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import reference BLAS routines which are not already implemented in Eigen : modified givens rotations, and packed and banded storages
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Gael Guennebaud
255
blas/chpr2.f
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255
blas/chpr2.f
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SUBROUTINE CHPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)
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* .. Scalar Arguments ..
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COMPLEX ALPHA
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INTEGER INCX,INCY,N
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CHARACTER UPLO
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* ..
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* .. Array Arguments ..
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COMPLEX AP(*),X(*),Y(*)
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* ..
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*
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* Purpose
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* =======
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*
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* CHPR2 performs the hermitian rank 2 operation
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*
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* A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A,
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*
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* where alpha is a scalar, x and y are n element vectors and A is an
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* n by n hermitian matrix, supplied in packed form.
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*
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* Arguments
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* ==========
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*
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* UPLO - CHARACTER*1.
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* On entry, UPLO specifies whether the upper or lower
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* triangular part of the matrix A is supplied in the packed
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* array AP as follows:
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*
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* UPLO = 'U' or 'u' The upper triangular part of A is
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* supplied in AP.
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*
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* UPLO = 'L' or 'l' The lower triangular part of A is
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* supplied in AP.
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*
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* Unchanged on exit.
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*
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* N - INTEGER.
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* On entry, N specifies the order of the matrix A.
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* N must be at least zero.
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* Unchanged on exit.
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*
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* ALPHA - COMPLEX .
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* On entry, ALPHA specifies the scalar alpha.
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* Unchanged on exit.
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*
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* X - COMPLEX array of dimension at least
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* ( 1 + ( n - 1 )*abs( INCX ) ).
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* Before entry, the incremented array X must contain the n
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* element vector x.
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* Unchanged on exit.
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*
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* INCX - INTEGER.
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* On entry, INCX specifies the increment for the elements of
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* X. INCX must not be zero.
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* Unchanged on exit.
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*
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* Y - COMPLEX array of dimension at least
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* ( 1 + ( n - 1 )*abs( INCY ) ).
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* Before entry, the incremented array Y must contain the n
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* element vector y.
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* Unchanged on exit.
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*
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* INCY - INTEGER.
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* On entry, INCY specifies the increment for the elements of
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* Y. INCY must not be zero.
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* Unchanged on exit.
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*
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* AP - COMPLEX array of DIMENSION at least
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* ( ( n*( n + 1 ) )/2 ).
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* Before entry with UPLO = 'U' or 'u', the array AP must
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* contain the upper triangular part of the hermitian matrix
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* packed sequentially, column by column, so that AP( 1 )
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* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
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* and a( 2, 2 ) respectively, and so on. On exit, the array
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* AP is overwritten by the upper triangular part of the
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* updated matrix.
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* Before entry with UPLO = 'L' or 'l', the array AP must
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* contain the lower triangular part of the hermitian matrix
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* packed sequentially, column by column, so that AP( 1 )
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* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
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* and a( 3, 1 ) respectively, and so on. On exit, the array
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* AP is overwritten by the lower triangular part of the
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* updated matrix.
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* Note that the imaginary parts of the diagonal elements need
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* not be set, they are assumed to be zero, and on exit they
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* are set to zero.
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*
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* Further Details
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* ===============
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*
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* Level 2 Blas routine.
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*
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* -- Written on 22-October-1986.
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* Jack Dongarra, Argonne National Lab.
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* Jeremy Du Croz, Nag Central Office.
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* Sven Hammarling, Nag Central Office.
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* Richard Hanson, Sandia National Labs.
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*
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* =====================================================================
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*
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* .. Parameters ..
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COMPLEX ZERO
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PARAMETER (ZERO= (0.0E+0,0.0E+0))
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* ..
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* .. Local Scalars ..
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COMPLEX TEMP1,TEMP2
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INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC CONJG,REAL
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* ..
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*
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* Test the input parameters.
