def test_hermemul(self):
# check values of result
for i in range(5):
pol1 = [0] * i + [1]
val1 = herme.hermeval(self.x, pol1)
for j in range(5):
msg = "At i=%d, j=%d" % (i, j)
pol2 = [0] * j + [1]
val2 = herme.hermeval(self.x, pol2)
pol3 = herme.hermemul(pol1, pol2)
val3 = herme.hermeval(self.x, pol3)
assert_(len(pol3) == i + j + 1, msg)
assert_almost_equal(val3, val1 * val2, err_msg=msg)
def test_hermevander(self):
# check for 1d x
x = np.arange(3)
v = herme.hermevander(x, 3)
assert_(v.shape == (3, 4))
for i in range(4):
coef = [0] * i + [1]
assert_almost_equal(v[..., i], herme.hermeval(x, coef))
# check for 2d x
x = np.array([[1, 2], [3, 4], [5, 6]])
v = herme.hermevander(x, 3)
assert_(v.shape == (3, 2, 4))
for i in range(4):
coef = [0] * i + [1]
assert_almost_equal(v[..., i], herme.hermeval(x, coef))
def test_hermefromroots(self):
res = herme.hermefromroots([])
assert_almost_equal(trim(res), [1])
for i in range(1, 5):
roots = np.cos(np.linspace(-np.pi, 0, 2 * i + 1)[1::2])
pol = herme.hermefromroots(roots)
res = herme.hermeval(roots, pol)
tgt = 0
assert_(len(pol) == i + 1)
assert_almost_equal(herme.herme2poly(pol)[-1], 1)
assert_almost_equal(res, tgt)
def test_hermeval(self):
#check empty input
assert_equal(herme.hermeval([], [1]).size, 0)
#check normal input)
x = np.linspace(-1, 1)
y = [polyval(x, c) for c in Helist]
for i in range(10):
msg = "At i=%d" % i
tgt = y[i]
res = herme.hermeval(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(herme.hermeval(x, [1]).shape, dims)
assert_equal(herme.hermeval(x, [1, 0]).shape, dims)
assert_equal(herme.hermeval(x, [1, 0, 0]).shape, dims)
def test_hermefit(self):
def f(x):
return x * (x - 1) * (x - 2)
def f2(x):
return x**4 + x**2 + 1
# Test exceptions
assert_raises(ValueError, herme.hermefit, [1], [1], -1)
assert_raises(TypeError, herme.hermefit, [[1]], [1], 0)
assert_raises(TypeError, herme.hermefit, [], [1], 0)
assert_raises(TypeError, herme.hermefit, [1], [[[1]]], 0)
assert_raises(TypeError, herme.hermefit, [1, 2], [1], 0)
assert_raises(TypeError, herme.hermefit, [1], [1, 2], 0)
assert_raises(TypeError, herme.hermefit, [1], [1], 0, w=[[1]])
assert_raises(TypeError, herme.hermefit, [1], [1], 0, w=[1, 1])
assert_raises(ValueError, herme.hermefit, [1], [1], [
-1,
])
assert_raises(ValueError, herme.hermefit, [1], [1], [2, -1, 6])
assert_raises(TypeError, herme.hermefit, [1], [1], [])
# Test fit
x = np.linspace(0, 2)
y = f(x)
#
coef3 = herme.hermefit(x, y, 3)
assert_equal(len(coef3), 4)
assert_almost_equal(herme.hermeval(x, coef3), y)
coef3 = herme.hermefit(x, y, [0, 1, 2, 3])
assert_equal(len(coef3), 4)
assert_almost_equal(herme.hermeval(x, coef3), y)
#
coef4 = herme.hermefit(x, y, 4)
assert_equal(len(coef4), 5)
assert_almost_equal(herme.hermeval(x, coef4), y)
coef4 = herme.hermefit(x, y, [0, 1, 2, 3, 4])
assert_equal(len(coef4), 5)
assert_almost_equal(herme.hermeval(x, coef4), y)
# check things still work if deg is not in strict increasing
coef4 = herme.hermefit(x, y, [2, 3, 4, 1, 0])
assert_equal(len(coef4), 5)
assert_almost_equal(herme.hermeval(x, coef4), y)
#
coef2d = herme.hermefit(x, np.array([y, y]).T, 3)
assert_almost_equal(coef2d, np.array([coef3, coef3]).T)
coef2d = herme.hermefit(x, np.array([y, y]).T, [0, 1, 2, 3])
assert_almost_equal(coef2d, np.array([coef3, coef3]).T)
# test weighting
w = np.zeros_like(x)
yw = y.copy()
w[1::2] = 1
y[0::2] = 0
wcoef3 = herme.hermefit(x, yw, 3, w=w)
assert_almost_equal(wcoef3, coef3)
wcoef3 = herme.hermefit(x, yw, [0, 1, 2, 3], w=w)
assert_almost_equal(wcoef3, coef3)
#
wcoef2d = herme.hermefit(x, np.array([yw, yw]).T, 3, w=w)
assert_almost_equal(wcoef2d, np.array([coef3, coef3]).T)
wcoef2d = herme.hermefit(x, np.array([yw, yw]).T, [0, 1, 2, 3], w=w)
assert_almost_equal(wcoef2d, np.array([coef3, coef3]).T)
# test scaling with complex values x points whose square
# is zero when summed.
x = [1, 1j, -1, -1j]
assert_almost_equal(herme.hermefit(x, x, 1), [0, 1])
assert_almost_equal(herme.hermefit(x, x, [0, 1]), [0, 1])
# test fitting only even Legendre polynomials
x = np.linspace(-1, 1)
y = f2(x)
coef1 = herme.hermefit(x, y, 4)
assert_almost_equal(herme.hermeval(x, coef1), y)
coef2 = herme.hermefit(x, y, [0, 2, 4])
assert_almost_equal(herme.hermeval(x, coef2), y)
assert_almost_equal(coef1, coef2)
def test_hermeint(self):
# check exceptions
assert_raises(ValueError, herme.hermeint, [0], .5)
assert_raises(ValueError, herme.hermeint, [0], -1)
assert_raises(ValueError, herme.hermeint, [0], 1, [0, 0])
assert_raises(ValueError, herme.hermeint, [0], lbnd=[0])
assert_raises(ValueError, herme.hermeint, [0], scl=[0])
assert_raises(ValueError, herme.hermeint, [0], axis=.5)
# test integration of zero polynomial
for i in range(2, 5):
k = [0] * (i - 2) + [1]
res = herme.hermeint([0], m=i, k=k)
assert_almost_equal(res, [0, 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]
hermepol = herme.poly2herme(pol)
hermeint = herme.hermeint(hermepol, m=1, k=[i])
res = herme.herme2poly(hermeint)
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]
hermepol = herme.poly2herme(pol)
hermeint = herme.hermeint(hermepol, m=1, k=[i], lbnd=-1)
assert_almost_equal(herme.hermeval(-1, hermeint), 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]
hermepol = herme.poly2herme(pol)
hermeint = herme.hermeint(hermepol, m=1, k=[i], scl=2)
res = herme.herme2poly(hermeint)
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 = herme.hermeint(tgt, m=1)
res = herme.hermeint(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 = herme.hermeint(tgt, m=1, k=[k])
res = herme.hermeint(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 = herme.hermeint(tgt, m=1, k=[k], lbnd=-1)
res = herme.hermeint(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 = herme.hermeint(tgt, m=1, k=[k], scl=2)
res = herme.hermeint(pol, m=j, k=list(range(j)), scl=2)
assert_almost_equal(trim(res), trim(tgt))