subroutine lmstr1(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 lmstr1 c c the purpose of lmstr1 is to minimize the sum of the squares of c m nonlinear functions in n variables by a modification of c the levenberg-marquardt algorithm which uses minimal storage. c this is done by using the more general least-squares solver c lmstr. the user must provide a subroutine which calculates c the functions and the rows of the jacobian. c c the subroutine statement is c c subroutine lmstr1(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 rows of the jacobian. c fcn must be declared in an external statement in the c user calling program, and should be written as follows. c c subroutine fcn(m,n,x,fvec,fjrow,iflag) c integer m,n,iflag c double precision x(n),fvec(m),fjrow(n) c ---------- c if iflag = 1 calculate the functions at x and c return this vector in fvec. c if iflag = i calculate the (i-1)-st row of the c jacobian at x and return this vector in fjrow. 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 lmstr1. 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 n by n array. the upper triangle of fjac c contains an upper triangular matrix r 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 triangular 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 n 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 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 ... lmstr c c argonne national laboratory. minpack project. march 1980. c burton s. garbow, dudley v. goetschel, kenneth e. hillstrom, c 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. n .or. tol .lt. zero * .or. lwa .lt. 5*n + m) go to 10 c c call lmstr. c maxfev = 100*(n + 1) ftol = tol xtol = tol gtol = zero mode = 1 nprint = 0 call lmstr(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 lmstr1. c end