randsvdfast
randsvdfast
test matrix
The MATLAB This repository contains a MATLAB function to generates a matrix with specified singular values or 2-norm condition number and the corresponding unit tests.
The function is named after the randsvd
matrix in the MATLAB gallery
, as it provides similar functionalities but uses a faster algorithm. The method was designed to generate test matrices for extreme-scale benchmarks such as the High-performance Linpack Benchmark (HPL) or the HPL-AI Mixed-Precision Benchmark.
Usage
The command
A = randsvdfast(n, kappa, mode, method, matrix, classname, realout)
generates a matrix A
of class classname
with condition number kappa
and singular values distributed according to mode
. The function generates a matrix of order n
if n
is a positive integer, and of size n(1)
by n(2)
if n
is a vector of length 2. By default, n
and kappa
are both set to 10.
The functions provides functionalities similar to those of the MATLAB function galley('randsvd', ...)
. The most notable difference is that this routine allows the user to specify a custom distribution of the singular values (see below), but does not implement the reduction to banded form.
The singular values can have one of the following distributions:
-
mode
= 0: one large singular value and one small singular value, -
mode
= 1: one large singular value, -
mode
= 2: one small singular value, -
mode
= 3 (default): geometric distribution, -
mode
= 4: arithmetic distribution, -
mode
= 5: random singular values with uniformly distributed magnitude, -
mode
= 6: the vectorkappa
contains the singular values.
The parameter method
selects the algorithm that will be used to generate the test matrix. It can take any of the following values:
-
method
= 1 (default): [Alg. 3.1, 1], -
method
= 2: [Alg. 3.2, 1], -
method
= 3: [Alg. 4.1, 1] (onlymode
= 0, 1, 2), -
method
= 4: [Alg. 4.2, 1] (onlymode
= 0, 1, 2).
This function is faster for method
= 3 or 4 than for method
= 1 or 2.
The algorithm uses an orthogonal matrix Q that depends on the value of the parameter matrix
, which can take the following values:
-
matrix
= 0 (default): Q is a Haar distributed random unitary generated as the Q factor of the QR decomposition of the matrixrandn(n(1),n(2))
. -
matrix
= an integer from 1 to 7: Q is the matrixgallery('orthog',n,matrix)
. -
matrix
is the function handle of a two-argument function that generates ann(1)
-by-n(2)
matrix with orthonormal columns.
The output matrix will be of class classname
where classname
is either
'single'
or 'double'
. Constants are computed in double precision, whereas
operations at the scalar level are performed in precision classname
. The
entries of A
will be real if realout
is true
, and complex otherwise. By
default the function generates a real matrix of doubles.
Tests
The class-based unit tests for the randsvdfast
function can be ran with the command test_run
.
Anymatrix
The repository can be downloaded as a remote group into the extensible matrix collection Anymatrix with
anymatrix('g', 'randsvdfast', 'mfasi/randsvdfast-matlab')
and the test matrix can be generated with
anymatrix('randsvdfast/randsvdfast', n, kappa, mode, method, matrix, classname, realout)
Reference
[1] M. Fasi & N. J. Higham. Generating extreme-scale matrices with specified singular values or condition numbers. SIAM J. Sci. Comput., 43(1), 663–684, 2021.
License
The code is distributed under the terms of the 2-Clause BSD License, see license.txt
Citar como
M. Fasi & N. J. Higham. Generating extreme-scale matrices with specified singular values or condition numbers. SIAM J. Sci. Comput., 43(1), 663–684, 2021.
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Versión | Publicado | Notas de la versión | |
---|---|---|---|
2.0 | See release notes for this release on GitHub: https://github.com/mfasi/randsvdfast-matlab/releases/tag/v2.0 |
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1.5.0 | Add unit tests. |
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1.1.0 | Update reference. |
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1.0.5 | Make error messages more informative. |
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1.0.2 | Fix bug in the ordering of mode and typos in documentation. |
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1.0.1 | Change summary. |
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1.0.0 |