Static code analysis and corrections
This commit is contained in:
Kristjan Komlosi
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@@ -0,0 +1,578 @@
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This directory contains numerical data for testing special functions.
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The data is in version control as text files.
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The data is automatically packed into npz files by setup.py.
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The npz files should not be checked in version control.
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The data in gsl is computed using the GNU scientific library, the data
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in local is computed using mpmath, and the data in boost is a copy of
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data distributed with the boost library and comes with the following
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license:
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Boost Software License - Version 1.0 - August 17th, 2003
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Permission is hereby granted, free of charge, to any person or organization
|
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obtaining a copy of the software and accompanying documentation covered by
|
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this license (the "Software") to use, reproduce, display, distribute,
|
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execute, and transmit the Software, and to prepare derivative works of the
|
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Software, and to permit third-parties to whom the Software is furnished to
|
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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
|
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SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
|
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FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
|
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ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
|
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DEALINGS IN THE SOFTWARE.
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|
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=========
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Copyright holders of each file are listed here:
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Jamfile.v2:# Copyright Daryle Walker, Hubert Holin, John Maddock 2006 - 2007
|
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acosh_data.ipp:// Copyright John Maddock 2008.
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acosh_test.hpp:// (C) Copyright Hubert Holin 2003.
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almost_equal.ipp:// Copyright (c) 2006 Johan Rade
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asinh_data.ipp:// Copyright John Maddock 2008.
|
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asinh_test.hpp:// (C) Copyright Hubert Holin 2003.
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assoc_legendre_p.ipp:// (C) Copyright John Maddock 2006-7.
|
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atanh_data.ipp:// Copyright John Maddock 2008.
|
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atanh_test.hpp:// (C) Copyright Hubert Holin 2003.
|
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bessel_i_data.ipp:// Copyright (c) 2007 John Maddock
|
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bessel_i_int_data.ipp:// Copyright (c) 2007 John Maddock
|
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bessel_j_data.ipp:// Copyright (c) 2007 John Maddock
|
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bessel_j_int_data.ipp:// Copyright (c) 2007 John Maddock
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bessel_j_large_data.ipp:// Copyright (c) 2007 John Maddock
|
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bessel_k_data.ipp:// Copyright (c) 2007 John Maddock
|
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bessel_k_int_data.ipp:// Copyright (c) 2007 John Maddock
|
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bessel_y01_data.ipp:// Copyright (c) 2007 John Maddock
|
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bessel_yn_data.ipp:// Copyright (c) 2007 John Maddock
|
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bessel_yv_data.ipp:// Copyright (c) 2007 John Maddock
|
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beta_exp_data.ipp:// (C) Copyright John Maddock 2006.
|
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beta_med_data.ipp:// (C) Copyright John Maddock 2006.
|
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beta_small_data.ipp:// (C) Copyright John Maddock 2006.
|
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binomial_data.ipp:// (C) Copyright John Maddock 2006-7.
|
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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.
|
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common_factor_test.cpp:// (C) Copyright Daryle Walker 2001, 2006.
|
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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.
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||||
compile_test/tools_stats_inc_test.cpp:// Copyright John Maddock 2006.
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||||
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.
|
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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.
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||||
compile_test/generate.sh:// Copyright John Maddock 2006.
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compile_test/generate.sh:// Copyright John Maddock 2006.
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compile_test/generate.sh:// Copyright John Maddock 2006.
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compile_test/distribution_concept_check.cpp:// Copyright John Maddock 2006.
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||||
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.
|
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compile_test/sf_modf_incl_test.cpp:// Copyright John Maddock 2006.
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compile_test/dist_find_location_incl_test.cpp:// Copyright John Maddock 2006.
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compile_test/compl_acos_incl_test.cpp:// Copyright John Maddock 2006.
|
||||
compile_test/sf_ellint_rd_incl_test.cpp:// Copyright John Maddock 2006.
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compile_test/tools_roots_inc_test.cpp:// Copyright John Maddock 2006.
