*> \brief \b ZHPR * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZHPR(UPLO,N,ALPHA,X,INCX,AP) * * .. Scalar Arguments .. * DOUBLE PRECISION ALPHA * INTEGER INCX,N * CHARACTER UPLO * .. * .. Array Arguments .. * COMPLEX*16 AP(*),X(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZHPR performs the hermitian rank 1 operation *> *> A := alpha*x*x**H + 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. *> \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 DOUBLE PRECISION. *> On entry, ALPHA specifies the scalar alpha. *> \endverbatim *> *> \param[in] X *> \verbatim *> X is COMPLEX*16 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,out] AP *> \verbatim *> AP is COMPLEX*16 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. * *> \ingroup complex16_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 ZHPR(UPLO,N,ALPHA,X,INCX,AP) * * -- Reference BLAS level2 routine -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. DOUBLE PRECISION ALPHA INTEGER INCX,N CHARACTER UPLO * .. * .. Array Arguments .. COMPLEX*16 AP(*),X(*) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ZERO PARAMETER (ZERO= (0.0D+0,0.0D+0)) * .. * .. Local Scalars .. COMPLEX*16 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