tmp
/
pip-install-ghxuqwgs
/numpy_78e94bf2b6094bf9a1f3d92042f9bf46
/numpy
/polynomial
/tests
/test_classes.py
"""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() | |