"""Test inter-conversion of different polynomial classes. This tests the convert and cast methods of all the polynomial classes. """ from __future__ import division import numpy as np from numpy.polynomial import ( Polynomial, Legendre, Chebyshev, Laguerre, Hermite, HermiteE) from numpy.testing import ( TestCase, assert_almost_equal, assert_raises, assert_equal, assert_, run_module_suite, dec) from numpy.testing.noseclasses import KnownFailure classes = ( Polynomial, Legendre, Chebyshev, Laguerre, Hermite, HermiteE) def test_class_methods(): for Poly1 in classes: for Poly2 in classes: yield check_conversion, Poly1, Poly2 yield check_cast, Poly1, Poly2 for Poly in classes: yield check_call, Poly yield check_identity, Poly yield check_basis, Poly yield check_fromroots, Poly yield check_fit, Poly yield check_equal, Poly yield check_not_equal, Poly yield check_add, Poly yield check_sub, Poly yield check_mul, Poly yield check_floordiv, Poly yield check_mod, Poly yield check_divmod, Poly yield check_pow, Poly yield check_integ, Poly yield check_deriv, Poly yield check_roots, Poly yield check_linspace, Poly yield check_mapparms, Poly yield check_degree, Poly yield check_copy, Poly yield check_cutdeg, Poly yield check_truncate, Poly yield check_trim, Poly # # helper functions # random = np.random.random def assert_poly_almost_equal(p1, p2, msg=""): try: assert_(np.all(p1.domain == p2.domain)) assert_(np.all(p1.window == p2.window)) assert_almost_equal(p1.coef, p2.coef) except AssertionError: msg = "Result: %s\nTarget: %s", (p1, p2) raise AssertionError(msg) # # conversion methods that depend on two classes # def check_conversion(Poly1, Poly2): x = np.linspace(0, 1, 10) coef = random((3,)) d1 = Poly1.domain + random((2,))*.25 w1 = Poly1.window + random((2,))*.25 p1 = Poly1(coef, domain=d1, window=w1) d2 = Poly2.domain + random((2,))*.25 w2 = Poly2.window + random((2,))*.25 p2 = p1.convert(kind=Poly2, domain=d2, window=w2) assert_almost_equal(p2.domain, d2) assert_almost_equal(p2.window, w2) assert_almost_equal(p2(x), p1(x)) def check_cast(Poly1, Poly2): x = np.linspace(0, 1, 10) coef = random((3,)) d1 = Poly1.domain + random((2,))*.25 w1 = Poly1.window + random((2,))*.25 p1 = Poly1(coef, domain=d1, window=w1) d2 = Poly2.domain + random((2,))*.25 w2 = Poly2.window + random((2,))*.25 p2 = Poly2.cast(p1, domain=d2, window=w2) assert_almost_equal(p2.domain, d2) assert_almost_equal(p2.window, w2) assert_almost_equal(p2(x), p1(x)) # # methods that depend on one class # def check_identity(Poly) : d = Poly.domain + random((2,))*.25 w = Poly.window + random((2,))*.25 x = np.linspace(d[0], d[1], 11) p = Poly.identity(domain=d, window=w) assert_equal(p.domain, d) assert_equal(p.window, w) assert_almost_equal(p(x), x) def check_basis(Poly): d = Poly.domain + random((2,))*.25 w = Poly.window + random((2,))*.25 p = Poly.basis(5, domain=d, window=w) assert_equal(p.domain, d) assert_equal(p.window, w) assert_equal(p.coef, [0]*5 + [1]) def check_fromroots(Poly): # check that requested roots are zeros of a polynomial # of correct degree, domain, and window. d = Poly.domain + random((2,))*.25 w = Poly.window + random((2,))*.25 r = random((5,)) p1 = Poly.fromroots(r, domain=d, window=w) assert_equal(p1.degree(), len(r)) assert_equal(p1.domain, d) assert_equal(p1.window, w) assert_almost_equal(p1(r), 0) # check that polynomial is monic p2 = Polynomial.cast(p1, domain=d, window=w) assert_almost_equal(p2.coef[-1], 1) def check_fit(Poly) : def f(x) : return x*(x - 1)*(x - 2) x = np.linspace(0,3) y = f(x) # check