Ttclass/amensolve.m - Revision history

Kuprov: Update function See also links and function index membership

2026-06-06T18:42:26Z

Update function See also links and function index membership

Kuprov: Rename Arguments section heading to Parameters

2026-06-05T17:52:59Z

Rename Arguments section heading to Parameters

Kuprov: Repair ttclass function page template

2026-06-05T17:04:02Z

Repair ttclass function page template

Kuprov: Normalise sequential blank lines

2026-04-25T11:31:34Z

Normalise sequential blank lines

Kuprov: /* See also */

2018-01-03T13:40:53Z

‎See also

Kuprov: Created page with "{{DISPLAYTITLE:ttclass/amensolve.m}} Solves the linear system Ax=y using the AMEn iteration. ==Syntax== x = amensolve(A,y,tol,opts,x0) ==Description== A very experimen..."

2018-01-03T13:40:41Z

Created page with "{{DISPLAYTITLE:ttclass/amensolve.m}} Solves the linear system Ax=y using the AMEn iteration. ==Syntax== x = amensolve(A,y,tol,opts,x0) ==Description== A very experimen..."

New page

{{DISPLAYTITLE:ttclass/amensolve.m}}
Solves the linear system Ax=y using the AMEn iteration.

==Syntax==

x = amensolve(A,y,tol,opts,x0)

==Description==
A very experimental tensor train format solver - see papers by Savostyanov and Dolgov.

==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.

==See also==
[[ttclass.m]], [[ttclass/amensum.m]]

''Version 2.1, authors: [[Dmitry Davostyanov]], [[Sergey Dolgov]]''

@@ Line 50: / Line 50: @@
 ==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 Savostyanov]], [[Sergey Dolgov]]''

@@ Line 6: / Line 6: @@
       x=amensolve(A,y,tol,opts,x0)
-==Arguments==
+==Parameters==
       A                    - ttclass representing a square matrix

← Older revision		Revision as of 13:40, 3 January 2018
Line 54:		Line 54:


−	''Version 2.1, authors: [[Dmitry ~~Davostyanov~~]], [[Sergey Dolgov]]''	+	''Version 2.1, authors: [[Dmitry Savostyanov]], [[Sergey Dolgov]]''

@@ Line 1: / Line 1: @@
-{{DISPLAYTITLE:ttclass/amensolve.m}}
+{{DISPLAYTITLE:ttclass/amensolve.m}} __NOTOC__
 Solves the linear system Ax=y using the AMEn iteration.
 ==Syntax==
-      x = amensolve(A,y,tol,opts,x0)
+      x=amensolve(A,y,tol,opts,x0)
 ==Arguments==
-   A    - ttclass representing a square matrix
+     A                    - ttclass representing a square matrix
-   y    - ttclass representing the right hand side
+     y                    - ttclass representing the right hand side
-   tol  - relative approximation and stopping tolerance,
+     tol                  - relative approximation and stopping tolerance,
 e-6 is a good start
-   x0   - ttclass representing the initial guess
+     x0                   - ttclass representing the initial guess
- Options (pass empty array for defaults):
+     Options (pass empty array for defaults):
-   opts.nswp - maximum number of AMEn sweeps
+     opts.nswp            - maximum number of AMEn sweeps
-   opts.init_guess_rank - the rank of the initial guess
+     opts.init_guess_rank - the rank of the initial guess
-   opts.enrichment_rank - the rank of the residual and
+     opts.enrichment_rank - the rank of the residual and
-                          enrichment
+                            enrichment
-   opts.resid_damp - local accuracy gap
+     opts.resid_damp      - local accuracy gap
-   opts.rmax - maximum TT rank limit for the solution
+     opts.rmax            - maximum TT rank limit for the solution
-   opts.max_full_size - direct vs iterative solver switch-
+     opts.max_full_size   - direct vs iterative solver switch-
-                        over dimension
+                            over dimension
-   opts.local_iters - maximum number of bicgstab iterations
+     opts.local_iters     - maximum number of bicgstab iterations
-                      for local problems
+                            for local problems
-   opts.verb - Verbosity level: silent (0), sweep (1) or full (2)
+     opts.verb            - Verbosity level: silent (0), sweep (1) or full (2)
 ==Outputs==
-   x    - ttclass representing the solution such that
+     x - ttclass representing the solution such that
-          |x-X| < tol |X| in Frobenius norm, where X is
+         |x-X| < tol |X| in Frobenius norm, where X is
-          the exact solution.
+         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.
 ==See also==