tf.raw_ops.MatrixTriangularSolve

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

tf.raw_ops.MatrixTriangularSolve( 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 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].

Note, the batch shapes for the inputs only need to broadcast.

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