tf.linalg.matmul

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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.compat.v2.linalg.matmul`, `tf.compat.v2.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 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:

# 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.