ctpsv.f

          SUBROUTINE CTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX)
    *     .. Scalar Arguments ..
          INTEGER INCX,N
          CHARACTER DIAG,TRANS,UPLO
    *     ..
    *     .. Array Arguments ..
          COMPLEX AP(*),X(*)
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  CTPSV  solves one of the systems of equations
    *
    *     A*x = b,   or   A'*x = b,   or   conjg( A' )*x = b,
    *
    *  where b and x are n element vectors and A is an n by n unit, or
    *  non-unit, upper or lower triangular matrix, supplied in packed form.
    *
    *  No test for singularity or near-singularity is included in this
    *  routine. Such tests must be performed before calling this routine.
    *
    *  Arguments
    *  ==========
    *
    *  UPLO   - CHARACTER*1.
    *           On entry, UPLO specifies whether the matrix is an upper or
    *           lower triangular matrix as follows:
    *
    *              UPLO = 'U' or 'u'   A is an upper triangular matrix.
    *
    *              UPLO = 'L' or 'l'   A is a lower triangular matrix.
    *
    *           Unchanged on exit.
    *
    *  TRANS  - CHARACTER*1.
    *           On entry, TRANS specifies the equations to be solved as
    *           follows:
    *
    *              TRANS = 'N' or 'n'   A*x = b.
    *
    *              TRANS = 'T' or 't'   A'*x = b.
    *
    *              TRANS = 'C' or 'c'   conjg( A' )*x = b.
    *
    *           Unchanged on exit.
    *
    *  DIAG   - CHARACTER*1.
    *           On entry, DIAG specifies whether or not A is unit
    *           triangular as follows:
    *
    *              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
    *
    *              DIAG = 'N' or 'n'   A is not assumed to be unit
    *                                  triangular.
    *
    *           Unchanged on exit.
    *
    *  N      - INTEGER.
    *           On entry, N specifies the order of the matrix A.
    *           N must be at least zero.
    *           Unchanged on exit.
    *
    *  AP     - COMPLEX          array of DIMENSION at least
    *           ( ( n*( n + 1 ) )/2 ).
    *           Before entry with  UPLO = 'U' or 'u', the array AP must
    *           contain the upper triangular matrix packed sequentially,
    *           column by column, so that AP( 1 ) contains a( 1, 1 ),
    *           AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
    *           respectively, and so on.
    *           Before entry with UPLO = 'L' or 'l', the array AP must
    *           contain the lower triangular matrix packed sequentially,
    *           column by column, so that AP( 1 ) contains a( 1, 1 ),
    *           AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
    *           respectively, and so on.
    *           Note that when  DIAG = 'U' or 'u', the diagonal elements of
    *           A are not referenced, but are assumed to be unity.
    *           Unchanged on exit.
    *
    *  X      - COMPLEX          array of dimension at least
    *           ( 1 + ( n - 1 )*abs( INCX ) ).
    *           Before entry, the incremented array X must contain the n
    *           element right-hand side vector b. On exit, X is overwritten
    *           with the solution vector x.
    *
    *  INCX   - INTEGER.
    *           On entry, INCX specifies the increment for the elements of
    *           X. INCX must not be zero.
    *           Unchanged on exit.
    *
    *
    *  Level 2 Blas routine.
    *
    *  -- Written on 22-October-1986.
    *     Jack Dongarra, Argonne National Lab.
    *     Jeremy Du Croz, Nag Central Office.
    *     Sven Hammarling, Nag Central Office.
    *     Richard Hanson, Sandia National Labs.
    *
    *
    *     .. Parameters ..
          COMPLEX ZERO
          PARAMETER (ZERO= (0.0E+0,0.0E+0))
    *     ..
    *     .. Local Scalars ..
          COMPLEX TEMP
          INTEGER I,INFO,IX,J,JX,K,KK,KX
          LOGICAL NOCONJ,NOUNIT
    *     ..
    *     .. External Functions ..
          LOGICAL LSAME
          EXTERNAL LSAME
    *     ..
    *     .. External Subroutines ..
          EXTERNAL XERBLA
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC CONJG
    *     ..
    *
    *     Test the input parameters.
    *
          INFO = 0
          IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
              INFO = 1
          ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
         +         .NOT.LSAME(TRANS,'C')) THEN
              INFO = 2
          ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
              INFO = 3
          ELSE IF (N.LT.0) THEN
              INFO = 4
          ELSE IF (INCX.EQ.0) THEN
              INFO = 7
          END IF
          IF (INFO.NE.0) THEN
              CALL XERBLA('CTPSV ',INFO)
              RETURN
          END IF
    *
    *     Quick return if possible.
    *
          IF (N.EQ.0) RETURN
    *
          NOCONJ = LSAME(TRANS,'T')
          NOUNIT = LSAME(DIAG,'N')
    *
    *     Set up the start point in X if the increment is not unity. This
    *     will be  ( N - 1 )*INCX  too small for descending loops.
    *
          IF (INCX.LE.0) THEN
              KX = 1 - (N-1)*INCX
          ELSE IF (INCX.NE.1) THEN
              KX = 1
          END IF
    *
    *     Start the operations. In this version the elements of AP are
    *     accessed sequentially with one pass through AP.
    *
          IF (LSAME(TRANS,'N')) THEN
    *
    *        Form  x := inv( A )*x.