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*
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INFO = 0
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IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
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INFO = 1
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ELSE IF (N.LT.0) THEN
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INFO = 2
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ELSE IF (INCX.EQ.0) THEN
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INFO = 5
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ELSE IF (INCY.EQ.0) THEN
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INFO = 7
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END IF
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IF (INFO.NE.0) THEN
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CALL XERBLA('CHPR2 ',INFO)
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RETURN
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END IF
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*
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* Quick return if possible.
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*
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IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN
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*
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* Set up the start points in X and Y if the increments are not both
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* unity.
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*
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IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN
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IF (INCX.GT.0) THEN
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KX = 1
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ELSE
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KX = 1 - (N-1)*INCX
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END IF
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IF (INCY.GT.0) THEN
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KY = 1
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ELSE
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KY = 1 - (N-1)*INCY
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END IF
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JX = KX
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JY = KY
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END IF
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*
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* Start the operations. In this version the elements of the array AP
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* are accessed sequentially with one pass through AP.
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*
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KK = 1
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IF (LSAME(UPLO,'U')) THEN
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*
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* Form A when upper triangle is stored in AP.
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*
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IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
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DO 20 J = 1,N
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IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN
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TEMP1 = ALPHA*CONJG(Y(J))
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TEMP2 = CONJG(ALPHA*X(J))
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K = KK
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DO 10 I = 1,J - 1
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AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2
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K = K + 1
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10 CONTINUE
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AP(KK+J-1) = REAL(AP(KK+J-1)) +
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+ REAL(X(J)*TEMP1+Y(J)*TEMP2)
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ELSE
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AP(KK+J-1) = REAL(AP(KK+J-1))
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END IF
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KK = KK + J
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20 CONTINUE
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ELSE
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DO 40 J = 1,N
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IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
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TEMP1 = ALPHA*CONJG(Y(JY))
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TEMP2 = CONJG(ALPHA*X(JX))
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IX = KX
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IY = KY
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DO 30 K = KK,KK + J - 2
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AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2
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IX = IX + INCX
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IY = IY + INCY
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30 CONTINUE
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AP(KK+J-1) = REAL(AP(KK+J-1)) +
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+ REAL(X(JX)*TEMP1+Y(JY)*TEMP2)
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ELSE
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AP(KK+J-1) = REAL(AP(KK+J-1))
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END IF
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JX = JX + INCX
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JY = JY + INCY
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KK = KK + J
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40 CONTINUE
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END IF
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ELSE
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*
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* Form A when lower triangle is stored in AP.
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*
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IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
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DO 60 J = 1,N
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IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN
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TEMP1 = ALPHA*CONJG(Y(J))
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TEMP2 = CONJG(ALPHA*X(J))
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AP(KK) = REAL(AP(KK)) +
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+ REAL(X(J)*TEMP1+Y(J)*TEMP2)
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K = KK + 1
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DO 50 I = J + 1,N
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AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2
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K = K + 1
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50 CONTINUE
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ELSE
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AP(KK) = REAL(AP(KK))
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END IF
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KK = KK + N - J + 1
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60 CONTINUE
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ELSE
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DO 80 J = 1,N
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IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
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TEMP1 = ALPHA*CONJG(Y(JY))
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TEMP2 = CONJG(ALPHA*X(JX))
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AP(KK) = REAL(AP(KK)) +
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+ REAL(X(JX)*TEMP1+Y(JY)*TEMP2)
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IX = JX
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IY = JY
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DO 70 K = KK + 1,KK + N - J
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IX = IX + INCX
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IY = IY + INCY
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AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2
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70 CONTINUE
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ELSE
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AP(KK) = REAL(AP(KK))
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END IF
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JX = JX + INCX
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JY = JY + INCY
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KK = KK + N - J + 1
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80 CONTINUE
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END IF
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END IF
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*
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RETURN
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*
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* End of CHPR2 .
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*
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END
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