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"""Tests for chebyshev module.
"""
from __future__ import division
import numpy as np
import numpy.polynomial.chebyshev as ch
from numpy.testing import *
from exceptions import TypeError, ValueError
def trim(x) :
return ch.chebtrim(x, tol=1e-6)
T0 = [ 1]
T1 = [ 0, 1]
T2 = [-1, 0, 2]
T3 = [ 0, -3, 0, 4]
T4 = [ 1, 0, -8, 0, 8]
T5 = [ 0, 5, 0, -20, 0, 16]
T6 = [-1, 0, 18, 0, -48, 0, 32]
T7 = [ 0, -7, 0, 56, 0, -112, 0, 64]
T8 = [ 1, 0, -32, 0, 160, 0, -256, 0, 128]
T9 = [ 0, 9, 0, -120, 0, 432, 0, -576, 0, 256]
Tlist = [T0, T1, T2, T3, T4, T5, T6, T7, T8, T9]
class TestPrivate(TestCase) :
def test__cseries_to_zseries(self) :
for i in range(5) :
inp = np.array([2] + [1]*i, np.double)
tgt = np.array([.5]*i + [2] + [.5]*i, np.double)
res = ch._cseries_to_zseries(inp)
assert_equal(res, tgt)
def test__zseries_to_cseries(self) :
for i in range(5) :
inp = np.array([.5]*i + [2] + [.5]*i, np.double)
tgt = np.array([2] + [1]*i, np.double)
res = ch._zseries_to_cseries(inp)
assert_equal(res, tgt)
class TestConstants(TestCase) :
def test_chebdomain(self) :
assert_equal(ch.chebdomain, [-1, 1])
def test_chebzero(self) :
assert_equal(ch.chebzero, [0])
def test_chebone(self) :
assert_equal(ch.chebone, [1])
def test_chebx(self) :
assert_equal(ch.chebx, [0, 1])
class TestArithmetic(TestCase) :
def test_chebadd(self) :
for i in range(5) :
for j in range(5) :
msg = "At i=%d, j=%d" % (i,j)
tgt = np.zeros(max(i,j) + 1)
tgt[i] += 1
tgt[j] += 1
res = ch.chebadd([0]*i + [1], [0]*j + [1])
assert_equal(trim(res), trim(tgt), err_msg=msg)
def test_chebsub(self) :
for i in range(5) :
for j in range(5) :
msg = "At i=%d, j=%d" % (i,j)
tgt = np.zeros(max(i,j) + 1)
tgt[i] += 1
tgt[j] -= 1
res = ch.chebsub([0]*i + [1], [0]*j + [1])
assert_equal(trim(res), trim(tgt), err_msg=msg)
def test_chebmul(self) :
for i in range(5) :
for j in range(5) :
msg = "At i=%d, j=%d" % (i,j)
tgt = np.zeros(i + j + 1)
tgt[i + j] += .5
tgt[abs(i - j)] += .5
res = ch.chebmul([0]*i + [1], [0]*j + [1])
assert_equal(trim(res), trim(tgt), err_msg=msg)
def test_chebdiv(self) :
for i in range(5) :
for j in range(5) :
msg = "At i=%d, j=%d" % (i,j)
ci = [0]*i + [1]
cj = [0]*j + [1]
tgt = ch.chebadd(ci, cj)
quo, rem = ch.chebdiv(tgt, ci)
res = ch.chebadd(ch.chebmul(quo, ci), rem)
assert_equal(trim(res), trim(tgt), err_msg=msg)
def test_chebval(self) :
def f(x) :
return x*(x**2 - 1)
#check empty input
assert_equal(ch.chebval([], [1]).size, 0)
#check normal input)
for i in range(5) :
tgt = 1
res = ch.chebval(1, [0]*i + [1])
assert_almost_equal(res, tgt)
tgt = (-1)**i
res = ch.chebval(-1, [0]*i + [1])
assert_almost_equal(res, tgt)
zeros = np.cos(np.linspace(-np.pi, 0, 2*i + 1)[1::2])
tgt = 0
res = ch.chebval(zeros, [0]*i + [1])
assert_almost_equal(res, tgt)
x = np.linspace(-1,1)
tgt = f(x)
res = ch.chebval(x, [0, -.25, 0, .25])
assert_almost_equal(res, tgt)
#check that shape is preserved
for i in range(3) :
dims = [2]*i
x = np.zeros(dims)
