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"""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)
classes = (
Polynomial, Legendre, Chebyshev, Laguerre,
Hermite, HermiteE)
class TestClassConversions(TestCase):
def test_conversion(self):
x = np.linspace(0, 1, 10)
window = np.array([0, 1])
domain = np.array([0, 1])
for Poly1 in classes:
d1 = domain + np.random.random((2,))*.25
w1 = window + np.random.random((2,))*.25
c1 = np.random.random((3,))
p1 = Poly1(c1, domain=d1, window=w1)
for Poly2 in classes:
msg = "-- %s -> %s" % (Poly1.__name__, Poly2.__name__)
d2 = domain + np.random.random((2,))*.25
w2 = window + np.random.random((2,))*.25
p2 = p1.convert(kind=Poly2, domain=d2, window=w2)
assert_almost_equal(p2.domain, d2, err_msg=msg)
assert_almost_equal(p2.window, w2, err_msg=msg)
assert_almost_equal(p2(x), p1(x), err_msg=msg)
def test_cast(self):
x = np.linspace(0, 1, 10)
window = np.array([0, 1])
domain = np.array([0, 1])
for Poly1 in classes:
d1 = domain + np.random.random((2,))*.25
w1 = window + np.random.random((2,))*.25
c1 = np.random.random((3,))
p1 = Poly1(c1, domain=d1, window=w1)
for Poly2 in classes:
msg = "-- %s -> %s" % (Poly1.__name__, Poly2.__name__)
d2 = domain + np.random.random((2,))*.25
w2 = window + np.random.random((2,))*.25
p2 = Poly2.cast(p1, domain=d2, window=w2)
assert_almost_equal(p2.domain, d2, err_msg=msg)
assert_almost_equal(p2.window, w2, err_msg=msg)
assert_almost_equal(p2(x), p1(x), err_msg=msg)
class TestClasses(TestCase):
def test_basis(self):
window = np.array([0, 1])
domain = np.array([0, 1])
for Poly in classes:
msg = "-- %s" % (Poly.__name__,)
d = domain + np.random.random((2,))*.25
w = window + np.random.random((2,))*.25
p = Poly.basis(5, domain=d, window=w)
assert_equal(p.domain, d, err_msg=msg)
assert_equal(p.window, w, err_msg=msg)
assert_equal(p.coef, [0]*5 + [1])
def test_fromroots(self):
window = np.array([0, 1])
domain = np.array([0, 1])
for Poly in classes:
msg = "-- %s" % (Poly.__name__,)
d = domain + np.random.random((2,))*.25
w = window + np.random.random((2,))*.25
r = np.random.random((5,))
p1 = Poly.fromroots(r, domain=d, window=w)
assert_equal(p1.domain, d, err_msg=msg)
assert_equal(p1.window, w, err_msg=msg)
assert_almost_equal(p1(r), 0, err_msg=msg)
# test monic with same domain and window
p2 = Polynomial.cast(p1, domain=d, window=w)
assert_almost_equal(p2.coef[-1], 1, err_msg=msg)
def test_roots(self):
window = np.array([0, 1])
domain = np.array([0, 1])
for Poly in classes:
msg = "-- %s" % (Poly.__name__,)
d = domain + np.random.random((2,))*.25
w = window + np.random.random((2,))*.25
tgt = np.sort(np.random.random((5,)))
res = np.sort(Poly.fromroots(tgt).roots())
assert_almost_equal(res, tgt, err_msg=msg)
def test_degree(self):
for Poly in classes:
msg = "-- %s" % (Poly.__name__,)
p = Poly.basis(5)
assert_equal(p.degree(), 5, err_msg=msg)
def test_copy(self):
for Poly in classes:
msg = "-- %s" % (Poly.__name__,)
p1 = Poly.basis(5)
p2 = p1.copy()
assert_(p1 == p2, msg)
assert_(p1 is not p2, msg)
assert_(p1.coef is not p2.coef, msg)
assert_(p1.domain is not p2.domain, msg)
assert_(p1.window is not p2.window, msg)
def test_deriv(self):
# Check that the derivative is the inverse of integration. It is
# assumes that the integration has been tested elsewhere.
window = np.array([0, 1])
domain = np.array([0, 1])
for Poly in classes:
msg = "-- %s" % (Poly.__name__,)
d = domain + np.random.random((2,))*.25
w = window + np.random.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, err_msg=msg)
assert_almost_equal(p2.deriv(2).coef, p1.coef, err_msg=msg)
def test_linspace(self):
window = np.array([0, 1])
domain = np.array([0, 1])
for Poly in classes:
msg = "-- %s" % (Poly.__name__,)
d = domain + np.random.random((2,))*.25
w = window + np.random.random((2,))*.25
p = Poly([1,2,3], domain=d, window=w)
# test default domain
xtgt = np.linspace(d[0], d[1], 20)
ytgt = p(xtgt)
xres, yres = p.linspace(20)
assert_almost_equal(xres, xtgt, err_msg=msg)
assert_almost_equal(yres, ytgt, err_msg=msg)
# test specified domain
xtgt = np.linspace(0, 2, 20)
ytgt = p(xtgt)
xres, yres = p.linspace(20, domain=[0, 2])
assert_almost_equal(xres, xtgt, err_msg=msg)
assert_almost_equal(yres, ytgt, err_msg=msg)
def test_fit(self) :
def f(x) :
return x*(x - 1)*(x - 2)
x = np.linspace(0,3)
y = f(x)
window = np.array([0, 1])
domain = np.array([0, 1])
for Poly in classes:
msg = "-- %s" % (Poly.__name__,)
# test default value of domain
p = Poly.fit(x, y, 3)
assert_almost_equal(p.domain, [0,3], err_msg=msg)
assert_almost_equal(p(x), y, err_msg=msg)
assert_equal(p.degree(), 3, err_msg=msg)
# test with given windows and domains
d = domain + np.random.random((2,))*.25
w = window + np.random.random((2,))*.25
p = Poly.fit(x, y, 3, domain=d, window=w)
assert_almost_equal(p(x), y, err_msg=msg)
assert_almost_equal(p.domain, d, err_msg=msg)
assert_almost_equal(p.window, w, err_msg=msg)
# test with class domain default
p = Poly.fit(x, y, 3, [])
assert_equal(p.domain, Poly.domain, err_msg=msg)
assert_equal(p.window, Poly.window, err_msg=msg)
# test that fit accepts weights.
w = np.zeros_like(x)
z = y + np.random.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), err_msg=msg)
if __name__ == "__main__":
run_module_suite()
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