zher2()

subroutine zher2	(	character	uplo,
		integer	n,
		complex*16	alpha,
		complex*16, dimension(*)	x,
		integer	incx,
		complex*16, dimension(*)	y,
		integer	incy,
		complex*16, dimension(lda,*)	a,
		integer	lda
	)

ZHER2

Purpose:

 ZHER2  performs the hermitian rank 2 operation

    A := alpha*x*y**H + conjg( alpha )*y*x**H + A,

 where alpha is a scalar, x and y are n element vectors and A is an n
 by n hermitian matrix.

Parameters

[in]	UPLO	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.
[in]	N	N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero.
[in]	ALPHA	ALPHA is COMPLEX*16 On entry, ALPHA specifies the scalar alpha.
[in]	X	X is COMPLEX*16 array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x.
[in]	INCX	INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero.
[in]	Y	Y is COMPLEX*16 array, dimension at least ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y.
[in]	INCY	INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero.
[in,out]	A	A is COMPLEX*16 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.
[in]	LDA	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 ).

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

  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.

Definition at line 149 of file zher2.f.

*
*  -- Reference BLAS level2 routine --
*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      COMPLEX*16 ALPHA
      INTEGER INCX,INCY,LDA,N
      CHARACTER UPLO
*     ..
*     .. Array Arguments ..
      COMPLEX*16 A(LDA,*),X(*),Y(*)
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      COMPLEX*16 ZERO
      parameter(zero= (0.0d+0,0.0d+0))
*     ..
*     .. Local Scalars ..
      COMPLEX*16 TEMP1,TEMP2
      INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY
*     ..
*     .. External Functions ..
      LOGICAL LSAME
      EXTERNAL lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC dble,dconjg,max
*     ..
*
*     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 (incy.EQ.0) THEN
          info = 7
      ELSE IF (lda.LT.max(1,n)) THEN
          info = 9
      END IF
      IF (info.NE.0) THEN
          CALL xerbla('ZHER2 ',info)
          RETURN
      END IF
*
*     Quick return if possible.
*
      IF ((n.EQ.0) .OR. (alpha.EQ.zero)) RETURN
*
*     Set up the start points in X and Y if the increments are not both
*     unity.
*
      IF ((incx.NE.1) .OR. (incy.NE.1)) THEN
          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
          jx = kx
          jy = ky
      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 the upper triangle.
*
          IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN
              DO 20 j = 1,n
                  IF ((x(j).NE.zero) .OR. (y(j).NE.zero)) THEN
                      temp1 = alpha*dconjg(y(j))
                      temp2 = dconjg(alpha*x(j))
                      DO 10 i = 1,j - 1
                          a(i,j) = a(i,j) + x(i)*temp1 + y(i)*temp2
   10                 CONTINUE
                      a(j,j) = dble(a(j,j)) +
     +                         dble(x(j)*temp1+y(j)*temp2)
                  ELSE
                      a(j,j) = dble(a(j,j))
                  END IF
   20         CONTINUE
          ELSE
              DO 40 j = 1,n
                  IF ((x(jx).NE.zero) .OR. (y(jy).NE.zero)) THEN
                      temp1 = alpha*dconjg(y(jy))
                      temp2 = dconjg(alpha*x(jx))
                      ix = kx
                      iy = ky
                      DO 30 i = 1,j - 1
                          a(i,j) = a(i,j) + x(ix)*temp1 + y(iy)*temp2
                          ix = ix + incx
                          iy = iy + incy
   30                 CONTINUE
                      a(j,j) = dble(a(j,j)) +
     +                         dble(x(jx)*temp1+y(jy)*temp2)
                  ELSE
                      a(j,j) = dble(a(j,j))
                  END IF
                  jx = jx + incx
                  jy = jy + incy
   40         CONTINUE
          END IF
      ELSE
*
*        Form  A  when A is stored in the lower triangle.
*
          IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN
              DO 60 j = 1,n
                  IF ((x(j).NE.zero) .OR. (y(j).NE.zero)) THEN
                      temp1 = alpha*dconjg(y(j))
                      temp2 = dconjg(alpha*x(j))
                      a(j,j) = dble(a(j,j)) +
     +                         dble(x(j)*temp1+y(j)*temp2)
                      DO 50 i = j + 1,n
                          a(i,j) = a(i,j) + x(i)*temp1 + y(i)*temp2
   50                 CONTINUE
                  ELSE
                      a(j,j) = dble(a(j,j))
                  END IF
   60         CONTINUE
          ELSE
              DO 80 j = 1,n
                  IF ((x(jx).NE.zero) .OR. (y(jy).NE.zero)) THEN
                      temp1 = alpha*dconjg(y(jy))
                      temp2 = dconjg(alpha*x(jx))
                      a(j,j) = dble(a(j,j)) +
     +                         dble(x(jx)*temp1+y(jy)*temp2)
                      ix = jx
                      iy = jy
                      DO 70 i = j + 1,n
                          ix = ix + incx
                          iy = iy + incy
                          a(i,j) = a(i,j) + x(ix)*temp1 + y(iy)*temp2
   70                 CONTINUE
                  ELSE
                      a(j,j) = dble(a(j,j))
                  END IF
                  jx = jx + incx
                  jy = jy + incy
   80         CONTINUE
          END IF
      END IF
*
      RETURN
*
*     End of ZHER2
*

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