def vdot(a, b):
"""Returns the dot product of 2 vectors (or anything that can be made into
a vector).
Note: this is not the same as `dot`, as it takes the conjugate of its first
argument if complex and always returns a scalar."""
return dot(asarray(a).ravel().conj(), asarray(b).ravel())
def vdot(a, b):
"""Returns the dot product of 2 vectors (or anything that can be made into
a vector).
Note: this is not the same as `dot`, as it takes the conjugate of its first
argument if complex and always returns a scalar."""
return dot(asarray(a).ravel().conj(), asarray(b).ravel())
def tensordot(a, b, axes=2):
"""tensordot returns the product for any (ndim >= 1) arrays.
r_{xxx, yyy} = \sum_k a_{xxx,k} b_{k,yyy} where
the axes to be summed over are given by the axes argument.
the first element of the sequence determines the axis or axes
in arr1 to sum over, and the second element in axes argument sequence
determines the axis or axes in arr2 to sum over.
When there is more than one axis to sum over, the corresponding
arguments to axes should be sequences of the same length with the first
axis to sum over given first in both sequences, the second axis second,
and so forth.
If the axes argument is an integer, N, then the last N dimensions of a
and first N dimensions of b are summed over.
"""
try:
iter(axes)
except:
axes_a = range(-axes,0)
axes_b = range(0,axes)
else:
axes_a, axes_b = axes
try:
na = len(axes_a)
axes_a = list(axes_a)
except TypeError:
axes_a = [axes_a]
na = 1
try:
nb = len(axes_b)
axes_b = list(axes_b)
except TypeError:
axes_b = [axes_b]
nb = 1
a, b = asarray(a), asarray(b)
as_ = a.shape
nda = len(a.shape)
bs = b.shape
ndb = len(b.shape)
equal = 1
if (na != nb): equal = 0
else:
for k in xrange(na):
if as_[axes_a[k]] != bs[axes_b[k]]:
equal = 0
break
if axes_a[k] < 0:
axes_a[k] += nda
if axes_b[k] < 0:
axes_b[k] += ndb
if not equal:
raise ValueError, "shape-mismatch for sum"
# Move the axes to sum over to the end of "a"
# and to the front of "b"
notin = [k for k in range(nda) if k not in axes_a]
newaxes_a = notin + axes_a
N2 = 1
for axis in axes_a:
N2 *= as_[axis]
newshape_a = (-1, N2)
olda = [as_[axis] for axis in notin]
notin = [k for k in range(ndb) if k not in axes_b]
newaxes_b = axes_b + notin
N2 = 1
for axis in axes_b:
N2 *= bs[axis]
newshape_b = (N2, -1)
oldb = [bs[axis] for axis in notin]
at = a.transpose(newaxes_a).reshape(newshape_a)
bt = b.transpose(newaxes_b).reshape(newshape_b)
res = dot(at, bt)
return res.reshape(olda + oldb)
def tensordot(a, b, axes=2):
"""tensordot returns the product for any (ndim >= 1) arrays.
r_{xxx, yyy} = \sum_k a_{xxx,k} b_{k,yyy} where
the axes to be summed over are given by the axes argument.
the first element of the sequence determines the axis or axes
in arr1 to sum over, and the second element in axes argument sequence
determines the axis or axes in arr2 to sum over.
When there is more than one axis to sum over, the corresponding
arguments to axes should be sequences of the same length with the first
axis to sum over given first in both sequences, the second axis second,
and so forth.
If the axes argument is an integer, N, then the last N dimensions of a
and first N dimensions of b are summed over.
"""
try:
iter(axes)
except:
axes_a = range(-axes, 0)
axes_b = range(0, axes)
else:
axes_a, axes_b = axes
try:
na = len(axes_a)
axes_a = list(axes_a)
except TypeError:
axes_a = [axes_a]
na = 1
try:
nb = len(axes_b)
axes_b = list(axes_b)
except TypeError:
axes_b = [axes_b]
nb = 1
a, b = asarray(a), asarray(b)
as_ = a.shape
nda = len(a.shape)
bs = b.shape
ndb = len(b.shape)
equal = 1
if (na != nb): equal = 0
else:
for k in xrange(na):
if as_[axes_a[k]] != bs[axes_b[k]]:
equal = 0
break
if axes_a[k] < 0:
axes_a[k] += nda
if axes_b[k] < 0:
axes_b[k] += ndb
if not equal:
raise ValueError, "shape-mismatch for sum"
# Move the axes to sum over to the end of "a"
# and to the front of "b"
notin = [k for k in range(nda) if k not in axes_a]
newaxes_a = notin + axes_a
N2 = 1
for axis in axes_a:
N2 *= as_[axis]
newshape_a = (-1, N2)
olda = [as_[axis] for axis in notin]
notin = [k for k in range(ndb) if k not in axes_b]
newaxes_b = axes_b + notin
N2 = 1
for axis in axes_b:
N2 *= bs[axis]
newshape_b = (N2, -1)
oldb = [bs[axis] for axis in notin]
at = a.transpose(newaxes_a).reshape(newshape_a)
bt = b.transpose(newaxes_b).reshape(newshape_b)
res = dot(at, bt)
return res.reshape(olda + oldb)