cgemm.f

          SUBROUTINE CGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
    *     .. Scalar Arguments ..
          COMPLEX ALPHA,BETA
          INTEGER K,LDA,LDB,LDC,M,N
          CHARACTER TRANSA,TRANSB
    *     ..
    *     .. Array Arguments ..
          COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  CGEMM  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.
    *
    *  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'.
    *
    *              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         .
    *           On entry, ALPHA specifies the scalar alpha.
    *           Unchanged on exit.
    *
    *  A      - COMPLEX          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          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         .
    *           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          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 CONJG,MAX
    *     ..
    *     .. Local Scalars ..
          COMPLEX TEMP
          INTEGER I,INFO,J,L,NCOLA,NROWA,NROWB
          LOGICAL CONJA,CONJB,NOTA,NOTB
    *     ..
    *     .. Parameters ..
          COMPLEX ONE
          PARAMETER (ONE= (1.0E+0,0.0E+0))
          COMPLEX ZERO
          PARAMETER (ZERO= (0.0E+0,0.0E+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('CGEMM ',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 + 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
    *
    *           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*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
    *
    *           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 + 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
    *
    *           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 + 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
    *
    *           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)*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
    *
    *           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 CGEMM .
    *
          END