default value of domain and window p = Poly.fit(x, y, 3) assert_almost_equal(p.domain, [0,3]) assert_almost_equal(p(x), y) assert_equal(p.degree(), 3) # check with given domains and window d = Poly.domain + random((2,))*.25 w = Poly.window + random((2,))*.25 p = Poly.fit(x, y, 3, domain=d, window=w) assert_almost_equal(p(x), y) assert_almost_equal(p.domain, d) assert_almost_equal(p.window, w) # check with class domain default p = Poly.fit(x, y, 3, []) assert_equal(p.domain, Poly.domain) assert_equal(p.window, Poly.window) # check that fit accepts weights. w = np.zeros_like(x) z = y + random(y.shape)*.25 w[::2] = 1 p1 = Poly.fit(x[::2], z[::2], 3) p2 = Poly.fit(x, z, 3, w=w) assert_almost_equal(p1(x), p2(x)) def check_equal(Poly) : p1 = Poly([1, 2, 3], domain=[0, 1], window=[2, 3]) p2 = Poly([1, 1, 1], domain=[0, 1], window=[2, 3]) p3 = Poly([1, 2, 3], domain=[1, 2], window=[2, 3]) p4 = Poly([1, 2, 3], domain=[0, 1], window=[1, 2]) assert_(p1 == p1) assert_(not p1 == p2) assert_(not p1 == p3) assert_(not p1 == p4) def check_not_equal(Poly) : p1 = Poly([1, 2, 3], domain=[0, 1], window=[2, 3]) p2 = Poly([1, 1, 1], domain=[0, 1], window=[2, 3]) p3 = Poly([1, 2, 3], domain=[1, 2], window=[2, 3]) p4 = Poly([1, 2, 3], domain=[0, 1], window=[1, 2]) assert_(not p1 != p1) assert_(p1 != p2) assert_(p1 != p3) assert_(p1 != p4) def check_add(Poly) : # This checks commutation, not numerical correctness c1 = list(random((4,)) + .5) c2 = list(random((3,)) + .5) p1 = Poly(c1) p2 = Poly(c2) p3 = p1 + p2 assert_poly_almost_equal(p2 + p1, p3) assert_poly_almost_equal(p1 + c2, p3) assert_poly_almost_equal(c2 + p1, p3) assert_poly_almost_equal(p1 + tuple(c2), p3) assert_poly_almost_equal(tuple(c2) + p1, p3) assert_poly_almost_equal(p1 + np.array(c2), p3) assert_poly_almost_equal(np.array(c2) + p1, p3) assert_raises(TypeError, p1.__add__, Poly([0], domain=Poly.domain + 1)) assert_raises(TypeError, p1.__add__, Poly([0], window=Poly.window + 1)) if Poly is Polynomial: assert_raises(TypeError, p1.__add__, Chebyshev([0])) else: assert_raises(TypeError, p1.__add__, Polynomial([0])) def check_sub(Poly) : # This checks commutation, not numerical correctness c1 = list(random((4,)) + .5) c2 = list(random((3,)) + .5) p1 = Poly(c1) p2 = Poly(c2) p3 = p1 - p2 assert_poly_almost_equal(p2 - p1, -p3) assert_poly_almost_equal(p1 - c2, p3) assert_poly_almost_equal(c2 - p1, -p3) assert_poly_almost_equal(p1 - tuple(c2), p3) assert_poly_almost_equal(tuple(c2) - p1, -p3) assert_poly_almost_equal(p1 - np.array(c2), p3) assert_poly_almost_equal(np.array(c2) - p1, -p3) assert_raises(TypeError, p1.__sub__, Poly([0], domain=Poly.domain + 1)) assert_raises(TypeError, p1.__sub__, Poly([0], window=Poly.window + 1)) if Poly is Polynomial: assert_raises(TypeError, p1.__sub__, Chebyshev([0])) else: assert_raises(TypeError, p1.__sub__, Polynomial([0])) def check_mul(Poly) : c1 = list(random((4,)) + .5) c2 = list(random((3,)) + .5) p1 = Poly(c1) p2 = Poly(c2) p3 = p1 * p2 assert_poly_almost_equal(p2 * p1, p3) assert_poly_almost_equal(p1 * c2, p3) assert_poly_almost_equal(c2 * p1, p3) assert_poly_almost_equal(p1 * tuple(c2), p3) assert_poly_almost_equal(tuple(c2) * p1, p3) assert_poly_almost_equal(p1 * np.array(c2), p3) assert_poly_almost_equal(np.array(c2) * p1, p3) assert_poly_almost_equal(p1 * 2, p1 * Poly([2])) assert_poly_almost_equal(2 * p1, p1 * Poly([2])) assert_raises(TypeError, p1.__mul__, Poly([0], domain=Poly.domain + 1)) assert_raises(TypeError, p1.__mul__, Poly([0], window=Poly.window + 1)) if Poly is Polynomial: assert_raises(TypeError, p1.