1), 5, rtol=2e-13),
+        data(gdtr_, 'igamma_big_data_ipp-igamma_big_data', (0,1), 5, rtol=2e-9),
+
+        data(gammaincc, 'igamma_small_data_ipp-igamma_small_data', (0,1), 3, rtol=1e-13),
+        data(gammaincc, 'igamma_med_data_ipp-igamma_med_data', (0,1), 3, rtol=2e-13),
+        data(gammaincc, 'igamma_int_data_ipp-igamma_int_data', (0,1), 3, rtol=4e-14),
+        data(gammaincc, 'igamma_big_data_ipp-igamma_big_data', (0,1), 3, rtol=1e-11),
+
+        data(gdtrc_, 'igamma_small_data_ipp-igamma_small_data', (0,1), 3, rtol=1e-13),
+        data(gdtrc_, 'igamma_med_data_ipp-igamma_med_data', (0,1), 3, rtol=2e-13),
+        data(gdtrc_, 'igamma_int_data_ipp-igamma_int_data', (0,1), 3, rtol=4e-14),
+        data(gdtrc_, 'igamma_big_data_ipp-igamma_big_data', (0,1), 3, rtol=1e-11),
+
+        data(gdtrib_, 'igamma_inva_data_ipp-igamma_inva_data', (1,0), 2, rtol=5e-9),
+        data(gdtrib_comp, 'igamma_inva_data_ipp-igamma_inva_data', (1,0), 3, rtol=5e-9),
+
+        data(poch_, 'tgamma_delta_ratio_data_ipp-tgamma_delta_ratio_data', (0,1), 2, rtol=2e-13),
+        data(poch_, 'tgamma_delta_ratio_int_ipp-tgamma_delta_ratio_int', (0,1), 2,),
+        data(poch_, 'tgamma_delta_ratio_int2_ipp-tgamma_delta_ratio_int2', (0,1), 2,),
+        data(poch_minus, 'tgamma_delta_ratio_data_ipp-tgamma_delta_ratio_data', (0,1), 3, rtol=2e-13),
+        data(poch_minus, 'tgamma_delta_ratio_int_ipp-tgamma_delta_ratio_int', (0,1), 3),
+        data(poch_minus, 'tgamma_delta_ratio_int2_ipp-tgamma_delta_ratio_int2', (0,1), 3),
+
+
+        data(eval_hermite_ld, 'hermite_ipp-hermite', (0,1), 2, rtol=2e-14),
+        data(eval_laguerre_ld, 'laguerre2_ipp-laguerre2', (0,1), 2, rtol=7e-12),
+        data(eval_laguerre_dd, 'laguerre2_ipp-laguerre2', (0,1), 2, knownfailure='hyp2f1 insufficiently accurate.'),
+        data(eval_genlaguerre_ldd, 'laguerre3_ipp-laguerre3', (0,1,2), 3, rtol=2e-13),
+        data(eval_genlaguerre_ddd, 'laguerre3_ipp-laguerre3', (0,1,2), 3, knownfailure='hyp2f1 insufficiently accurate.'),
+
+        data(log1p, 'log1p_expm1_data_ipp-log1p_expm1_data', 0, 1),
+        data(expm1, 'log1p_expm1_data_ipp-log1p_expm1_data', 0, 2),
+
+        data(iv, 'bessel_i_data_ipp-bessel_i_data', (0,1), 2, rtol=1e-12),
+        data(iv, 'bessel_i_data_ipp-bessel_i_data', (0,1j), 2, rtol=2e-10, atol=1e-306),
+        data(iv, 'bessel_i_int_data_ipp-bessel_i_int_data', (0,1), 2, rtol=1e-9),
+        data(iv, 'bessel_i_int_data_ipp-bessel_i_int_data', (0,1j), 2, rtol=2e-10),
+
+        data(jn, 'bessel_j_int_data_ipp-bessel_j_int_data', (0,1), 2, rtol=1e-12),
+        data(jn, 'bessel_j_int_data_ipp-bessel_j_int_data', (0,1j), 2, rtol=1e-12),
+        data(jn, 'bessel_j_large_data_ipp-bessel_j_large_data', (0,1), 2, rtol=6e-11),
+        data(jn, 'bessel_j_large_data_ipp-bessel_j_large_data', (0,1j), 2, rtol=6e-11),
+
+        data(jv, 'bessel_j_int_data_ipp-bessel_j_int_data', (0,1), 2, rtol=1e-12),
+        data(jv, 'bessel_j_int_data_ipp-bessel_j_int_data', (0,1j), 2, rtol=1e-12),
+        data(jv, 'bessel_j_data_ipp-bessel_j_data', (0,1), 2, rtol=1e-12),
+        data(jv, 'bessel_j_data_ipp-bessel_j_data', (0,1j), 2, rtol=1e-12),
+
+        data(kn, 'bessel_k_int_data_ipp-bessel_k_int_data', (0,1), 2, rtol=1e-12),
+
+        data(kv, 'bessel_k_int_data_ipp-bessel_k_int_data', (0,1), 2, rtol=1e-12),
+        data(kv, 'bessel_k_int_data_ipp-bessel_k_int_data', (0,1j), 2, rtol=1e-12),
+        data(kv, 'bessel_k_data_ipp-bessel_k_data', (0,1), 2, rtol=1e-12),
+        data(kv, 'bessel_k_data_ipp-bessel_k_data', (0,1j), 2, rtol=1e-12),
+
+        data(yn, 'bessel_y01_data_ipp-bessel_y01_data', (0,1), 2, rtol=1e-12),
+        data(yn, 'bessel_yn_data_ipp-bessel_yn_data', (0,1), 2, rtol=1e-12),
+
+        data(yv, 'bessel_yn_data_ipp-bessel_yn_data', (0,1), 2, rtol=1e-12),
+        data(yv, 'bessel_yn_data_ipp-bessel_yn_data', (0,1j), 2, rtol=1e-12),
+        data(yv, 'bessel_yv_data_ipp-bessel_yv_data', (0,1), 2, rtol=1e-10),
+        data(yv, 'bessel_yv_data_ipp-bessel_yv_data', (0,1j), 2, rtol=1e-10),
+
+        data(zeta_, 'zeta_data_ipp-zeta_data', 0, 1, param_filter=(lambda s: s > 1)),
+        data(zeta_, 'zeta_neg_data_ipp-zeta_neg_data', 0, 1, param_filter=(lambda s: s > 1)),
+        data(zeta_, 'zeta_1_up_data_ipp-zeta_1_up_data', 0, 1, param_filter=(lambda s: s > 1)),
+        data(zeta_, 'zeta_1_below_data_ipp-zeta_1_below_data', 0, 1, param_filter=(lambda s: s > 1)),
+
+        data(gammaincinv, 'gamma_inv_small_data_ipp-gamma_inv_small_data', (0,1), 2, rtol=1e-11),
+        data(gammaincinv, 'gamma_inv_data_ipp-gamma_inv_data', (0,1), 2, rtol=1e-14),
+        data(gammaincinv, 'gamma_inv_big_data_ipp-gamma_inv_big_data', (0,1), 2, rtol=1e-11),
+
+        data(gammainccinv, 'gamma_inv_small_data_ipp-gamma_inv_small_data', (0,1), 3, rtol=1e-12),
+        data(gammainccinv, 'gamma_inv_data_ipp-gamma_inv_data', (0,1), 3, rtol=1e-14),
+        data(gammainccinv, 'gamma_inv_big_data_ipp-gamma_inv_big_data', (0,1), 3, rtol=1e-14),
+
+        data(gdtrix_, 'gamma_inv_small_data_ipp-gamma_inv_small_data', (0,1), 2, rtol=3e-13, knownfailure='gdtrix unflow some points'),
+        data(gdtrix_, 'gamma_inv_data_ipp-gamma_inv_data', (0,1), 2, rtol=3e-15),
+        data(gdtrix_, 'gamma_inv_big_data_ipp-gamma_inv_big_data', (0,1), 2),
+        data(gdtrix_comp, 'gamma_inv_small_data_ipp-gamma_inv_small_data', (0,1), 2, knownfailure='gdtrix bad some points'),
+        data(gdtrix_comp, 'gamma_inv_data_ipp-gamma_inv_data', (0,1), 3, rtol=6e-15),
+        data(gdtrix_comp, 'gamma_inv_big_data_ipp-gamma_inv_big_data', (0,1), 3),
+
+        data(chndtr, 'nccs_ipp-nccs', (2,0,1), 3, rtol=3e-5),
+        data(chndtr, 'nccs_big_ipp-nccs_big', (2,0,1), 3, rtol=5e-4, knownfailure='chndtr inaccurate some points'),
+
+        data(sph_harm_, 'spherical_harmonic_ipp-spherical_harmonic', (1,0,3,2), (4,5), rtol=5e-11,
+             param_filter=(lambda p: np.ones(p.shape, '?'),
+                           lambda p: np.ones(p.shape, '?'),
+                           lambda p: np.logical_and(p < 2*np.pi, p >= 0),
+                           lambda p: np.logical_and(p < np.pi, p >= 0))),
+
+        data(spherical_jn_, 'sph_bessel_data_ipp-sph_bessel_data', (0,1), 2, rtol=1e-13),
+        data(spherical_yn_, 'sph_neumann_data_ipp-sph_neumann_data', (0,1), 2, rtol=8e-15),
+
+        data(owens_t, 'owenst_data_ipp-owens_t', (0, 1), 2, rtol=5e-14),
+        data(owens_t, 'owenst_data_ipp-owens_t_alarge', (0, 1), 2, rtol=5e-15),
+
+        # -- not used yet (function does not exist in scipy):
+        # 'ellint_pi2_data_ipp-ellint_pi2_data',
+        # 'ellint_pi3_data_ipp-ellint_pi3_data',
+        # 'ellint_pi3_large_data_ipp-ellint_pi3_large_data',
+        # 'ellint_rc_data_ipp-ellint_rc_data',
+        # 'ellint_rd_data_ipp-ellint_rd_data',
+        # 'ellint_rf_data_ipp-ellint_rf_data',
+        # 'ellint_rj_data_ipp-ellint_rj_data',
+        # 'ncbeta_big_ipp-ncbeta_big',
+        # 'ncbeta_ipp-ncbeta',
+        # 'powm1_sqrtp1m1_test_cpp-powm1_data',
+        # 'powm1_sqrtp1m1_test_cpp-sqrtp1m1_data',
+        # 'test_gamma_data_ipp-gammap1m1_data',
+        # 'tgamma_ratio_data_ipp-tgamma_ratio_data',
+]
+
+
+@pytest.mark.parametrize('test', BOOST_TESTS, ids=repr)
+def test_boost(test):
+    _test_factory(test)
+
+
+GSL_TESTS = [
+        data_gsl(mathieu_a, 'mathieu_ab', (0, 1), 2, rtol=1e-13, atol=1e-13),
+        data_gsl(mathieu_b, 'mathieu_ab', (0, 1), 3, rtol=1e-13, atol=1e-13),
+
+        # Also the GSL output has limited accuracy...
+        data_gsl(mathieu_ce_rad, 'mathieu_ce_se', (0, 1, 2), 3, rtol=1e-7, atol=1e-13),
+        data_gsl(mathieu_se_rad, 'mathieu_ce_se', (0, 1, 2), 4, rtol=1e-7, atol=1e-13),
+
+        data_gsl(mathieu_mc1_scaled, 'mathieu_mc_ms', (0, 1, 2), 3, rtol=1e-7, atol=1e-13),
+        data_gsl(mathieu_ms1_scaled, 'mathieu_mc_ms', (0, 1, 2), 4, rtol=1e-7, atol=1e-13),
+
+        data_gsl(mathieu_mc2_scaled, 'mathieu_mc_ms', (0, 1, 2), 5, rtol=1e-7, atol=1e-13),
+        data_gsl(mathieu_ms2_scaled, 'mathieu_mc_ms', (0, 1, 2), 6, rtol=1e-7, atol=1e-13),
+]
+
+
+@pytest.mark.parametrize('test', GSL_TESTS, ids=repr)
+def test_gsl(test):
+    _test_factory(test)
+
+
+LOCAL_TESTS = [
+    data_local(ellipkinc, 'ellipkinc_neg_m', (0, 1), 2),
+    data_local(ellipkm1, 'ellipkm1', 0, 1),
+    data_local(ellipeinc, 'ellipeinc_neg_m', (0, 1), 2),
+    data_local(clog1p, 'log1p_expm1_complex', (0,1), (2,3), rtol=1e-14),
+    data_local(cexpm1, 'log1p_expm1_complex', (0,1), (4,5), rtol=1e-14),
+    data_local(gammainc, 'gammainc', (0, 1), 2, rtol=1e-12),
+    data_local(gammaincc, 'gammaincc', (0, 1), 2, rtol=1e-11),
+    data_local(ellip_harm_2, 'ellip',(0, 1, 2, 3, 4), 6, rtol=1e-10, atol=1e-13),
+    data_local(ellip_harm, 'ellip',(0, 1, 2, 3, 4), 5, rtol=1e-10, atol=1e-13),
+]
+
+
+@pytest.mark.parametrize('test', LOCAL_TESTS, ids=repr)
+def test_local(test):
+    _test_factory(test)
+
+
+def _test_factory(test, dtype=np.double):
+    """Boost test"""
+    with suppress_warnings() as sup:
+        sup.filter(IntegrationWarning, "The occurrence of roundoff error is detected")
+        with np.errstate(all='ignore'):
+            test.check(dtype=dtype)

venv/Lib/site-packages/scipy/special/tests/test_digamma.py

@@ -0,0 +1,42 @@
+import numpy as np
+from numpy import pi, log, sqrt
+from numpy.testing import assert_, assert_equal
+
+from scipy.special._testutils import FuncData
+import scipy.special as sc
+
+# Euler-Mascheroni constant
+euler = 0.57721566490153286
+
+
+def test_consistency():
+    # Make sure the implementation of digamma for real arguments
+    # agrees with the implementation of digamma for complex arguments.
+
+    # It's all poles after -1e16
+    x = np.r_[-np.logspace(15, -30, 200), np.logspace(-30, 300, 200)]
+    dataset = np.vstack((x + 0j, sc.digamma(x))).T
+    FuncData(sc.digamma, dataset, 0, 1, rtol=5e-14, nan_ok=True).check()
+
+
+def test_special_values():
+    # Test special values from Gauss's digamma theorem. See
+    #
+    # https://en.wikipedia.org/wiki/Digamma_function
+
+    dataset = [(1, -euler),
+               (0.5, -2*log(2) - euler),
+               (1/3, -pi/(2*sqrt(3)) - 3*log(3)/2 - euler),
+               (1/4, -pi/2 - 3*log(2) - euler),
+               (1/6, -pi*sqrt(3)/2 - 2*log(2) - 3*log(3)/2 - euler),
+               (1/8, -pi/2 - 4*log(2) - (pi + log(2 + sqrt(2)) - log(2 - sqrt(2)))/sqrt(2) - euler)]
+
+    dataset = np.asarray(dataset)
+    FuncData(sc.digamma, dataset, 0, 1, rtol=1e-14).check()
+
+
+def test_nonfinite():
+    pts = [0.0, -0.0, np.inf]
+    std = [-np.inf, np.inf, np.inf]
+    assert_equal(sc.digamma(pts), std)
+    assert_(all(np.isnan(sc.digamma([-np.inf, -1]))))

venv/Lib/site-packages/scipy/special/tests/test_ellip_harm.py

@@ -0,0 +1,278 @@
+#
+# Tests for the Ellipsoidal Harmonic Function,
+# Distributed under the same license as SciPy itself.
+#
+
+import numpy as np
+from numpy.testing import (assert_equal, assert_almost_equal, assert_allclose,
+                           assert_, suppress_warnings)
+from scipy.special._testutils import assert_func_equal
+from scipy.special import ellip_harm, ellip_harm_2, ellip_normal
+from scipy.integrate import IntegrationWarning
+from numpy import sqrt, pi
+
+
+def test_ellip_potential():
+    def change_coefficient(lambda1, mu, nu, h2, k2):
+        x = sqrt(lambda1**2*mu**2*nu**2/(h2*k2))
+        y = sqrt((lambda1**2 - h2)*(mu**2 - h2)*(h2 - nu**2)/(h2*(k2 - h2)))
+        z = sqrt((lambda1**2 - k2)*(k2 - mu**2)*(k2 - nu**2)/(k2*(k2 - h2)))
+        return x, y, z
+
+    def solid_int_ellip(lambda1, mu, nu, n, p, h2, k2):
+        return (ellip_harm(h2, k2, n, p, lambda1)*ellip_harm(h2, k2, n, p, mu)
+               * ellip_harm(h2, k2, n, p, nu))
+
+    def solid_int_ellip2(lambda1, mu, nu, n, p, h2, k2):
+        return (ellip_harm_2(h2, k2, n, p, lambda1)
+                * ellip_harm(h2, k2, n, p, mu)*ellip_harm(h2, k2, n, p, nu))
+
+    def summation(lambda1, mu1, nu1, lambda2, mu2, nu2, h2, k2):
+        tol = 1e-8
+        sum1 = 0
+        for n in range(20):
+            xsum = 0
+            for p in range(1, 2*n+2):
+                xsum += (4*pi*(solid_int_ellip(lambda2, mu2, nu2, n, p, h2, k2)
+                    * solid_int_ellip2(lambda1, mu1, nu1, n, p, h2, k2)) /
+                    (ellip_normal(h2, k2, n, p)*(2*n + 1)))
+            if abs(xsum) < 0.1*tol*abs(sum1):
+                break
+            sum1 += xsum
+        return sum1, xsum
+
+    def potential(lambda1, mu1, nu1, lambda2, mu2, nu2, h2, k2):
+        x1, y1, z1 = change_coefficient(lambda1, mu1, nu1, h2, k2)
+        x2, y2, z2 = change_coefficient(lambda2, mu2, nu2, h2, k2)
+        res = sqrt((x2 - x1)**2 + (y2 - y1)**2 + (z2 - z1)**2)
+        return 1/res
+
+    pts = [
+        (120, sqrt(19), 2, 41, sqrt(17), 2, 15, 25),
+        (120, sqrt(16), 3.2, 21, sqrt(11), 2.9, 11, 20),
+       ]
+
+    with suppress_warnings() as sup:
+        sup.filter(IntegrationWarning, "The occurrence of roundoff error")
+        sup.filter(IntegrationWarning, "The maximum number of subdivisions")
+
+        for p in pts:
+            err_msg = repr(p)
+            exact = potential(*p)
+            result, last_term = summation(*p)
+            assert_allclose(exact, result, atol=0, rtol=1e-8, err_msg=err_msg)
+            assert_(abs(result - exact) < 10*abs(last_term), err_msg)
+
+
+def test_ellip_norm():
+
+    def G01(h2, k2):
+        return 4*pi
+
+    def G11(h2, k2):
+        return 4*pi*h2*k2/3
+
+    def G12(h2, k2):
+        return 4*pi*h2*(k2 - h2)/3
+
+    def G13(h2, k2):
+        return 4*pi*k2*(k2 - h2)/3
+
+    def G22(h2, k2):
+        res = (2*(h2**4 + k2**4) - 4*h2*k2*(h2**2 + k2**2) + 6*h2**2*k2**2 +
+        sqrt(h2**2 + k2**2 - h2*k2)*(-2*(h2**3 + k2**3) + 3*h2*k2*(h2 + k2)))
+        return 16*pi/405*res
+
+    def G21(h2, k2):
+        res = (2*(h2**4 + k2**4) - 4*h2*k2*(h2**2 + k2**2) + 6*h2**2*k2**2
+        + sqrt(h2**2 + k2**2 - h2*k2)*(2*(h2**3 + k2**3) - 3*h2*k2*(h2 + k2)))
+        return 16*pi/405*res
+
+    def G23(h2, k2):
+        return 4*pi*h2**2*k2*(k2 - h2)/15
+
+    def G24(h2, k2):
+        return 4*pi*h2*k2**2*(k2 - h2)/15
+
+    def G25(h2, k2):
+        return 4*pi*h2*k2*(k2 - h2)**2/15
+
+    def G32(h2, k2):
+        res = (16*(h2**4 + k2**4) - 36*h2*k2*(h2**2 + k2**2) + 46*h2**2*k2**2
+        + sqrt(4*(h2**2 + k2**2) - 7*h2*k2)*(-8*(h2**3 + k2**3) +
+        11*h2*k2*(h2 + k2)))
+        return 16*pi/13125*k2*h2*res
+
+    def G31(h2, k2):
+        res = (16*(h2**4 + k2**4) - 36*h2*k2*(h2**2 + k2**2) + 46*h2**2*k2**2
+        + sqrt(4*(h2**2 + k2**2) - 7*h2*k2)*(8*(h2**3 + k2**3) -
+        11*h2*k2*(h2 + k2)))
+        return 16*pi/13125*h2*k2*res
+
+    def G34(h2, k2):
+        res = (6*h2**4 + 16*k2**4 - 12*h2**3*k2 - 28*h2*k2**3 + 34*h2**2*k2**2
+        + sqrt(h2**2 + 4*k2**2 - h2*k2)*(-6*h2**3 - 8*k2**3 + 9*h2**2*k2 +
+                                            13*h2*k2**2))
+        return 16*pi/13125*h2*(k2 - h2)*res
+
+    def G33(h2, k2):
+        res = (6*h2**4 + 16*k2**4 - 12*h2**3*k2 - 28*h2*k2**3 + 34*h2**2*k2**2
+        + sqrt(h2**2 + 4*k2**2 - h2*k2)*(6*h2**3 + 8*k2**3 - 9*h2**2*k2 -
+        13*h2*k2**2))
+        return 16*pi/13125*h2*(k2 - h2)*res
+
+    def G36(h2, k2):
+        res = (16*h2**4 + 6*k2**4 - 28*h2**3*k2 - 12*h2*k2**3 + 34*h2**2*k2**2
+        + sqrt(4*h2**2 + k2**2 - h2*k2)*(-8*h2**3 - 6*k2**3 + 13*h2**2*k2 +
+        9*h2*k2**2))
+        return 16*pi/13125*k2*(k2 - h2)*res
+
+    def G35(h2, k2):
+        res = (16*h2**4 + 6*k2**4 - 28*h2**3*k2 - 12*h2*k2**3 + 34*h2**2*k2**2
+        + sqrt(4*h2**2 + k2**2 - h2*k2)*(8*h2**3 + 6*k2**3 - 13*h2**2*k2 -
+        9*h2*k2**2))
+        return 16*pi/13125*k2*(k2 - h2)*res
+
+    def G37(h2, k2):
+        return 4*pi*h2**2*k2**2*(k2 - h2)**2/105
+
+    known_funcs = {(0, 1): G01, (1, 1): G11, (1, 2): G12, (1, 3): G13,
+                   (2, 1): G21, (2, 2): G22, (2, 3): G23, (2, 4): G24,
+                   (2, 5): G25, (3, 1): G31, (3, 2): G32, (3, 3): G33,
+                   (3, 4): G34, (3, 5): G35, (3, 6): G36, (3, 7): G37}
+
+    def _ellip_norm(n, p, h2, k2):
+        func = known_funcs[n, p]
+        return func(h2, k2)
+    _ellip_norm = np.vectorize(_ellip_norm)
+
+    def ellip_normal_known(h2, k2, n, p):
+        return _ellip_norm(n, p, h2, k2)
+
+    # generate both large and small h2 < k2 pairs
+    np.random.seed(1234)
+    h2 = np.random.pareto(0.5, size=1)
+    k2 = h2 * (1 + np.random.pareto(0.5, size=h2.size))
+
+    points = []
+    for n in range(4):
+        for p in range(1, 2*n+2):
+            points.append((h2, k2, np.full(h2.size, n), np.full(h2.size, p)))
+    points = np.array(points)
+    with suppress_warnings() as sup:
+        sup.filter(IntegrationWarning, "The occurrence of roundoff error")
+        assert_func_equal(ellip_normal, ellip_normal_known, points, rtol=1e-12)
+
+
+def test_ellip_harm_2():
+
+    def I1(h2, k2, s):
+        res = (ellip_harm_2(h2, k2, 1, 1, s)/(3 * ellip_harm(h2, k2, 1, 1, s))
+        + ellip_harm_2(h2, k2, 1, 2, s)/(3 * ellip_harm(h2, k2, 1, 2, s)) +
+        ellip_harm_2(h2, k2, 1, 3, s)/(3 * ellip_harm(h2, k2, 1, 3, s)))
+        return res
+
+    with suppress_warnings() as sup:
+        sup.filter(IntegrationWarning, "The occurrence of roundoff error")
+        assert_almost_equal(I1(5, 8, 10), 1/(10*sqrt((100-5)*(100-8))))
+
+        # Values produced by code from arXiv:1204.0267
+        assert_almost_equal(ellip_harm_2(5, 8, 2, 1, 10), 0.00108056853382)
+        assert_almost_equal(ellip_harm_2(5, 8, 2, 2, 10), 0.00105820513809)
+        assert_almost_equal(ellip_harm_2(5, 8, 2, 3, 10), 0.00106058384743)
+        assert_almost_equal(ellip_harm_2(5, 8, 2, 4, 10), 0.00106774492306)
+        assert_almost_equal(ellip_harm_2(5, 8, 2, 5, 10), 0.00107976356454)
+
+
+def test_ellip_harm():
+
+    def E01(h2, k2, s):
+        return 1
+
+    def E11(h2, k2, s):
+        return s
+
+    def E12(h2, k2, s):
+        return sqrt(abs(s*s - h2))
+
+    def E13(h2, k2, s):
+        return sqrt(abs(s*s - k2))
+
+    def E21(h2, k2, s):
+        return s*s - 1/3*((h2 + k2) + sqrt(abs((h2 + k2)*(h2 + k2)-3*h2*k2)))
+
+    def E22(h2, k2, s):
+        return s*s - 1/3*((h2 + k2) - sqrt(abs((h2 + k2)*(h2 + k2)-3*h2*k2)))
+
+    def E23(h2, k2, s):
+        return s * sqrt(abs(s*s - h2))
+
+    def E24(h2, k2, s):
+        return s * sqrt(abs(s*s - k2))
+
+    def E25(h2, k2, s):
+        return sqrt(abs((s*s - h2)*(s*s - k2)))
+
+    def E31(h2, k2, s):
+        return s*s*s - (s/5)*(2*(h2 + k2) + sqrt(4*(h2 + k2)*(h2 + k2) -
+        15*h2*k2))
+
+    def E32(h2, k2, s):
+        return s*s*s - (s/5)*(2*(h2 + k2) - sqrt(4*(h2 + k2)*(h2 + k2) -
+        15*h2*k2))
+
+    def E33(h2, k2, s):
+        return sqrt(abs(s*s - h2))*(s*s - 1/5*((h2 + 2*k2) + sqrt(abs((h2 +
+        2*k2)*(h2 + 2*k2) - 5*h2*k2))))
+
+    def E34(h2, k2, s):
+        return sqrt(abs(s*s - h2))*(s*s - 1/5*((h2 + 2*k2) - sqrt(abs((h2 +
+        2*k2)*(h2 + 2*k2) - 5*h2*k2))))
+
+    def E35(h2, k2, s):
+        return sqrt(abs(s*s - k2))*(s*s - 1/5*((2*h2 + k2) + sqrt(abs((2*h2
+        + k2)*(2*h2 + k2) - 5*h2*k2))))
+
+    def E36(h2, k2, s):
+        return sqrt(abs(s*s - k2))*(s*s - 1/5*((2*h2 + k2) - sqrt(abs((2*h2
+        + k2)*(2*h2 + k2) - 5*h2*k2))))
+
+    def E37(h2, k2, s):
+        return s * sqrt(abs((s*s - h2)*(s*s - k2)))
+
+    assert_equal(ellip_harm(5, 8, 1, 2, 2.5, 1, 1),
+    ellip_harm(5, 8, 1, 2, 2.5))
+
+    known_funcs = {(0, 1): E01, (1, 1): E11, (1, 2): E12, (1, 3): E13,
+                   (2, 1): E21, (2, 2): E22, (2, 3): E23, (2, 4): E24,
+                   (2, 5): E25, (3, 1): E31, (3, 2): E32, (3, 3): E33,
+                   (3, 4): E34, (3, 5): E35, (3, 6): E36, (3, 7): E37}
+
+    point_ref = []
+
+    def ellip_harm_known(h2, k2, n, p, s):
+        for i in range(h2.size):
+            func = known_funcs[(int(n[i]), int(p[i]))]
+            point_ref.append(func(h2[i], k2[i], s[i]))
+        return point_ref
+
+    np.random.seed(1234)
+    h2 = np.random.pareto(0.5, size=30)
+    k2 = h2*(1 + np.random.pareto(0.5, size=h2.size))
+    s = np.random.pareto(0.5, size=h2.size)
+    points = []
+    for i in range(h2.size):
+        for n in range(4):
+            for p in range(1, 2*n+2):
+                points.append((h2[i], k2[i], n, p, s[i]))
+    points = np.array(points)
+    assert_func_equal(ellip_harm, ellip_harm_known, points, rtol=1e-12)
+
+
+def test_ellip_harm_invalid_p():
+    # Regression test. This should return nan.
+    n = 4
+    # Make p > 2*n + 1.
+    p = 2*n + 2
+    result = ellip_harm(0.5, 2.0, n, p, 0.2)
+    assert np.isnan(result)

