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

*> \brief \b SSBMV
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE SSBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*
*       .. Scalar Arguments ..
*       REAL ALPHA,BETA
*       INTEGER INCX,INCY,K,LDA,N
*       CHARACTER UPLO
*       ..
*       .. Array Arguments ..
*       REAL A(LDA,*),X(*),Y(*)
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> SSBMV  performs the matrix-vector  operation
*>
*>    y := alpha*A*x + beta*y,
*>
*> where alpha and beta are scalars, x and y are n element vectors and
*> A is an n by n symmetric band matrix, with k super-diagonals.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>           On entry, UPLO specifies whether the upper or lower
*>           triangular part of the band matrix A is being supplied as
*>           follows:
*>
*>              UPLO = 'U' or 'u'   The upper triangular part of A is
*>                                  being supplied.
*>
*>              UPLO = 'L' or 'l'   The lower triangular part of A is
*>                                  being supplied.
*> \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, K specifies the number of super-diagonals of the
*>           matrix A. K must satisfy  0 .le. K.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*>          ALPHA is REAL
*>           On entry, ALPHA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is REAL 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 symmetric matrix, 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 the upper
*>           triangular part of a symmetric 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 symmetric matrix, 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 the lower
*>           triangular part of a symmetric 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
*> \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] X
*> \verbatim
*>          X is REAL array, dimension at least
*>           ( 1 + ( n - 1 )*abs( INCX ) ).
*>           Before entry, the incremented array X must contain the
*>           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
*>
*> \param[in] BETA
*> \verbatim
*>          BETA is REAL
*>           On entry, BETA specifies the scalar beta.
*> \endverbatim
*>
*> \param[in,out] Y
*> \verbatim
*>          Y is REAL array, dimension at least
*>           ( 1 + ( n - 1 )*abs( INCY ) ).
*>           Before entry, the incremented array Y must contain the
*>           vector y. On exit, Y is overwritten by the updated vector y.
*> \endverbatim
*>
*> \param[in] INCY
*> \verbatim
*>          INCY is INTEGER
*>           On entry, INCY specifies the increment for the elements of
*>           Y. INCY 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 single_blas_level2
*
*> \par Further Details:
*  =====================
*>
*> \verbatim
*>
*>  Level 2 Blas routine.
*>  The vector and matrix arguments are not referenced when N = 0, or M = 0
*>
*>  -- 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 SSBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*
*  -- 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 ..
      REAL ALPHA,BETA
      INTEGER INCX,INCY,K,LDA,N
      CHARACTER UPLO
*     ..
*     .. Array Arguments ..
      REAL A(LDA,*),X(*),Y(*)
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL ONE,ZERO
      PARAMETER (ONE=1.0E+0,ZERO=0.0E+0)
*     ..
*     .. Local Scalars ..
      REAL TEMP1,TEMP2
      INTEGER I,INFO,IX,IY,J,JX,JY,KPLUS1,KX,KY,L
*     ..
*     .. External Functions ..
      LOGICAL LSAME
      EXTERNAL LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC MAX,MIN
*     ..
*
*     Test the input parameters.
*
      INFO = 0
      IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
          INFO = 1
      ELSE IF (N.LT.0) THEN
          INFO = 2
      ELSE IF (K.LT.0) THEN
          INFO = 3
      ELSE IF (LDA.LT. (K+1)) THEN
          INFO = 6
      ELSE IF (INCX.EQ.0) THEN
          INFO = 8
      ELSE IF (INCY.EQ.0) THEN
          INFO = 11
      END IF
      IF (INFO.NE.0) THEN
          CALL XERBLA('SSBMV ',INFO)
          RETURN
      END IF
*
*     Quick return if possible.
*
      IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
*
*     Set up the start points in  X  and  Y.
*
      IF (INCX.GT.0) THEN
          KX = 1
      ELSE
          KX = 1 - (N-1)*INCX
      END IF
      IF (INCY.GT.0) THEN
          KY = 1
      ELSE
          KY = 1 - (N-1)*INCY
      END IF
*
*     Start the operations. In this version the elements of the array A
*     are accessed sequentially with one pass through A.
