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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))
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)
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