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compile_test/tools_test_data_inc_test.cpp:// Copyright John Maddock 2006.
|
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compile_test/compl_abs_incl_test.cpp:// Copyright John Maddock 2006.
|
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compile_test/dist_nc_t_incl_test.cpp:// Copyright John Maddock 2008.
|
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compile_test/sf_factorials_incl_test.cpp:// Copyright John Maddock 2006.
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compile_test/sf_gamma_incl_test.cpp:// Copyright John Maddock 2006.
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compile_test/compl_atan_incl_test.cpp:// Copyright John Maddock 2006.
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compile_test/sf_powm1_incl_test.cpp:// Copyright John Maddock 2006.
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compile_test/sf_hypot_incl_test.cpp:// Copyright John Maddock 2006.
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compile_test/dist_pareto_incl_test.cpp:// Copyright John Maddock 2006.
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compile_test/sf_round_incl_test.cpp:// Copyright John Maddock 2006.
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compile_test/dist_weibull_incl_test.cpp:// Copyright John Maddock 2006.
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compile_test/std_real_concept_check.cpp:// Copyright John Maddock 2006.
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compile_test/dist_hypergeo_incl_test.cpp:// Copyright John Maddock 2008.
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compile_test/dist_inv_chi_sq_incl_test.cpp:// Copyright John Maddock 2006.
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compile_test/sf_sqrt1pm1_incl_test.cpp:// Copyright John Maddock 2006.
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compile_test/sf_log1p_incl_test.cpp:// Copyright John Maddock 2006.
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compile_test/sf_jacobi_incl_test.cpp:// Copyright John Maddock 2012.
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compile_test/dist_neg_binom_incl_test.cpp:// Copyright John Maddock 2006.
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compile_test/dist_nc_f_incl_test.cpp:// Copyright John Maddock 2008.
|
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compile_test/dist_find_scale_incl_test.cpp:// Copyright John Maddock 2006.
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compile_test/sf_bessel_incl_test.cpp:// Copyright John Maddock 2006.
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compile_test/tools_minima_inc_test.cpp:// Copyright John Maddock 2006.
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compile_test/compl_asin_incl_test.cpp:// Copyright John Maddock 2006.
|
||||
compile_test/dist_extreme_val_incl_test.cpp:// Copyright John Maddock 2006.
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compile_test/sf_lanczos_incl_test.cpp:// Copyright John Maddock 2006.
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compile_test/dist_uniform_incl_test.cpp:// Copyright John Maddock 2006.
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compile_test/test_compile_result.hpp:// Copyright John Maddock 2007.
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compile_test/tools_series_inc_test.cpp:// Copyright John Maddock 2006.
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compile_test/sf_ellint_3_incl_test.cpp:// Copyright John Maddock 2006.
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compile_test/sf_ellint_rf_incl_test.cpp:// Copyright John Maddock 2006.
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compile_test/sf_ellint_2_incl_test.cpp:// Copyright John Maddock 2006.
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compile_test/sf_hermite_incl_test.cpp:// Copyright John Maddock 2006.
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compile_test/poison.hpp:// Copyright John Maddock 2013.
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compile_test/sf_zeta_incl_test.cpp:// Copyright John Maddock 2007.
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compile_test/dist_laplace_incl_test.cpp:// Copyright John Maddock 2008.
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compile_test/sf_expint_incl_test.cpp:// Copyright John Maddock 2007.
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compile_test/sf_expm1_incl_test.cpp:// Copyright John Maddock 2006.
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compile_test/dist_bernoulli_incl_test.cpp:// Copyright John Maddock 2006.
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compile_test/compl_asinh_incl_test.cpp:// Copyright John Maddock 2006.
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||||
compile_test/sf_beta_incl_test.cpp:// Copyright John Maddock 2006.
|
||||
compile_test/tools_fraction_inc_test.cpp:// Copyright John Maddock 2006.
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compile_test/sf_owens_t_incl_test.cpp:// Copyright John Maddock 2012.
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compile_test/tools_toms748_inc_test.cpp:// Copyright John Maddock 2006.
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compile_test/sf_ellint_1_incl_test.cpp:// Copyright John Maddock 2006.
