Mercurial > hg > vamp-build-and-test
diff DEPENDENCIES/mingw32/Python27/Lib/site-packages/numpy/polynomial/tests/test_classes.py @ 87:2a2c65a20a8b
Add Python libs and headers
| author | Chris Cannam |
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| date | Wed, 25 Feb 2015 14:05:22 +0000 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/DEPENDENCIES/mingw32/Python27/Lib/site-packages/numpy/polynomial/tests/test_classes.py Wed Feb 25 14:05:22 2015 +0000 @@ -0,0 +1,570 @@ +"""Test inter-conversion of different polynomial classes. + +This tests the convert and cast methods of all the polynomial classes. + +""" +from __future__ import division, absolute_import, print_function + +import operator as op +from numbers import Number + +import numpy as np +from numpy.polynomial import ( + Polynomial, Legendre, Chebyshev, Laguerre, Hermite, HermiteE) +from numpy.testing import ( + assert_almost_equal, assert_raises, assert_equal, assert_, + run_module_suite) +from numpy.compat import long + + +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_truediv, 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 + pdom = Polynomial.domain + pwin = Polynomial.window + p2 = Polynomial.cast(p1, domain=pdom, window=pwin) + 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, op.add, p1, Poly([0], domain=Poly.domain + 1)) + assert_raises(TypeError, op.add, p1, Poly([0], window=Poly.window + 1)) + if Poly is Polynomial: + assert_raises(TypeError, op.add, p1, Chebyshev([0])) + else: + assert_raises(TypeError, op.add, p1, 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, op.sub, p1, Poly([0], domain=Poly.domain + 1)) + assert_raises(TypeError, op.sub, p1, Poly([0], window=Poly.window + 1)) + if Poly is Polynomial: + assert_raises(TypeError, op.sub, p1, Chebyshev([0])) + else: + assert_raises(TypeError, op.sub, p1, 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, op.mul, p1, Poly([0], domain=Poly.domain + 1)) + assert_raises(TypeError, op.mul, p1, Poly([0], window=Poly.window + 1)) + if Poly is Polynomial: + assert_raises(TypeError, op.mul, p1, Chebyshev([0])) + else: + assert_raises(TypeError, op.mul, p1, 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, op.floordiv, p1, Poly([0], domain=Poly.domain + 1)) + assert_raises( + TypeError, op.floordiv, p1, Poly([0], window=Poly.window + 1)) + if Poly is Polynomial: + assert_raises(TypeError, op.floordiv, p1, Chebyshev([0])) + else: + assert_raises(TypeError, op.floordiv, p1, Polynomial([0])) + + +def check_truediv(Poly): + # true division is valid only if the denominator is a Number and + # not a python bool. + p1 = Poly([1,2,3]) + p2 = p1 * 5 + + for stype in np.ScalarType: + if not issubclass(stype, Number) or issubclass(stype, bool): + continue + s = stype(5) + assert_poly_almost_equal(op.truediv(p2, s), p1) + assert_raises(TypeError, op.truediv, s, p2) + for stype in (int, long, float): + s = stype(5) + assert_poly_almost_equal(op.truediv(p2, s), p1) + assert_raises(TypeError, op.truediv, s, p2) + for stype in [complex]: + s = stype(5, 0) + assert_poly_almost_equal(op.truediv(p2, s), p1) + assert_raises(TypeError, op.truediv, s, p2) + for s in [tuple(), list(), dict(), bool(), np.array([1])]: + assert_raises(TypeError, op.truediv, p2, s) + assert_raises(TypeError, op.truediv, s, p2) + for ptype in classes: + assert_raises(TypeError, op.truediv, p2, ptype(1)) + + +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, op.mod, p1, Poly([0], domain=Poly.domain + 1)) + assert_raises(TypeError, op.mod, p1, Poly([0], window=Poly.window + 1)) + if Poly is Polynomial: + assert_raises(TypeError, op.mod, p1, Chebyshev([0])) + else: + assert_raises(TypeError, op.mod, p1, 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, domain=d, window=w).roots()) + assert_almost_equal(res, tgt) + # default domain and window + 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) + # default domain and window + p1 = Poly([1, 2, 3]) + 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=w) + tst = Poly([1, 2, 3], domain=d, window=w) + for i in range(5): + assert_poly_almost_equal(tst**i, tgt) + tgt = tgt * tst + # default domain and window + tgt = Poly([1]) + tst = Poly([1, 2, 3]) + for i in range(5): + assert_poly_almost_equal(tst**i, tgt) + tgt = tgt * tst + # check error for invalid powers + assert_raises(ValueError, op.pow, tgt, 1.5) + assert_raises(ValueError, op.pow, tgt, -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()