--- /dev/null
+*> \brief \b DGEMM
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
+*
+* .. Scalar Arguments ..
+* DOUBLE PRECISION ALPHA,BETA
+* INTEGER K,LDA,LDB,LDC,M,N
+* CHARACTER TRANSA,TRANSB
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*)
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DGEMM performs one of the matrix-matrix operations
+*>
+*> C := alpha*op( A )*op( B ) + beta*C,
+*>
+*> where op( X ) is one of
+*>
+*> op( X ) = X or op( X ) = X**T,
+*>
+*> alpha and beta are scalars, and A, B and C are matrices, with op( A )
+*> an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] TRANSA
+*> \verbatim
+*> TRANSA is CHARACTER*1
+*> On entry, TRANSA specifies the form of op( A ) to be used in
+*> the matrix multiplication as follows:
+*>
+*> TRANSA = 'N' or 'n', op( A ) = A.
+*>
+*> TRANSA = 'T' or 't', op( A ) = A**T.
+*>
+*> TRANSA = 'C' or 'c', op( A ) = A**T.
+*> \endverbatim
+*>
+*> \param[in] TRANSB
+*> \verbatim
+*> TRANSB is CHARACTER*1
+*> On entry, TRANSB specifies the form of op( B ) to be used in
+*> the matrix multiplication as follows:
+*>
+*> TRANSB = 'N' or 'n', op( B ) = B.
+*>
+*> TRANSB = 'T' or 't', op( B ) = B**T.
+*>
+*> TRANSB = 'C' or 'c', op( B ) = B**T.
+*> \endverbatim
+*>
+*> \param[in] M
+*> \verbatim
+*> M is INTEGER
+*> On entry, M specifies the number of rows of the matrix
+*> op( A ) and of the matrix C. M must be at least zero.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> On entry, N specifies the number of columns of the matrix
+*> op( B ) and the number of columns of the matrix C. N must be
+*> at least zero.
+*> \endverbatim
+*>
+*> \param[in] K
+*> \verbatim
+*> K is INTEGER
+*> On entry, K specifies the number of columns of the matrix
+*> op( A ) and the number of rows of the matrix op( 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 TRANSA = 'N' or 'n', and is m otherwise.
+*> Before entry with TRANSA = 'N' or 'n', the leading m by k
+*> part of the array A must contain the matrix A, otherwise
+*> the leading k by m 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 TRANSA = 'N' or 'n' then
+*> LDA must be at least max( 1, m ), 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
+*> n when TRANSB = 'N' or 'n', and is k otherwise.
+*> Before entry with TRANSB = 'N' or 'n', the leading k by n
+*> part of the array B must contain the matrix B, otherwise
+*> the leading n by k 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 TRANSB = 'N' or 'n' then
+*> LDB must be at least max( 1, k ), otherwise LDB must be at
+*> least max( 1, n ).
+*> \endverbatim
+*>
+*> \param[in] BETA
+*> \verbatim
+*> BETA is DOUBLE PRECISION.
+*> On entry, BETA specifies the scalar beta. When BETA is
+*> supplied as zero then C need not be set on input.
+*> \endverbatim
+*>
+*> \param[in,out] C
+*> \verbatim
+*> C is DOUBLE PRECISION array of DIMENSION ( LDC, n ).
+*> Before entry, the leading m by n part of the array C must
+*> contain the matrix C, except when beta is zero, in which
+*> case C need not be set on entry.
+*> On exit, the array C is overwritten by the m by n matrix
+*> ( alpha*op( A )*op( B ) + beta*C ).
+*> \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, m ).
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2015
+*
+*> \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 DGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
+*
+* -- Reference BLAS level3 routine (version 3.6.0) --
+* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2015
+*
+* .. Scalar Arguments ..
+ DOUBLE PRECISION ALPHA,BETA
+ INTEGER K,LDA,LDB,LDC,M,N
+ CHARACTER TRANSA,TRANSB
+* ..
+* .. 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 TEMP
+ INTEGER I,INFO,J,L,NCOLA,NROWA,NROWB
+ LOGICAL NOTA,NOTB
+* ..
+* .. Parameters ..
+ DOUBLE PRECISION ONE,ZERO
+ PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
+* ..
+*
+* Set NOTA and NOTB as true if A and B respectively are not
+* transposed and set NROWA, NCOLA and NROWB as the number of rows
+* and columns of A and the number of rows of B respectively.
+*
+ NOTA = LSAME(TRANSA,'N')
+ NOTB = LSAME(TRANSB,'N')
+ IF (NOTA) THEN
+ NROWA = M
+ NCOLA = K
+ ELSE
+ NROWA = K
+ NCOLA = M
+ END IF
+ IF (NOTB) THEN
+ NROWB = K
+ ELSE
+ NROWB = N
+ END IF
+*
+* Test the input parameters.
