#include "ESMF_LapackBlas.inc" !> \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, 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, 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, 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 December 2016 ! !> \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 3.7.0) -- ! -- 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,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