numpy.dot — NumPy v2.6.dev0 Manual

numpy.dot(a, b, out=None)

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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

matmul

or a@b is preferred.

If either a or b is 0-D (scalar), it is equivalent to

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:aarray_likeFirst argument.

barray_likeSecond argument.

outndarray, optionalOutput 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:outputndarrayReturns 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:ValueErrorIf 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.

vecdot

Vector dot product of two arrays.

tensordot

Sum products over arbitrary axes.

einsum

Einstein summation convention.

matmul

‘@’ operator as method with out parameter.

linalg.multi_dot

Chained dot product.

Examples

>>> importnumpyasnp>>> np.dot(3,4)12Neither 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