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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.** 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.** =====================================================================** .. 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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