OpenBLAS/reference/ctrsmf.f

      SUBROUTINE CTRSMF ( SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA,
     $                   B, LDB )
*     .. Scalar Arguments ..
      CHARACTER*1        SIDE, UPLO, TRANSA, DIAG
      INTEGER            M, N, LDA, LDB
      COMPLEX            ALPHA
*     .. Array Arguments ..
      COMPLEX            A( LDA, * ), B( LDB, * )
*     ..
*
*  Purpose
*  =======
*
*  CTRSM  solves one of the matrix equations
*
*     op( A )*X = alpha*B,   or   X*op( A ) = alpha*B,
*
*  where alpha is a scalar, X and B are m by n matrices, 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' ).
*
*  The matrix X is overwritten on B.
*
*  Parameters
*  ==========
*
*  SIDE   - CHARACTER*1.
*           On entry, SIDE specifies whether op( A ) appears on the left
*           or right of X as follows:
*
*              SIDE = 'L' or 'l'   op( A )*X = alpha*B.
*
*              SIDE = 'R' or 'r'   X*op( A ) = alpha*B.
*
*           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  right-hand  side  matrix  B,  and  on exit  is
*           overwritten by the solution matrix  X.
*
*  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 ..
      LOGICAL            LSIDE, NOCONJ, NOUNIT, UPPER
      INTEGER            I, INFO, J, K, NROWA
      COMPLEX            TEMP
*     .. Parameters ..
      COMPLEX            ONE
      PARAMETER        ( ONE  = ( 1.0E+0, 0.0E+0 ) )
      COMPLEX            ZERO
      PARAMETER        ( ZERO = ( 0.0E+0, 0.0E+0 ) )
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      LSIDE  = LSAME( SIDE  , 'L' )
      IF( LSIDE )THEN
         NROWA = M
      ELSE
         NROWA = N
      END IF
      NOCONJ = (LSAME( TRANSA, 'N' ) .OR. 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, 'R' ) ).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( 'CTRSM ', 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' ) .OR. LSAME( TRANSA, 'R' ))THEN
*
*           Form  B := alpha*inv( A )*B.
*
            IF( UPPER )THEN
               DO 60, J = 1, N
                  IF( ALPHA.NE.ONE )THEN
                     DO 30, I = 1, M
                        B( I, J ) = ALPHA*B( I, J )
   30                CONTINUE
                  END IF

                  DO 50, K = M, 1, -1
                     IF( B( K, J ).NE.ZERO )THEN

                        IF( NOUNIT ) THEN
                           IF (NOCONJ) THEN
                              B( K, J ) = B( K, J )/A( K, K )
                           ELSE
                              B( K, J ) = B( K, J )/CONJG(A( K, K ))
                           ENDIF
                        ENDIF