assert_equal(ch.chebval(x, [1]).shape, dims)
assert_equal(ch.chebval(x, [1,0]).shape, dims)
assert_equal(ch.chebval(x, [1,0,0]).shape, dims)
class TestCalculus(TestCase) :
def test_chebint(self) :
# check exceptions
assert_raises(ValueError, ch.chebint, [0], -1)
assert_raises(ValueError, ch.chebint, [0], 1, [0,0])
assert_raises(ValueError, ch.chebint, [0], 1, lbnd=[0,0])
assert_raises(ValueError, ch.chebint, [0], 1, scl=[0,0])
# check single integration with integration constant
for i in range(5) :
scl = i + 1
pol = [0]*i + [1]
tgt = [i] + [0]*i + [1/scl]
chebpol = ch.poly2cheb(pol)
chebint = ch.chebint(chebpol, m=1, k=[i])
res = ch.cheb2poly(chebint)
assert_almost_equal(trim(res), trim(tgt))
# check single integration with integration constant and lbnd
for i in range(5) :
scl = i + 1
pol = [0]*i + [1]
chebpol = ch.poly2cheb(pol)
chebint = ch.chebint(chebpol, m=1, k=[i], lbnd=-1)
assert_almost_equal(ch.chebval(-1, chebint), i)
# check single integration with integration constant and scaling
for i in range(5) :
scl = i + 1
pol = [0]*i + [1]
tgt = [i] + [0]*i + [2/scl]
chebpol = ch.poly2cheb(pol)
chebint = ch.chebint(chebpol, m=1, k=[i], scl=2)
res = ch.cheb2poly(chebint)
assert_almost_equal(trim(res), trim(tgt))
# check multiple integrations with default k
for i in range(5) :
for j in range(2,5) :
pol = [0]*i + [1]
tgt = pol[:]
for k in range(j) :
tgt = ch.chebint(tgt, m=1)
res = ch.chebint(pol, m=j)
assert_almost_equal(trim(res), trim(tgt))
# check multiple integrations with defined k
for i in range(5) :
for j in range(2,5) :
pol = [0]*i + [1]
tgt = pol[:]
for k in range(j) :
tgt = ch.chebint(tgt, m=1, k=[k])
res = ch.chebint(pol, m=j, k=range(j))
assert_almost_equal(trim(res), trim(tgt))
# check multiple integrations with lbnd
for i in range(5) :
for j in range(2,5) :
pol = [0]*i + [1]
tgt = pol[:]
for k in range(j) :
tgt = ch.chebint(tgt, m=1, k=[k], lbnd=-1)
res = ch.chebint(pol, m=j, k=range(j), lbnd=-1)
assert_almost_equal(trim(res), trim(tgt))
# check multiple integrations with scaling
for i in range(5) :
for j in range(2,5) :
pol = [0]*i + [1]
tgt = pol[:]
for k in range(j) :
tgt = ch.chebint(tgt, m=1, k=[k], scl=2)
res = ch.chebint(pol, m=j, k=range(j), scl=2)
assert_almost_equal(trim(res), trim(tgt))
def test_chebder(self) :
# check exceptions
assert_raises(ValueError, ch.chebder, [0], -1)
# check that zeroth deriviative does nothing
for i in range(5) :
tgt = [1] + [0]*i
res = ch.chebder(tgt, m=0)
assert_equal(trim(res), trim(tgt))
# check that derivation is the inverse of integration
for i in range(5) :
for j in range(2,5) :
tgt = [1] + [0]*i
res = ch.chebder(ch.chebint(tgt, m=j), m=j)
assert_almost_equal(trim(res), trim(tgt))
# check derivation with scaling
for i in range(5) :
for j in range(2,5) :
tgt = [1] + [0]*i
res = ch.chebder(ch.chebint(tgt, m=j, scl=2), m=j, scl=.5)
assert_almost_equal(trim(res), trim(tgt))
class TestMisc(TestCase) :
def test_chebfromroots(self) :
res = ch.chebfromroots([])
assert_almost_equal(trim(res), [1])
for i in range(1,5) :