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compile_test/sf_erf_incl_test.cpp:// Copyright John Maddock 2006.
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compile_test/main.cpp:// Copyright John Maddock 2009.
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compile_test/sf_math_fwd_incl_test.cpp:// Copyright John Maddock 2006.
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compile_test/sf_airy_incl_test.cpp:// Copyright John Maddock 2012.
|
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compile_test/dist_lognormal_incl_test.cpp:// Copyright John Maddock 2006.
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compile_test/dist_cauchy_incl_test.cpp:// Copyright John Maddock 2006.
|
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complex_test.cpp:// (C) Copyright John Maddock 2005.
|
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digamma_data.ipp:// (C) Copyright John Maddock 2006-7.
|
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digamma_neg_data.ipp:// (C) Copyright John Maddock 2006-7.
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digamma_root_data.ipp:// (C) Copyright John Maddock 2006-7.
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digamma_small_data.ipp:// (C) Copyright John Maddock 2006-7.
|
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e_float_concept_check.cpp:// Copyright John Maddock 2011.
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ellint_e2_data.ipp:// Copyright (c) 2006 John Maddock
|
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ellint_e_data.ipp:// Copyright (c) 2006 John Maddock
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ellint_f_data.ipp:// Copyright (c) 2006 John Maddock
|
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ellint_k_data.ipp:// (C) Copyright John Maddock 2006-7.
|
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ellint_pi2_data.ipp:// Copyright (c) 2006 John Maddock
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ellint_pi3_data.ipp:// Copyright (c) 2006 John Maddock
|
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ellint_pi3_large_data.ipp:// Copyright (c) 2006 John Maddock
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ellint_rc_data.ipp:// Copyright (c) 2006 John Maddock
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ellint_rd_data.ipp:// Copyright (c) 2006 John Maddock
|
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ellint_rf_data.ipp:// Copyright (c) 2006 John Maddock
|
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ellint_rj_data.ipp:// Copyright (c) 2006 John Maddock
|
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erf_data.ipp:// (C) Copyright John Maddock 2006-7.
|
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erf_inv_data.ipp:// (C) Copyright John Maddock 2006-7.
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erf_large_data.ipp:// (C) Copyright John Maddock 2006-7.
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erf_small_data.ipp:// (C) Copyright John Maddock 2006.
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erfc_inv_big_data.ipp:// (C) Copyright John Maddock 2006-7.
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erfc_inv_data.ipp:// (C) Copyright John Maddock 2006-7.
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expint_1_data.ipp:// Copyright John Maddock 2008.
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expint_data.ipp:// Copyright John Maddock 2008.
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expint_small_data.ipp:// Copyright John Maddock 2008.
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expinti_data.ipp:// Copyright John Maddock 2008.
|
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expinti_data_double.ipp:// Copyright John Maddock 2008.
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expinti_data_long.ipp:// Copyright John Maddock 2008.
|
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functor.hpp:// (C) Copyright John Maddock 2007.
|
||||
gamma_inv_big_data.ipp:// (C) Copyright John Maddock 2006-7.
|
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gamma_inv_data.ipp:// (C) Copyright John Maddock 2006-7.
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gamma_inv_small_data.ipp:// (C) Copyright John Maddock 2006-7.
|
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handle_test_result.hpp:// (C) Copyright John Maddock 2006-7.
|
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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.
|
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ibeta_data.ipp:// (C) Copyright John Maddock 2006.
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||||
ibeta_int_data.ipp:// (C) Copyright John Maddock 2006-7.
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ibeta_inv_data.ipp:// (C) Copyright John Maddock 2006-7.
|
||||
ibeta_inva_data.ipp:// (C) Copyright John Maddock 2006-7.
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ibeta_large_data.ipp:// (C) Copyright John Maddock 2006.
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ibeta_small_data.ipp:// (C) Copyright John Maddock 2006.
|
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igamma_big_data.ipp:// (C) Copyright John Maddock 2006.
