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| """Tests for chebyshev module. | |
| """ | |
| from functools import reduce | |
| import numpy as np | |
| import numpy.polynomial.chebyshev as cheb | |
| from numpy.polynomial.polynomial import polyval | |
| from numpy.testing import ( | |
| assert_almost_equal, assert_raises, assert_equal, assert_, | |
| ) | |
| def trim(x): | |
| return cheb.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: | |
| 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 = cheb._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 = cheb._zseries_to_cseries(inp) | |
| assert_equal(res, tgt) | |
| class TestConstants: | |
| def test_chebdomain(self): | |
| assert_equal(cheb.chebdomain, [-1, 1]) | |
| def test_chebzero(self): | |
| assert_equal(cheb.chebzero, [0]) | |
| def test_chebone(self): | |
| assert_equal(cheb.chebone, [1]) | |
| def test_chebx(self): | |
| assert_equal(cheb.chebx, [0, 1]) | |
| class TestArithmetic: | |
| def test_chebadd(self): | |
| for i in range(5): | |
| for j in range(5): | |
| msg = f"At i={i}, j={j}" | |
| tgt = np.zeros(max(i, j) + 1) | |
| tgt[i] += 1 | |
| tgt[j] += 1 | |
| res = cheb.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 = f"At i={i}, j={j}" | |
| tgt = np.zeros(max(i, j) + 1) | |
| tgt[i] += 1 | |
| tgt[j] -= 1 | |
| res = cheb.chebsub([0]*i + [1], [0]*j + [1]) | |
| assert_equal(trim(res), trim(tgt), err_msg=msg) | |
| def test_chebmulx(self): | |
| assert_equal(cheb.chebmulx([0]), [0]) | |
| assert_equal(cheb.chebmulx([1]), [0, 1]) | |
| for i in range(1, 5): | |
| ser = [0]*i + [1] | |
| tgt = [0]*(i - 1) + [.5, 0, .5] | |
| assert_equal(cheb.chebmulx(ser), tgt) | |
| def test_chebmul(self): | |
| for i in range(5): | |
| for j in range(5): | |
| msg = f"At i={i}, j={j}" | |
| tgt = np.zeros(i + j + 1) | |
| tgt[i + j] += .5 | |
| tgt[abs(i - j)] += .5 | |
| res = cheb.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 = f"At i={i}, j={j}" | |
| ci = [0]*i + [1] | |
| cj = [0]*j + [1] | |
| tgt = cheb.chebadd(ci, cj) | |
| quo, rem = cheb.chebdiv(tgt, ci) | |
| res = cheb.chebadd(cheb.chebmul(quo, ci), rem) | |
| assert_equal(trim(res), trim(tgt), err_msg=msg) | |
| def test_chebpow(self): | |
| for i in range(5): | |
| for j in range(5): | |
| msg = f"At i={i}, j={j}" | |
| c = np.arange(i + 1) | |
| tgt = reduce(cheb.chebmul, [c]*j, np.array([1])) | |
| res = cheb.chebpow(c, j) | |
| assert_equal(trim(res), trim(tgt), err_msg=msg) | |
| class TestEvaluation: | |
| # coefficients of 1 + 2*x + 3*x**2 | |
| c1d = np.array([2.5, 2., 1.5]) | |
| c2d = np.einsum('i,j->ij', c1d, c1d) | |
| c3d = np.einsum('i,j,k->ijk', c1d, c1d, c1d) | |
| # some random values in [-1, 1) | |
| x = np.random.random((3, 5))*2 - 1 | |
| y = polyval(x, [1., 2., 3.]) | |
| def test_chebval(self): | |
| #check empty input | |
| assert_equal(cheb.chebval([], [1]).size, 0) | |
| #check normal input) | |
| x = np.linspace(-1, 1) | |
| y = [polyval(x, c) for c in Tlist] | |
| for i in range(10): | |
| msg = f"At i={i}" | |
| tgt = y[i] | |
| res = cheb.chebval(x, [0]*i + [1]) | |
| assert_almost_equal(res, tgt, err_msg=msg) | |
| #check that shape is preserved | |
| for i in range(3): | |
| dims = [2]*i | |
| x = np.zeros(dims) | |
