SUBROUTINE ZGTSVX_F95(DL, D, DU, B, X, DLF, DF, DUF, DU2, & IPIV, FACT, TRANS, 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: GTSVX_F77 => LA_GTSVX ! .. IMPLICIT STATEMENT .. IMPLICIT NONE ! .. SCALAR ARGUMENTS .. CHARACTER(LEN=1), INTENT(IN), OPTIONAL :: TRANS, FACT INTEGER, INTENT(OUT), OPTIONAL :: INFO REAL(WP), INTENT(OUT), OPTIONAL :: RCOND ! .. ARRAY ARGUMENTS .. COMPLEX(WP), INTENT(IN) :: DL(:), D(:), DU(:), B(:,:) INTEGER, INTENT(INOUT), OPTIONAL, TARGET :: IPIV(:) COMPLEX(WP), INTENT(INOUT), OPTIONAL, TARGET :: DLF(:), DF(:), DUF(:), DU2(:) REAL(WP), INTENT(OUT), OPTIONAL, TARGET :: FERR(:), BERR(:) COMPLEX(WP), INTENT(OUT) :: X(:,:) !---------------------------------------------------------------------- ! ! Purpose ! ======= ! ! LA_GTSVX computes the solution to a real or complex linear system ! of equations of the form A*X = B, A^T*X = B or A^H*X = B, where A is a ! square tridiagonal matrix and X and B are rectangular matrices or ! vectors. ! LA_GTSVX can also optionally estimate the condition number of A and ! compute error bounds. ! ! ========= ! ! SUBROUTINE LA_GTSVX( DL, D, DU, B, X, DLF=dlf, DF=df, DUF=duf, & ! DU2=du2, IPIV=ipiv, FACT=fact, TRANS=trans, FERR=ferr, & ! BERR=berr, RCOND=rcond, INFO=info ) ! (), INTENT(IN) :: DL(:), D(:), DU(:), ! (), INTENT(OUT) :: ! (), INTENT(INOUT), OPTIONAL :: DLF(:), DF(:), & ! DUF(:), DU2(:) ! INTEGER, INTENT(INOUT), OPTIONAL :: IPIV(:) ! CHARACTER(LEN=1), INTENT(IN), OPTIONAL :: FACT, TRANS ! 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 ! ========= ! ! DL (input) REAL or COMPLEX array, shape (:) with size(DL) = n-1. ! The subdiagonal of A. ! D (input) REAL or COMPLEX array, shape (:) with size(D) = n. ! The diagonal of A. ! DU (input) REAL or COMPLEX array, shape (:) with size(DU) = n-1. ! The superdiagonal of A. ! B (input/output) REAL or COMPLEX array, shape (:,:) with ! size(B,1) = n or shape (:) with size(B) = n. ! The matrix B. ! X (output) REAL or COMPLEX array, shape (:,:) with size(X,1) = n ! and size(X,2) = size(B,2), or shape (:) with size(X) = n. ! The solution matrix X . ! DLF Optional (input or output) REAL or COMPLEX array, shape (:) with ! size(DLF)= n-1. ! If FACT = 'F' then DLF is an input argument that contains the ! multipliers that define the matrix L from the LU factorization ! of A. ! If FACT = 'N' then DLF is an output argument that contains the ! multipliers that define the matrix L from the LU factorization ! of A. ! DF Optional (input or output) REAL or COMPLEX array, shape (:) with ! size(DF)= n. ! If FACT = 'F' then DF is an input argument that contains the ! diagonal of the matrix U . ! If FACT = 'N' then DF is an output argument that contains the ! diagonal of the matrix U . ! DUF Optional (input or output) REAL or COMPLEX array, shape (:) with ! size(DUF) = n-1. ! If FACT = 'F' then DUF is an input argument that contains the ! first superdiagonal of U. ! If FACT = 'N' then DUF is an output argument that contains the ! first superdiagonal of U. ! DU2 Optional (input or output) REAL or COMPLEX array, shape (:) with ! size(DU2) = n-2. ! If FACT = 'F', then DU2 is an input argument that contains the ! second superdiagonal of U. ! If FACT = 'N', then DU2 is an output argument that contains the ! second superdiagonal of U. ! IPIV Optional (input or output) INTEGER array, shape (:) with ! size(IPIV) = n. ! If FACT = 'F' then IPIV is an input argument that contains the ! pivot indices from the LU factorization of A. ! If FACT = 'N', then IPIV is an output argument that contains the ! pivot indices from the LU factorization of A; row i of the ! matrix was interchanged with row IPIV(i). IPIV(i) will always ! be either i or i+1; IPIV(i) = i indicates a row interchange was ! not required. ! FACT Optional (input) CHARACTER(LEN=1). ! Specifies whether the factored form of A is supplied on entry. ! = 'N': The matrix will be copied to DLF, DF and DUF and ! factored. ! = 'F': DLF, DF, DUF, DU2 and IPIV contain the factored form ! of A. ! Default value: 'N'. ! TRANS Optional (input) CHARACTER(LEN=1). ! Specifies the form of the system of equations: ! = 'N': A*X = B (No transpose) ! = 'T': A^T*X = B (Transpose) ! = 'C': A^H*X = B (Conjugate transpose) ! Default value: 'N'. ! 