inverse.f

一个基于打靶法的最优控制求解软件 求解过程中采用参数延续算法

     $         CALL DSWAP( N, A( I, 1 ), LDA, A( IP, 1 ), LDA )
            IX = IX + INCX
   20    CONTINUE
      ELSE IF( INCX.LT.0 ) THEN
         DO 30 I = K2, K1, -1
            IP = IPIV( IX )
            IF( IP.NE.I )
     $         CALL DSWAP( N, A( I, 1 ), LDA, A( IP, 1 ), LDA )
            IX = IX + INCX
   30    CONTINUE
      END IF
*
      RETURN
*
*     End of DLASWP
*
      END



c      subroutine  dscal(n,da,dx,incx)
cc
cc     scales a vector by a constant.
cc     uses unrolled loops for increment equal to one.
cc     jack dongarra, linpack, 3/11/78.
cc     modified to correct problem with negative increment, 8/21/90.
cc
c      double precision da,dx(1)
c      integer i,incx,ix,m,mp1,n
cc
c      if(n.le.0)return
c      if(incx.eq.1)go to 20
cc
cc        code for increment not equal to 1
cc
c      ix = 1
c      if(incx.lt.0)ix = (-n+1)*incx + 1
c      do 10 i = 1,n
c        dx(ix) = da*dx(ix)
c        ix = ix + incx
c   10 continue
c      return
cc
cc        code for increment equal to 1
cc
cc
cc        clean-up loop
cc
c   20 m = mod(n,5)
c      if( m .eq. 0 ) go to 40
c      do 30 i = 1,m
c        dx(i) = da*dx(i)
c   30 continue
c      if( n .lt. 5 ) return
c   40 mp1 = m + 1
c      do 50 i = mp1,n,5
c        dx(i) = da*dx(i)
c        dx(i + 1) = da*dx(i + 1)
c        dx(i + 2) = da*dx(i + 2)
c        dx(i + 3) = da*dx(i + 3)
c        dx(i + 4) = da*dx(i + 4)
c   50 continue
c      return
c      end


      subroutine  dswap (n,dx,incx,dy,incy)
c
c     interchanges two vectors.
c     uses unrolled loops for increments equal one.
c     jack dongarra, linpack, 3/11/78.
c
      double precision dx(1),dy(1),dtemp
      integer i,incx,incy,ix,iy,m,mp1,n
c
      if(n.le.0)return
      if(incx.eq.1.and.incy.eq.1)go to 20
c
c       code for unequal increments or equal increments not equal
c         to 1
c
      ix = 1
      iy = 1
      if(incx.lt.0)ix = (-n+1)*incx + 1
      if(incy.lt.0)iy = (-n+1)*incy + 1
      do 10 i = 1,n
        dtemp = dx(ix)
        dx(ix) = dy(iy)
        dy(iy) = dtemp
        ix = ix + incx
        iy = iy + incy
   10 continue
      return
c
c       code for both increments equal to 1
c
c
c       clean-up loop
c
   20 m = mod(n,3)
      if( m .eq. 0 ) go to 40
      do 30 i = 1,m
        dtemp = dx(i)
        dx(i) = dy(i)
        dy(i) = dtemp
   30 continue
      if( n .lt. 3 ) return
   40 mp1 = m + 1
      do 50 i = mp1,n,3
        dtemp = dx(i)
        dx(i) = dy(i)
        dy(i) = dtemp
        dtemp = dx(i + 1)
        dx(i + 1) = dy(i + 1)
        dy(i + 1) = dtemp
        dtemp = dx(i + 2)
        dx(i + 2) = dy(i + 2)
        dy(i + 2) = dtemp
   50 continue
      return
      end