roots = np.cos(np.linspace(-np.pi, 0, 2*i + 1)[1::2])
tgt = [0]*i + [1]
res = ch.chebfromroots(roots)*2**(i-1)
assert_almost_equal(trim(res),trim(tgt))
def test_chebroots(self) :
assert_almost_equal(ch.chebroots([1]), [])
assert_almost_equal(ch.chebroots([1, 2]), [-.5])
for i in range(2,5) :
tgt = np.linspace(-1, 1, i)
res = ch.chebroots(ch.chebfromroots(tgt))
assert_almost_equal(trim(res), trim(tgt))
def test_chebvander(self) :
# check for 1d x
x = np.arange(3)
v = ch.chebvander(x, 3)
assert_(v.shape == (3,4))
for i in range(4) :
coef = [0]*i + [1]
assert_almost_equal(v[...,i], ch.chebval(x, coef))
# check for 2d x
x = np.array([[1,2],[3,4],[5,6]])
v = ch.chebvander(x, 3)
assert_(v.shape == (3,2,4))
for i in range(4) :
coef = [0]*i + [1]
assert_almost_equal(v[...,i], ch.chebval(x, coef))
def test_chebfit(self) :
def f(x) :
return x*(x - 1)*(x - 2)
# Test exceptions
assert_raises(ValueError, ch.chebfit, [1], [1], -1)
assert_raises(TypeError, ch.chebfit, [[1]], [1], 0)
assert_raises(TypeError, ch.chebfit, [], [1], 0)
assert_raises(TypeError, ch.chebfit, [1], [[[1]]], 0)
assert_raises(TypeError, ch.chebfit, [1, 2], [1], 0)
assert_raises(TypeError, ch.chebfit, [1], [1, 2], 0)
# Test fit
x = np.linspace(0,2)
y = f(x)
coef = ch.chebfit(x, y, 3)
assert_equal(len(coef), 4)
assert_almost_equal(ch.chebval(x, coef), y)
coef = ch.chebfit(x, y, 4)
assert_equal(len(coef), 5)
assert_almost_equal(ch.chebval(x, coef), y)
coef2d = ch.chebfit(x, np.array([y,y]).T, 4)
assert_almost_equal(coef2d, np.array([coef,coef]).T)
def test_chebtrim(self) :
coef = [2, -1, 1, 0]
# Test exceptions
assert_raises(ValueError, ch.chebtrim, coef, -1)
# Test results
assert_equal(ch.chebtrim(coef), coef[:-1])
assert_equal(ch.chebtrim(coef, 1), coef[:-3])
assert_equal(ch.chebtrim(coef, 2), [0])
def test_chebline(self) :
assert_equal(ch.chebline(3,4), [3, 4])
def test_cheb2poly(self) :
for i in range(10) :
assert_equal(ch.cheb2poly([0]*i + [1]), Tlist[i])
def test_poly2cheb(self) :
for i in range(10) :
assert_equal(ch.poly2cheb(Tlist[i]), [0]*i + [1])
class TestChebyshevClass(TestCase) :
p1 = ch.Chebyshev([1,2,3])
p2 = ch.Chebyshev([1,2,3], [0,1])
p3 = ch.Chebyshev([1,2])
p4 = ch.Chebyshev([2,2,3])
p5 = ch.Chebyshev([3,2,3])
def test_equal(self) :
assert_(self.p1 == self.p1)
assert_(self.p2 == self.p2)
assert_(not self.p1 == self.p2)
assert_(not self.p1 == self.p3)
assert_(not self.p1 == [1,2,3])
def test_not_equal(self) :
assert_(not self.p1 != self.p1)
assert_(not self.p2 != self.p2)
assert_(self.p1 != self.p2)
assert_(self.p1 != self.p3)
assert_(self.p1 != [1,2,3])
def test_add(self) :
tgt = ch.Chebyshev([2,4,6])
assert_(self.p1 + self.p1 == tgt)
assert_(self.p1 + [1,2,3] == tgt)
assert_([1,2,3] + self.p1 == tgt)
def test_sub(self) :
tgt = ch.Chebyshev([1])
assert_(self.p4 - self.p1 == tgt)
assert_(self.p4 - [1,2,3] == tgt)
assert_([2,2,3] - self.p1 == tgt)
def test_mul(self) :
tgt = ch.Chebyshev([7.5, 10., 8., 6., 4.5])
assert_(self.p1 * self.p1 == tgt)
assert_(self.p1 * [1,2,3] == tgt)