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igamma_int_data.ipp:// (C) Copyright John Maddock 2006-7.
|
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igamma_inva_data.ipp:// (C) Copyright John Maddock 2006-7.
|
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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
|
||||
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File diff suppressed because it is too large
Load Diff
@@ -0,0 +1,108 @@
|
||||
from __future__ import division, print_function, absolute_import
|
||||
|
||||
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)
|
||||
|
||||
@@ -0,0 +1,409 @@
|
||||
"""
|
||||
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
|
||||
|
||||
"""
|
||||
from __future__ import division, print_function, absolute_import
|
||||
|
||||
import itertools
|
||||
|
||||
import numpy as np
|
||||
from numpy.testing import assert_equal
|
||||
import pytest
|
||||
|
||||
import scipy.special as sp
|
||||
from scipy._lib.six import with_metaclass
|
||||
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
|
||||
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
|
||||
@@ -0,0 +1,332 @@
|
||||
from __future__ import division, print_function, absolute_import
|
||||
|
||||
from itertools import product
|
||||
|
||||
from numpy.testing import assert_allclose
|
||||
import pytest
|
||||
|
||||
from scipy import special
|
||||
from scipy.special import cython_special
|
||||
|
||||
|
||||
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 = {
|
||||
'f': 'float',
|
||||
'd': 'double',
|
||||
'g': 'long double',
|
||||
'F': 'float complex',
|
||||
'D': 'double complex',
|
||||
'G': 'long double complex',
|
||||
'i':'int',
|
||||
'l': 'long'
|
||||
}
|
||||
|
||||
|
||||
TEST_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, ('lld', 'ddd'), None),
|
||||
(special.bdtrc, cython_special.bdtrc, ('lld', 'ddd'), None),
|
||||
(special.bdtri, cython_special.bdtri, ('lld', '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.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.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, ('ld', 'dd'), None),
|
||||
(special.pdtrc, cython_special.pdtrc, ('ld', '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.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.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
|
||||
skip = {'hyp2f0', 'hyp1f2', 'hyp3f0'}
|
||||
for name in dir(cython_special):
|
||||
func = getattr(cython_special, name)
|
||||
if callable(func) and not (name.startswith('_') or name in skip):
|
||||
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
|
||||
values = [set() for code in specializations[0]]
|
||||
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 = []
|
||||
for j, code in enumerate(typecodes):
|
||||
if is_fused_code[j]:
|
||||
signature.append(CYTHON_SIGNATURE_MAP[code])
|
||||
|
||||
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:
|
||||
pyval = pyfunc(*pt)
|
||||
cyval = cy_spec_func(*pt)
|
||||
assert_allclose(cyval, pyval, err_msg="{} {} {}".format(pt, typecodes, signature))
|
||||
@@ -0,0 +1,500 @@
|
||||
from __future__ import division, print_function, absolute_import
|
||||
|
||||
import os
|
||||
|
||||
import numpy as np
|
||||
from numpy import arccosh, arcsinh, arctanh
|
||||
from scipy._lib._numpy_compat 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=7e-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=7e-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")
|
||||
olderr = np.seterr(all='ignore')
|
||||
try:
|
||||
test.check(dtype=dtype)
|
||||
finally:
|
||||
np.seterr(**olderr)
|
||||
@@ -0,0 +1,44 @@
|
||||
from __future__ import division, print_function, absolute_import
|
||||
|
||||
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]))))
|
||||
@@ -0,0 +1,273 @@
|
||||
#
|
||||
# Tests for the Ellipsoidal Harmonic Function,
|
||||
# Distributed under the same license as SciPy itself.
|
||||
#
|
||||
|
||||
from __future__ import division, print_function, absolute_import
|
||||
|
||||
import numpy as np
|
||||
from numpy.testing import (assert_equal, assert_almost_equal, assert_allclose,
|
||||
assert_)
|
||||
from scipy._lib._numpy_compat import 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, n*np.ones(h2.size), p*np.ones(h2.size)))
|
||||
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)
|
||||
|
||||
@@ -0,0 +1,46 @@
|
||||
from __future__ import division, print_function, absolute_import
|
||||
|
||||
import numpy as np
|
||||
from numpy.testing import assert_allclose
|
||||
|
||||
import scipy.special as sc
|
||||
from scipy.special._testutils import FuncData
|
||||
|
||||
|
||||
def test_line():