      SUBROUTINE DTRMM (SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA,
     $   B, LDB)
C***BEGIN PROLOGUE  DTRMM
C***PURPOSE  Perform one of the matrix-matrix operations.
C***LIBRARY   SLATEC (BLAS)
C***CATEGORY  D1B6
C***TYPE      DOUBLE PRECISION (STRMM-S, DTRMM-D, CTRMM-C)
C***KEYWORDS  LEVEL 3 BLAS, LINEAR ALGEBRA
C***AUTHOR  Dongarra, J., (ANL)
C           Duff, I., (AERE)
C           Du Croz, J., (NAG)
C           Hammarling, S. (NAG)
C***DESCRIPTION
C
C  DTRMM  performs one of the matrix-matrix operations
C
C     B := alpha*op( A )*B,   or   B := alpha*B*op( A ),
C
C  where  alpha  is a scalar,  B  is an m by n matrix,  A  is a unit, or
C  non-unit,  upper or lower triangular matrix  and  op( A )  is one  of
C
C     op( A ) = A   or   op( A ) = A'.
C
C  Parameters
C  ==========
C
C  SIDE   - CHARACTER*1.
C           On entry,  SIDE specifies whether  op( A ) multiplies B from
C           the left or right as follows:
C
C              SIDE = 'L' or 'l'   B := alpha*op( A )*B.
C
C              SIDE = 'R' or 'r'   B := alpha*B*op( A ).
C
C           Unchanged on exit.
C
C  UPLO   - CHARACTER*1.
C           On entry, UPLO specifies whether the matrix A is an upper or
C           lower triangular matrix as follows:
C
C              UPLO = 'U' or 'u'   A is an upper triangular matrix.
C
C              UPLO = 'L' or 'l'   A is a lower triangular matrix.
C
C           Unchanged on exit.
C
C  TRANSA - CHARACTER*1.
C           On entry, TRANSA specifies the form of op( A ) to be used in
C           the matrix multiplication as follows:
C
C              TRANSA = 'N' or 'n'   op( A ) = A.
C
C              TRANSA = 'T' or 't'   op( A ) = A'.
C
C              TRANSA = 'C' or 'c'   op( A ) = A'.
C
C           Unchanged on exit.
C
C  DIAG   - CHARACTER*1.
C           On entry, DIAG specifies whether or not A is unit triangular
C           as follows:
C
C              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
C
C              DIAG = 'N' or 'n'   A is not assumed to be unit
C                                  triangular.
C
C           Unchanged on exit.
C
C  M      - INTEGER.
C           On entry, M specifies the number of rows of B. M must be at
C           least zero.
C           Unchanged on exit.
C
C  N      - INTEGER.
C           On entry, N specifies the number of columns of B.  N must be
C           at least zero.
C           Unchanged on exit.
C
C  ALPHA  - DOUBLE PRECISION.
C           On entry,  ALPHA specifies the scalar  alpha. When  alpha is
C           zero then  A is not referenced and  B need not be set before
C           entry.
C           Unchanged on exit.
C
C  A      - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m
C           when  SIDE = 'L' or 'l'  and is  n  when  SIDE = 'R' or 'r'.
C           Before entry  with  UPLO = 'U' or 'u',  the  leading  k by k
C           upper triangular part of the array  A must contain the upper
C           triangular matrix  and the strictly lower triangular part of
C           A is not referenced.
C           Before entry  with  UPLO = 'L' or 'l',  the  leading  k by k
C           lower triangular part of the array  A must contain the lower
C           triangular matrix  and the strictly upper triangular part of
C           A is not referenced.
C           Note that when  DIAG = 'U' or 'u',  the diagonal elements of
C           A  are not referenced either,  but are assumed to be  unity.
C           Unchanged on exit.
C
C  LDA    - INTEGER.
C           On entry, LDA specifies the first dimension of A as declared
C           in the calling (sub) program.  When  SIDE = 'L' or 'l'  then
C           LDA  must be at least  max( 1, m ),  when  SIDE = 'R' or 'r'
C           then LDA must be at least max( 1, n ).
C           Unchanged on exit.
C
C  B      - DOUBLE PRECISION array of DIMENSION ( LDB, n ).
C           Before entry,  the leading  m by n part of the array  B must
C           contain the matrix  B,  and  on exit  is overwritten  by the
C           transformed matrix.
C
C  LDB    - INTEGER.
C           On entry, LDB specifies the first dimension of B as declared
C           in  the  calling  (sub)  program.   LDB  must  be  at  least
C           max( 1, m ).
