ctrmm.f

          SUBROUTINE CTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
    *     .. Scalar Arguments ..
          COMPLEX ALPHA
          INTEGER LDA,LDB,M,N
          CHARACTER DIAG,SIDE,TRANSA,UPLO
    *     ..
    *     .. Array Arguments ..
          COMPLEX A(LDA,*),B(LDB,*)
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  CTRMM  performs one of the matrix-matrix operations
    *
    *     B := alpha*op( A )*B,   or   B := alpha*B*op( A )
    *
    *  where  alpha  is a scalar,  B  is an m by n matrix,  A  is a unit, or
    *  non-unit,  upper or lower triangular matrix  and  op( A )  is one  of
    *
    *     op( A ) = A   or   op( A ) = A'   or   op( A ) = conjg( A' ).
    *
    *  Arguments
    *  ==========
    *
    *  SIDE   - CHARACTER*1.
    *           On entry,  SIDE specifies whether  op( A ) multiplies B from
    *           the left or right as follows:
    *
    *              SIDE = 'L' or 'l'   B := alpha*op( A )*B.
    *
    *              SIDE = 'R' or 'r'   B := alpha*B*op( A ).
    *
    *           Unchanged on exit.
    *
    *  UPLO   - CHARACTER*1.
    *           On entry, UPLO specifies whether the matrix A is an upper or
    *           lower triangular matrix as follows:
    *
    *              UPLO = 'U' or 'u'   A is an upper triangular matrix.
    *
    *              UPLO = 'L' or 'l'   A is a lower triangular matrix.
    *
    *           Unchanged on exit.
    *
    *  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.
    *
    *  DIAG   - CHARACTER*1.
    *           On entry, DIAG specifies whether or not A is unit triangular
    *           as follows:
    *
    *              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
    *
    *              DIAG = 'N' or 'n'   A is not assumed to be unit
    *                                  triangular.
    *
    *           Unchanged on exit.
    *
    *  M      - INTEGER.
    *           On entry, M specifies the number of rows of B. M must be at
    *           least zero.
    *           Unchanged on exit.
    *
    *  N      - INTEGER.
    *           On entry, N specifies the number of columns of B.  N must be
    *           at least zero.
    *           Unchanged on exit.
    *
    *  ALPHA  - COMPLEX         .
    *           On entry,  ALPHA specifies the scalar  alpha. When  alpha is
    *           zero then  A is not referenced and  B need not be set before
    *           entry.
    *           Unchanged on exit.
    *
    *  A      - COMPLEX          array of DIMENSION ( LDA, k ), where k is m
    *           when  SIDE = 'L' or 'l'  and is  n  when  SIDE = 'R' or 'r'.
    *           Before entry  with  UPLO = 'U' or 'u',  the  leading  k by k
    *           upper triangular part of the array  A must contain the upper
    *           triangular matrix  and the strictly lower triangular part of
    *           A is not referenced.
    *           Before entry  with  UPLO = 'L' or 'l',  the  leading  k by k
    *           lower triangular part of the array  A must contain the lower
    *           triangular matrix  and the strictly upper triangular part of
    *           A is not referenced.
    *           Note that when  DIAG = 'U' or 'u',  the diagonal elements of
    *           A  are not referenced either,  but are assumed to be  unity.
    *           Unchanged on exit.
    *
    *  LDA    - INTEGER.
    *           On entry, LDA specifies the first dimension of A as declared
    *           in the calling (sub) program.  When  SIDE = 'L' or 'l'  then
    *           LDA  must be at least  max( 1, m ),  when  SIDE = 'R' or 'r'
    *           then LDA must be at least max( 1, n ).
    *           Unchanged on exit.
    *
    *  B      - COMPLEX          array of DIMENSION ( LDB, n ).
    *           Before entry,  the leading  m by n part of the array  B must
    *           contain the matrix  B,  and  on exit  is overwritten  by the
    *           transformed matrix.
    *
    *  LDB    - INTEGER.
    *           On entry, LDB specifies the first dimension of B as declared
    *           in  the  calling  (sub)  program.   LDB  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,K,NROWA
          LOGICAL LSIDE,NOCONJ,NOUNIT,UPPER
    *     ..
    *     .. Parameters ..
