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(*)
* ..
*
* Purpose
* =======
*
* CHPR2 performs the hermitian rank 2 operation
*
* A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + 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.
*
* Arguments
* ==========
*
* UPLO - 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.
*
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the order of the matrix A.
* N must be at least zero.
* Unchanged on exit.
*
* ALPHA - COMPLEX .
* On entry, ALPHA specifies the scalar alpha.
* Unchanged on exit.
*
* X - COMPLEX array of dimension at least
* ( 1 + ( n - 1 )*abs( INCX ) ).
* Before entry, the incremented array X must contain the n
* element vector x.
* Unchanged on exit.
*
* INCX - INTEGER.
* On entry, INCX specifies the increment for the elements of
* X. INCX must not be zero.
* Unchanged on exit.
*
* Y - COMPLEX array of dimension at least
* ( 1 + ( n - 1 )*abs( INCY ) ).
* Before entry, the incremented array Y must contain the n
* element vector y.
* Unchanged on exit.
*
* INCY - INTEGER.
* On entry, INCY specifies the increment for the elements of
* Y. INCY must not be zero.
* Unchanged on exit.
*
* AP - COMPLEX array of 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.
*
*
* 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.
*
*
* .. 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