C           Unchanged on exit.
C
C***REFERENCES  Dongarra, J., Du Croz, J., Duff, I., and Hammarling, S.
C                 A set of level 3 basic linear algebra subprograms.
C                 ACM TOMS, Vol. 16, No. 1, pp. 1-17, March 1990.
C***ROUTINES CALLED  LSAME, XERBLA
C***REVISION HISTORY  (YYMMDD)
C   890208  DATE WRITTEN
C   910605  Modified to meet SLATEC prologue standards.  Only comment
C           lines were modified.  (BKS)
C***END PROLOGUE  DTRMM
C     .. Scalar Arguments ..
      CHARACTER*1        SIDE, UPLO, TRANSA, DIAG
      INTEGER            M, N, LDA, LDB
      DOUBLE PRECISION   ALPHA
C     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), B( LDB, * )
C     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
C     .. External Subroutines ..
      EXTERNAL           XERBLA
C     .. Intrinsic Functions ..
      INTRINSIC          MAX
C     .. Local Scalars ..
      LOGICAL            LSIDE, NOUNIT, UPPER
      INTEGER            I, INFO, J, K, NROWA
      DOUBLE PRECISION   TEMP
C     .. Parameters ..
      DOUBLE PRECISION   ONE         , ZERO
      PARAMETER        ( ONE = 1D+0, ZERO = 0D+0 )
C***FIRST EXECUTABLE STATEMENT  DTRMM
C
C     Test the input parameters.
C
      LSIDE  = LSAME( SIDE  , 'L' )
      IF( LSIDE )THEN
         NROWA = M
      ELSE
         NROWA = N
      END IF
      NOUNIT = LSAME( DIAG  , 'N' )
      UPPER  = LSAME( UPLO  , 'U' )
C
      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( 'DTRMM ', INFO )
         RETURN
      END IF
C
C     Quick return if possible.
C
      IF( N.EQ.0 )
     $   RETURN
C
C     And when  alpha.eq.zero.
C
      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
C
C     Start the operations.
C
      IF( LSIDE )THEN
         IF( LSAME( TRANSA, 'N' ) )THEN
C
C           Form  B := alpha*A*B.
C
            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
C
C           Form  B := alpha*B*A'.
C
            IF( UPPER )THEN
               DO 110, J = 1, N
                  DO 100, I = M, 1, -1
                     TEMP = B( I, J )
                     IF( NOUNIT )
     $                  TEMP = TEMP*A( I, I )
                     DO 90, K = 1, I - 1
                        TEMP = TEMP + A( K, I )*B( K, J )
   90                CONTINUE
                     B( I, J ) = ALPHA*TEMP
  100             CONTINUE
  110          CONTINUE
            ELSE
               DO 140, J = 1, N
                  DO 130, I = 1, M
                     TEMP = B( I, J )
                     IF( NOUNIT )
     $                  TEMP = TEMP*A( I, I )
                     DO 120, K = I + 1, M
                        TEMP = TEMP + A( K, I )*B( K, J )
  120                CONTINUE
                     B( I, J ) = ALPHA*TEMP
  130             CONTINUE
  140          CONTINUE
            END IF
         END IF
      ELSE
         IF( LSAME( TRANSA, 'N' ) )THEN
C
C           Form  B := alpha*B*A.
C
            IF( UPPER )THEN
               DO 180, J = N, 1, -1
                  TEMP = ALPHA
                  IF( NOUNIT )
     $               TEMP = TEMP*A( J, J )
                  DO 150, I = 1, M
                     B( I, J ) = TEMP*B( I, J )
  150             CONTINUE
                  DO 170, K = 1, J - 1
                     IF( A( K, J ).NE.ZERO )THEN
                        TEMP = ALPHA*A( K, J )
                        DO 160, I = 1, M
                           B( I, J ) = B( I, J ) + TEMP*B( I, K )
  160                   CONTINUE
                     END IF
  170             CONTINUE
  180          CONTINUE
            ELSE
               DO 220, J = 1, N
                  TEMP = ALPHA
                  IF( NOUNIT )
     $               TEMP = TEMP*A( J, J )
                  DO 190, I = 1, M
                     B( I, J ) = TEMP*B( I, J )
  190             CONTINUE
                  DO 210, K = J + 1, N
                     IF( A( K, J ).NE.ZERO )THEN
                        TEMP = ALPHA*A( K, J )
                        DO 200, I = 1, M
                           B( I, J ) = B( I, J ) + TEMP*B( I, K )
  200                   CONTINUE
                     END IF
  210             CONTINUE
  220          CONTINUE
            END IF
         ELSE
C
C           Form  B := alpha*B*A'.