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.
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 is a positive integer, and of size
n is a vector of length 2. By default,
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 vector
kappacontains the singular values.
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] (only
mode= 0, 1, 2),
method= 4: [Alg. 4.2, 1] (only
mode= 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 matrix
matrix= an integer from 1 to 7: Q is the matrix
matrixis the function handle of a two-argument function that generates an
n(2)matrix with orthonormal columns.
The output matrix will be of class
classname is either
'double'. Constants are computed in double precision, whereas
operations at the scalar level are performed in precision
A will be real if
true, and complex otherwise. By
default the function generates a real matrix of doubles.
The class-based unit tests for the
randsvdfast function can be ran with the command
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)
 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.
The code is distributed under the terms of the 2-Clause BSD License, see license.txt
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.
MATLAB Release Compatibility
Platform CompatibilityWindows macOS Linux
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