venv/Lib/site-packages/scipy/special/tests/test_erfinv.py

@@ -0,0 +1,59 @@
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal
+import pytest
+
+import scipy.special as sc
+
+class TestInverseErrorFunction:
+    def test_compliment(self):
+        # Test erfcinv(1 - x) == erfinv(x)
+        x = np.linspace(-1, 1, 101)
+        assert_allclose(sc.erfcinv(1 - x), sc.erfinv(x), rtol=0, atol=1e-15)
+
+    def test_literal_values(self):
+        # calculated via https://keisan.casio.com/exec/system/1180573448
+        # for y = 0, 0.1, ... , 0.9
+        actual = sc.erfinv(np.linspace(0, 0.9, 10))
+        expected = [
+            0,
+            0.08885599049425768701574,
+            0.1791434546212916764928,
+            0.27246271472675435562,
+            0.3708071585935579290583,
+            0.4769362762044698733814,
+            0.5951160814499948500193,
+            0.7328690779592168522188,
+            0.9061938024368232200712,
+            1.163087153676674086726,
+        ]
+        assert_allclose(actual, expected, rtol=0, atol=1e-15)
+
+    @pytest.mark.parametrize(
+        'f, x, y',
+        [
+            (sc.erfinv, -1, -np.inf),
+            (sc.erfinv, 0, 0),
+            (sc.erfinv, 1, np.inf),
+            (sc.erfinv, -100, np.nan),
+            (sc.erfinv, 100, np.nan),
+            (sc.erfcinv, 0, np.inf),
+            (sc.erfcinv, 1, -0.0),
+            (sc.erfcinv, 2, -np.inf),
+            (sc.erfcinv, -100, np.nan),
+            (sc.erfcinv, 100, np.nan),
+        ],
+        ids=[
+            'erfinv at lower bound',
+            'erfinv at midpoint',
+            'erfinv at upper bound',
+            'erfinv below lower bound',
+            'erfinv above upper bound',
+            'erfcinv at lower bound',
+            'erfcinv at midpoint',
+            'erfcinv at upper bound',
+            'erfcinv below lower bound',
+            'erfcinv above upper bound',
+        ]
+    )
+    def test_domain_bounds(self, f, x, y):
+        assert_equal(f(x), y)

venv/Lib/site-packages/scipy/special/tests/test_exponential_integrals.py

@@ -0,0 +1,75 @@
+import pytest
+
+import numpy as np
+from numpy.testing import assert_allclose
+import scipy.special as sc
+
+
+class TestExp1(object):
+
+    def test_branch_cut(self):
+        assert np.isnan(sc.exp1(-1))
+        assert sc.exp1(complex(-1, 0)).imag == (
+            -sc.exp1(complex(-1, -0.0)).imag
+        )
+
+        assert_allclose(
+            sc.exp1(complex(-1, 0)),
+            sc.exp1(-1 + 1e-20j),
+            atol=0,
+            rtol=1e-15
+        )
+        assert_allclose(
+            sc.exp1(complex(-1, -0.0)),
+            sc.exp1(-1 - 1e-20j),
+            atol=0,
+            rtol=1e-15
+        )
+
+    def test_834(self):
+        # Regression test for #834
+        a = sc.exp1(-complex(19.9999990))
+        b = sc.exp1(-complex(19.9999991))
+        assert_allclose(a.imag, b.imag, atol=0, rtol=1e-15)
+
+
+class TestExpi(object):
+
+    @pytest.mark.parametrize('result', [
+        sc.expi(complex(-1, 0)),
+        sc.expi(complex(-1, -0.0)),
+        sc.expi(-1)
+    ])
+    def test_branch_cut(self, result):
+        desired = -0.21938393439552027368  # Computed using Mpmath
+        assert_allclose(result, desired, atol=0, rtol=1e-14)
+
+    def test_near_branch_cut(self):
+        lim_from_above = sc.expi(-1 + 1e-20j)
+        lim_from_below = sc.expi(-1 - 1e-20j)
+        assert_allclose(
+            lim_from_above.real,
+            lim_from_below.real,
+            atol=0,
+            rtol=1e-15
+        )
+        assert_allclose(
+            lim_from_above.imag,
+            -lim_from_below.imag,
+            atol=0,
+            rtol=1e-15
+        )
+
+    def test_continuity_on_positive_real_axis(self):
+        assert_allclose(
+            sc.expi(complex(1, 0)),
+            sc.expi(complex(1, -0.0)),
+            atol=0,
+            rtol=1e-15
+        )
+
+
+class TestExpn(object):
+
+    def test_out_of_domain(self):
+        assert all(np.isnan([sc.expn(-1, 1.0), sc.expn(1, -1.0)]))

venv/Lib/site-packages/scipy/special/tests/test_faddeeva.py

@@ -0,0 +1,85 @@
+import pytest
+
+import numpy as np
+from numpy.testing import assert_allclose
+import scipy.special as sc
+from scipy.special._testutils import FuncData
+
+
+class TestVoigtProfile(object):
+
+    @pytest.mark.parametrize('x, sigma, gamma', [
+        (np.nan, 1, 1),
+        (0, np.nan, 1),
+        (0, 1, np.nan),
+        (1, np.nan, 0),
+        (np.nan, 1, 0),
+        (1, 0, np.nan),
+        (np.nan, 0, 1),
+        (np.nan, 0, 0)
+    ])
+    def test_nan(self, x, sigma, gamma):
+        assert np.isnan(sc.voigt_profile(x, sigma, gamma))
+
+    @pytest.mark.parametrize('x, desired', [
+        (-np.inf, 0),
+        (np.inf, 0)
+    ])
+    def test_inf(self, x, desired):
+        assert sc.voigt_profile(x, 1, 1) == desired
+
+    def test_against_mathematica(self):
+        # Results obtained from Mathematica by computing
+        #
+        # PDF[VoigtDistribution[gamma, sigma], x]
+        #
+        points = np.array([
+            [-7.89, 45.06, 6.66, 0.0077921073660388806401],
+            [-0.05, 7.98, 24.13, 0.012068223646769913478],
+            [-13.98, 16.83, 42.37, 0.0062442236362132357833],
+            [-12.66, 0.21, 6.32, 0.010052516161087379402],
+            [11.34, 4.25, 21.96, 0.0113698923627278917805],
+            [-11.56, 20.40, 30.53, 0.0076332760432097464987],
+            [-9.17, 25.61, 8.32, 0.011646345779083005429],
+            [16.59, 18.05, 2.50, 0.013637768837526809181],
+            [9.11, 2.12, 39.33, 0.0076644040807277677585],
+            [-43.33, 0.30, 45.68, 0.0036680463875330150996]
+        ])
+        FuncData(
+            sc.voigt_profile,
+            points,
+            (0, 1, 2),
+            3,
+            atol=0,
+            rtol=1e-15
+        ).check()
+
+    def test_symmetry(self):
+        x = np.linspace(0, 10, 20)
+        assert_allclose(
+            sc.voigt_profile(x, 1, 1),
+            sc.voigt_profile(-x, 1, 1),
+            rtol=1e-15,
+            atol=0
+        )
+
+    @pytest.mark.parametrize('x, sigma, gamma, desired', [
+        (0, 0, 0, np.inf),
+        (1, 0, 0, 0)
+    ])
+    def test_corner_cases(self, x, sigma, gamma, desired):
+        assert sc.voigt_profile(x, sigma, gamma) == desired
+
+    @pytest.mark.parametrize('sigma1, gamma1, sigma2, gamma2', [
+        (0, 1, 1e-16, 1),
+        (1, 0, 1, 1e-16),
+        (0, 0, 1e-16, 1e-16)
+    ])
+    def test_continuity(self, sigma1, gamma1, sigma2, gamma2):
+        x = np.linspace(1, 10, 20)
+        assert_allclose(
+            sc.voigt_profile(x, sigma1, gamma1),
+            sc.voigt_profile(x, sigma2, gamma2),
+            rtol=1e-16,
+            atol=1e-16
+        )

venv/Lib/site-packages/scipy/special/tests/test_gamma.py

@@ -0,0 +1,12 @@
+import numpy as np
+import scipy.special as sc
+
+
+class TestRgamma:
+
+    def test_gh_11315(self):
+        assert sc.rgamma(-35) == 0
+
+    def test_rgamma_zeros(self):
+        x = np.array([0, -10, -100, -1000, -10000])
+        assert np.all(sc.rgamma(x) == 0)

venv/Lib/site-packages/scipy/special/tests/test_gammainc.py

@@ -0,0 +1,136 @@
+import pytest
+
+import numpy as np
+from numpy.testing import assert_allclose, assert_array_equal
+
+import scipy.special as sc
+from scipy.special._testutils import FuncData
+
+
+INVALID_POINTS = [
+    (1, -1),
+    (0, 0),
+    (-1, 1),
+    (np.nan, 1),
+    (1, np.nan)
+]
+
+
+class TestGammainc(object):
+
+    @pytest.mark.parametrize('a, x', INVALID_POINTS)
+    def test_domain(self, a, x):
+        assert np.isnan(sc.gammainc(a, x))
+
+    def test_a_eq_0_x_gt_0(self):
+        assert sc.gammainc(0, 1) == 1
+
+    @pytest.mark.parametrize('a, x, desired', [
+        (np.inf, 1, 0),
+        (np.inf, 0, 0),
+        (np.inf, np.inf, np.nan),
+        (1, np.inf, 1)
+    ])
+    def test_infinite_arguments(self, a, x, desired):
+        result = sc.gammainc(a, x)
+        if np.isnan(desired):
+            assert np.isnan(result)
+        else:
+            assert result == desired
+
+    def test_infinite_limits(self):
+        # Test that large arguments converge to the hard-coded limits
+        # at infinity.
+        assert_allclose(
+            sc.gammainc(1000, 100),
+            sc.gammainc(np.inf, 100),
+            atol=1e-200,  # Use `atol` since the function converges to 0.
+            rtol=0
+        )
+        assert sc.gammainc(100, 1000) == sc.gammainc(100, np.inf)
+
+    def test_x_zero(self):
+        a = np.arange(1, 10)
+        assert_array_equal(sc.gammainc(a, 0), 0)
+
+    def test_limit_check(self):
+        result = sc.gammainc(1e-10, 1)
+        limit = sc.gammainc(0, 1)
+        assert np.isclose(result, limit)
+
+    def gammainc_line(self, x):
+        # The line a = x where a simpler asymptotic expansion (analog
+        # of DLMF 8.12.15) is available.
+        c = np.array([-1/3, -1/540, 25/6048, 101/155520,
+                      -3184811/3695155200, -2745493/8151736420])
+        res = 0
+        xfac = 1
+        for ck in c:
+            res -= ck*xfac
+            xfac /= x
+        res /= np.sqrt(2*np.pi*x)
+        res += 0.5
+        return res
+
+    def test_line(self):
+        x = np.logspace(np.log10(25), 300, 500)
+        a = x
+        dataset = np.vstack((a, x, self.gammainc_line(x))).T
+        FuncData(sc.gammainc, dataset, (0, 1), 2, rtol=1e-11).check()
+
+    def test_roundtrip(self):
+        a = np.logspace(-5, 10, 100)
+        x = np.logspace(-5, 10, 100)
+
+        y = sc.gammaincinv(a, sc.gammainc(a, x))
+        assert_allclose(x, y, rtol=1e-10)
+
+
+class TestGammaincc(object):
+
+    @pytest.mark.parametrize('a, x', INVALID_POINTS)
+    def test_domain(self, a, x):
+        assert np.isnan(sc.gammaincc(a, x))
+
+    def test_a_eq_0_x_gt_0(self):
+        assert sc.gammaincc(0, 1) == 0
+
+    @pytest.mark.parametrize('a, x, desired', [
+        (np.inf, 1, 1),
+        (np.inf, 0, 1),
+        (np.inf, np.inf, np.nan),
+        (1, np.inf, 0)
+    ])
+    def test_infinite_arguments(self, a, x, desired):
+        result = sc.gammaincc(a, x)
+        if np.isnan(desired):
+            assert np.isnan(result)
+        else:
+            assert result == desired
+
+    def test_infinite_limits(self):
+        # Test that large arguments converge to the hard-coded limits
+        # at infinity.
+        assert sc.gammaincc(1000, 100) == sc.gammaincc(np.inf, 100)
+        assert_allclose(
+            sc.gammaincc(100, 1000),
+            sc.gammaincc(100, np.inf),
+            atol=1e-200,  # Use `atol` since the function converges to 0.
+            rtol=0
+        )
+
+    def test_limit_check(self):
+        result = sc.gammaincc(1e-10,1)
+        limit = sc.gammaincc(0,1)
+        assert np.isclose(result, limit)
+
+    def test_x_zero(self):
+        a = np.arange(1, 10)
+        assert_array_equal(sc.gammaincc(a, 0), 1)
+
+    def test_roundtrip(self):
+        a = np.logspace(-5, 10, 100)
+        x = np.logspace(-5, 10, 100)
+
+        y = sc.gammainccinv(a, sc.gammaincc(a, x))
+        assert_allclose(x, y, rtol=1e-14)

venv/Lib/site-packages/scipy/special/tests/test_hypergeometric.py

@@ -0,0 +1,107 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_allclose
+from numpy.testing import assert_equal
+
+import scipy.special as sc
+
+
+class TestHyperu(object):
+
+    def test_negative_x(self):
+        a, b, x = np.meshgrid(
+            [-1, -0.5, 0, 0.5, 1],
+            [-1, -0.5, 0, 0.5, 1],
+            np.linspace(-100, -1, 10),
+        )
+        assert np.all(np.isnan(sc.hyperu(a, b, x)))
+
+    def test_special_cases(self):
+        assert sc.hyperu(0, 1, 1) == 1.0
+
+    @pytest.mark.parametrize('a', [0.5, 1, np.nan])
+    @pytest.mark.parametrize('b', [1, 2, np.nan])
+    @pytest.mark.parametrize('x', [0.25, 3, np.nan])
+    def test_nan_inputs(self, a, b, x):
+        assert np.isnan(sc.hyperu(a, b, x)) == np.any(np.isnan([a, b, x]))
+
+class TestHyp1f1(object):
+
+    @pytest.mark.parametrize('a, b, x', [
+        (np.nan, 1, 1),
+        (1, np.nan, 1),
+        (1, 1, np.nan)
+    ])
+    def test_nan_inputs(self, a, b, x):
+        assert np.isnan(sc.hyp1f1(a, b, x))
+
+    def test_poles(self):
+        assert_equal(sc.hyp1f1(1, [0, -1, -2, -3, -4], 0.5), np.infty)
+
+    @pytest.mark.parametrize('a, b, x, result', [
+        (-1, 1, 0.5, 0.5),
+        (1, 1, 0.5, 1.6487212707001281468),
+        (2, 1, 0.5, 2.4730819060501922203),
+        (1, 2, 0.5, 1.2974425414002562937),
+        (-10, 1, 0.5, -0.38937441413785204475)
+    ])
+    def test_special_cases(self, a, b, x, result):
+        # Hit all the special case branches at the beginning of the
+        # function. Desired answers computed using Mpmath.
+        assert_allclose(sc.hyp1f1(a, b, x), result, atol=0, rtol=1e-15)
+
+    @pytest.mark.parametrize('a, b, x, result', [
+        (1, 1, 0.44, 1.5527072185113360455),
+        (-1, 1, 0.44, 0.55999999999999999778),
+        (100, 100, 0.89, 2.4351296512898745592),
+        (-100, 100, 0.89, 0.40739062490768104667),
+        (1.5, 100, 59.99, 3.8073513625965598107),
+        (-1.5, 100, 59.99, 0.25099240047125826943)
+    ])
+    def test_geometric_convergence(self, a, b, x, result):
+        # Test the region where we are relying on the ratio of
+        #
+        # (|a| + 1) * |x| / |b|
+        #
+        # being small. Desired answers computed using Mpmath
+        assert_allclose(sc.hyp1f1(a, b, x), result, atol=0, rtol=1e-15)
+
+    @pytest.mark.parametrize('a, b, x, result', [
+        (-1, 1, 1.5, -0.5),
+        (-10, 1, 1.5, 0.41801777430943080357),
+        (-25, 1, 1.5, 0.25114491646037839809),
+        (-50, 1, 1.5, -0.25683643975194756115),
+        (-51, 1, 1.5, -0.19843162753845452972)
+    ])
+    def test_a_negative_integer(self, a, b, x, result):
+        # Desired answers computed using Mpmath. After -51 the
+        # relative error becomes unsatisfactory and we start returning
+        # NaN.
+        assert_allclose(sc.hyp1f1(a, b, x), result, atol=0, rtol=1e-9)
+
+    def test_gh_3492(self):
+        desired = 0.99973683897677527773  # Computed using Mpmath
+        assert_allclose(
+            sc.hyp1f1(0.01, 150, -4),
+            desired,
+            atol=0,
+            rtol=1e-15
+        )
+
+    def test_gh_3593(self):
+        desired = 1.0020033381011970966  # Computed using Mpmath
+        assert_allclose(
+            sc.hyp1f1(1, 5, 0.01),
+            desired,
+            atol=0,
+            rtol=1e-15
+        )
+
+    @pytest.mark.parametrize('a, b, x, desired', [
+        (-1, -2, 2, 2),
+        (-1, -4, 10, 3.5),
+        (-2, -2, 1, 2.5)
+    ])
+    def test_gh_11099(self, a, b, x, desired):
+        # All desired results computed using Mpmath
+        assert sc.hyp1f1(a, b, x) == desired

