def mat_pow(M, N):
"""Returns matrix M in N-th power using
Chebyshev polinomials of second kind
M – Unimodular matrix
N – power
return = M^N
"""
import numpy as np
from scipy.special import eval_chebyu
p = (M[0,0] + M[1,1])/2
U_m1 = eval_chebyu(N-1, p)
U_m2 = eval_chebyu(N-2, p)
a = M[0,0]*U_m1 - U_m2
b = M[0,1]*U_m1
c = M[1,0]*U_m1
d = M[1,1]*U_m1 - U_m2
X = np.matrix([[a, b],
[c, d]])
return X
def test_chebyshev():
allTrue = True
for order in range(ORDER_MAX):
x = np.random.rand(1).item()
valuePy = sp.eval_chebyt(order, x)
valueCpp = NumCpp.chebyshev_t_Scaler(order, x)
if np.round(valuePy, DECIMALS_ROUND) != np.round(
valueCpp, DECIMALS_ROUND):
allTrue = False
assert allTrue
allTrue = True
for order in range(ORDER_MAX):
shapeInput = np.random.randint(10, 100, [
2,
], dtype=np.uint32)
shape = NumCpp.Shape(*shapeInput)
cArray = NumCpp.NdArray(shape)
x = np.random.rand(*shapeInput)
cArray.setArray(x)
valuePy = sp.eval_chebyt(order, x)
valueCpp = NumCpp.chebyshev_t_Array(order, cArray)
if not np.array_equal(np.round(valuePy, DECIMALS_ROUND),
np.round(valueCpp, DECIMALS_ROUND)):
allTrue = False
assert allTrue
allTrue = True
for order in range(ORDER_MAX):
x = np.random.rand(1).item()
valuePy = sp.eval_chebyu(order, x)
valueCpp = NumCpp.chebyshev_u_Scaler(order, x)
if np.round(valuePy, DECIMALS_ROUND) != np.round(
valueCpp, DECIMALS_ROUND):
allTrue = False
assert allTrue
allTrue = True
for order in range(ORDER_MAX):
shapeInput = np.random.randint(10, 100, [
2,
], dtype=np.uint32)
shape = NumCpp.Shape(*shapeInput)
cArray = NumCpp.NdArray(shape)
x = np.random.rand(*shapeInput)
cArray.setArray(x)
valuePy = sp.eval_chebyu(order, x)
valueCpp = NumCpp.chebyshev_u_Array(order, cArray)
if not np.array_equal(np.round(valuePy, DECIMALS_ROUND),
np.round(valueCpp, DECIMALS_ROUND)):
allTrue = False
assert allTrue
def gradchebyquad(x):
"""
Evaluation of the gradient function of chebyquad
"""
chq = chebyquad_fcn(x)
UM = 4. / len(x) * array([[(i+1) * eval_chebyu(i, 2. * xj - 1.)
for xj in x] for i in xrange(len(x) - 1)])
return dot(chq[1:].reshape((1, -1)), UM).reshape((-1, ))
def test_chebyshev():
if NumCpp.NO_USE_BOOST:
return
for order in range(ORDER_MAX):
x = np.random.rand(1).item()
valuePy = sp.eval_chebyt(order, x)
valueCpp = NumCpp.chebyshev_t_Scaler(order, x)
assert np.round(valuePy,
DECIMALS_ROUND) == np.round(valueCpp, DECIMALS_ROUND)
for order in range(ORDER_MAX):
shapeInput = np.random.randint(10, 100, [
2,
], dtype=np.uint32)
shape = NumCpp.Shape(*shapeInput)
cArray = NumCpp.NdArray(shape)
x = np.random.rand(*shapeInput)
cArray.setArray(x)
valuePy = sp.eval_chebyt(order, x)
valueCpp = NumCpp.chebyshev_t_Array(order, cArray)
assert np.array_equal(np.round(valuePy, DECIMALS_ROUND),
np.round(valueCpp, DECIMALS_ROUND))
for order in range(ORDER_MAX):
x = np.random.rand(1).item()
valuePy = sp.eval_chebyu(order, x)
valueCpp = NumCpp.chebyshev_u_Scaler(order, x)
assert np.round(valuePy,
DECIMALS_ROUND) == np.round(valueCpp, DECIMALS_ROUND)
for order in range(ORDER_MAX):
shapeInput = np.random.randint(10, 100, [
2,
], dtype=np.uint32)
shape = NumCpp.Shape(*shapeInput)
cArray = NumCpp.NdArray(shape)
x = np.random.rand(*shapeInput)
cArray.setArray(x)
valuePy = sp.eval_chebyu(order, x)
valueCpp = NumCpp.chebyshev_u_Array(order, cArray)
assert np.array_equal(np.round(valuePy, DECIMALS_ROUND),
np.round(valueCpp, DECIMALS_ROUND))
def _eval_numpy_(self, n, x):
"""
Evaluate ``self`` using numpy.
EXAMPLES::
sage: import numpy
sage: z = numpy.array([1,2])
sage: z2 = numpy.array([[1,2],[1,2]])
sage: z3 = numpy.array([1,2,3.])
sage: chebyshev_U(1,z)
array([ 2., 4.])
sage: chebyshev_U(1,z2)
array([[ 2., 4.],
[ 2., 4.]])
sage: chebyshev_U(1,z3)
array([ 2., 4., 6.])
sage: chebyshev_U(z,0.1)
array([ 0.2 , -0.96])
"""
from scipy.special import eval_chebyu
return eval_chebyu(n, x)
