Source module last modified on Thu, 2 Jul 1998, 23:17;
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SUBROUTINE DGEMM ( TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB,
$ BETA, C, LDC )
# .. Scalar Arguments ..
CHARACTER*1 TRANSA, TRANSB
INTEGER M, N, K, LDA, LDB, LDC
DOUBLE PRECISION ALPHA, BETA
# .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * )
# ..
#
# Purpose
# =======
#
# 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',
#
# 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.
#
# Parameters
# ==========
#
# TRANSA - 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'.
#
# TRANSA = 'C' or 'c', op( A ) = A'.
#
# Unchanged on exit.
#
# TRANSB - 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'.
#
# TRANSB = 'C' or 'c', op( B ) = B'.
#
# Unchanged on exit.
#
# M - 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.
# Unchanged on exit.
#
# N - 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.
# Unchanged on exit.
#
# K - 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.
# Unchanged on exit.
#
# ALPHA - DOUBLE PRECISION.
# On entry, ALPHA specifies the scalar alpha.
# Unchanged on exit.
#
# A - 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.
# Unchanged on exit.
#
# LDA - 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 ).
# Unchanged on exit.
#
# B - 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.
# Unchanged on exit.
#
# LDB - 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 ).
# Unchanged on exit.
#
# BETA - DOUBLE PRECISION.
# On entry, BETA specifies the scalar beta. When BETA is
# supplied as zero then C need not be set on input.
# Unchanged on exit.
#
# C - 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 ).
#
# LDC - 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 ).
# Unchanged on exit.
#
#
# 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.
#
#
# .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
# .. External Subroutines ..
EXTERNAL XERBLA
# .. Intrinsic Functions ..
INTRINSIC MAX
# .. Local Scalars ..
LOGICAL NOTA, NOTB
INTEGER I, INFO, J, L, NCOLA, NROWA, NROWB
DOUBLE PRECISION TEMP
# .. Parameters ..
DOUBLE PRECISION ONE , ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
# ..
# .. Executable Statements ..
#
# 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( ( ! NOTA )&&
$ ( ! LSAME( TRANSA, 'C' ) )&&
$ ( ! LSAME( TRANSA, 'T' ) ) )THEN
INFO = 1
ELSE IF( ( ! NOTB )&&
$ ( ! LSAME( TRANSB, 'C' ) )&&
$ ( ! LSAME( TRANSB, 'T' ) ) )THEN
INFO = 2
ELSE IF( M <0 )THEN
INFO = 3
ELSE IF( N <0 )THEN
INFO = 4
ELSE IF( K <0 )THEN
INFO = 5
ELSE IF( LDA<MAX( 1, NROWA ) )THEN
INFO = 8
ELSE IF( LDB<MAX( 1, NROWB ) )THEN
INFO = 10
ELSE IF( LDC<MAX( 1, M ) )THEN
INFO = 13
END IF
IF( INFO!=0 )THEN
CALL XERBLA( 'DGEMM ', INFO )
RETURN
END IF
#
# Quick return if possible.
#
IF( ( M==0 )||( N==0 )||
$ ( ( ( ALPHA==ZERO )||( K==0 ) )&&( BETA==ONE ) ) )
$ RETURN
#
# And if alpha.eq.zero.
#
IF( ALPHA==ZERO )THEN
IF( BETA==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==ZERO )THEN
DO 50, I = 1, M
C( I, J ) = ZERO
50 CONTINUE
ELSE IF( BETA!=ONE )THEN
DO 60, I = 1, M
C( I, J ) = BETA*C( I, J )
60 CONTINUE
END IF
DO 80, L = 1, K
IF( B( L, J )!=ZERO )THEN
TEMP = ALPHA*B( L, J )
DO 70, I = 1, M
C( I, J ) = C( I, J ) + TEMP*A( I, L )
70 CONTINUE
END IF
80 CONTINUE
90 CONTINUE
ELSE
#
# Form C := alpha*A'*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==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' + beta*C
#
DO 170, J = 1, N
IF( BETA==ZERO )THEN
DO 130, I = 1, M
C( I, J ) = ZERO
130 CONTINUE
ELSE IF( BETA!=ONE )THEN
DO 140, I = 1, M
C( I, J ) = BETA*C( I, J )
140 CONTINUE
END IF
DO 160, L = 1, K
IF( B( J, L )!=ZERO )THEN
TEMP = ALPHA*B( J, L )
DO 150, I = 1, M
C( I, J ) = C( I, J ) + TEMP*A( I, L )
150 CONTINUE
END IF
160 CONTINUE
170 CONTINUE
ELSE
#
# Form C := alpha*A'*B' + 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==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