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Diffstat (limited to 'math/minpack/lmdif1.f')
| -rw-r--r-- | math/minpack/lmdif1.f | 135 |
1 files changed, 135 insertions, 0 deletions
diff --git a/math/minpack/lmdif1.f b/math/minpack/lmdif1.f new file mode 100644 index 00000000..70f8aae0 --- /dev/null +++ b/math/minpack/lmdif1.f @@ -0,0 +1,135 @@ + subroutine lmdif1(fcn,m,n,x,fvec,tol,info,iwa,wa,lwa) + integer m,n,info,lwa + integer iwa(n) + double precision tol + double precision x(n),fvec(m),wa(lwa) + external fcn +c ********** +c +c subroutine lmdif1 +c +c the purpose of lmdif1 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 lmdif. the user must provide a +c subroutine which calculates the functions. the jacobian is +c then calculated by a forward-difference approximation. +c +c the subroutine statement is +c +c subroutine lmdif1(fcn,m,n,x,fvec,tol,info,iwa,wa,lwa) +c +c where +c +c fcn is the name of the user-supplied subroutine which +c calculates the functions. fcn must be declared +c in an external statement in the user calling +c program, and should be written as follows. +c +c subroutine fcn(m,n,x,fvec,iflag) +c integer m,n,iflag +c double precision x(n),fvec(m) +c ---------- +c calculate the functions at x and +c return this vector in 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 lmdif1. +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 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 has reached or +c exceeded 200*(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 iwa is an integer work array of length n. +c +c wa is a work array of length lwa. +c +c lwa is a positive integer input variable not less than +c m*n+5*n+m. +c +c subprograms called +c +c user-supplied ...... fcn +c +c minpack-supplied ... lmdif +c +c argonne national laboratory. minpack project. march 1980. +c burton s. garbow, kenneth e. hillstrom, jorge j. more +c +c ********** + integer maxfev,mode,mp5n,nfev,nprint + double precision epsfcn,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. tol .lt. zero + * .or. lwa .lt. m*n + 5*n + m) go to 10 +c +c call lmdif. +c + maxfev = 200*(n + 1) + ftol = tol + xtol = tol + gtol = zero + epsfcn = zero + mode = 1 + nprint = 0 + mp5n = m + 5*n + call lmdif(fcn,m,n,x,fvec,ftol,xtol,gtol,maxfev,epsfcn,wa(1), + * mode,factor,nprint,info,nfev,wa(mp5n+1),m,iwa, + * 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 lmdif1. +c + end |