	Test Matrices:

	The files in this directory are translations of the files in
	the testmatrix distribution available from netlib. The
	following is the original README file.

	Obviously all of the mfiles are not translated yet.

My paper ``A Collection of Test Matrices in MATLAB'' has been accepted for
publication in ACM Trans. Math. Soft., and in revising the paper I have
prepared a new version of the collection of M-files.  The version previously in
Netlib was `Version 1.1, November 15 1989' (as returned by the command
`matrix(-1)') and the new one is `Version 1.2, May 30 1990'.

Here is a summary of the changes in going from the original Version 1.0 of
July 4, 1989 to Version 1.2.   Those marked with a `*' were already (partially)
present at Version 1.1.

(1]  Some improvements to the documentation in the comment lines of the
M-files, including correction of errors, improved wording, and extra
references.

(2]  A few minor bugs or inefficiencies corrected.

(3]  Added a new matrix, bringing the total to 45:

%AUGMENT  AUGMENT(A) is the square matrix [EYE(m) A; A' ZEROS(n)] of dimension
%         m+n, where A is m-by-n.  It is the symmetric and indefinite
%         coefficient matrix of the augmented system associated with a least
%         squares problem minimize NORM(A*x-b).
%         Special case: if A is a scalar, n say, then AUGMENT(A) is the same
%                       as AUGMENT(RAND(p,q)) where n = p+q and p = ROUND(n/2),
%                       that is, a random augmented matrix of dimension n is
%                       produced.

(4]  Added an extra option to ORTHOG:

function Q = orthog(n, k)
%ORTHOG Orthogonal and nearly orthogonal matrices.
%       Q = ORTHOG(N, K) selects the K'th type of matrix of order N.
...
%       K = 4:  Helmert matrix: a permutation of a lower Hessenberg matrix,
%               whose first row is ONES(1:N)/SQRT(N).

(5]  Changed second parameter in SPARSE from a character selecting the plot
type to a tolerance such that elements smaller than the tolerance are
regarded as zero.

(6)  Added extra functionality to RANDSVD:

function A = randsvd(n, kappa, mode, kl, ku)
%RANDSVD  Random matrices with pre-assigned singular values.
...
%      Special case: if KAPPA < 0 then a random full symmetric positive
%                    definite matrix is produced with COND(A) = -KAPPA and
%                    eigenvalues distributed according to MODE.
%                    KL and KU, if present, are ignored.

(7)  Changed SEE.  It now works for rectangular matrices.  Instead of the
inverse, the pseudo-inverse is plotted in the second window.  The plot of
columns of A versus the row index in the third window is replaced in this
new version by a plot of the singular values of A on a logarithmic scale.

(8)  HOUSE now avoids division by zero when it is given a zero vector
(BANDRED is the only routine that calls HOUSE).


---Nick Higham
   Dept. of Mathematics
   University of Manchester
   na.nhigham@na-net.stanford.edu
   October 10, 1990
