OpenBLAS/lapack-netlib/BLAS/SRC/ctbsv.f

*> \brief \b CTBSV
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE CTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
*
*       .. Scalar Arguments ..
*       INTEGER INCX,K,LDA,N
*       CHARACTER DIAG,TRANS,UPLO
*       ..
*       .. Array Arguments ..
*       COMPLEX A(LDA,*),X(*)
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> CTBSV  solves one of the systems of equations
*>
*>    A*x = b,   or   A**T*x = b,   or   A**H*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 band matrix, with ( k + 1 )
*> diagonals.
*>
*> No test for singularity or near-singularity is included in this
*> routine. Such tests must be performed before calling this routine.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is 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.
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*>          TRANS is 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**T*x = b.
*>
*>              TRANS = 'C' or 'c'   A**H*x = b.
*> \endverbatim
*>
*> \param[in] DIAG
*> \verbatim
*>          DIAG is 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.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>           On entry, N specifies the order of the matrix A.
*>           N must be at least zero.
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*>          K is INTEGER
*>           On entry with UPLO = 'U' or 'u', K specifies the number of
*>           super-diagonals of the matrix A.
*>           On entry with UPLO = 'L' or 'l', K specifies the number of
*>           sub-diagonals of the matrix A.
*>           K must satisfy  0 .le. K.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is COMPLEX array, dimension ( LDA, N )
*>           Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
*>           by n part of the array A must contain the upper triangular
*>           band part of the matrix of coefficients, supplied column by
*>           column, with the leading diagonal of the matrix in row
*>           ( k + 1 ) of the array, the first super-diagonal starting at
*>           position 2 in row k, and so on. The top left k by k triangle
*>           of the array A is not referenced.
*>           The following program segment will transfer an upper
*>           triangular band matrix from conventional full matrix storage
*>           to band storage:
*>
*>                 DO 20, J = 1, N
*>                    M = K + 1 - J
*>                    DO 10, I = MAX( 1, J - K ), J
*>                       A( M + I, J ) = matrix( I, J )
*>              10    CONTINUE
*>              20 CONTINUE
*>
*>           Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
*>           by n part of the array A must contain the lower triangular
*>           band part of the matrix of coefficients, supplied column by
*>           column, with the leading diagonal of the matrix in row 1 of
*>           the array, the first sub-diagonal starting at position 1 in
*>           row 2, and so on. The bottom right k by k triangle of the
*>           array A is not referenced.
*>           The following program segment will transfer a lower
*>           triangular band matrix from conventional full matrix storage
*>           to band storage:
*>
*>                 DO 20, J = 1, N
*>                    M = 1 - J
*>                    DO 10, I = J, MIN( N, J + K )
*>                       A( M + I, J ) = matrix( I, J )
*>              10    CONTINUE
*>              20 CONTINUE
*>
*>           Note that when DIAG = 'U' or 'u' the elements of the array A
*>           corresponding to the diagonal elements of the matrix are not
*>           referenced, but are assumed to be unity.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>           On entry, LDA specifies the first dimension of A as declared
*>           in the calling (sub) program. LDA must be at least
*>           ( k + 1 ).
*> \endverbatim
*>
*> \param[in,out] X
*> \verbatim
*>          X is COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*>          INCX is INTEGER
*>           On entry, INCX specifies the increment for the elements of
*>           X. INCX must not be zero.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup complex_blas_level2
*
*> \par Further Details:
*  =====================
*>
*> \verbatim
*>
*>  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.
*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE CTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
*
*  -- Reference BLAS level2 routine (version 3.7.0) --
*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     December 2016
*
*     .. Scalar Arguments ..
      INTEGER INCX,K,LDA,N
      CHARACTER DIAG,TRANS,UPLO
*     ..
*     .. Array Arguments ..
      COMPLEX A(LDA,*),X(*)
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      COMPLEX ZERO
      PARAMETER (ZERO= (0.0E+0,0.0E+0))
*     ..
*     .. Local Scalars ..
      COMPLEX TEMP
      INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L
      LOGICAL NOCONJ,NOUNIT
*     ..
*     .. External Functions ..
      LOGICAL LSAME
      EXTERNAL LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC CONJG,MAX,MIN
*     ..
*
*     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 (K.LT.0) THEN
          INFO = 5
      ELSE IF (LDA.LT. (K+1)) THEN
          INFO = 7
      ELSE IF (INCX.EQ.0) THEN
          INFO = 9
      END IF
      IF (INFO.NE.0) THEN
          CALL XERBLA('CTBSV ',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 A are
*     accessed by sequentially with one pass through A.
*
      IF (LSAME(TRANS,'N')) THEN
*
*        Form  x := inv( A )*x.
