High Performance Computing
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This is a crosspost from   Cleve’s Corner: Cleve Moler on Mathematics and Computing Cleve Moler is the author of the first MATLAB, one of the founders of MathWorks, and is currently Chief Mathematician at the company. He writes here about MATLAB, scientific computing and interesting mathematics.. See the original post here.

MiniGallery, Sampler of MATLAB Test Matrices

MATLAB has dozens of test matrices. Here are a few.



  • Random. A = sprand(n,n,0.25). Random sparse, density = 0.25.
  • Bucky. A = bucky. Sparse connectivity graph of the geodesic dome, the soccer ball, and the carbon-60 molecule.
  • Wilkinson. A = wilkinson(n). Wn+. Nearly equal double eigenvalues.
  • Band. A = triu(tril(A,2),-2). Elements near diagonal.
  • Triangular. A = triu(A). Elements on and above diagonal.
  • Hessenberg. A = triu(A,-1). Upper triangular plus one subdiagonal. See schur.
  • Permutation. A = sparse(randperm(n),1:n,1). One +1 in each row and column.
  • Companion. c = charpoly(A); A = [-c(2:end); eye(n-1,n)]. Traditional companion matrix.
  • Fiedler. c = charpoly(A); A = fiedler(-c(2:end)). Fiedler companion matrix.
  • Hankel. A = flip(gallery('toeppd',n)). Constant antidiagonals.
  • Toeplitz. A = gallery('toeppd',n). Constant diagonals.
  • Magic. A = magic(n). Magic square.




Get the MATLAB code

Published with MATLAB® R2023a