Conjugate gradient solver.
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 .
|