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dot(a, b, out=None)

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])
```

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 :None:None:`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.

Raises

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

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 :None:None:`out` is given, then it is returned.

Dot product of two arrays. Specifically,

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

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.interpolate._fitpack2.RectSphereBivariateSpline numpy.ma.core.dot numpy.einsum numpy.vdot scipy.linalg._basic.pinvh scipy.linalg._decomp_svd.svd numpy.inner numpy.core._multiarray_umath.c_einsum numpy.linalg.multi_dot numpy.ma.core.inner numpy.core._multiarray_umath.inner numpy.core._multiarray_umath.vdot

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