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subroutine lmdif1(fcn,m,n,x,fvec,tol,info,iwa,wa,lwa)
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double precision x(n),fvec(m),wa(lwa)
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c the purpose of lmdif1 is to minimize the sum of the squares of
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c m nonlinear functions in n variables by a modification of the
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c levenberg-marquardt algorithm. this is done by using the more
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c general least-squares solver lmdif. the user must provide a
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c subroutine which calculates the functions. the jacobian is
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c then calculated by a forward-difference approximation.
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c the subroutine statement is
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c subroutine lmdif1(fcn,m,n,x,fvec,tol,info,iwa,wa,lwa)
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c fcn is the name of the user-supplied subroutine which
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c calculates the functions. fcn must be declared
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c in an external statement in the user calling
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c program, and should be written as follows.
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c subroutine fcn(m,n,x,fvec,iflag)
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c double precision x(n),fvec(m)
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c calculate the functions at x and
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c return this vector in fvec.
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c the value of iflag should not be changed by fcn unless
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c the user wants to terminate execution of lmdif1.
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c in this case set iflag to a negative integer.
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c m is a positive integer input variable set to the number
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c n is a positive integer input variable set to the number
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c of variables. n must not exceed m.
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c x is an array of length n. on input x must contain
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c an initial estimate of the solution vector. on output x
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c contains the final estimate of the solution vector.
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c fvec is an output array of length m which contains
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c the functions evaluated at the output x.
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c tol is a nonnegative input variable. termination occurs
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c when the algorithm estimates either that the relative
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c error in the sum of squares is at most tol or that
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c the relative error between x and the solution is at
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c info is an integer output variable. if the user has
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c terminated execution, info is set to the (negative)
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c value of iflag. see description of fcn. otherwise,
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c info is set as follows.
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c info = 0 improper input parameters.
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c info = 1 algorithm estimates that the relative error
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c in the sum of squares is at most tol.
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c info = 2 algorithm estimates that the relative error
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c between x and the solution is at most tol.
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c info = 3 conditions for info = 1 and info = 2 both hold.
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c info = 4 fvec is orthogonal to the columns of the
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c jacobian to machine precision.
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c info = 5 number of calls to fcn has reached or
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c info = 6 tol is too small. no further reduction in
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c the sum of squares is possible.
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c info = 7 tol is too small. no further improvement in
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c the approximate solution x is possible.
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c iwa is an integer work array of length n.
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c wa is a work array of length lwa.
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c lwa is a positive integer input variable not less than
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c user-supplied ...... fcn
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c minpack-supplied ... lmdif
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c argonne national laboratory. minpack project. march 1980.
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c burton s. garbow, kenneth e. hillstrom, jorge j. more
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integer maxfev,mode,mp5n,nfev,nprint
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double precision epsfcn,factor,ftol,gtol,xtol,zero
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data factor,zero /1.0d2,0.0d0/
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c check the input parameters for errors.
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if (n .le. 0 .or. m .lt. n .or. tol .lt. zero
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* .or. lwa .lt. m*n + 5*n + m) go to 10
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call lmdif(fcn,m,n,x,fvec,ftol,xtol,gtol,maxfev,epsfcn,wa(1),
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* mode,factor,nprint,info,nfev,wa(mp5n+1),m,iwa,
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* wa(n+1),wa(2*n+1),wa(3*n+1),wa(4*n+1),wa(5*n+1))
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if (info .eq. 8) info = 4
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c last card of subroutine lmdif1.
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removed
Lib/optimize/minpack/lmdif1.f
