397 lines
12 KiB
Fortran
397 lines
12 KiB
Fortran
*> \brief \b ZHERK
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE ZHERK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* DOUBLE PRECISION ALPHA,BETA
|
|
* INTEGER K,LDA,LDC,N
|
|
* CHARACTER TRANS,UPLO
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* COMPLEX*16 A(LDA,*),C(LDC,*)
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> ZHERK performs one of the hermitian rank k operations
|
|
*>
|
|
*> C := alpha*A*A**H + beta*C,
|
|
*>
|
|
*> or
|
|
*>
|
|
*> C := alpha*A**H*A + beta*C,
|
|
*>
|
|
*> where alpha and beta are real scalars, C is an n by n hermitian
|
|
*> matrix and A is an n by k matrix in the first case and a k by n
|
|
*> matrix in the second case.
|
|
*> \endverbatim
|
|
*
|
|
* Arguments:
|
|
* ==========
|
|
*
|
|
*> \param[in] UPLO
|
|
*> \verbatim
|
|
*> UPLO is CHARACTER*1
|
|
*> On entry, UPLO specifies whether the upper or lower
|
|
*> triangular part of the array C is to be referenced as
|
|
*> follows:
|
|
*>
|
|
*> UPLO = 'U' or 'u' Only the upper triangular part of C
|
|
*> is to be referenced.
|
|
*>
|
|
*> UPLO = 'L' or 'l' Only the lower triangular part of C
|
|
*> is to be referenced.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] TRANS
|
|
*> \verbatim
|
|
*> TRANS is CHARACTER*1
|
|
*> On entry, TRANS specifies the operation to be performed as
|
|
*> follows:
|
|
*>
|
|
*> TRANS = 'N' or 'n' C := alpha*A*A**H + beta*C.
|
|
*>
|
|
*> TRANS = 'C' or 'c' C := alpha*A**H*A + beta*C.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] N
|
|
*> \verbatim
|
|
*> N is INTEGER
|
|
*> On entry, N specifies the order of the matrix C. N must be
|
|
*> at least zero.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] K
|
|
*> \verbatim
|
|
*> K is INTEGER
|
|
*> On entry with TRANS = 'N' or 'n', K specifies the number
|
|
*> of columns of the matrix A, and on entry with
|
|
*> TRANS = 'C' or 'c', K specifies the number of rows of the
|
|
*> matrix A. K must be at least zero.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] ALPHA
|
|
*> \verbatim
|
|
*> ALPHA is DOUBLE PRECISION .
|
|
*> On entry, ALPHA specifies the scalar alpha.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] A
|
|
*> \verbatim
|
|
*> A is COMPLEX*16 array, dimension ( LDA, ka ), where ka is
|
|
*> k when TRANS = 'N' or 'n', and is n otherwise.
|
|
*> Before entry with TRANS = 'N' or 'n', the leading n by k
|
|
*> part of the array A must contain the matrix A, otherwise
|
|
*> the leading k by n part of the array A must contain the
|
|
*> matrix A.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] LDA
|
|
*> \verbatim
|
|
*> LDA is INTEGER
|
|
*> On entry, LDA specifies the first dimension of A as declared
|
|
*> in the calling (sub) program. When TRANS = 'N' or 'n'
|
|
*> then LDA must be at least max( 1, n ), otherwise LDA must
|
|
*> be at least max( 1, k ).
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] BETA
|
|
*> \verbatim
|
|
*> BETA is DOUBLE PRECISION.
|
|
*> On entry, BETA specifies the scalar beta.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in,out] C
|
|
*> \verbatim
|
|
*> C is COMPLEX*16 array, dimension ( LDC, N )
|
|
*> Before entry with UPLO = 'U' or 'u', the leading n by n
|
|
*> upper triangular part of the array C must contain the upper
|
|
*> triangular part of the hermitian matrix and the strictly
|
|
*> lower triangular part of C is not referenced. On exit, the
|
|
*> upper triangular part of the array C 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 C must contain the lower
|
|
*> triangular part of the hermitian matrix and the strictly
|
|
*> upper triangular part of C is not referenced. On exit, the
|
|
*> lower triangular part of the array C 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] LDC
|
|
*> \verbatim
|
|
*> LDC is INTEGER
|
|
*> On entry, LDC specifies the first dimension of C as declared
|
|
*> in the calling (sub) program. LDC 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_level3
|
|
*
|
|
*> \par Further Details:
|
|
* =====================
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> Level 3 Blas routine.