+*
+ INFO = 0
+ IF ((.NOT.NOTA) .AND. (.NOT.LSAME(TRANSA,'C')) .AND.
+ + (.NOT.LSAME(TRANSA,'T'))) THEN
+ INFO = 1
+ ELSE IF ((.NOT.NOTB) .AND. (.NOT.LSAME(TRANSB,'C')) .AND.
+ + (.NOT.LSAME(TRANSB,'T'))) THEN
+ INFO = 2
+ ELSE IF (M.LT.0) THEN
+ INFO = 3
+ ELSE IF (N.LT.0) THEN
+ INFO = 4
+ ELSE IF (K.LT.0) THEN
+ INFO = 5
+ ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
+ INFO = 8
+ ELSE IF (LDB.LT.MAX(1,NROWB)) THEN
+ INFO = 10
+ ELSE IF (LDC.LT.MAX(1,M)) THEN
+ INFO = 13
+ END IF
+ IF (INFO.NE.0) THEN
+ CALL XERBLA('DGEMM ',INFO)
+ RETURN
+ END IF
+*
+* Quick return if possible.
+*
+ IF ((M.EQ.0) .OR. (N.EQ.0) .OR.
+ + (((ALPHA.EQ.ZERO).OR. (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN
+*
+* And if alpha.eq.zero.
+*
+ IF (ALPHA.EQ.ZERO) THEN
+ IF (BETA.EQ.ZERO) THEN
+ DO 20 J = 1,N
+ DO 10 I = 1,M
+ C(I,J) = ZERO
+ 10 CONTINUE
+ 20 CONTINUE
+ ELSE
+ DO 40 J = 1,N
+ DO 30 I = 1,M
+ C(I,J) = BETA*C(I,J)
+ 30 CONTINUE
+ 40 CONTINUE
+ END IF
+ RETURN
+ END IF
+*
+* Start the operations.
+*
+ IF (NOTB) THEN
+ IF (NOTA) THEN
+*
+* Form C := alpha*A*B + beta*C.
+*
+ DO 90 J = 1,N
+ IF (BETA.EQ.ZERO) THEN
+ DO 50 I = 1,M
+ C(I,J) = ZERO
+ 50 CONTINUE
+ ELSE IF (BETA.NE.ONE) THEN
+ DO 60 I = 1,M
+ C(I,J) = BETA*C(I,J)
+ 60 CONTINUE
+ END IF
+ DO 80 L = 1,K
+ TEMP = ALPHA*B(L,J)
+ DO 70 I = 1,M
+ C(I,J) = C(I,J) + TEMP*A(I,L)
+ 70 CONTINUE
+ 80 CONTINUE
+ 90 CONTINUE
+ ELSE
+*
+* Form C := alpha*A**T*B + beta*C
+*
+ DO 120 J = 1,N
+ DO 110 I = 1,M
+ TEMP = ZERO
+ DO 100 L = 1,K
+ TEMP = TEMP + A(L,I)*B(L,J)
+ 100 CONTINUE
+ IF (BETA.EQ.ZERO) THEN
+ C(I,J) = ALPHA*TEMP
+ ELSE
+ C(I,J) = ALPHA*TEMP + BETA*C(I,J)
+ END IF
+ 110 CONTINUE
+ 120 CONTINUE
+ END IF
+ ELSE
+ IF (NOTA) THEN
+*
+* Form C := alpha*A*B**T + beta*C
+*
+ DO 170 J = 1,N
+ IF (BETA.EQ.ZERO) THEN
+ DO 130 I = 1,M
+ C(I,J) = ZERO
+ 130 CONTINUE
+ ELSE IF (BETA.NE.ONE) THEN
+ DO 140 I = 1,M
+ C(I,J) = BETA*C(I,J)
+ 140 CONTINUE
+ END IF
+ DO 160 L = 1,K
+ TEMP = ALPHA*B(J,L)
+ DO 150 I = 1,M
+ C(I,J) = C(I,J) + TEMP*A(I,L)
+ 150 CONTINUE
+ 160 CONTINUE
+ 170 CONTINUE
+ ELSE
+*
+* Form C := alpha*A**T*B**T + beta*C
+*
+ DO 200 J = 1,N
+ DO 190 I = 1,M
+ TEMP = ZERO
+ DO 180 L = 1,K
+ TEMP = TEMP + A(L,I)*B(J,L)
+ 180 CONTINUE
+ IF (BETA.EQ.ZERO) THEN
+ C(I,J) = ALPHA*TEMP
+ ELSE
+ C(I,J) = ALPHA*TEMP + BETA*C(I,J)
+ END IF
+ 190 CONTINUE
+ 200 CONTINUE
+ END IF
+ END IF
+*
+ RETURN
+*
+* End of DGEMM .
+*
+ END
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