|
||||
# Test on the line a = x where a simpler asymptotic expansion
|
||||
# (analog of DLMF 8.12.15) is available.
|
||||
|
||||
def gammainc_line(x):
|
||||
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
|
||||
|
||||
x = np.logspace(np.log10(25), 300, 500)
|
||||
a = x.copy()
|
||||
dataset = np.vstack((a, x, gammainc_line(x))).T
|
||||
|
||||
FuncData(sc.gammainc, dataset, (0, 1), 2, rtol=1e-11).check()
|
||||
|
||||
|
||||
def test_gammainc_roundtrip():
|
||||
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)
|
||||
|
||||
|
||||
def test_gammaincc_roundtrip():
|
||||
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)
|
||||
@@ -0,0 +1,414 @@
|
||||
from __future__ import division, print_function, absolute_import
|
||||
|
||||
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()
|
||||
@@ -0,0 +1,103 @@
|
||||
#
|
||||
# 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
|
||||
|
||||
from __future__ import division, print_function, absolute_import
|
||||
|
||||
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))
|
||||
olderr = np.seterr(all='ignore')
|
||||
try:
|
||||
FuncData(w, data, (0,1), 2, rtol=1e-10, atol=1e-13).check()
|
||||
finally:
|
||||
np.seterr(**olderr)
|
||||
|
||||
|
||||
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)
|
||||
@@ -0,0 +1,72 @@
|
||||
from __future__ import division, print_function, absolute_import
|
||||
|
||||
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)
|
||||
@@ -0,0 +1,81 @@
|
||||
from __future__ import division, print_function, absolute_import
|
||||
|
||||
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)
|
||||
olderr = np.seterr(divide='ignore')
|
||||
try:
|
||||
actual = logit(a)
|
||||
finally:
|
||||
np.seterr(**olderr)
|
||||
|
||||
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)
|
||||
olderr = np.seterr(invalid='ignore')
|
||||
try:
|
||||
actual = logit(np.array([-3., -2., 2., 3.]))
|
||||
finally:
|
||||
np.seterr(**olderr)
|
||||
|
||||
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)
|
||||
@@ -0,0 +1,196 @@
|
||||
from __future__ import division, print_function, absolute_import
|
||||
|
||||
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)
|
||||
File diff suppressed because it is too large
Load Diff
@@ -0,0 +1,64 @@
|
||||
"""Test how the ufuncs in special handle nan inputs.
|
||||
|
||||
"""
|
||||
from __future__ import division, print_function, absolute_import
|
||||
|
||||
import numpy as np
|
||||
from numpy.testing import assert_array_equal, assert_
|
||||
import pytest
|
||||
|
||||
import scipy.special as sc
|
||||
from scipy._lib._numpy_compat import suppress_warnings
|
||||
|
||||
|
||||
KNOWNFAILURES = {}
|
||||
|
||||
POSTPROCESSING = {}
|
||||
|
||||
|
||||
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:
|
||||
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))
|
||||
@@ -0,0 +1,756 @@
|
||||
from __future__ import division, print_function, absolute_import
|
||||
|
||||
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._lib.six import xrange
|
||||
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)
|
||||
olderr = np.seterr(all='ignore')
|
||||
try:
|
||||
C2 = orth.chebyc(2)
|
||||
C3 = orth.chebyc(3)
|
||||
C4 = orth.chebyc(4)
|
||||
C5 = orth.chebyc(5)
|
||||
finally:
|
||||
np.seterr(**olderr)
|
||||
|
||||
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*orth.poch(a,3),0,-6*a*(a+1),
|
||||
0])/3.0,11)
|
||||
assert_array_almost_equal(Ca4.c,array([4*orth.poch(a,4),0,-12*orth.poch(a,3),
|
||||
0,3*a*(a+1)])/6.0,11)
|
||||
assert_array_almost_equal(Ca5.c,array([4*orth.poch(a,5),0,-20*orth.poch(a,4),
|
||||
0,15*orth.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 xrange(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()
|
||||
])
|
||||
olderr = np.seterr(all='ignore')
|
||||
try:
|
||||
for pstr in poly:
|
||||
p = eval(pstr)
|
||||
assert_almost_equal(p(0.315), np.poly1d(p.coef)(0.315),
|
||||
err_msg=pstr)
|
||||
