function b = r8cbb_mtv ( n1, n2, ml, mu, a, x )
%*****************************************************************************80
%
%% R8CBB_MTV multiplies a vector by 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:
%
% 26 February 2004
%
% Author:
%
% John Burkardt
%
% Parameters:
%
% Input, integer ML, MU, the lower and upper bandwidths.
% ML and MU must be nonnegative, and no greater than N1-1.
%
% 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, real A((ML+MU+1)*N1 + 2*N1*N2 + N2*N2), the R8CBB matrix.
%
% Input, real X(N1+N2), the vector to multiply the matrix.
%
% Output, real B(N1+N2), the product X * A.
%
%
% Destroy all row vectors!
%
a = a(:);
x = x(:);
%
% Set B to zero.
%
b = zeros ( n1 + n2, 1 );
%
% Multiply by A1.
%
for j = 1 : n1
ilo = max ( 1, j - mu );
ihi = min ( n1, j + ml );
ij = ( j - 1 ) * ( ml + mu + 1 ) - j + mu + 1;
b(j) = b(j) + x(ilo:ihi)' * a(ij+ilo:ij+ihi);
end
%
% Multiply by A2.
%
for j = n1 + 1 : n1 + n2
ij = ( ml + mu + 1 ) * n1 + ( j - n1 - 1 ) * n1;
b(j) = b(j) + x(1:n1)' * a(ij+1:ij+n1);
end
%
% Multiply by A3 and A4.
%
for j = 1 : n1 + n2
ij = ( ml + mu + 1 ) * n1 + n1 * n2 + ( j - 1 ) * n2 - n1;
b(j) = b(j) + x(n1+1:n1+n2)' * a(ij+n1+1:ij+n1+n2);
end
return
end