"""Tests for laguerre module.
"""
from functools import reduce
import numpy as np
import numpy.polynomial.laguerre as lag
from numpy.polynomial.polynomial import polyval
from numpy.testing import (
assert_almost_equal, assert_raises, assert_equal, assert_,
)
L0 = np.array([1])/1
L1 = np.array([1, -1])/1
L2 = np.array([2, -4, 1])/2
L3 = np.array([6, -18, 9, -1])/6
L4 = np.array([24, -96, 72, -16, 1])/24
L5 = np.array([120, -600, 600, -200, 25, -1])/120
L6 = np.array([720, -4320, 5400, -2400, 450, -36, 1])/720
Llist = [L0, L1, L2, L3, L4, L5, L6]
def trim(x):
return lag.lagtrim(x, tol=1e-6)
class TestConstants:
def test_lagdomain(self):
assert_equal(lag.lagdomain, [0, 1])
def test_lagzero(self):
assert_equal(lag.lagzero, [0])
def test_lagone(self):
assert_equal(lag.lagone, [1])
def test_lagx(self):
assert_equal(lag.lagx, [1, -1])
class TestArithmetic:
x = np.linspace(-3, 3, 100)
def test_lagadd(self):
for i in range(5):
for j in range(5):
msg = f"At i={i}, j={j}"
tgt = np.zeros(max(i, j) + 1)
tgt[i] += 1
tgt[j] += 1
res = lag.lagadd([0]*i + [1], [0]*j + [1])
assert_equal(trim(res), trim(tgt), err_msg=msg)
def test_lagsub(self):
for i in range(5):
for j in range(5):
msg = f"At i={i}, j={j}"
tgt = np.zeros(max(i, j) + 1)
tgt[i] += 1
tgt[j] -= 1
res = lag.lagsub([0]*i + [1], [0]*j + [1])
assert_equal(trim(res), trim(tgt), err_msg=msg)
def test_lagmulx(self):
assert_equal(lag.lagmulx([0]), [0])
assert_equal(lag.lagmulx([1]), [1, -1])
for i in range(1, 5):
ser = [0]*i + [1]
tgt = [0]*(i - 1) + [-i, 2*i + 1, -(i + 1)]
assert_almost_equal(lag.lagmulx(ser), tgt)
def test_lagmul(self):
# check values of result
for i in range(5):
pol1 = [0]*i + [1]
val1 = lag.lagval(self.x, pol1)
for j in range(5):
msg = f"At i={i}, j={j}"
pol2 = [0]*j + [1]
val2 = lag.lagval(self.x, pol2)
pol3 = lag.lagmul(pol1, pol2)
val3 = lag.lagval(self.x, pol3)
assert_(len(pol3) == i + j + 1, msg)
assert_almost_equal(val3, val1*val2, err_msg=msg)
def test_lagdiv(self):
for i in range(5):
for j in range(5):
msg = f"At i={i}, j={j}"
ci = [0]*i + [1]
cj = [0]*j + [1]
tgt = lag.lagadd(ci, cj)
quo, rem = lag.lagdiv(tgt, ci)
res = lag.lagadd(lag.lagmul(quo, ci), rem)
assert_almost_equal(trim(res), trim(tgt), err_msg=msg)
def test_lagpow(self):
for i in range(5):
for j in range(5):
msg = f"At i={i}, j={j}"
c = np.arange(i + 1)
tgt = reduce(lag.lagmul, [c]*j, np.array([1]))
res = lag.lagpow(c, j)
assert_equal(trim(res), trim(tgt), err_msg=msg)
class TestEvaluation:
# coefficients of 1 + 2*x + 3*x**2
c1d = np.array([9., -14., 6.])
c2d = np.einsum('i,j->ij', c1d, c1d)
c3d = np.einsum('i,j,k->ijk', c1d, c1d, c1d)
# some random values in [-1, 1)
x = np.random.random((3, 5))*2 - 1
y = polyval(x, [1., 2., 3.])