          COMPLEX ONE
          PARAMETER (ONE= (1.0E+0,0.0E+0))
          COMPLEX ZERO
          PARAMETER (ZERO= (0.0E+0,0.0E+0))
    *     ..
    *
    *     Test the input parameters.
    *
          LSIDE = LSAME(SIDE,'L')
          IF (LSIDE) THEN
              NROWA = M
          ELSE
              NROWA = N
          END IF
          NOCONJ = LSAME(TRANSA,'T')
          NOUNIT = LSAME(DIAG,'N')
          UPPER = LSAME(UPLO,'U')
    *
          INFO = 0
          IF ((.NOT.LSIDE) .AND. (.NOT.LSAME(SIDE,'R'))) THEN
              INFO = 1
          ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
              INFO = 2
          ELSE IF ((.NOT.LSAME(TRANSA,'N')) .AND.
         +         (.NOT.LSAME(TRANSA,'T')) .AND.
         +         (.NOT.LSAME(TRANSA,'C'))) THEN
              INFO = 3
          ELSE IF ((.NOT.LSAME(DIAG,'U')) .AND. (.NOT.LSAME(DIAG,'N'))) THEN
              INFO = 4
          ELSE IF (M.LT.0) THEN
              INFO = 5
          ELSE IF (N.LT.0) THEN
              INFO = 6
          ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
              INFO = 9
          ELSE IF (LDB.LT.MAX(1,M)) THEN
              INFO = 11
          END IF
          IF (INFO.NE.0) THEN
              CALL XERBLA('CTRMM ',INFO)
              RETURN
          END IF
    *
    *     Quick return if possible.
    *
          IF (N.EQ.0) RETURN
    *
    *     And when  alpha.eq.zero.
    *
          IF (ALPHA.EQ.ZERO) THEN
              DO 20 J = 1,N
                  DO 10 I = 1,M
                      B(I,J) = ZERO
       10         CONTINUE
       20     CONTINUE
              RETURN
          END IF
    *
    *     Start the operations.
    *
          IF (LSIDE) THEN
              IF (LSAME(TRANSA,'N')) THEN
    *
    *           Form  B := alpha*A*B.
    *
                  IF (UPPER) THEN
                      DO 50 J = 1,N
                          DO 40 K = 1,M
                              IF (B(K,J).NE.ZERO) THEN
                                  TEMP = ALPHA*B(K,J)
                                  DO 30 I = 1,K - 1
                                      B(I,J) = B(I,J) + TEMP*A(I,K)
       30                         CONTINUE
                                  IF (NOUNIT) TEMP = TEMP*A(K,K)
                                  B(K,J) = TEMP
                              END IF
       40                 CONTINUE
       50             CONTINUE
                  ELSE
                      DO 80 J = 1,N
                          DO 70 K = M,1,-1
                              IF (B(K,J).NE.ZERO) THEN
                                  TEMP = ALPHA*B(K,J)
                                  B(K,J) = TEMP
                                  IF (NOUNIT) B(K,J) = B(K,J)*A(K,K)
                                  DO 60 I = K + 1,M
                                      B(I,J) = B(I,J) + TEMP*A(I,K)
       60                         CONTINUE
                              END IF
       70                 CONTINUE
       80             CONTINUE
                  END IF
              ELSE
    *
    *           Form  B := alpha*A'*B   or   B := alpha*conjg( A' )*B.
    *
                  IF (UPPER) THEN
                      DO 120 J = 1,N
                          DO 110 I = M,1,-1
                              TEMP = B(I,J)
                              IF (NOCONJ) THEN
                                  IF (NOUNIT) TEMP = TEMP*A(I,I)
                                  DO 90 K = 1,I - 1
                                      TEMP = TEMP + A(K,I)*B(K,J)
       90                         CONTINUE
                              ELSE
                                  IF (NOUNIT) TEMP = TEMP*CONJG(A(I,I))
                                  DO 100 K = 1,I - 1
                                      TEMP = TEMP + CONJG(A(K,I))*B(K,J)
      100                         CONTINUE
                              END IF
                              B(I,J) = ALPHA*TEMP
      110                 CONTINUE
      120             CONTINUE
                  ELSE
                      DO 160 J = 1,N
                          DO 150 I = 1,M
                              TEMP = B(I,J)
                              IF (NOCONJ) THEN
                                  IF (NOUNIT) TEMP = TEMP*A(I,I)
                                  DO 130 K = I + 1,M
                                      TEMP = TEMP + A(K,I)*B(K,J)
      130                         CONTINUE
                              ELSE
                                  IF (NOUNIT) TEMP = TEMP*CONJG(A(I,I))
                                  DO 140 K = I + 1,M
                                      TEMP = TEMP + CONJG(A(K,I))*B(K,J)
      140                         CONTINUE
                              END IF
                              B(I,J) = ALPHA*TEMP
      150                 CONTINUE
      160             CONTINUE
                  END IF
              END IF
          ELSE
              IF (LSAME(TRANSA,'N')) THEN
    *
    *           Form  B := alpha*B*A.
