Purpose ======= LA_SPSV computes the solution to a linear system of equations A*X = B, where A is a real or complex symmetric matrix stored in packed format 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_HPSV computes the solution to a linear system of equations A*X = B, where A is a complex Hermitian matrix stored in packed format 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_SPSV / LA_HESV( AP, B, UPLO=uplo, & IPIV=ipiv, INFO=info ) (), INTENT(INOUT) :: AP(:), 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 ========= AP (input/output) REAL or COMPLEX array, shape (:) with size(AP)= n*(n + 1)=2, where n is the order of A. On entry, the upper or lower triangle of matrix A in packed storage. The elements are stored columnwise as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j<=n; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for 1<=j<=i<=n. On exit, the block diagonal matrix D and the multipliers used to obtain U or L from the factorization of A, stored as a packed triangular matrix 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'. IPIV Optional (output) INTEGER array, shape (:) with size(IPIV)=n. 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.