from brian2 import dot)
dot(a, b, out=None)¶
Dot product of two arrays.
For 2-D arrays it is equivalent to matrix multiplication, and for 1-D arrays to inner product of vectors (without complex conjugation). For N dimensions it is a sum product over the last axis of
aand the second-to-last of
dot(a, b)[i,j,k,m] = sum(a[i,j,:] * b[k,:,m])
a : array_like
b : array_like
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.
output : ndarray
Returns the dot product of
bare both scalars or both 1-D arrays then a scalar is returned; otherwise an array is returned. If
outis given, then it is returned.
- If the last dimension of
ais not the same size as the second-to-last dimension of
- Complex-conjugating dot product.
- Sum products over arbitrary axes.
- Einstein summation convention.
>>> np.dot(3, 4) 12
Neither argument is complex-conjugated:
>>> np.dot([2j, 3j], [2j, 3j]) (-13+0j)
For 2-D arrays it’s 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