Difference between revisions of "Ttclass/amensolve.m"
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Solves the linear system Ax=y using the AMEn iteration. | Solves the linear system Ax=y using the AMEn iteration. | ||
==Syntax== | ==Syntax== | ||
| − | x = amensolve(A,y,tol,opts,x0) | + | x=amensolve(A,y,tol,opts,x0) |
| − | |||
| − | |||
| − | |||
==Arguments== | ==Arguments== | ||
| − | + | A - ttclass representing a square matrix | |
| − | + | y - ttclass representing the right hand side | |
| − | + | tol - relative approximation and stopping tolerance, | |
| − | + | 1e-6 is a good start | |
| − | + | x0 - ttclass representing the initial guess | |
| − | + | Options (pass empty array for defaults): | |
| − | + | opts.nswp - maximum number of AMEn sweeps | |
| − | + | opts.init_guess_rank - the rank of the initial guess | |
| − | + | opts.enrichment_rank - the rank of the residual and | |
| − | + | enrichment | |
| − | + | opts.resid_damp - local accuracy gap | |
| − | + | opts.rmax - maximum TT rank limit for the solution | |
| − | + | opts.max_full_size - direct vs iterative solver switch- | |
| − | + | over dimension | |
| − | + | opts.local_iters - maximum number of bicgstab iterations | |
| − | + | for local problems | |
| − | + | opts.verb - Verbosity level: silent (0), sweep (1) or full (2) | |
==Outputs== | ==Outputs== | ||
| − | + | x - ttclass representing the solution such that | |
| − | + | |x-X| < tol |X| in Frobenius norm, where X is | |
| − | + | the exact solution. | |
==Notes== | ==Notes== | ||
A, y and x0 should have ntrains==1. Call [[ttclass/shrink.m]] on all three if that is not the case. | A, y and x0 should have ntrains==1. Call [[ttclass/shrink.m]] on all three if that is not the case. | ||
| + | |||
| + | A very experimental tensor train format solver - see papers by Savostyanov and Dolgov. | ||
==See also== | ==See also== | ||
Revision as of 18:04, 5 June 2026
Solves the linear system Ax=y using the AMEn iteration.
Syntax
x=amensolve(A,y,tol,opts,x0)
Arguments
A - ttclass representing a square matrix
y - ttclass representing the right hand side
tol - relative approximation and stopping tolerance,
1e-6 is a good start
x0 - ttclass representing the initial guess
Options (pass empty array for defaults):
opts.nswp - maximum number of AMEn sweeps
opts.init_guess_rank - the rank of the initial guess
opts.enrichment_rank - the rank of the residual and
enrichment
opts.resid_damp - local accuracy gap
opts.rmax - maximum TT rank limit for the solution
opts.max_full_size - direct vs iterative solver switch-
over dimension
opts.local_iters - maximum number of bicgstab iterations
for local problems
opts.verb - Verbosity level: silent (0), sweep (1) or full (2)
Outputs
x - ttclass representing the solution such that
|x-X| < tol |X| in Frobenius norm, where X is
the exact solution.
Notes
A, y and x0 should have ntrains==1. Call ttclass/shrink.m on all three if that is not the case.
A very experimental tensor train format solver - see papers by Savostyanov and Dolgov.
See also
Version 2.1, authors: Dmitry Savostyanov, Sergey Dolgov