def test_lagval(self):
#check empty input
assert_equal(lag.lagval([], [1]).size, 0)
#check normal input)
x = np.linspace(-1, 1)
y = [polyval(x, c) for c in Llist]
for i in range(7):
msg = f"At i={i}"
tgt = y[i]
res = lag.lagval(x, [0]*i + [1])
assert_almost_equal(res, tgt, err_msg=msg)
#check that shape is preserved
for i in range(3):
dims = [2]*i
x = np.zeros(dims)
assert_equal(lag.lagval(x, [1]).shape, dims)
assert_equal(lag.lagval(x, [1, 0]).shape, dims)
assert_equal(lag.lagval(x, [1, 0, 0]).shape, dims)
def test_lagval2d(self):
x1, x2, x3 = self.x
y1, y2, y3 = self.y
#test exceptions
assert_raises(ValueError, lag.lagval2d, x1, x2[:2], self.c2d)
#test values
tgt = y1*y2
res = lag.lagval2d(x1, x2, self.c2d)
assert_almost_equal(res, tgt)
#test shape
z = np.ones((2, 3))
res = lag.lagval2d(z, z, self.c2d)
assert_(res.shape == (2, 3))
def test_lagval3d(self):
x1, x2, x3 = self.x
y1, y2, y3 = self.y
#test exceptions
assert_raises(ValueError, lag.lagval3d, x1, x2, x3[:2], self.c3d)
#test values
tgt = y1*y2*y3
res = lag.lagval3d(x1, x2, x3, self.c3d)
assert_almost_equal(res, tgt)
#test shape
z = np.ones((2, 3))
res = lag.lagval3d(z, z, z, self.c3d)
assert_(res.shape == (2, 3))
def test_laggrid2d(self):
x1, x2, x3 = self.x
y1, y2, y3 = self.y
#test values
tgt = np.einsum('i,j->ij', y1, y2)
res = lag.laggrid2d(x1, x2, self.c2d)
assert_almost_equal(res, tgt)
#test shape
z = np.ones((2, 3))
res = lag.laggrid2d(z, z, self.c2d)
assert_(res.shape == (2, 3)*2)
def test_laggrid3d(self):
x1, x2, x3 = self.x
y1, y2, y3 = self.y
#test values
tgt = np.einsum('i,j,k->ijk', y1, y2, y3)
res = lag.laggrid3d(x1, x2, x3, self.c3d)
assert_almost_equal(res, tgt)
#test shape
z = np.ones((2, 3))
res = lag.laggrid3d(z, z, z, self.c3d)
assert_(res.shape == (2, 3)*3)
class TestIntegral:
def test_lagint(self):
# check exceptions
assert_raises(TypeError, lag.lagint, [0], .5)
assert_raises(ValueError, lag.lagint, [0], -1)
assert_raises(ValueError, lag.lagint, [0], 1, [0, 0])
assert_raises(ValueError, lag.lagint, [0], lbnd=[0])
assert_raises(ValueError, lag.lagint, [0], scl=[0])
assert_raises(TypeError, lag.lagint, [0], axis=.5)
# test integration of zero polynomial
for i in range(2, 5):
k = [0]*(i - 2) + [1]
res = lag.lagint([0], m=i, k=k)
assert_almost_equal(res, [1, -1])
# check single integration with integration constant
for i in range(5):
scl = i + 1
pol = [0]*i + [1]
tgt = [i] + [0]*i + [1/scl]
lagpol = lag.poly2lag(pol)
lagint = lag.lagint(lagpol, m=1, k=[i])
res = lag.lag2poly(lagint)
assert_almost_equal(trim(res), trim(tgt))
# check single integration with integration constant and lbnd
for i in range(5):
scl = i + 1
pol = [0]*i + [1]
lagpol = lag.poly2lag(pol)
lagint = lag.lagint(lagpol, m=1, k=[i], lbnd=-1)
assert_almost_equal(lag.lagval(-1, lagint), i)
