Purpose ======= LA_GBSV computes the solution to a real or complex linear system of equations A*X = B, where A is a square band matrix and X and B are rectangular matrices or vectors. The LU decomposition with row interchanges is used to factor A as A = L*U , where L is a product of permutation and unit lower triangular matrices with kl subdiagonals, and U is upper triangular with kl + ku superdiagonals. The factored form of A is then used to solve the above system. ========= SUBROUTINE LA_GBSV( AB, B, KL=kl, IPIV=ipiv, INFO=info ) (), INTENT(INOUT) :: AB(:,:), INTEGER, INTENT(IN), OPTIONAL :: KL INTEGER, INTENT(OUT), OPTIONAL :: IPIV(:) INTEGER, INTENT(OUT), OPTIONAL :: INFO where ::= REAL | COMPLEX ::= KIND(1.0) | KIND(1.0D0) ::= B(:,:) | B(:) Arguments ========= AB (input/output) REAL or COMPLEX rectangular array, shape (:,:) with size(AB,1) = 2*kl+ku+1 and size(AB,2) = n, where kl and ku are, respectively, the numbers of subdiagonals and superdiagonals in the band of A, and n is the order of A. On entry, the matrix A in band storage. The (kl + ku + 1) diagonals of A are stored in rows (kl + 1) to (2*kl + ku + 1) of AB, so that the j-th column of A is stored in the j-th column of AB as follows: AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl) 1<=j<=n The remaining elements in AB need not be set. On exit, details of the factorization. U is an upper triangular band matrix with (kl + ku + 1) diagonals. These are stored in the first (kl + ku + 1) rows of AB. The multipliers that arise during the factorization are stored in the remaining rows. B (input/output) REAL or COMPLEX array, shape (:,:) with size(B,1) = n or shape (:) with size(B) = n. On entry, the matrix B. On exit, the solution matrix X. KL Optional (input) INTEGER. The number of subdiagonals in the band of A (KL = kl). The number of superdiagonals in the band is given by ku = size(AB,1) - 2 * kl - 1. Default value: (size(AB,1)-1)/3. IPIV Optional (output) INTEGER array, shape (:) with size(IPIV) = n. The pivot indices that define the row interchanges; row i of the matrix was interchanged with row IPIV(i). INFO Optional (output) INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: if INFO = i, U(i,i) = 0. The factorization has been completed, but the factor U is singular, so the solution could not be computed. If INFO is not present and an error occurs, then the program is terminated with an error message.