Chris@87: """Tests for chebyshev module.
Chris@87: 
Chris@87: """
Chris@87: from __future__ import division, absolute_import, print_function
Chris@87: 
Chris@87: import numpy as np
Chris@87: import numpy.polynomial.chebyshev as cheb
Chris@87: from numpy.polynomial.polynomial import polyval
Chris@87: from numpy.testing import (
Chris@87:     TestCase, assert_almost_equal, assert_raises,
Chris@87:     assert_equal, assert_, run_module_suite)
Chris@87: 
Chris@87: 
Chris@87: def trim(x):
Chris@87:     return cheb.chebtrim(x, tol=1e-6)
Chris@87: 
Chris@87: T0 = [1]
Chris@87: T1 = [0, 1]
Chris@87: T2 = [-1, 0, 2]
Chris@87: T3 = [0, -3, 0, 4]
Chris@87: T4 = [1, 0, -8, 0, 8]
Chris@87: T5 = [0, 5, 0, -20, 0, 16]
Chris@87: T6 = [-1, 0, 18, 0, -48, 0, 32]
Chris@87: T7 = [0, -7, 0, 56, 0, -112, 0, 64]
Chris@87: T8 = [1, 0, -32, 0, 160, 0, -256, 0, 128]
Chris@87: T9 = [0, 9, 0, -120, 0, 432, 0, -576, 0, 256]
Chris@87: 
Chris@87: Tlist = [T0, T1, T2, T3, T4, T5, T6, T7, T8, T9]
Chris@87: 
Chris@87: 
Chris@87: class TestPrivate(TestCase):
Chris@87: 
Chris@87:     def test__cseries_to_zseries(self):
Chris@87:         for i in range(5):
Chris@87:             inp = np.array([2] + [1]*i, np.double)
Chris@87:             tgt = np.array([.5]*i + [2] + [.5]*i, np.double)
Chris@87:             res = cheb._cseries_to_zseries(inp)
Chris@87:             assert_equal(res, tgt)
Chris@87: 
Chris@87:     def test__zseries_to_cseries(self):
Chris@87:         for i in range(5):
Chris@87:             inp = np.array([.5]*i + [2] + [.5]*i, np.double)
Chris@87:             tgt = np.array([2] + [1]*i, np.double)
Chris@87:             res = cheb._zseries_to_cseries(inp)
Chris@87:             assert_equal(res, tgt)
Chris@87: 
Chris@87: 
Chris@87: class TestConstants(TestCase):
Chris@87: 
Chris@87:     def test_chebdomain(self):
Chris@87:         assert_equal(cheb.chebdomain, [-1, 1])
Chris@87: 
Chris@87:     def test_chebzero(self):
Chris@87:         assert_equal(cheb.chebzero, [0])
Chris@87: 
Chris@87:     def test_chebone(self):
Chris@87:         assert_equal(cheb.chebone, [1])
Chris@87: 
Chris@87:     def test_chebx(self):
Chris@87:         assert_equal(cheb.chebx, [0, 1])
Chris@87: 
Chris@87: 
Chris@87: class TestArithmetic(TestCase):
Chris@87: 
Chris@87:     def test_chebadd(self):
Chris@87:         for i in range(5):
Chris@87:             for j in range(5):
Chris@87:                 msg = "At i=%d, j=%d" % (i, j)
Chris@87:                 tgt = np.zeros(max(i, j) + 1)
Chris@87:                 tgt[i] += 1
Chris@87:                 tgt[j] += 1
Chris@87:                 res = cheb.chebadd([0]*i + [1], [0]*j + [1])
Chris@87:                 assert_equal(trim(res), trim(tgt), err_msg=msg)
Chris@87: 
Chris@87:     def test_chebsub(self):
Chris@87:         for i in range(5):
Chris@87:             for j in range(5):
Chris@87:                 msg = "At i=%d, j=%d" % (i, j)
Chris@87:                 tgt = np.zeros(max(i, j) + 1)
Chris@87:                 tgt[i] += 1
Chris@87:                 tgt[j] -= 1
Chris@87:                 res = cheb.chebsub([0]*i + [1], [0]*j + [1])
Chris@87:                 assert_equal(trim(res), trim(tgt), err_msg=msg)
Chris@87: 
Chris@87:     def test_chebmulx(self):
Chris@87:         assert_equal(cheb.chebmulx([0]), [0])