assert_([1,2,3] * self.p1 == tgt)
def test_floordiv(self) :
tgt = ch.Chebyshev([1])
assert_(self.p4 // self.p1 == tgt)
assert_(self.p4 // [1,2,3] == tgt)
assert_([2,2,3] // self.p1 == tgt)
def test_mod(self) :
tgt = ch.Chebyshev([1])
assert_((self.p4 % self.p1) == tgt)
assert_((self.p4 % [1,2,3]) == tgt)
assert_(([2,2,3] % self.p1) == tgt)
def test_divmod(self) :
tquo = ch.Chebyshev([1])
trem = ch.Chebyshev([2])
quo, rem = divmod(self.p5, self.p1)
assert_(quo == tquo and rem == trem)
quo, rem = divmod(self.p5, [1,2,3])
assert_(quo == tquo and rem == trem)
quo, rem = divmod([3,2,3], self.p1)
assert_(quo == tquo and rem == trem)
def test_pow(self) :
tgt = ch.Chebyshev([1])
for i in range(5) :
res = self.p1**i
assert_(res == tgt)
tgt *= self.p1
def test_call(self) :
# domain = [-1, 1]
x = np.linspace(-1, 1)
tgt = 3*(2*x**2 - 1) + 2*x + 1
assert_almost_equal(self.p1(x), tgt)
# domain = [0, 1]
x = np.linspace(0, 1)
xx = 2*x - 1
assert_almost_equal(self.p2(x), self.p1(xx))
def test_convert(self) :
x = np.linspace(-1,1)
p = self.p1.convert(domain=[0,1])
assert_almost_equal(p(x), self.p1(x))
def test_mapparms(self) :
parms = self.p2.mapparms()
assert_almost_equal(parms, [-1, 2])
def test_trim(self) :
coef = [1, 1e-6, 1e-12, 0]
p = ch.Chebyshev(coef)
assert_equal(p.trim().coef, coef[:3])
assert_equal(p.trim(1e-10).coef, coef[:2])
assert_equal(p.trim(1e-5).coef, coef[:1])
def test_truncate(self) :
assert_raises(ValueError, self.p1.truncate, 0)
assert_equal(len(self.p1.truncate(4)), 3)
assert_equal(len(self.p1.truncate(3)), 3)
assert_equal(len(self.p1.truncate(2)), 2)
assert_equal(len(self.p1.truncate(1)), 1)
def test_copy(self) :
p = self.p1.copy()
assert_(self.p1 == p)
def test_integ(self) :
p = self.p2.integ()
assert_almost_equal(p.coef, ch.chebint([1,2,3], 1, 0, scl=.5))
p = self.p2.integ(lbnd=0)
assert_almost_equal(p(0), 0)
p = self.p2.integ(1, 1)
assert_almost_equal(p.coef, ch.chebint([1,2,3], 1, 1, scl=.5))
p = self.p2.integ(2, [1, 2])
assert_almost_equal(p.coef, ch.chebint([1,2,3], 2, [1,2], scl=.5))
def test_deriv(self) :
p = self.p2.integ(2, [1, 2])
assert_almost_equal(p.deriv(1).coef, self.p2.integ(1, [1]).coef)
assert_almost_equal(p.deriv(2).coef, self.p2.coef)
def test_roots(self) :
p = ch.Chebyshev(ch.poly2cheb([0, -1, 0, 1]), [0, 1])
res = p.roots()
tgt = [0, .5, 1]
assert_almost_equal(res, tgt)
def test_fromroots(self) :
roots = [0, .5, 1]
p = ch.Chebyshev.fromroots(roots, domain=[0, 1])
res = p.coef
tgt = ch.poly2cheb([0, -1, 0, 1])
assert_almost_equal(res, tgt)
def test_fit(self) :
def f(x) :
return x*(x - 1)*(x - 2)
x = np.linspace(0,3)
y = f(x)
p = ch.Chebyshev.fit(x, y, 3)
assert_almost_equal(p(x), y)
p = ch.Chebyshev.fit(x, y, 3, None)
assert_almost_equal(p(x), y)
assert_almost_equal(p.domain, [0,3])
def test_identity(self) :
x = np.linspace(0,3)
p = ch.Chebyshev.identity()
assert_almost_equal(p(x), x)
p = ch.Chebyshev.identity([1,3])
assert_almost_equal(p(x), x)
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