    *
              IF (LSAME(UPLO,'U')) THEN
                  KK = (N* (N+1))/2
                  IF (INCX.EQ.1) THEN
                      DO 20 J = N,1,-1
                          IF (X(J).NE.ZERO) THEN
                              IF (NOUNIT) X(J) = X(J)/AP(KK)
                              TEMP = X(J)
                              K = KK - 1
                              DO 10 I = J - 1,1,-1
                                  X(I) = X(I) - TEMP*AP(K)
                                  K = K - 1
       10                     CONTINUE
                          END IF
                          KK = KK - J
       20             CONTINUE
                  ELSE
                      JX = KX + (N-1)*INCX
                      DO 40 J = N,1,-1
                          IF (X(JX).NE.ZERO) THEN
                              IF (NOUNIT) X(JX) = X(JX)/AP(KK)
                              TEMP = X(JX)
                              IX = JX
                              DO 30 K = KK - 1,KK - J + 1,-1
                                  IX = IX - INCX
                                  X(IX) = X(IX) - TEMP*AP(K)
       30                     CONTINUE
                          END IF
                          JX = JX - INCX
                          KK = KK - J
       40             CONTINUE
                  END IF
              ELSE
                  KK = 1
                  IF (INCX.EQ.1) THEN
                      DO 60 J = 1,N
                          IF (X(J).NE.ZERO) THEN
                              IF (NOUNIT) X(J) = X(J)/AP(KK)
                              TEMP = X(J)
                              K = KK + 1
                              DO 50 I = J + 1,N
                                  X(I) = X(I) - TEMP*AP(K)
                                  K = K + 1
       50                     CONTINUE
                          END IF
                          KK = KK + (N-J+1)
       60             CONTINUE
                  ELSE
                      JX = KX
                      DO 80 J = 1,N
                          IF (X(JX).NE.ZERO) THEN
                              IF (NOUNIT) X(JX) = X(JX)/AP(KK)
                              TEMP = X(JX)
                              IX = JX
                              DO 70 K = KK + 1,KK + N - J
                                  IX = IX + INCX
                                  X(IX) = X(IX) - TEMP*AP(K)
       70                     CONTINUE
                          END IF
                          JX = JX + INCX
                          KK = KK + (N-J+1)
       80             CONTINUE
                  END IF
              END IF
          ELSE
    *
    *        Form  x := inv( A' )*x  or  x := inv( conjg( A' ) )*x.
    *
              IF (LSAME(UPLO,'U')) THEN
                  KK = 1
                  IF (INCX.EQ.1) THEN
                      DO 110 J = 1,N
                          TEMP = X(J)
                          K = KK
                          IF (NOCONJ) THEN
                              DO 90 I = 1,J - 1
                                  TEMP = TEMP - AP(K)*X(I)
                                  K = K + 1
       90                     CONTINUE
                              IF (NOUNIT) TEMP = TEMP/AP(KK+J-1)
                          ELSE
                              DO 100 I = 1,J - 1
                                  TEMP = TEMP - CONJG(AP(K))*X(I)
                                  K = K + 1
      100                     CONTINUE
                              IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK+J-1))
                          END IF
                          X(J) = TEMP
                          KK = KK + J
      110             CONTINUE
                  ELSE
                      JX = KX
                      DO 140 J = 1,N
                          TEMP = X(JX)
                          IX = KX
                          IF (NOCONJ) THEN
                              DO 120 K = KK,KK + J - 2
                                  TEMP = TEMP - AP(K)*X(IX)
                                  IX = IX + INCX
      120                     CONTINUE
                              IF (NOUNIT) TEMP = TEMP/AP(KK+J-1)
                          ELSE
                              DO 130 K = KK,KK + J - 2
                                  TEMP = TEMP - CONJG(AP(K))*X(IX)
                                  IX = IX + INCX
      130                     CONTINUE
                              IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK+J-1))
                          END IF
                          X(JX) = TEMP
                          JX = JX + INCX
                          KK = KK + J
      140             CONTINUE
                  END IF
              ELSE
                  KK = (N* (N+1))/2
                  IF (INCX.EQ.1) THEN
                      DO 170 J = N,1,-1
                          TEMP = X(J)
                          K = KK
                          IF (NOCONJ) THEN
                              DO 150 I = N,J + 1,-1
                                  TEMP = TEMP - AP(K)*X(I)
                                  K = K - 1
      150                     CONTINUE
                              IF (NOUNIT) TEMP = TEMP/AP(KK-N+J)
                          ELSE
                              DO 160 I = N,J + 1,-1
                                  TEMP = TEMP - CONJG(AP(K))*X(I)
                                  K = K - 1
      160                     CONTINUE
                              IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK-N+J))
                          END IF
                          X(J) = TEMP
                          KK = KK - (N-J+1)
      170             CONTINUE
                  ELSE
                      KX = KX + (N-1)*INCX
                      JX = KX
                      DO 200 J = N,1,-1
                          TEMP = X(JX)
                          IX = KX
                          IF (NOCONJ) THEN
                              DO 180 K = KK,KK - (N- (J+1)),-1
                                  TEMP = TEMP - AP(K)*X(IX)
                                  IX = IX - INCX
      180                     CONTINUE
                              IF (NOUNIT) TEMP = TEMP/AP(KK-N+J)
                          ELSE
                              DO 190 K = KK,KK - (N- (J+1)),-1
                                  TEMP = TEMP - CONJG(AP(K))*X(IX)
                                  IX = IX - INCX
      190                     CONTINUE
                              IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK-N+J))
                          END IF
                          X(JX) = TEMP
                          JX = JX - INCX
                          KK = KK - (N-J+1)
      200             CONTINUE
                  END IF
              END IF
          END IF
    *
          RETURN
    *
    *     End of CTPSV .
    *
          END