venv/Lib/site-packages/scipy/special/tests/test_kolmogorov.py

@@ -0,0 +1,412 @@
+import itertools
+import sys
+import pytest
+
+import numpy as np
+from numpy.testing import assert_
+from scipy.special._testutils import FuncData
+
+from scipy.special import kolmogorov, kolmogi, smirnov, smirnovi
+from scipy.special._ufuncs import (_kolmogc, _kolmogci, _kolmogp,
+                                   _smirnovc, _smirnovci, _smirnovp)
+
+_rtol = 1e-10
+
+class TestSmirnov(object):
+    def test_nan(self):
+        assert_(np.isnan(smirnov(1, np.nan)))
+
+    def test_basic(self):
+        dataset = [(1, 0.1, 0.9),
+                   (1, 0.875, 0.125),
+                   (2, 0.875, 0.125 * 0.125),
+                   (3, 0.875, 0.125 * 0.125 * 0.125)]
+
+        dataset = np.asarray(dataset)
+        FuncData(smirnov, dataset, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+        dataset[:, -1] = 1 - dataset[:, -1]
+        FuncData(_smirnovc, dataset, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+
+    def test_x_equals_0(self):
+        dataset = [(n, 0, 1) for n in itertools.chain(range(2, 20), range(1010, 1020))]
+        dataset = np.asarray(dataset)
+        FuncData(smirnov, dataset, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+        dataset[:, -1] = 1 - dataset[:, -1]
+        FuncData(_smirnovc, dataset, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+
+    def test_x_equals_1(self):
+        dataset = [(n, 1, 0) for n in itertools.chain(range(2, 20), range(1010, 1020))]
+        dataset = np.asarray(dataset)
+        FuncData(smirnov, dataset, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+        dataset[:, -1] = 1 - dataset[:, -1]
+        FuncData(_smirnovc, dataset, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+
+    def test_x_equals_0point5(self):
+        dataset = [(1, 0.5, 0.5),
+                   (2, 0.5, 0.25),
+                   (3, 0.5, 0.166666666667),
+                   (4, 0.5, 0.09375),
+                   (5, 0.5, 0.056),
+                   (6, 0.5, 0.0327932098765),
+                   (7, 0.5, 0.0191958707681),
+                   (8, 0.5, 0.0112953186035),
+                   (9, 0.5, 0.00661933257355),
+                   (10, 0.5, 0.003888705)]
+
+        dataset = np.asarray(dataset)
+        FuncData(smirnov, dataset, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+        dataset[:, -1] = 1 - dataset[:, -1]
+        FuncData(_smirnovc, dataset, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+
+    def test_n_equals_1(self):
+        x = np.linspace(0, 1, 101, endpoint=True)
+        dataset = np.column_stack([[1]*len(x), x, 1-x])
+        FuncData(smirnov, dataset, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+        dataset[:, -1] = 1 - dataset[:, -1]
+        FuncData(_smirnovc, dataset, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+
+    def test_n_equals_2(self):
+        x = np.linspace(0.5, 1, 101, endpoint=True)
+        p = np.power(1-x, 2)
+        n = np.array([2] * len(x))
+        dataset = np.column_stack([n, x, p])
+        FuncData(smirnov, dataset, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+        dataset[:, -1] = 1 - dataset[:, -1]
+        FuncData(_smirnovc, dataset, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+
+    def test_n_equals_3(self):
+        x = np.linspace(0.7, 1, 31, endpoint=True)
+        p = np.power(1-x, 3)
+        n = np.array([3] * len(x))
+        dataset = np.column_stack([n, x, p])
+        FuncData(smirnov, dataset, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+        dataset[:, -1] = 1 - dataset[:, -1]
+        FuncData(_smirnovc, dataset, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+
+    def test_n_large(self):
+        # test for large values of n
+        # Probabilities should go down as n goes up
+        x = 0.4
+        pvals = np.array([smirnov(n, x) for n in range(400, 1100, 20)])
+        dfs = np.diff(pvals)
+        assert_(np.all(dfs <= 0), msg='Not all diffs negative %s' % dfs)
+
+
+class TestSmirnovi(object):
+    def test_nan(self):
+        assert_(np.isnan(smirnovi(1, np.nan)))
+
+    def test_basic(self):
+        dataset = [(1, 0.4, 0.6),
+                   (1, 0.6, 0.4),
+                   (1, 0.99, 0.01),
+                   (1, 0.01, 0.99),
+                   (2, 0.125 * 0.125, 0.875),
+                   (3, 0.125 * 0.125 * 0.125, 0.875),
+                   (10, 1.0 / 16 ** 10, 1 - 1.0 / 16)]
+
+        dataset = np.asarray(dataset)
+        FuncData(smirnovi, dataset, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+        dataset[:, 1] = 1 - dataset[:, 1]
+        FuncData(_smirnovci, dataset, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+
+    def test_x_equals_0(self):
+        dataset = [(n, 0, 1) for n in itertools.chain(range(2, 20), range(1010, 1020))]
+        dataset = np.asarray(dataset)
+        FuncData(smirnovi, dataset, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+        dataset[:, 1] = 1 - dataset[:, 1]
+        FuncData(_smirnovci, dataset, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+
+    def test_x_equals_1(self):
+        dataset = [(n, 1, 0) for n in itertools.chain(range(2, 20), range(1010, 1020))]
+        dataset = np.asarray(dataset)
+        FuncData(smirnovi, dataset, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+        dataset[:, 1] = 1 - dataset[:, 1]
+        FuncData(_smirnovci, dataset, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+
+    def test_n_equals_1(self):
+        pp = np.linspace(0, 1, 101, endpoint=True)
+        # dataset = np.array([(1, p, 1-p) for p in pp])
+        dataset = np.column_stack([[1]*len(pp), pp, 1-pp])
+        FuncData(smirnovi, dataset, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+        dataset[:, 1] = 1 - dataset[:, 1]
+        FuncData(_smirnovci, dataset, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+
+    def test_n_equals_2(self):
+        x = np.linspace(0.5, 1, 101, endpoint=True)
+        p = np.power(1-x, 2)
+        n = np.array([2] * len(x))
+        dataset = np.column_stack([n, p, x])
+        FuncData(smirnovi, dataset, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+        dataset[:, 1] = 1 - dataset[:, 1]
+        FuncData(_smirnovci, dataset, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+
+    def test_n_equals_3(self):
+        x = np.linspace(0.7, 1, 31, endpoint=True)
+        p = np.power(1-x, 3)
+        n = np.array([3] * len(x))
+        dataset = np.column_stack([n, p, x])
+        FuncData(smirnovi, dataset, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+        dataset[:, 1] = 1 - dataset[:, 1]
+        FuncData(_smirnovci, dataset, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+
+    def test_round_trip(self):
+        def _sm_smi(n, p):
+            return smirnov(n, smirnovi(n, p))
+
+        def _smc_smci(n, p):
+            return _smirnovc(n, _smirnovci(n, p))
+
+        dataset = [(1, 0.4, 0.4),
+                   (1, 0.6, 0.6),
+                   (2, 0.875, 0.875),
+                   (3, 0.875, 0.875),
+                   (3, 0.125, 0.125),
+                   (10, 0.999, 0.999),
+                   (10, 0.0001, 0.0001)]
+
+        dataset = np.asarray(dataset)
+        FuncData(_sm_smi, dataset, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+        FuncData(_smc_smci, dataset, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+
+    def test_x_equals_0point5(self):
+        dataset = [(1, 0.5, 0.5),
+                   (2, 0.5, 0.366025403784),
+                   (2, 0.25, 0.5),
+                   (3, 0.5, 0.297156508177),
+                   (4, 0.5, 0.255520481121),
+                   (5, 0.5, 0.234559536069),
+                   (6, 0.5, 0.21715965898),
+                   (7, 0.5, 0.202722580034),
+                   (8, 0.5, 0.190621765256),
+                   (9, 0.5, 0.180363501362),
+                   (10, 0.5, 0.17157867006)]
+
+        dataset = np.asarray(dataset)
+        FuncData(smirnovi, dataset, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+        dataset[:, 1] = 1 - dataset[:, 1]
+        FuncData(_smirnovci, dataset, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+
+
+class TestSmirnovp(object):
+    def test_nan(self):
+        assert_(np.isnan(_smirnovp(1, np.nan)))
+
+    def test_basic(self):
+        # Check derivative at endpoints
+        n1_10 = np.arange(1, 10)
+        dataset0 = np.column_stack([n1_10, np.full_like(n1_10, 0), np.full_like(n1_10, -1)])
+        FuncData(_smirnovp, dataset0, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+
+        n2_10 = np.arange(2, 10)
+        dataset1 = np.column_stack([n2_10, np.full_like(n2_10, 1.0), np.full_like(n2_10, 0)])
+        FuncData(_smirnovp, dataset1, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+
+    def test_oneminusoneovern(self):
+        # Check derivative at x=1-1/n
+        n = np.arange(1, 20)
+        x = 1.0/n
+        xm1 = 1-1.0/n
+        pp1 = -n * x**(n-1)
+        pp1 -= (1-np.sign(n-2)**2) * 0.5  # n=2, x=0.5, 1-1/n = 0.5, need to adjust
+        dataset1 = np.column_stack([n, xm1, pp1])
+        FuncData(_smirnovp, dataset1, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+
+    def test_oneovertwon(self):
+        # Check derivative at x=1/2n  (Discontinuous at x=1/n, so check at x=1/2n)
+        n = np.arange(1, 20)
+        x = 1.0/2/n
+        pp = -(n*x+1) * (1+x)**(n-2)
+        dataset0 = np.column_stack([n, x, pp])
+        FuncData(_smirnovp, dataset0, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+
+    def test_oneovern(self):
+        # Check derivative at x=1/n  (Discontinuous at x=1/n, hard to tell if x==1/n, only use n=power of 2)
+        n = 2**np.arange(1, 10)
+        x = 1.0/n
+        pp = -(n*x+1) * (1+x)**(n-2) + 0.5
+        dataset0 = np.column_stack([n, x, pp])
+        FuncData(_smirnovp, dataset0, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+
+    @pytest.mark.xfail(sys.maxsize <= 2**32,
+                       reason="requires 64-bit platform")
+    def test_oneovernclose(self):
+        # Check derivative at x=1/n  (Discontinuous at x=1/n, test on either side: x=1/n +/- 2epsilon)
+        n = np.arange(3, 20)
+
+        x = 1.0/n - 2*np.finfo(float).eps
+        pp = -(n*x+1) * (1+x)**(n-2)
+        dataset0 = np.column_stack([n, x, pp])
+        FuncData(_smirnovp, dataset0, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+
+        x = 1.0/n + 2*np.finfo(float).eps
+        pp = -(n*x+1) * (1+x)**(n-2) + 1
+        dataset1 = np.column_stack([n, x, pp])
+        FuncData(_smirnovp, dataset1, (0, 1), 2, rtol=_rtol).check(dtypes=[int, float, float])
+
+
+class TestKolmogorov(object):
+    def test_nan(self):
+        assert_(np.isnan(kolmogorov(np.nan)))
+
+    def test_basic(self):
+        dataset = [(0, 1.0),
+                   (0.5, 0.96394524366487511),
+                   (0.8275735551899077, 0.5000000000000000),
+                   (1, 0.26999967167735456),
+                   (2, 0.00067092525577969533)]
+
+        dataset = np.asarray(dataset)
+        FuncData(kolmogorov, dataset, (0,), 1, rtol=_rtol).check()
+
+    def test_linspace(self):
+        x = np.linspace(0, 2.0, 21)
+        dataset = [1.0000000000000000, 1.0000000000000000, 0.9999999999994950,
+                   0.9999906941986655, 0.9971923267772983, 0.9639452436648751,
+                   0.8642827790506042, 0.7112351950296890, 0.5441424115741981,
+                   0.3927307079406543, 0.2699996716773546, 0.1777181926064012,
+                   0.1122496666707249, 0.0680922218447664, 0.0396818795381144,
+                   0.0222179626165251, 0.0119520432391966, 0.0061774306344441,
+                   0.0030676213475797, 0.0014636048371873, 0.0006709252557797]
+
+        dataset_c = [0.0000000000000000, 6.609305242245699e-53, 5.050407338670114e-13,
+                     9.305801334566668e-06, 0.0028076732227017, 0.0360547563351249,
+                     0.1357172209493958, 0.2887648049703110, 0.4558575884258019,
+                     0.6072692920593457, 0.7300003283226455, 0.8222818073935988,
+                     0.8877503333292751, 0.9319077781552336, 0.9603181204618857,
+                     0.9777820373834749, 0.9880479567608034, 0.9938225693655559,
+                     0.9969323786524203, 0.9985363951628127, 0.9993290747442203]
+
+        dataset = np.column_stack([x, dataset])
+        FuncData(kolmogorov, dataset, (0,), 1, rtol=_rtol).check()
+        dataset_c = np.column_stack([x, dataset_c])
+        FuncData(_kolmogc, dataset_c, (0,), 1, rtol=_rtol).check()
+
+    def test_linspacei(self):
+        p = np.linspace(0, 1.0, 21, endpoint=True)
+        dataset = [np.inf, 1.3580986393225507, 1.2238478702170823,
+                   1.1379465424937751, 1.0727491749396481, 1.0191847202536859,
+                   0.9730633753323726, 0.9320695842357622, 0.8947644549851197,
+                   0.8601710725555463, 0.8275735551899077, 0.7964065373291559,
+                   0.7661855555617682, 0.7364542888171910, 0.7067326523068980,
+                   0.6764476915028201, 0.6448126061663567, 0.6105590999244391,
+                   0.5711732651063401, 0.5196103791686224, 0.0000000000000000]
+
+        dataset_c = [0.0000000000000000, 0.5196103791686225, 0.5711732651063401,
+                     0.6105590999244391, 0.6448126061663567, 0.6764476915028201,
+                     0.7067326523068980, 0.7364542888171910, 0.7661855555617682,
+                     0.7964065373291559, 0.8275735551899077, 0.8601710725555463,
+                     0.8947644549851196, 0.9320695842357622, 0.9730633753323727,
+                     1.0191847202536859, 1.0727491749396481, 1.1379465424937754,
+                     1.2238478702170825, 1.3580986393225509, np.inf]
+
+        dataset = np.column_stack([p[1:], dataset[1:]])
+        FuncData(kolmogi, dataset, (0,), 1, rtol=_rtol).check()
+        dataset_c = np.column_stack([p[:-1], dataset_c[:-1]])
+        FuncData(_kolmogci, dataset_c, (0,), 1, rtol=_rtol).check()
+
+    def test_smallx(self):
+        epsilon = 0.1 ** np.arange(1, 14)
+        x = np.array([0.571173265106, 0.441027698518, 0.374219690278, 0.331392659217,
+                      0.300820537459, 0.277539353999, 0.259023494805, 0.243829561254,
+                      0.231063086389, 0.220135543236, 0.210641372041, 0.202290283658,
+                      0.19487060742])
+
+        dataset = np.column_stack([x, 1-epsilon])
+        FuncData(kolmogorov, dataset, (0,), 1, rtol=_rtol).check()
+
+    def test_round_trip(self):
+        def _ki_k(_x):
+            return kolmogi(kolmogorov(_x))
+
+        def _kci_kc(_x):
+            return _kolmogci(_kolmogc(_x))
+
+        x = np.linspace(0.0, 2.0, 21, endpoint=True)
+        x02 = x[(x == 0) | (x > 0.21)]  # Exclude 0.1, 0.2.  0.2 almost makes succeeds, but 0.1 has no chance.
+        dataset02 = np.column_stack([x02, x02])
+        FuncData(_ki_k, dataset02, (0,), 1, rtol=_rtol).check()
+
+        dataset = np.column_stack([x, x])
+        FuncData(_kci_kc, dataset, (0,), 1, rtol=_rtol).check()
+
+
+class TestKolmogi(object):
+    def test_nan(self):
+        assert_(np.isnan(kolmogi(np.nan)))
+
+    def test_basic(self):
+        dataset = [(1.0, 0),
+                   (0.96394524366487511, 0.5),
+                   (0.9, 0.571173265106),
+                   (0.5000000000000000, 0.8275735551899077),
+                   (0.26999967167735456, 1),
+                   (0.00067092525577969533, 2)]
+
+        dataset = np.asarray(dataset)
+        FuncData(kolmogi, dataset, (0,), 1, rtol=_rtol).check()
+
+    def test_smallpcdf(self):
+        epsilon = 0.5 ** np.arange(1, 55, 3)
+        # kolmogi(1-p) == _kolmogci(p) if  1-(1-p) == p, but not necessarily otherwise
+        # Use epsilon s.t. 1-(1-epsilon)) == epsilon, so can use same x-array for both results
+
+        x = np.array([0.8275735551899077, 0.5345255069097583, 0.4320114038786941,
+                      0.3736868442620478, 0.3345161714909591, 0.3057833329315859,
+                      0.2835052890528936, 0.2655578150208676, 0.2506869966107999,
+                      0.2380971058736669, 0.2272549289962079, 0.2177876361600040,
+                      0.2094254686862041, 0.2019676748836232, 0.1952612948137504,
+                      0.1891874239646641, 0.1836520225050326, 0.1785795904846466])
+
+        dataset = np.column_stack([1-epsilon, x])
+        FuncData(kolmogi, dataset, (0,), 1, rtol=_rtol).check()
+
+        dataset = np.column_stack([epsilon, x])
+        FuncData(_kolmogci, dataset, (0,), 1, rtol=_rtol).check()
+
+    def test_smallpsf(self):
+        epsilon = 0.5 ** np.arange(1, 55, 3)
+        # kolmogi(p) == _kolmogci(1-p) if  1-(1-p) == p, but not necessarily otherwise
+        # Use epsilon s.t. 1-(1-epsilon)) == epsilon, so can use same x-array for both results
+
+        x = np.array([0.8275735551899077, 1.3163786275161036, 1.6651092133663343,
+                      1.9525136345289607, 2.2027324540033235, 2.4272929437460848,
+                      2.6327688477341593, 2.8233300509220260, 3.0018183401530627,
+                      3.1702735084088891, 3.3302184446307912, 3.4828258153113318,
+                      3.6290214150152051, 3.7695513262825959, 3.9050272690877326,
+                      4.0359582187082550, 4.1627730557884890, 4.2858371743264527])
+
+        dataset = np.column_stack([epsilon, x])
+        FuncData(kolmogi, dataset, (0,), 1, rtol=_rtol).check()
+
+        dataset = np.column_stack([1-epsilon, x])
+        FuncData(_kolmogci, dataset, (0,), 1, rtol=_rtol).check()
+
+    def test_round_trip(self):
+        def _k_ki(_p):
+            return kolmogorov(kolmogi(_p))
+
+        p = np.linspace(0.1, 1.0, 10, endpoint=True)
+        dataset = np.column_stack([p, p])
+        FuncData(_k_ki, dataset, (0,), 1, rtol=_rtol).check()
+
+
+class TestKolmogp(object):
+    def test_nan(self):
+        assert_(np.isnan(_kolmogp(np.nan)))
+
+    def test_basic(self):
+        dataset = [(0.000000, -0.0),
+                   (0.200000, -1.532420541338916e-10),
+                   (0.400000, -0.1012254419260496),
+                   (0.600000, -1.324123244249925),
+                   (0.800000, -1.627024345636592),
+                   (1.000000, -1.071948558356941),
+                   (1.200000, -0.538512430720529),
+                   (1.400000, -0.2222133182429472),
+                   (1.600000, -0.07649302775520538),
+                   (1.800000, -0.02208687346347873),
+                   (2.000000, -0.005367402045629683)]
+
+        dataset = np.asarray(dataset)
+        FuncData(_kolmogp, dataset, (0,), 1, rtol=_rtol).check()

venv/Lib/site-packages/scipy/special/tests/test_lambertw.py

@@ -0,0 +1,98 @@
+#
+# Tests for the lambertw function,
+# Adapted from the MPMath tests [1] by Yosef Meller, mellerf@netvision.net.il
+# Distributed under the same license as SciPy itself.
+#
+# [1] mpmath source code, Subversion revision 992
+#     http://code.google.com/p/mpmath/source/browse/trunk/mpmath/tests/test_functions2.py?spec=svn994&r=992
+
+import numpy as np
+from numpy.testing import assert_, assert_equal, assert_array_almost_equal
+from scipy.special import lambertw
+from numpy import nan, inf, pi, e, isnan, log, r_, array, complex_
+
+from scipy.special._testutils import FuncData
+
+
+def test_values():
+    assert_(isnan(lambertw(nan)))
+    assert_equal(lambertw(inf,1).real, inf)
+    assert_equal(lambertw(inf,1).imag, 2*pi)
+    assert_equal(lambertw(-inf,1).real, inf)
+    assert_equal(lambertw(-inf,1).imag, 3*pi)
+
+    assert_equal(lambertw(1.), lambertw(1., 0))
+
+    data = [
+        (0,0, 0),
+        (0+0j,0, 0),
+        (inf,0, inf),
+        (0,-1, -inf),
+        (0,1, -inf),
+        (0,3, -inf),
+        (e,0, 1),
+        (1,0, 0.567143290409783873),
+        (-pi/2,0, 1j*pi/2),
+        (-log(2)/2,0, -log(2)),
+        (0.25,0, 0.203888354702240164),
+        (-0.25,0, -0.357402956181388903),
+        (-1./10000,0, -0.000100010001500266719),
+        (-0.25,-1, -2.15329236411034965),
+        (0.25,-1, -3.00899800997004620-4.07652978899159763j),
+        (-0.25,-1, -2.15329236411034965),
+        (0.25,1, -3.00899800997004620+4.07652978899159763j),
+        (-0.25,1, -3.48973228422959210+7.41405453009603664j),
+        (-4,0, 0.67881197132094523+1.91195078174339937j),
+        (-4,1, -0.66743107129800988+7.76827456802783084j),
+        (-4,-1, 0.67881197132094523-1.91195078174339937j),
+        (1000,0, 5.24960285240159623),
+        (1000,1, 4.91492239981054535+5.44652615979447070j),
+        (1000,-1, 4.91492239981054535-5.44652615979447070j),
+        (1000,5, 3.5010625305312892+29.9614548941181328j),
+        (3+4j,0, 1.281561806123775878+0.533095222020971071j),
+        (-0.4+0.4j,0, -0.10396515323290657+0.61899273315171632j),
+        (3+4j,1, -0.11691092896595324+5.61888039871282334j),
+        (3+4j,-1, 0.25856740686699742-3.85211668616143559j),
+        (-0.5,-1, -0.794023632344689368-0.770111750510379110j),
+        (-1./10000,1, -11.82350837248724344+6.80546081842002101j),
+        (-1./10000,-1, -11.6671145325663544),
+        (-1./10000,-2, -11.82350837248724344-6.80546081842002101j),
+        (-1./100000,4, -14.9186890769540539+26.1856750178782046j),
+        (-1./100000,5, -15.0931437726379218666+32.5525721210262290086j),
+        ((2+1j)/10,0, 0.173704503762911669+0.071781336752835511j),
+        ((2+1j)/10,1, -3.21746028349820063+4.56175438896292539j),
+        ((2+1j)/10,-1, -3.03781405002993088-3.53946629633505737j),
+        ((2+1j)/10,4, -4.6878509692773249+23.8313630697683291j),
+        (-(2+1j)/10,0, -0.226933772515757933-0.164986470020154580j),
+        (-(2+1j)/10,1, -2.43569517046110001+0.76974067544756289j),
+        (-(2+1j)/10,-1, -3.54858738151989450-6.91627921869943589j),
+        (-(2+1j)/10,4, -4.5500846928118151+20.6672982215434637j),
+        (pi,0, 1.073658194796149172092178407024821347547745350410314531),
+
+        # Former bug in generated branch,
+        (-0.5+0.002j,0, -0.78917138132659918344 + 0.76743539379990327749j),
+        (-0.5-0.002j,0, -0.78917138132659918344 - 0.76743539379990327749j),
+        (-0.448+0.4j,0, -0.11855133765652382241 + 0.66570534313583423116j),
+        (-0.448-0.4j,0, -0.11855133765652382241 - 0.66570534313583423116j),
+    ]
+    data = array(data, dtype=complex_)
+
+    def w(x, y):
+        return lambertw(x, y.real.astype(int))
+    with np.errstate(all='ignore'):
+        FuncData(w, data, (0,1), 2, rtol=1e-10, atol=1e-13).check()
+
+
+def test_ufunc():
+    assert_array_almost_equal(
+        lambertw(r_[0., e, 1.]), r_[0., 1., 0.567143290409783873])
+
+
+def test_lambertw_ufunc_loop_selection():
+    # see https://github.com/scipy/scipy/issues/4895
+    dt = np.dtype(np.complex128)
+    assert_equal(lambertw(0, 0, 0).dtype, dt)
+    assert_equal(lambertw([0], 0, 0).dtype, dt)
+    assert_equal(lambertw(0, [0], 0).dtype, dt)
+    assert_equal(lambertw(0, 0, [0]).dtype, dt)
+    assert_equal(lambertw([0], [0], [0]).dtype, dt)

