mxnet.ndarray.sparse.dot¶

mxnet.ndarray.sparse.dot(lhs=None, rhs=None, transpose_a=_Null, transpose_b=_Null, forward_stype=_Null, out=None, name=None, **kwargs)¶

Dot product of two arrays.

dot’s behavior depends on the input array dimensions:

1-D arrays: inner product of vectors
2-D arrays: matrix multiplication
N-D arrays: a sum product over the last axis of the first input and the first axis of the second input

For example, given 3-D x with shape (n,m,k) and y with shape (k,r,s), the result array will have shape (n,m,r,s). It is computed by:
```
dot(x,y)[i,j,a,b] = sum(x[i,j,:]*y[:,a,b])
```
Example:
```
x = reshape([0,1,2,3,4,5,6,7], shape=(2,2,2))
y = reshape([7,6,5,4,3,2,1,0], shape=(2,2,2))
dot(x,y)[0,0,1,1] = 0
sum(x[0,0,:]*y[:,1,1]) = 0
```

The storage type of dot output depends on storage types of inputs, transpose option and forward_stype option for output storage type. Implemented sparse operations include:

dot(default, default, transpose_a=True/False, transpose_b=True/False) = default
dot(csr, default, transpose_a=True) = default
dot(csr, default, transpose_a=True) = row_sparse
dot(csr, default) = default
dot(csr, row_sparse) = default
dot(default, csr) = csr (CPU only)
dot(default, csr, forward_stype=’default’) = default
dot(default, csr, transpose_b=True, forward_stype=’default’) = default

If the combination of input storage types and forward_stype does not match any of the above patterns, dot will fallback and generate output with default storage.

Note

If the storage type of the lhs is “csr”, the storage type of gradient w.r.t rhs will be “row_sparse”. Only a subset of optimizers support sparse gradients, including SGD, AdaGrad and Adam. Note that by default lazy updates is turned on, which may perform differently from standard updates. For more details, please check the Optimization API at: https://mxnet.incubator.apache.org/api/python/optimization/optimization.html

Defined in src/operator/tensor/dot.cc:L77

Parameters

lhs (NDArray) – The first input
rhs (NDArray) – The second input
transpose_a (boolean, optional, default=0) – If true then transpose the first input before dot.
transpose_b (boolean, optional, default=0) – If true then transpose the second input before dot.
forward_stype ({None, 'csr', 'default', 'row_sparse'},optional, default='None') – The desired storage type of the forward output given by user, if thecombination of input storage types and this hint does not matchany implemented ones, the dot operator will perform fallback operationand still produce an output of the desired storage type.
out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays