SUBROUTINE ZPOSVX_F95(A, B, X, UPLO, AF, FACT, EQUED, S, FERR, BERR, RCOND, 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: LSAME, ERINFO USE F77_LAPACK, ONLY: POSVX_F77 => LA_POSVX ! .. IMPLICIT STATEMENT .. IMPLICIT NONE ! .. SCALAR ARGUMENTS .. CHARACTER(LEN=1), INTENT(IN), OPTIONAL :: UPLO, FACT CHARACTER(LEN=1), INTENT(INOUT), OPTIONAL :: EQUED INTEGER, INTENT(OUT), OPTIONAL :: INFO REAL(WP), INTENT(OUT), OPTIONAL :: RCOND ! .. ARRAY ARGUMENTS .. COMPLEX(WP), INTENT(INOUT) :: A(:,:), B(:,:) COMPLEX(WP), INTENT(OUT) :: X(:,:) REAL(WP), INTENT(INOUT), OPTIONAL, TARGET :: S(:) COMPLEX(WP), INTENT(INOUT), OPTIONAL, TARGET :: AF(:,:) REAL(WP), INTENT(OUT), OPTIONAL, TARGET :: FERR(:), BERR(:) !---------------------------------------------------------------------- ! ! Purpose ! ======= ! ! LA_POSVX computes the solution to a linear system of equations ! A*X = B, where A is real symmetric or complex Hermitian and, in either ! case, positive definite, and where X and B are rectangular matrices or ! vectors. ! LA_POSVX can also optionally equilibrate the system if A is poorly ! scaled, estimate the condition number of (the equilibrated) A, and ! compute error bounds. ! ! ========= ! ! SUBROUTINE LA_POSVX( A, B, X, UPLO=uplo, AF=af, FACT=fact, & ! EQUED=equed, S=s, FERR=ferr, BERR=berr, & ! RCOND=rcond, INFO=info ) ! (), INTENT(INOUT) :: A(:,:), ! (), INTENT(OUT) :: ! CHARACTER(LEN=1), INTENT(IN), OPTIONAL :: UPLO ! (), INTENT(INOUT), OPTIONAL :: AF(:,:) ! CHARACTER(LEN=1), INTENT(IN), OPTIONAL :: FACT ! CHARACTER(LEN=1), INTENT(INOUT), OPTIONAL :: EQUED ! REAL(), INTENT(INOUT), OPTIONAL :: S(:) ! REAL(), INTENT(OUT), OPTIONAL :: ! REAL(), INTENT(OUT), OPTIONAL :: RCOND ! INTEGER, INTENT(OUT), OPTIONAL :: INFO ! where ! ::= REAL | COMPLEX ! ::= KIND(1.0) | KIND(1.0D0) ! ::= B(:,:) | B(:) ! ::= X(:,:) | X(:) ! ::= FERR(:), BERR(:) | FERR, BERR ! ! Arguments ! ========= ! ! A (input/output) REAL or COMPLEX square array, shape (:,:). ! On entry, the matrix A or its equilibration: ! If UPLO = 'U', then the upper triangular part of A contains ! the upper triangular part of (the equilibrated) A, and the ! strictly lower triangular part of A is not referenced. ! If UPLO = 'L', then the lower triangular part of A contains ! the lower triangular part of (the equilibrated) A, and the ! strictly upper triangular part of A is not referenced. ! If FACT = 'F' and EQUED = 'Y', then A has been equilibrated ! by the scaling factors in S during a previous call to ! LA_POSVX. ! On exit, if FACT = 'E', then the equilibrated version of A is ! stored in A; otherwise, A is unchanged. ! 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 scaled version of B if the system has been ! equilibrated; otherwise, B is unchanged. ! X (output) REAL or COMPLEX array, shape (:,:) with size(X,1) = ! size(A,1) and size(X,2) = size(B,2), or shape (:) with size(X) ! = size(A,1). ! 