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61.1 Introduction to minpack | ||
61.2 Functions and Variables for minpack |
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Minpack
is a Common Lisp translation (via f2cl
) of the
Fortran library MINPACK, as obtained from Netlib.
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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]
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.
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