forked from lijiext/lammps
280 lines
7.9 KiB
Fortran
280 lines
7.9 KiB
Fortran
*> \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 of 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 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.
|
|
*> \endverbatim
|
|
*
|
|
* Authors:
|
|
* ========
|
|
*
|
|
*> \author Univ. of Tennessee
|
|
*> \author Univ. of California Berkeley
|
|
*> \author Univ. of Colorado Denver
|
|
*> \author NAG Ltd.
|
|
*
|
|
*> \date November 2011
|
|
*
|
|
*> \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 (version 3.4.0) --
|
|
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
|
* November 2011
|
|
*
|
|
* .. 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
|