318 lines
9.3 KiB
Fortran
318 lines
9.3 KiB
Fortran
*> \brief \b ZHER2
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE ZHER2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA)
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* COMPLEX*16 ALPHA
|
|
* INTEGER INCX,INCY,LDA,N
|
|
* CHARACTER UPLO
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* COMPLEX*16 A(LDA,*),X(*),Y(*)
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> ZHER2 performs the hermitian rank 2 operation
|
|
*>
|
|
*> A := alpha*x*y**H + conjg( alpha )*y*x**H + A,
|
|
*>
|
|
*> where alpha is a scalar, x and y are n element vectors and A is an n
|
|
*> by n hermitian matrix.
|
|
*> \endverbatim
|
|
*
|
|
* Arguments:
|
|
* ==========
|
|
*
|
|
*> \param[in] UPLO
|
|
*> \verbatim
|
|
*> UPLO is CHARACTER*1
|
|
*> On entry, UPLO specifies whether the upper or lower
|
|
*> triangular part of the array A is to be referenced as
|
|
*> follows:
|
|
*>
|
|
*> UPLO = 'U' or 'u' Only the upper triangular part of A
|
|
*> is to be referenced.
|
|
*>
|
|
*> UPLO = 'L' or 'l' Only the lower triangular part of A
|
|
*> is to be referenced.
|
|
*> \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 COMPLEX*16
|
|
*> 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] Y
|
|
*> \verbatim
|
|
*> Y is COMPLEX*16 array, dimension at least
|
|
*> ( 1 + ( n - 1 )*abs( INCY ) ).
|
|
*> Before entry, the incremented array Y must contain the n
|
|
*> element vector y.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] INCY
|
|
*> \verbatim
|
|
*> INCY is INTEGER
|
|
*> On entry, INCY specifies the increment for the elements of
|
|
*> Y. INCY must not be zero.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in,out] A
|
|
*> \verbatim
|
|
*> A is COMPLEX*16 array, dimension ( LDA, N )
|
|
*> Before entry with UPLO = 'U' or 'u', the leading n by n
|
|
*> upper triangular part of the array A must contain the upper
|
|
*> triangular part of the hermitian matrix and the strictly
|
|
*> lower triangular part of A is not referenced. On exit, the
|
|
*> upper triangular part of the array A is overwritten by the
|
|
*> upper triangular part of the updated matrix.
|
|
*> Before entry with UPLO = 'L' or 'l', the leading n by n
|
|
*> lower triangular part of the array A must contain the lower
|
|
*> triangular part of the hermitian matrix and the strictly
|
|
*> upper triangular part of A is not referenced. On exit, the
|
|
*> lower triangular part of the array A 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
|
|
*>
|
|
*> \param[in] LDA
|
|
*> \verbatim
|
|
*> LDA is INTEGER
|
|
*> On entry, LDA specifies the first dimension of A as declared
|
|
*> in the calling (sub) program. LDA must be at least
|
|
*> max( 1, n ).
|
|
*> \endverbatim
|
|
*
|
|
* Authors:
|
|
* ========
|
|
*
|
|
*> \author Univ. of Tennessee
|
|
*> \author Univ. of California Berkeley
|
|
*> \author Univ. of Colorado Denver
|
|
*> \author NAG Ltd.
|
|
*
|
|
*> \date December 2016
|
|
*
|
|
*> \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 ZHER2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA)
|
|
*
|
|
* -- Reference BLAS level2 routine (version 3.7.0) --
|
|
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
|
* December 2016
|
|
*
|
|
* .. Scalar Arguments ..
|
|
COMPLEX*16 ALPHA
|
|
INTEGER INCX,INCY,LDA,N
|
|
CHARACTER UPLO
|
|
* ..
|
|
* .. Array Arguments ..
|
|
COMPLEX*16 A(LDA,*),X(*),Y(*)
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
COMPLEX*16 ZERO
|
|
PARAMETER (ZERO= (0.0D+0,0.0D+0))
|
|
* ..
|
|
* .. Local Scalars ..
