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

*> \brief \b CHER
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE CHER(UPLO,N,ALPHA,X,INCX,A,LDA)
*
*       .. Scalar Arguments ..
*       REAL ALPHA
*       INTEGER INCX,LDA,N
*       CHARACTER UPLO
*       ..
*       .. Array Arguments ..
*       COMPLEX A(LDA,*),X(*)
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> CHER   performs the hermitian rank 1 operation
*>
*>    A := alpha*x*x**H + A,
*>
*> where alpha is a real scalar, x is an n element vector and A is an
*> n by n hermitian matrix.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>           On entry, UPLO specifies whether the upper or lower
*>           triangular part of the array A is to be referenced as
*>           follows:
*>
*>              UPLO = 'U' or 'u'   Only the upper triangular part of A
*>                                  is to be referenced.
*>
*>              UPLO = 'L' or 'l'   Only the lower triangular part of A
*>                                  is to be referenced.
*> \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] ALPHA
*> \verbatim
*>          ALPHA is REAL
*>           On entry, ALPHA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] 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 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,out] A
*> \verbatim
*>          A is COMPLEX array, dimension ( LDA, N )
*>           Before entry with  UPLO = 'U' or 'u', the leading n by n
*>           upper triangular part of the array A must contain the upper
*>           triangular part of the hermitian matrix and the strictly
*>           lower triangular part of A is not referenced. On exit, the
*>           upper triangular part of the array A is overwritten by the
*>           upper triangular part of the updated matrix.
*>           Before entry with UPLO = 'L' or 'l', the leading n by n
*>           lower triangular part of the array A must contain the lower
*>           triangular part of the hermitian matrix and the strictly
*>           upper triangular part of A is not referenced. On exit, the
*>           lower triangular part of the array A is overwritten by the
*>           lower triangular part of the updated matrix.
*>           Note that the imaginary parts of the diagonal elements need
*>           not be set, they are assumed to be zero, and on exit they
*>           are set to zero.
*> \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
*>           max( 1, n ).
*> \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 CHER(UPLO,N,ALPHA,X,INCX,A,LDA)
*
*  -- 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
      INTEGER INCX,LDA,N
      CHARACTER 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,KX
*     ..
*     .. External Functions ..
      LOGICAL LSAME
      EXTERNAL LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC CONJG,MAX,REAL
*     ..
*
*     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 (INCX.EQ.0) THEN
          INFO = 5
      ELSE IF (LDA.LT.MAX(1,N)) THEN
          INFO = 7
      END IF
      IF (INFO.NE.0) THEN
          CALL XERBLA('CHER  ',INFO)
          RETURN
      END IF
*
*     Quick return if possible.
*
      IF ((N.EQ.0) .OR. (ALPHA.EQ.REAL(ZERO))) RETURN
*
*     Set the start point in X if the increment is not unity.
*
      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 sequentially with one pass through the triangular part
*     of A.
*
      IF (LSAME(UPLO,'U')) THEN
*
*        Form  A  when A is stored in upper triangle.
*
          IF (INCX.EQ.1) THEN
              DO 20 J = 1,N
                  IF (X(J).NE.ZERO) THEN
                      TEMP = ALPHA*CONJG(X(J))
                      DO 10 I = 1,J - 1
                          A(I,J) = A(I,J) + X(I)*TEMP
   10                 CONTINUE
                      A(J,J) = REAL(A(J,J)) + REAL(X(J)*TEMP)
                  ELSE
                      A(J,J) = REAL(A(J,J))
                  END IF
   20         CONTINUE
          ELSE
              JX = KX
              DO 40 J = 1,N
                  IF (X(JX).NE.ZERO) THEN
                      TEMP = ALPHA*CONJG(X(JX))
                      IX = KX
                      DO 30 I = 1,J - 1
                          A(I,J) = A(I,J) + X(IX)*TEMP
                          IX = IX + INCX
   30                 CONTINUE
                      A(J,J) = REAL(A(J,J)) + REAL(X(JX)*TEMP)
                  ELSE
                      A(J,J) = REAL(A(J,J))
                  END IF
                  JX = JX + INCX
   40         CONTINUE
          END IF
      ELSE
*
*        Form  A  when A is stored in lower triangle.
*
          IF (INCX.EQ.1) THEN
              DO 60 J = 1,N
                  IF (X(J).NE.ZERO) THEN
                      TEMP = ALPHA*CONJG(X(J))
                      A(J,J) = REAL(A(J,J)) + REAL(TEMP*X(J))
                      DO 50 I = J + 1,N
                          A(I,J) = A(I,J) + X(I)*TEMP
   50                 CONTINUE
                  ELSE
                      A(J,J) = REAL(A(J,J))
                  END IF
   60         CONTINUE
          ELSE
              JX = KX
              DO 80 J = 1,N
                  IF (X(JX).NE.ZERO) THEN
                      TEMP = ALPHA*CONJG(X(JX))
                      A(J,J) = REAL(A(J,J)) + REAL(TEMP*X(JX))
                      IX = JX
                      DO 70 I = J + 1,N
                          IX = IX + INCX
                          A(I,J) = A(I,J) + X(IX)*TEMP
   70                 CONTINUE
                  ELSE
                      A(J,J) = REAL(A(J,J))
                  END IF
                  JX = JX + INCX
   80         CONTINUE
          END IF
      END IF
*
      RETURN
*
*     End of CHER  .
*
      END