|
|
*>
|
|
*> -- Written on 8-February-1989.
|
|
*> Jack Dongarra, Argonne National Laboratory.
|
|
*> Iain Duff, AERE Harwell.
|
|
*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
|
|
*> Sven Hammarling, Numerical Algorithms Group Ltd.
|
|
*>
|
|
*> -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1.
|
|
*> Ed Anderson, Cray Research Inc.
|
|
*> \endverbatim
|
|
*>
|
|
* =====================================================================
|
|
SUBROUTINE ZHERK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
|
|
*
|
|
* -- Reference BLAS level3 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 ..
|
|
DOUBLE PRECISION ALPHA,BETA
|
|
INTEGER K,LDA,LDC,N
|
|
CHARACTER TRANS,UPLO
|
|
* ..
|
|
* .. Array Arguments ..
|
|
COMPLEX*16 A(LDA,*),C(LDC,*)
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. External Functions ..
|
|
LOGICAL LSAME
|
|
EXTERNAL LSAME
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL XERBLA
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC DBLE,DCMPLX,DCONJG,MAX
|
|
* ..
|
|
* .. Local Scalars ..
|
|
COMPLEX*16 TEMP
|
|
DOUBLE PRECISION RTEMP
|
|
INTEGER I,INFO,J,L,NROWA
|
|
LOGICAL UPPER
|
|
* ..
|
|
* .. Parameters ..
|
|
DOUBLE PRECISION ONE,ZERO
|
|
PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
|
|
* ..
|
|
*
|
|
* Test the input parameters.
|
|
*
|
|
IF (LSAME(TRANS,'N')) THEN
|
|
NROWA = N
|
|
ELSE
|
|
NROWA = K
|
|
END IF
|
|
UPPER = LSAME(UPLO,'U')
|
|
*
|
|
INFO = 0
|
|
IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
|
|
INFO = 1
|
|
ELSE IF ((.NOT.LSAME(TRANS,'N')) .AND.
|
|
+ (.NOT.LSAME(TRANS,'C'))) THEN
|
|
INFO = 2
|
|
ELSE IF (N.LT.0) THEN
|
|
INFO = 3
|
|
ELSE IF (K.LT.0) THEN
|
|
INFO = 4
|
|
ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
|
|
INFO = 7
|
|
ELSE IF (LDC.LT.MAX(1,N)) THEN
|
|
INFO = 10
|
|
END IF
|
|
IF (INFO.NE.0) THEN
|
|
CALL XERBLA('ZHERK ',INFO)
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Quick return if possible.
|
|
*
|
|
IF ((N.EQ.0) .OR. (((ALPHA.EQ.ZERO).OR.
|
|
+ (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN
|
|
*
|
|
* And when alpha.eq.zero.
|
|
*
|
|
IF (ALPHA.EQ.ZERO) THEN
|
|
IF (UPPER) THEN
|
|
IF (BETA.EQ.ZERO) THEN
|
|
DO 20 J = 1,N
|
|
DO 10 I = 1,J
|
|
C(I,J) = ZERO
|
|
10 CONTINUE
|
|
20 CONTINUE
|
|
ELSE
|
|
DO 40 J = 1,N
|
|
DO 30 I = 1,J - 1
|
|
C(I,J) = BETA*C(I,J)
|
|
30 CONTINUE
|
|
C(J,J) = BETA*DBLE(C(J,J))
|
|
40 CONTINUE
|
|
END IF
|
|
ELSE
|
|
IF (BETA.EQ.ZERO) THEN
|
|
DO 60 J = 1,N
|
|
DO 50 I = J,N
|
|
C(I,J) = ZERO
|
|
50 CONTINUE
|
|
60 CONTINUE
|
|
ELSE
|
|
DO 80 J = 1,N
|
|
C(J,J) = BETA*DBLE(C(J,J))
|
|
DO 70 I = J + 1,N
|
|
C(I,J) = BETA*C(I,J)
|
|
70 CONTINUE
|
|
80 CONTINUE
|
|
END IF
|
|
END IF
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Start the operations.
|
|
*
|
|
IF (LSAME(TRANS,'N')) THEN
|
|
*
|
|
* Form C := alpha*A*A**H + beta*C.