| assert_equal(cheb.chebval(x, [1]).shape, dims) | |
| assert_equal(cheb.chebval(x, [1, 0]).shape, dims) | |
| assert_equal(cheb.chebval(x, [1, 0, 0]).shape, dims) | |
| def test_chebval2d(self): | |
| x1, x2, x3 = self.x | |
| y1, y2, y3 = self.y | |
| #test exceptions | |
| assert_raises(ValueError, cheb.chebval2d, x1, x2[:2], self.c2d) | |
| #test values | |
| tgt = y1*y2 | |
| res = cheb.chebval2d(x1, x2, self.c2d) | |
| assert_almost_equal(res, tgt) | |
| #test shape | |
| z = np.ones((2, 3)) | |
| res = cheb.chebval2d(z, z, self.c2d) | |
| assert_(res.shape == (2, 3)) | |
| def test_chebval3d(self): | |
| x1, x2, x3 = self.x | |
| y1, y2, y3 = self.y | |
| #test exceptions | |
| assert_raises(ValueError, cheb.chebval3d, x1, x2, x3[:2], self.c3d) | |
| #test values | |
| tgt = y1*y2*y3 | |
| res = cheb.chebval3d(x1, x2, x3, self.c3d) | |
| assert_almost_equal(res, tgt) | |
| #test shape | |
| z = np.ones((2, 3)) | |
| res = cheb.chebval3d(z, z, z, self.c3d) | |
| assert_(res.shape == (2, 3)) | |
| def test_chebgrid2d(self): | |
| x1, x2, x3 = self.x | |
| y1, y2, y3 = self.y | |
| #test values | |
| tgt = np.einsum('i,j->ij', y1, y2) | |
| res = cheb.chebgrid2d(x1, x2, self.c2d) | |
| assert_almost_equal(res, tgt) | |
| #test shape | |
| z = np.ones((2, 3)) | |
| res = cheb.chebgrid2d(z, z, self.c2d) | |
| assert_(res.shape == (2, 3)*2) | |
| def test_chebgrid3d(self): | |
| x1, x2, x3 = self.x | |
| y1, y2, y3 = self.y | |
| #test values | |
| tgt = np.einsum('i,j,k->ijk', y1, y2, y3) | |
| res = cheb.chebgrid3d(x1, x2, x3, self.c3d) | |
| assert_almost_equal(res, tgt) | |
| #test shape | |
| z = np.ones((2, 3)) | |
| res = cheb.chebgrid3d(z, z, z, self.c3d) | |
| assert_(res.shape == (2, 3)*3) | |
| class TestIntegral: | |
| def test_chebint(self): | |
| # check exceptions | |
| assert_raises(TypeError, cheb.chebint, [0], .5) | |
| assert_raises(ValueError, cheb.chebint, [0], -1) | |
| assert_raises(ValueError, cheb.chebint, [0], 1, [0, 0]) | |
| assert_raises(ValueError, cheb.chebint, [0], lbnd=[0]) | |
| assert_raises(ValueError, cheb.chebint, [0], scl=[0]) | |
| assert_raises(TypeError, cheb.chebint, [0], axis=.5) | |
| # test integration of zero polynomial | |
| for i in range(2, 5): | |
| k = [0]*(i - 2) + [1] | |
| res = cheb.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 = cheb.poly2cheb(pol) | |
| chebint = cheb.chebint(chebpol, m=1, k=[i]) | |
| res = cheb.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 = cheb.poly2cheb(pol) | |
| chebint = cheb.chebint(chebpol, m=1, k=[i], lbnd=-1) | |
| assert_almost_equal(cheb.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 = cheb.poly2cheb(pol) | |
| chebint = cheb.chebint(chebpol, m=1, k=[i], scl=2) | |
| res = cheb.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 = cheb.chebint(tgt, m=1) | |
| res = cheb.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 = cheb.chebint(tgt, m=1, k=[k]) | |
| res = cheb.chebint(pol, m=j, k=list(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 = cheb.chebint(tgt, m=1, k=[k], lbnd=-1) | |
| res = cheb.chebint(pol, m=j, k=list(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 = cheb.chebint(tgt, m=1, k=[k], scl=2) | |
| res = cheb.chebint(pol, m=j, k=list(range(j)), scl=2) | |
| assert_almost_equal(trim(res), trim(tgt)) | |
