hpl_ai_matrix is a MATLAB function that constructs an n-by-n matrix
designed for use in the HPL-AI Mixed Precision Benchmark. The matrix has a specified
infinity-norm condition number, LU factorization with partial pivoting is
numerically stable for it, and it can be formed in O(n^2) flops.
Other program files are
test_run: runs a series of unit tests for thehpl_ai_matrixfunction.fun_based_unit_tests: used bytest_runand not intended to be called directly.
A = hpl_ai_matrix(n,kappa) returns an n-by-n matrix A for which which
cond(A,inf) = kappa > 1 and LU factorization with partial pivoting
requires no row interchanges. The matrices are generated using the
strategy discussed in the reference below. The default value of kappa is 1000.
This function is not intended for small n, and an error is returned
for n < 100.
[A,alpha,beta] = hpl_ai_matrix(n,kappa,rho) specifies the value of rho
satisfying 0 < rho < 1 (default 1/2) such that the parameters alpha
and beta defining the matrix satisfy alpha = rho*beta.
A = hpl_ai_matrix(n,kappa,rho,alpha,beta) uses the specified values
of alpha and beta. Both parameters must be specified, and their
values must satisfy the two conditions 0 < alpha < beta and
alpha < 1. kappa and rho are ignored in this case, and a warning is
emitted if kappa or rho are not empty.
The code was developed in MATLAB R2019b and R2020a and works with versions
back to R2017a. (hpl_ai_matrix works in earlier versions but the test code
does not as it uses string arrays.).
M. Fasi and N. J. Higham. Matrices with tunable infinity-norm condition number and no need for pivoting in LU factorization. SIAM J. Matrix Anal. Appl., 42(1):417–435, 2021.
See license.txt for licensing information.