tf.linalg.experimental.conjugate_gradient

Conjugate gradient solver.

View aliases

Compat aliases for migration

See Migration guide for more details.

tf.compat.v1.linalg.experimental.conjugate_gradient

tf.linalg.experimental.conjugate_gradient(
    operator, rhs, preconditioner=None, x=None, tol=1e-05, max_iter=20,
    name='conjugate_gradient'
)

Solves a linear system of equations A*x = rhs for self-adjoint, positive definite matrix A and right-hand side vector rhs, using an iterative, matrix-free algorithm where the action of the matrix A is represented by operator. The iteration terminates when either the number of iterations exceeds max_iter or when the residual norm has been reduced to tol times its initial value, i.e. \(||rhs - A x_k|| <= tol ||rhs||\).

Args
operator	A LinearOperator that is self-adjoint and positive definite.
rhs	A possibly batched vector of shape [..., N] containing the right-hand size vector.
preconditioner	A LinearOperator that approximates the inverse of A. An efficient preconditioner could dramatically improve the rate of convergence. If preconditioner represents matrix M(M approximates A^{-1}), the algorithm uses preconditioner.apply(x) to estimate A^{-1}x. For this to be useful, the cost of applying M should be much lower than computing A^{-1} directly.
x	A possibly batched vector of shape [..., N] containing the initial guess for the solution.
tol	A float scalar convergence tolerance.
max_iter	An integer giving the maximum number of iterations.
name	A name scope for the operation.

Returns
output	A namedtuple representing the final state with fields: i: A scalar int32 Tensor. Number of iterations executed. x: A rank-1 Tensor of shape [..., N] containing the computed solution. r: A rank-1 Tensor of shape [.., M] containing the residual vector. p: A rank-1 Tensor of shape [..., N]. A-conjugate basis vector. gamma: \(r \dot M \dot r\), equivalent to \(||r||_2^2\) when preconditioner=None.