strsm.f

          SUBROUTINE STRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
    *     .. Scalar Arguments ..
          REAL ALPHA
          INTEGER LDA,LDB,M,N
          CHARACTER DIAG,SIDE,TRANSA,UPLO
    *     ..
    *     .. Array Arguments ..
          REAL A(LDA,*),B(LDB,*)
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  STRSM  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'.
    *
    *  The matrix X is overwritten on B.
    *
    *  Arguments
    *  ==========
    *
    *  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 ) = 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  - REAL            .
    *           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      - REAL             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      - REAL             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 MAX
    *     ..
    *     .. Local Scalars ..
          REAL TEMP
          INTEGER I,INFO,J,K,NROWA
          LOGICAL LSIDE,NOUNIT,UPPER
    *     ..
    *     .. Parameters ..
          REAL ONE,ZERO
          PARAMETER (ONE=1.0E+0,ZERO=0.0E+0)
    *     ..
    *
    *     Test the input parameters.
    *
          LSIDE = LSAME(SIDE,'L')
          IF (LSIDE) THEN
              NROWA = M
          ELSE
              NROWA = N
          END IF
          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('STRSM ',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*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) B(K,J) = B(K,J)/A(K,K)
                                  DO 40 I = 1,K - 1
                                      B(I,J) = B(I,J) - B(K,J)*A(I,K)
       40                         CONTINUE
                              END IF
       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 (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
       90                 CONTINUE
      100             CONTINUE
                  END IF
              ELSE
    *
    *           Form  B := alpha*inv( A' )*B.
    *
                  IF (UPPER) THEN
                      DO 130 J = 1,N
                          DO 120 I = 1,M
                              TEMP = ALPHA*B(I,J)
                              DO 110 K = 1,I - 1
                                  TEMP = TEMP - A(K,I)*B(K,J)
      110                     CONTINUE
                              IF (NOUNIT) TEMP = TEMP/A(I,I)
                              B(I,J) = TEMP
      120                 CONTINUE
      130             CONTINUE
                  ELSE
                      DO 160 J = 1,N
                          DO 150 I = M,1,-1
                              TEMP = ALPHA*B(I,J)
                              DO 140 K = I + 1,M
                                  TEMP = TEMP - A(K,I)*B(K,J)
      140                     CONTINUE
                              IF (NOUNIT) TEMP = TEMP/A(I,I)
                              B(I,J) = TEMP
      150                 CONTINUE
      160             CONTINUE
                  END IF
              END IF
          ELSE
              IF (LSAME(TRANSA,'N')) THEN
    *
    *           Form  B := alpha*B*inv( A ).
    *
                  IF (UPPER) THEN
                      DO 210 J = 1,N
                          IF (ALPHA.NE.ONE) THEN
                              DO 170 I = 1,M
                                  B(I,J) = ALPHA*B(I,J)
      170                     CONTINUE
                          END IF
                          DO 190 K = 1,J - 1
                              IF (A(K,J).NE.ZERO) THEN
                                  DO 180 I = 1,M
                                      B(I,J) = B(I,J) - A(K,J)*B(I,K)
      180                         CONTINUE
                              END IF
      190                 CONTINUE
                          IF (NOUNIT) THEN
                              TEMP = ONE/A(J,J)
                              DO 200 I = 1,M
                                  B(I,J) = TEMP*B(I,J)
      200                     CONTINUE
                          END IF
      210             CONTINUE
                  ELSE
                      DO 260 J = N,1,-1
                          IF (ALPHA.NE.ONE) THEN
                              DO 220 I = 1,M
                                  B(I,J) = ALPHA*B(I,J)
      220                     CONTINUE
                          END IF
                          DO 240 K = J + 1,N
                              IF (A(K,J).NE.ZERO) THEN
                                  DO 230 I = 1,M
                                      B(I,J) = B(I,J) - A(K,J)*B(I,K)
      230                         CONTINUE
                              END IF
      240                 CONTINUE
                          IF (NOUNIT) THEN
                              TEMP = ONE/A(J,J)
                              DO 250 I = 1,M
                                  B(I,J) = TEMP*B(I,J)
      250                     CONTINUE
                          END IF
      260             CONTINUE
                  END IF
              ELSE
    *
    *           Form  B := alpha*B*inv( A' ).
    *
                  IF (UPPER) THEN
                      DO 310 K = N,1,-1
                          IF (NOUNIT) THEN
                              TEMP = ONE/A(K,K)
                              DO 270 I = 1,M
                                  B(I,K) = TEMP*B(I,K)
      270                     CONTINUE
                          END IF
                          DO 290 J = 1,K - 1
                              IF (A(J,K).NE.ZERO) THEN
                                  TEMP = A(J,K)
                                  DO 280 I = 1,M
                                      B(I,J) = B(I,J) - TEMP*B(I,K)
      280                         CONTINUE
                              END IF
      290                 CONTINUE
                          IF (ALPHA.NE.ONE) THEN
                              DO 300 I = 1,M
                                  B(I,K) = ALPHA*B(I,K)
      300                     CONTINUE
                          END IF
      310             CONTINUE
                  ELSE
                      DO 360 K = 1,N
                          IF (NOUNIT) THEN
                              TEMP = ONE/A(K,K)
                              DO 320 I = 1,M
                                  B(I,K) = TEMP*B(I,K)
      320                     CONTINUE
                          END IF
                          DO 340 J = K + 1,N
                              IF (A(J,K).NE.ZERO) THEN
                                  TEMP = A(J,K)
                                  DO 330 I = 1,M
                                      B(I,J) = B(I,J) - TEMP*B(I,K)
      330                         CONTINUE
                              END IF
      340                 CONTINUE
                          IF (ALPHA.NE.ONE) THEN
                              DO 350 I = 1,M
                                  B(I,K) = ALPHA*B(I,K)
      350                     CONTINUE
                          END IF
      360             CONTINUE
                  END IF
              END IF
          END IF
    *
          RETURN
    *
    *     End of STRSM .
    *
          END