*> \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, 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, 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, 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.
*
*> \ingroup gemm
*
*> \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 --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. 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,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 and NROWB as the number of rows of A
* and B respectively.
*
nota = lsame(transa,'N')
notb = lsame(transb,'N')
IF (nota) THEN
nrowa = m
ELSE
nrowa = k
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