tf.linalg.matmul

Multiplies matrix a by matrix b, producing a * b.

View aliases

Main aliases

tf.matmul

Compat aliases for migration

See Migration guide for more details.

tf.compat.v1.linalg.matmul, tf.compat.v1.matmul

tf.linalg.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
)

The inputs must, following any transpositions, be tensors of rank >= 2 where the inner 2 dimensions specify valid matrix multiplication dimensions, and any further outer dimensions specify matching batch size.

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.

A simple 2-D tensor matrix multiplication:

a = tf.constant([1, 2, 3, 4, 5, 6], shape=[2, 3])
a  # 2-D tensor
<tf.Tensor: shape=(2, 3), dtype=int32, numpy=
array([[1, 2, 3],
       [4, 5, 6]], dtype=int32)>
b = tf.constant([7, 8, 9, 10, 11, 12], shape=[3, 2])
b  # 2-D tensor
<tf.Tensor: shape=(3, 2), dtype=int32, numpy=
array([[ 7,  8],
       [ 9, 10],
       [11, 12]], dtype=int32)>
c = tf.matmul(a, b)
c  # `a` * `b`
<tf.Tensor: shape=(2, 2), dtype=int32, numpy=
array([[ 58,  64],
       [139, 154]], dtype=int32)>

A batch matrix multiplication with batch shape [2]:

a = tf.constant(np.arange(1, 13, dtype=np.int32), shape=[2, 2, 3])
a  # 3-D tensor
<tf.Tensor: shape=(2, 2, 3), dtype=int32, numpy=
array([[[ 1,  2,  3],
        [ 4,  5,  6]],
       [[ 7,  8,  9],
        [10, 11, 12]]], dtype=int32)>
b = tf.constant(np.arange(13, 25, dtype=np.int32), shape=[2, 3, 2])
b  # 3-D tensor
<tf.Tensor: shape=(2, 3, 2), dtype=int32, numpy=
array([[[13, 14],
        [15, 16],
        [17, 18]],
       [[19, 20],
        [21, 22],
        [23, 24]]], dtype=int32)>
c = tf.matmul(a, b)
c  # `a` * `b`
<tf.Tensor: shape=(2, 2, 2), dtype=int32, numpy=
array([[[ 94, 100],
        [229, 244]],
       [[508, 532],
        [697, 730]]], dtype=int32)>

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]])