*
          IF (LSAME(UPLO,'U')) THEN
              KPLUS1 = K + 1
              IF (INCX.EQ.1) THEN
                  DO 20 J = N,1,-1
                      IF (X(J).NE.ZERO) THEN
                          L = KPLUS1 - J
                          IF (NOUNIT) X(J) = X(J)/A(KPLUS1,J)
                          TEMP = X(J)
                          DO 10 I = J - 1,MAX(1,J-K),-1
                              X(I) = X(I) - TEMP*A(L+I,J)
   10                     CONTINUE
                      END IF
   20             CONTINUE
              ELSE
                  KX = KX + (N-1)*INCX
                  JX = KX
                  DO 40 J = N,1,-1
                      KX = KX - INCX
                      IF (X(JX).NE.ZERO) THEN
                          IX = KX
                          L = KPLUS1 - J
                          IF (NOUNIT) X(JX) = X(JX)/A(KPLUS1,J)
                          TEMP = X(JX)
                          DO 30 I = J - 1,MAX(1,J-K),-1
                              X(IX) = X(IX) - TEMP*A(L+I,J)
                              IX = IX - INCX
   30                     CONTINUE
                      END IF
                      JX = JX - INCX
   40             CONTINUE
              END IF
          ELSE
              IF (INCX.EQ.1) THEN
                  DO 60 J = 1,N
                      IF (X(J).NE.ZERO) THEN
                          L = 1 - J
                          IF (NOUNIT) X(J) = X(J)/A(1,J)
                          TEMP = X(J)
                          DO 50 I = J + 1,MIN(N,J+K)
                              X(I) = X(I) - TEMP*A(L+I,J)
   50                     CONTINUE
                      END IF
   60             CONTINUE
              ELSE
                  JX = KX
                  DO 80 J = 1,N
                      KX = KX + INCX
                      IF (X(JX).NE.ZERO) THEN
                          IX = KX
                          L = 1 - J
                          IF (NOUNIT) X(JX) = X(JX)/A(1,J)
                          TEMP = X(JX)
                          DO 70 I = J + 1,MIN(N,J+K)
                              X(IX) = X(IX) - TEMP*A(L+I,J)
                              IX = IX + INCX
   70                     CONTINUE
                      END IF
                      JX = JX + INCX
   80             CONTINUE
              END IF
          END IF
      ELSE
*
*        Form  x := inv( A**T )*x  or  x := inv( A**H )*x.
*
          IF (LSAME(UPLO,'U')) THEN
              KPLUS1 = K + 1
              IF (INCX.EQ.1) THEN
                  DO 110 J = 1,N
                      TEMP = X(J)
                      L = KPLUS1 - J
                      IF (NOCONJ) THEN
                          DO 90 I = MAX(1,J-K),J - 1
                              TEMP = TEMP - A(L+I,J)*X(I)
   90                     CONTINUE
                          IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J)
                      ELSE
                          DO 100 I = MAX(1,J-K),J - 1
                              TEMP = TEMP - CONJG(A(L+I,J))*X(I)
  100                     CONTINUE
                          IF (NOUNIT) TEMP = TEMP/CONJG(A(KPLUS1,J))
                      END IF
                      X(J) = TEMP
  110             CONTINUE
              ELSE
                  JX = KX
                  DO 140 J = 1,N
                      TEMP = X(JX)
                      IX = KX
                      L = KPLUS1 - J
                      IF (NOCONJ) THEN
                          DO 120 I = MAX(1,J-K),J - 1
                              TEMP = TEMP - A(L+I,J)*X(IX)
                              IX = IX + INCX
  120                     CONTINUE
                          IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J)
                      ELSE
                          DO 130 I = MAX(1,J-K),J - 1
                              TEMP = TEMP - CONJG(A(L+I,J))*X(IX)
                              IX = IX + INCX
  130                     CONTINUE
                          IF (NOUNIT) TEMP = TEMP/CONJG(A(KPLUS1,J))
                      END IF
                      X(JX) = TEMP
                      JX = JX + INCX
                      IF (J.GT.K) KX = KX + INCX
  140             CONTINUE
              END IF
          ELSE
              IF (INCX.EQ.1) THEN
                  DO 170 J = N,1,-1
                      TEMP = X(J)
                      L = 1 - J
                      IF (NOCONJ) THEN
                          DO 150 I = MIN(N,J+K),J + 1,-1
                              TEMP = TEMP - A(L+I,J)*X(I)
  150                     CONTINUE
                          IF (NOUNIT) TEMP = TEMP/A(1,J)
                      ELSE
                          DO 160 I = MIN(N,J+K),J + 1,-1
                              TEMP = TEMP - CONJG(A(L+I,J))*X(I)
  160                     CONTINUE
                          IF (NOUNIT) TEMP = TEMP/CONJG(A(1,J))
                      END IF
                      X(J) = TEMP
  170             CONTINUE
              ELSE
                  KX = KX + (N-1)*INCX
                  JX = KX
                  DO 200 J = N,1,-1
                      TEMP = X(JX)
                      IX = KX
                      L = 1 - J
                      IF (NOCONJ) THEN
                          DO 180 I = MIN(N,J+K),J + 1,-1
                              TEMP = TEMP - A(L+I,J)*X(IX)
                              IX = IX - INCX
  180                     CONTINUE
                          IF (NOUNIT) TEMP = TEMP/A(1,J)
                      ELSE
                          DO 190 I = MIN(N,J+K),J + 1,-1
                              TEMP = TEMP - CONJG(A(L+I,J))*X(IX)
                              IX = IX - INCX
  190                     CONTINUE
                          IF (NOUNIT) TEMP = TEMP/CONJG(A(1,J))
                      END IF
                      X(JX) = TEMP
                      JX = JX - INCX
                      IF ((N-J).GE.K) KX = KX - INCX
  200             CONTINUE
              END IF
          END IF
      END IF
*
      RETURN
*
*     End of CTBSV .
*
      END