/* Last edited on 2011-05-15 01:36:12 by stolfi */ /* lmdif.f -- translated by f2c (version of 17 January 1992 0:17:58). You must link the resulting object file with the libraries: -lf77 -li77 -lm -lc (in that order) */ #ifndef lmdif_H #define lmdif_H #include typedef void fcn_t(int *m, int *n, double *x, double *fvec, int *iflag); int lmdif ( fcn_t *fcn, int *m, int *n, double *x, double *fvec, double *ftol, double *xtol, double *gtol, int *maxfev, double *epsfcn, double *diag, int *mode, double *factor, int *nprint, int *info, int *nfev, double *fjac, int *ldfjac, int *ipvt, double *qtf, double *wa1, double *wa2, double *wa3, double *wa4 ); /* ********** */ /* subroutine lmdif */ /* the purpose of lmdif is to minimize the sum of the squares of */ /* m nonlinear functions in n variables by a modification of */ /* the levenberg-marquardt algorithm. the user must provide a */ /* subroutine which calculates the functions. the jacobian is */ /* then calculated by a forward-difference approximation. */ /* the subroutine statement is */ /* subroutine lmdif(fcn,m,n,x,fvec,ftol,xtol,gtol,maxfev,epsfcn, */ /* diag,mode,factor,nprint,info,nfev,fjac, */ /* ldfjac,ipvt,qtf,wa1,wa2,wa3,wa4) */ /* where */ /* fcn is the name of the user-supplied subroutine which */ /* calculates the functions. fcn must be declared */ /* in an external statement in the user calling */ /* program, and should be written as follows. */ /* subroutine fcn(m,n,x,fvec,iflag) */ /* int m,n,iflag */ /* double precision x(n),fvec(m) */ /* ---------- */ /* calculate the functions at x and */ /* return this vector in fvec. */ /* ---------- */ /* return */ /* end */ /* the value of iflag should not be changed by fcn unless */ /* the user wants to terminate execution of lmdif. */ /* in this case set iflag to a negative int. */ /* m is a positive int input variable set to the number */ /* of functions. */ /* n is a positive int input variable set to the number */ /* of variables. n must not exceed m. */ /* x is an array of length n. on input x must contain */ /* an initial estimate of the solution vector. on output x */ /* contains the final estimate of the solution vector. */ /* fvec is an output array of length m which contains */ /* the functions evaluated at the output x. */ /* ftol is a nonnegative input variable. termination */ /* occurs when both the actual and predicted relative */ /* reductions in the sum of squares are at most ftol. */ /* therefore, ftol measures the relative error desired */ /* in the sum of squares. */ /* xtol is a nonnegative input variable. termination */ /* occurs when the relative error between two consecutive */ /* iterates is at most xtol. therefore, xtol measures the */ /* relative error desired in the approximate solution. */ /* gtol is a nonnegative input variable. termination */ /* occurs when the cosine of the angle between fvec and */ /* any column of the jacobian is at most gtol in absolute */ /* value. therefore, gtol measures the orthogonality */ /* desired between the function vector and the columns */ /* of the jacobian. */ /* maxfev is a positive int input variable. termination */ /* occurs when the number of calls to fcn is at least */ /* maxfev by the end of an iteration. */ /* epsfcn is an input variable used in determining a suitable */ /* step length for the forward-difference approximation. this */ /* approximation assumes that the relative errors in the */ /* functions are of the order of epsfcn. if epsfcn is less */ /* than the machine precision, it is assumed that the relative */ /* errors in the functions are of the order of the machine */ /* precision. */ /* diag is an array of length n. if mode = 1 (see */ /* below), diag is internally set. if mode = 2, diag */ /* must contain positive entries that serve as */ /* multiplicative scale factors for the variables. */ /* mode is an int input variable. if mode = 1, the */ /* variables will be scaled internally. if mode = 2, */ /* the scaling is specified by the input diag. other */ /* values of mode are equivalent to mode = 1. */ /* factor is a positive input variable used in determining the */ /* initial step bound. this bound is set to the product of */ /* factor and the euclidean norm of diag*x if nonzero, or else */ /* to factor itself. in most cases factor should lie in the */ /* interval (.1,100.). 100. is a generally recommended value. */ /* nprint is an int input variable that enables controlled */ /* printing of iterates if it is positive. in this case, */ /* fcn is called with iflag = 0 at the beginning of the first */ /* iteration and every nprint iterations thereafter and */ /* immediately prior to return, with x and fvec available */ /* for printing. if nprint is not positive, no special calls */ /* of fcn with iflag = 0 are made. */ /* info is an int output variable. if the user has */ /* terminated execution, info is set to the (negative) */ /* value of iflag. see description of fcn. otherwise, */ /* info is set as follows. */ /* info = 0 improper input parameters. */ /* info = 1 both actual and predicted relative reductions */ /* in the sum of squares are at most ftol. */ /* info = 2 relative error between two consecutive iterates */ /* is at most xtol. */ /* info = 3 conditions for info = 1 and info = 2 both hold. */ /* info = 4 the cosine of the angle between fvec and any */ /* column of the jacobian is at most gtol in */ /* absolute value. */ /* info = 5 number of calls to fcn has reached or */ /* exceeded maxfev. */ /* info = 6 ftol is too small. no further reduction in */ /* the sum of squares is possible. */ /* info = 7 xtol is too small. no further improvement in */ /* the approximate solution x is possible. */ /* info = 8 gtol is too small. fvec is orthogonal to the */ /* columns of the jacobian to machine precision. */ /* nfev is an int output variable set to the number of */ /* calls to fcn. */ /* fjac is an output m by n array. the upper n by n submatrix */ /* of fjac contains an upper triangular matrix r with */ /* diagonal elements of nonincreasing magnitude such that */ /* t t t */ /* p *(jac *jac)*p = r *r, */ /* where p is a permutation matrix and jac is the final */ /* calculated jacobian. column j of p is column ipvt(j) */ /* (see below) of the identity matrix. the lower trapezoidal */ /* part of fjac contains information generated during */ /* the computation of r. */ /* ldfjac is a positive int input variable not less than m */ /* which specifies the leading dimension of the array fjac. */ /* ipvt is an int output array of length n. ipvt */ /* defines a permutation matrix p such that jac*p = q*r, */ /* where jac is the final calculated jacobian, q is */ /* orthogonal (not stored), and r is upper triangular */ /* with diagonal elements of nonincreasing magnitude. */ /* column j of p is column ipvt(j) of the identity matrix. */ /* qtf is an output array of length n which contains */ /* the first n elements of the vector (q transpose)*fvec. */ /* wa1, wa2, and wa3 are work arrays of length n. */ /* wa4 is a work array of length m. */ /* subprograms called */ /* user-supplied ...... fcn */ /* minpack-supplied ... dpmpar,enorm,fdjac2,lmpar,qrfac */ /* fortran-supplied ... dabs,dmax1,dmin1,dsqrt,mod */ /* argonne national laboratory. minpack project. march 1980. */ /* burton s. garbow, kenneth e. hillstrom, jorge j. more */ /* ********** */ #endif