function [ a, seed ] = r8cbb_random ( n1, n2, ml, mu, seed )
%*****************************************************************************80
%
%% R8CBB_RANDOM randomizes a R8CBB matrix.
%
% Discussion:
%
% The R8CBB storage format is for a compressed border banded matrix.
% Such a matrix has the logical form:
%
% A1 | A2
% ---+---
% A3 | A4
%
% with A1 a (usually large) N1 by N1 banded matrix, while A2, A3 and A4
% are dense rectangular matrices of orders N1 by N2, N2 by N1, and N2 by N2,
% respectively.
%
% The R8CBB format is the same as the DBB format, except that the banded
% matrix A1 is stored in compressed band form rather than standard
% banded form. In other words, we do not include the extra room
% set aside for fill in during pivoting.
%
% A should be defined as a vector. The user must then store
% the entries of the four blocks of the matrix into the vector A.
% Each block is stored by columns.
%
% A1, the banded portion of the matrix, is stored in
% the first (ML+MU+1)*N1 entries of A, using the obvious variant
% of the LINPACK general band format.
%
% The following formulas should be used to determine how to store
% the entry corresponding to row I and column J in the original matrix:
%
% Entries of A1:
%
% 1 <= I <= N1, 1 <= J <= N1, (J-I) <= MU and (I-J) <= ML.
%
% Store the I, J entry into location
% (I-J+MU+1)+(J-1)*(ML+MU+1).
%
% Entries of A2:
%
% 1 <= I <= N1, N1+1 <= J <= N1+N2.
%
% Store the I, J entry into location
% (ML+MU+1)*N1+(J-N1-1)*N1+I.
%
% Entries of A3:
%
% N1+1 <= I <= N1+N2, 1 <= J <= N1.
%
% Store the I, J entry into location
% (ML+MU+1)*N1+N1*N2+(J-1)*N2+(I-N1).
%
% Entries of A4:
%
% N1+1 <= I <= N1+N2, N1+1 <= J <= N1+N2
%
% Store the I, J entry into location
% (ML+MU+1)*N1+N1*N2+(J-1)*N2+(I-N1).
% (same formula used for A3).
%
% Licensing:
%
% This code is distributed under the MIT license.
%
% Modified:
%
% 16 February 2005
%
% Author:
%
% John Burkardt
%
% Parameters:
%
% Input, integer N1, N2, the order of the banded and dense blocks.
% N1 and N2 must be nonnegative, and at least one must be positive.
%
% Input, integer ML, MU, the lower and upper bandwidths.
% ML and MU must be nonnegative and no greater than N1-1.
%
% Input, integer SEED, a seed for the random number generator.
%
% Output, real A((ML+MU+1)*N1 + 2*N1*N2 + N2*N2), the R8CBB matrix.
%
% Output, integer SEED, a seed for the random number generator.
%
%
% Randomize the banded matrix A1.
% We still believe that the "junk" entries should be set to 0.
%
for j = 1 : n1
for row = 1 : ml+mu+1
i = row + j - mu - 1;
if ( 1 <= i && i <= n1 )
[ r, seed ] = r8_uniform_01 ( seed );
else
r = 0.0;
end
a(row+(j-1)*(ml+mu+1)) = r;
end
end
%
% Randomize the rectangular strips A2+A3+A4.
%
for k = (ml+mu+1) * n1 + 1 : (ml+mu+1) * n1 + 2*n1*n2 + n2*n2
[ a(k), seed ] = r8_uniform_01 ( seed );
end
return
end