matmul(a, b, transpose_a=False, transpose_b=False, adjoint_a=False, adjoint_b=False, a_is_sparse=False, b_is_sparse=False, name=None)
Multiplies matrix `a` by matrix `b`, producing `a` * `b`.
The inputs must, following any transpositions, be tensors of rank >= 2
where the inner 2 dimensions specify valid matrix multiplication arguments,
and any further outer dimensions match.
Both matrices must be of the same type. The supported types are:
`float16`, `float32`, `float64`, `int32`, `complex64`, `complex128`.
Either matrix can be transposed or adjointed (conjugated and transposed) on
the fly by setting one of the corresponding flag to `True`. These are `False`
by default.
If one or both of the matrices contain a lot of zeros, a more efficient
multiplication algorithm can be used by setting the corresponding
`a_is_sparse` or `b_is_sparse` flag to `True`. These are `False` by default.
This optimization is only available for plain matrices (rank-2 tensors) with
datatypes `bfloat16` or `float32`.
For example:
```python
# 2-D tensor `a`
# [[1, 2, 3],
# [4, 5, 6]]
a = tf.constant([1, 2, 3, 4, 5, 6], shape=[2, 3])
# 2-D tensor `b`
# [[ 7, 8],
# [ 9, 10],
# [11, 12]]
b = tf.constant([7, 8, 9, 10, 11, 12], shape=[3, 2])
# `a` * `b`
# [[ 58, 64],
# [139, 154]]
c = tf.matmul(a, b)
# 3-D tensor `a`
# [[[ 1, 2, 3],
# [ 4, 5, 6]],
# [[ 7, 8, 9],
# [10, 11, 12]]]
a = tf.constant(np.arange(1, 13, dtype=np.int32),
shape=[2, 2, 3])
# 3-D tensor `b`
# [[[13, 14],
# [15, 16],
# [17, 18]],
# [[19, 20],
# [21, 22],
# [23, 24]]]
b = tf.constant(np.arange(13, 25, dtype=np.int32),
shape=[2, 3, 2])
# `a` * `b`
# [[[ 94, 100],
# [229, 244]],
# [[508, 532],
# [697, 730]]]
c = tf.matmul(a, b)
# Since python >= 3.5 the @ operator is supported (see PEP 465).
# In TensorFlow, it simply calls the `tf.matmul()` function, so the
# following lines are equivalent:
d = a @ b @ [[10.], [11.]]
d = tf.matmul(tf.matmul(a, b), [[10.], [11.]])
```
Args:
a: `Tensor` of type `float16`, `float32`, `float64`, `int32`, `complex64`,
`complex128` and rank > 1.
b: `Tensor` with same type and rank as `a`.
transpose_a: If `True`, `a` is transposed before multiplication.
transpose_b: If `True`, `b` is transposed before multiplication.
adjoint_a: If `True`, `a` is conjugated and transposed before
multiplication.
adjoint_b: If `True`, `b` is conjugated and transposed before
multiplication.
a_is_sparse: If `True`, `a` is treated as a sparse matrix.
b_is_sparse: If `True`, `b` is treated as a sparse matrix.
name: Name for the operation (optional).
Returns:
A `Tensor` of the same type as `a` and `b` where each inner-most matrix is
the product of the corresponding matrices in `a` and `b`, e.g. if all
transpose or adjoint attributes are `False`:
`output`[..., i, j] = sum_k (`a`[..., i, k] * `b`[..., k, j]),
for all indices i, j.
Note: This is matrix product, not element-wise product.
Raises:
ValueError: If transpose_a and adjoint_a, or transpose_b and adjoint_b
are both set to True.
