U Hv f;@sddlZddlZddlmZmZddlmZddlm Z m Z ej ddddddd gej d dddddd gd d Z ej d dddddd gej d dddddgddZej ddddddd gej d ddddd gej d ddddddd dgddZedddddgdddddgdddddgdddd d!gd"d#d$d%d&gd"dd$d'ejgd(d#d$d)d&gd(dd$d*ejgd+d,d-d.d&gd+d/d-d0d&gd+d1d-d2d&gd+d3d-d4d&gd+dd-d5d6gd+d#d$d7d8gd+dd$d9ejggZej jej d:edddd;fded?d@ZdS)AN) assert_equalassert_allclose)rgamma wright_besselagư>g?g? bcCstt||dt|dS)zTest at x = 0.N)rrr)rr r J/tmp/pip-unpacked-wheel-96ln3f52/scipy/special/tests/test_wright_bessel.pytest_wright_bessel_zerosr xcCsT|dkrP|d}td|d|dd}tt|d||t||ddddS) zTest relation of wright_bessel and modified bessel function iv. iv(z) = (1/2*z)**v * Phi(1, v+1; 1/4*z**2). See https://dlmf.nist.gov/10.46.E2 rrg@g@dy=rtolZatolN)rrnppowerscZiv)r rvwbr r r test_wright_bessel_iv"s rgjt?rdcCsHtt||d|||t|||||dt|||ddddS)a=Test functional relation of wright_bessel. Phi(a, b-1, z) = a*z*Phi(a, b+a, z) + (b-1)*Phi(a, b, z) Note that d/dx Phi(a, b, x) = Phi(a, b-1, x) See Eq. (22) of B. Stankovic, On the Function of E. M. Wright, Publ. de l' Institut Mathematique, Beograd, Nouvelle S`er. 10 (1970), 113-124. r:0yE>rNrr)rr rr r r test_wright_functional4srgY@g9B.@gS [.Gg:0yU>g$@gUqZ+YIgv(x>g@@g]a(aaHMrg 5U4'g+i)+p>g?g4@gj@g+^%ngp ~=g +eDgd?g'^%ngc+eDg?r g@@guc& Bg=gsc& Bg|=gB& Bgh㈵>g]% BgKӨwqBgdy=g@ IgA:)>gmxi%%z a, b, x, phicCstt||||dddS)zDTest cases of test_data that do not reach relative accuracy of 1e-11rrNr)rr rphir r r test_wright_data_grid_failures_sr!za, b, x, phi, accuracycCs<t|r"tt|||s8tntt|||||ddS)z}Test cases of test_data that do not reach relative accuracy of 1e-11 Here we test for reduced accuracy or even nan. rN)risnanrAssertionErrorr)rr rr Zaccuracyr r r #test_wright_data_grid_less_accuratehs r$)ZpytestZnumpyrZ numpy.testingrrZ scipy.specialspecialrrrmarkZ parametrizer rrarraynanZgrid_a_b_x_value_accZxfailtolistr!r$r r r r sT