def kroneckerproduct(a,b):
'''Computes a otimes b where otimes is the Kronecker product operator.
Note: the Kronecker product is also known as the matrix direct product
or tensor product. It is defined as follows for 2D arrays a and b
where shape(a)=(m,n) and shape(b)=(p,q):
c = a otimes b => cij = a[i,j]*b where cij is the ij-th submatrix of c.
So shape(c)=(m*p,n*q).
>>> print kroneckerproduct([[1,2]],[[3],[4]])
[[3 6]
[4 8]]
>>> print kroneckerproduct([[1,2]],[[3,4]])
[ [3 4 6 8]]
>>> print kroneckerproduct([[1],[2]],[[3],[4]])
[[3]
[4]
[6]
[8]]
'''
a, b = _na.asarray(a), _na.asarray(b)
if not (len(a.shape)==2 and len(b.shape)==2):
raise ValueError, 'Input must be 2D arrays.'
if not a.iscontiguous():
a = _gen.reshape(a, a.shape)
if not b.iscontiguous():
b = _gen.reshape(b, b.shape)
o = outerproduct(a,b)
o.shape = a.shape + b.shape
return _gen.concatenate(_gen.concatenate(o, axis=1), axis=1)
def kroneckerproduct(a, b):
'''Computes a otimes b where otimes is the Kronecker product operator.
Note: the Kronecker product is also known as the matrix direct product
or tensor product. It is defined as follows for 2D arrays a and b
where shape(a)=(m,n) and shape(b)=(p,q):
c = a otimes b => cij = a[i,j]*b where cij is the ij-th submatrix of c.
So shape(c)=(m*p,n*q).
>>> print kroneckerproduct([[1,2]],[[3],[4]])
[[3 6]
[4 8]]
>>> print kroneckerproduct([[1,2]],[[3,4]])
[ [3 4 6 8]]
>>> print kroneckerproduct([[1],[2]],[[3],[4]])
[[3]
[4]
[6]
[8]]
'''
a, b = _na.asarray(a), _na.asarray(b)
if not (len(a.shape) == 2 and len(b.shape) == 2):
raise ValueError, 'Input must be 2D arrays.'
if not a.iscontiguous():
a = _gen.reshape(a, a.shape)
if not b.iscontiguous():
b = _gen.reshape(b, b.shape)
o = outerproduct(a, b)
o.shape = a.shape + b.shape
return _gen.concatenate(_gen.concatenate(o, axis=1), axis=1)
def outerproduct(array1, array2):
"""outerproduct(array1, array2) computes the NxM outerproduct of N vector
'array1' and M vector 'array2', where result[i,j] = array1[i]*array2[j].
"""
array1=_gen.reshape(
_na.asarray(array1), (-1,1)) # ravel array1 into an Nx1
array2=_gen.reshape(
_na.asarray(array2), (1,-1)) # ravel array2 into a 1xM
return matrixmultiply(array1,array2) # return NxM result
def outerproduct(array1, array2):
"""outerproduct(array1, array2) computes the NxM outerproduct of N vector
'array1' and M vector 'array2', where result[i,j] = array1[i]*array2[j].
"""
array1 = _gen.reshape(_na.asarray(array1),
(-1, 1)) # ravel array1 into an Nx1
array2 = _gen.reshape(_na.asarray(array2),
(1, -1)) # ravel array2 into a 1xM
return matrixmultiply(array1, array2) # return NxM result
def tensormultiply(array1, array2):
"""tensormultiply returns the product for any rank >=1 arrays, defined as:
r_{xxx, yyy} = \sum_k array1_{xxx, k} array2_{k, yyyy}
where xxx, yyy denote the rest of the a and b dimensions.
"""
array1, array2 = _na.asarray(array1), _na.asarray(array2)
if array1.shape[-1] != array2.shape[0]:
raise ValueError, "Unmatched dimensions"
shape = array1.shape[:-1] + array2.shape[1:]
return _gen.reshape(dot(_gen.reshape(array1, (-1, array1.shape[-1])),
_gen.reshape(array2, (array2.shape[0], -1))), shape)
def tensormultiply(array1, array2):
"""tensormultiply returns the product for any rank >=1 arrays, defined as:
r_{xxx, yyy} = \sum_k array1_{xxx, k} array2_{k, yyyy}
where xxx, yyy denote the rest of the a and b dimensions.
