"""Tests for hermendre module. """ from __future__ import division import numpy as np import numpy.polynomial.hermite as herm import numpy.polynomial.polynomial as poly from numpy.testing import * H0 = np.array([ 1]) H1 = np.array([0, 2]) H2 = np.array([ -2, 0, 4]) H3 = np.array([0, -12, 0, 8]) H4 = np.array([ 12, 0, -48, 0, 16]) H5 = np.array([0, 120, 0, -160, 0, 32]) H6 = np.array([-120, 0, 720, 0, -480, 0, 64]) H7 = np.array([0, -1680, 0, 3360, 0, -1344, 0, 128]) H8 = np.array([1680, 0, -13440, 0, 13440, 0, -3584, 0, 256]) H9 = np.array([0, 30240, 0, -80640, 0, 48384, 0, -9216, 0, 512]) Hlist = [H0, H1, H2, H3, H4, H5, H6, H7, H8, H9] def trim(x) : return herm.hermtrim(x, tol=1e-6) class TestConstants(TestCase) : def test_hermdomain(self) : assert_equal(herm.hermdomain, [-1, 1]) def test_hermzero(self) : assert_equal(herm.hermzero, [0]) def test_hermone(self) : assert_equal(herm.hermone, [1]) def test_hermx(self) : assert_equal(herm.hermx, [0, .5]) class TestArithmetic(TestCase) : x = np.linspace(-3, 3, 100) y0 = poly.polyval(x, H0) y1 = poly.polyval(x, H1) y2 = poly.polyval(x, H2) y3 = poly.polyval(x, H3) y4 = poly.polyval(x, H4) y5 = poly.polyval(x, H5) y6 = poly.polyval(x, H6) y7 = poly.polyval(x, H7) y8 = poly.polyval(x, H8) y9 = poly.polyval(x, H9) y = [y0, y1, y2, y3, y4, y5, y6, y7, y8, y9] def test_hermval(self) : def f(x) : return x*(x**2 - 1) #check empty input assert_equal(herm.hermval([], [1]).size, 0) #check normal input) for i in range(10) : msg = "At i=%d" % i ser = np.zeros tgt = self.y[i] res = herm.hermval(self.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(herm.hermval(x, [1]).shape, dims) assert_equal(herm.hermval(x, [1,0]).shape, dims) assert_equal(herm.hermval(x, [1,0,0]).shape, dims) def test_hermadd(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 = herm.hermadd([0]*i + [1], [0]*j + [1]) assert_equal(trim(res), trim(tgt), err_msg=msg) def test_hermsub(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 = herm.hermsub([0]*i + [1], [0]*j + [1]) assert_equal(trim(res), trim(tgt), err_msg=msg) def test_hermmulx(self): assert_equal(herm.hermmulx([0]), [0]) assert_equal(herm.hermmulx([1]), [0,.5]) for i in range(1, 5): ser = [0]*i + [1] tgt = [0]*(i - 1) + [i, 0, .5] assert_equal(herm.hermmulx(ser), tgt) def test_hermmul(self) : # check values of result for i in range(5) : pol1 = [0]*i + [1] val1 = herm.hermval(self.x, pol1) for j in range(5) : msg = "At i=%d, j=%d" % (i,j) pol2 = [0]*j + [1] val2 = herm.hermval(self.x, pol2) pol3 = herm.hermmul(pol1, pol2) val3 = herm.hermval(self.x, pol3) assert_(len(pol3) == i + j + 1, msg) assert_almost_equal(val3, val1*val2, err_msg=msg) def test_hermdiv(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 = herm.hermadd(ci, cj) quo, rem = herm.hermdiv(tgt, ci) res = herm.hermadd(herm.hermmul(quo, ci), rem) assert_equal(trim(res), trim(tgt), err_msg=msg) class TestCalculus(TestCase) : def test_hermint(self) : # check exceptions assert_raises(ValueError, herm.hermint, [0], .5) assert_raises(ValueError, herm.hermint, [0], -1) assert_raises(ValueError, herm.hermint, [0], 1, [0,0]) # test integration of zero polynomial for i in range(2, 5): k = [0]*(i - 2) + [1] res = herm.hermint([0], m=i, k=k) assert_almost_equal(res, [0, .5]) # check single integration with integration constant for i in range(5) : scl = i + 1 pol = [0]*i + [1] tgt = [i] + [0]*i + [1/scl] hermpol = herm.poly2herm(pol) hermint = herm.hermint(hermpol, m=1, k=[i]) res = herm.herm2poly(hermint) 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] hermpol = herm.poly2herm(pol) hermint = herm.hermint(hermpol, m=1, k=[i], lbnd=-1) assert_almost_equal(herm.hermval(-1, hermint), 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] hermpol = herm.poly2herm(pol) hermint = herm.hermint(hermpol, m=1, k=[i], scl=2) res = herm.herm2poly(hermint) 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 = herm.hermint(tgt, m=1) res = herm.hermint(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 = herm.hermint(tgt, m=1, k=[k]) res = herm.hermint(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 = herm.hermint(tgt, m=1, k=[k], lbnd=-1) res = herm.hermint(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 = herm.hermint(tgt, m=1, k=[k], scl=2) res = herm.hermint(pol, m=j, k=range(j), scl=2) assert_almost_equal(trim(res), trim(tgt)) def test_hermder(self) : # check exceptions assert_raises(ValueError, herm.hermder, [0], .5) assert_raises(ValueError, herm.hermder, [0], -1) # check that zeroth deriviative does nothing for i in range(5) : tgt = [1] + [0]*i res = herm.hermder(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 = herm.hermder(herm.hermint(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 = herm.hermder(herm.hermint(tgt, m=j, scl=2), m=j, scl=.5) assert_almost_equal(trim(res), trim(tgt)) class TestMisc(TestCase) : def