# check single integration with integration constant and scaling
for i in range(5):
scl = i + 1
pol = [0]*i + [1]
tgt = [i] + [0]*i + [2/scl]
lagpol = lag.poly2lag(pol)
lagint = lag.lagint(lagpol, m=1, k=[i], scl=2)
res = lag.lag2poly(lagint)
assert_almost_equal(trim(res), trim(tgt))
# check multiple integrations with default k
for i in range(5):
for j in range(2, 5):
pol = [0]*i + [1]
tgt = pol[:]
for k in range(j):
tgt = lag.lagint(tgt, m=1)
res = lag.lagint(pol, m=j)
assert_almost_equal(trim(res), trim(tgt))
# check multiple integrations with defined k
for i in range(5):
for j in range(2, 5):
pol = [0]*i + [1]
tgt = pol[:]
for k in range(j):
tgt = lag.lagint(tgt, m=1, k=[k])
res = lag.lagint(pol, m=j, k=list(range(j)))
assert_almost_equal(trim(res), trim(tgt))
# check multiple integrations with lbnd
for i in range(5):
for j in range(2, 5):
pol = [0]*i + [1]
tgt = pol[:]
for k in range(j):
tgt = lag.lagint(tgt, m=1, k=[k], lbnd=-1)
res = lag.lagint(pol, m=j, k=list(range(j)), lbnd=-1)
assert_almost_equal(trim(res), trim(tgt))
# check multiple integrations with scaling
for i in range(5):
for j in range(2, 5):
pol = [0]*i + [1]
tgt = pol[:]
for k in range(j):
tgt = lag.lagint(tgt, m=1, k=[k], scl=2)
res = lag.lagint(pol, m=j, k=list(range(j)), scl=2)
assert_almost_equal(trim(res), trim(tgt))
def test_lagint_axis(self):
# check that axis keyword works
c2d = np.random.random((3, 4))
tgt = np.vstack([lag.lagint(c) for c in c2d.T]).T
res = lag.lagint(c2d, axis=0)
assert_almost_equal(res, tgt)
tgt = np.vstack([lag.lagint(c) for c in c2d])
res = lag.lagint(c2d, axis=1)
assert_almost_equal(res, tgt)
tgt = np.vstack([lag.lagint(c, k=3) for c in c2d])
res = lag.lagint(c2d, k=3, axis=1)
assert_almost_equal(res, tgt)
class TestDerivative:
def test_lagder(self):
# check exceptions
assert_raises(TypeError, lag.lagder, [0], .5)
assert_raises(ValueError, lag.lagder, [0], -1)
# check that zeroth derivative does nothing
for i in range(5):
tgt = [0]*i + [1]
res = lag.lagder(tgt, m=0)
assert_equal(trim(res), trim(tgt))
# check that derivation is the inverse of integration
for i in range(5):
for j in range(2, 5):
tgt = [0]*i + [1]
res = lag.lagder(lag.lagint(tgt, m=j), m=j)
assert_almost_equal(trim(res), trim(tgt))
# check derivation with scaling
for i in range(5):
for j in range(2, 5):
tgt = [0]*i + [1]
res = lag.lagder(lag.lagint(tgt, m=j, scl=2), m=j, scl=.5)
assert_almost_equal(trim(res), trim(tgt))
def test_lagder_axis(self):
# check that axis keyword works
c2d = np.random.random((3, 4))
tgt = np.vstack([lag.lagder(c) for c in c2d.T]).T
res = lag.lagder(c2d, axis=0)
assert_almost_equal(res, tgt)
tgt = np.vstack([lag.lagder(c) for c in c2d])
res = lag.lagder(c2d, axis=1)
assert_almost_equal(res, tgt)
class TestVander:
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