Initial commit

1 files changed, 156 insertions, 0 deletions

diff --git a/math/minpack/lmder1.f b/math/minpack/lmder1.f
new file mode 100644
index 00000000..d691940f
--- /dev/null
+++ b/math/minpack/lmder1.f
@@ -0,0 +1,156 @@
+      subroutine lmder1(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 lmder1
+c
+c     the purpose of lmder1 is to minimize the sum of the squares of
+c     m nonlinear functions in n variables by a modification of the
+c     levenberg-marquardt algorithm. this is done by using the more
+c     general least-squares solver lmder. the user must provide a
+c     subroutine which calculates the functions and the jacobian.
+c
+c     the subroutine statement is
+c
+c       subroutine lmder1(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 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(m,n,x,fvec,fjac,ldfjac,iflag)
+c         integer m,n,ldfjac,iflag
+c         double precision x(n),fvec(m),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 lmder1.
+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 m by n array. the upper n by n submatrix
+c         of fjac contains an upper triangular matrix r with
+c         diagonal elements of nonincreasing magnitude 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 trapezoidal
+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 m
+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         with diagonal elements of nonincreasing magnitude.
+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 ... lmder
+c
+c     argonne national laboratory. minpack project. march 1980.
+c     burton s. garbow, kenneth e. hillstrom, 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. m .or. tol .lt. zero
+     *    .or. lwa .lt. 5*n + m) go to 10
+c
+c     call lmder.
+c
+      maxfev = 100*(n + 1)
+      ftol = tol
+      xtol = tol
+      gtol = zero
+      mode = 1
+      nprint = 0
+      call lmder(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 lmder1.
+c
+      end