pwkit/lmmin.py: import; and fix up lsqmdl

lmmin_reference/dataf

@@ -0,0 +1,29 @@
+    1    5   10    1
+    1    5   50    1
+    2    5   10    1
+    2    5   50    1
+    3    5   10    1
+    3    5   50    1
+    4    2    2    3
+    5    3    3    3
+    6    4    4    3
+    7    2    2    3
+    8    3   15    3
+    9    4   11    3
+   10    3   16    2
+   11    6   31    3
+   11    9   31    3
+   11   12   31    3
+   12    3   10    1
+   13    2   10    1
+   14    4   20    3
+   15    1    8    3
+   15    8    8    1
+   15    9    9    1
+   15   10   10    1
+   16   10   10    3
+   16   30   30    1
+   16   40   40    1
+   17    5   33    1
+   18   11   65    1
+    0    0    0    0

lmmin_reference/fdjac2.f

@@ -0,0 +1,107 @@
+      subroutine fdjac2(fcn,m,n,x,fvec,fjac,ldfjac,iflag,epsfcn,wa)
+      integer m,n,ldfjac,iflag
+      double precision epsfcn
+      double precision 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         double precision 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 ... dpmpar
+c
+c       fortran-supplied ... dabs,dmax1,dsqrt
+c
+c     argonne national laboratory. minpack project. march 1980.
+c     burton s. garbow, kenneth e. hillstrom, jorge j. more
+c
+c     **********
+      integer i,j
+      double precision eps,epsmch,h,temp,zero
+      double precision dpmpar
+      data zero /0.0d0/
+c
+c     epsmch is the machine precision.
+c
+      epsmch = dpmpar(1)
+c
+      eps = dsqrt(dmax1(epsfcn,epsmch))
+      do 20 j = 1, n
+         temp = x(j)
+         h = eps*dabs(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