Purpose ======= LA_PBSV computes the solution to a linear system of equations A*X = B, where A has band form and is real symmetric or complex Hermitian and, in either case, positive definite, and where X and B are rectangular matrices or vectors. The Cholesky decomposition is used to factor A as A = U^H*U if UPLO = 'U', or A = L*L^H if UPLO = 'L' where U is an upper triangular band matrix and L is a lower triangular band matrix, each with the same number of superdiagonals or subdiagonals as A. The factored form of A is then used to solve the above system. ========= SUBROUTINE LA_PBSV( AB, B, UPLO=uplo, INFO=info ) (), INTENT(INOUT) :: AB(:,:), CHARACTER(LEN=1), INTENT(IN), OPTIONAL :: UPLO INTEGER, INTENT(OUT), OPTIONAL :: INFO where ::= REAL | COMPLEX ::= KIND(1.0) | KIND(1.0D0) ::= B(:,:) | B(:) Arguments ========= AB (input/output) REAL or COMPLEX array, shape (:,:) with size(AB,1) = kd + 1 and size(AB,2) = n, where kd is the number of superdiagonals or subdiagonals in the band and n is the order of A. On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L') triangle of matrix A in band storage. The (kd + 1) diagonals of A are stored in the rows of AB so that the j-th column of A is stored in the j-th column of AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j 1<=j<=n if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd) 1<=j<=n. On exit, the factor U or L from the Cholesky factorization A = U^H*U = L*L^H in the same storage format as A. 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 . UPLO Optional (input) CHARACTER(LEN=1) = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. Default value: 'U'. INFO Optional (output) INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: if INFO = i, the leading minor of order i of A is not positive definite, so the factorization could not be completed and the solution could not be computed. If INFO is not present and an error occurs, then the program is terminated with an error message.