# mars.tensor.dot¶

mars.tensor.dot(a, b, out=None, sparse=None)[source]

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])
```
Parameters
• a (array_like) – First argument.

• b (array_like) – Second argument.

• out (Tensor, 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 – 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 a tensor is returned. If out is given, then it is returned.

Return type

Tensor

Raises

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

`vdot`

Complex-conjugating dot product.

`tensordot`

Sum products over arbitrary axes.

`einsum`

Einstein summation convention.

`matmul`

‘@’ operator as method with out parameter.

Examples

```>>> import mars.tensor as mt
```
```>>> mt.dot(3, 4).execute()
12
```

Neither argument is complex-conjugated:

```>>> mt.dot([2j, 3j], [2j, 3j]).execute()
(-13+0j)
```

For 2-D arrays it is the matrix product:

```>>> a = [[1, 0], [0, 1]]
>>> b = [[4, 1], [2, 2]]
>>> mt.dot(a, b).execute()
array([[4, 1],
[2, 2]])
```
```>>> a = mt.arange(3*4*5*6).reshape((3,4,5,6))
>>> b = mt.arange(3*4*5*6)[::-1].reshape((5,4,6,3))
>>> mt.dot(a, b)[2,3,2,1,2,2].execute()
499128
>>> mt.sum(a[2,3,2,:] * b[1,2,:,2]).execute()
499128
```