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Mini Shell
"""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
yield check_ufunc_override, 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)
p = Poly.fit(x, y, [0, 1, 2, 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)
p = Poly.fit(x, y, [0, 1, 2, 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)
p3 = Poly.fit(x, z, [0, 1, 2, 3], w=w)
assert_almost_equal(p1(x), p2(x))
assert_almost_equal(p2(x), p3(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())
def check_ufunc_override(Poly):
p = Poly([1, 2, 3])
x = np.ones(3)
assert_raises(TypeError, np.add, p, x)
assert_raises(TypeError, np.add, x, p)
if __name__ == "__main__":
run_module_suite()
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