| def test_chebint_axis(self): | |
| # check that axis keyword works | |
| c2d = np.random.random((3, 4)) | |
| tgt = np.vstack([cheb.chebint(c) for c in c2d.T]).T | |
| res = cheb.chebint(c2d, axis=0) | |
| assert_almost_equal(res, tgt) | |
| tgt = np.vstack([cheb.chebint(c) for c in c2d]) | |
| res = cheb.chebint(c2d, axis=1) | |
| assert_almost_equal(res, tgt) | |
| tgt = np.vstack([cheb.chebint(c, k=3) for c in c2d]) | |
| res = cheb.chebint(c2d, k=3, axis=1) | |
| assert_almost_equal(res, tgt) | |
| class TestDerivative: | |
| def test_chebder(self): | |
| # check exceptions | |
| assert_raises(TypeError, cheb.chebder, [0], .5) | |
| assert_raises(ValueError, cheb.chebder, [0], -1) | |
| # check that zeroth derivative does nothing | |
| for i in range(5): | |
| tgt = [0]*i + [1] | |
| res = cheb.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 = [0]*i + [1] | |
| res = cheb.chebder(cheb.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 = [0]*i + [1] | |
| res = cheb.chebder(cheb.chebint(tgt, m=j, scl=2), m=j, scl=.5) | |
| assert_almost_equal(trim(res), trim(tgt)) | |
| def test_chebder_axis(self): | |
| # check that axis keyword works | |
| c2d = np.random.random((3, 4)) | |
| tgt = np.vstack([cheb.chebder(c) for c in c2d.T]).T | |
| res = cheb.chebder(c2d, axis=0) | |
| assert_almost_equal(res, tgt) | |
| tgt = np.vstack([cheb.chebder(c) for c in c2d]) | |
| res = cheb.chebder(c2d, axis=1) | |
| assert_almost_equal(res, tgt) | |
| class TestVander: | |
| # some random values in [-1, 1) | |
| x = np.random.random((3, 5))*2 - 1 | |
| def test_chebvander(self): | |
| # check for 1d x | |
| x = np.arange(3) | |
| v = cheb.chebvander(x, 3) | |
| assert_(v.shape == (3, 4)) | |
| for i in range(4): | |
| coef = [0]*i + [1] | |
| assert_almost_equal(v[..., i], cheb.chebval(x, coef)) | |
| # check for 2d x | |
| x = np.array([[1, 2], [3, 4], [5, 6]]) | |
| v = cheb.chebvander(x, 3) | |
| assert_(v.shape == (3, 2, 4)) | |
| for i in range(4): | |
| coef = [0]*i + [1] | |
| assert_almost_equal(v[..., i], cheb.chebval(x, coef)) | |
| def test_chebvander2d(self): | |
| # also tests chebval2d for non-square coefficient array | |
| x1, x2, x3 = self.x | |
| c = np.random.random((2, 3)) | |
| van = cheb.chebvander2d(x1, x2, [1, 2]) | |
| tgt = cheb.chebval2d(x1, x2, c) | |
| res = np.dot(van, c.flat) | |
| assert_almost_equal(res, tgt) | |
| # check shape | |
| van = cheb.chebvander2d([x1], [x2], [1, 2]) | |
| assert_(van.shape == (1, 5, 6)) | |
| def test_chebvander3d(self): | |
| # also tests chebval3d for non-square coefficient array | |
| x1, x2, x3 = self.x | |
| c = np.random.random((2, 3, 4)) | |
| van = cheb.chebvander3d(x1, x2, x3, [1, 2, 3]) | |
| tgt = cheb.chebval3d(x1, x2, x3, c) | |
| res = np.dot(van, c.flat) | |
| assert_almost_equal(res, tgt) | |
| # check shape | |
| van = cheb.chebvander3d([x1], [x2], [x3], [1, 2, 3]) | |
| assert_(van.shape == (1, 5, 24)) | |
| class TestFitting: | |
| def test_chebfit(self): | |
| def f(x): | |
| return x*(x - 1)*(x - 2) | |
| def f2(x): | |
| return x**4 + x**2 + 1 | |
| # Test exceptions | |
| assert_raises(ValueError, cheb.chebfit, [1], [1], -1) | |
| assert_raises(TypeError, cheb.chebfit, [[1]], [1], 0) | |
| assert_raises(TypeError, cheb.chebfit, [], [1], 0) | |
