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SUBROUTINE ZGEMM ( 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
COMPLEX*16 ALPHA, BETA
* .. Array Arguments ..
COMPLEX*16 A( LDA, * ), B( LDB, * ), C( LDC, * )
* ..
*
* Purpose
* =======
*
* ZGEMM 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' or op( X ) = conjg( 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 ) = conjg( 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 ) = conjg( 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 - COMPLEX*16 .
* On entry, ALPHA specifies the scalar alpha.
* Unchanged on exit.
*
* A - COMPLEX*16 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 - COMPLEX*16 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 - COMPLEX*16 .
* 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 - COMPLEX*16 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 DCONJG, MAX
* .. Local Scalars ..
LOGICAL CONJA, CONJB, NOTA, NOTB
INTEGER I, INFO, J, L, NCOLA, NROWA, NROWB
COMPLEX*16 TEMP
* .. Parameters ..
COMPLEX*16 ONE
PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
COMPLEX*16 ZERO
PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
* ..
* .. Executable Statements ..
*
* Set NOTA and NOTB as true if A and B respectively are not
* conjugated or transposed, set CONJA and CONJB as true if A and
* B respectively are to be transposed but not conjugated 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' )
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
*
* Test the input parameters.
*
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( 'ZGEMM ', 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 when 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
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
*
* Form C := alpha*conjg( A' )*B + beta*C.
*
DO 120, J = 1, N
DO 110, I = 1, M
TEMP = ZERO
DO 100, L = 1, K
TEMP = TEMP + DCONJG( 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
*
* Form C := alpha*A'*B + beta*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
*
* Form C := alpha*A*conjg( B' ) + beta*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*DCONJG( 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
*
* Form C := alpha*A*B' + beta*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
*
* Form C := alpha*conjg( A' )*conjg( B' ) + beta*C.
*
DO 280, J = 1, N
DO 270, I = 1, M
TEMP = ZERO
DO 260, L = 1, K
TEMP = TEMP +
$ DCONJG( A( L, I ) )*DCONJG( 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
*
* Form C := alpha*conjg( A' )*B' + beta*C
*
DO 310, J = 1, N
DO 300, I = 1, M
TEMP = ZERO
DO 290, L = 1, K
TEMP = TEMP + DCONJG( 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
*
* Form C := alpha*A'*conjg( B' ) + beta*C
*
DO 340, J = 1, N
DO 330, I = 1, M
TEMP = ZERO
DO 320, L = 1, K
TEMP = TEMP + A( L, I )*DCONJG( 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
*
* Form C := alpha*A'*B' + beta*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
*
RETURN
*
* End of ZGEMM .
*
END
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