Chris@87:         assert_equal(cheb.chebmulx([1]), [0, 1])
Chris@87:         for i in range(1, 5):
Chris@87:             ser = [0]*i + [1]
Chris@87:             tgt = [0]*(i - 1) + [.5, 0, .5]
Chris@87:             assert_equal(cheb.chebmulx(ser), tgt)
Chris@87: 
Chris@87:     def test_chebmul(self):
Chris@87:         for i in range(5):
Chris@87:             for j in range(5):
Chris@87:                 msg = "At i=%d, j=%d" % (i, j)
Chris@87:                 tgt = np.zeros(i + j + 1)
Chris@87:                 tgt[i + j] += .5
Chris@87:                 tgt[abs(i - j)] += .5
Chris@87:                 res = cheb.chebmul([0]*i + [1], [0]*j + [1])
Chris@87:                 assert_equal(trim(res), trim(tgt), err_msg=msg)
Chris@87: 
Chris@87:     def test_chebdiv(self):
Chris@87:         for i in range(5):
Chris@87:             for j in range(5):
Chris@87:                 msg = "At i=%d, j=%d" % (i, j)
Chris@87:                 ci = [0]*i + [1]
Chris@87:                 cj = [0]*j + [1]
Chris@87:                 tgt = cheb.chebadd(ci, cj)
Chris@87:                 quo, rem = cheb.chebdiv(tgt, ci)
Chris@87:                 res = cheb.chebadd(cheb.chebmul(quo, ci), rem)
Chris@87:                 assert_equal(trim(res), trim(tgt), err_msg=msg)
Chris@87: 
Chris@87: 
Chris@87: class TestEvaluation(TestCase):
Chris@87:     # coefficients of 1 + 2*x + 3*x**2
Chris@87:     c1d = np.array([2.5, 2., 1.5])
Chris@87:     c2d = np.einsum('i,j->ij', c1d, c1d)
Chris@87:     c3d = np.einsum('i,j,k->ijk', c1d, c1d, c1d)
Chris@87: 
Chris@87:     # some random values in [-1, 1)
Chris@87:     x = np.random.random((3, 5))*2 - 1
Chris@87:     y = polyval(x, [1., 2., 3.])
Chris@87: 
Chris@87:     def test_chebval(self):
Chris@87:         #check empty input
Chris@87:         assert_equal(cheb.chebval([], [1]).size, 0)
Chris@87: 
Chris@87:         #check normal input)
Chris@87:         x = np.linspace(-1, 1)
Chris@87:         y = [polyval(x, c) for c in Tlist]
Chris@87:         for i in range(10):
Chris@87:             msg = "At i=%d" % i
Chris@87:             tgt = y[i]
Chris@87:             res = cheb.chebval(x, [0]*i + [1])
Chris@87:             assert_almost_equal(res, tgt, err_msg=msg)
Chris@87: 
Chris@87:         #check that shape is preserved
Chris@87:         for i in range(3):
Chris@87:             dims = [2]*i
Chris@87:             x = np.zeros(dims)
Chris@87:             assert_equal(cheb.chebval(x, [1]).shape, dims)
Chris@87:             assert_equal(cheb.chebval(x, [1, 0]).shape, dims)
Chris@87:             assert_equal(cheb.chebval(x, [1, 0, 0]).shape, dims)
Chris@87: 
Chris@87:     def test_chebval2d(self):
Chris@87:         x1, x2, x3 = self.x
Chris@87:         y1, y2, y3 = self.y
Chris@87: 
Chris@87:         #test exceptions
Chris@87:         assert_raises(ValueError, cheb.chebval2d, x1, x2[:2], self.c2d)
Chris@87: 
Chris@87:         #test values
Chris@87:         tgt = y1*y2
Chris@87:         res = cheb.chebval2d(x1, x2, self.c2d)
Chris@87:         assert_almost_equal(res, tgt)
Chris@87: 
Chris@87:         #test shape
Chris@87:         z = np.ones((2, 3))
Chris@87:         res = cheb.chebval2d(z, z, self.c2d)
Chris@87:         assert_(res.shape == (2, 3))
Chris@87: 
Chris@87:     def test_chebval3d(self):
Chris@87:         x1, x2, x3 = self.x
