openfermion.utils.channel_state.dot

dot(a, b, out=None)

openfermion.utils.channel_state.dot()

Dot product of two arrays. Specifically,

  • If both a and b are 1-D arrays, it is inner product of vectors (without complex conjugation).

  • If both a and b are 2-D arrays, it is matrix multiplication, but using :func:matmul or a @ b is preferred.

  • If either a or b is 0-D (scalar), it is equivalent to :func:multiply and using numpy.multiply(a, b) or a * b is preferred.

  • If a is an N-D array and b is a 1-D array, it is a sum product over the last axis of a and b.

  • If a is an N-D array and b is an M-D array (where M>=2), it is a sum product over the last axis of a and the second-to-last axis of b::

    dot(a, b)[i,j,k,m] = sum(a[i,j,:] * b[k,:,m])

It uses an optimized BLAS library when possible (see numpy.linalg).

Parameters

a : array_like First argument. b : array_like Second argument. out : ndarray, optional Output argument. This must have the exact kind that would be returned if it was not used. In particular, it must have the right type, must be C-contiguous, and its dtype must be the dtype that would be returned for dot(a,b). This is a performance feature. Therefore, if these conditions are not met, an exception is raised, instead of attempting to be flexible.

Returns

output : ndarray Returns the dot product of a and b. If a and b are both scalars or both 1-D arrays then a scalar is returned; otherwise an array is returned. If out is given, then it is returned.

Raises

ValueError If the last dimension of a is not the same size as the second-to-last dimension of b.

See Also

vdot : Complex-conjugating dot product. tensordot : Sum products over arbitrary axes. einsum : Einstein summation convention. matmul : '@' operator as method with out parameter. linalg.multi_dot : Chained dot product.

Examples

>>> np.dot(3, 4)
12

Neither argument is complex-conjugated:

np.dot([2j, 3j], [2j, 3j])
(-13+0j)

For 2-D arrays it is the matrix product:

a = [[1, 0], [0, 1]]
b = [[4, 1], [2, 2]]
np.dot(a, b)
array([[4, 1],
       [2, 2]])

a = np.arange(3*4*5*6).reshape((3,4,5,6))
b = np.arange(3*4*5*6)[::-1].reshape((5,4,6,3))
np.dot(a, b)[2,3,2,1,2,2]
499128
sum(a[2,3,2,:] * b[1,2,:,2])
499128