finally:
|
||||
np.seterr(**olderr)
|
||||
|
||||
|
||||
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: orth.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=1e-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)
|
||||
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: orth.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=1e-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 = orth.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 xrange(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 = orth.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: orth.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), orth.eval_chebyt, weightf(0), -1., 1., 5)
|
||||
vgq(rootf(0), orth.eval_chebyt, weightf(0), -1., 1., 25)
|
||||
vgq(rootf(0), orth.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, orth.eval_chebyt, weightf, -1., 1., 5)
|
||||
verify_gauss_quad(sc.roots_chebyt, orth.eval_chebyt, weightf, -1., 1., 25)
|
||||
verify_gauss_quad(sc.roots_chebyt, orth.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, orth.eval_chebyu, weightf, -1., 1., 5)
|
||||
verify_gauss_quad(sc.roots_chebyu, orth.eval_chebyu, weightf, -1., 1., 25)
|
||||
verify_gauss_quad(sc.roots_chebyu, orth.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, orth.eval_chebyc, weightf, -2., 2., 5)
|
||||
verify_gauss_quad(sc.roots_chebyc, orth.eval_chebyc, weightf, -2., 2., 25)
|
||||
verify_gauss_quad(sc.roots_chebyc, orth.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, orth.eval_chebys, weightf, -2., 2., 5)
|
||||
verify_gauss_quad(sc.roots_chebys, orth.eval_chebys, weightf, -2., 2., 25)
|
||||
verify_gauss_quad(sc.roots_chebys, orth.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, orth.eval_sh_chebyt, weightf, 0., 1., 5)
|
||||
verify_gauss_quad(sc.roots_sh_chebyt, orth.eval_sh_chebyt, weightf, 0., 1., 25)
|
||||
verify_gauss_quad(sc.roots_sh_chebyt, orth.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, orth.eval_sh_chebyu, weightf, 0., 1., 5)
|
||||
verify_gauss_quad(sc.roots_sh_chebyu, orth.eval_sh_chebyu, weightf, 0., 1., 25)
|
||||
verify_gauss_quad(sc.roots_sh_chebyu, orth.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, orth.eval_legendre, weightf, -1., 1., 5)
|
||||
verify_gauss_quad(sc.roots_legendre, orth.eval_legendre, weightf, -1., 1.,
|
||||
25, atol=1e-13)
|
||||
verify_gauss_quad(sc.roots_legendre, orth.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, orth.eval_sh_legendre, weightf, 0., 1., 5)
|
||||
verify_gauss_quad(sc.roots_sh_legendre, orth.eval_sh_legendre, weightf, 0., 1.,
|
||||
25, atol=1e-13)
|
||||
verify_gauss_quad(sc.roots_sh_legendre, orth.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, orth.eval_laguerre, weightf, 0., np.inf, 5)
|
||||
verify_gauss_quad(sc.roots_laguerre, orth.eval_laguerre, weightf, 0., np.inf,
|
||||
25, atol=1e-13)
|
||||
verify_gauss_quad(sc.roots_laguerre, orth.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: orth.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=1e-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=1e-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)
|
||||
@@ -0,0 +1,248 @@
|
||||
from __future__ import division, print_function, absolute_import
|
||||
|
||||
import numpy as np
|
||||
from numpy.testing import assert_, assert_allclose
|
||||
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
|
||||
olderr = np.seterr(all='raise')
|
||||
try:
|
||||
# these should raise no fp warnings
|
||||
orth.eval_legendre(1, 0)
|
||||
orth.eval_laguerre(1, 1)
|
||||
orth.eval_gegenbauer(1, 1, 0)
|
||||
finally:
|
||||
np.seterr(**olderr)
|
||||
|
||||
|
||||
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)
|
||||
|
||||
olderr = np.seterr(all='raise')
|
||||
try:
|
||||
ds = FuncData(polyfunc, dataset, list(range(len(param_ranges)+2)), -1,
|
||||
rtol=rtol)
|
||||
ds.check()
|
||||
finally:
|
||||
np.seterr(**olderr)
|
||||
|
||||
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):
