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SUBROUTINE ZGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
* .. Scalar Arguments ..
COMPLEX*16 ALPHA,BETA
INTEGER K,LDA,LDB,LDC,M,N
CHARACTER TRANSA,TRANSB
* ..
* .. 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**T or op( X ) = X**H,
*
* 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.
*
* Arguments
* ==========
*
* 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**T.
*
* TRANSA = 'C' or 'c', op( A ) = A**H.
*
* 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**T.
*
* TRANSB = 'C' or 'c', op( B ) = B**H.
*
* 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.
*
* Further Details
* ===============
*
* 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 ..
COMPLEX*16 TEMP
INTEGER I,INFO,J,L,NCOLA,NROWA,NROWB
LOGICAL CONJA,CONJB,NOTA,NOTB
* ..
* .. Parameters ..
COMPLEX*16 ONE
PARAMETER (ONE= (1.0D+0,0.0D+0))
COMPLEX*16 ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
* ..
*
* 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*A**H*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**T*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*B**H + 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**T + 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*A**H*B**H + 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*A**H*B**T + 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**T*B**H + 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**T*B**T + 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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