Chris@87:         y1, y2, y3 = self.y
Chris@87: 
Chris@87:         #test exceptions
Chris@87:         assert_raises(ValueError, cheb.chebval3d, x1, x2, x3[:2], self.c3d)
Chris@87: 
Chris@87:         #test values
Chris@87:         tgt = y1*y2*y3
Chris@87:         res = cheb.chebval3d(x1, x2, x3, self.c3d)
Chris@87:         assert_almost_equal(res, tgt)
Chris@87: 
Chris@87:         #test shape
Chris@87:         z = np.ones((2, 3))
Chris@87:         res = cheb.chebval3d(z, z, z, self.c3d)
Chris@87:         assert_(res.shape == (2, 3))
Chris@87: 
Chris@87:     def test_chebgrid2d(self):
Chris@87:         x1, x2, x3 = self.x
Chris@87:         y1, y2, y3 = self.y
Chris@87: 
Chris@87:         #test values
Chris@87:         tgt = np.einsum('i,j->ij', y1, y2)
Chris@87:         res = cheb.chebgrid2d(x1, x2, self.c2d)
Chris@87:         assert_almost_equal(res, tgt)
Chris@87: 
Chris@87:         #test shape
Chris@87:         z = np.ones((2, 3))
Chris@87:         res = cheb.chebgrid2d(z, z, self.c2d)
Chris@87:         assert_(res.shape == (2, 3)*2)
Chris@87: 
Chris@87:     def test_chebgrid3d(self):
Chris@87:         x1, x2, x3 = self.x
Chris@87:         y1, y2, y3 = self.y
Chris@87: 
Chris@87:         #test values
Chris@87:         tgt = np.einsum('i,j,k->ijk', y1, y2, y3)
Chris@87:         res = cheb.chebgrid3d(x1, x2, x3, self.c3d)
Chris@87:         assert_almost_equal(res, tgt)
Chris@87: 
Chris@87:         #test shape
Chris@87:         z = np.ones((2, 3))
Chris@87:         res = cheb.chebgrid3d(z, z, z, self.c3d)
Chris@87:         assert_(res.shape == (2, 3)*3)
Chris@87: 
Chris@87: 
Chris@87: class TestIntegral(TestCase):
Chris@87: 
Chris@87:     def test_chebint(self):
Chris@87:         # check exceptions
Chris@87:         assert_raises(ValueError, cheb.chebint, [0], .5)
Chris@87:         assert_raises(ValueError, cheb.chebint, [0], -1)
Chris@87:         assert_raises(ValueError, cheb.chebint, [0], 1, [0, 0])
Chris@87: 
Chris@87:         # test integration of zero polynomial
Chris@87:         for i in range(2, 5):
Chris@87:             k = [0]*(i - 2) + [1]
Chris@87:             res = cheb.chebint([0], m=i, k=k)
Chris@87:             assert_almost_equal(res, [0, 1])
Chris@87: 
Chris@87:         # check single integration with integration constant
Chris@87:         for i in range(5):
Chris@87:             scl = i + 1
Chris@87:             pol = [0]*i + [1]
Chris@87:             tgt = [i] + [0]*i + [1/scl]
Chris@87:             chebpol = cheb.poly2cheb(pol)
Chris@87:             chebint = cheb.chebint(chebpol, m=1, k=[i])
Chris@87:             res = cheb.cheb2poly(chebint)
Chris@87:             assert_almost_equal(trim(res), trim(tgt))
Chris@87: 
Chris@87:         # check single integration with integration constant and lbnd
Chris@87:         for i in range(5):
Chris@87:             scl = i + 1
Chris@87:             pol = [0]*i + [1]
Chris@87:             chebpol = cheb.poly2cheb(pol)
Chris@87:             chebint = cheb.chebint(chebpol, m=1, k=[i], lbnd=-1)
Chris@87:             assert_almost_equal(cheb.chebval(-1, chebint), i)
Chris@87: 
Chris@87:         # check single integration with integration constant and scaling
Chris@87:         for i in range(5):
Chris@87:             scl = i + 1
