"""Tests for chebyshev module. """ from __future__ import division import numpy as np import numpy.polynomial.chebyshev as ch from numpy.testing import * 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_chebmulx(self): assert_equal(ch.chebmulx([0]), [0]) assert_equal(ch.chebmulx([1]), [0,1]) for i in range(1, 5): ser = [0]*i + [1] tgt = [0]*(i - 1) + [.5, 0, .5] assert_equal(ch.chebmulx(ser), tgt) 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], .5) assert_raises(ValueError, ch.chebint, [0], -1) assert_raises(ValueError, ch.chebint, [0], 1, [0,0]) # test integration of zero polynomial for i in range(2, 5): k = [0]*(i - 2) + [1] res = ch.chebint([0], m=i, k=k) assert_almost_equal(res, [0, 1]) # 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], .5) 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) assert_raises(TypeError, ch.chebfit, [1], [1], 0, w=[[1]]) assert_raises(TypeError, ch.chebfit, [1], [1], 0, w=[1,1]) # Test fit x = np.linspace(0,2) y = f(x) # coef3 = ch.chebfit(x, y, 3) assert_equal(len(coef3), 4) assert_almost_equal(ch.chebval(x, coef3), y) # coef4 = ch.chebfit(x, y, 4) assert_equal(len(coef4), 5) assert_almost_equal(ch.chebval(x, coef4), y) # coef2d = ch.chebfit(x, np.array([y,y]).T, 3) assert_almost_equal(coef2d, np.array([coef3,coef3]).T) # test weighting w = np.zeros_like(x) yw = y.copy() w[1::2] = 1 y[0::2] = 0 wcoef3 = ch.chebfit(x, yw, 3, w=w) assert_almost_equal(wcoef3, coef3) # wcoef2d = ch.chebfit(x, np.array([yw,yw]).T, 3, w=w) assert_almost_equal(wcoef2d, np.array([coef3,coef3]).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_almost_equal(ch.cheb2poly([0]*i + [1]), Tlist[i]) def test_poly2cheb(self) : for i in range(10) : assert_almost_equal(ch.poly2cheb(Tlist[i]), [0]*i + [1]) def test_chebpts1(self): #test exceptions assert_raises(ValueError, ch.chebpts1, 1.5) assert_raises(ValueError, ch.chebpts1, 0) #test points tgt = [0] assert_almost_equal(ch.chebpts1(1), tgt) tgt = [-0.70710678118654746, 0.70710678118654746] assert_almost_equal(ch.chebpts1(2), tgt) tgt = [-0.86602540378443871, 0, 0.86602540378443871] assert_almost_equal(ch.chebpts1(3), tgt) tgt = [-0.9238795325, -0.3826834323, 0.3826834323, 0.9238795325] assert_almost_equal(ch.chebpts1(4), tgt) def test_chebpts2(self): #test exceptions assert_raises(ValueError, ch.chebpts2, 1.5) assert_raises(ValueError, ch.chebpts2, 1) #test points tgt = [-1, 1] assert_almost_equal(ch.chebpts2(2), tgt) tgt = [-1, 0, 1] assert_almost_equal(ch.chebpts2(3), tgt) tgt = [-1, -0.5, .5, 1] assert_almost_equal(ch.chebpts2(4), tgt) tgt = [-1.0, -0.707106781187, 0, 0.707106781187, 1.0] assert_almost_equal(ch.chebpts2(5), tgt) 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_degree(self) : assert_equal(self.p1.degree(), 2) def test_trimdeg(self) : assert_raises(ValueError, self.p1.cutdeg, .5) assert_raises(ValueError, self.p1.cutdeg, -1) assert_equal(len(self.p1.cutdeg(3)), 3) assert_equal(len(self.p1.cutdeg(2)), 3) assert_equal(len(self.p1.cutdeg(1)), 2) assert_equal(len(self.p1.cutdeg(0)), 1) 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, .5) 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_linspace(self): xdes = np.linspace(0, 1, 20) ydes = self.p2(xdes) xres, yres = self.p2.linspace(20) assert_almost_equal(xres, xdes) assert_almost_equal(yres, ydes) 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) # test default value of domain p = ch.Chebyshev.fit(x, y, 3) assert_almost_equal(p.domain, [0,3]) # test that fit works in given domains p = ch.Chebyshev.fit(x, y, 3, None) assert_almost_equal(p(x), y) assert_almost_equal(p.domain, [0,3]) p = ch.Chebyshev.fit(x, y, 3, []) assert_almost_equal(p(x), y) assert_almost_equal(p.domain, [-1, 1]) # test that fit accepts weights. w = np.zeros_like(x) yw = y.copy() w[1::2] = 1 yw[0::2] = 0 p = ch.Chebyshev.fit(x, yw, 3, w=w) assert_almost_equal(p(x), y) 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)