venv/Lib/site-packages/scipy/special/tests/test_log_softmax.py

@@ -0,0 +1,109 @@
+import numpy as np
+from numpy.testing import assert_allclose
+
+import pytest
+
+import scipy.special as sc
+
+
+@pytest.mark.parametrize('x, expected', [
+    (np.array([1000, 1]), np.array([0, -999])),
+
+    # Expected value computed using mpmath (with mpmath.mp.dps = 200) and then
+    # converted to float.
+    (np.arange(4), np.array([-3.4401896985611953,
+                             -2.4401896985611953,
+                             -1.4401896985611953,
+                             -0.44018969856119533]))
+])
+def test_log_softmax(x, expected):
+    assert_allclose(sc.log_softmax(x), expected, rtol=1e-13)
+
+
+@pytest.fixture
+def log_softmax_x():
+    x = np.arange(4)
+    return x
+
+
+@pytest.fixture
+def log_softmax_expected():
+    # Expected value computed using mpmath (with mpmath.mp.dps = 200) and then
+    # converted to float.
+    expected = np.array([-3.4401896985611953,
+                         -2.4401896985611953,
+                         -1.4401896985611953,
+                         -0.44018969856119533])
+    return expected
+
+
+def test_log_softmax_translation(log_softmax_x, log_softmax_expected):
+    # Translation property.  If all the values are changed by the same amount,
+    # the softmax result does not change.
+    x = log_softmax_x + 100
+    expected = log_softmax_expected
+    assert_allclose(sc.log_softmax(x), expected, rtol=1e-13)
+
+
+def test_log_softmax_noneaxis(log_softmax_x, log_softmax_expected):
+    # When axis=None, softmax operates on the entire array, and preserves
+    # the shape.
+    x = log_softmax_x.reshape(2, 2)
+    expected = log_softmax_expected.reshape(2, 2)
+    assert_allclose(sc.log_softmax(x), expected, rtol=1e-13)
+
+
+@pytest.mark.parametrize('axis_2d, expected_2d', [
+    (0, np.log(0.5) * np.ones((2, 2))),
+    (1, np.array([[0, -999], [0, -999]]))
+])
+def test_axes(axis_2d, expected_2d):
+    assert_allclose(
+        sc.log_softmax([[1000, 1], [1000, 1]], axis=axis_2d),
+        expected_2d,
+        rtol=1e-13,
+    )
+
+
+@pytest.fixture
+def log_softmax_2d_x():
+    x = np.arange(8).reshape(2, 4)
+    return x
+
+
+@pytest.fixture
+def log_softmax_2d_expected():
+    # Expected value computed using mpmath (with mpmath.mp.dps = 200) and then
+    # converted to float.
+    expected = np.array([[-3.4401896985611953,
+                         -2.4401896985611953,
+                         -1.4401896985611953,
+                         -0.44018969856119533],
+                        [-3.4401896985611953,
+                         -2.4401896985611953,
+                         -1.4401896985611953,
+                         -0.44018969856119533]])
+    return expected
+
+
+def test_log_softmax_2d_axis1(log_softmax_2d_x, log_softmax_2d_expected):
+    x = log_softmax_2d_x
+    expected = log_softmax_2d_expected
+    assert_allclose(sc.log_softmax(x, axis=1), expected, rtol=1e-13)
+
+
+def test_log_softmax_2d_axis0(log_softmax_2d_x, log_softmax_2d_expected):
+    x = log_softmax_2d_x.T
+    expected = log_softmax_2d_expected.T
+    assert_allclose(sc.log_softmax(x, axis=0), expected, rtol=1e-13)
+
+
+def test_log_softmax_3d(log_softmax_2d_x, log_softmax_2d_expected):
+    # 3-d input, with a tuple for the axis.
+    x_3d = log_softmax_2d_x.reshape(2, 2, 2)
+    expected_3d = log_softmax_2d_expected.reshape(2, 2, 2)
+    assert_allclose(sc.log_softmax(x_3d, axis=(1, 2)), expected_3d, rtol=1e-13)
+
+
+def test_log_softmax_scalar():
+    assert_allclose(sc.log_softmax(1.0), 0.0, rtol=1e-13)

venv/Lib/site-packages/scipy/special/tests/test_loggamma.py

@@ -0,0 +1,70 @@
+import numpy as np
+from numpy.testing import assert_allclose, assert_
+
+from scipy.special._testutils import FuncData
+from scipy.special import gamma, gammaln, loggamma
+
+
+def test_identities1():
+    # test the identity exp(loggamma(z)) = gamma(z)
+    x = np.array([-99.5, -9.5, -0.5, 0.5, 9.5, 99.5])
+    y = x.copy()
+    x, y = np.meshgrid(x, y)
+    z = (x + 1J*y).flatten()
+    dataset = np.vstack((z, gamma(z))).T
+
+    def f(z):
+        return np.exp(loggamma(z))
+
+    FuncData(f, dataset, 0, 1, rtol=1e-14, atol=1e-14).check()
+
+
+def test_identities2():
+    # test the identity loggamma(z + 1) = log(z) + loggamma(z)
+    x = np.array([-99.5, -9.5, -0.5, 0.5, 9.5, 99.5])
+    y = x.copy()
+    x, y = np.meshgrid(x, y)
+    z = (x + 1J*y).flatten()
+    dataset = np.vstack((z, np.log(z) + loggamma(z))).T
+
+    def f(z):
+        return loggamma(z + 1)
+
+    FuncData(f, dataset, 0, 1, rtol=1e-14, atol=1e-14).check()
+
+
+def test_complex_dispatch_realpart():
+    # Test that the real parts of loggamma and gammaln agree on the
+    # real axis.
+    x = np.r_[-np.logspace(10, -10), np.logspace(-10, 10)] + 0.5
+
+    dataset = np.vstack((x, gammaln(x))).T
+
+    def f(z):
+        z = np.array(z, dtype='complex128')
+        return loggamma(z).real
+
+    FuncData(f, dataset, 0, 1, rtol=1e-14, atol=1e-14).check()
+
+
+def test_real_dispatch():
+    x = np.logspace(-10, 10) + 0.5
+    dataset = np.vstack((x, gammaln(x))).T
+
+    FuncData(loggamma, dataset, 0, 1, rtol=1e-14, atol=1e-14).check()
+    assert_(loggamma(0) == np.inf)
+    assert_(np.isnan(loggamma(-1)))
+
+
+def test_gh_6536():
+    z = loggamma(complex(-3.4, +0.0))
+    zbar = loggamma(complex(-3.4, -0.0))
+    assert_allclose(z, zbar.conjugate(), rtol=1e-15, atol=0)
+
+
+def test_branch_cut():
+    # Make sure negative zero is treated correctly
+    x = -np.logspace(300, -30, 100)
+    z = np.asarray([complex(x0, 0.0) for x0 in x])
+    zbar = np.asarray([complex(x0, -0.0) for x0 in x])
+    assert_allclose(z, zbar.conjugate(), rtol=1e-15, atol=0)

venv/Lib/site-packages/scipy/special/tests/test_logit.py

@@ -0,0 +1,73 @@
+import numpy as np
+from numpy.testing import (assert_equal, assert_almost_equal,
+        assert_allclose)
+from scipy.special import logit, expit
+
+
+class TestLogit(object):
+    def check_logit_out(self, dtype, expected):
+        a = np.linspace(0,1,10)
+        a = np.array(a, dtype=dtype)
+        with np.errstate(divide='ignore'):
+            actual = logit(a)
+
+        assert_almost_equal(actual, expected)
+
+        assert_equal(actual.dtype, np.dtype(dtype))
+
+    def test_float32(self):
+        expected = np.array([-np.inf, -2.07944155,
+                            -1.25276291, -0.69314718,
+                            -0.22314353, 0.22314365,
+                            0.6931473, 1.25276303,
+                            2.07944155, np.inf], dtype=np.float32)
+        self.check_logit_out('f4', expected)
+
+    def test_float64(self):
+        expected = np.array([-np.inf, -2.07944154,
+                            -1.25276297, -0.69314718,
+                            -0.22314355, 0.22314355,
+                            0.69314718, 1.25276297,
+                            2.07944154, np.inf])
+        self.check_logit_out('f8', expected)
+
+    def test_nan(self):
+        expected = np.array([np.nan]*4)
+        with np.errstate(invalid='ignore'):
+            actual = logit(np.array([-3., -2., 2., 3.]))
+
+        assert_equal(expected, actual)
+
+
+class TestExpit(object):
+    def check_expit_out(self, dtype, expected):
+        a = np.linspace(-4,4,10)
+        a = np.array(a, dtype=dtype)
+        actual = expit(a)
+        assert_almost_equal(actual, expected)
+        assert_equal(actual.dtype, np.dtype(dtype))
+
+    def test_float32(self):
+        expected = np.array([0.01798621, 0.04265125,
+                            0.09777259, 0.20860852,
+                            0.39068246, 0.60931754,
+                            0.79139149, 0.9022274,
+                            0.95734876, 0.98201376], dtype=np.float32)
+        self.check_expit_out('f4',expected)
+
+    def test_float64(self):
+        expected = np.array([0.01798621, 0.04265125,
+                            0.0977726, 0.20860853,
+                            0.39068246, 0.60931754,
+                            0.79139147, 0.9022274,
+                            0.95734875, 0.98201379])
+        self.check_expit_out('f8', expected)
+
+    def test_large(self):
+        for dtype in (np.float32, np.float64, np.longdouble):
+            for n in (88, 89, 709, 710, 11356, 11357):
+                n = np.array(n, dtype=dtype)
+                assert_allclose(expit(n), 1.0, atol=1e-20)
+                assert_allclose(expit(-n), 0.0, atol=1e-20)
+                assert_equal(expit(n).dtype, dtype)
+                assert_equal(expit(-n).dtype, dtype)

venv/Lib/site-packages/scipy/special/tests/test_logsumexp.py

@@ -0,0 +1,194 @@
+import numpy as np
+from numpy.testing import (assert_almost_equal, assert_equal, assert_allclose,
+                           assert_array_almost_equal, assert_)
+
+from scipy.special import logsumexp, softmax
+
+
+def test_logsumexp():
+    # Test whether logsumexp() function correctly handles large inputs.
+    a = np.arange(200)
+    desired = np.log(np.sum(np.exp(a)))
+    assert_almost_equal(logsumexp(a), desired)
+
+    # Now test with large numbers
+    b = [1000, 1000]
+    desired = 1000.0 + np.log(2.0)
+    assert_almost_equal(logsumexp(b), desired)
+
+    n = 1000
+    b = np.full(n, 10000, dtype='float64')
+    desired = 10000.0 + np.log(n)
+    assert_almost_equal(logsumexp(b), desired)
+
+    x = np.array([1e-40] * 1000000)
+    logx = np.log(x)
+
+    X = np.vstack([x, x])
+    logX = np.vstack([logx, logx])
+    assert_array_almost_equal(np.exp(logsumexp(logX)), X.sum())
+    assert_array_almost_equal(np.exp(logsumexp(logX, axis=0)), X.sum(axis=0))
+    assert_array_almost_equal(np.exp(logsumexp(logX, axis=1)), X.sum(axis=1))
+
+    # Handling special values properly
+    assert_equal(logsumexp(np.inf), np.inf)
+    assert_equal(logsumexp(-np.inf), -np.inf)
+    assert_equal(logsumexp(np.nan), np.nan)
+    assert_equal(logsumexp([-np.inf, -np.inf]), -np.inf)
+
+    # Handling an array with different magnitudes on the axes
+    assert_array_almost_equal(logsumexp([[1e10, 1e-10],
+                                         [-1e10, -np.inf]], axis=-1),
+                              [1e10, -1e10])
+
+    # Test keeping dimensions
+    assert_array_almost_equal(logsumexp([[1e10, 1e-10],
+                                         [-1e10, -np.inf]],
+                                        axis=-1,
+                                        keepdims=True),
+                              [[1e10], [-1e10]])
+
+    # Test multiple axes
+    assert_array_almost_equal(logsumexp([[1e10, 1e-10],
+                                         [-1e10, -np.inf]],
+                                        axis=(-1,-2)),
+                              1e10)
+
+
+def test_logsumexp_b():
+    a = np.arange(200)
+    b = np.arange(200, 0, -1)
+    desired = np.log(np.sum(b*np.exp(a)))
+    assert_almost_equal(logsumexp(a, b=b), desired)
+
+    a = [1000, 1000]
+    b = [1.2, 1.2]
+    desired = 1000 + np.log(2 * 1.2)
+    assert_almost_equal(logsumexp(a, b=b), desired)
+
+    x = np.array([1e-40] * 100000)
+    b = np.linspace(1, 1000, 100000)
+    logx = np.log(x)
+
+    X = np.vstack((x, x))
+    logX = np.vstack((logx, logx))
+    B = np.vstack((b, b))
+    assert_array_almost_equal(np.exp(logsumexp(logX, b=B)), (B * X).sum())
+    assert_array_almost_equal(np.exp(logsumexp(logX, b=B, axis=0)),
+                                (B * X).sum(axis=0))
+    assert_array_almost_equal(np.exp(logsumexp(logX, b=B, axis=1)),
+                                (B * X).sum(axis=1))
+
+
+def test_logsumexp_sign():
+    a = [1,1,1]
+    b = [1,-1,-1]
+
+    r, s = logsumexp(a, b=b, return_sign=True)
+    assert_almost_equal(r,1)
+    assert_equal(s,-1)
+
+
+def test_logsumexp_sign_zero():
+    a = [1,1]
+    b = [1,-1]
+
+    r, s = logsumexp(a, b=b, return_sign=True)
+    assert_(not np.isfinite(r))
+    assert_(not np.isnan(r))
+    assert_(r < 0)
+    assert_equal(s,0)
+
+
+def test_logsumexp_sign_shape():
+    a = np.ones((1,2,3,4))
+    b = np.ones_like(a)
+
+    r, s = logsumexp(a, axis=2, b=b, return_sign=True)
+
+    assert_equal(r.shape, s.shape)
+    assert_equal(r.shape, (1,2,4))
+
+    r, s = logsumexp(a, axis=(1,3), b=b, return_sign=True)
+
+    assert_equal(r.shape, s.shape)
+    assert_equal(r.shape, (1,3))
+
+
+def test_logsumexp_shape():
+    a = np.ones((1, 2, 3, 4))
+    b = np.ones_like(a)
+
+    r = logsumexp(a, axis=2, b=b)
+    assert_equal(r.shape, (1, 2, 4))
+
+    r = logsumexp(a, axis=(1, 3), b=b)
+    assert_equal(r.shape, (1, 3))
+
+
+def test_logsumexp_b_zero():
+    a = [1,10000]
+    b = [1,0]
+
+    assert_almost_equal(logsumexp(a, b=b), 1)
+
+
+def test_logsumexp_b_shape():
+    a = np.zeros((4,1,2,1))
+    b = np.ones((3,1,5))
+
+    logsumexp(a, b=b)
+
+
+def test_softmax_fixtures():
+    assert_allclose(softmax([1000, 0, 0, 0]), np.array([1, 0, 0, 0]),
+                    rtol=1e-13)
+    assert_allclose(softmax([1, 1]), np.array([.5, .5]), rtol=1e-13)
+    assert_allclose(softmax([0, 1]), np.array([1, np.e])/(1 + np.e),
+                    rtol=1e-13)
+
+    # Expected value computed using mpmath (with mpmath.mp.dps = 200) and then
+    # converted to float.
+    x = np.arange(4)
+    expected = np.array([0.03205860328008499,
+                         0.08714431874203256,
+                         0.23688281808991013,
+                         0.6439142598879722])
+
+    assert_allclose(softmax(x), expected, rtol=1e-13)
+
+    # Translation property.  If all the values are changed by the same amount,
+    # the softmax result does not change.
+    assert_allclose(softmax(x + 100), expected, rtol=1e-13)
+
+    # When axis=None, softmax operates on the entire array, and preserves
+    # the shape.
+    assert_allclose(softmax(x.reshape(2, 2)), expected.reshape(2, 2),
+                    rtol=1e-13)
+
+
+def test_softmax_multi_axes():
+    assert_allclose(softmax([[1000, 0], [1000, 0]], axis=0),
+                    np.array([[.5, .5], [.5, .5]]), rtol=1e-13)
+    assert_allclose(softmax([[1000, 0], [1000, 0]], axis=1),
+                    np.array([[1, 0], [1, 0]]), rtol=1e-13)
+
+    # Expected value computed using mpmath (with mpmath.mp.dps = 200) and then
+    # converted to float.
+    x = np.array([[-25, 0, 25, 50],
+                  [1, 325, 749, 750]])
+    expected = np.array([[2.678636961770877e-33,
+                          1.9287498479371314e-22,
+                          1.3887943864771144e-11,
+                          0.999999999986112],
+                         [0.0,
+                          1.9444526359919372e-185,
+                          0.2689414213699951,
+                          0.7310585786300048]])
+    assert_allclose(softmax(x, axis=1), expected, rtol=1e-13)
+    assert_allclose(softmax(x.T, axis=0), expected.T, rtol=1e-13)
+
+    # 3-d input, with a tuple for the axis.
+    x3d = x.reshape(2, 2, 2)
+    assert_allclose(softmax(x3d, axis=(1, 2)), expected.reshape(2, 2, 2),
+                    rtol=1e-13)

venv/Lib/site-packages/scipy/special/tests/test_nan_inputs.py

@@ -0,0 +1,64 @@
+"""Test how the ufuncs in special handle nan inputs.
+
+"""
+from typing import Callable, Dict
+
+import numpy as np
+from numpy.testing import assert_array_equal, assert_, suppress_warnings
+import pytest
+import scipy.special as sc
+
+
+KNOWNFAILURES: Dict[str, Callable] = {}
+
+POSTPROCESSING: Dict[str, Callable] = {}
+
+
+def _get_ufuncs():
+    ufuncs = []
+    ufunc_names = []
+    for name in sorted(sc.__dict__):
+        obj = sc.__dict__[name]
+        if not isinstance(obj, np.ufunc):
+            continue
+        msg = KNOWNFAILURES.get(obj)
+        if msg is None:
+            ufuncs.append(obj)
+            ufunc_names.append(name)
+        else:
+            fail = pytest.mark.xfail(run=False, reason=msg)
+            ufuncs.append(pytest.param(obj, marks=fail))
+            ufunc_names.append(name)
+    return ufuncs, ufunc_names
+
+
+UFUNCS, UFUNC_NAMES = _get_ufuncs()
+
+
+@pytest.mark.parametrize("func", UFUNCS, ids=UFUNC_NAMES)
+def test_nan_inputs(func):
+    args = (np.nan,)*func.nin
+    with suppress_warnings() as sup:
+        # Ignore warnings about unsafe casts from legacy wrappers
+        sup.filter(RuntimeWarning,
+                   "floating point number truncated to an integer")
+        try:
+            with suppress_warnings() as sup:
+                sup.filter(DeprecationWarning)
+                res = func(*args)
+        except TypeError:
+            # One of the arguments doesn't take real inputs
+            return
+    if func in POSTPROCESSING:
+        res = POSTPROCESSING[func](*res)
+
+    msg = "got {} instead of nan".format(res)
+    assert_array_equal(np.isnan(res), True, err_msg=msg)
+
+
+def test_legacy_cast():
+    with suppress_warnings() as sup:
+        sup.filter(RuntimeWarning,
+                   "floating point number truncated to an integer")
+        res = sc.bdtrc(np.nan, 1, 0.5)
+        assert_(np.isnan(res))

venv/Lib/site-packages/scipy/special/tests/test_ndtr.py

@@ -0,0 +1,20 @@
+import numpy as np
+from numpy.testing import assert_equal, assert_almost_equal
+import scipy.special as sc
+
+
+def test_ndtr():
+    assert_equal(sc.ndtr(0), 0.5)
+    assert_almost_equal(sc.ndtr(1), 0.84134474606)
+
+
+class TestNdtri:
+
+    def test_zero(self):
+        assert sc.ndtri(0.5) == 0.0
+
+    def test_asymptotes(self):
+        assert_equal(sc.ndtri([0.0, 1.0]), [-np.inf, np.inf])
+
+    def test_outside_of_domain(self):
+        assert all(np.isnan(sc.ndtri([-1.5, 1.5])))