Chris@87:             pol = [0]*i + [1]
Chris@87:             tgt = [i] + [0]*i + [2/scl]
Chris@87:             chebpol = cheb.poly2cheb(pol)
Chris@87:             chebint = cheb.chebint(chebpol, m=1, k=[i], scl=2)
Chris@87:             res = cheb.cheb2poly(chebint)
Chris@87:             assert_almost_equal(trim(res), trim(tgt))
Chris@87: 
Chris@87:         # check multiple integrations with default k
Chris@87:         for i in range(5):
Chris@87:             for j in range(2, 5):
Chris@87:                 pol = [0]*i + [1]
Chris@87:                 tgt = pol[:]
Chris@87:                 for k in range(j):
Chris@87:                     tgt = cheb.chebint(tgt, m=1)
Chris@87:                 res = cheb.chebint(pol, m=j)
Chris@87:                 assert_almost_equal(trim(res), trim(tgt))
Chris@87: 
Chris@87:         # check multiple integrations with defined k
Chris@87:         for i in range(5):
Chris@87:             for j in range(2, 5):
Chris@87:                 pol = [0]*i + [1]
Chris@87:                 tgt = pol[:]
Chris@87:                 for k in range(j):
Chris@87:                     tgt = cheb.chebint(tgt, m=1, k=[k])
Chris@87:                 res = cheb.chebint(pol, m=j, k=list(range(j)))
Chris@87:                 assert_almost_equal(trim(res), trim(tgt))
Chris@87: 
Chris@87:         # check multiple integrations with lbnd
Chris@87:         for i in range(5):
Chris@87:             for j in range(2, 5):
Chris@87:                 pol = [0]*i + [1]
Chris@87:                 tgt = pol[:]
Chris@87:                 for k in range(j):
Chris@87:                     tgt = cheb.chebint(tgt, m=1, k=[k], lbnd=-1)
Chris@87:                 res = cheb.chebint(pol, m=j, k=list(range(j)), lbnd=-1)
Chris@87:                 assert_almost_equal(trim(res), trim(tgt))
Chris@87: 
Chris@87:         # check multiple integrations with scaling
Chris@87:         for i in range(5):
Chris@87:             for j in range(2, 5):
Chris@87:                 pol = [0]*i + [1]
Chris@87:                 tgt = pol[:]
Chris@87:                 for k in range(j):
Chris@87:                     tgt = cheb.chebint(tgt, m=1, k=[k], scl=2)
Chris@87:                 res = cheb.chebint(pol, m=j, k=list(range(j)), scl=2)
Chris@87:                 assert_almost_equal(trim(res), trim(tgt))
Chris@87: 
Chris@87:     def test_chebint_axis(self):
Chris@87:         # check that axis keyword works
Chris@87:         c2d = np.random.random((3, 4))
Chris@87: 
Chris@87:         tgt = np.vstack([cheb.chebint(c) for c in c2d.T]).T
Chris@87:         res = cheb.chebint(c2d, axis=0)
Chris@87:         assert_almost_equal(res, tgt)
Chris@87: 
Chris@87:         tgt = np.vstack([cheb.chebint(c) for c in c2d])
Chris@87:         res = cheb.chebint(c2d, axis=1)
Chris@87:         assert_almost_equal(res, tgt)
Chris@87: 
Chris@87:         tgt = np.vstack([cheb.chebint(c, k=3) for c in c2d])
Chris@87:         res = cheb.chebint(c2d, k=3, axis=1)
Chris@87:         assert_almost_equal(res, tgt)
Chris@87: 
Chris@87: 
Chris@87: class TestDerivative(TestCase):
Chris@87: 
Chris@87:     def test_chebder(self):
Chris@87:         # check exceptions
Chris@87:         assert_raises(ValueError, cheb.chebder, [0], .5)
Chris@87:         assert_raises(ValueError, cheb.chebder, [0], -1)
Chris@87: 
