subroutine hybrd1(fcn,n,x,fvec,tol,info,wa,lwa) integer n,info,lwa real tol real x(n),fvec(n),wa(lwa) external fcn c ********** c c subroutine hybrd1 c c the purpose of hybrd1 is to find a zero of a system of c n nonlinear functions in n variables by a modification c of the powell hybrid method. this is done by using the c more general nonlinear equation solver hybrd. the user c must provide a subroutine which calculates the functions. c the jacobian is then calculated by a forward-difference c approximation. c c the subroutine statement is c c subroutine hybrd1(fcn,n,x,fvec,tol,info,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(n,x,fvec,iflag) c integer n,iflag c real x(n),fvec(n) 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 hybrd1. c in this case set iflag to a negative integer. c c n is a positive integer input variable set to the number c of functions and variables. 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 n 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 that the relative error c between x and the solution is at 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 between x and the solution is at most tol. c c info = 2 number of calls to fcn has reached or exceeded c 200*(n+1). c c info = 3 tol is too small. no further improvement in c the approximate solution x is possible. c c info = 4 iteration is not making good progress. c c wa is a work array of length lwa. c c lwa is a positive integer input variable not less than c (n*(3*n+13))/2. c c subprograms called c c user-supplied ...... fcn c c minpack-supplied ... hybrd c c argonne national laboratory. minpack project. march 1980. c burton s. garbow, kenneth e. hillstrom, jorge j. more c c ********** integer index,j,lr,maxfev,ml,mode,mu,nfev,nprint real epsfcn,factor,one,xtol,zero data factor,one,zero /1.0e2,1.0e0,0.0e0/ info = 0 c c check the input parameters for errors. c if (n .le. 0 .or. tol .lt. zero .or. lwa .lt. (n*(3*n + 13))/2) * go to 20 c c call hybrd. c maxfev = 200*(n + 1) xtol = tol ml = n - 1 mu = n - 1 epsfcn = zero mode = 2 do 10 j = 1, n wa(j) = one 10 continue nprint = 0 lr = (n*(n + 1))/2 index = 6*n + lr call hybrd(fcn,n,x,fvec,xtol,maxfev,ml,mu,epsfcn,wa(1),mode, * factor,nprint,info,nfev,wa(index+1),n,wa(6*n+1),lr, * wa(n+1),wa(2*n+1),wa(3*n+1),wa(4*n+1),wa(5*n+1)) if (info .eq. 5) info = 4 20 continue return c c last card of subroutine hybrd1. c end