| assert_raises(TypeError, cheb.chebfit, [1], [[[1]]], 0) | |
| assert_raises(TypeError, cheb.chebfit, [1, 2], [1], 0) | |
| assert_raises(TypeError, cheb.chebfit, [1], [1, 2], 0) | |
| assert_raises(TypeError, cheb.chebfit, [1], [1], 0, w=[[1]]) | |
| assert_raises(TypeError, cheb.chebfit, [1], [1], 0, w=[1, 1]) | |
| assert_raises(ValueError, cheb.chebfit, [1], [1], [-1,]) | |
| assert_raises(ValueError, cheb.chebfit, [1], [1], [2, -1, 6]) | |
| assert_raises(TypeError, cheb.chebfit, [1], [1], []) | |
| # Test fit | |
| x = np.linspace(0, 2) | |
| y = f(x) | |
| # | |
| coef3 = cheb.chebfit(x, y, 3) | |
| assert_equal(len(coef3), 4) | |
| assert_almost_equal(cheb.chebval(x, coef3), y) | |
| coef3 = cheb.chebfit(x, y, [0, 1, 2, 3]) | |
| assert_equal(len(coef3), 4) | |
| assert_almost_equal(cheb.chebval(x, coef3), y) | |
| # | |
| coef4 = cheb.chebfit(x, y, 4) | |
| assert_equal(len(coef4), 5) | |
| assert_almost_equal(cheb.chebval(x, coef4), y) | |
| coef4 = cheb.chebfit(x, y, [0, 1, 2, 3, 4]) | |
| assert_equal(len(coef4), 5) | |
| assert_almost_equal(cheb.chebval(x, coef4), y) | |
| # check things still work if deg is not in strict increasing | |
| coef4 = cheb.chebfit(x, y, [2, 3, 4, 1, 0]) | |
| assert_equal(len(coef4), 5) | |
| assert_almost_equal(cheb.chebval(x, coef4), y) | |
| # | |
| coef2d = cheb.chebfit(x, np.array([y, y]).T, 3) | |
| assert_almost_equal(coef2d, np.array([coef3, coef3]).T) | |
| coef2d = cheb.chebfit(x, np.array([y, y]).T, [0, 1, 2, 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 = cheb.chebfit(x, yw, 3, w=w) | |
| assert_almost_equal(wcoef3, coef3) | |
| wcoef3 = cheb.chebfit(x, yw, [0, 1, 2, 3], w=w) | |
| assert_almost_equal(wcoef3, coef3) | |
| # | |
| wcoef2d = cheb.chebfit(x, np.array([yw, yw]).T, 3, w=w) | |
| assert_almost_equal(wcoef2d, np.array([coef3, coef3]).T) | |
| wcoef2d = cheb.chebfit(x, np.array([yw, yw]).T, [0, 1, 2, 3], w=w) | |
| assert_almost_equal(wcoef2d, np.array([coef3, coef3]).T) | |
| # test scaling with complex values x points whose square | |
| # is zero when summed. | |
| x = [1, 1j, -1, -1j] | |
| assert_almost_equal(cheb.chebfit(x, x, 1), [0, 1]) | |
| assert_almost_equal(cheb.chebfit(x, x, [0, 1]), [0, 1]) | |
| # test fitting only even polynomials | |
| x = np.linspace(-1, 1) | |
| y = f2(x) | |
| coef1 = cheb.chebfit(x, y, 4) | |
| assert_almost_equal(cheb.chebval(x, coef1), y) | |
| coef2 = cheb.chebfit(x, y, [0, 2, 4]) | |
| assert_almost_equal(cheb.chebval(x, coef2), y) | |
| assert_almost_equal(coef1, coef2) | |
| class TestInterpolate: | |
| def f(self, x): | |
| return x * (x - 1) * (x - 2) | |
| def test_raises(self): | |
| assert_raises(ValueError, cheb.chebinterpolate, self.f, -1) | |
| assert_raises(TypeError, cheb.chebinterpolate, self.f, 10.) | |
| def test_dimensions(self): | |
| for deg in range(1, 5): | |
| assert_(cheb.chebinterpolate(self.f, deg).shape == (deg + 1,)) | |
| def test_approximation(self): | |
| def powx(x, p): | |
| return x**p | |
| x = np.linspace(-1, 1, 10) | |
| for deg in range(0, 10): | |
| for p in range(0, deg + 1): | |
| c = cheb.chebinterpolate(powx, deg, (p,)) | |
| assert_almost_equal(cheb.chebval(x, c), powx(x, p), decimal=12) | |
| class TestCompanion: | |
| def test_raises(self): | |
| assert_raises(ValueError, cheb.chebcompanion, []) | |
