tf.linalg.triangular_solve

Solve systems of linear equations with upper or lower triangular matrices.

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, N].

The output is a tensor of shape [..., M, N]. If adjoint is True then the innermost matrices in output satisfy matrix equations sum_k matrix[..., i, k] * output[..., k, j] = rhs[..., i, j]. If adjoint is False then the innermost matrices in output satisfy matrix equations sum_k 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: shape=(4, 1), dtype=float32, numpy=
array([[ 1.3333334 ],
       [-0.66666675],
       [ 2.6666665 ],
       [-1.3333331 ]], dtype=float32)>
tf.matmul(a, x)
<tf.Tensor: shape=(4, 1), dtype=float32, numpy=
array([[4.],
       [2.],
       [4.],
       [2.]], dtype=float32)>

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, N]. 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).

A Tensor. Has the same type as matrix, and shape is [..., M, N].