venv/Lib/site-packages/scipy/special/tests/test_orthogonal.py

@@ -0,0 +1,748 @@
+import numpy as np
+from numpy import array, sqrt
+from numpy.testing import (assert_array_almost_equal, assert_equal,
+                           assert_almost_equal, assert_allclose)
+from pytest import raises as assert_raises
+
+from scipy import integrate
+import scipy.special as sc
+from scipy.special import gamma
+import scipy.special.orthogonal as orth
+
+
+class TestCheby(object):
+    def test_chebyc(self):
+        C0 = orth.chebyc(0)
+        C1 = orth.chebyc(1)
+        with np.errstate(all='ignore'):
+            C2 = orth.chebyc(2)
+            C3 = orth.chebyc(3)
+            C4 = orth.chebyc(4)
+            C5 = orth.chebyc(5)
+
+        assert_array_almost_equal(C0.c,[2],13)
+        assert_array_almost_equal(C1.c,[1,0],13)
+        assert_array_almost_equal(C2.c,[1,0,-2],13)
+        assert_array_almost_equal(C3.c,[1,0,-3,0],13)
+        assert_array_almost_equal(C4.c,[1,0,-4,0,2],13)
+        assert_array_almost_equal(C5.c,[1,0,-5,0,5,0],13)
+
+    def test_chebys(self):
+        S0 = orth.chebys(0)
+        S1 = orth.chebys(1)
+        S2 = orth.chebys(2)
+        S3 = orth.chebys(3)
+        S4 = orth.chebys(4)
+        S5 = orth.chebys(5)
+        assert_array_almost_equal(S0.c,[1],13)
+        assert_array_almost_equal(S1.c,[1,0],13)
+        assert_array_almost_equal(S2.c,[1,0,-1],13)
+        assert_array_almost_equal(S3.c,[1,0,-2,0],13)
+        assert_array_almost_equal(S4.c,[1,0,-3,0,1],13)
+        assert_array_almost_equal(S5.c,[1,0,-4,0,3,0],13)
+
+    def test_chebyt(self):
+        T0 = orth.chebyt(0)
+        T1 = orth.chebyt(1)
+        T2 = orth.chebyt(2)
+        T3 = orth.chebyt(3)
+        T4 = orth.chebyt(4)
+        T5 = orth.chebyt(5)
+        assert_array_almost_equal(T0.c,[1],13)
+        assert_array_almost_equal(T1.c,[1,0],13)
+        assert_array_almost_equal(T2.c,[2,0,-1],13)
+        assert_array_almost_equal(T3.c,[4,0,-3,0],13)
+        assert_array_almost_equal(T4.c,[8,0,-8,0,1],13)
+        assert_array_almost_equal(T5.c,[16,0,-20,0,5,0],13)
+
+    def test_chebyu(self):
+        U0 = orth.chebyu(0)
+        U1 = orth.chebyu(1)
+        U2 = orth.chebyu(2)
+        U3 = orth.chebyu(3)
+        U4 = orth.chebyu(4)
+        U5 = orth.chebyu(5)
+        assert_array_almost_equal(U0.c,[1],13)
+        assert_array_almost_equal(U1.c,[2,0],13)
+        assert_array_almost_equal(U2.c,[4,0,-1],13)
+        assert_array_almost_equal(U3.c,[8,0,-4,0],13)
+        assert_array_almost_equal(U4.c,[16,0,-12,0,1],13)
+        assert_array_almost_equal(U5.c,[32,0,-32,0,6,0],13)
+
+
+class TestGegenbauer(object):
+
+    def test_gegenbauer(self):
+        a = 5*np.random.random() - 0.5
+        if np.any(a == 0):
+            a = -0.2
+        Ca0 = orth.gegenbauer(0,a)
+        Ca1 = orth.gegenbauer(1,a)
+        Ca2 = orth.gegenbauer(2,a)
+        Ca3 = orth.gegenbauer(3,a)
+        Ca4 = orth.gegenbauer(4,a)
+        Ca5 = orth.gegenbauer(5,a)
+
+        assert_array_almost_equal(Ca0.c,array([1]),13)
+        assert_array_almost_equal(Ca1.c,array([2*a,0]),13)
+        assert_array_almost_equal(Ca2.c,array([2*a*(a+1),0,-a]),13)
+        assert_array_almost_equal(Ca3.c,array([4*sc.poch(a,3),0,-6*a*(a+1),
+                                               0])/3.0,11)
+        assert_array_almost_equal(Ca4.c,array([4*sc.poch(a,4),0,-12*sc.poch(a,3),
+                                               0,3*a*(a+1)])/6.0,11)
+        assert_array_almost_equal(Ca5.c,array([4*sc.poch(a,5),0,-20*sc.poch(a,4),
+                                               0,15*sc.poch(a,3),0])/15.0,11)
+
+
+class TestHermite(object):
+    def test_hermite(self):
+        H0 = orth.hermite(0)
+        H1 = orth.hermite(1)
+        H2 = orth.hermite(2)
+        H3 = orth.hermite(3)
+        H4 = orth.hermite(4)
+        H5 = orth.hermite(5)
+        assert_array_almost_equal(H0.c,[1],13)
+        assert_array_almost_equal(H1.c,[2,0],13)
+        assert_array_almost_equal(H2.c,[4,0,-2],13)
+        assert_array_almost_equal(H3.c,[8,0,-12,0],13)
+        assert_array_almost_equal(H4.c,[16,0,-48,0,12],12)
+        assert_array_almost_equal(H5.c,[32,0,-160,0,120,0],12)
+
+    def test_hermitenorm(self):
+        # He_n(x) = 2**(-n/2) H_n(x/sqrt(2))
+        psub = np.poly1d([1.0/sqrt(2),0])
+        H0 = orth.hermitenorm(0)
+        H1 = orth.hermitenorm(1)
+        H2 = orth.hermitenorm(2)
+        H3 = orth.hermitenorm(3)
+        H4 = orth.hermitenorm(4)
+        H5 = orth.hermitenorm(5)
+        he0 = orth.hermite(0)(psub)
+        he1 = orth.hermite(1)(psub) / sqrt(2)
+        he2 = orth.hermite(2)(psub) / 2.0
+        he3 = orth.hermite(3)(psub) / (2*sqrt(2))
+        he4 = orth.hermite(4)(psub) / 4.0
+        he5 = orth.hermite(5)(psub) / (4.0*sqrt(2))
+
+        assert_array_almost_equal(H0.c,he0.c,13)
+        assert_array_almost_equal(H1.c,he1.c,13)
+        assert_array_almost_equal(H2.c,he2.c,13)
+        assert_array_almost_equal(H3.c,he3.c,13)
+        assert_array_almost_equal(H4.c,he4.c,13)
+        assert_array_almost_equal(H5.c,he5.c,13)
+
+
+class _test_sh_legendre(object):
+
+    def test_sh_legendre(self):
+        # P*_n(x) = P_n(2x-1)
+        psub = np.poly1d([2,-1])
+        Ps0 = orth.sh_legendre(0)
+        Ps1 = orth.sh_legendre(1)
+        Ps2 = orth.sh_legendre(2)
+        Ps3 = orth.sh_legendre(3)
+        Ps4 = orth.sh_legendre(4)
+        Ps5 = orth.sh_legendre(5)
+        pse0 = orth.legendre(0)(psub)
+        pse1 = orth.legendre(1)(psub)
+        pse2 = orth.legendre(2)(psub)
+        pse3 = orth.legendre(3)(psub)
+        pse4 = orth.legendre(4)(psub)
+        pse5 = orth.legendre(5)(psub)
+        assert_array_almost_equal(Ps0.c,pse0.c,13)
+        assert_array_almost_equal(Ps1.c,pse1.c,13)
+        assert_array_almost_equal(Ps2.c,pse2.c,13)
+        assert_array_almost_equal(Ps3.c,pse3.c,13)
+        assert_array_almost_equal(Ps4.c,pse4.c,12)
+        assert_array_almost_equal(Ps5.c,pse5.c,12)
+
+
+class _test_sh_chebyt(object):
+
+    def test_sh_chebyt(self):
+        # T*_n(x) = T_n(2x-1)
+        psub = np.poly1d([2,-1])
+        Ts0 = orth.sh_chebyt(0)
+        Ts1 = orth.sh_chebyt(1)
+        Ts2 = orth.sh_chebyt(2)
+        Ts3 = orth.sh_chebyt(3)
+        Ts4 = orth.sh_chebyt(4)
+        Ts5 = orth.sh_chebyt(5)
+        tse0 = orth.chebyt(0)(psub)
+        tse1 = orth.chebyt(1)(psub)
+        tse2 = orth.chebyt(2)(psub)
+        tse3 = orth.chebyt(3)(psub)
+        tse4 = orth.chebyt(4)(psub)
+        tse5 = orth.chebyt(5)(psub)
+        assert_array_almost_equal(Ts0.c,tse0.c,13)
+        assert_array_almost_equal(Ts1.c,tse1.c,13)
+        assert_array_almost_equal(Ts2.c,tse2.c,13)
+        assert_array_almost_equal(Ts3.c,tse3.c,13)
+        assert_array_almost_equal(Ts4.c,tse4.c,12)
+        assert_array_almost_equal(Ts5.c,tse5.c,12)
+
+
+class _test_sh_chebyu(object):
+
+    def test_sh_chebyu(self):
+        # U*_n(x) = U_n(2x-1)
+        psub = np.poly1d([2,-1])
+        Us0 = orth.sh_chebyu(0)
+        Us1 = orth.sh_chebyu(1)
+        Us2 = orth.sh_chebyu(2)
+        Us3 = orth.sh_chebyu(3)
+        Us4 = orth.sh_chebyu(4)
+        Us5 = orth.sh_chebyu(5)
+        use0 = orth.chebyu(0)(psub)
+        use1 = orth.chebyu(1)(psub)
+        use2 = orth.chebyu(2)(psub)
+        use3 = orth.chebyu(3)(psub)
+        use4 = orth.chebyu(4)(psub)
+        use5 = orth.chebyu(5)(psub)
+        assert_array_almost_equal(Us0.c,use0.c,13)
+        assert_array_almost_equal(Us1.c,use1.c,13)
+        assert_array_almost_equal(Us2.c,use2.c,13)
+        assert_array_almost_equal(Us3.c,use3.c,13)
+        assert_array_almost_equal(Us4.c,use4.c,12)
+        assert_array_almost_equal(Us5.c,use5.c,11)
+
+
+class _test_sh_jacobi(object):
+    def test_sh_jacobi(self):
+        # G^(p,q)_n(x) = n! gamma(n+p)/gamma(2*n+p) * P^(p-q,q-1)_n(2*x-1)
+        conv = lambda n,p: gamma(n+1)*gamma(n+p)/gamma(2*n+p)
+        psub = np.poly1d([2,-1])
+        q = 4 * np.random.random()
+        p = q-1 + 2*np.random.random()
+        # print("shifted jacobi p,q = ", p, q)
+        G0 = orth.sh_jacobi(0,p,q)
+        G1 = orth.sh_jacobi(1,p,q)
+        G2 = orth.sh_jacobi(2,p,q)
+        G3 = orth.sh_jacobi(3,p,q)
+        G4 = orth.sh_jacobi(4,p,q)
+        G5 = orth.sh_jacobi(5,p,q)
+        ge0 = orth.jacobi(0,p-q,q-1)(psub) * conv(0,p)
+        ge1 = orth.jacobi(1,p-q,q-1)(psub) * conv(1,p)
+        ge2 = orth.jacobi(2,p-q,q-1)(psub) * conv(2,p)
+        ge3 = orth.jacobi(3,p-q,q-1)(psub) * conv(3,p)
+        ge4 = orth.jacobi(4,p-q,q-1)(psub) * conv(4,p)
+        ge5 = orth.jacobi(5,p-q,q-1)(psub) * conv(5,p)
+
+        assert_array_almost_equal(G0.c,ge0.c,13)
+        assert_array_almost_equal(G1.c,ge1.c,13)
+        assert_array_almost_equal(G2.c,ge2.c,13)
+        assert_array_almost_equal(G3.c,ge3.c,13)
+        assert_array_almost_equal(G4.c,ge4.c,13)
+        assert_array_almost_equal(G5.c,ge5.c,13)
+
+
+class TestCall(object):
+    def test_call(self):
+        poly = []
+        for n in range(5):
+            poly.extend([x.strip() for x in
+                ("""
+                orth.jacobi(%(n)d,0.3,0.9)
+                orth.sh_jacobi(%(n)d,0.3,0.9)
+                orth.genlaguerre(%(n)d,0.3)
+                orth.laguerre(%(n)d)
+                orth.hermite(%(n)d)
+                orth.hermitenorm(%(n)d)
+                orth.gegenbauer(%(n)d,0.3)
+                orth.chebyt(%(n)d)
+                orth.chebyu(%(n)d)
+                orth.chebyc(%(n)d)
+                orth.chebys(%(n)d)
+                orth.sh_chebyt(%(n)d)
+                orth.sh_chebyu(%(n)d)
+                orth.legendre(%(n)d)
+                orth.sh_legendre(%(n)d)
+                """ % dict(n=n)).split()
+            ])
+        with np.errstate(all='ignore'):
+            for pstr in poly:
+                p = eval(pstr)
+                assert_almost_equal(p(0.315), np.poly1d(p.coef)(0.315),
+                                    err_msg=pstr)
+
+
+class TestGenlaguerre(object):
+    def test_regression(self):
+        assert_equal(orth.genlaguerre(1, 1, monic=False)(0), 2.)
+        assert_equal(orth.genlaguerre(1, 1, monic=True)(0), -2.)
+        assert_equal(orth.genlaguerre(1, 1, monic=False), np.poly1d([-1, 2]))
+        assert_equal(orth.genlaguerre(1, 1, monic=True), np.poly1d([1, -2]))
+
+
+def verify_gauss_quad(root_func, eval_func, weight_func, a, b, N,
+                      rtol=1e-15, atol=1e-14):
+    # this test is copied from numpy's TestGauss in test_hermite.py
+    x, w, mu = root_func(N, True)
+
+    n = np.arange(N)
+    v = eval_func(n[:,np.newaxis], x)
+    vv = np.dot(v*w, v.T)
+    vd = 1 / np.sqrt(vv.diagonal())
+    vv = vd[:, np.newaxis] * vv * vd
+    assert_allclose(vv, np.eye(N), rtol, atol)
+
+    # check that the integral of 1 is correct
+    assert_allclose(w.sum(), mu, rtol, atol)
+
+    # compare the results of integrating a function with quad.
+    f = lambda x: x**3 - 3*x**2 + x - 2
+    resI = integrate.quad(lambda x: f(x)*weight_func(x), a, b)
+    resG = np.vdot(f(x), w)
+    rtol = 1e-6 if 1e-6 < resI[1] else resI[1] * 10
+    assert_allclose(resI[0], resG, rtol=rtol)
+
+def test_roots_jacobi():
+    rf = lambda a, b: lambda n, mu: sc.roots_jacobi(n, a, b, mu)
+    ef = lambda a, b: lambda n, x: sc.eval_jacobi(n, a, b, x)
+    wf = lambda a, b: lambda x: (1 - x)**a * (1 + x)**b
+
+    vgq = verify_gauss_quad
+    vgq(rf(-0.5, -0.75), ef(-0.5, -0.75), wf(-0.5, -0.75), -1., 1., 5)
+    vgq(rf(-0.5, -0.75), ef(-0.5, -0.75), wf(-0.5, -0.75), -1., 1.,
+        25, atol=1e-12)
+    vgq(rf(-0.5, -0.75), ef(-0.5, -0.75), wf(-0.5, -0.75), -1., 1.,
+        100, atol=1e-11)
+
+    vgq(rf(0.5, -0.5), ef(0.5, -0.5), wf(0.5, -0.5), -1., 1., 5)
+    vgq(rf(0.5, -0.5), ef(0.5, -0.5), wf(0.5, -0.5), -1., 1., 25, atol=1.5e-13)
+    vgq(rf(0.5, -0.5), ef(0.5, -0.5), wf(0.5, -0.5), -1., 1., 100, atol=2e-12)
+
+    vgq(rf(1, 0.5), ef(1, 0.5), wf(1, 0.5), -1., 1., 5, atol=2e-13)
+    vgq(rf(1, 0.5), ef(1, 0.5), wf(1, 0.5), -1., 1., 25, atol=2e-13)
+    vgq(rf(1, 0.5), ef(1, 0.5), wf(1, 0.5), -1., 1., 100, atol=1e-12)
+
+    vgq(rf(0.9, 2), ef(0.9, 2), wf(0.9, 2), -1., 1., 5)
+    vgq(rf(0.9, 2), ef(0.9, 2), wf(0.9, 2), -1., 1., 25, atol=1e-13)
+    vgq(rf(0.9, 2), ef(0.9, 2), wf(0.9, 2), -1., 1., 100, atol=3e-13)
+
+    vgq(rf(18.24, 27.3), ef(18.24, 27.3), wf(18.24, 27.3), -1., 1., 5)
+    vgq(rf(18.24, 27.3), ef(18.24, 27.3), wf(18.24, 27.3), -1., 1., 25,
+        atol=1.1e-14)
+    vgq(rf(18.24, 27.3), ef(18.24, 27.3), wf(18.24, 27.3), -1., 1.,
+        100, atol=1e-13)
+
+    vgq(rf(47.1, -0.2), ef(47.1, -0.2), wf(47.1, -0.2), -1., 1., 5, atol=1e-13)
+    vgq(rf(47.1, -0.2), ef(47.1, -0.2), wf(47.1, -0.2), -1., 1., 25, atol=2e-13)
+    vgq(rf(47.1, -0.2), ef(47.1, -0.2), wf(47.1, -0.2), -1., 1.,
+        100, atol=1e-11)
+
+    vgq(rf(2.25, 68.9), ef(2.25, 68.9), wf(2.25, 68.9), -1., 1., 5)
+    vgq(rf(2.25, 68.9), ef(2.25, 68.9), wf(2.25, 68.9), -1., 1., 25, atol=1e-13)
+    vgq(rf(2.25, 68.9), ef(2.25, 68.9), wf(2.25, 68.9), -1., 1.,
+        100, atol=1e-13)
+
+    # when alpha == beta == 0, P_n^{a,b}(x) == P_n(x)
+    xj, wj = sc.roots_jacobi(6, 0.0, 0.0)
+    xl, wl = sc.roots_legendre(6)
+    assert_allclose(xj, xl, 1e-14, 1e-14)
+    assert_allclose(wj, wl, 1e-14, 1e-14)
+
+    # when alpha == beta != 0, P_n^{a,b}(x) == C_n^{alpha+0.5}(x)
+    xj, wj = sc.roots_jacobi(6, 4.0, 4.0)
+    xc, wc = sc.roots_gegenbauer(6, 4.5)
+    assert_allclose(xj, xc, 1e-14, 1e-14)
+    assert_allclose(wj, wc, 1e-14, 1e-14)
+
+    x, w = sc.roots_jacobi(5, 2, 3, False)
+    y, v, m = sc.roots_jacobi(5, 2, 3, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(wf(2,3), -1, 1)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_jacobi, 0, 1, 1)
+    assert_raises(ValueError, sc.roots_jacobi, 3.3, 1, 1)
+    assert_raises(ValueError, sc.roots_jacobi, 3, -2, 1)
+    assert_raises(ValueError, sc.roots_jacobi, 3, 1, -2)
+    assert_raises(ValueError, sc.roots_jacobi, 3, -2, -2)
+
+def test_roots_sh_jacobi():
+    rf = lambda a, b: lambda n, mu: sc.roots_sh_jacobi(n, a, b, mu)
+    ef = lambda a, b: lambda n, x: sc.eval_sh_jacobi(n, a, b, x)
+    wf = lambda a, b: lambda x: (1. - x)**(a - b) * (x)**(b - 1.)
+
+    vgq = verify_gauss_quad
+    vgq(rf(-0.5, 0.25), ef(-0.5, 0.25), wf(-0.5, 0.25), 0., 1., 5)
+    vgq(rf(-0.5, 0.25), ef(-0.5, 0.25), wf(-0.5, 0.25), 0., 1.,
+        25, atol=1e-12)
+    vgq(rf(-0.5, 0.25), ef(-0.5, 0.25), wf(-0.5, 0.25), 0., 1.,
+        100, atol=1e-11)
+
+    vgq(rf(0.5, 0.5), ef(0.5, 0.5), wf(0.5, 0.5), 0., 1., 5)
+    vgq(rf(0.5, 0.5), ef(0.5, 0.5), wf(0.5, 0.5), 0., 1., 25, atol=1e-13)
+    vgq(rf(0.5, 0.5), ef(0.5, 0.5), wf(0.5, 0.5), 0., 1., 100, atol=1e-12)
+
+    vgq(rf(1, 0.5), ef(1, 0.5), wf(1, 0.5), 0., 1., 5)
+    vgq(rf(1, 0.5), ef(1, 0.5), wf(1, 0.5), 0., 1., 25, atol=1.5e-13)
+    vgq(rf(1, 0.5), ef(1, 0.5), wf(1, 0.5), 0., 1., 100, atol=2e-12)
+
+    vgq(rf(2, 0.9), ef(2, 0.9), wf(2, 0.9), 0., 1., 5)
+    vgq(rf(2, 0.9), ef(2, 0.9), wf(2, 0.9), 0., 1., 25, atol=1e-13)
+    vgq(rf(2, 0.9), ef(2, 0.9), wf(2, 0.9), 0., 1., 100, atol=1e-12)
+
+    vgq(rf(27.3, 18.24), ef(27.3, 18.24), wf(27.3, 18.24), 0., 1., 5)
+    vgq(rf(27.3, 18.24), ef(27.3, 18.24), wf(27.3, 18.24), 0., 1., 25)
+    vgq(rf(27.3, 18.24), ef(27.3, 18.24), wf(27.3, 18.24), 0., 1.,
+        100, atol=1e-13)
+
+    vgq(rf(47.1, 0.2), ef(47.1, 0.2), wf(47.1, 0.2), 0., 1., 5, atol=1e-12)
+    vgq(rf(47.1, 0.2), ef(47.1, 0.2), wf(47.1, 0.2), 0., 1., 25, atol=1e-11)
+    vgq(rf(47.1, 0.2), ef(47.1, 0.2), wf(47.1, 0.2), 0., 1., 100, atol=1e-10)
+
+    vgq(rf(68.9, 2.25), ef(68.9, 2.25), wf(68.9, 2.25), 0., 1., 5, atol=3.5e-14)
+    vgq(rf(68.9, 2.25), ef(68.9, 2.25), wf(68.9, 2.25), 0., 1., 25, atol=2e-13)
+    vgq(rf(68.9, 2.25), ef(68.9, 2.25), wf(68.9, 2.25), 0., 1.,
+        100, atol=1e-12)
+
+    x, w = sc.roots_sh_jacobi(5, 3, 2, False)
+    y, v, m = sc.roots_sh_jacobi(5, 3, 2, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(wf(3,2), 0, 1)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_sh_jacobi, 0, 1, 1)
+    assert_raises(ValueError, sc.roots_sh_jacobi, 3.3, 1, 1)
+    assert_raises(ValueError, sc.roots_sh_jacobi, 3, 1, 2)    # p - q <= -1
+    assert_raises(ValueError, sc.roots_sh_jacobi, 3, 2, -1)   # q <= 0
+    assert_raises(ValueError, sc.roots_sh_jacobi, 3, -2, -1)  # both
+
+def test_roots_hermite():
+    rootf = sc.roots_hermite
+    evalf = sc.eval_hermite
+    weightf = orth.hermite(5).weight_func
+
+    verify_gauss_quad(rootf, evalf, weightf, -np.inf, np.inf, 5)
+    verify_gauss_quad(rootf, evalf, weightf, -np.inf, np.inf, 25, atol=1e-13)
+    verify_gauss_quad(rootf, evalf, weightf, -np.inf, np.inf, 100, atol=1e-12)
+
+    # Golub-Welsch branch
+    x, w = sc.roots_hermite(5, False)
+    y, v, m = sc.roots_hermite(5, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf, -np.inf, np.inf)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    # Asymptotic branch (switch over at n >= 150)
+    x, w = sc.roots_hermite(200, False)
+    y, v, m = sc.roots_hermite(200, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+    assert_allclose(sum(v), m, 1e-14, 1e-14)
+
+    assert_raises(ValueError, sc.roots_hermite, 0)
+    assert_raises(ValueError, sc.roots_hermite, 3.3)
+
+def test_roots_hermite_asy():
+    # Recursion for Hermite functions
+    def hermite_recursion(n, nodes):
+        H = np.zeros((n, nodes.size))
+        H[0,:] = np.pi**(-0.25) * np.exp(-0.5*nodes**2)
+        if n > 1:
+            H[1,:] = sqrt(2.0) * nodes * H[0,:]
+            for k in range(2, n):
+                H[k,:] = sqrt(2.0/k) * nodes * H[k-1,:] - sqrt((k-1.0)/k) * H[k-2,:]
+        return H
+
+    # This tests only the nodes
+    def test(N, rtol=1e-15, atol=1e-14):
+        x, w = orth._roots_hermite_asy(N)
+        H = hermite_recursion(N+1, x)
+        assert_allclose(H[-1,:], np.zeros(N), rtol, atol)
+        assert_allclose(sum(w), sqrt(np.pi), rtol, atol)
+
+    test(150, atol=1e-12)
+    test(151, atol=1e-12)
+    test(300, atol=1e-12)
+    test(301, atol=1e-12)
+    test(500, atol=1e-12)
+    test(501, atol=1e-12)
+    test(999, atol=1e-12)
+    test(1000, atol=1e-12)
+    test(2000, atol=1e-12)
+    test(5000, atol=1e-12)
+
+def test_roots_hermitenorm():
+    rootf = sc.roots_hermitenorm
+    evalf = sc.eval_hermitenorm
+    weightf = orth.hermitenorm(5).weight_func
+
+    verify_gauss_quad(rootf, evalf, weightf, -np.inf, np.inf, 5)
+    verify_gauss_quad(rootf, evalf, weightf, -np.inf, np.inf, 25, atol=1e-13)
+    verify_gauss_quad(rootf, evalf, weightf, -np.inf, np.inf, 100, atol=1e-12)
+
+    x, w = sc.roots_hermitenorm(5, False)
+    y, v, m = sc.roots_hermitenorm(5, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf, -np.inf, np.inf)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_hermitenorm, 0)
+    assert_raises(ValueError, sc.roots_hermitenorm, 3.3)
+
+def test_roots_gegenbauer():
+    rootf = lambda a: lambda n, mu: sc.roots_gegenbauer(n, a, mu)
+    evalf = lambda a: lambda n, x: sc.eval_gegenbauer(n, a, x)
+    weightf = lambda a: lambda x: (1 - x**2)**(a - 0.5)
+
+    vgq = verify_gauss_quad
+    vgq(rootf(-0.25), evalf(-0.25), weightf(-0.25), -1., 1., 5)
+    vgq(rootf(-0.25), evalf(-0.25), weightf(-0.25), -1., 1., 25, atol=1e-12)
+    vgq(rootf(-0.25), evalf(-0.25), weightf(-0.25), -1., 1., 100, atol=1e-11)
+
+    vgq(rootf(0.1), evalf(0.1), weightf(0.1), -1., 1., 5)
+    vgq(rootf(0.1), evalf(0.1), weightf(0.1), -1., 1., 25, atol=1e-13)
+    vgq(rootf(0.1), evalf(0.1), weightf(0.1), -1., 1., 100, atol=1e-12)
+
+    vgq(rootf(1), evalf(1), weightf(1), -1., 1., 5)
+    vgq(rootf(1), evalf(1), weightf(1), -1., 1., 25, atol=1e-13)
+    vgq(rootf(1), evalf(1), weightf(1), -1., 1., 100, atol=1e-12)
+
+    vgq(rootf(10), evalf(10), weightf(10), -1., 1., 5)
+    vgq(rootf(10), evalf(10), weightf(10), -1., 1., 25, atol=1e-13)
+    vgq(rootf(10), evalf(10), weightf(10), -1., 1., 100, atol=1e-12)
+
+    vgq(rootf(50), evalf(50), weightf(50), -1., 1., 5, atol=1e-13)
+    vgq(rootf(50), evalf(50), weightf(50), -1., 1., 25, atol=1e-12)
+    vgq(rootf(50), evalf(50), weightf(50), -1., 1., 100, atol=1e-11)
+
+    # this is a special case that the old code supported.
+    # when alpha = 0, the gegenbauer polynomial is uniformly 0. but it goes
+    # to a scaled down copy of T_n(x) there.
+    vgq(rootf(0), sc.eval_chebyt, weightf(0), -1., 1., 5)
+    vgq(rootf(0), sc.eval_chebyt, weightf(0), -1., 1., 25)
+    vgq(rootf(0), sc.eval_chebyt, weightf(0), -1., 1., 100, atol=1e-12)
+
+    x, w = sc.roots_gegenbauer(5, 2, False)
+    y, v, m = sc.roots_gegenbauer(5, 2, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf(2), -1, 1)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_gegenbauer, 0, 2)
+    assert_raises(ValueError, sc.roots_gegenbauer, 3.3, 2)
+    assert_raises(ValueError, sc.roots_gegenbauer, 3, -.75)
+
+def test_roots_chebyt():
+    weightf = orth.chebyt(5).weight_func
+    verify_gauss_quad(sc.roots_chebyt, sc.eval_chebyt, weightf, -1., 1., 5)
+    verify_gauss_quad(sc.roots_chebyt, sc.eval_chebyt, weightf, -1., 1., 25)
+    verify_gauss_quad(sc.roots_chebyt, sc.eval_chebyt, weightf, -1., 1., 100, atol=1e-12)
+
+    x, w = sc.roots_chebyt(5, False)
+    y, v, m = sc.roots_chebyt(5, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf, -1, 1)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_chebyt, 0)
+    assert_raises(ValueError, sc.roots_chebyt, 3.3)
+
+def test_chebyt_symmetry():
+    x, w = sc.roots_chebyt(21)
+    pos, neg = x[:10], x[11:]
+    assert_equal(neg, -pos[::-1])
+    assert_equal(x[10], 0)
+
+def test_roots_chebyu():
+    weightf = orth.chebyu(5).weight_func
+    verify_gauss_quad(sc.roots_chebyu, sc.eval_chebyu, weightf, -1., 1., 5)
+    verify_gauss_quad(sc.roots_chebyu, sc.eval_chebyu, weightf, -1., 1., 25)
+    verify_gauss_quad(sc.roots_chebyu, sc.eval_chebyu, weightf, -1., 1., 100)
+
+    x, w = sc.roots_chebyu(5, False)
+    y, v, m = sc.roots_chebyu(5, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf, -1, 1)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_chebyu, 0)
+    assert_raises(ValueError, sc.roots_chebyu, 3.3)
+
+def test_roots_chebyc():
+    weightf = orth.chebyc(5).weight_func
+    verify_gauss_quad(sc.roots_chebyc, sc.eval_chebyc, weightf, -2., 2., 5)
+    verify_gauss_quad(sc.roots_chebyc, sc.eval_chebyc, weightf, -2., 2., 25)
+    verify_gauss_quad(sc.roots_chebyc, sc.eval_chebyc, weightf, -2., 2., 100, atol=1e-12)
+
+    x, w = sc.roots_chebyc(5, False)
+    y, v, m = sc.roots_chebyc(5, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf, -2, 2)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_chebyc, 0)
+    assert_raises(ValueError, sc.roots_chebyc, 3.3)
+
+def test_roots_chebys():
+    weightf = orth.chebys(5).weight_func
+    verify_gauss_quad(sc.roots_chebys, sc.eval_chebys, weightf, -2., 2., 5)
+    verify_gauss_quad(sc.roots_chebys, sc.eval_chebys, weightf, -2., 2., 25)
+    verify_gauss_quad(sc.roots_chebys, sc.eval_chebys, weightf, -2., 2., 100)
+
+    x, w = sc.roots_chebys(5, False)
+    y, v, m = sc.roots_chebys(5, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf, -2, 2)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_chebys, 0)
+    assert_raises(ValueError, sc.roots_chebys, 3.3)
+
+def test_roots_sh_chebyt():
+    weightf = orth.sh_chebyt(5).weight_func
+    verify_gauss_quad(sc.roots_sh_chebyt, sc.eval_sh_chebyt, weightf, 0., 1., 5)
+    verify_gauss_quad(sc.roots_sh_chebyt, sc.eval_sh_chebyt, weightf, 0., 1., 25)
+    verify_gauss_quad(sc.roots_sh_chebyt, sc.eval_sh_chebyt, weightf, 0., 1.,
+                      100, atol=1e-13)
+
+    x, w = sc.roots_sh_chebyt(5, False)
+    y, v, m = sc.roots_sh_chebyt(5, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf, 0, 1)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_sh_chebyt, 0)
+    assert_raises(ValueError, sc.roots_sh_chebyt, 3.3)
+
+def test_roots_sh_chebyu():
+    weightf = orth.sh_chebyu(5).weight_func
+    verify_gauss_quad(sc.roots_sh_chebyu, sc.eval_sh_chebyu, weightf, 0., 1., 5)
+    verify_gauss_quad(sc.roots_sh_chebyu, sc.eval_sh_chebyu, weightf, 0., 1., 25)
+    verify_gauss_quad(sc.roots_sh_chebyu, sc.eval_sh_chebyu, weightf, 0., 1.,
+                      100, atol=1e-13)
+
+    x, w = sc.roots_sh_chebyu(5, False)
+    y, v, m = sc.roots_sh_chebyu(5, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf, 0, 1)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_sh_chebyu, 0)
+    assert_raises(ValueError, sc.roots_sh_chebyu, 3.3)
+
+def test_roots_legendre():
+    weightf = orth.legendre(5).weight_func
+    verify_gauss_quad(sc.roots_legendre, sc.eval_legendre, weightf, -1., 1., 5)
+    verify_gauss_quad(sc.roots_legendre, sc.eval_legendre, weightf, -1., 1.,
+                      25, atol=1e-13)
+    verify_gauss_quad(sc.roots_legendre, sc.eval_legendre, weightf, -1., 1.,
+                      100, atol=1e-12)
+
+    x, w = sc.roots_legendre(5, False)
+    y, v, m = sc.roots_legendre(5, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf, -1, 1)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_legendre, 0)
+    assert_raises(ValueError, sc.roots_legendre, 3.3)
+
+def test_roots_sh_legendre():
+    weightf = orth.sh_legendre(5).weight_func
+    verify_gauss_quad(sc.roots_sh_legendre, sc.eval_sh_legendre, weightf, 0., 1., 5)
+    verify_gauss_quad(sc.roots_sh_legendre, sc.eval_sh_legendre, weightf, 0., 1.,
+                      25, atol=1e-13)
+    verify_gauss_quad(sc.roots_sh_legendre, sc.eval_sh_legendre, weightf, 0., 1.,
+                      100, atol=1e-12)
+
+    x, w = sc.roots_sh_legendre(5, False)
+    y, v, m = sc.roots_sh_legendre(5, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf, 0, 1)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_sh_legendre, 0)
+    assert_raises(ValueError, sc.roots_sh_legendre, 3.3)
+
+def test_roots_laguerre():
+    weightf = orth.laguerre(5).weight_func
+    verify_gauss_quad(sc.roots_laguerre, sc.eval_laguerre, weightf, 0., np.inf, 5)
+    verify_gauss_quad(sc.roots_laguerre, sc.eval_laguerre, weightf, 0., np.inf,
+                      25, atol=1e-13)
+    verify_gauss_quad(sc.roots_laguerre, sc.eval_laguerre, weightf, 0., np.inf,
+                      100, atol=1e-12)
+
+    x, w = sc.roots_laguerre(5, False)
+    y, v, m = sc.roots_laguerre(5, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf, 0, np.inf)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_laguerre, 0)
+    assert_raises(ValueError, sc.roots_laguerre, 3.3)
+
+def test_roots_genlaguerre():
+    rootf = lambda a: lambda n, mu: sc.roots_genlaguerre(n, a, mu)
+    evalf = lambda a: lambda n, x: sc.eval_genlaguerre(n, a, x)
+    weightf = lambda a: lambda x: x**a * np.exp(-x)
+
+    vgq = verify_gauss_quad
+    vgq(rootf(-0.5), evalf(-0.5), weightf(-0.5), 0., np.inf, 5)
+    vgq(rootf(-0.5), evalf(-0.5), weightf(-0.5), 0., np.inf, 25, atol=1e-13)
+    vgq(rootf(-0.5), evalf(-0.5), weightf(-0.5), 0., np.inf, 100, atol=1e-12)
+
+    vgq(rootf(0.1), evalf(0.1), weightf(0.1), 0., np.inf, 5)
+    vgq(rootf(0.1), evalf(0.1), weightf(0.1), 0., np.inf, 25, atol=1e-13)
+    vgq(rootf(0.1), evalf(0.1), weightf(0.1), 0., np.inf, 100, atol=1.6e-13)
+
+    vgq(rootf(1), evalf(1), weightf(1), 0., np.inf, 5)
+    vgq(rootf(1), evalf(1), weightf(1), 0., np.inf, 25, atol=1e-13)
+    vgq(rootf(1), evalf(1), weightf(1), 0., np.inf, 100, atol=1.03e-13)
+
+    vgq(rootf(10), evalf(10), weightf(10), 0., np.inf, 5)
+    vgq(rootf(10), evalf(10), weightf(10), 0., np.inf, 25, atol=1e-13)
+    vgq(rootf(10), evalf(10), weightf(10), 0., np.inf, 100, atol=1e-12)
+
+    vgq(rootf(50), evalf(50), weightf(50), 0., np.inf, 5)
+    vgq(rootf(50), evalf(50), weightf(50), 0., np.inf, 25, atol=1e-13)
+    vgq(rootf(50), evalf(50), weightf(50), 0., np.inf, 100, rtol=1e-14, atol=2e-13)
+
+    x, w = sc.roots_genlaguerre(5, 2, False)
+    y, v, m = sc.roots_genlaguerre(5, 2, True)
+    assert_allclose(x, y, 1e-14, 1e-14)
+    assert_allclose(w, v, 1e-14, 1e-14)
+
+    muI, muI_err = integrate.quad(weightf(2.), 0., np.inf)
+    assert_allclose(m, muI, rtol=muI_err)
+
+    assert_raises(ValueError, sc.roots_genlaguerre, 0, 2)
+    assert_raises(ValueError, sc.roots_genlaguerre, 3.3, 2)
+    assert_raises(ValueError, sc.roots_genlaguerre, 3, -1.1)
+
+
+def test_gh_6721():
+    # Regresssion test for gh_6721. This should not raise.
+    sc.chebyt(65)(0.2)

