tf.linalg.matvec

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

tf.linalg.matvec(
    a, b, transpose_a=False, adjoint_a=False, a_is_sparse=False, b_is_sparse=False,
    name=None
)

The matrix a must, following any transpositions, be a tensor of rank >= 2, with shape(a)[-1] == shape(b)[-1], and shape(a)[:-2] able to broadcast with shape(b)[:-1].

Both a and b must be of the same type. The supported types are: float16, float32, float64, int32, complex64, complex128.

Matrix a 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 inputs 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/vectors (rank-2/1 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])

# 1-D tensor `b`
# [7, 9, 11]
b = tf.constant([7, 9, 11], shape=[3])

# `a` * `b`
# [ 58,  64]
c = tf.linalg.matvec(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])

# 2-D tensor `b`
# [[13, 14, 15],
#  [16, 17, 18]]
b = tf.constant(np.arange(13, 19, dtype=np.int32),
                shape=[2, 3])

# `a` * `b`
# [[ 86, 212],
#  [410, 563]]
c = tf.linalg.matvec(a, b)

Args:

• a: Tensor of type float16, float32, float64, int32, complex64, complex128 and rank > 1.
• b: Tensor with same type as a and compatible dimensions.
• transpose_a: If True, a is transposed before multiplication.
• adjoint_a: If True, a 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 vector is the product of the corresponding matrices in a and vectors in b, e.g. if all transpose or adjoint attributes are False:

output[..., i] = sum_k (a[..., i, k] * b[..., k]), for all indices i.

• Note: This is matrix-vector product, not element-wise product.

Raises:

• ValueError: If transpose_a and adjoint_a are both set to True.