|
|
*
|
|
IF (UPPER) THEN
|
|
DO 130 J = 1,N
|
|
IF (BETA.EQ.ZERO) THEN
|
|
DO 90 I = 1,J
|
|
C(I,J) = ZERO
|
|
90 CONTINUE
|
|
ELSE IF (BETA.NE.ONE) THEN
|
|
DO 100 I = 1,J - 1
|
|
C(I,J) = BETA*C(I,J)
|
|
100 CONTINUE
|
|
C(J,J) = BETA*DBLE(C(J,J))
|
|
ELSE
|
|
C(J,J) = DBLE(C(J,J))
|
|
END IF
|
|
DO 120 L = 1,K
|
|
IF (A(J,L).NE.DCMPLX(ZERO)) THEN
|
|
TEMP = ALPHA*DCONJG(A(J,L))
|
|
DO 110 I = 1,J - 1
|
|
C(I,J) = C(I,J) + TEMP*A(I,L)
|
|
110 CONTINUE
|
|
C(J,J) = DBLE(C(J,J)) + DBLE(TEMP*A(I,L))
|
|
END IF
|
|
120 CONTINUE
|
|
130 CONTINUE
|
|
ELSE
|
|
DO 180 J = 1,N
|
|
IF (BETA.EQ.ZERO) THEN
|
|
DO 140 I = J,N
|
|
C(I,J) = ZERO
|
|
140 CONTINUE
|
|
ELSE IF (BETA.NE.ONE) THEN
|
|
C(J,J) = BETA*DBLE(C(J,J))
|
|
DO 150 I = J + 1,N
|
|
C(I,J) = BETA*C(I,J)
|
|
150 CONTINUE
|
|
ELSE
|
|
C(J,J) = DBLE(C(J,J))
|
|
END IF
|
|
DO 170 L = 1,K
|
|
IF (A(J,L).NE.DCMPLX(ZERO)) THEN
|
|
TEMP = ALPHA*DCONJG(A(J,L))
|
|
C(J,J) = DBLE(C(J,J)) + DBLE(TEMP*A(J,L))
|
|
DO 160 I = J + 1,N
|
|
C(I,J) = C(I,J) + TEMP*A(I,L)
|
|
160 CONTINUE
|
|
END IF
|
|
170 CONTINUE
|
|
180 CONTINUE
|
|
END IF
|
|
ELSE
|
|
*
|
|
* Form C := alpha*A**H*A + beta*C.
|
|
*
|
|
IF (UPPER) THEN
|
|
DO 220 J = 1,N
|
|
DO 200 I = 1,J - 1
|
|
TEMP = ZERO
|
|
DO 190 L = 1,K
|
|
TEMP = TEMP + DCONJG(A(L,I))*A(L,J)
|
|
190 CONTINUE
|
|
IF (BETA.EQ.ZERO) THEN
|
|
C(I,J) = ALPHA*TEMP
|
|
ELSE
|
|
C(I,J) = ALPHA*TEMP + BETA*C(I,J)
|
|
END IF
|
|
200 CONTINUE
|
|
RTEMP = ZERO
|
|
DO 210 L = 1,K
|
|
RTEMP = RTEMP + DCONJG(A(L,J))*A(L,J)
|
|
210 CONTINUE
|
|
IF (BETA.EQ.ZERO) THEN
|
|
C(J,J) = ALPHA*RTEMP
|
|
ELSE
|
|
C(J,J) = ALPHA*RTEMP + BETA*DBLE(C(J,J))
|
|
END IF
|
|
220 CONTINUE
|
|
ELSE
|
|
DO 260 J = 1,N
|
|
RTEMP = ZERO
|
|
DO 230 L = 1,K
|
|
RTEMP = RTEMP + DCONJG(A(L,J))*A(L,J)
|
|
230 CONTINUE
|
|
IF (BETA.EQ.ZERO) THEN
|
|
C(J,J) = ALPHA*RTEMP
|
|
ELSE
|
|
C(J,J) = ALPHA*RTEMP + BETA*DBLE(C(J,J))
|
|
END IF
|
|
DO 250 I = J + 1,N
|
|
TEMP = ZERO
|
|
DO 240 L = 1,K
|
|
TEMP = TEMP + DCONJG(A(L,I))*A(L,J)
|
|
240 CONTINUE
|
|
IF (BETA.EQ.ZERO) THEN
|
|
C(I,J) = ALPHA*TEMP
|
|
ELSE
|
|
C(I,J) = ALPHA*TEMP + BETA*C(I,J)
|
|
END IF
|
|
250 CONTINUE
|
|
260 CONTINUE
|
|
END IF
|
|
END IF
|
|
*
|
|
RETURN
|
|
*
|
|
* End of ZHERK .
|
|
*
|
|
END
|