def _gemmdot(a, b, alpha=1.0, beta=1.0, out=None, trans='n'):
"""Matrix multiplication using gemm.
return reference to out, where::
out <- alpha * a . b + beta * out
If out is None, a suitably sized zero array will be created.
``a.b`` denotes matrix multiplication, where the product-sum is
over the last dimension of a, and either
the first dimension of b (for trans='n'), or
the last dimension of b (for trans='t' or 'c').
If trans='c', the complex conjugate of b is used.
"""
# Store original shapes
ashape = a.shape
bshape = b.shape
# Vector-vector multiplication is handled by dotu
if a.ndim == 1 and b.ndim == 1:
assert out is None
if trans == 'c':
return alpha * _gpaw.dotc(b, a) # dotc conjugates *first* argument
else:
return alpha * _gpaw.dotu(a, b)
## # Use gemv if a or b is a vector, and the other is a matrix??
## if a.ndim == 1 and trans == 'n':
## gemv(alpha, b, a, beta, out, trans='n')
## if b.ndim == 1 and trans == 'n':
## gemv(alpha, a, b, beta, out, trans='t')
# Map all arrays to 2D arrays
a = a.reshape(-1, a.shape[-1])
if trans == 'n':
b = b.reshape(b.shape[0], -1)
outshape = a.shape[0], b.shape[1]
else: # 't' or 'c'
b = b.reshape(-1, b.shape[-1])
# Apply BLAS gemm routine
outshape = a.shape[0], b.shape[trans == 'n']
if out is None:
# (ATLAS can't handle uninitialized output array)
out = np.zeros(outshape, a.dtype)
else:
out = out.reshape(outshape)
gemm(alpha, b, a, beta, out, trans)
# Determine actual shape of result array
if trans == 'n':
outshape = ashape[:-1] + bshape[1:]
else: # 't' or 'c'
outshape = ashape[:-1] + bshape[:-1]
return out.reshape(outshape)
def _gemmdot(a, b, alpha=1.0, beta=1.0, out=None, trans='n'):
"""Matrix multiplication using gemm.
return reference to out, where::
out <- alpha * a . b + beta * out
If out is None, a suitably sized zero array will be created.
``a.b`` denotes matrix multiplication, where the product-sum is
over the last dimension of a, and either
the first dimension of b (for trans='n'), or
the last dimension of b (for trans='t' or 'c').
If trans='c', the complex conjugate of b is used.
"""
# Store original shapes
ashape = a.shape
bshape = b.shape
# Vector-vector multiplication is handled by dotu
if a.ndim == 1 and b.ndim == 1:
assert out is None
if trans == 'c':
return alpha * _gpaw.dotc(b, a) # dotc conjugates *first* argument
else:
return alpha * _gpaw.dotu(a, b)
## # Use gemv if a or b is a vector, and the other is a matrix??
## if a.ndim == 1 and trans == 'n':
## gemv(alpha, b, a, beta, out, trans='n')
## if b.ndim == 1 and trans == 'n':
## gemv(alpha, a, b, beta, out, trans='t')
# Map all arrays to 2D arrays
a = a.reshape(-1, a.shape[-1])
if trans == 'n':
b = b.reshape(b.shape[0], -1)
outshape = a.shape[0], b.shape[1]
else: # 't' or 'c'
b = b.reshape(-1, b.shape[-1])
# Apply BLAS gemm routine
outshape = a.shape[0], b.shape[trans == 'n']
if out is None:
# (ATLAS can't handle uninitialized output array)
out = np.zeros(outshape, a.dtype)
else:
out = out.reshape(outshape)
gemm(alpha, b, a, beta, out, trans)
# Determine actual shape of result array
if trans == 'n':
outshape = ashape[:-1] + bshape[1:]
else: # 't' or 'c'
outshape = ashape[:-1] + bshape[:-1]
return out.reshape(outshape)
def dotc(a, b):
"""Dot product, conjugating the first vector with complex arguments.
Returns the value of the operation::
_
\ cc
) a * b
/_ ijk... ijk...
ijk...
``cc`` denotes complex conjugation.
"""
assert ((is_contiguous(a, float) and is_contiguous(b, float)) or
(is_contiguous(a, complex) and is_contiguous(b,complex)))
assert a.shape == b.shape
return _gpaw.dotc(a, b)
def dotc(a, b):
"""Dot product, conjugating the first vector with complex arguments.
Returns the value of the operation::
_
\ cc
) a * b
/_ ijk... ijk...
ijk...
``cc`` denotes complex conjugation.
"""
assert ((is_contiguous(a, float) and is_contiguous(b, float)) or
(is_contiguous(a, complex) and is_contiguous(b, complex)))
assert a.shape == b.shape
return _gpaw.dotc(a, b)