tf.linalg.triangular_solve

Solves systems of linear equations with upper or lower triangular matrices by backsubstitution.

View aliases

Main aliases

`tf.matrix_triangular_solve`

Compat aliases for migration

See Migration guide for more details.

tf.compat.v1.linalg.triangular_solve, tf.compat.v1.matrix_triangular_solve, `tf.compat.v2.linalg.triangular_solve`

tf.linalg.triangular_solve(
    matrix, rhs, lower=True, adjoint=False, name=None
)

matrix is a tensor of shape [..., M, M] whose inner-most 2 dimensions form square matrices. If lower is True then the strictly upper triangular part of each inner-most matrix is assumed to be zero and not accessed. If lower is False then the strictly lower triangular part of each inner-most matrix is assumed to be zero and not accessed. rhs is a tensor of shape [..., M, K].

The output is a tensor of shape [..., M, K]. If adjoint is True then the innermost matrices in output satisfy matrix equations matrix[..., :, :] * output[..., :, :] = rhs[..., :, :]. If adjoint is False then the strictly then the innermost matrices in output satisfy matrix equations adjoint(matrix[..., i, k]) * output[..., k, j] = rhs[..., i, j].

Example:

a = tf.constant([[3,  0,  0,  0],
                 [2,  1,  0,  0],
                 [1,  0,  1,  0],
                 [1,  1,  1,  1]], dtype=tf.float32)

b = tf.constant([[4],
                 [2],
                 [4],
                 [2]], dtype=tf.float32)

x = tf.linalg.triangular_solve(a, b, lower=True)
x
# <tf.Tensor: id=257, shape=(4, 1), dtype=float32, numpy=
# array([[ 1.3333334 ],
#        [-0.66666675],
#        [ 2.6666665 ],
#        [-1.3333331 ]], dtype=float32)>

# in python3 one can use `a@x`
tf.matmul(a, x)
# <tf.Tensor: id=263, shape=(4, 1), dtype=float32, numpy=
# array([[4.       ],
#        [2.       ],
#        [4.       ],
#        [1.9999999]], dtype=float32)>

Args
matrix	A Tensor. Must be one of the following types: float64, float32, half, complex64, complex128. Shape is [..., M, M].
rhs	A Tensor. Must have the same type as matrix. Shape is [..., M, K].
lower	An optional bool. Defaults to True. Boolean indicating whether the innermost matrices in matrix are lower or upper triangular.
adjoint	An optional bool. Defaults to False. Boolean indicating whether to solve with matrix or its (block-wise) adjoint.
name	A name for the operation (optional).

Returns
A Tensor. Has the same type as matrix.

Numpy Compatibility

Equivalent to scipy.linalg.solve_triangular