*DECK CGEMM SUBROUTINE CGEMM (TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, \$ BETA, C, LDC) C***BEGIN PROLOGUE CGEMM C***PURPOSE Multiply a complex general matrix by a complex general C matrix. C***LIBRARY SLATEC (BLAS) C***CATEGORY D1B6 C***TYPE COMPLEX (SGEMM-S, DGEMM-D, CGEMM-C) C***KEYWORDS LEVEL 3 BLAS, LINEAR ALGEBRA C***AUTHOR Dongarra, J., (ANL) C Duff, I., (AERE) C Du Croz, J., (NAG) C Hammarling, S. (NAG) C***DESCRIPTION C C CGEMM performs one of the matrix-matrix operations C C C := alpha*op( A )*op( B ) + beta*C, C C where op( X ) is one of C C op( X ) = X or op( X ) = X' or op( X ) = conjg( X' ), C C alpha and beta are scalars, and A, B and C are matrices, with op( A ) C an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. C C Parameters C ========== C C TRANSA - CHARACTER*1. C On entry, TRANSA specifies the form of op( A ) to be used in C the matrix multiplication as follows: C C TRANSA = 'N' or 'n', op( A ) = A. C C TRANSA = 'T' or 't', op( A ) = A'. C C TRANSA = 'C' or 'c', op( A ) = conjg( A' ). C C Unchanged on exit. C C TRANSB - CHARACTER*1. C On entry, TRANSB specifies the form of op( B ) to be used in C the matrix multiplication as follows: C C TRANSB = 'N' or 'n', op( B ) = B. C C TRANSB = 'T' or 't', op( B ) = B'. C C TRANSB = 'C' or 'c', op( B ) = conjg( B' ). C C Unchanged on exit. C C M - INTEGER. C On entry, M specifies the number of rows of the matrix C op( A ) and of the matrix C. M must be at least zero. C Unchanged on exit. C C N - INTEGER. C On entry, N specifies the number of columns of the matrix C op( B ) and the number of columns of the matrix C. N must be C at least zero. C Unchanged on exit. C C K - INTEGER. C On entry, K specifies the number of columns of the matrix C op( A ) and the number of rows of the matrix op( B ). K must C be at least zero. C Unchanged on exit. C C ALPHA - COMPLEX . C On entry, ALPHA specifies the scalar alpha. C Unchanged on exit. C C A - COMPLEX array of DIMENSION ( LDA, ka ), where ka is C k when TRANSA = 'N' or 'n', and is m otherwise. C Before entry with TRANSA = 'N' or 'n', the leading m by k C part of the array A must contain the matrix A, otherwise C the leading k by m part of the array A must contain the C matrix A. C Unchanged on exit. C C LDA - INTEGER. C On entry, LDA specifies the first dimension of A as declared C in the calling (sub) program. When TRANSA = 'N' or 'n' then C LDA must be at least max( 1, m ), otherwise LDA must be at C least max( 1, k ). C Unchanged on exit. C C B - COMPLEX array of DIMENSION ( LDB, kb ), where kb is C n when TRANSB = 'N' or 'n', and is k otherwise. C Before entry with TRANSB = 'N' or 'n', the leading k by n C part of the array B must contain the matrix B, otherwise C the leading n by k part of the array B must contain the C matrix B. C Unchanged on exit. C C LDB - INTEGER. C On entry, LDB specifies the first dimension of B as declared C in the calling (sub) program. When TRANSB = 'N' or 'n' then C LDB must be at least max( 1, k ), otherwise LDB must be at C least max( 1, n ). C Unchanged on exit. C C BETA - COMPLEX . C On entry, BETA specifies the scalar beta. When BETA is C supplied as zero then C need not be set on input. C Unchanged on exit. C C C - COMPLEX array of DIMENSION ( LDC, n ). C Before entry, the leading m by n part of the array C must C contain the matrix C, except when beta is zero, in which C case C need not be set on entry. C On exit, the array C is overwritten by the m by n matrix C ( alpha*op( A )*op( B ) + beta*C ). C C LDC - INTEGER. C On entry, LDC specifies the first dimension of C as declared C in the calling (sub) program. LDC must be at least C max( 1, m ). C Unchanged on exit. C C***REFERENCES Dongarra, J., Du Croz, J., Duff, I., and Hammarling, S. C A set of level 3 basic linear algebra subprograms. C ACM TOMS, Vol. 16, No. 1, pp. 1-17, March 1990. C***ROUTINES CALLED LSAME, XERBLA C***REVISION HISTORY (YYMMDD) C 890208 DATE WRITTEN C 910605 Modified to meet SLATEC prologue standards. Only comment C lines were modified. (BKS) C***END PROLOGUE CGEMM C .. Scalar Arguments .. CHARACTER*1 TRANSA, TRANSB INTEGER M, N, K, LDA, LDB, LDC COMPLEX ALPHA, BETA C .. Array Arguments .. COMPLEX A( LDA, * ), B( LDB, * ), C( LDC, * ) C .. External Functions .. LOGICAL