SUBROUTINE ZHPSV_F95( AP, B, UPLO, IPIV, INFO ) ! ! -- LAPACK95 interface driver routine (version 3.0) -- ! UNI-C, Denmark; Univ. of Tennessee, USA; NAG Ltd., UK ! September, 2000 ! ! .. USE STATEMENTS .. USE LA_PRECISION, ONLY: WP => DP USE LA_AUXMOD, ONLY: ERINFO, LSAME USE F77_LAPACK, ONLY: HPSV_F77 => LA_HPSV ! .. IMPLICIT STATEMENT .. IMPLICIT NONE ! .. SCALAR ARGUMENTS .. CHARACTER(LEN=1), INTENT(IN), OPTIONAL :: UPLO INTEGER, INTENT(OUT), OPTIONAL :: INFO ! .. ARRAY ARGUMENTS .. INTEGER, INTENT(OUT), OPTIONAL, TARGET :: IPIV(:) COMPLEX(WP), INTENT(INOUT) :: AP(:), B(:,:) !---------------------------------------------------------------------- ! ! 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. !---------------------------------------------------------------------- ! .. PARAMETERS .. CHARACTER(LEN=7), PARAMETER :: SRNAME = 'LA_HPSV' ! .. LOCAL SCALARS .. CHARACTER(LEN=1) :: LUPLO INTEGER :: LINFO, N, NN, NRHS, SIPIV, ISTAT, ISTAT1 COMPLEX(WP) :: WW ! .. LOCAL POINTERS .. INTEGER, POINTER :: LPIV(:) ! .. INTRINSIC FUNCTIONS .. INTRINSIC SIZE, PRESENT, REAL, INT, AIMAG ! .. EXECUTABLE STATEMENTS .. LINFO = 0; ISTAT = 0; NN = SIZE(AP); NRHS = SIZE(B,2) WW = (-1+SQRT(1+8*REAL(NN,WP)))*0.5; N = INT(WW) IF( PRESENT(UPLO) )THEN; LUPLO = UPLO; ELSE; LUPLO = 'U'; END IF IF( PRESENT(IPIV) )THEN; SIPIV = SIZE(IPIV); ELSE; SIPIV = N; END IF ! .. TEST THE ARGUMENTS IF( NN < 0 .OR. AIMAG(WW) /= 0 .OR. REAL(N,WP) /= REAL(WW) ) THEN; LINFO = -1 ELSE IF( SIZE( B, 1 ) /= N .OR. NRHS < 0 ) THEN; LINFO = -2 ELSE IF( .NOT.LSAME(LUPLO,'U') .AND. .NOT.LSAME(LUPLO,'L') )THEN; LINFO = -3 ELSE IF( SIPIV /= N )THEN; LINFO = -4 ELSE IF ( N > 0 ) THEN IF( PRESENT(IPIV) )THEN; LPIV => IPIV ELSE; ALLOCATE( LPIV(N), STAT = ISTAT ); END IF IF( ISTAT == 0 ) THEN CALL HPSV_F77( LUPLO, N, NRHS, AP, LPIV, B, N, LINFO ) ELSE; LINFO = -100; END IF IF( .NOT.PRESENT(IPIV) )DEALLOCATE(LPIV, STAT = ISTAT1 ) END IF CALL ERINFO( LINFO, SRNAME, INFO, ISTAT ) END SUBROUTINE ZHPSV_F95