tf.linalg.triangular_solve  |  TensorFlow v2.16.1 (original) (raw)

tf.linalg.triangular_solve

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

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tf.compat.v1.linalg.triangular_solve, tf.compat.v1.matrix_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 loweris 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 equationssum_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)>