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|
*> \brief \b CHER2K
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE CHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
*
* .. Scalar Arguments ..
* COMPLEX ALPHA
* REAL BETA
* INTEGER K,LDA,LDB,LDC,N
* CHARACTER TRANS,UPLO
* ..
* .. Array Arguments ..
* COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CHER2K performs one of the hermitian rank 2k operations
*>
*> C := alpha*A*B**H + conjg( alpha )*B*A**H + beta*C,
*>
*> or
*>
*> C := alpha*A**H*B + conjg( alpha )*B**H*A + beta*C,
*>
*> where alpha and beta are scalars with beta real, C is an n by n
*> hermitian matrix and A and B are n by k matrices in the first case
*> and k by n matrices 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*B**H +
*> conjg( alpha )*B*A**H +
*> beta*C.
*>
*> TRANS = 'C' or 'c' C := alpha*A**H*B +
*> conjg( alpha )*B**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 matrices A and B, and on entry with
*> TRANS = 'C' or 'c', K specifies the number of rows of the
*> matrices A and B. K must be at least zero.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*> ALPHA is COMPLEX
*> On entry, ALPHA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is COMPLEX 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] B
*> \verbatim
*> B is COMPLEX array, dimension ( LDB, kb ), where kb 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 B must contain the matrix B, otherwise
*> the leading k by n part of the array B must contain the
*> matrix B.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> On entry, LDB specifies the first dimension of B as declared
*> in the calling (sub) program. When TRANS = 'N' or 'n'
*> then LDB must be at least max( 1, n ), otherwise LDB must
*> be at least max( 1, k ).
*> \endverbatim
*>
*> \param[in] BETA
*> \verbatim
*> BETA is REAL
*> On entry, BETA specifies the scalar beta.
*> \endverbatim
*>
*> \param[in,out] C
*> \verbatim
*> C is COMPLEX 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 complex_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 REAL( C(J,J) ) when BETA = 1.
*> Ed Anderson, Cray Research Inc.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE CHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,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 ..
COMPLEX ALPHA
REAL BETA
INTEGER K,LDA,LDB,LDC,N
CHARACTER TRANS,UPLO
* ..
* .. Array Arguments ..
COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
* ..
*
* =====================================================================
*
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC CONJG,MAX,REAL
* ..
* .. Local Scalars ..
COMPLEX TEMP1,TEMP2
INTEGER I,INFO,J,L,NROWA
LOGICAL UPPER
* ..
* .. Parameters ..
REAL ONE
PARAMETER (ONE=1.0E+0)
COMPLEX ZERO
PARAMETER (ZERO= (0.0E+0,0.0E+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 (LDB.LT.MAX(1,NROWA)) THEN
INFO = 9
ELSE IF (LDC.LT.MAX(1,N)) THEN
INFO = 12
END IF
IF (INFO.NE.0) THEN
CALL XERBLA('CHER2K',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.REAL(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*REAL(C(J,J))
40 CONTINUE
END IF
ELSE
IF (BETA.EQ.REAL(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*REAL(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*B**H + conjg( alpha )*B*A**H +
* C.
*
IF (UPPER) THEN
DO 130 J = 1,N
IF (BETA.EQ.REAL(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*REAL(C(J,J))
ELSE
C(J,J) = REAL(C(J,J))
END IF
DO 120 L = 1,K
IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN
TEMP1 = ALPHA*CONJG(B(J,L))
TEMP2 = CONJG(ALPHA*A(J,L))
DO 110 I = 1,J - 1
C(I,J) = C(I,J) + A(I,L)*TEMP1 +
+ B(I,L)*TEMP2
110 CONTINUE
C(J,J) = REAL(C(J,J)) +
+ REAL(A(J,L)*TEMP1+B(J,L)*TEMP2)
END IF
120 CONTINUE
130 CONTINUE
ELSE
DO 180 J = 1,N
IF (BETA.EQ.REAL(ZERO)) THEN
DO 140 I = J,N
C(I,J) = ZERO
140 CONTINUE
ELSE IF (BETA.NE.ONE) THEN
DO 150 I = J + 1,N
C(I,J) = BETA*C(I,J)
150 CONTINUE
C(J,J) = BETA*REAL(C(J,J))
ELSE
C(J,J) = REAL(C(J,J))
END IF
DO 170 L = 1,K
IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN
TEMP1 = ALPHA*CONJG(B(J,L))
TEMP2 = CONJG(ALPHA*A(J,L))
DO 160 I = J + 1,N
C(I,J) = C(I,J) + A(I,L)*TEMP1 +
+ B(I,L)*TEMP2
160 CONTINUE
C(J,J) = REAL(C(J,J)) +
+ REAL(A(J,L)*TEMP1+B(J,L)*TEMP2)
END IF
170 CONTINUE
180 CONTINUE
END IF
ELSE
*
* Form C := alpha*A**H*B + conjg( alpha )*B**H*A +
* C.
*
IF (UPPER) THEN
DO 210 J = 1,N
DO 200 I = 1,J
TEMP1 = ZERO
TEMP2 = ZERO
DO 190 L = 1,K
TEMP1 = TEMP1 + CONJG(A(L,I))*B(L,J)
TEMP2 = TEMP2 + CONJG(B(L,I))*A(L,J)
190 CONTINUE
IF (I.EQ.J) THEN
IF (BETA.EQ.REAL(ZERO)) THEN
C(J,J) = REAL(ALPHA*TEMP1+
+ CONJG(ALPHA)*TEMP2)
ELSE
C(J,J) = BETA*REAL(C(J,J)) +
+ REAL(ALPHA*TEMP1+
+ CONJG(ALPHA)*TEMP2)
END IF
ELSE
IF (BETA.EQ.REAL(ZERO)) THEN
C(I,J) = ALPHA*TEMP1 + CONJG(ALPHA)*TEMP2
ELSE
C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 +
+ CONJG(ALPHA)*TEMP2
END IF
END IF
200 CONTINUE
210 CONTINUE
ELSE
DO 240 J = 1,N
DO 230 I = J,N
TEMP1 = ZERO
TEMP2 = ZERO
DO 220 L = 1,K
TEMP1 = TEMP1 + CONJG(A(L,I))*B(L,J)
TEMP2 = TEMP2 + CONJG(B(L,I))*A(L,J)
220 CONTINUE
IF (I.EQ.J) THEN
IF (BETA.EQ.REAL(ZERO)) THEN
C(J,J) = REAL(ALPHA*TEMP1+
+ CONJG(ALPHA)*TEMP2)
ELSE
C(J,J) = BETA*REAL(C(J,J)) +
+ REAL(ALPHA*TEMP1+
+ CONJG(ALPHA)*TEMP2)
END IF
ELSE
IF (BETA.EQ.REAL(ZERO)) THEN
C(I,J) = ALPHA*TEMP1 + CONJG(ALPHA)*TEMP2
ELSE
C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 +
+ CONJG(ALPHA)*TEMP2
END IF
END IF
230 CONTINUE
240 CONTINUE
END IF
END IF
*
RETURN
*
* End of CHER2K.
*
END
|