test_hermfromroots(self) : res = herm.hermfromroots([]) 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]) pol = herm.hermfromroots(roots) res = herm.hermval(roots, pol) tgt = 0 assert_(len(pol) == i + 1) assert_almost_equal(herm.herm2poly(pol)[-1], 1) assert_almost_equal(res, tgt) def test_hermroots(self) : assert_almost_equal(herm.hermroots([1]), []) assert_almost_equal(herm.hermroots([1, 1]), [-.5]) for i in range(2,5) : tgt = np.linspace(-1, 1, i) res = herm.hermroots(herm.hermfromroots(tgt)) assert_almost_equal(trim(res), trim(tgt)) def test_hermvander(self) : # check for 1d x x = np.arange(3) v = herm.hermvander(x, 3) assert_(v.shape == (3,4)) for i in range(4) : coef = [0]*i + [1] assert_almost_equal(v[...,i], herm.hermval(x, coef)) # check for 2d x x = np.array([[1,2],[3,4],[5,6]]) v = herm.hermvander(x, 3) assert_(v.shape == (3,2,4)) for i in range(4) : coef = [0]*i + [1] assert_almost_equal(v[...,i], herm.hermval(x, coef)) def test_hermfit(self) : def f(x) : return x*(x - 1)*(x - 2) # Test exceptions assert_raises(ValueError, herm.hermfit, [1], [1], -1) assert_raises(TypeError, herm.hermfit, [[1]], [1], 0) assert_raises(TypeError, herm.hermfit, [], [1], 0) assert_raises(TypeError, herm.hermfit, [1], [[[1]]], 0) assert_raises(TypeError, herm.hermfit, [1, 2], [1], 0) assert_raises(TypeError, herm.hermfit, [1], [1, 2], 0) assert_raises(TypeError, herm.hermfit, [1], [1], 0, w=[[1]]) assert_raises(TypeError, herm.hermfit, [1], [1], 0, w=[1,1]) # Test fit x = np.linspace(0,2) y = f(x) # coef3 = herm.hermfit(x, y, 3) assert_equal(len(coef3), 4) assert_almost_equal(herm.hermval(x, coef3), y) # coef4 = herm.hermfit(x, y, 4) assert_equal(len(coef4), 5) assert_almost_equal(herm.hermval(x, coef4), y) # coef2d = herm.hermfit(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 = herm.hermfit(x, yw, 3, w=w) assert_almost_equal(wcoef3, coef3) # wcoef2d = herm.hermfit(x, np.array([yw,yw]).T, 3, w=w) assert_almost_equal(wcoef2d, np.array([coef3,coef3]).T) def test_hermtrim(self) : coef = [2, -1, 1, 0] # Test exceptions assert_raises(ValueError, herm.hermtrim, coef, -1) # Test results assert_equal(herm.hermtrim(coef), coef[:-1]) assert_equal(herm.hermtrim(coef, 1), coef[:-3]) assert_equal(herm.hermtrim(coef, 2), [0]) def test_hermline(self) : assert_equal(herm.hermline(3,4), [3, 2]) def test_herm2poly(self) : for i in range(10) : assert_almost_equal(herm.herm2poly([0]*i + [1]), Hlist[i]) def test_poly2herm(self) : for i in range(10) : assert_almost_equal(herm.poly2herm(Hlist[i]), [0]*i + [1]) def assert_poly_almost_equal(p1, p2): assert_almost_equal(p1.coef, p2.coef) assert_equal(p1.domain, p2.domain) class TestHermiteClass(TestCase) : p1 = herm.Hermite([1,2,3]) p2 = herm.Hermite([1,2,3], [0,1]) p3 = herm.Hermite([1,2]) p4 = herm.Hermite([2,2,3]) p5 = herm.Hermite([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 = herm.Hermite([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 = herm.Hermite([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 = herm.Hermite([ 81., 52., 82., 12., 9.]) assert_poly_almost_equal(self.p1 * self.p1, tgt) assert_poly_almost_equal(self.p1 * [1,2,3], tgt) assert_poly_almost_equal([1,2,3] * self.p1, tgt) def test_floordiv(self) : tgt = herm.Hermite([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 = herm.Hermite([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 = herm.Hermite([1]) trem = herm.Hermite([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 = herm.Hermite([1]) for i in range(5) : res = self.p1**i assert_(res == tgt) tgt = tgt*self.p1 def test_call(self) : # domain = [-1, 1] x = np.linspace(-1, 1) tgt = 3*(4*x**2 - 2) + 2*(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_cutdeg(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 = herm.Hermite(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, herm.hermint([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, herm.hermint([1,2,3], 1, 1, scl=.5)) p = self.p2.integ(2, [1, 2]) assert_almost_equal(p.coef, herm.hermint([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 = herm.Hermite(herm.poly2herm([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 = herm.Hermite.fromroots(roots, domain=[0, 1]) res = p.coef tgt = herm.poly2herm([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 = herm.Hermite.fit(x, y, 3) assert_almost_equal(p.domain, [0,3]) # test that fit works in given domains p = herm.Hermite.fit(x, y, 3, None) assert_almost_equal(p(x), y) assert_almost_equal(p.domain, [0,3]) p = herm.Hermite.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 = herm.Hermite.fit(x, yw, 3, w=w) assert_almost_equal(p(x), y) def test_identity(self) : x = np.linspace(0,3) p = herm.Hermite.identity() assert_almost_equal(p(x), x) p = herm.Hermite.identity([1,3]) assert_almost_equal(p(x), x) # if __name__ == "__main__": run_module_suite()