lmder1.f 5.54 KB
Newer Older
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156
      subroutine lmder1(fcn,m,n,x,fvec,fjac,ldfjac,tol,info,ipvt,wa,
     *                  lwa)
      integer m,n,ldfjac,info,lwa
      integer ipvt(n)
      double precision tol
      double precision x(n),fvec(m),fjac(ldfjac,n),wa(lwa)
      external fcn
c     **********
c
c     subroutine lmder1
c
c     the purpose of lmder1 is to minimize the sum of the squares of
c     m nonlinear functions in n variables by a modification of the
c     levenberg-marquardt algorithm. this is done by using the more
c     general least-squares solver lmder. the user must provide a
c     subroutine which calculates the functions and the jacobian.
c
c     the subroutine statement is
c
c       subroutine lmder1(fcn,m,n,x,fvec,fjac,ldfjac,tol,info,
c                         ipvt,wa,lwa)
c
c     where
c
c       fcn is the name of the user-supplied subroutine which
c         calculates the functions and the jacobian. fcn must
c         be declared in an external statement in the user
c         calling program, and should be written as follows.
c
c         subroutine fcn(m,n,x,fvec,fjac,ldfjac,iflag)
c         integer m,n,ldfjac,iflag
c         double precision x(n),fvec(m),fjac(ldfjac,n)
c         ----------
c         if iflag = 1 calculate the functions at x and
c         return this vector in fvec. do not alter fjac.
c         if iflag = 2 calculate the jacobian at x and
c         return this matrix in fjac. do not alter fvec.
c         ----------
c         return
c         end
c
c         the value of iflag should not be changed by fcn unless
c         the user wants to terminate execution of lmder1.
c         in this case set iflag to a negative integer.
c
c       m is a positive integer input variable set to the number
c         of functions.
c
c       n is a positive integer input variable set to the number
c         of variables. n must not exceed m.
c
c       x is an array of length n. on input x must contain
c         an initial estimate of the solution vector. on output x
c         contains the final estimate of the solution vector.
c
c       fvec is an output array of length m which contains
c         the functions evaluated at the output x.
c
c       fjac is an output m by n array. the upper n by n submatrix
c         of fjac contains an upper triangular matrix r with
c         diagonal elements of nonincreasing magnitude such that
c
c                t     t           t
c               p *(jac *jac)*p = r *r,
c
c         where p is a permutation matrix and jac is the final
c         calculated jacobian. column j of p is column ipvt(j)
c         (see below) of the identity matrix. the lower trapezoidal
c         part of fjac contains information generated during
c         the computation of r.
c
c       ldfjac is a positive integer input variable not less than m
c         which specifies the leading dimension of the array fjac.
c
c       tol is a nonnegative input variable. termination occurs
c         when the algorithm estimates either that the relative
c         error in the sum of squares is at most tol or that
c         the relative error between x and the solution is at
c         most tol.
c
c       info is an integer output variable. if the user has
c         terminated execution, info is set to the (negative)
c         value of iflag. see description of fcn. otherwise,
c         info is set as follows.
c
c         info = 0  improper input parameters.
c
c         info = 1  algorithm estimates that the relative error
c                   in the sum of squares is at most tol.
c
c         info = 2  algorithm estimates that the relative error
c                   between x and the solution is at most tol.
c
c         info = 3  conditions for info = 1 and info = 2 both hold.
c
c         info = 4  fvec is orthogonal to the columns of the
c                   jacobian to machine precision.
c
c         info = 5  number of calls to fcn with iflag = 1 has
c                   reached 100*(n+1).
c
c         info = 6  tol is too small. no further reduction in
c                   the sum of squares is possible.
c
c         info = 7  tol is too small. no further improvement in
c                   the approximate solution x is possible.
c
c       ipvt is an integer output array of length n. ipvt
c         defines a permutation matrix p such that jac*p = q*r,
c         where jac is the final calculated jacobian, q is
c         orthogonal (not stored), and r is upper triangular
c         with diagonal elements of nonincreasing magnitude.
c         column j of p is column ipvt(j) of the identity matrix.
c
c       wa is a work array of length lwa.
c
c       lwa is a positive integer input variable not less than 5*n+m.
c
c     subprograms called
c
c       user-supplied ...... fcn
c
c       minpack-supplied ... lmder
c
c     argonne national laboratory. minpack project. march 1980.
c     burton s. garbow, kenneth e. hillstrom, jorge j. more
c
c     **********
      integer maxfev,mode,nfev,njev,nprint
      double precision factor,ftol,gtol,xtol,zero
      data factor,zero /1.0d2,0.0d0/
      info = 0
c
c     check the input parameters for errors.
c
      if (n .le. 0 .or. m .lt. n .or. ldfjac .lt. m .or. tol .lt. zero
     *    .or. lwa .lt. 5*n + m) go to 10
c
c     call lmder.
c
      maxfev = 100*(n + 1)
      ftol = tol
      xtol = tol
      gtol = zero
      mode = 1
      nprint = 0
      call lmder(fcn,m,n,x,fvec,fjac,ldfjac,ftol,xtol,gtol,maxfev,
     *           wa(1),mode,factor,nprint,info,nfev,njev,ipvt,wa(n+1),
     *           wa(2*n+1),wa(3*n+1),wa(4*n+1),wa(5*n+1))
      if (info .eq. 8) info = 4
   10 continue
      return
c
c     last card of subroutine lmder1.
c
      end