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*> \brief \b DSYR2K
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
*
* .. Scalar Arguments ..
* DOUBLE PRECISION ALPHA,BETA
* INTEGER K,LDA,LDB,LDC,N
* CHARACTER TRANS,UPLO
* ..
* .. Array Arguments ..
* DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DSYR2K performs one of the symmetric rank 2k operations
*>
*> C := alpha*A*B**T + alpha*B*A**T + beta*C,
*>
*> or
*>
*> C := alpha*A**T*B + alpha*B**T*A + beta*C,
*>
*> where alpha and beta are scalars, C is an n by n symmetric 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**T + alpha*B*A**T +
*> beta*C.
*>
*> TRANS = 'T' or 't' C := alpha*A**T*B + alpha*B**T*A +
*> beta*C.
*>
*> TRANS = 'C' or 'c' C := alpha*A**T*B + alpha*B**T*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 = 'T' or 't' or '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 DOUBLE PRECISION.
*> On entry, ALPHA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE PRECISION array of 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 DOUBLE PRECISION array of 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 DOUBLE PRECISION.
*> On entry, BETA specifies the scalar beta.
*> \endverbatim
*>
*> \param[in,out] C
*> \verbatim
*> C is DOUBLE PRECISION array of 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 symmetric 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 symmetric 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.
*> \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 November 2011
*
*> \ingroup double_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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE DSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
*
* -- Reference BLAS level3 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,BETA
INTEGER K,LDA,LDB,LDC,N
CHARACTER TRANS,UPLO
* ..
* .. Array Arguments ..
DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*)
* ..
*
* =====================================================================
*
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Local Scalars ..
DOUBLE PRECISION TEMP1,TEMP2
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,'T')) .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('DSYR2K',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
C(I,J) = BETA*C(I,J)
30 CONTINUE
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
DO 70 I = J,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**T + alpha*B*A**T + 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
C(I,J) = BETA*C(I,J)
100 CONTINUE
END IF
DO 120 L = 1,K
IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN
TEMP1 = ALPHA*B(J,L)
TEMP2 = ALPHA*A(J,L)
DO 110 I = 1,J
C(I,J) = C(I,J) + A(I,L)*TEMP1 +
+ B(I,L)*TEMP2
110 CONTINUE
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
DO 150 I = J,N
C(I,J) = BETA*C(I,J)
150 CONTINUE
END IF
DO 170 L = 1,K
IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN
TEMP1 = ALPHA*B(J,L)
TEMP2 = ALPHA*A(J,L)
DO 160 I = J,N
C(I,J) = C(I,J) + A(I,L)*TEMP1 +
+ B(I,L)*TEMP2
160 CONTINUE
END IF
170 CONTINUE
180 CONTINUE
END IF
ELSE
*
* Form C := alpha*A**T*B + alpha*B**T*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 + A(L,I)*B(L,J)
TEMP2 = TEMP2 + B(L,I)*A(L,J)
190 CONTINUE
IF (BETA.EQ.ZERO) THEN
C(I,J) = ALPHA*TEMP1 + ALPHA*TEMP2
ELSE
C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 +
+ ALPHA*TEMP2
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 + A(L,I)*B(L,J)
TEMP2 = TEMP2 + B(L,I)*A(L,J)
220 CONTINUE
IF (BETA.EQ.ZERO) THEN
C(I,J) = ALPHA*TEMP1 + ALPHA*TEMP2
ELSE
C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 +
+ ALPHA*TEMP2
END IF
230 CONTINUE
240 CONTINUE
END IF
END IF
*
RETURN
*
* End of DSYR2K.
*
END
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