(maxima.info)Functions and Variables for minpack

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71.2 Functions and Variables for minpack
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 -- Function: minpack_lsquares (<flist>, <varlist>, <guess> [,
          <tolerance>, <jacobian>])

     Compute the point that minimizes the sum of the squares of the
     functions in the list <flist>.  The variables are in the list
     <varlist>.  An initial guess of the optimum point must be provided
     in <guess>.

     The optional keyword arguments, <tolerance> and <jacobian> provide
     some control over the algorithm.  <tolerance> is the estimated
     relative error desired in the sum of squares.  <jacobian> can be
     used to specify the Jacobian.  If <jacobian> is not given or is
     'true' (the default), the Jacobian is computed from <flist>.  If
     <jacobian> is 'false', a numerical approximation is used.

     'minpack_lsquares' returns a list.  The first item is the estimated
     solution; the second is the sum of squares, and the third indicates
     the success of the algorithm.  The possible values are

     '0'
          improper input parameters.
     '1'
          algorithm estimates that the relative error in the sum of
          squares is at most 'tolerance'.
     '2'
          algorithm estimates that the relative error between x and the
          solution is at most 'tolerance'.
     '3'
          conditions for info = 1 and info = 2 both hold.
     '4'
          fvec is orthogonal to the columns of the jacobian to machine
          precision.
     '5'
          number of calls to fcn with iflag = 1 has reached 100*(n+1).
     '6'
          tol is too small.  no further reduction in the sum of squares
          is possible.
     '7'
          tol is too small.  no further improvement in the approximate
          solution x is possible.

          /* Problem 6: Powell singular function */
          (%i1) powell(x1,x2,x3,x4) :=
                   [x1+10*x2, sqrt(5)*(x3-x4), (x2-2*x3)^2,
                        sqrt(10)*(x1-x4)^2]$
          (%i2) minpack_lsquares(powell(x1,x2,x3,x4), [x1,x2,x3,x4],
                                 [3,-1,0,1]);
          (%o2) [[1.652117596168394e-17, - 1.652117596168393e-18,
                  2.643388153869468e-18, 2.643388153869468e-18],
                 6.109327859207777e-34, 4]

          /* Same problem but use numerical approximation to Jacobian */
          (%i3) minpack_lsquares(powell(x1,x2,x3,x4), [x1,x2,x3,x4],
                                 [3,-1,0,1], jacobian = false);
          (%o3) [[5.060282149485331e-11, - 5.060282149491206e-12,
                  2.179447843547218e-11, 2.179447843547218e-11],
                 3.534491794847031e-21, 5]

 -- Function: minpack_solve (<flist>, <varlist>, <guess> [, <tolerance>,
          <jacobian>])
     Solve a system of 'n' equations in 'n' unknowns.  The 'n' equations
     are given in the list <flist>, and the unknowns are in <varlist>.
     An initial guess of the solution must be provided in <guess>.

     The optional keyword arguments, <tolerance> and <jacobian> provide
     some control over the algorithm.  <tolerance> is the estimated
     relative error desired in the sum of squares.  <jacobian> can be
     used to specify the Jacobian.  If <jacobian> is not given or is
     'true' (the default), the Jacobian is computed from <flist>.  If
     <jacobian> is 'false', a numerical approximation is used.

     'minpack_solve' returns a list.  The first item is the estimated
     solution; the second is the sum of squares, and the third indicates
     the success of the algorithm.  The possible values are

     '0'
          improper input parameters.
     '1'
          algorithm estimates that the relative error in the solution is
          at most 'tolerance'.
     '2'
          number of calls to fcn with iflag = 1 has reached 100*(n+1).
     '3'
          tol is too small.  no further reduction in the sum of squares
          is possible.
     '4'
          Iteration is not making good progress.