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*> \brief \b CHPR2
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE CHPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)
*
* .. Scalar Arguments ..
* COMPLEX ALPHA
* INTEGER INCX,INCY,N
* CHARACTER UPLO
* ..
* .. Array Arguments ..
* COMPLEX AP(*),X(*),Y(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CHPR2 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, supplied in packed form.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> On entry, UPLO specifies whether the upper or lower
*> triangular part of the matrix A is supplied in the packed
*> array AP as follows:
*>
*> UPLO = 'U' or 'u' The upper triangular part of A is
*> supplied in AP.
*>
*> UPLO = 'L' or 'l' The lower triangular part of A is
*> supplied in AP.
*> \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 COMPLEX
*> 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] Y
*> \verbatim
*> Y is COMPLEX array, dimension at least
*> ( 1 + ( n - 1 )*abs( INCY ) ).
*> Before entry, the incremented array Y must contain the n
*> element 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
*>
*> \param[in,out] AP
*> \verbatim
*> AP is COMPLEX array, dimension at least
*> ( ( n*( n + 1 ) )/2 ).
*> Before entry with UPLO = 'U' or 'u', the array AP must
*> contain the upper triangular part of the hermitian 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. On exit, the array
*> AP is overwritten by the upper triangular part of the
*> updated matrix.
*> Before entry with UPLO = 'L' or 'l', the array AP must
*> contain the lower triangular part of the hermitian 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. On exit, the array
*> AP 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
*
* 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 CHPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)
*
* -- 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 ..
COMPLEX ALPHA
INTEGER INCX,INCY,N
CHARACTER UPLO
* ..
* .. Array Arguments ..
COMPLEX AP(*),X(*),Y(*)
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX ZERO
PARAMETER (ZERO= (0.0E+0,0.0E+0))
* ..
* .. Local Scalars ..
COMPLEX TEMP1,TEMP2
INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC CONJG,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 (INCY.EQ.0) THEN
INFO = 7
END IF
IF (INFO.NE.0) THEN
CALL XERBLA('CHPR2 ',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 the array AP
* are accessed sequentially with one pass through AP.
*
KK = 1
IF (LSAME(UPLO,'U')) THEN
*
* Form A when upper triangle is stored in AP.
*
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*CONJG(Y(J))
TEMP2 = CONJG(ALPHA*X(J))
K = KK
DO 10 I = 1,J - 1
AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2
K = K + 1
10 CONTINUE
AP(KK+J-1) = REAL(AP(KK+J-1)) +
+ REAL(X(J)*TEMP1+Y(J)*TEMP2)
ELSE
AP(KK+J-1) = REAL(AP(KK+J-1))
END IF
KK = KK + J
20 CONTINUE
ELSE
DO 40 J = 1,N
IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
TEMP1 = ALPHA*CONJG(Y(JY))
TEMP2 = CONJG(ALPHA*X(JX))
IX = KX
IY = KY
DO 30 K = KK,KK + J - 2
AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2
IX = IX + INCX
IY = IY + INCY
30 CONTINUE
AP(KK+J-1) = REAL(AP(KK+J-1)) +
+ REAL(X(JX)*TEMP1+Y(JY)*TEMP2)
ELSE
AP(KK+J-1) = REAL(AP(KK+J-1))
END IF
JX = JX + INCX
JY = JY + INCY
KK = KK + J
40 CONTINUE
END IF
ELSE
*
* Form A when lower triangle is stored in AP.
*
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*CONJG(Y(J))
TEMP2 = CONJG(ALPHA*X(J))
AP(KK) = REAL(AP(KK)) +
+ REAL(X(J)*TEMP1+Y(J)*TEMP2)
K = KK + 1
DO 50 I = J + 1,N
AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2
K = K + 1
50 CONTINUE
ELSE
AP(KK) = REAL(AP(KK))
END IF
KK = KK + N - J + 1
60 CONTINUE
ELSE
DO 80 J = 1,N
IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
TEMP1 = ALPHA*CONJG(Y(JY))
TEMP2 = CONJG(ALPHA*X(JX))
AP(KK) = REAL(AP(KK)) +
+ REAL(X(JX)*TEMP1+Y(JY)*TEMP2)
IX = JX
IY = JY
DO 70 K = KK + 1,KK + N - J
IX = IX + INCX
IY = IY + INCY
AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2
70 CONTINUE
ELSE
AP(KK) = REAL(AP(KK))
END IF
JX = JX + INCX
JY = JY + INCY
KK = KK + N - J + 1
80 CONTINUE
END IF
END IF
*
RETURN
*
* End of CHPR2 .
*
END
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