def test_mon_mult_random():
np.random.seed(988)
#test with random matrices
possible_dim = np.random.randint(1,5, (1,10))
dim = possible_dim[0, np.random.randint(1,9)]
shape = list()
for i in range(dim):
shape.append(np.random.randint(2,4))
matrix1 = np.random.randint(1,11,(shape))
M1 = MultiPower(matrix1)
shape2 = list()
for i in range(dim):
shape2.append(np.random.randint(2,4))
matrix2 = np.ones(shape2)
M2 = MultiPower(matrix2)
M3 = M1*M2
for index, i in np.ndenumerate(M2.coeff):
if sum(index) == 0:
M4 = MultiPower.mon_mult(M1, index)
else:
M4 = M4 + MultiPower.mon_mult(M1, index)
if M3.shape != M4.shape:
new_M3_coeff, new_M4_coeff = utils.match_size(M3.coeff,M4.coeff)
else:
new_M3_coeff, new_M4_coeff = M3.coeff, M4.coeff
assert np.allclose(new_M3_coeff, new_M4_coeff)
def reduce_poly(poly, divisors, basisSet, permitted_round_error=1e-10):
'''
Divides a polynomial by a set of divisor polynomials using the standard
multivariate division algorithm and returns the remainder
parameters
----------
poly : polynomial object
the polynomial to be divided by the Groebner basis
divisors : list of polynomial objects
polynomials to divide poly by
basisSet : set of tuples
The monomials that make up a basis for the vector space
returns
-------
polynomial object
the remainder of poly / divisors
'''
remainder_shape = np.maximum.reduce([p.shape for p in divisors])
remainder = np.zeros(remainder_shape)
for term in zip(*np.where(poly.coeff != 0)):
if term in basisSet:
remainder[term] += poly.coeff[term]
poly.coeff[term] = 0
poly.__init__(poly.coeff, clean_zeros=False)
# while poly is not the zero polynomial
while np.any(poly.coeff):
divisible = False
# Go through polynomials in set of divisors
for divisor in divisors:
# If the LT of the divisor divides the LT of poly
if divides(divisor.lead_term, poly.lead_term):
# Get the quotient LT(poly)/LT(divisor)
LT_quotient = np.subtract(poly.lead_term, divisor.lead_term)
poly_to_subtract_coeff = divisor.mon_mult(LT_quotient,
returnType='Matrix')
# Match sizes of poly_to_subtract and poly so
# poly_to_subtract.coeff can be subtracted from poly.coeff
poly_coeff, poly_to_subtract_coeff = match_size(
poly.coeff, poly_to_subtract_coeff)
new_coeff = poly_coeff - \
(poly.lead_coeff/poly_to_subtract_coeff[tuple(divisor.lead_term+LT_quotient)])*poly_to_subtract_coeff
new_coeff[np.where(
np.abs(new_coeff) < permitted_round_error)] = 0
for term in zip(*np.where(new_coeff != 0)):
if term in basisSet:
remainder[term] += new_coeff[term]
new_coeff[term] = 0
poly.__init__(new_coeff, clean_zeros=False)
divisible = True
break
return remainder
def __sub__(self, other):
'''
Subtraction of two MultiCheb polynomials.
Parameters
----------
other : MultiCheb
Returns
-------
MultiCheb
The coeff values are the result of self.coeff - other.coeff.
'''
if self.shape != other.shape:
new_self, new_other = match_size(self.coeff, other.coeff)
else:
new_self, new_other = self.coeff, other.coeff
return MultiCheb((new_self - (new_other)), clean_zeros=False)
def __add__(self, other):
'''
Addition of two MultiPower polynomials.
Parameters
----------
other : MultiPower
Returns
-------
MultiPower object
The sum of the coeff of self and coeff of other.
'''
if self.shape != other.shape:
new_self, new_other = match_size(self.coeff, other.coeff)
else:
new_self, new_other = self.coeff, other.coeff
return MultiPower((new_self + new_other), clean_zeros=False)
def __mul__(self, other):
'''
Multiplication of two MultiPower polynomials.
Parameters
----------
other : MultiPower object
Returns
-------
MultiPower object
The result of self*other.
'''
if self.shape != other.shape:
new_self, new_other = match_size(self.coeff, other.coeff)
else:
new_self, new_other = self.coeff, other.coeff
return MultiPower(convolve(new_self, new_other))
def __add__(self, other):
'''
Addition of two MultiCheb polynomials.
Parameters
----------
other : MultiCheb
Returns
-------
MultiCheb
The sum of the coeff of self and coeff of other.
'''
if self.shape != other.shape:
new_self, new_other = match_size(self.coeff, other.coeff)
else:
new_self, new_other = self.coeff, other.coeff
return MultiCheb(new_self + new_other)
def bivariate_roots(f, g):
"""Calculates the common roots of f and g using the bezout resultant method.
Parameters
----------
f, g : MultiCheb objects
Returns
-------
roots
"""
F, G = utils.match_size(f.coeff, g.coeff)
n = max(F.shape)
# F, G = np.zeros((n,n)), np.zeros((n,n))
# F = F + utils.match_size(F, f_coeffs)[1] # Square matrix for f
# G = G + utils.match_size(G, g_coeffs)[1] # Square matrix for g
A = np.zeros((n - 1, n - 1, 2 * n - 1))
a, b, c = (np.vstack([np.ones(
(n - 1, 1)), 2]) / 2).T, np.zeros(n), np.ones(n) / 2
for i in range(1, n + 1):
for j in range(1, n + 1):
AA = np.array([[0] + list(F[:, i - 1][::-1])])
v = G[:, j - 1][::-1].reshape((-1, 1))
X, ignored = DLP(AA, v, a, b, c)
if i == 1 or j == 1:
cc = np.zeros(max(i, j))
cc[0] = 1
else:
cc = np.zeros(i + j - 1)
cc[-1] = .5
cc[abs(i - j)] = .5
cc = cc[::-1]
for k in range(len(cc)):
A[:, :, -1 - k] = A[:, :, -1 - k] + X[1:, 1:] * cc[-1 - k]
nrmA = np.linalg.norm(A[:, :, -1], 'fro')
for ii in range(A.shape[2]):
if np.linalg.norm(A[:, :, ii], 'fro') / nrmA > 1e-20:
break
A = A[:, :, ii:]
ns = A.shape
AA = A.reshape(ns[0], ns[1] * ns[2], order='F')
n = ns[0]
v = np.random.rand(n, 1)
a, b, c = (np.vstack([np.ones(
(n - 1, 1)), 2]) / 2).T, np.zeros(n), np.ones(n) / 2
X, Y = DLP(AA, v, a, b, c)
yvals, V = sLA.eig(Y, -X)
y = yvals
x = np.divide(V[-2, :], V[-1, :])
t = np.copy(x)
x = x[np.logical_and(np.logical_and(np.imag(y) == 0,
abs(y) < 1),
abs(x) < 1)]
y = y[np.logical_and(np.logical_and(np.imag(y) == 0,
abs(y) < 1),
abs(t) < 1)]
return list(zip(x, y))