    *
                  IF (UPPER) THEN
                      DO 200 J = N,1,-1
                          TEMP = ALPHA
                          IF (NOUNIT) TEMP = TEMP*A(J,J)
                          DO 170 I = 1,M
                              B(I,J) = TEMP*B(I,J)
      170                 CONTINUE
                          DO 190 K = 1,J - 1
                              IF (A(K,J).NE.ZERO) THEN
                                  TEMP = ALPHA*A(K,J)
                                  DO 180 I = 1,M
                                      B(I,J) = B(I,J) + TEMP*B(I,K)
      180                         CONTINUE
                              END IF
      190                 CONTINUE
      200             CONTINUE
                  ELSE
                      DO 240 J = 1,N
                          TEMP = ALPHA
                          IF (NOUNIT) TEMP = TEMP*A(J,J)
                          DO 210 I = 1,M
                              B(I,J) = TEMP*B(I,J)
      210                 CONTINUE
                          DO 230 K = J + 1,N
                              IF (A(K,J).NE.ZERO) THEN
                                  TEMP = ALPHA*A(K,J)
                                  DO 220 I = 1,M
                                      B(I,J) = B(I,J) + TEMP*B(I,K)
      220                         CONTINUE
                              END IF
      230                 CONTINUE
      240             CONTINUE
                  END IF
              ELSE
    *
    *           Form  B := alpha*B*A'   or   B := alpha*B*conjg( A' ).
    *
                  IF (UPPER) THEN
                      DO 280 K = 1,N
                          DO 260 J = 1,K - 1
                              IF (A(J,K).NE.ZERO) THEN
                                  IF (NOCONJ) THEN
                                      TEMP = ALPHA*A(J,K)
                                  ELSE
                                      TEMP = ALPHA*CONJG(A(J,K))
                                  END IF
                                  DO 250 I = 1,M
                                      B(I,J) = B(I,J) + TEMP*B(I,K)
      250                         CONTINUE
                              END IF
      260                 CONTINUE
                          TEMP = ALPHA
                          IF (NOUNIT) THEN
                              IF (NOCONJ) THEN
                                  TEMP = TEMP*A(K,K)
                              ELSE
                                  TEMP = TEMP*CONJG(A(K,K))
                              END IF
                          END IF
                          IF (TEMP.NE.ONE) THEN
                              DO 270 I = 1,M
                                  B(I,K) = TEMP*B(I,K)
      270                     CONTINUE
                          END IF
      280             CONTINUE
                  ELSE
                      DO 320 K = N,1,-1
                          DO 300 J = K + 1,N
                              IF (A(J,K).NE.ZERO) THEN
                                  IF (NOCONJ) THEN
                                      TEMP = ALPHA*A(J,K)
                                  ELSE
                                      TEMP = ALPHA*CONJG(A(J,K))
                                  END IF
                                  DO 290 I = 1,M
                                      B(I,J) = B(I,J) + TEMP*B(I,K)
      290                         CONTINUE
                              END IF
      300                 CONTINUE
                          TEMP = ALPHA
                          IF (NOUNIT) THEN
                              IF (NOCONJ) THEN
                                  TEMP = TEMP*A(K,K)
                              ELSE
                                  TEMP = TEMP*CONJG(A(K,K))
                              END IF
                          END IF
                          IF (TEMP.NE.ONE) THEN
                              DO 310 I = 1,M
                                  B(I,K) = TEMP*B(I,K)
      310                     CONTINUE
                          END IF
      320             CONTINUE
                  END IF
              END IF
          END IF
    *
          RETURN
    *
    *     End of CTRMM .
    *
          END