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SUBROUTINE ZHPR(UPLO,N,ALPHA,X,INCX,AP)* .. Scalar Arguments .. DOUBLE PRECISION ALPHA INTEGER INCX,N CHARACTER UPLO* ..* .. Array Arguments .. DOUBLE COMPLEX AP(*),X(*)* ..** Purpose* =======** ZHPR performs the hermitian rank 1 operation** A := alpha*x*conjg( x' ) + A,** where alpha is a real scalar, x is an n element vector 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 - DOUBLE PRECISION.* On entry, ALPHA specifies the scalar alpha.* Unchanged on exit.** X - COMPLEX*16 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.** AP - COMPLEX*16 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 .. DOUBLE COMPLEX ZERO PARAMETER (ZERO= (0.0D+0,0.0D+0))* ..* .. Local Scalars .. DOUBLE COMPLEX TEMP INTEGER I,INFO,IX,J,JX,K,KK,KX* ..* .. External Functions .. LOGICAL LSAME EXTERNAL LSAME* ..* .. External Subroutines .. EXTERNAL XERBLA* ..* .. Intrinsic Functions .. INTRINSIC DBLE,DCONJG* ..** 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 END IF IF (INFO.NE.0) THEN CALL XERBLA('ZHPR ',INFO) RETURN END IF** Quick return if possible.* IF ((N.EQ.0) .OR. (ALPHA.EQ.DBLE(ZERO))) RETURN** Set the start point in X if the increment is not unity.* IF (INCX.LE.0) THEN KX = 1 - (N-1)*INCX ELSE IF (INCX.NE.1) THEN KX = 1 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) THEN DO 20 J = 1,N IF (X(J).NE.ZERO) THEN TEMP = ALPHA*DCONJG(X(J)) K = KK DO 10 I = 1,J - 1 AP(K) = AP(K) + X(I)*TEMP K = K + 1 10 CONTINUE AP(KK+J-1) = DBLE(AP(KK+J-1)) + DBLE(X(J)*TEMP) ELSE AP(KK+J-1) = DBLE(AP(KK+J-1)) END IF KK = KK + J 20 CONTINUE ELSE JX = KX DO 40 J = 1,N IF (X(JX).NE.ZERO) THEN TEMP = ALPHA*DCONJG(X(JX)) IX = KX DO 30 K = KK,KK + J - 2 AP(K) = AP(K) + X(IX)*TEMP IX = IX + INCX 30 CONTINUE AP(KK+J-1) = DBLE(AP(KK+J-1)) + DBLE(X(JX)*TEMP) ELSE AP(KK+J-1) = DBLE(AP(KK+J-1)) END IF JX = JX + INCX KK = KK + J 40 CONTINUE END IF ELSE** Form A when lower triangle is stored in AP.* IF (INCX.EQ.1) THEN DO 60 J = 1,N IF (X(J).NE.ZERO) THEN TEMP = ALPHA*DCONJG(X(J)) AP(KK) = DBLE(AP(KK)) + DBLE(TEMP*X(J)) K = KK + 1 DO 50 I = J + 1,N AP(K) = AP(K) + X(I)*TEMP K = K + 1 50 CONTINUE ELSE AP(KK) = DBLE(AP(KK)) END IF KK = KK + N - J + 1 60 CONTINUE ELSE JX = KX DO 80 J = 1,N IF (X(JX).NE.ZERO) THEN TEMP = ALPHA*DCONJG(X(JX)) AP(KK) = DBLE(AP(KK)) + DBLE(TEMP*X(JX)) IX = JX DO 70 K = KK + 1,KK + N - J IX = IX + INCX AP(K) = AP(K) + X(IX)*TEMP 70 CONTINUE ELSE AP(KK) = DBLE(AP(KK)) END IF JX = JX + INCX KK = KK + N - J + 1 80 CONTINUE END IF END IF* RETURN** End of ZHPR .* END
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