"""
array1, array2 = _na.asarray(array1), _na.asarray(array2)
if array1.shape[-1] != array2.shape[0]:
raise ValueError, "Unmatched dimensions"
shape = array1.shape[:-1] + array2.shape[1:]
return _gen.reshape(
dot(_gen.reshape(array1, (-1, array1.shape[-1])),
_gen.reshape(array2, (array2.shape[0], -1))), shape)
def num2char(n, format, itemsize=32):
"""num2char formats NumArray 'num' into a CharArray using 'format'
>>> num2char(_na.arange(0.0,5), '%2.2f')
CharArray(['0.00', '1.00', '2.00', '3.00', '4.00'])
>>> num2char(_na.arange(0.0,5), '%d')
CharArray(['0', '1', '2', '3', '4'])
>>> num2char(_na.arange(5), "%02d")
CharArray(['00', '01', '02', '03', '04'])
Limitations:
1. When formatted values are too large to fit into strings of
length itemsize, the values are truncated, possibly losing
significant information.
2. Complex numbers are not supported.
"""
n = _na.asarray(n)
if isinstance(n.type(), _nt.ComplexType):
raise NotImplementedError("num2char doesn't support complex types yet.")
if n.type() == _na.Float64:
wnum = n
else:
wnum = n.astype(_na.Float64)
char = CharArray(shape=n.getshape(), itemsize=itemsize)
_chararray.Format(format, wnum, char)
return char
def num2char(n, format, itemsize=32):
"""num2char formats NumArray 'num' into a CharArray using 'format'
>>> num2char(_na.arange(0.0,5), '%2.2f')
CharArray(['0.00', '1.00', '2.00', '3.00', '4.00'])
>>> num2char(_na.arange(0.0,5), '%d')
CharArray(['0', '1', '2', '3', '4'])
>>> num2char(_na.arange(5), "%02d")
CharArray(['00', '01', '02', '03', '04'])
Limitations:
1. When formatted values are too large to fit into strings of
length itemsize, the values are truncated, possibly losing
significant information.
2. Complex numbers are not supported.
"""
n = _na.asarray(n)
if isinstance(n.type(), _nt.ComplexType):
raise NotImplementedError(
"num2char doesn't support complex types yet.")
if n.type() == _na.Float64:
wnum = n
else:
wnum = n.astype(_na.Float64)
char = CharArray(shape=n.getshape(), itemsize=itemsize)
_chararray.Format(format, wnum, char)
return char
def mask(a, m):
"""mask(a, m) returns the values of 'a' satisfying category 'm'.
mask does a parallel check for values which are not classifyable
by the categorization code, raising a RuntimeError exception if
any are found.
"""
a = _na.asarray(a)
if isinstance(a.type(), _na.IntegralType):
a = a.astype('Float64')
if isinstance(a.type(), _na.ComplexType):
f = _na.ieeemask(a.real, m) | _na.ieeemask(a.imag, m)
g = _na.ieeemask(a.real, BUG) | _na.ieeemask(a.imag, BUG)
else:
f = _na.ieeemask(a, m)
g = _na.ieeemask(a, BUG)
if _na.bitwise_or.reduce(_na.ravel(g)) != 0:
raise RuntimeError("Unclassifyable floating point values.")
if f.rank == 0:
f = f[()]
return f
def mask(a, m):
"""mask(a, m) returns the values of 'a' satisfying category 'm'.
mask does a parallel check for values which are not classifyable
by the categorization code, raising a RuntimeError exception if
any are found.
"""
a = _na.asarray(a)
if isinstance(a.type(), _na.IntegralType):
a = a.astype('Float64')
if isinstance(a.type(), _na.ComplexType):
f = _na.ieeemask(a.real, m) | _na.ieeemask(a.imag, m)
g = _na.ieeemask(a.real, BUG) | _na.ieeemask(a.imag, BUG)
else:
f = _na.ieeemask(a, m)
g = _na.ieeemask(a, BUG)
if _na.bitwise_or.reduce(_na.ravel(g)) != 0:
raise RuntimeError("Unclassifyable floating point values.")
if f.rank == 0:
f = f[()]
return f