*
*     First form  y := beta*y.
*
      IF (BETA.NE.ONE) THEN
          IF (INCY.EQ.1) THEN
              IF (BETA.EQ.ZERO) THEN
                  DO 10 I = 1,N
                      Y(I) = ZERO
   10             CONTINUE
              ELSE
                  DO 20 I = 1,N
                      Y(I) = BETA*Y(I)
   20             CONTINUE
              END IF
          ELSE
              IY = KY
              IF (BETA.EQ.ZERO) THEN
                  DO 30 I = 1,N
                      Y(IY) = ZERO
                      IY = IY + INCY
   30             CONTINUE
              ELSE
                  DO 40 I = 1,N
                      Y(IY) = BETA*Y(IY)
                      IY = IY + INCY
   40             CONTINUE
              END IF
          END IF
      END IF
      IF (ALPHA.EQ.ZERO) RETURN
      IF (LSAME(UPLO,'U')) THEN
*
*        Form  y  when upper triangle of A is stored.
*
          KPLUS1 = K + 1
          IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
              DO 60 J = 1,N
                  TEMP1 = ALPHA*X(J)
                  TEMP2 = ZERO
                  L = KPLUS1 - J
                  DO 50 I = MAX(1,J-K),J - 1
                      Y(I) = Y(I) + TEMP1*A(L+I,J)
                      TEMP2 = TEMP2 + A(L+I,J)*X(I)
   50             CONTINUE
                  Y(J) = Y(J) + TEMP1*A(KPLUS1,J) + ALPHA*TEMP2
   60         CONTINUE
          ELSE
              JX = KX
              JY = KY
              DO 80 J = 1,N
                  TEMP1 = ALPHA*X(JX)
                  TEMP2 = ZERO
                  IX = KX
                  IY = KY
                  L = KPLUS1 - J
                  DO 70 I = MAX(1,J-K),J - 1
                      Y(IY) = Y(IY) + TEMP1*A(L+I,J)
                      TEMP2 = TEMP2 + A(L+I,J)*X(IX)
                      IX = IX + INCX
                      IY = IY + INCY
   70             CONTINUE
                  Y(JY) = Y(JY) + TEMP1*A(KPLUS1,J) + ALPHA*TEMP2
                  JX = JX + INCX
                  JY = JY + INCY
                  IF (J.GT.K) THEN
                      KX = KX + INCX
                      KY = KY + INCY
                  END IF
   80         CONTINUE
          END IF
      ELSE
*
*        Form  y  when lower triangle of A is stored.
*
          IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
              DO 100 J = 1,N
                  TEMP1 = ALPHA*X(J)
                  TEMP2 = ZERO
                  Y(J) = Y(J) + TEMP1*A(1,J)
                  L = 1 - J
                  DO 90 I = J + 1,MIN(N,J+K)
                      Y(I) = Y(I) + TEMP1*A(L+I,J)
                      TEMP2 = TEMP2 + A(L+I,J)*X(I)
   90             CONTINUE
                  Y(J) = Y(J) + ALPHA*TEMP2
  100         CONTINUE
          ELSE
              JX = KX
              JY = KY
              DO 120 J = 1,N
                  TEMP1 = ALPHA*X(JX)
                  TEMP2 = ZERO
                  Y(JY) = Y(JY) + TEMP1*A(1,J)
                  L = 1 - J
                  IX = JX
                  IY = JY
                  DO 110 I = J + 1,MIN(N,J+K)
                      IX = IX + INCX
                      IY = IY + INCY
                      Y(IY) = Y(IY) + TEMP1*A(L+I,J)
                      TEMP2 = TEMP2 + A(L+I,J)*X(IX)
  110             CONTINUE
                  Y(JY) = Y(JY) + ALPHA*TEMP2
                  JX = JX + INCX
                  JY = JY + INCY
  120         CONTINUE
          END IF
      END IF
*
      RETURN
*
*     End of SSBMV .
*
      END