venv/Lib/site-packages/scipy/special/tests/test_orthogonal_eval.py

@@ -0,0 +1,266 @@
+import numpy as np
+from numpy.testing import assert_, assert_allclose
+import pytest
+
+import scipy.special.orthogonal as orth
+from scipy.special._testutils import FuncData
+
+
+def test_eval_chebyt():
+    n = np.arange(0, 10000, 7)
+    x = 2*np.random.rand() - 1
+    v1 = np.cos(n*np.arccos(x))
+    v2 = orth.eval_chebyt(n, x)
+    assert_(np.allclose(v1, v2, rtol=1e-15))
+
+
+def test_eval_genlaguerre_restriction():
+    # check it returns nan for alpha <= -1
+    assert_(np.isnan(orth.eval_genlaguerre(0, -1, 0)))
+    assert_(np.isnan(orth.eval_genlaguerre(0.1, -1, 0)))
+
+
+def test_warnings():
+    # ticket 1334
+    with np.errstate(all='raise'):
+        # these should raise no fp warnings
+        orth.eval_legendre(1, 0)
+        orth.eval_laguerre(1, 1)
+        orth.eval_gegenbauer(1, 1, 0)
+
+
+class TestPolys(object):
+    """
+    Check that the eval_* functions agree with the constructed polynomials
+
+    """
+
+    def check_poly(self, func, cls, param_ranges=[], x_range=[], nn=10,
+                   nparam=10, nx=10, rtol=1e-8):
+        np.random.seed(1234)
+
+        dataset = []
+        for n in np.arange(nn):
+            params = [a + (b-a)*np.random.rand(nparam) for a,b in param_ranges]
+            params = np.asarray(params).T
+            if not param_ranges:
+                params = [0]
+            for p in params:
+                if param_ranges:
+                    p = (n,) + tuple(p)
+                else:
+                    p = (n,)
+                x = x_range[0] + (x_range[1] - x_range[0])*np.random.rand(nx)
+                x[0] = x_range[0]  # always include domain start point
+                x[1] = x_range[1]  # always include domain end point
+                poly = np.poly1d(cls(*p).coef)
+                z = np.c_[np.tile(p, (nx,1)), x, poly(x)]
+                dataset.append(z)
+
+        dataset = np.concatenate(dataset, axis=0)
+
+        def polyfunc(*p):
+            p = (p[0].astype(int),) + p[1:]
+            return func(*p)
+
+        with np.errstate(all='raise'):
+            ds = FuncData(polyfunc, dataset, list(range(len(param_ranges)+2)), -1,
+                          rtol=rtol)
+            ds.check()
+
+    def test_jacobi(self):
+        self.check_poly(orth.eval_jacobi, orth.jacobi,
+                   param_ranges=[(-0.99, 10), (-0.99, 10)], x_range=[-1, 1],
+                   rtol=1e-5)
+
+    def test_sh_jacobi(self):
+        self.check_poly(orth.eval_sh_jacobi, orth.sh_jacobi,
+                   param_ranges=[(1, 10), (0, 1)], x_range=[0, 1],
+                   rtol=1e-5)
+
+    def test_gegenbauer(self):
+        self.check_poly(orth.eval_gegenbauer, orth.gegenbauer,
+                   param_ranges=[(-0.499, 10)], x_range=[-1, 1],
+                   rtol=1e-7)
+
+    def test_chebyt(self):
+        self.check_poly(orth.eval_chebyt, orth.chebyt,
+                   param_ranges=[], x_range=[-1, 1])
+
+    def test_chebyu(self):
+        self.check_poly(orth.eval_chebyu, orth.chebyu,
+                   param_ranges=[], x_range=[-1, 1])
+
+    def test_chebys(self):
+        self.check_poly(orth.eval_chebys, orth.chebys,
+                   param_ranges=[], x_range=[-2, 2])
+
+    def test_chebyc(self):
+        self.check_poly(orth.eval_chebyc, orth.chebyc,
+                   param_ranges=[], x_range=[-2, 2])
+
+    def test_sh_chebyt(self):
+        with np.errstate(all='ignore'):
+            self.check_poly(orth.eval_sh_chebyt, orth.sh_chebyt,
+                            param_ranges=[], x_range=[0, 1])
+
+    def test_sh_chebyu(self):
+        self.check_poly(orth.eval_sh_chebyu, orth.sh_chebyu,
+                   param_ranges=[], x_range=[0, 1])
+
+    def test_legendre(self):
+        self.check_poly(orth.eval_legendre, orth.legendre,
+                   param_ranges=[], x_range=[-1, 1])
+
+    def test_sh_legendre(self):
+        with np.errstate(all='ignore'):
+            self.check_poly(orth.eval_sh_legendre, orth.sh_legendre,
+                            param_ranges=[], x_range=[0, 1])
+
+    def test_genlaguerre(self):
+        self.check_poly(orth.eval_genlaguerre, orth.genlaguerre,
+                   param_ranges=[(-0.99, 10)], x_range=[0, 100])
+
+    def test_laguerre(self):
+        self.check_poly(orth.eval_laguerre, orth.laguerre,
+                   param_ranges=[], x_range=[0, 100])
+
+    def test_hermite(self):
+        self.check_poly(orth.eval_hermite, orth.hermite,
+                   param_ranges=[], x_range=[-100, 100])
+
+    def test_hermitenorm(self):
+        self.check_poly(orth.eval_hermitenorm, orth.hermitenorm,
+                        param_ranges=[], x_range=[-100, 100])
+
+
+class TestRecurrence(object):
+    """
+    Check that the eval_* functions sig='ld->d' and 'dd->d' agree.
+
+    """
+
+    def check_poly(self, func, param_ranges=[], x_range=[], nn=10,
+                   nparam=10, nx=10, rtol=1e-8):
+        np.random.seed(1234)
+
+        dataset = []
+        for n in np.arange(nn):
+            params = [a + (b-a)*np.random.rand(nparam) for a,b in param_ranges]
+            params = np.asarray(params).T
+            if not param_ranges:
+                params = [0]
+            for p in params:
+                if param_ranges:
+                    p = (n,) + tuple(p)
+                else:
+                    p = (n,)
+                x = x_range[0] + (x_range[1] - x_range[0])*np.random.rand(nx)
+                x[0] = x_range[0]  # always include domain start point
+                x[1] = x_range[1]  # always include domain end point
+                kw = dict(sig=(len(p)+1)*'d'+'->d')
+                z = np.c_[np.tile(p, (nx,1)), x, func(*(p + (x,)), **kw)]
+                dataset.append(z)
+
+        dataset = np.concatenate(dataset, axis=0)
+
+        def polyfunc(*p):
+            p = (p[0].astype(int),) + p[1:]
+            kw = dict(sig='l'+(len(p)-1)*'d'+'->d')
+            return func(*p, **kw)
+
+        with np.errstate(all='raise'):
+            ds = FuncData(polyfunc, dataset, list(range(len(param_ranges)+2)), -1,
+                          rtol=rtol)
+            ds.check()
+
+    def test_jacobi(self):
+        self.check_poly(orth.eval_jacobi,
+                   param_ranges=[(-0.99, 10), (-0.99, 10)], x_range=[-1, 1])
+
+    def test_sh_jacobi(self):
+        self.check_poly(orth.eval_sh_jacobi,
+                   param_ranges=[(1, 10), (0, 1)], x_range=[0, 1])
+
+    def test_gegenbauer(self):
+        self.check_poly(orth.eval_gegenbauer,
+                   param_ranges=[(-0.499, 10)], x_range=[-1, 1])
+
+    def test_chebyt(self):
+        self.check_poly(orth.eval_chebyt,
+                   param_ranges=[], x_range=[-1, 1])
+
+    def test_chebyu(self):
+        self.check_poly(orth.eval_chebyu,
+                   param_ranges=[], x_range=[-1, 1])
+
+    def test_chebys(self):
+        self.check_poly(orth.eval_chebys,
+                   param_ranges=[], x_range=[-2, 2])
+
+    def test_chebyc(self):
+        self.check_poly(orth.eval_chebyc,
+                   param_ranges=[], x_range=[-2, 2])
+
+    def test_sh_chebyt(self):
+        self.check_poly(orth.eval_sh_chebyt,
+                   param_ranges=[], x_range=[0, 1])
+
+    def test_sh_chebyu(self):
+        self.check_poly(orth.eval_sh_chebyu,
+                   param_ranges=[], x_range=[0, 1])
+
+    def test_legendre(self):
+        self.check_poly(orth.eval_legendre,
+                   param_ranges=[], x_range=[-1, 1])
+
+    def test_sh_legendre(self):
+        self.check_poly(orth.eval_sh_legendre,
+                   param_ranges=[], x_range=[0, 1])
+
+    def test_genlaguerre(self):
+        self.check_poly(orth.eval_genlaguerre,
+                   param_ranges=[(-0.99, 10)], x_range=[0, 100])
+
+    def test_laguerre(self):
+        self.check_poly(orth.eval_laguerre,
+                   param_ranges=[], x_range=[0, 100])
+
+    def test_hermite(self):
+        v = orth.eval_hermite(70, 1.0)
+        a = -1.457076485701412e60
+        assert_allclose(v,a)
+
+
+def test_hermite_domain():
+    # Regression test for gh-11091.
+    assert np.isnan(orth.eval_hermite(-1, 1.0))
+    assert np.isnan(orth.eval_hermitenorm(-1, 1.0))
+
+
+@pytest.mark.parametrize("n", [0, 1, 2])
+@pytest.mark.parametrize("x", [0, 1, np.nan])
+def test_hermite_nan(n, x):
+    # Regression test for gh-11369.
+    assert np.isnan(orth.eval_hermite(n, x)) == np.any(np.isnan([n, x]))
+    assert np.isnan(orth.eval_hermitenorm(n, x)) == np.any(np.isnan([n, x]))
+
+
+@pytest.mark.parametrize('n', [0, 1, 2, 3.2])
+@pytest.mark.parametrize('alpha', [1, np.nan])
+@pytest.mark.parametrize('x', [2, np.nan])
+def test_genlaguerre_nan(n, alpha, x):
+    # Regression test for gh-11361.
+    nan_laguerre = np.isnan(orth.eval_genlaguerre(n, alpha, x))
+    nan_arg = np.any(np.isnan([n, alpha, x]))
+    assert nan_laguerre == nan_arg
+
+
+@pytest.mark.parametrize('n', [0, 1, 2, 3.2])
+@pytest.mark.parametrize('alpha', [0.0, 1, np.nan])
+@pytest.mark.parametrize('x', [1e-6, 2, np.nan])
+def test_gegenbauer_nan(n, alpha, x):
+    # Regression test for gh-11370.
+    nan_gegenbauer = np.isnan(orth.eval_gegenbauer(n, alpha, x))
+    nan_arg = np.any(np.isnan([n, alpha, x]))
+    assert nan_gegenbauer == nan_arg

venv/Lib/site-packages/scipy/special/tests/test_owens_t.py

@@ -0,0 +1,42 @@
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose
+
+import scipy.special as sc
+
+
+def test_symmetries():
+    np.random.seed(1234)
+    a, h = np.random.rand(100), np.random.rand(100)
+    assert_equal(sc.owens_t(h, a), sc.owens_t(-h, a))
+    assert_equal(sc.owens_t(h, a), -sc.owens_t(h, -a))
+
+
+def test_special_cases():
+    assert_equal(sc.owens_t(5, 0), 0)
+    assert_allclose(sc.owens_t(0, 5), 0.5*np.arctan(5)/np.pi,
+                    rtol=5e-14)
+    # Target value is 0.5*Phi(5)*(1 - Phi(5)) for Phi the CDF of the
+    # standard normal distribution
+    assert_allclose(sc.owens_t(5, 1), 1.4332574485503512543e-07,
+                    rtol=5e-14)
+
+
+def test_nans():
+    assert_equal(sc.owens_t(20, np.nan), np.nan)
+    assert_equal(sc.owens_t(np.nan, 20), np.nan)
+    assert_equal(sc.owens_t(np.nan, np.nan), np.nan)
+
+
+def test_infs():
+    h = 1
+    res = 0.5*sc.erfc(h/np.sqrt(2))
+    assert_allclose(sc.owens_t(h, np.inf), res, rtol=5e-14)
+    assert_allclose(sc.owens_t(h, -np.inf), -res, rtol=5e-14)
+
+    assert_equal(sc.owens_t(np.inf, 1), 0)
+    assert_equal(sc.owens_t(-np.inf, 1), 0)
+
+    assert_equal(sc.owens_t(np.inf, np.inf), 0)
+    assert_equal(sc.owens_t(-np.inf, np.inf), 0)
+    assert_equal(sc.owens_t(np.inf, -np.inf), -0.0)
+    assert_equal(sc.owens_t(-np.inf, -np.inf), -0.0)