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'. ! AF Optional (input or output) REAL or COMPLEX array, shape (:,:) ! with the same size as A. ! If FACT = 'F' then AF is an input argument that contains the ! factor U or L from the Cholesky factorization of (the ! equilibrated) A, in the same storage format as A, returned by ! a previous call to LA_POSVX ! If FACT /= 'F' then AF is an output argument that contains the ! factor U or L from the Cholesky factorization of (the ! equilibrated) A in the same storage format as A. ! FACT Optional (input) CHARACTER(LEN=1). ! Specifies whether the factored form of the matrix A is ! supplied on entry, and, if not, whether A should be ! equilibrated before it is factored. ! = 'N': The matrix A will be copied to AF and factored ! (no equilibration). ! = 'E': The matrix A will be equilibrated, then copied to AF ! and factored. ! = 'F': AF contains the factored form of (the equilibrated) ! A. ! Default value: 'N'. ! EQUED Optional (input or output) CHARACTER(LEN=1). ! Specifies the form of equilibration that was done. ! EQUED is an input argument if FACT = 'F', otherwise it is an ! output argument: ! = 'N': No equilibration (always true if FACT = 'N'). ! = 'Y': Equilibration, i.e., A has been premultiplied and ! postmultiplied by diag(S). ! Default value: 'N'. ! S Optional (input or output) REAL array, shape (:) with size(S)= ! size(A,1). ! The scaling factors for A. ! S is an input argument if FACT = 'F' and EQUED = 'Y'. ! S is an output argument if FACT = 'E' and EQUED = 'Y'. ! FERR Optional (output) REAL array of shape (:), with size(FERR) = ! size(X,2), or REAL scalar. ! The estimated forward error bound for each solution vector ! X(j) (the j-th column of the solution matrix X). If XTRUE is ! the true solution corresponding to X(j), FERR(j) is an ! estimated upper bound for the magnitude of the largest element ! in (X(j)-XTRUE) divided by the magnitude of the largest ! element in X(j). The estimate is as reliable as the estimate ! for RCOND, and is almost always a slight overestimate of the ! true error. ! BERR Optional (output) REAL array of shape (:), with size(BERR) = ! size(X,2), or REAL scalar. ! The componentwise relative backward error of each solution ! vector X(j) (i.e., the smallest relative change in any element ! of A or B that makes X(j) an exact solution). ! RCOND Optional (output) REAL ! The estimate of the reciprocal condition number of (the ! equilibrated) A. If RCOND is less than the machine precision, ! the matrix is singular to working precision. This condition is ! indicated by a return code of INFO > 0. ! INFO Optional (output) INTEGER ! = 0: successful exit. ! < 0: if INFO = -i, the i-th argument had an illegal value. ! > 0: if INFO = i, and i is ! <= n: the leading minor of order i of (the equilibrated) ! A is not positive definite, so the factorization ! could not be completed and the solution and error ! bounds could not be computed. RCOND= 0 is returned. ! = n+1: U or L is nonsingular, but RCOND is less than ! machine precision, so the matrix is singular to ! working precision. Nevertheless, the solution and ! error bounds are computed because the computed ! solution can be more accurate than the value of ! RCOND would suggest. ! If INFO is not present and an error occurs, then the program ! is terminated with an error message. !