function b = r8bb_to_r8ge ( n1, n2, ml, mu, a ) %*****************************************************************************80 % %% R8BB_TO_R8GE copies a R8BB matrix to a R8GE matrix. % % Discussion: % % The R8BB storage format is for a 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. % % 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 (2*ML+MU+1)*N1 entries of A, using standard LINPACK % general band format. The reason for the factor of 2 in front of % ML is to allocate space that may be required if pivoting occurs. % % 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+ML+MU+1)+(J-1)*(2*ML+MU+1). % % Entries of A2: % % 1 <= I <= N1, N1+1 <= J <= N1+N2. % % Store the I, J entry into location % (2*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 % (2*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 % (2*ML+MU+1)*N1+N1*N2+(J-1)*N2+(I-N1). % (same formula used for A3). % % Licensing: % % This code is distributed under the GNU LGPL license. % % Modified: % % 02 March 2004 % % 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, real A((2*ML+MU+1)*N1+2*N1*N2+N2*N2), the R8BB matrix. % % Output, real B(N1+N2,N1+N2), the R8GE matrix. % for i = 1 : n1 for j = 1 : n1 if ( mu+ml < (j-i) | ml < (i-j) ) b(i,j) = 0.0; else ij = (i-j+ml+mu+1)+(j-1)*(2*ml+mu+1); b(i,j) = a(ij); end end end for i = 1 : n1 for j = n1+1 : n2 ij = (2*ml+mu+1)*n1+(j-n1-1)*n1+i; b(i,j) = a(ij); end end for i = n1+1 : n2 for j = 1 : n1+n2 ij = (2*ml+mu+1)*n1+n2*n1+(j-1)*n2+(i-n1); b(i,j) = a(ij); end end return end