venv/Lib/site-packages/scipy/special/tests/test_pcf.py

@@ -0,0 +1,24 @@
+"""Tests for parabolic cylinder functions.
+
+"""
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal
+import scipy.special as sc
+
+
+def test_pbwa_segfault():
+    # Regression test for https://github.com/scipy/scipy/issues/6208.
+    #
+    # Data generated by mpmath.
+    #
+    w = 1.02276567211316867161
+    wp = -0.48887053372346189882
+    assert_allclose(sc.pbwa(0, 0), (w, wp), rtol=1e-13, atol=0)
+
+
+def test_pbwa_nan():
+    # Check that NaN's are returned outside of the range in which the
+    # implementation is accurate.
+    pts = [(-6, -6), (-6, 6), (6, -6), (6, 6)]
+    for p in pts:
+        assert_equal(sc.pbwa(*p), (np.nan, np.nan))

venv/Lib/site-packages/scipy/special/tests/test_pdtr.py

@@ -0,0 +1,48 @@
+import numpy as np
+import scipy.special as sc
+from numpy.testing import assert_almost_equal, assert_array_equal
+
+
+class TestPdtr(object):
+    def test(self):
+        val = sc.pdtr(0, 1)
+        assert_almost_equal(val, np.exp(-1))
+
+    def test_m_zero(self):
+        val = sc.pdtr([0, 1, 2], 0)
+        assert_array_equal(val, [1, 1, 1])
+
+    def test_rounding(self):
+        double_val = sc.pdtr([0.1, 1.1, 2.1], 1.0)
+        int_val = sc.pdtr([0, 1, 2], 1.0)
+        assert_array_equal(double_val, int_val)
+
+    def test_inf(self):
+        val = sc.pdtr(np.inf, 1.0)
+        assert_almost_equal(val, 1.0)
+
+    def test_domain(self):
+        val = sc.pdtr(-1.1, 1.0)
+        assert np.isnan(val)
+
+class TestPdtrc(object):
+    def test_value(self):
+        val = sc.pdtrc(0, 1)
+        assert_almost_equal(val, 1 - np.exp(-1))
+
+    def test_m_zero(self):
+        val = sc.pdtrc([0, 1, 2], 0.0)
+        assert_array_equal(val, [0, 0, 0])
+
+    def test_rounding(self):
+        double_val = sc.pdtrc([0.1, 1.1, 2.1], 1.0)
+        int_val = sc.pdtrc([0, 1, 2], 1.0)
+        assert_array_equal(double_val, int_val)
+
+    def test_inf(self):
+        val = sc.pdtrc(np.inf, 1.0)
+        assert_almost_equal(val, 0.0)
+
+    def test_domain(self):
+        val = sc.pdtrc(-1.1, 1.0)
+        assert np.isnan(val)

venv/Lib/site-packages/scipy/special/tests/test_precompute_expn_asy.py

@@ -0,0 +1,24 @@
+from numpy.testing import assert_equal
+
+from scipy.special._testutils import check_version, MissingModule
+from scipy.special._precompute.expn_asy import generate_A
+
+try:
+    import sympy  # type: ignore[import]
+    from sympy import Poly
+except ImportError:
+    sympy = MissingModule("sympy")
+
+
+@check_version(sympy, "1.0")
+def test_generate_A():
+    # Data from DLMF 8.20.5
+    x = sympy.symbols('x')
+    Astd = [Poly(1, x),
+            Poly(1, x),
+            Poly(1 - 2*x),
+            Poly(1 - 8*x + 6*x**2)]
+    Ares = generate_A(len(Astd))
+
+    for p, q in zip(Astd, Ares):
+        assert_equal(p, q)

venv/Lib/site-packages/scipy/special/tests/test_precompute_gammainc.py

@@ -0,0 +1,109 @@
+import numpy as np  # np is actually used, in the decorators below.
+import pytest
+
+from scipy.special._testutils import MissingModule, check_version
+from scipy.special._mptestutils import (
+    Arg, IntArg, mp_assert_allclose, assert_mpmath_equal)
+from scipy.special._precompute.gammainc_asy import (
+    compute_g, compute_alpha, compute_d)
+from scipy.special._precompute.gammainc_data import gammainc, gammaincc
+
+try:
+    import sympy  # type: ignore[import]
+except ImportError:
+    sympy = MissingModule('sympy')
+
+try:
+    import mpmath as mp  # type: ignore[import]
+except ImportError:
+    mp = MissingModule('mpmath')
+
+
+@check_version(mp, '0.19')
+def test_g():
+    # Test data for the g_k. See DLMF 5.11.4.
+    with mp.workdps(30):
+        g = [mp.mpf(1), mp.mpf(1)/12, mp.mpf(1)/288,
+             -mp.mpf(139)/51840, -mp.mpf(571)/2488320,
+             mp.mpf(163879)/209018880, mp.mpf(5246819)/75246796800]
+        mp_assert_allclose(compute_g(7), g)
+
+
+@pytest.mark.slow
+@check_version(mp, '0.19')
+@check_version(sympy, '0.7')
+@pytest.mark.xfail_on_32bit("rtol only 2e-11, see gh-6938")
+def test_alpha():
+    # Test data for the alpha_k. See DLMF 8.12.14.
+    with mp.workdps(30):
+        alpha = [mp.mpf(0), mp.mpf(1), mp.mpf(1)/3, mp.mpf(1)/36,
+                 -mp.mpf(1)/270, mp.mpf(1)/4320, mp.mpf(1)/17010,
+                 -mp.mpf(139)/5443200, mp.mpf(1)/204120]
+        mp_assert_allclose(compute_alpha(9), alpha)
+
+
+@pytest.mark.xslow
+@check_version(mp, '0.19')
+@check_version(sympy, '0.7')
+def test_d():
+    # Compare the d_{k, n} to the results in appendix F of [1].
+    #
+    # Sources
+    # -------
+    # [1] DiDonato and Morris, Computation of the Incomplete Gamma
+    #     Function Ratios and their Inverse, ACM Transactions on
+    #     Mathematical Software, 1986.
+
+    with mp.workdps(50):
+        dataset = [(0, 0, -mp.mpf('0.333333333333333333333333333333')),
+                   (0, 12, mp.mpf('0.102618097842403080425739573227e-7')),
+                   (1, 0, -mp.mpf('0.185185185185185185185185185185e-2')),
+                   (1, 12, mp.mpf('0.119516285997781473243076536700e-7')),
+                   (2, 0, mp.mpf('0.413359788359788359788359788360e-2')),
+                   (2, 12, -mp.mpf('0.140925299108675210532930244154e-7')),
+                   (3, 0, mp.mpf('0.649434156378600823045267489712e-3')),
+                   (3, 12, -mp.mpf('0.191111684859736540606728140873e-7')),
+                   (4, 0, -mp.mpf('0.861888290916711698604702719929e-3')),
+                   (4, 12, mp.mpf('0.288658297427087836297341274604e-7')),
+                   (5, 0, -mp.mpf('0.336798553366358150308767592718e-3')),
+                   (5, 12, mp.mpf('0.482409670378941807563762631739e-7')),
+                   (6, 0, mp.mpf('0.531307936463992223165748542978e-3')),
+                   (6, 12, -mp.mpf('0.882860074633048352505085243179e-7')),
+                   (7, 0, mp.mpf('0.344367606892377671254279625109e-3')),
+                   (7, 12, -mp.mpf('0.175629733590604619378669693914e-6')),
+                   (8, 0, -mp.mpf('0.652623918595309418922034919727e-3')),
+                   (8, 12, mp.mpf('0.377358774161109793380344937299e-6')),
+                   (9, 0, -mp.mpf('0.596761290192746250124390067179e-3')),
+                   (9, 12, mp.mpf('0.870823417786464116761231237189e-6'))]
+        d = compute_d(10, 13)
+        res = [d[k][n] for k, n, std in dataset]
+        std = map(lambda x: x[2], dataset)
+        mp_assert_allclose(res, std)
+
+
+@check_version(mp, '0.19')
+def test_gammainc():
+    # Quick check that the gammainc in
+    # special._precompute.gammainc_data agrees with mpmath's
+    # gammainc.
+    assert_mpmath_equal(gammainc,
+                        lambda a, x: mp.gammainc(a, b=x, regularized=True),
+                        [Arg(0, 100, inclusive_a=False), Arg(0, 100)],
+                        nan_ok=False, rtol=1e-17, n=50, dps=50)
+
+
+@pytest.mark.xslow
+@check_version(mp, '0.19')
+def test_gammaincc():
+    # Check that the gammaincc in special._precompute.gammainc_data
+    # agrees with mpmath's gammainc.
+    assert_mpmath_equal(lambda a, x: gammaincc(a, x, dps=1000),
+                        lambda a, x: mp.gammainc(a, a=x, regularized=True),
+                        [Arg(20, 100), Arg(20, 100)],
+                        nan_ok=False, rtol=1e-17, n=50, dps=1000)
+
+    # Test the fast integer path
+    assert_mpmath_equal(gammaincc,
+                        lambda a, x: mp.gammainc(a, a=x, regularized=True),
+                        [IntArg(1, 100), Arg(0, 100)],
+                        nan_ok=False, rtol=1e-17, n=50, dps=50)

venv/Lib/site-packages/scipy/special/tests/test_precompute_utils.py

@@ -0,0 +1,36 @@
+import pytest
+
+from scipy.special._testutils import MissingModule, check_version
+from scipy.special._mptestutils import mp_assert_allclose
+from scipy.special._precompute.utils import lagrange_inversion
+
+try:
+    import sympy  # type: ignore[import]
+except ImportError:
+    sympy = MissingModule('sympy')
+
+try:
+    import mpmath as mp  # type: ignore[import]
+except ImportError:
+    mp = MissingModule('mpmath')
+
+
+@pytest.mark.slow
+@check_version(sympy, '0.7')
+@check_version(mp, '0.19')
+class TestInversion(object):
+    @pytest.mark.xfail_on_32bit("rtol only 2e-9, see gh-6938")
+    def test_log(self):
+        with mp.workdps(30):
+            logcoeffs = mp.taylor(lambda x: mp.log(1 + x), 0, 10)
+            expcoeffs = mp.taylor(lambda x: mp.exp(x) - 1, 0, 10)
+            invlogcoeffs = lagrange_inversion(logcoeffs)
+            mp_assert_allclose(invlogcoeffs, expcoeffs)
+
+    @pytest.mark.xfail_on_32bit("rtol only 1e-15, see gh-6938")
+    def test_sin(self):
+        with mp.workdps(30):
+            sincoeffs = mp.taylor(mp.sin, 0, 10)
+            asincoeffs = mp.taylor(mp.asin, 0, 10)
+            invsincoeffs = lagrange_inversion(sincoeffs)
+            mp_assert_allclose(invsincoeffs, asincoeffs, atol=1e-30)

venv/Lib/site-packages/scipy/special/tests/test_round.py

@@ -0,0 +1,16 @@
+import numpy as np
+import pytest
+
+from scipy.special import _test_round
+
+
+@pytest.mark.skipif(not _test_round.have_fenv(), reason="no fenv()")
+def test_add_round_up():
+    np.random.seed(1234)
+    _test_round.test_add_round(10**5, 'up')
+
+
+@pytest.mark.skipif(not _test_round.have_fenv(), reason="no fenv()")
+def test_add_round_down():
+    np.random.seed(1234)
+    _test_round.test_add_round(10**5, 'down')

venv/Lib/site-packages/scipy/special/tests/test_sf_error.py

@@ -0,0 +1,112 @@
+import warnings
+
+from numpy.testing import assert_, assert_equal
+import pytest
+from pytest import raises as assert_raises
+
+import scipy.special as sc
+from scipy.special._ufuncs import _sf_error_test_function
+
+_sf_error_code_map = {
+    # skip 'ok'
+    'singular': 1,
+    'underflow': 2,
+    'overflow': 3,
+    'slow': 4,
+    'loss': 5,
+    'no_result': 6,
+    'domain': 7,
+    'arg': 8,
+    'other': 9
+}
+
+_sf_error_actions = [
+    'ignore',
+    'warn',
+    'raise'
+]
+
+
+def _check_action(fun, args, action):
+    if action == 'warn':
+        with pytest.warns(sc.SpecialFunctionWarning):
+            fun(*args)
+    elif action == 'raise':
+        with assert_raises(sc.SpecialFunctionError):
+            fun(*args)
+    else:
+        # action == 'ignore', make sure there are no warnings/exceptions
+        with warnings.catch_warnings():
+            warnings.simplefilter("error")
+            fun(*args)
+
+
+def test_geterr():
+    err = sc.geterr()
+    for key, value in err.items():
+        assert_(key in _sf_error_code_map.keys())
+        assert_(value in _sf_error_actions)
+
+
+def test_seterr():
+    entry_err = sc.geterr()
+    try:
+        for category in _sf_error_code_map.keys():
+            for action in _sf_error_actions:
+                geterr_olderr = sc.geterr()
+                seterr_olderr = sc.seterr(**{category: action})
+                assert_(geterr_olderr == seterr_olderr)
+                newerr = sc.geterr()
+                assert_(newerr[category] == action)
+                geterr_olderr.pop(category)
+                newerr.pop(category)
+                assert_(geterr_olderr == newerr)
+                _check_action(_sf_error_test_function,
+                              (_sf_error_code_map[category],),
+                               action)
+    finally:
+        sc.seterr(**entry_err)
+
+
+def test_errstate_pyx_basic():
+    olderr = sc.geterr()
+    with sc.errstate(singular='raise'):
+        with assert_raises(sc.SpecialFunctionError):
+            sc.loggamma(0)
+    assert_equal(olderr, sc.geterr())
+
+
+def test_errstate_c_basic():
+    olderr = sc.geterr()
+    with sc.errstate(domain='raise'):
+        with assert_raises(sc.SpecialFunctionError):
+            sc.spence(-1)
+    assert_equal(olderr, sc.geterr())
+
+
+def test_errstate_cpp_basic():
+    olderr = sc.geterr()
+    with sc.errstate(underflow='raise'):
+        with assert_raises(sc.SpecialFunctionError):
+            sc.wrightomega(-1000)
+    assert_equal(olderr, sc.geterr())
+
+
+def test_errstate():
+    for category in _sf_error_code_map.keys():
+        for action in _sf_error_actions:
+            olderr = sc.geterr()
+            with sc.errstate(**{category: action}):
+                _check_action(_sf_error_test_function,
+                              (_sf_error_code_map[category],),
+                              action)
+            assert_equal(olderr, sc.geterr())
+
+
+def test_errstate_all_but_one():
+    olderr = sc.geterr()
+    with sc.errstate(all='raise', singular='ignore'):
+        sc.gammaln(0)
+        with assert_raises(sc.SpecialFunctionError):
+            sc.spence(-1.0)
+    assert_equal(olderr, sc.geterr())

venv/Lib/site-packages/scipy/special/tests/test_sici.py

@@ -0,0 +1,36 @@
+import numpy as np
+
+import scipy.special as sc
+from scipy.special._testutils import FuncData
+
+
+def test_sici_consistency():
+    # Make sure the implementation of sici for real arguments agrees
+    # with the implementation of sici for complex arguments.
+
+    # On the negative real axis Cephes drops the imaginary part in ci
+    def sici(x):
+        si, ci = sc.sici(x + 0j)
+        return si.real, ci.real
+    
+    x = np.r_[-np.logspace(8, -30, 200), 0, np.logspace(-30, 8, 200)]
+    si, ci = sc.sici(x)
+    dataset = np.column_stack((x, si, ci))
+    FuncData(sici, dataset, 0, (1, 2), rtol=1e-12).check()
+
+
+def test_shichi_consistency():
+    # Make sure the implementation of shichi for real arguments agrees
+    # with the implementation of shichi for complex arguments.
+
+    # On the negative real axis Cephes drops the imaginary part in chi
+    def shichi(x):
+        shi, chi = sc.shichi(x + 0j)
+        return shi.real, chi.real
+
+    # Overflow happens quickly, so limit range
+    x = np.r_[-np.logspace(np.log10(700), -30, 200), 0,
+              np.logspace(-30, np.log10(700), 200)]
+    shi, chi = sc.shichi(x)
+    dataset = np.column_stack((x, shi, chi))
+    FuncData(shichi, dataset, 0, (1, 2), rtol=1e-14).check()

venv/Lib/site-packages/scipy/special/tests/test_spence.py

@@ -0,0 +1,32 @@
+import numpy as np
+from numpy import sqrt, log, pi
+from scipy.special._testutils import FuncData
+from scipy.special import spence
+
+
+def test_consistency():
+    # Make sure the implementation of spence for real arguments
+    # agrees with the implementation of spence for imaginary arguments.
+
+    x = np.logspace(-30, 300, 200)
+    dataset = np.vstack((x + 0j, spence(x))).T
+    FuncData(spence, dataset, 0, 1, rtol=1e-14).check()
+
+
+def test_special_points():
+    # Check against known values of Spence's function.
+
+    phi = (1 + sqrt(5))/2
+    dataset = [(1, 0),
+               (2, -pi**2/12),
+               (0.5, pi**2/12 - log(2)**2/2),
+               (0, pi**2/6),
+               (-1, pi**2/4 - 1j*pi*log(2)),
+               ((-1 + sqrt(5))/2, pi**2/15 - log(phi)**2),
+               ((3 - sqrt(5))/2, pi**2/10 - log(phi)**2),
+               (phi, -pi**2/15 + log(phi)**2/2),
+               # Corrected from Zagier, "The Dilogarithm Function"
+               ((3 + sqrt(5))/2, -pi**2/10 - log(phi)**2)]
+
+    dataset = np.asarray(dataset)
+    FuncData(spence, dataset, 0, 1, rtol=1e-14).check()

venv/Lib/site-packages/scipy/special/tests/test_spfun_stats.py

@@ -0,0 +1,61 @@
+import numpy as np
+from numpy.testing import (assert_array_equal,
+        assert_array_almost_equal_nulp, assert_almost_equal)
+from pytest import raises as assert_raises
+
+from scipy.special import gammaln, multigammaln
+
+
+class TestMultiGammaLn(object):
+
+    def test1(self):
+        # A test of the identity
+        #     Gamma_1(a) = Gamma(a)
+        np.random.seed(1234)
+        a = np.abs(np.random.randn())
+        assert_array_equal(multigammaln(a, 1), gammaln(a))
+
+    def test2(self):
+        # A test of the identity
+        #     Gamma_2(a) = sqrt(pi) * Gamma(a) * Gamma(a - 0.5)
+        a = np.array([2.5, 10.0])
+        result = multigammaln(a, 2)
+        expected = np.log(np.sqrt(np.pi)) + gammaln(a) + gammaln(a - 0.5)
+        assert_almost_equal(result, expected)
+
+    def test_bararg(self):
+        assert_raises(ValueError, multigammaln, 0.5, 1.2)
+
+
+def _check_multigammaln_array_result(a, d):
+    # Test that the shape of the array returned by multigammaln
+    # matches the input shape, and that all the values match
+    # the value computed when multigammaln is called with a scalar.
+    result = multigammaln(a, d)
+    assert_array_equal(a.shape, result.shape)
+    a1 = a.ravel()
+    result1 = result.ravel()
+    for i in range(a.size):
+        assert_array_almost_equal_nulp(result1[i], multigammaln(a1[i], d))
+
+
+def test_multigammaln_array_arg():
+    # Check that the array returned by multigammaln has the correct
+    # shape and contains the correct values.  The cases have arrays
+    # with several differnent shapes.
+    # The cases include a regression test for ticket #1849
+    # (a = np.array([2.0]), an array with a single element).
+    np.random.seed(1234)
+
+    cases = [
+        # a, d
+        (np.abs(np.random.randn(3, 2)) + 5, 5),
+        (np.abs(np.random.randn(1, 2)) + 5, 5),
+        (np.arange(10.0, 18.0).reshape(2, 2, 2), 3),
+        (np.array([2.0]), 3),
+        (np.float64(2.0), 3),
+    ]
+
+    for a, d in cases:
+        _check_multigammaln_array_result(a, d)
+

venv/Lib/site-packages/scipy/special/tests/test_sph_harm.py

@@ -0,0 +1,37 @@
+import numpy as np
+from numpy.testing import assert_allclose
+import scipy.special as sc
+
+
+def test_first_harmonics():
+    # Test against explicit representations of the first four
+    # spherical harmonics which use `theta` as the azimuthal angle,
+    # `phi` as the polar angle, and include the Condon-Shortley
+    # phase.
+
+    # Notation is Ymn
+    def Y00(theta, phi):
+        return 0.5*np.sqrt(1/np.pi)
+
+    def Yn11(theta, phi):
+        return 0.5*np.sqrt(3/(2*np.pi))*np.exp(-1j*theta)*np.sin(phi)
+
+    def Y01(theta, phi):
+        return 0.5*np.sqrt(3/np.pi)*np.cos(phi)
+
+    def Y11(theta, phi):
+        return -0.5*np.sqrt(3/(2*np.pi))*np.exp(1j*theta)*np.sin(phi)
+
+    harms = [Y00, Yn11, Y01, Y11]
+    m = [0, -1, 0, 1]
+    n = [0, 1, 1, 1]
+
+    theta = np.linspace(0, 2*np.pi)
+    phi = np.linspace(0, np.pi)
+    theta, phi = np.meshgrid(theta, phi)
+
+    for harm, m, n in zip(harms, m, n):
+        assert_allclose(sc.sph_harm(m, n, theta, phi),
+                        harm(theta, phi),
+                        rtol=1e-15, atol=1e-15,
+                        err_msg="Y^{}_{} incorrect".format(m, n))

