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