__mul__, Chebyshev([0])) else: assert_raises(TypeError, p1.__mul__, Polynomial([0])) def check_floordiv(Poly) : c1 = list(random((4,)) + .5) c2 = list(random((3,)) + .5) c3 = list(random((2,)) + .5) p1 = Poly(c1) p2 = Poly(c2) p3 = Poly(c3) p4 = p1 * p2 + p3 c4 = list(p4.coef) assert_poly_almost_equal(p4 // p2, p1) assert_poly_almost_equal(p4 // c2, p1) assert_poly_almost_equal(c4 // p2, p1) assert_poly_almost_equal(p4 // tuple(c2), p1) assert_poly_almost_equal(tuple(c4) // p2, p1) assert_poly_almost_equal(p4 // np.array(c2), p1) assert_poly_almost_equal(np.array(c4) // p2, p1) assert_poly_almost_equal(2 // p2, Poly([0])) assert_poly_almost_equal(p2 // 2, 0.5*p2) assert_raises(TypeError, p1.__floordiv__, Poly([0], domain=Poly.domain + 1)) assert_raises(TypeError, p1.__floordiv__, Poly([0], window=Poly.window + 1)) if Poly is Polynomial: assert_raises(TypeError, p1.__floordiv__, Chebyshev([0])) else: assert_raises(TypeError, p1.__floordiv__, Polynomial([0])) def check_mod(Poly) : # This checks commutation, not numerical correctness c1 = list(random((4,)) + .5) c2 = list(random((3,)) + .5) c3 = list(random((2,)) + .5) p1 = Poly(c1) p2 = Poly(c2) p3 = Poly(c3) p4 = p1 * p2 + p3 c4 = list(p4.coef) assert_poly_almost_equal(p4 % p2, p3) assert_poly_almost_equal(p4 % c2, p3) assert_poly_almost_equal(c4 % p2, p3) assert_poly_almost_equal(p4 % tuple(c2), p3) assert_poly_almost_equal(tuple(c4) % p2, p3) assert_poly_almost_equal(p4 % np.array(c2), p3) assert_poly_almost_equal(np.array(c4) % p2, p3) assert_poly_almost_equal(2 % p2, Poly([2])) assert_poly_almost_equal(p2 % 2, Poly([0])) assert_raises(TypeError, p1.__mod__, Poly([0], domain=Poly.domain + 1)) assert_raises(TypeError, p1.__mod__, Poly([0], window=Poly.window + 1)) if Poly is Polynomial: assert_raises(TypeError, p1.__mod__, Chebyshev([0])) else: assert_raises(TypeError, p1.__mod__, Polynomial([0])) def check_divmod(Poly) : # This checks commutation, not numerical correctness c1 = list(random((4,)) + .5) c2 = list(random((3,)) + .5) c3 = list(random((2,)) + .5) p1 = Poly(c1) p2 = Poly(c2) p3 = Poly(c3) p4 = p1 * p2 + p3 c4 = list(p4.coef) quo, rem = divmod(p4, p2) assert_poly_almost_equal(quo, p1) assert_poly_almost_equal(rem, p3) quo, rem = divmod(p4, c2) assert_poly_almost_equal(quo, p1) assert_poly_almost_equal(rem, p3) quo, rem = divmod(c4, p2) assert_poly_almost_equal(quo, p1) assert_poly_almost_equal(rem, p3) quo, rem = divmod(p4, tuple(c2)) assert_poly_almost_equal(quo, p1) assert_poly_almost_equal(rem, p3) quo, rem = divmod(tuple(c4), p2) assert_poly_almost_equal(quo, p1) assert_poly_almost_equal(rem, p3) quo, rem = divmod(p4, np.array(c2)) assert_poly_almost_equal(quo, p1) assert_poly_almost_equal(rem, p3) quo, rem = divmod(np.array(c4), p2) assert_poly_almost_equal(quo, p1) assert_poly_almost_equal(rem, p3) quo, rem = divmod(p2, 2) assert_poly_almost_equal(quo, 0.5*p2) assert_poly_almost_equal(rem, Poly([0])) quo, rem = divmod(2, p2) assert_poly_almost_equal(quo, Poly([0])) assert_poly_almost_equal(rem, Poly([2])) assert_raises(TypeError, divmod, p1, Poly([0], domain=Poly.domain + 1)) assert_raises(TypeError, divmod, p1, Poly([0], window=Poly.window + 1)) if Poly is Polynomial: assert_raises(TypeError, divmod, p1, Chebyshev([0])) else: assert_raises(TypeError, divmod, p1, Polynomial([0])) def check_roots(Poly): d = Poly.domain + random((2,))*.25 w = Poly.window + random((2,))*.25 tgt = np.sort(random((5,))) res = np.sort(Poly.fromroots(tgt).roots()) assert_almost_equal(res, tgt) def check_degree(Poly): p = Poly.basis(5) assert_equal(p.degree(), 5) def check_copy(Poly): p1 = Poly.basis(5) p2 = p1.copy() assert_(p1 == p2) assert_(p1 is not p2) assert_(p1.coef is not p2.coef) assert_(p1.domain is not p2.domain) assert_(p1.window is not p2.window) def check_integ(Poly) : P = Polynomial # Check defaults p0 = Poly.cast(P([1*2, 2*3, 3*4])) p1 = P.cast(p0.integ()) p2 = P.cast(p0.integ(2)) assert_poly_almost_equal(p1, P([0, 2, 3, 4])) assert_poly_almost_equal(p2, P([0, 0, 1, 1, 1])) # Check with k p0 = Poly.cast(P([1*2, 2*3, 3*4])) p1 = P.cast(p0.integ(k=1)) p2 = P.cast(p0.integ(2, k=[1, 1])) assert_poly_almost_equal(p1, P([1, 2, 3, 4])) assert_poly_almost_equal(p2, P([1, 1, 1, 1, 1])) # Check with lbnd p0 = Poly.cast(P([1*2, 2*3, 3*4])) p1 = P.cast(p0.integ(lbnd=1)) p2 = P.cast(p0.integ(2, lbnd=1)) assert_poly_almost_equal(p1, P([-9, 2, 3, 4])) assert_poly_almost_equal(p2, P([6, -9, 1, 1, 1])) # Check scaling d = 2*Poly.domain p0 = Poly.cast(P([1*2, 2*3, 3*4]), domain=d) p1 = P.cast(p0.integ()) p2 = P.cast(p0.integ(2)) assert_poly_almost_equal(p1, P([0, 2, 3, 4])) assert_poly_almost_equal(p2, P([0, 0, 1, 1, 1])) def check_deriv(Poly): # Check that the derivative is the inverse of integration. It is # assumes that the integration has been checked elsewhere. d = Poly.domain + random((2,))*.25 w = Poly.window + random((2,))*.25 p1 = Poly([1, 2, 3], domain=d, window=w) p2 = p1.integ(2, k=[1, 2]) p3 = p1.integ(1, k=[1]) assert_almost_equal(p2.deriv(1).coef, p3.coef) assert_almost_equal(p2.deriv(2).coef, p1.coef) def check_linspace(Poly): d = Poly.domain + random((2,))*.25 w = Poly.window + random((2,))*.25 p = Poly([1,2,3], domain=d, window=w) # check default domain xtgt = np.linspace(d[0], d[1], 20) ytgt = p(xtgt) xres, yres = p.linspace(20) assert_almost_equal(xres, xtgt) assert_almost_equal(yres, ytgt) # check specified domain xtgt = np.linspace(0, 2, 20) ytgt = p(xtgt) xres, yres = p.linspace(20, domain=[0, 2]) assert_almost_equal(xres, xtgt) assert_almost_equal(yres, ytgt) def check_pow(Poly) : d = Poly.domain + random((2,))*.25 w = Poly.window + random((2,))*.25 tgt = Poly([1], domain=d, window=d) tst = Poly([1, 2, 3], domain=d, window=d) for i in range(5) : assert_poly_almost_equal(tst**i, tgt) tgt = tgt * tst assert_raises(ValueError, tgt.__pow__, 1.5) assert_raises(ValueError, tgt.__pow__, -1) def check_call(Poly) : P = Polynomial d = Poly.domain x = np.linspace(d[0], d[1], 11) # Check defaults p = Poly.cast(P([1, 2, 3])) tgt = 1 + x*(2 + 3*x) res = p(x) assert_almost_equal(res, tgt) def check_cutdeg(Poly) : p = Poly([1, 2, 3]) assert_raises(ValueError, p.cutdeg, .5) assert_raises(ValueError, p.cutdeg, -1) assert_equal(len(p.cutdeg(3)), 3) assert_equal(len(p.cutdeg(2)), 3) assert_equal(len(p.cutdeg(1)), 2) assert_equal(len(p.cutdeg(0)), 1) def check_truncate(Poly) : p = Poly([1, 2, 3]) assert_raises(ValueError, p.truncate, .5) assert_raises(ValueError, p.truncate, 0) assert_equal(len(p.truncate(4)), 3) assert_equal(len(p.truncate(3)), 3) assert_equal(len(p.truncate(2)), 2) assert_equal(len(p.truncate(1)), 1) def check_trim(Poly) : c = [1, 1e-6, 1e-12, 0] p = Poly(c) assert_equal(p.trim().coef, c[:3]) assert_equal(p.trim(1e-10).coef, c[:2]) assert_equal(p.trim(1e-5).coef, c[:1]) def check_mapparms(Poly) : # check with defaults. Should be identity. d = Poly.domain w = Poly.window p = Poly([1], domain=d, window=w) assert_almost_equal([0, 1], p.mapparms()) # w = 2*d + 1 p = Poly([1], domain=d, window=w) assert_almost_equal([1, 2], p.mapparms()) if __name__ == "__main__": run_module_suite()