|
||||
olderr = np.seterr(all='ignore')
|
||||
try:
|
||||
self.check_poly(orth.eval_sh_chebyt, orth.sh_chebyt,
|
||||
param_ranges=[], x_range=[0, 1])
|
||||
finally:
|
||||
np.seterr(**olderr)
|
||||
|
||||
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):
|
||||
olderr = np.seterr(all='ignore')
|
||||
try:
|
||||
self.check_poly(orth.eval_sh_legendre, orth.sh_legendre,
|
||||
param_ranges=[], x_range=[0, 1])
|
||||
finally:
|
||||
np.seterr(**olderr)
|
||||
|
||||
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)
|
||||
|
||||
olderr = np.seterr(all='raise')
|
||||
try:
|
||||
ds = FuncData(polyfunc, dataset, list(range(len(param_ranges)+2)), -1,
|
||||
rtol=rtol)
|
||||
ds.check()
|
||||
finally:
|
||||
np.seterr(**olderr)
|
||||
|
||||
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)
|
||||
@@ -0,0 +1,44 @@
|
||||
from __future__ import division, print_function, absolute_import
|
||||
|
||||
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)
|
||||
@@ -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))
|
||||
+26
@@ -0,0 +1,26 @@
|
||||
from __future__ import division, print_function, absolute_import
|
||||
|
||||
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
|
||||
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)
|
||||
+116
@@ -0,0 +1,116 @@
|
||||
from __future__ import division, print_function, absolute_import
|
||||
|
||||
import numpy as np
|
||||
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
|
||||
except ImportError:
|
||||
sympy = MissingModule('sympy')
|
||||
|
||||
try:
|
||||
import mpmath as mp
|
||||
except ImportError:
|
||||
mp = MissingModule('mpmath')
|
||||
|
||||
|
||||
_is_32bit_platform = np.intp(0).itemsize < 8
|
||||
|
||||
|
||||
@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(condition=_is_32bit_platform, reason="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 = []
|
||||
for k, n, std in dataset:
|
||||
res.append(d[k][n])
|
||||
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)
|
||||
@@ -0,0 +1,42 @@
|
||||
from __future__ import division, print_function, absolute_import
|
||||
import numpy as np
|
||||
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
|
||||
except ImportError:
|
||||
sympy = MissingModule('sympy')
|
||||
|
||||
try:
|
||||
import mpmath as mp
|
||||
except ImportError:
|
||||
mp = MissingModule('mpmath')
|
||||
|
||||
|
||||
_is_32bit_platform = np.intp(0).itemsize < 8
|
||||
|
||||
|
||||
@pytest.mark.slow
|
||||
@check_version(sympy, '0.7')
|
||||
@check_version(mp, '0.19')
|
||||
class TestInversion(object):
|
||||
@pytest.mark.xfail(condition=_is_32bit_platform, reason="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(condition=_is_32bit_platform, reason="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)
|
||||
|
||||
@@ -0,0 +1,18 @@
|
||||
from __future__ import division, print_function, absolute_import
|
||||
|
||||
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')
|
||||
@@ -0,0 +1,115 @@
|
||||
from __future__ import division, print_function, absolute_import
|
||||
|
||||
import warnings
|
||||
|
||||
from numpy.testing import assert_, assert_equal
|
||||
from scipy._lib._numpy_compat import suppress_warnings
|
||||
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())
|
||||
@@ -0,0 +1,38 @@
|
||||
from __future__ import division, print_function, absolute_import
|
||||
|
||||
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()
|
||||
@@ -0,0 +1,34 @@
|
||||
from __future__ import division, print_function, absolute_import
|
||||
|
||||
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()
|
||||
@@ -0,0 +1,63 @@
|
||||
from __future__ import division, print_function, absolute_import
|
||||
|
||||
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)
|
||||
|
||||
@@ -0,0 +1,39 @@
|
||||
from __future__ import division, print_function, absolute_import
|
||||
|
||||
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))
