subroutine hybrj1(fcn,n,x,fvec,fjac,ldfjac,tol,info,wa,lwa) integer n,ldfjac,info,lwa real tol real x(n),fvec(n),fjac(ldfjac,n),wa(lwa) external fcn c ********** c c subroutine hybrj1 c c the purpose of hybrj1 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 hybrj. the user c must provide a subroutine which calculates the functions c and the jacobian. c c the subroutine statement is c c subroutine hybrj1(fcn,n,x,fvec,fjac,ldfjac,tol,info,wa,lwa) c c where c c fcn is the name of the user-supplied subroutine which c calculates the functions and the jacobian. fcn must c be declared in an external statement in the user c calling program, and should be written as follows. c c subroutine fcn(n,x,fvec,fjac,ldfjac,iflag) c integer n,ldfjac,iflag c real x(n),fvec(n),fjac(ldfjac,n) c ---------- c if iflag = 1 calculate the functions at x and c return this vector in fvec. do not alter fjac. c if iflag = 2 calculate the jacobian at x and c return this matrix in fjac. do not alter 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 hybrj1. 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 fjac is an output n by n array which contains the c orthogonal matrix q produced by the qr factorization c of the final approximate jacobian. 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 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 with iflag = 1 has c reached 100*(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*(n+13))/2. c c subprograms called c c user-supplied ...... fcn c c minpack-supplied ... hybrj c c argonne national laboratory. minpack project. march 1980. c burton s. garbow, kenneth e. hillstrom, jorge j. more c c ********** integer j,lr,maxfev,mode,nfev,njev,nprint real 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. ldfjac .lt. n .or. tol .lt. zero * .or. lwa .lt. (n*(n + 13))/2) go to 20 c c call hybrj. c maxfev = 100*(n + 1) xtol = tol mode = 2 do 10 j = 1, n wa(j) = one 10 continue nprint = 0 lr = (n*(n + 1))/2 call hybrj(fcn,n,x,fvec,fjac,ldfjac,xtol,maxfev,wa(1),mode, * factor,nprint,info,nfev,njev,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 hybrj1. c end