Chris@87:         # check that zeroth deriviative does nothing
Chris@87:         for i in range(5):
Chris@87:             tgt = [0]*i + [1]
Chris@87:             res = cheb.chebder(tgt, m=0)
Chris@87:             assert_equal(trim(res), trim(tgt))
Chris@87: 
Chris@87:         # check that derivation is the inverse of integration
Chris@87:         for i in range(5):
Chris@87:             for j in range(2, 5):
Chris@87:                 tgt = [0]*i + [1]
Chris@87:                 res = cheb.chebder(cheb.chebint(tgt, m=j), m=j)
Chris@87:                 assert_almost_equal(trim(res), trim(tgt))
Chris@87: 
Chris@87:         # check derivation with scaling
Chris@87:         for i in range(5):
Chris@87:             for j in range(2, 5):
Chris@87:                 tgt = [0]*i + [1]
Chris@87:                 res = cheb.chebder(cheb.chebint(tgt, m=j, scl=2), m=j, scl=.5)
Chris@87:                 assert_almost_equal(trim(res), trim(tgt))
Chris@87: 
Chris@87:     def test_chebder_axis(self):
Chris@87:         # check that axis keyword works
Chris@87:         c2d = np.random.random((3, 4))
Chris@87: 
Chris@87:         tgt = np.vstack([cheb.chebder(c) for c in c2d.T]).T
Chris@87:         res = cheb.chebder(c2d, axis=0)
Chris@87:         assert_almost_equal(res, tgt)
Chris@87: 
Chris@87:         tgt = np.vstack([cheb.chebder(c) for c in c2d])
Chris@87:         res = cheb.chebder(c2d, axis=1)
Chris@87:         assert_almost_equal(res, tgt)
Chris@87: 
Chris@87: 
Chris@87: class TestVander(TestCase):
Chris@87:     # some random values in [-1, 1)
Chris@87:     x = np.random.random((3, 5))*2 - 1
Chris@87: 
Chris@87:     def test_chebvander(self):
Chris@87:         # check for 1d x
Chris@87:         x = np.arange(3)
Chris@87:         v = cheb.chebvander(x, 3)
Chris@87:         assert_(v.shape == (3, 4))
Chris@87:         for i in range(4):
Chris@87:             coef = [0]*i + [1]
Chris@87:             assert_almost_equal(v[..., i], cheb.chebval(x, coef))
Chris@87: 
Chris@87:         # check for 2d x
Chris@87:         x = np.array([[1, 2], [3, 4], [5, 6]])
Chris@87:         v = cheb.chebvander(x, 3)
Chris@87:         assert_(v.shape == (3, 2, 4))
Chris@87:         for i in range(4):
Chris@87:             coef = [0]*i + [1]
Chris@87:             assert_almost_equal(v[..., i], cheb.chebval(x, coef))
Chris@87: 
Chris@87:     def test_chebvander2d(self):
Chris@87:         # also tests chebval2d for non-square coefficient array
Chris@87:         x1, x2, x3 = self.x
Chris@87:         c = np.random.random((2, 3))
Chris@87:         van = cheb.chebvander2d(x1, x2, [1, 2])
Chris@87:         tgt = cheb.chebval2d(x1, x2, c)
Chris@87:         res = np.dot(van, c.flat)
Chris@87:         assert_almost_equal(res, tgt)
Chris@87: 
Chris@87:         # check shape
Chris@87:         van = cheb.chebvander2d([x1], [x2], [1, 2])
Chris@87:         assert_(van.shape == (1, 5, 6))
Chris@87: 
Chris@87:     def test_chebvander3d(self):
Chris@87:         # also tests chebval3d for non-square coefficient array
Chris@87:         x1, x2, x3 = self.x
Chris@87:         c = np.random.random((2, 3, 4))
Chris@87:         van = cheb.chebvander3d(x1, x2, x3, [1, 2, 3])
Chris@87:         tgt = cheb.chebval3d(x1, x2, x3, c)
Chris@87:         res = np.dot(van, c.flat)