                        IF (NOCONJ) THEN
                           DO 40, I = 1, K - 1
                            B( I, J ) = B( I, J ) - B( K, J )*A( I, K )
   40                      CONTINUE
                        ELSE
                           DO 45, I = 1, K - 1
                      B( I, J ) = B( I, J ) - B( K, J )*CONJG(A( I, K ))
   45                      CONTINUE
                        ENDIF
                     ENDIF
   50             CONTINUE
   60          CONTINUE
            ELSE
               DO 100, J = 1, N
                  IF( ALPHA.NE.ONE )THEN
                     DO 70, I = 1, M
                        B( I, J ) = ALPHA*B( I, J )
   70                CONTINUE
                  END IF
                  DO 90 K = 1, M
                     IF (NOCONJ) THEN
                     IF( B( K, J ).NE.ZERO )THEN
                        IF( NOUNIT )
     $                     B( K, J ) = B( K, J )/A( K, K )
                        DO 80, I = K + 1, M
                           B( I, J ) = B( I, J ) - B( K, J )*A( I, K )
   80                   CONTINUE
                     END IF
                     ELSE
                     IF( B( K, J ).NE.ZERO )THEN
                        IF( NOUNIT )
     $                     B( K, J ) = B( K, J )/CONJG(A( K, K ))
                        DO 85, I = K + 1, M
                      B( I, J ) = B( I, J ) - B( K, J )*CONJG(A( I, K ))
   85                   CONTINUE
                     END IF
                     ENDIF
   90             CONTINUE
  100          CONTINUE
            END IF
         ELSE
*
*           Form  B := alpha*inv( A' )*B
*           or    B := alpha*inv( conjg( A' ) )*B.
*
            IF( UPPER )THEN
               DO 140, J = 1, N
                  DO 130, I = 1, M
                     TEMP = ALPHA*B( I, J )
                     IF( NOCONJ )THEN
                        DO 110, K = 1, I - 1
                           TEMP = TEMP - A( K, I )*B( K, J )
  110                   CONTINUE
                        IF( NOUNIT )
     $                     TEMP = TEMP/A( I, I )
                     ELSE
                        DO 120, K = 1, I - 1
                           TEMP = TEMP - CONJG( A( K, I ) )*B( K, J )
  120                   CONTINUE
                        IF( NOUNIT )
     $                     TEMP = TEMP/CONJG( A( I, I ) )
                     END IF
                     B( I, J ) = TEMP
  130             CONTINUE
  140          CONTINUE
            ELSE
               DO 180, J = 1, N
                  DO 170, I = M, 1, -1
                     TEMP = ALPHA*B( I, J )
                     IF( NOCONJ )THEN
                        DO 150, K = I + 1, M
                           TEMP = TEMP - A( K, I )*B( K, J )
  150                   CONTINUE
                        IF( NOUNIT )
     $                     TEMP = TEMP/A( I, I )
                     ELSE
                        DO 160, K = I + 1, M
                           TEMP = TEMP - CONJG( A( K, I ) )*B( K, J )
  160                   CONTINUE
                        IF( NOUNIT )
     $                     TEMP = TEMP/CONJG( A( I, I ) )
                     END IF
                     B( I, J ) = TEMP
  170             CONTINUE
  180          CONTINUE
            END IF
         END IF
      ELSE
         IF( LSAME( TRANSA, 'N' ) .OR. LSAME( TRANSA, 'R' ))THEN
*
*           Form  B := alpha*B*inv( A ).
*
            IF( UPPER )THEN
               DO 230, J = 1, N
                  IF( ALPHA.NE.ONE )THEN
                     DO 190, I = 1, M
                        B( I, J ) = ALPHA*B( I, J )
  190                CONTINUE
                  END IF
                  DO 210, K = 1, J - 1
                     IF( A( K, J ).NE.ZERO )THEN
                        IF (NOCONJ) THEN
                        DO 200, I = 1, M
                           B( I, J ) = B( I, J ) - A( K, J )*B( I, K )
  200                   CONTINUE
                        ELSE
                        DO 205, I = 1, M
                     B( I, J ) = B( I, J ) - CONJG(A( K, J ))*B( I, K )
 205                    CONTINUE
                        ENDIF
                     END IF
  210             CONTINUE
                  IF( NOUNIT )THEN
                     IF (NOCONJ) THEN
                     TEMP = ONE/A( J, J )
                     ELSE
                     TEMP = ONE/CONJG(A( J, J ))
                     ENDIF
                     DO 220, I = 1, M
                        B( I, J ) = TEMP*B( I, J )
  220                CONTINUE
                  END IF
  230          CONTINUE
            ELSE
               DO 280, J = N, 1, -1
                  IF( ALPHA.NE.ONE )THEN
                     DO 240, I = 1, M
                        B( I, J ) = ALPHA*B( I, J )
  240                CONTINUE
                  END IF
                  DO 260, K = J + 1, N
                     IF( A( K, J ).NE.ZERO )THEN
                        IF (NOCONJ) THEN
                        DO 250, I = 1, M
                           B( I, J ) = B( I, J ) - A( K, J )*B( I, K )
  250                   CONTINUE
                        ELSE
                        DO 255, I = 1, M
                    B( I, J ) = B( I, J ) - CONJG(A( K, J ))*B( I, K )
 255                    CONTINUE
                        ENDIF
                     END IF
  260             CONTINUE
                  IF( NOUNIT )THEN
                     IF (NOCONJ) THEN
                     TEMP = ONE/A( J, J )
                     ELSE
                     TEMP = ONE/CONJG(A( J, J ))
                     ENDIF
                     DO 270, I = 1, M
                       B( I, J ) = TEMP*B( I, J )
  270                CONTINUE
                  END IF
  280          CONTINUE
            END IF
         ELSE
*
*           Form  B := alpha*B*inv( A' )
*           or    B := alpha*B*inv( conjg( A' ) ).
*
            IF( UPPER )THEN
               DO 330, K = N, 1, -1
                  IF( NOUNIT )THEN
                     IF( NOCONJ )THEN
                        TEMP = ONE/A( K, K )
                     ELSE
                        TEMP = ONE/CONJG( A( K, K ) )
                     END IF
                     DO 290, I = 1, M
                        B( I, K ) = TEMP*B( I, K )
  290                CONTINUE
                  END IF
                  DO 310, J = 1, K - 1
                     IF( A( J, K ).NE.ZERO )THEN
                        IF( NOCONJ )THEN
                           TEMP = A( J, K )
                        ELSE
                           TEMP = CONJG( A( J, K ) )
                        END IF
                        DO 300, I = 1, M
                           B( I, J ) = B( I, J ) - TEMP*B( I, K )
  300                   CONTINUE
                     END IF
  310             CONTINUE
                  IF( ALPHA.NE.ONE )THEN
                     DO 320, I = 1, M
                        B( I, K ) = ALPHA*B( I, K )
  320                CONTINUE
                  END IF
  330          CONTINUE
            ELSE
               DO 380, K = 1, N
                  IF( NOUNIT )THEN
                     IF( NOCONJ )THEN
                        TEMP = ONE/A( K, K )
                     ELSE
                        TEMP = ONE/CONJG( A( K, K ) )
                     END IF
                     DO 340, I = 1, M
                        B( I, K ) = TEMP*B( I, K )
  340                CONTINUE
                  END IF
                  DO 360, J = K + 1, N
                     IF( A( J, K ).NE.ZERO )THEN
                        IF( NOCONJ )THEN
                           TEMP = A( J, K )
                        ELSE
                           TEMP = CONJG( A( J, K ) )
                        END IF
                        DO 350, I = 1, M
                           B( I, J ) = B( I, J ) - TEMP*B( I, K )
  350                   CONTINUE
                     END IF
  360             CONTINUE
                  IF( ALPHA.NE.ONE )THEN
                     DO 370, I = 1, M
                        B( I, K ) = ALPHA*B( I, K )
  370                CONTINUE
                  END IF
  380          CONTINUE
            END IF
         END IF
      END IF
*
      RETURN
*
*     End of CTRSM .
*
      END