LSAME EXTERNAL LSAME C .. External Subroutines .. EXTERNAL XERBLA C .. Intrinsic Functions .. INTRINSIC CONJG, MAX C .. Local Scalars .. LOGICAL CONJA, CONJB, NOTA, NOTB INTEGER I, INFO, J, L, NCOLA, NROWA, NROWB COMPLEX TEMP C .. Parameters .. COMPLEX ONE PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) ) COMPLEX ZERO PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) ) C***FIRST EXECUTABLE STATEMENT CGEMM C C Set NOTA and NOTB as true if A and B respectively are not C conjugated or transposed, set CONJA and CONJB as true if A and C B respectively are to be transposed but not conjugated and set C NROWA, NCOLA and NROWB as the number of rows and columns of A C and the number of rows of B respectively. C NOTA = LSAME( TRANSA, 'N' ) NOTB = LSAME( TRANSB, 'N' ) CONJA = LSAME( TRANSA, 'C' ) CONJB = LSAME( TRANSB, 'C' ) IF( NOTA )THEN NROWA = M NCOLA = K ELSE NROWA = K NCOLA = M END IF IF( NOTB )THEN NROWB = K ELSE NROWB = N END IF C C Test the input parameters. C INFO = 0 IF( ( .NOT.NOTA ).AND. \$ ( .NOT.CONJA ).AND. \$ ( .NOT.LSAME( TRANSA, 'T' ) ) )THEN INFO = 1 ELSE IF( ( .NOT.NOTB ).AND. \$ ( .NOT.CONJB ).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( 'CGEMM ', INFO ) RETURN END IF C C Quick return if possible. C IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR. \$ ( ( ( ALPHA.EQ.ZERO ).OR.( K.EQ.0 ) ).AND.( BETA.EQ.ONE ) ) ) \$ RETURN C C And when alpha.eq.zero. C 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 C C Start the operations. C IF( NOTB )THEN IF( NOTA )THEN C C Form C := alpha*A*B + beta*C. 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 IF( B( L, J ).NE.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 IF( CONJA )THEN C C Form C := alpha*conjg( A' )*B + beta*C. C DO 120, J = 1, N DO 110, I = 1, M TEMP = ZERO DO 100, L = 1, K TEMP = TEMP + CONJG( 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 ELSE C C Form C := alpha*A'*B + beta*C C DO 150, J = 1, N DO 140, I = 1, M TEMP = ZERO DO 130, L = 1, K TEMP = TEMP + A( L, I )*B( L, J ) 130 CONTINUE IF( BETA.EQ.ZERO )THEN C( I, J ) = ALPHA*TEMP ELSE C( I, J ) = ALPHA*TEMP + BETA*C( I, J ) END IF 140 CONTINUE 150 CONTINUE END IF ELSE IF( NOTA )THEN IF( CONJB )THEN C C Form C := alpha*A*conjg( B' ) + beta*C. C DO 200, J = 1, N IF( BETA.EQ.ZERO )THEN DO 160, I = 1, M C( I, J ) = ZERO 160 CONTINUE ELSE IF( BETA.NE.ONE )THEN DO 170, I = 1, M C( I, J ) = BETA*C( I, J ) 170 CONTINUE END IF DO 190, L = 1, K IF( B( J, L ).NE.ZERO )THEN TEMP = ALPHA*CONJG( B( J, L ) ) DO 180, I = 1, M C( I, J ) = C( I, J ) + TEMP*A( I, L ) 180 CONTINUE END IF 190 CONTINUE 200 CONTINUE ELSE C C Form C := alpha*A*B' + beta*C C DO 250, J = 1, N IF( BETA.EQ.ZERO )THEN DO 210, I = 1, M C( I, J ) = ZERO 210 CONTINUE ELSE IF( BETA.NE.ONE )THEN DO 220, I = 1, M C( I, J ) = BETA*C( I, J ) 220 CONTINUE END IF DO 240, L = 1, K IF( B( J, L ).NE.ZERO )THEN TEMP = ALPHA*B( J, L ) DO 230, I = 1, M C( I, J ) = C( I, J ) + TEMP*A( I, L ) 230 CONTINUE END IF 240 CONTINUE 250 CONTINUE END IF ELSE IF( CONJA )THEN IF( CONJB )THEN C C Form C := alpha*conjg( A' )*conjg( B' ) + beta*C. C DO 280, J = 1, N DO 270, I = 1, M TEMP = ZERO DO 260, L = 1, K TEMP = TEMP + CONJG( A( L, I ) )*CONJG( B( J, L ) ) 260 CONTINUE IF( BETA.EQ.ZERO )THEN C( I, J ) = ALPHA*TEMP ELSE C( I, J ) = ALPHA*TEMP + BETA*C( I, J ) END IF 270 CONTINUE 280 CONTINUE ELSE C C Form C := alpha*conjg( A' )*B' + beta*C C DO 310, J = 1, N DO 300, I = 1, M TEMP = ZERO DO 290, L = 1, K TEMP = TEMP + CONJG( A( L, I ) )*B( J, L ) 290 CONTINUE IF( BETA.EQ.ZERO )THEN C( I, J ) = ALPHA*TEMP ELSE C( I, J ) = ALPHA*TEMP + BETA*C( I, J ) END IF 300 CONTINUE 310 CONTINUE END IF ELSE IF( CONJB )THEN C C Form C := alpha*A'*conjg( B' ) + beta*C C DO 340, J = 1, N DO 330, I = 1, M TEMP = ZERO DO 320, L = 1, K TEMP = TEMP + A( L, I )*CONJG( B( J, L ) ) 320 CONTINUE IF( BETA.EQ.ZERO )THEN C( I, J ) = ALPHA*TEMP ELSE C( I, J ) = ALPHA*TEMP + BETA*C( I, J ) END IF 330 CONTINUE 340 CONTINUE ELSE C C Form C := alpha*A'*B' + beta*C C DO 370, J = 1, N DO 360, I = 1, M TEMP = ZERO DO 350, L = 1, K TEMP = TEMP + A( L, I )*B( J, L ) 350 CONTINUE IF( BETA.EQ.ZERO )THEN C( I, J ) = ALPHA*TEMP ELSE C( I, J ) = ALPHA*TEMP + BETA*C( I, J ) END IF 360 CONTINUE 370 CONTINUE END IF END IF C RETURN C C End of CGEMM . C END