Chris@87:         assert_almost_equal(res, tgt)
Chris@87: 
Chris@87:         # check shape
Chris@87:         van = cheb.chebvander3d([x1], [x2], [x3], [1, 2, 3])
Chris@87:         assert_(van.shape == (1, 5, 24))
Chris@87: 
Chris@87: 
Chris@87: class TestFitting(TestCase):
Chris@87: 
Chris@87:     def test_chebfit(self):
Chris@87:         def f(x):
Chris@87:             return x*(x - 1)*(x - 2)
Chris@87: 
Chris@87:         # Test exceptions
Chris@87:         assert_raises(ValueError, cheb.chebfit, [1], [1], -1)
Chris@87:         assert_raises(TypeError, cheb.chebfit, [[1]], [1], 0)
Chris@87:         assert_raises(TypeError, cheb.chebfit, [], [1], 0)
Chris@87:         assert_raises(TypeError, cheb.chebfit, [1], [[[1]]], 0)
Chris@87:         assert_raises(TypeError, cheb.chebfit, [1, 2], [1], 0)
Chris@87:         assert_raises(TypeError, cheb.chebfit, [1], [1, 2], 0)
Chris@87:         assert_raises(TypeError, cheb.chebfit, [1], [1], 0, w=[[1]])
Chris@87:         assert_raises(TypeError, cheb.chebfit, [1], [1], 0, w=[1, 1])
Chris@87: 
Chris@87:         # Test fit
Chris@87:         x = np.linspace(0, 2)
Chris@87:         y = f(x)
Chris@87:         #
Chris@87:         coef3 = cheb.chebfit(x, y, 3)
Chris@87:         assert_equal(len(coef3), 4)
Chris@87:         assert_almost_equal(cheb.chebval(x, coef3), y)
Chris@87:         #
Chris@87:         coef4 = cheb.chebfit(x, y, 4)
Chris@87:         assert_equal(len(coef4), 5)
Chris@87:         assert_almost_equal(cheb.chebval(x, coef4), y)
Chris@87:         #
Chris@87:         coef2d = cheb.chebfit(x, np.array([y, y]).T, 3)
Chris@87:         assert_almost_equal(coef2d, np.array([coef3, coef3]).T)
Chris@87:         # test weighting
Chris@87:         w = np.zeros_like(x)
Chris@87:         yw = y.copy()
Chris@87:         w[1::2] = 1
Chris@87:         y[0::2] = 0
Chris@87:         wcoef3 = cheb.chebfit(x, yw, 3, w=w)
Chris@87:         assert_almost_equal(wcoef3, coef3)
Chris@87:         #
Chris@87:         wcoef2d = cheb.chebfit(x, np.array([yw, yw]).T, 3, w=w)
Chris@87:         assert_almost_equal(wcoef2d, np.array([coef3, coef3]).T)
Chris@87:         # test scaling with complex values x points whose square
Chris@87:         # is zero when summed.
Chris@87:         x = [1, 1j, -1, -1j]
Chris@87:         assert_almost_equal(cheb.chebfit(x, x, 1), [0, 1])
Chris@87: 
Chris@87: 
Chris@87: class TestCompanion(TestCase):
Chris@87: 
Chris@87:     def test_raises(self):
Chris@87:         assert_raises(ValueError, cheb.chebcompanion, [])
Chris@87:         assert_raises(ValueError, cheb.chebcompanion, [1])
Chris@87: 
Chris@87:     def test_dimensions(self):
Chris@87:         for i in range(1, 5):
Chris@87:             coef = [0]*i + [1]
Chris@87:             assert_(cheb.chebcompanion(coef).shape == (i, i))
Chris@87: 
Chris@87:     def test_linear_root(self):
Chris@87:         assert_(cheb.chebcompanion([1, 2])[0, 0] == -.5)
Chris@87: 
Chris@87: 
Chris@87: class TestGauss(TestCase):
Chris@87: 
Chris@87:     def test_100(self):
Chris@87:         x, w = cheb.chebgauss(100)
Chris@87: 
Chris@87:         # test orthogonality. Note that the results need to be normalized,
Chris@87:         # otherwise the huge values that can arise from fast growing
Chris@87:         # functions like Laguerre can be very confusing.
