Purpose ======= LA_SYSV computes the solution to a linear system of equations A*X = B, where A is a real or complex symmetric matrix and X and B are rectangular matrices or vectors. A diagonal pivoting method is used to factor A as A = U*D*U^T if UPLO = 'U', or A = L*D*L^T if UPLO = 'L' where U (or L) is a product of permutation and unit upper (or lower) triangular matrices, and D is a symmetric block diagonal matrix with 1 by 1 and 2 by 2 diagonal blocks. The factored form of A is then used to solve the above system. LA_HESV computes the solution to a linear system of equations A*X = B, where A is a complex Hermitian matrix and X and B are rectangular matrices or vectors. A diagonal pivoting method is used to factor A as A = U*D*U^H if UPLO = 'U', or A = L*D*L^H if UPLO = 'L' where U (or L) is a product of permutation and unit upper (or lower) triangular matrices, and D is a complex Hermitian block diagonal matrix with 1 by 1 and 2 by 2 diagonal blocks. The factored form of A is then used to solve the above system. ========= SUBROUTINE LA_SYSV / LA_HESV( A, B, UPLO=uplo, & IPIV=ipiv, INFO=info ) (), INTENT(INOUT) :: A(:,:), CHARACTER(LEN=1), INTENT(IN), OPTIONAL :: UPLO INTEGER, INTENT(OUT), OPTIONAL :: IPIV(:) INTEGER, INTENT(OUT), OPTIONAL :: INFO where ::= REAL | COMPLEX ::= KIND(1.0) | KIND(1.0D0) ::= B(:,:) | B(:) Arguments ========= A (input/output) REAL or COMPLEX square array, shape (:,:). On entry, the matrix A. If UPLO = 'U', the upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization of A. B (input/output) REAL or COMPLEX array, shape (:,:) with size(B,1) = size(A,1) or shape (:) with size(B) = size(A,1). 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'. IPIV Optional (output) INTEGER array, shape (:) with size(IPIV) = size(A,1). Details of the row and column interchanges and the block structure of D. If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged, and D(k,k) is a 1 by 1 diagonal block. If IPIV k < 0, then there are two cases: 1. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and columns (k-1) and -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2 by 2 diagonal block. 2. If UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0, then rows and columns (k + 1) and -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2 by 2 diagonal block. INFO Optional (output) INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: if INFO = i, D(i,i) = 0. The factorization has been completed, but the block diagonal matrix D 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.