Difference between revisions of "Ttclass/amensolve.m"
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| − | {{DISPLAYTITLE:ttclass/amensolve.m}} | + | {{DISPLAYTITLE:ttclass/amensolve.m}} __NOTOC__ |
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) |
| − | == | + | ==Parameters== |
| − | |||
| − | + | 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== | ||
| − | [[ttclass.m]], [[ttclass/amensum.m]] | + | [[ttclass.m]], [[ttclass/amensum.m]], [[ttclass/shrink.m]], [[ttclass/clearcoeff.m]], [[ttclass/conj.m]], [[ttclass/ctranspose.m]], [[ttclass/diag.m]], [[ttclass/dot.m]], [[ttclass/full.m]], [[ttclass/hdot.m]], [[ttclass/ismatrix.m]], [[ttclass/isnumeric.m]], [[ttclass/isreal.m]], [[ttclass/kron.m]], [[ttclass/mean.m]], [[ttclass/minus.m]], [[ttclass/mldivide.m]], [[ttclass/mrdivide.m]], [[ttclass/mtimes.m]], [[ttclass/nnz.m]], [[ttclass/norm.m]], [[ttclass/numel.m]], [[ttclass/pack.m]], [[ttclass/plus.m]], [[ttclass/rand.m]], [[ttclass/ranks.m]], [[ttclass/rdivide.m]], [[ttclass/revert.m]], [[ttclass/size.m]], [[ttclass/sizes.m]], [[ttclass/subsref.m]], [[ttclass/sum.m]], [[ttclass/trace.m]], [[ttclass/transpose.m]], [[ttclass/truncate.m]], [[ttclass/ttort.m]], [[ttclass/unit_like.m]], [[ttclass/vec.m]], [[Tensor_train_module]] |
| − | |||
| − | ''Version 2.1, authors: [[Dmitry | + | ''Version 2.1, authors: [[Dmitry Savostyanov]], [[Sergey Dolgov]]'' |
Latest revision as of 19:42, 6 June 2026
Solves the linear system Ax=y using the AMEn iteration.
Syntax
x=amensolve(A,y,tol,opts,x0)
Parameters
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
ttclass.m, ttclass/amensum.m, ttclass/shrink.m, ttclass/clearcoeff.m, ttclass/conj.m, ttclass/ctranspose.m, ttclass/diag.m, ttclass/dot.m, ttclass/full.m, ttclass/hdot.m, ttclass/ismatrix.m, ttclass/isnumeric.m, ttclass/isreal.m, ttclass/kron.m, ttclass/mean.m, ttclass/minus.m, ttclass/mldivide.m, ttclass/mrdivide.m, ttclass/mtimes.m, ttclass/nnz.m, ttclass/norm.m, ttclass/numel.m, ttclass/pack.m, ttclass/plus.m, ttclass/rand.m, ttclass/ranks.m, ttclass/rdivide.m, ttclass/revert.m, ttclass/size.m, ttclass/sizes.m, ttclass/subsref.m, ttclass/sum.m, ttclass/trace.m, ttclass/transpose.m, ttclass/truncate.m, ttclass/ttort.m, ttclass/unit_like.m, ttclass/vec.m, Tensor_train_module
Version 2.1, authors: Dmitry Savostyanov, Sergey Dolgov
