flopscope.

flopscope.numpy.dot

fnp.dot(a, b)[flopscope source]

Dot product of two arrays. Specifically,

Adapted from NumPy docs np.dot

Areacore
Typecustom
NumPy Refnp.dot
Cost
m⋅k⋅nm \cdot k \cdot n
Flopscope Context

Dot product; cost = M*K*N (FMA=1).

  • 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 matmul or a @ b is preferred.

  • If either a or b is 0-D (scalar), it is equivalent to multiply and using flops.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 flops.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

Examples

>>> import flopscope.numpy as fnp
>>> flops.dot(3, 4)
12

Neither argument is complex-conjugated:

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