|
|
COMPLEX*16 TEMP1,TEMP2
|
|
INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY
|
|
* ..
|
|
* .. External Functions ..
|
|
LOGICAL LSAME
|
|
EXTERNAL LSAME
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL XERBLA
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC DBLE,DCONJG,MAX
|
|
* ..
|
|
*
|
|
* 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
|
|
ELSE IF (LDA.LT.MAX(1,N)) THEN
|
|
INFO = 9
|
|
END IF
|
|
IF (INFO.NE.0) THEN
|
|
CALL XERBLA('ZHER2 ',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 A are
|
|
* accessed sequentially with one pass through the triangular part
|
|
* of A.
|
|
*
|
|
IF (LSAME(UPLO,'U')) THEN
|
|
*
|
|
* Form A when A is stored in the upper triangle.
|
|
*
|
|
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*DCONJG(Y(J))
|
|
TEMP2 = DCONJG(ALPHA*X(J))
|
|
DO 10 I = 1,J - 1
|
|
A(I,J) = A(I,J) + X(I)*TEMP1 + Y(I)*TEMP2
|
|
10 CONTINUE
|
|
A(J,J) = DBLE(A(J,J)) +
|
|
+ DBLE(X(J)*TEMP1+Y(J)*TEMP2)
|
|
ELSE
|
|
A(J,J) = DBLE(A(J,J))
|
|
END IF
|
|
20 CONTINUE
|
|
ELSE
|
|
DO 40 J = 1,N
|
|
IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
|
|
TEMP1 = ALPHA*DCONJG(Y(JY))
|
|
TEMP2 = DCONJG(ALPHA*X(JX))
|
|
IX = KX
|
|
IY = KY
|
|
DO 30 I = 1,J - 1
|
|
A(I,J) = A(I,J) + X(IX)*TEMP1 + Y(IY)*TEMP2
|
|
IX = IX + INCX
|
|
IY = IY + INCY
|
|
30 CONTINUE
|
|
A(J,J) = DBLE(A(J,J)) +
|
|
+ DBLE(X(JX)*TEMP1+Y(JY)*TEMP2)
|
|
ELSE
|
|
A(J,J) = DBLE(A(J,J))
|
|
END IF
|
|
JX = JX + INCX
|
|
JY = JY + INCY
|
|
40 CONTINUE
|
|
END IF
|
|
ELSE
|
|
*
|
|
* Form A when A is stored in the lower triangle.
|
|
*
|
|
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*DCONJG(Y(J))
|
|
TEMP2 = DCONJG(ALPHA*X(J))
|
|
A(J,J) = DBLE(A(J,J)) +
|
|
+ DBLE(X(J)*TEMP1+Y(J)*TEMP2)
|
|
DO 50 I = J + 1,N
|
|
A(I,J) = A(I,J) + X(I)*TEMP1 + Y(I)*TEMP2
|
|
50 CONTINUE
|
|
ELSE
|
|
A(J,J) = DBLE(A(J,J))
|
|
END IF
|
|
60 CONTINUE
|
|
ELSE
|
|
DO 80 J = 1,N
|
|
IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
|
|
TEMP1 = ALPHA*DCONJG(Y(JY))
|
|
TEMP2 = DCONJG(ALPHA*X(JX))
|
|
A(J,J) = DBLE(A(J,J)) +
|
|
+ DBLE(X(JX)*TEMP1+Y(JY)*TEMP2)
|
|
IX = JX
|
|
IY = JY
|
|
DO 70 I = J + 1,N
|
|
IX = IX + INCX
|
|
IY = IY + INCY
|
|
A(I,J) = A(I,J) + X(IX)*TEMP1 + Y(IY)*TEMP2
|
|
70 CONTINUE
|
|
ELSE
|
|
A(J,J) = DBLE(A(J,J))
|
|
END IF
|
|
JX = JX + INCX
|
|
JY = JY + INCY
|
|
80 CONTINUE
|
|
END IF
|
|
END IF
|
|
*
|
|
RETURN
|
|
*
|
|
* End of ZHER2 .
|
|
*
|
|
END
|