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 matrix 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: U(i,i) = 0. The factorization has not been completed ! unless i = n. The factor U is singular, so the solution ! could not be computed. ! = n+1: U is nonsingular, but RCOND is less than machine ! precision, meaning that 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_GTSVX' ! .. LOCAL SCALARS .. CHARACTER(LEN=1) :: LFACT, LTRANS INTEGER :: LINFO, NRHS, N, ISTAT, ISTAT1, SIPIV, SDLF, SDF, SDUF, SDU2, & SFERR, SBERR REAL(WP) :: LRCOND ! .. LOCAL POINTERS .. INTEGER, POINTER :: LPIV(:) REAL(WP), POINTER :: RWORK(:), LFERR(:), LBERR(:) COMPLEX(WP), POINTER :: WORK(:), LDLF(:), LDF(:), LDUF(:), LDU2(:) ! .. INTRINSIC FUNCTIONS .. INTRINSIC PRESENT, SIZE ! .. EXECUTABLE STATEMENTS .. LINFO = 0; ISTAT = 0 N = SIZE(D); NRHS = SIZE(B,2) IF( PRESENT(RCOND) ) RCOND = 1.0_WP IF( PRESENT(FACT) )THEN; LFACT = FACT; ELSE; LFACT='N'; END IF IF( PRESENT(IPIV) )THEN; SIPIV = SIZE(IPIV); ELSE; SIPIV = N; END IF IF( PRESENT(DLF) )THEN; SDLF = SIZE(DLF); ELSE; SDLF = N-1; END IF IF( PRESENT(DF) )THEN; SDF = SIZE(DF); ELSE; SDF = N; END IF IF( PRESENT(DUF) )THEN; SDUF = SIZE(DUF); ELSE; SDUF = N-1; END IF IF( PRESENT(DU2) )THEN; SDU2 = SIZE(DU2); ELSE; SDU2 = N-2; END IF 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(TRANS))THEN; LTRANS = TRANS; ELSE; LTRANS='N'; END IF ! PRINT *, LINFO, ISTAT, N, NRHS, LFACT, SIPIV, SDLF, SDF, SDUF, SDU2, SFERR, SBERR, LTRANS ! .. TEST THE ARGUMENTS IF( SIZE( DL ) /= N-1 .AND. N/=0 ) THEN; LINFO = -1 ELSE IF( N < 0 ) THEN; LINFO = -2 ELSE IF( SIZE( DU ) /= N-1 .AND. N/=0) THEN; LINFO = -3 ELSE IF( SIZE(B, 1) /= N .OR. NRHS < 0 )THEN; LINFO = -4 ELSE IF( SIZE(X, 1) /= N .OR. SIZE(X, 2) /= NRHS )THEN; LINFO = -5 ELSE IF( SDLF /= N-1 .AND. N/=0) THEN; LINFO = -6 ELSE IF( SDF /= N ) THEN; LINFO = -7 ELSE IF( SDUF /= N-1 .AND. N/=0 ) THEN; LINFO = -8 ELSE IF( SDU2 /= N-2 .AND. N>1 ) THEN; LINFO = -9 ELSE IF( SIPIV /= N )THEN; LINFO = -10 ELSE IF( SFERR /= NRHS )THEN; LINFO = -13 ELSE IF( SBERR /= NRHS )THEN; LINFO = -14 ELSE IF( ( .NOT. ( LSAME(LFACT,'F') .OR. LSAME(LFACT,'N') ) ) .OR. & ( LSAME(LFACT,'F') .AND. .NOT.( PRESENT(DF) .AND. PRESENT(IPIV) ) ) )THEN LINFO = -11 ELSE IF( .NOT.( LSAME(LTRANS,'N') .OR. LSAME(LTRANS,'T') .OR. & LSAME(LTRANS,'C') ) )THEN; LINFO = -12 ELSE IF ( N > 0 )THEN IF( .NOT.PRESENT(DF) ) THEN ALLOCATE( LDLF(N-1),LDF(N),LDUF(N-1),LDU2(N-2), STAT=ISTAT ) ELSE; LDLF => DLF; LDF => DF; LDUF => DUF; LDU2 => DU2; END IF IF( ISTAT == 0 )THEN IF( .NOT.PRESENT(IPIV) )THEN; ALLOCATE( LPIV(N), STAT=ISTAT ) ELSE; LPIV => IPIV; 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 GTSVX_F77( LFACT, LTRANS, N, NRHS, DL, D, DU, LDLF, LDF, LDUF, & LDU2, LPIV, B, N, X, N, LRCOND, LFERR, LBERR, & WORK, RWORK, LINFO ) ELSE; LINFO = -100; END IF IF( .NOT.PRESENT(DLF) ) DEALLOCATE( LDLF, LDF, LDUF, LDU2, STAT=ISTAT1 ) IF( .NOT.PRESENT(IPIV) ) DEALLOCATE( LPIV, STAT=ISTAT1 ) IF( .NOT.PRESENT(FERR) ) DEALLOCATE( LFERR, STAT=ISTAT1 ) IF( .NOT.PRESENT(BERR) ) DEALLOCATE( LBERR, STAT=ISTAT1 ) IF( PRESENT(RCOND) ) RCOND=LRCOND DEALLOCATE( WORK, RWORK, STAT=ISTAT1 ) END IF CALL ERINFO( LINFO, SRNAME, INFO, ISTAT ) END SUBROUTINE ZGTSVX_F95