|
||||
@@ -0,0 +1,383 @@
|
||||
#
|
||||
# Tests of spherical Bessel functions.
|
||||
#
|
||||
from __future__ import division, print_function, absolute_import
|
||||
|
||||
import numpy as np
|
||||
from numpy.testing import (assert_almost_equal, assert_allclose,
|
||||
assert_array_almost_equal)
|
||||
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
|
||||
|
||||
from scipy._lib._numpy_compat import suppress_warnings
|
||||
|
||||
|
||||
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), -inf*np.ones(shape=n.shape))
|
||||
|
||||
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), nan*np.ones(shape=n.shape))
|
||||
|
||||
|
||||
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), inf*np.ones(shape=n.shape))
|
||||
|
||||
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), nan*np.ones(shape=n.shape))
|
||||
|
||||
|
||||
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).
|
||||
@@ -0,0 +1,77 @@
|
||||
from __future__ import division, print_function, absolute_import
|
||||
|
||||
import sys
|
||||
|
||||
import numpy as np
|
||||
from numpy.testing import assert_equal, assert_allclose
|
||||
import pytest
|
||||
|
||||
from scipy.special._ufuncs import _sinpi as sinpi
|
||||
from scipy.special._ufuncs import _cospi as cospi
|
||||
|
||||
from scipy._lib._numpy_compat import suppress_warnings
|
||||
|
||||
|
||||
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)
|
||||
|
||||
|
||||
@pytest.mark.xfail('win32' in sys.platform
|
||||
and np.intp(0).itemsize < 8
|
||||
and sys.version_info < (3, 5),
|
||||
reason="fails on 32-bit Windows with old MSVC")
|
||||
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)
|
||||
@@ -0,0 +1,55 @@
|
||||
from __future__ import division, print_function, absolute_import
|
||||
|
||||
import numpy as np
|
||||
from numpy.testing import assert_, assert_equal
|
||||
|
||||
import scipy.special as sc
|
||||
|
||||
|
||||
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)
|
||||
@@ -0,0 +1,39 @@
|
||||
from __future__ import division, print_function, absolute_import
|
||||
|
||||
import scipy.special as sc
|
||||
import numpy as np
|
||||
from numpy.testing import assert_, assert_equal, assert_allclose
|
||||
|
||||
|
||||
def test_zeta():
|
||||
assert_allclose(sc.zeta(2,2), np.pi**2/6 - 1, rtol=1e-12)
|
||||
|
||||
|
||||
def test_zeta_1arg():
|
||||
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_zetac():
|
||||
assert_equal(sc.zetac(0), -1.5)
|
||||
assert_equal(sc.zetac(1.0), np.inf)
|
||||
# Expected values in the following were computed using
|
||||
# Wolfram Alpha `Zeta[x] - 1`:
|
||||
rtol = 1e-12
|
||||
assert_allclose(sc.zetac(-2.1), -0.9972705002153750, rtol=rtol)
|
||||
assert_allclose(sc.zetac(0.8), -5.437538415895550, rtol=rtol)
|
||||
assert_allclose(sc.zetac(0.9999), -10000.42279161673, rtol=rtol)
|
||||
assert_allclose(sc.zetac(9), 0.002008392826082214, rtol=rtol)
|
||||
assert_allclose(sc.zetac(50), 8.881784210930816e-16, rtol=rtol)
|
||||
assert_allclose(sc.zetac(75), 2.646977960169853e-23, rtol=rtol)
|
||||
|
||||
|
||||
def test_zetac_negative_even():
|
||||
pts = [-2, -50, -100]
|
||||
for p in pts:
|
||||
assert_equal(sc.zetac(p), -1)
|
||||
|
||||
|
||||
def test_zetac_inf():
|
||||
assert_equal(sc.zetac(np.inf), 0.0)
|
||||
assert_(np.isnan(sc.zetac(-np.inf)))
|
||||
Reference in New Issue
Block a user