| assert_raises(ValueError, cheb.chebcompanion, [1]) | |
| def test_dimensions(self): | |
| for i in range(1, 5): | |
| coef = [0]*i + [1] | |
| assert_(cheb.chebcompanion(coef).shape == (i, i)) | |
| def test_linear_root(self): | |
| assert_(cheb.chebcompanion([1, 2])[0, 0] == -.5) | |
| class TestGauss: | |
| def test_100(self): | |
| x, w = cheb.chebgauss(100) | |
| # test orthogonality. Note that the results need to be normalized, | |
| # otherwise the huge values that can arise from fast growing | |
| # functions like Laguerre can be very confusing. | |
| v = cheb.chebvander(x, 99) | |
| vv = np.dot(v.T * w, v) | |
| vd = 1/np.sqrt(vv.diagonal()) | |
| vv = vd[:, None] * vv * vd | |
| assert_almost_equal(vv, np.eye(100)) | |
| # check that the integral of 1 is correct | |
| tgt = np.pi | |
| assert_almost_equal(w.sum(), tgt) | |
| class TestMisc: | |
| def test_chebfromroots(self): | |
| res = cheb.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 = cheb.chebfromroots(roots)*2**(i-1) | |
| assert_almost_equal(trim(res), trim(tgt)) | |
| def test_chebroots(self): | |
| assert_almost_equal(cheb.chebroots([1]), []) | |
| assert_almost_equal(cheb.chebroots([1, 2]), [-.5]) | |
| for i in range(2, 5): | |
| tgt = np.linspace(-1, 1, i) | |
| res = cheb.chebroots(cheb.chebfromroots(tgt)) | |
| assert_almost_equal(trim(res), trim(tgt)) | |
| def test_chebtrim(self): | |
| coef = [2, -1, 1, 0] | |
| # Test exceptions | |
| assert_raises(ValueError, cheb.chebtrim, coef, -1) | |
| # Test results | |
| assert_equal(cheb.chebtrim(coef), coef[:-1]) | |
| assert_equal(cheb.chebtrim(coef, 1), coef[:-3]) | |
| assert_equal(cheb.chebtrim(coef, 2), [0]) | |
| def test_chebline(self): | |
| assert_equal(cheb.chebline(3, 4), [3, 4]) | |
| def test_cheb2poly(self): | |
| for i in range(10): | |
| assert_almost_equal(cheb.cheb2poly([0]*i + [1]), Tlist[i]) | |
| def test_poly2cheb(self): | |
| for i in range(10): | |
| assert_almost_equal(cheb.poly2cheb(Tlist[i]), [0]*i + [1]) | |
| def test_weight(self): | |
| x = np.linspace(-1, 1, 11)[1:-1] | |
| tgt = 1./(np.sqrt(1 + x) * np.sqrt(1 - x)) | |
| res = cheb.chebweight(x) | |
| assert_almost_equal(res, tgt) | |
| def test_chebpts1(self): | |
| #test exceptions | |
| assert_raises(ValueError, cheb.chebpts1, 1.5) | |
| assert_raises(ValueError, cheb.chebpts1, 0) | |
| #test points | |
| tgt = [0] | |
| assert_almost_equal(cheb.chebpts1(1), tgt) | |
| tgt = [-0.70710678118654746, 0.70710678118654746] | |
| assert_almost_equal(cheb.chebpts1(2), tgt) | |
| tgt = [-0.86602540378443871, 0, 0.86602540378443871] | |
| assert_almost_equal(cheb.chebpts1(3), tgt) | |
| tgt = [-0.9238795325, -0.3826834323, 0.3826834323, 0.9238795325] | |
| assert_almost_equal(cheb.chebpts1(4), tgt) | |
| def test_chebpts2(self): | |
| #test exceptions | |
| assert_raises(ValueError, cheb.chebpts2, 1.5) | |
| assert_raises(ValueError, cheb.chebpts2, 1) | |
| #test points | |
| tgt = [-1, 1] | |
| assert_almost_equal(cheb.chebpts2(2), tgt) | |
| tgt = [-1, 0, 1] | |
| assert_almost_equal(cheb.chebpts2(3), tgt) | |
| tgt = [-1, -0.5, .5, 1] | |
| assert_almost_equal(cheb.chebpts2(4), tgt) | |
| tgt = [-1.0, -0.707106781187, 0, 0.707106781187, 1.0] | |
| assert_almost_equal(cheb.chebpts2(5), tgt) | |