def differential(P, Q):
"""Polynomial differential operator
Parameters
----------
P : Poly
Polynomial to be differentiated.
Q : Poly
Polynomial to differentiate by. Must be decomposed. If
polynomial array, the output is the Jacobian matrix.
"""
P, Q = Poly(P), Poly(Q)
if not is_decomposed(Q):
differential(decompose(Q)).sum(0)
if Q.shape:
return Poly([differential(P, q) for q in Q])
if Q.dim > P.dim:
P = setdim(P, Q.dim)
else:
Q = setdim(Q, P.dim)
qkey = Q.keys[0]
A = {}
for key in P.keys:
newkey = np.array(key) - np.array(qkey)
if np.any(newkey < 0):
continue
A[tuple(newkey)] = P.A[key]*np.prod([fac(key[i], \
exact=True)/fac(newkey[i], exact=True) \
for i in xrange(P.dim)])
return Poly(A, P.dim, None)
def differential(P, Q):
"""Polynomial differential operator
Parameters
----------
P : Poly
Polynomial to be differentiated.
Q : Poly
Polynomial to differentiate by. Must be decomposed. If
polynomial array, the output is the Jacobian matrix.
"""
P, Q = Poly(P), Poly(Q)
if not is_decomposed(Q):
differential(decompose(Q)).sum(0)
if Q.shape:
return Poly([differential(P, q) for q in Q])
if Q.dim > P.dim:
P = setdim(P, Q.dim)
else:
Q = setdim(Q, P.dim)
qkey = Q.keys[0]
A = {}
for key in P.keys:
newkey = np.array(key) - np.array(qkey)
if np.any(newkey < 0):
continue
A[tuple(newkey)] = P.A[key] * np.prod(
[fac(key[i], exact=True) / fac(newkey[i], exact=True) for i in xrange(P.dim)]
)
return Poly(A, P.dim, None)
def swapdim(P, dim1=1, dim2=0):
"""
Swap the dim between two variables.
Parameters
----------
P : Poly
Input polynomial.
dim1 : int
First dim
dim2 : int
Second dim.
Returns
-------
Q : Poly
Polynomial with swapped dimensions.
Examples
--------
>>> x,y = variable(2)
>>> P = x**4-y
>>> print P
q0^4-q1
>>> print swapdim(P)
q1^4-q0
"""
if not isinstance(P, Poly):
return np.swapaxes(P, dim1, dim2)
if dim1 == dim2:
return P
m = max(dim1, dim2)
if P.dim <= m:
P = setdim(P, m + 1)
A = {}
for key in P.keys:
val = P.A[key]
key = list(key)
key[dim1], key[dim2] = key[dim2], key[dim1]
A[tuple(key)] = val
return Poly(A)
def swapdim(P, dim1=1, dim2=0):
"""
Swap the dim between two variables.
Parameters
----------
P : Poly
Input polynomial.
dim1 : int
First dim
dim2 : int
Second dim.
Returns
-------
Q : Poly
Polynomial with swapped dimensions.
Examples
--------
>>> x,y = variable(2)
>>> P = x**4-y
>>> print P
q0^4-q1
>>> print swapdim(P)
q1^4-q0
"""
if not isinstance(P, Poly):
return np.swapaxes(P, dim1, dim2)
if dim1 == dim2:
return P
m = max(dim1, dim2)
if P.dim <= m:
P = setdim(P, m + 1)
A = {}
for key in P.keys:
val = P.A[key]
key = list(key)
key[dim1], key[dim2] = key[dim2], key[dim1]
A[tuple(key)] = val
return Poly(A)