---------------------------------------------------------------------- ! .. PARAMETERS .. CHARACTER(LEN=8), PARAMETER :: SRNAME = 'LA_POSVX' ! .. LOCAL SCALARS .. CHARACTER(LEN=1) :: LFACT, LUPLO, LEQUED INTEGER :: LINFO, NRHS, N, ISTAT, ISTAT1, S1AF, S2AF, SS, SFERR, SBERR REAL(WP) :: LRCOND, MVS ! .. LOCAL POINTERS .. REAL(WP), POINTER :: RWORK(:), LFERR(:), LBERR(:), LS(:) COMPLEX(WP), POINTER :: WORK(:), LAF(:, :) ! .. INTRINSIC FUNCTIONS .. INTRINSIC PRESENT, SIZE, MINVAL, TINY ! .. EXECUTABLE STATEMENTS .. LINFO = 0; ISTAT = 0; N = SIZE(A, 1); NRHS = SIZE(B, 2) IF( PRESENT(RCOND) ) RCOND = 1.0_WP IF( PRESENT(FACT) )THEN; LFACT = FACT; ELSE; LFACT='N'; END IF IF( PRESENT(EQUED) .AND. LSAME(LFACT,'F') )THEN; LEQUED = EQUED ELSE; LEQUED='N'; END IF IF( PRESENT(AF) )THEN; S1AF = SIZE(AF,1); S2AF = SIZE(AF,2) ELSE; S1AF = N; S2AF = N; END IF IF( ( PRESENT(S) ) )THEN; SS = SIZE(S); ELSE; SS = N; END IF IF( PRESENT(S) .AND. LSAME(LFACT,'F') .AND. LSAME(LEQUED,'Y') ) THEN MVS = MINVAL(S); ELSE; MVS = TINY(1.0_WP); ENDIF IF( PRESENT(FERR) )THEN; SFERR = SIZE(FERR); ELSE; SFERR = NRHS; END IF IF( PRESENT(BERR) )THEN; SBERR = SIZE(BERR); ELSE; SBERR = NRHS; END IF IF(PRESENT(UPLO))THEN; LUPLO = UPLO; ELSE; LUPLO='U'; END IF ! .. TEST THE ARGUMENTS IF( SIZE(A, 2) /= N .OR. N < 0 )THEN; LINFO = -1 ELSE IF( SIZE(B, 1) /= N .OR. NRHS < 0 )THEN; LINFO = -2 ELSE IF( SIZE(X, 1) /= N .OR. SIZE(X, 2) /= NRHS )THEN; LINFO = -3 ELSE IF( .NOT.LSAME(LUPLO,'U') .AND. .NOT.LSAME(LUPLO,'L') )THEN; LINFO = -4 ELSE IF( S1AF /= N .OR. S2AF /= N ) THEN; LINFO = -5 ELSE IF( ( .NOT. ( LSAME(LFACT,'F') .OR. LSAME(LFACT,'N') .OR. & LSAME(LFACT,'E') ) ) .OR. & ( LSAME(LFACT,'F') .AND. .NOT.PRESENT(AF) ) )THEN; LINFO = -6 ELSE IF( .NOT.LSAME(LEQUED,'N') .AND. .NOT.LSAME(LEQUED,'Y') )THEN; LINFO = -7 ELSE IF( SS /= N .OR. LSAME(LFACT,'F') .AND. LSAME(LEQUED,'Y') & .AND. MVS <= 0.0_WP )THEN; LINFO = -8 ELSE IF( SFERR /= NRHS )THEN; LINFO = -9 ELSE IF( SBERR /= NRHS )THEN; LINFO = -10 ELSE IF ( N > 0 )THEN IF( .NOT.PRESENT(AF) ) THEN; ALLOCATE( LAF(N,N), STAT=ISTAT ) ELSE; LAF => AF; END IF IF( ISTAT == 0 )THEN IF( .NOT.PRESENT(S) )THEN; ALLOCATE( LS(N), STAT=ISTAT ) ELSE; LS => S; END IF END IF IF( ISTAT == 0 )THEN IF( .NOT.PRESENT(FERR) )THEN; ALLOCATE( LFERR(NRHS), STAT=ISTAT ) ELSE; LFERR => FERR; END IF END IF IF( ISTAT == 0 )THEN IF( .NOT.PRESENT(BERR) )THEN; ALLOCATE( LBERR(NRHS), STAT=ISTAT ) ELSE; LBERR => BERR; END IF END IF IF( ISTAT == 0 ) ALLOCATE(WORK(2*N), RWORK(N), STAT=ISTAT ) IF( ISTAT == 0 )THEN CALL POSVX_F77( LFACT, LUPLO, N, NRHS, A, N, LAF, N, LEQUED, LS, & B, N, X, N, LRCOND, LFERR, LBERR, WORK, RWORK, LINFO ) ELSE; LINFO = -100; END IF IF( .NOT.PRESENT(S) ) DEALLOCATE( LS, STAT=ISTAT1 ) IF( .NOT.PRESENT(AF) ) DEALLOCATE( LAF, STAT=ISTAT1 ) IF( .NOT.PRESENT(FERR) ) DEALLOCATE( LFERR, STAT=ISTAT1 ) IF( .NOT.PRESENT(BERR) ) DEALLOCATE( LBERR, STAT=ISTAT1 ) IF( PRESENT(RCOND) ) RCOND=LRCOND IF( PRESENT(EQUED) .AND. .NOT.LSAME(LFACT,'F') ) EQUED=LEQUED DEALLOCATE( WORK, RWORK, STAT=ISTAT1 ) END IF CALL ERINFO( LINFO, SRNAME, INFO, ISTAT ) END SUBROUTINE ZPOSVX_F95