def mon_mult(self, mon, returnType='Poly'):
'''
Multiplies a polynomial by a monomial.
Parameters
----------
mon : tuple
The powers in the monomial.
Ex: x^3*y^4*z^2 would be input as (3,4,2)
returnType : str
Which type of object to return.
Returns
-------
MultiPower object if returnType is 'Poly'
ndarray if returnType is 'Matrix'
'''
mon = np.array(mon)
result = np.zeros(self.shape + mon)
result[slice_bottom(self.coeff)] = self.coeff
if returnType == 'Poly':
return MultiPower(result,
clean_zeros=False,
lead_term=self.lead_term + mon)
elif returnType == 'Matrix':
return result
def _mon_mult1(initial_matrix, idx, dim_mult):
"""
Executes monomial multiplication in one dimension.
Parameters
----------
initial_matrix : array_like
Matrix of coefficients that represent a Chebyshev polynomial.
idx : tuple of ints
The index of a monomial of one variable to multiply by initial_matrix.
dim_mult : int
The location of the non-zero value in idx.
Returns
-------
ndarray
Coeff that are the result of the one dimensial monomial multiplication.
"""
p1 = np.zeros(initial_matrix.shape + idx)
p1[slice_bottom(initial_matrix)] = initial_matrix
largest_idx = [i - 1 for i in initial_matrix.shape]
new_shape = [
max(i, j)
for i, j in itertools.zip_longest(largest_idx, idx, fillvalue=0)
] #finds the largest length in each dimmension
if initial_matrix.shape[dim_mult] <= idx[dim_mult]:
add_a = [
i - j for i, j in itertools.zip_longest(
new_shape, largest_idx, fillvalue=0)
]
add_a_list = np.zeros((len(new_shape), 2))
#changes the second column to the values of add_a and add_b.
add_a_list[:, 1] = add_a
#uses add_a_list and add_b_list to pad each polynomial appropriately.
initial_matrix = np.pad(initial_matrix, add_a_list.astype(int),
'constant')
number_of_dim = initial_matrix.ndim
shape_of_self = initial_matrix.shape
#Loop iterates through each dimension of the polynomial and folds in that dimension
for i in range(number_of_dim):
if idx[i] != 0:
initial_matrix = MultiCheb._fold_in_i_dir(
initial_matrix, number_of_dim, i, shape_of_self[i], idx[i])
if p1.shape != initial_matrix.shape:
idx = [i - j for i, j in zip(p1.shape, initial_matrix.shape)]
result = np.zeros(np.array(initial_matrix.shape) + idx)
result[slice_top(initial_matrix)] = initial_matrix
initial_matrix = result
Pf = p1 + initial_matrix
return .5 * Pf