subroutine fdjac2(fcn,m,n,x,fvec,fjac,ldfjac,iflag,epsfcn,wa)
integer m,n,ldfjac,iflag
real epsfcn
real x(n),fvec(m),fjac(ldfjac,n),wa(m)
c **********
c
c subroutine fdjac2
c
c this subroutine computes a forward-difference approximation
c to the m by n jacobian matrix associated with a specified
c problem of m functions in n variables.
c
c the subroutine statement is
c
c subroutine fdjac2(fcn,m,n,x,fvec,fjac,ldfjac,iflag,epsfcn,wa)
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(m,n,x,fvec,iflag)
c integer m,n,iflag
c real x(n),fvec(m)
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 fdjac2.
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 input array of length n.
c
c fvec is an input array of length m which must contain the
c functions evaluated at x.
c
c fjac is an output m by n array which contains the
c approximation to the jacobian matrix evaluated at x.
c
c ldfjac is a positive integer input variable not less than m
c which specifies the leading dimension of the array fjac.
c
c iflag is an integer variable which can be used to terminate
c the execution of fdjac2. see description of fcn.
c
c epsfcn is an input variable used in determining a suitable
c step length for the forward-difference approximation. this
c approximation assumes that the relative errors in the
c functions are of the order of epsfcn. if epsfcn is less
c than the machine precision, it is assumed that the relative
c errors in the functions are of the order of the machine
c precision.
c
c wa is a work array of length m.
c
c subprograms called
c
c user-supplied ...... fcn
c
c minpack-supplied ... spmpar
c
c fortran-supplied ... abs,amax1,sqrt
c
c argonne national laboratory. minpack project. march 1980.
c burton s. garbow, kenneth e. hillstrom, jorge j. more
c
c **********
integer i,j
real eps,epsmch,h,temp,zero
real spmpar
data zero /0.0e0/
c
c epsmch is the machine precision.
c
epsmch = spmpar(1)
c
eps = sqrt(amax1(epsfcn,epsmch))
do 20 j = 1, n
temp = x(j)
h = eps*abs(temp)
if (h .eq. zero) h = eps
x(j) = temp + h
call fcn(m,n,x,wa,iflag)
if (iflag .lt. 0) go to 30
x(j) = temp
do 10 i = 1, m
fjac(i,j) = (wa(i) - fvec(i))/h
10 continue
20 continue
30 continue
return
c
c last card of subroutine fdjac2.
c
end