venv/Lib/site-packages/scipy/special/tests/test_spherical_bessel.py

@@ -0,0 +1,379 @@
+#
+# Tests of spherical Bessel functions.
+#
+import numpy as np
+from numpy.testing import (assert_almost_equal, assert_allclose,
+                           assert_array_almost_equal, suppress_warnings)
+import pytest
+from numpy import sin, cos, sinh, cosh, exp, inf, nan, r_, pi
+
+from scipy.special import spherical_jn, spherical_yn, spherical_in, spherical_kn
+from scipy.integrate import quad
+
+
+class TestSphericalJn:
+    def test_spherical_jn_exact(self):
+        # https://dlmf.nist.gov/10.49.E3
+        # Note: exact expression is numerically stable only for small
+        # n or z >> n.
+        x = np.array([0.12, 1.23, 12.34, 123.45, 1234.5])
+        assert_allclose(spherical_jn(2, x),
+                        (-1/x + 3/x**3)*sin(x) - 3/x**2*cos(x))
+
+    def test_spherical_jn_recurrence_complex(self):
+        # https://dlmf.nist.gov/10.51.E1
+        n = np.array([1, 2, 3, 7, 12])
+        x = 1.1 + 1.5j
+        assert_allclose(spherical_jn(n - 1, x) + spherical_jn(n + 1, x),
+                        (2*n + 1)/x*spherical_jn(n, x))
+
+    def test_spherical_jn_recurrence_real(self):
+        # https://dlmf.nist.gov/10.51.E1
+        n = np.array([1, 2, 3, 7, 12])
+        x = 0.12
+        assert_allclose(spherical_jn(n - 1, x) + spherical_jn(n + 1,x),
+                        (2*n + 1)/x*spherical_jn(n, x))
+
+    def test_spherical_jn_inf_real(self):
+        # https://dlmf.nist.gov/10.52.E3
+        n = 6
+        x = np.array([-inf, inf])
+        assert_allclose(spherical_jn(n, x), np.array([0, 0]))
+
+    def test_spherical_jn_inf_complex(self):
+        # https://dlmf.nist.gov/10.52.E3
+        n = 7
+        x = np.array([-inf + 0j, inf + 0j, inf*(1+1j)])
+        with suppress_warnings() as sup:
+            sup.filter(RuntimeWarning, "invalid value encountered in multiply")
+            assert_allclose(spherical_jn(n, x), np.array([0, 0, inf*(1+1j)]))
+
+    def test_spherical_jn_large_arg_1(self):
+        # https://github.com/scipy/scipy/issues/2165
+        # Reference value computed using mpmath, via
+        # besselj(n + mpf(1)/2, z)*sqrt(pi/(2*z))
+        assert_allclose(spherical_jn(2, 3350.507), -0.00029846226538040747)
+
+    def test_spherical_jn_large_arg_2(self):
+        # https://github.com/scipy/scipy/issues/1641
+        # Reference value computed using mpmath, via
+        # besselj(n + mpf(1)/2, z)*sqrt(pi/(2*z))
+        assert_allclose(spherical_jn(2, 10000), 3.0590002633029811e-05)
+
+    def test_spherical_jn_at_zero(self):
+        # https://dlmf.nist.gov/10.52.E1
+        # But note that n = 0 is a special case: j0 = sin(x)/x -> 1
+        n = np.array([0, 1, 2, 5, 10, 100])
+        x = 0
+        assert_allclose(spherical_jn(n, x), np.array([1, 0, 0, 0, 0, 0]))
+
+
+class TestSphericalYn:
+    def test_spherical_yn_exact(self):
+        # https://dlmf.nist.gov/10.49.E5
+        # Note: exact expression is numerically stable only for small
+        # n or z >> n.
+        x = np.array([0.12, 1.23, 12.34, 123.45, 1234.5])
+        assert_allclose(spherical_yn(2, x),
+                        (1/x - 3/x**3)*cos(x) - 3/x**2*sin(x))
+
+    def test_spherical_yn_recurrence_real(self):
+        # https://dlmf.nist.gov/10.51.E1
+        n = np.array([1, 2, 3, 7, 12])
+        x = 0.12
+        assert_allclose(spherical_yn(n - 1, x) + spherical_yn(n + 1,x),
+                        (2*n + 1)/x*spherical_yn(n, x))
+
+    def test_spherical_yn_recurrence_complex(self):
+        # https://dlmf.nist.gov/10.51.E1
+        n = np.array([1, 2, 3, 7, 12])
+        x = 1.1 + 1.5j
+        assert_allclose(spherical_yn(n - 1, x) + spherical_yn(n + 1, x),
+                        (2*n + 1)/x*spherical_yn(n, x))
+
+    def test_spherical_yn_inf_real(self):
+        # https://dlmf.nist.gov/10.52.E3
+        n = 6
+        x = np.array([-inf, inf])
+        assert_allclose(spherical_yn(n, x), np.array([0, 0]))
+
+    def test_spherical_yn_inf_complex(self):
+        # https://dlmf.nist.gov/10.52.E3
+        n = 7
+        x = np.array([-inf + 0j, inf + 0j, inf*(1+1j)])
+        with suppress_warnings() as sup:
+            sup.filter(RuntimeWarning, "invalid value encountered in multiply")
+            assert_allclose(spherical_yn(n, x), np.array([0, 0, inf*(1+1j)]))
+
+    def test_spherical_yn_at_zero(self):
+        # https://dlmf.nist.gov/10.52.E2
+        n = np.array([0, 1, 2, 5, 10, 100])
+        x = 0
+        assert_allclose(spherical_yn(n, x), np.full(n.shape, -inf))
+
+    def test_spherical_yn_at_zero_complex(self):
+        # Consistently with numpy:
+        # >>> -np.cos(0)/0
+        # -inf
+        # >>> -np.cos(0+0j)/(0+0j)
+        # (-inf + nan*j)
+        n = np.array([0, 1, 2, 5, 10, 100])
+        x = 0 + 0j
+        assert_allclose(spherical_yn(n, x), np.full(n.shape, nan))
+
+
+class TestSphericalJnYnCrossProduct:
+    def test_spherical_jn_yn_cross_product_1(self):
+        # https://dlmf.nist.gov/10.50.E3
+        n = np.array([1, 5, 8])
+        x = np.array([0.1, 1, 10])
+        left = (spherical_jn(n + 1, x) * spherical_yn(n, x) -
+                spherical_jn(n, x) * spherical_yn(n + 1, x))
+        right = 1/x**2
+        assert_allclose(left, right)
+
+    def test_spherical_jn_yn_cross_product_2(self):
+        # https://dlmf.nist.gov/10.50.E3
+        n = np.array([1, 5, 8])
+        x = np.array([0.1, 1, 10])
+        left = (spherical_jn(n + 2, x) * spherical_yn(n, x) -
+                spherical_jn(n, x) * spherical_yn(n + 2, x))
+        right = (2*n + 3)/x**3
+        assert_allclose(left, right)
+
+
+class TestSphericalIn:
+    def test_spherical_in_exact(self):
+        # https://dlmf.nist.gov/10.49.E9
+        x = np.array([0.12, 1.23, 12.34, 123.45])
+        assert_allclose(spherical_in(2, x),
+                        (1/x + 3/x**3)*sinh(x) - 3/x**2*cosh(x))
+
+    def test_spherical_in_recurrence_real(self):
+        # https://dlmf.nist.gov/10.51.E4
+        n = np.array([1, 2, 3, 7, 12])
+        x = 0.12
+        assert_allclose(spherical_in(n - 1, x) - spherical_in(n + 1,x),
+                        (2*n + 1)/x*spherical_in(n, x))
+
+    def test_spherical_in_recurrence_complex(self):
+        # https://dlmf.nist.gov/10.51.E1
+        n = np.array([1, 2, 3, 7, 12])
+        x = 1.1 + 1.5j
+        assert_allclose(spherical_in(n - 1, x) - spherical_in(n + 1,x),
+                        (2*n + 1)/x*spherical_in(n, x))
+
+    def test_spherical_in_inf_real(self):
+        # https://dlmf.nist.gov/10.52.E3
+        n = 5
+        x = np.array([-inf, inf])
+        assert_allclose(spherical_in(n, x), np.array([-inf, inf]))
+
+    def test_spherical_in_inf_complex(self):
+        # https://dlmf.nist.gov/10.52.E5
+        # Ideally, i1n(n, 1j*inf) = 0 and i1n(n, (1+1j)*inf) = (1+1j)*inf, but
+        # this appears impossible to achieve because C99 regards any complex
+        # value with at least one infinite  part as a complex infinity, so
+        # 1j*inf cannot be distinguished from (1+1j)*inf.  Therefore, nan is
+        # the correct return value.
+        n = 7
+        x = np.array([-inf + 0j, inf + 0j, inf*(1+1j)])
+        assert_allclose(spherical_in(n, x), np.array([-inf, inf, nan]))
+
+    def test_spherical_in_at_zero(self):
+        # https://dlmf.nist.gov/10.52.E1
+        # But note that n = 0 is a special case: i0 = sinh(x)/x -> 1
+        n = np.array([0, 1, 2, 5, 10, 100])
+        x = 0
+        assert_allclose(spherical_in(n, x), np.array([1, 0, 0, 0, 0, 0]))
+
+
+class TestSphericalKn:
+    def test_spherical_kn_exact(self):
+        # https://dlmf.nist.gov/10.49.E13
+        x = np.array([0.12, 1.23, 12.34, 123.45])
+        assert_allclose(spherical_kn(2, x),
+                        pi/2*exp(-x)*(1/x + 3/x**2 + 3/x**3))
+
+    def test_spherical_kn_recurrence_real(self):
+        # https://dlmf.nist.gov/10.51.E4
+        n = np.array([1, 2, 3, 7, 12])
+        x = 0.12
+        assert_allclose((-1)**(n - 1)*spherical_kn(n - 1, x) - (-1)**(n + 1)*spherical_kn(n + 1,x),
+                        (-1)**n*(2*n + 1)/x*spherical_kn(n, x))
+
+    def test_spherical_kn_recurrence_complex(self):
+        # https://dlmf.nist.gov/10.51.E4
+        n = np.array([1, 2, 3, 7, 12])
+        x = 1.1 + 1.5j
+        assert_allclose((-1)**(n - 1)*spherical_kn(n - 1, x) - (-1)**(n + 1)*spherical_kn(n + 1,x),
+                        (-1)**n*(2*n + 1)/x*spherical_kn(n, x))
+
+    def test_spherical_kn_inf_real(self):
+        # https://dlmf.nist.gov/10.52.E6
+        n = 5
+        x = np.array([-inf, inf])
+        assert_allclose(spherical_kn(n, x), np.array([-inf, 0]))
+
+    def test_spherical_kn_inf_complex(self):
+        # https://dlmf.nist.gov/10.52.E6
+        # The behavior at complex infinity depends on the sign of the real
+        # part: if Re(z) >= 0, then the limit is 0; if Re(z) < 0, then it's
+        # z*inf.  This distinction cannot be captured, so we return nan.
+        n = 7
+        x = np.array([-inf + 0j, inf + 0j, inf*(1+1j)])
+        assert_allclose(spherical_kn(n, x), np.array([-inf, 0, nan]))
+
+    def test_spherical_kn_at_zero(self):
+        # https://dlmf.nist.gov/10.52.E2
+        n = np.array([0, 1, 2, 5, 10, 100])
+        x = 0
+        assert_allclose(spherical_kn(n, x), np.full(n.shape, inf))
+
+    def test_spherical_kn_at_zero_complex(self):
+        # https://dlmf.nist.gov/10.52.E2
+        n = np.array([0, 1, 2, 5, 10, 100])
+        x = 0 + 0j
+        assert_allclose(spherical_kn(n, x), np.full(n.shape, nan))
+
+
+class SphericalDerivativesTestCase:
+    def fundamental_theorem(self, n, a, b):
+        integral, tolerance = quad(lambda z: self.df(n, z), a, b)
+        assert_allclose(integral,
+                        self.f(n, b) - self.f(n, a),
+                        atol=tolerance)
+
+    @pytest.mark.slow
+    def test_fundamental_theorem_0(self):
+        self.fundamental_theorem(0, 3.0, 15.0)
+
+    @pytest.mark.slow
+    def test_fundamental_theorem_7(self):
+        self.fundamental_theorem(7, 0.5, 1.2)
+
+
+class TestSphericalJnDerivatives(SphericalDerivativesTestCase):
+    def f(self, n, z):
+        return spherical_jn(n, z)
+
+    def df(self, n, z):
+        return spherical_jn(n, z, derivative=True)
+
+    def test_spherical_jn_d_zero(self):
+        n = np.array([0, 1, 2, 3, 7, 15])
+        assert_allclose(spherical_jn(n, 0, derivative=True),
+                        np.array([0, 1/3, 0, 0, 0, 0]))
+
+
+class TestSphericalYnDerivatives(SphericalDerivativesTestCase):
+    def f(self, n, z):
+        return spherical_yn(n, z)
+
+    def df(self, n, z):
+        return spherical_yn(n, z, derivative=True)
+
+
+class TestSphericalInDerivatives(SphericalDerivativesTestCase):
+    def f(self, n, z):
+        return spherical_in(n, z)
+
+    def df(self, n, z):
+        return spherical_in(n, z, derivative=True)
+
+    def test_spherical_in_d_zero(self):
+        n = np.array([1, 2, 3, 7, 15])
+        assert_allclose(spherical_in(n, 0, derivative=True),
+                        np.zeros(5))
+
+
+class TestSphericalKnDerivatives(SphericalDerivativesTestCase):
+    def f(self, n, z):
+        return spherical_kn(n, z)
+
+    def df(self, n, z):
+        return spherical_kn(n, z, derivative=True)
+
+
+class TestSphericalOld:
+    # These are tests from the TestSpherical class of test_basic.py,
+    # rewritten to use spherical_* instead of sph_* but otherwise unchanged.
+
+    def test_sph_in(self):
+        # This test reproduces test_basic.TestSpherical.test_sph_in.
+        i1n = np.empty((2,2))
+        x = 0.2
+
+        i1n[0][0] = spherical_in(0, x)
+        i1n[0][1] = spherical_in(1, x)
+        i1n[1][0] = spherical_in(0, x, derivative=True)
+        i1n[1][1] = spherical_in(1, x, derivative=True)
+
+        inp0 = (i1n[0][1])
+        inp1 = (i1n[0][0] - 2.0/0.2 * i1n[0][1])
+        assert_array_almost_equal(i1n[0],np.array([1.0066800127054699381,
+                                                0.066933714568029540839]),12)
+        assert_array_almost_equal(i1n[1],[inp0,inp1],12)
+
+    def test_sph_in_kn_order0(self):
+        x = 1.
+        sph_i0 = np.empty((2,))
+        sph_i0[0] = spherical_in(0, x)
+        sph_i0[1] = spherical_in(0, x, derivative=True)
+        sph_i0_expected = np.array([np.sinh(x)/x,
+                                    np.cosh(x)/x-np.sinh(x)/x**2])
+        assert_array_almost_equal(r_[sph_i0], sph_i0_expected)
+
+        sph_k0 = np.empty((2,))
+        sph_k0[0] = spherical_kn(0, x)
+        sph_k0[1] = spherical_kn(0, x, derivative=True)
+        sph_k0_expected = np.array([0.5*pi*exp(-x)/x,
+                                    -0.5*pi*exp(-x)*(1/x+1/x**2)])
+        assert_array_almost_equal(r_[sph_k0], sph_k0_expected)
+
+    def test_sph_jn(self):
+        s1 = np.empty((2,3))
+        x = 0.2
+
+        s1[0][0] = spherical_jn(0, x)
+        s1[0][1] = spherical_jn(1, x)
+        s1[0][2] = spherical_jn(2, x)
+        s1[1][0] = spherical_jn(0, x, derivative=True)
+        s1[1][1] = spherical_jn(1, x, derivative=True)
+        s1[1][2] = spherical_jn(2, x, derivative=True)
+
+        s10 = -s1[0][1]
+        s11 = s1[0][0]-2.0/0.2*s1[0][1]
+        s12 = s1[0][1]-3.0/0.2*s1[0][2]
+        assert_array_almost_equal(s1[0],[0.99334665397530607731,
+                                      0.066400380670322230863,
+                                      0.0026590560795273856680],12)
+        assert_array_almost_equal(s1[1],[s10,s11,s12],12)
+
+    def test_sph_kn(self):
+        kn = np.empty((2,3))
+        x = 0.2
+
+        kn[0][0] = spherical_kn(0, x)
+        kn[0][1] = spherical_kn(1, x)
+        kn[0][2] = spherical_kn(2, x)
+        kn[1][0] = spherical_kn(0, x, derivative=True)
+        kn[1][1] = spherical_kn(1, x, derivative=True)
+        kn[1][2] = spherical_kn(2, x, derivative=True)
+
+        kn0 = -kn[0][1]
+        kn1 = -kn[0][0]-2.0/0.2*kn[0][1]
+        kn2 = -kn[0][1]-3.0/0.2*kn[0][2]
+        assert_array_almost_equal(kn[0],[6.4302962978445670140,
+                                         38.581777787067402086,
+                                         585.15696310385559829],12)
+        assert_array_almost_equal(kn[1],[kn0,kn1,kn2],9)
+
+    def test_sph_yn(self):
+        sy1 = spherical_yn(2, 0.2)
+        sy2 = spherical_yn(0, 0.2)
+        assert_almost_equal(sy1,-377.52483,5)  # previous values in the system
+        assert_almost_equal(sy2,-4.9003329,5)
+        sphpy = (spherical_yn(0, 0.2) - 2*spherical_yn(2, 0.2))/3
+        sy3 = spherical_yn(1, 0.2, derivative=True)
+        assert_almost_equal(sy3,sphpy,4)  # compare correct derivative val. (correct =-system val).

venv/Lib/site-packages/scipy/special/tests/test_trig.py

@@ -0,0 +1,66 @@
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose, suppress_warnings
+
+from scipy.special._ufuncs import _sinpi as sinpi
+from scipy.special._ufuncs import _cospi as cospi
+
+
+def test_integer_real_part():
+    x = np.arange(-100, 101)
+    y = np.hstack((-np.linspace(310, -30, 10), np.linspace(-30, 310, 10)))
+    x, y = np.meshgrid(x, y)
+    z = x + 1j*y
+    # In the following we should be *exactly* right
+    res = sinpi(z)
+    assert_equal(res.real, 0.0)
+    res = cospi(z)
+    assert_equal(res.imag, 0.0)
+
+
+def test_half_integer_real_part():
+    x = np.arange(-100, 101) + 0.5
+    y = np.hstack((-np.linspace(310, -30, 10), np.linspace(-30, 310, 10)))
+    x, y = np.meshgrid(x, y)
+    z = x + 1j*y
+    # In the following we should be *exactly* right
+    res = sinpi(z)
+    assert_equal(res.imag, 0.0)
+    res = cospi(z)
+    assert_equal(res.real, 0.0)
+
+
+def test_intermediate_overlow():
+    # Make sure we avoid overflow in situations where cosh/sinh would
+    # overflow but the product with sin/cos would not
+    sinpi_pts = [complex(1 + 1e-14, 227),
+                 complex(1e-35, 250),
+                 complex(1e-301, 445)]
+    # Data generated with mpmath
+    sinpi_std = [complex(-8.113438309924894e+295, -np.inf),
+                 complex(1.9507801934611995e+306, np.inf),
+                 complex(2.205958493464539e+306, np.inf)]
+    with suppress_warnings() as sup:
+        sup.filter(RuntimeWarning, "invalid value encountered in multiply")
+        for p, std in zip(sinpi_pts, sinpi_std):
+            assert_allclose(sinpi(p), std)
+
+    # Test for cosine, less interesting because cos(0) = 1.
+    p = complex(0.5 + 1e-14, 227)
+    std = complex(-8.113438309924894e+295, -np.inf)
+    with suppress_warnings() as sup:
+        sup.filter(RuntimeWarning, "invalid value encountered in multiply")
+        assert_allclose(cospi(p), std)
+
+
+def test_zero_sign():
+    y = sinpi(-0.0)
+    assert y == 0.0
+    assert np.signbit(y)
+
+    y = sinpi(0.0)
+    assert y == 0.0
+    assert not np.signbit(y)
+
+    y = cospi(0.5)
+    assert y == 0.0
+    assert not np.signbit(y)

venv/Lib/site-packages/scipy/special/tests/test_wrightomega.py

@@ -0,0 +1,117 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_, assert_equal, assert_allclose
+
+import scipy.special as sc
+from scipy.special._testutils import assert_func_equal
+
+
+def test_wrightomega_nan():
+    pts = [complex(np.nan, 0),
+           complex(0, np.nan),
+           complex(np.nan, np.nan),
+           complex(np.nan, 1),
+           complex(1, np.nan)]
+    for p in pts:
+        res = sc.wrightomega(p)
+        assert_(np.isnan(res.real))
+        assert_(np.isnan(res.imag))
+
+
+def test_wrightomega_inf_branch():
+    pts = [complex(-np.inf, np.pi/4),
+           complex(-np.inf, -np.pi/4),
+           complex(-np.inf, 3*np.pi/4),
+           complex(-np.inf, -3*np.pi/4)]
+    expected_results = [complex(0.0, 0.0),
+                        complex(0.0, -0.0),
+                        complex(-0.0, 0.0),
+                        complex(-0.0, -0.0)]
+    for p, expected in zip(pts, expected_results):
+        res = sc.wrightomega(p)
+        # We can't use assert_equal(res, expected) because in older versions of
+        # numpy, assert_equal doesn't check the sign of the real and imaginary
+        # parts when comparing complex zeros. It does check the sign when the
+        # arguments are *real* scalars.
+        assert_equal(res.real, expected.real)
+        assert_equal(res.imag, expected.imag)
+
+
+def test_wrightomega_inf():
+    pts = [complex(np.inf, 10),
+           complex(-np.inf, 10),
+           complex(10, np.inf),
+           complex(10, -np.inf)]
+    for p in pts:
+        assert_equal(sc.wrightomega(p), p)
+
+
+def test_wrightomega_singular():
+    pts = [complex(-1.0, np.pi),
+           complex(-1.0, -np.pi)]
+    for p in pts:
+        res = sc.wrightomega(p)
+        assert_equal(res, -1.0)
+        assert_(np.signbit(res.imag) == False)
+
+
+@pytest.mark.parametrize('x, desired', [
+    (-np.inf, 0),
+    (np.inf, np.inf),
+])
+def test_wrightomega_real_infinities(x, desired):
+    assert sc.wrightomega(x) == desired
+
+
+def test_wrightomega_real_nan():
+    assert np.isnan(sc.wrightomega(np.nan))
+
+
+def test_wrightomega_real_series_crossover():
+    desired_error = 2 * np.finfo(float).eps
+    crossover = 1e20
+    x_before_crossover = np.nextafter(crossover, -np.inf)
+    x_after_crossover = np.nextafter(crossover, np.inf)
+    # Computed using Mpmath
+    desired_before_crossover = 99999999999999983569.948
+    desired_after_crossover = 100000000000000016337.948
+    assert_allclose(
+        sc.wrightomega(x_before_crossover),
+        desired_before_crossover,
+        atol=0,
+        rtol=desired_error,
+    )
+    assert_allclose(
+        sc.wrightomega(x_after_crossover),
+        desired_after_crossover,
+        atol=0,
+        rtol=desired_error,
+    )
+
+
+def test_wrightomega_exp_approximation_crossover():
+    desired_error = 2 * np.finfo(float).eps
+    crossover = -50
+    x_before_crossover = np.nextafter(crossover, np.inf)
+    x_after_crossover = np.nextafter(crossover, -np.inf)
+    # Computed using Mpmath
+    desired_before_crossover = 1.9287498479639314876e-22
+    desired_after_crossover = 1.9287498479639040784e-22
+    assert_allclose(
+        sc.wrightomega(x_before_crossover),
+        desired_before_crossover,
+        atol=0,
+        rtol=desired_error,
+    )
+    assert_allclose(
+        sc.wrightomega(x_after_crossover),
+        desired_after_crossover,
+        atol=0,
+        rtol=desired_error,
+    )
+
+
+def test_wrightomega_real_versus_complex():
+    x = np.linspace(-500, 500, 1001)
+    results = sc.wrightomega(x + 0j).real
+    assert_func_equal(sc.wrightomega, results, x, atol=0, rtol=1e-14)

venv/Lib/site-packages/scipy/special/tests/test_zeta.py

@@ -0,0 +1,49 @@
+import scipy.special as sc
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose
+
+
+def test_zeta():
+    assert_allclose(sc.zeta(2,2), np.pi**2/6 - 1, rtol=1e-12)
+
+
+def test_zetac():
+    # Expected values in the following were computed using Wolfram
+    # Alpha's `Zeta[x] - 1`
+    x = [-2.1, 0.8, 0.9999, 9, 50, 75]
+    desired = [
+        -0.9972705002153750,
+        -5.437538415895550,
+        -10000.42279161673,
+        0.002008392826082214,
+        8.881784210930816e-16,
+        2.646977960169853e-23,
+    ]
+    assert_allclose(sc.zetac(x), desired, rtol=1e-12)
+
+
+def test_zetac_special_cases():
+    assert sc.zetac(np.inf) == 0
+    assert np.isnan(sc.zetac(-np.inf))
+    assert sc.zetac(0) == -1.5
+    assert sc.zetac(1.0) == np.inf
+
+    assert_equal(sc.zetac([-2, -50, -100]), -1)
+
+
+def test_riemann_zeta_special_cases():
+    assert np.isnan(sc.zeta(np.nan))
+    assert sc.zeta(np.inf) == 1
+    assert sc.zeta(0) == -0.5
+
+    # Riemann zeta is zero add negative even integers.
+    assert_equal(sc.zeta([-2, -4, -6, -8, -10]), 0)
+
+    assert_allclose(sc.zeta(2), np.pi**2/6, rtol=1e-12)
+    assert_allclose(sc.zeta(4), np.pi**4/90, rtol=1e-12)
+
+
+def test_riemann_zeta_avoid_overflow():
+    s = -260.00000000001
+    desired = -5.6966307844402683127e+297  # Computed with Mpmath
+    assert_allclose(sc.zeta(s), desired, atol=0, rtol=5e-14)