Chris@87:         v = cheb.chebvander(x, 99)
Chris@87:         vv = np.dot(v.T * w, v)
Chris@87:         vd = 1/np.sqrt(vv.diagonal())
Chris@87:         vv = vd[:, None] * vv * vd
Chris@87:         assert_almost_equal(vv, np.eye(100))
Chris@87: 
Chris@87:         # check that the integral of 1 is correct
Chris@87:         tgt = np.pi
Chris@87:         assert_almost_equal(w.sum(), tgt)
Chris@87: 
Chris@87: 
Chris@87: class TestMisc(TestCase):
Chris@87: 
Chris@87:     def test_chebfromroots(self):
Chris@87:         res = cheb.chebfromroots([])
Chris@87:         assert_almost_equal(trim(res), [1])
Chris@87:         for i in range(1, 5):
Chris@87:             roots = np.cos(np.linspace(-np.pi, 0, 2*i + 1)[1::2])
Chris@87:             tgt = [0]*i + [1]
Chris@87:             res = cheb.chebfromroots(roots)*2**(i-1)
Chris@87:             assert_almost_equal(trim(res), trim(tgt))
Chris@87: 
Chris@87:     def test_chebroots(self):
Chris@87:         assert_almost_equal(cheb.chebroots([1]), [])
Chris@87:         assert_almost_equal(cheb.chebroots([1, 2]), [-.5])
Chris@87:         for i in range(2, 5):
Chris@87:             tgt = np.linspace(-1, 1, i)
Chris@87:             res = cheb.chebroots(cheb.chebfromroots(tgt))
Chris@87:             assert_almost_equal(trim(res), trim(tgt))
Chris@87: 
Chris@87:     def test_chebtrim(self):
Chris@87:         coef = [2, -1, 1, 0]
Chris@87: 
Chris@87:         # Test exceptions
Chris@87:         assert_raises(ValueError, cheb.chebtrim, coef, -1)
Chris@87: 
Chris@87:         # Test results
Chris@87:         assert_equal(cheb.chebtrim(coef), coef[:-1])
Chris@87:         assert_equal(cheb.chebtrim(coef, 1), coef[:-3])
Chris@87:         assert_equal(cheb.chebtrim(coef, 2), [0])
Chris@87: 
Chris@87:     def test_chebline(self):
Chris@87:         assert_equal(cheb.chebline(3, 4), [3, 4])
Chris@87: 
Chris@87:     def test_cheb2poly(self):
Chris@87:         for i in range(10):
Chris@87:             assert_almost_equal(cheb.cheb2poly([0]*i + [1]), Tlist[i])
Chris@87: 
Chris@87:     def test_poly2cheb(self):
Chris@87:         for i in range(10):
Chris@87:             assert_almost_equal(cheb.poly2cheb(Tlist[i]), [0]*i + [1])
Chris@87: 
Chris@87:     def test_weight(self):
Chris@87:         x = np.linspace(-1, 1, 11)[1:-1]
Chris@87:         tgt = 1./(np.sqrt(1 + x) * np.sqrt(1 - x))
Chris@87:         res = cheb.chebweight(x)
Chris@87:         assert_almost_equal(res, tgt)
Chris@87: 
Chris@87:     def test_chebpts1(self):
Chris@87:         #test exceptions
Chris@87:         assert_raises(ValueError, cheb.chebpts1, 1.5)
Chris@87:         assert_raises(ValueError, cheb.chebpts1, 0)
Chris@87: 
Chris@87:         #test points
Chris@87:         tgt = [0]
Chris@87:         assert_almost_equal(cheb.chebpts1(1), tgt)
Chris@87:         tgt = [-0.70710678118654746, 0.70710678118654746]
Chris@87:         assert_almost_equal(cheb.chebpts1(2), tgt)
Chris@87:         tgt = [-0.86602540378443871, 0, 0.86602540378443871]
Chris@87:         assert_almost_equal(cheb.chebpts1(3), tgt)
Chris@87:         tgt = [-0.9238795325, -0.3826834323, 0.3826834323, 0.9238795325]
Chris@87:         assert_almost_equal(cheb.chebpts1(4), tgt)
Chris@87: 
Chris@87:     def test_chebpts2(self):
Chris@87:         #test exceptions
Chris@87:         assert_raises(ValueError, cheb.chebpts2, 1.5)
Chris@87:         assert_raises(ValueError, cheb.chebpts2, 1)
Chris@87: 
Chris@87:         #test points
Chris@87:         tgt = [-1, 1]
Chris@87:         assert_almost_equal(cheb.chebpts2(2), tgt)
Chris@87:         tgt = [-1, 0, 1]
Chris@87:         assert_almost_equal(cheb.chebpts2(3), tgt)
Chris@87:         tgt = [-1, -0.5, .5, 1]
Chris@87:         assert_almost_equal(cheb.chebpts2(4), tgt)
Chris@87:         tgt = [-1.0, -0.707106781187, 0, 0.707106781187, 1.0]
Chris@87:         assert_almost_equal(cheb.chebpts2(5), tgt)
Chris@87: 
Chris@87: if __name__ == "__main__":
Chris@87:     run_module_suite()