From 17ee31b51081b8281b652fa06b997918003f7772 Mon Sep 17 00:00:00 2001 From: Karl Berry Date: Wed, 8 Jul 2009 01:04:31 +0000 Subject: asymptote 1.80 git-svn-id: svn://tug.org/texlive/trunk@14179 c570f23f-e606-0410-a88d-b1316a301751 --- Master/texmf/asymptote/lmfit.asy | 89 +++++++++++++++++++++++++++++----------- 1 file changed, 66 insertions(+), 23 deletions(-) (limited to 'Master/texmf/asymptote/lmfit.asy') diff --git a/Master/texmf/asymptote/lmfit.asy b/Master/texmf/asymptote/lmfit.asy index d0367547b74..72745625824 100644 --- a/Master/texmf/asymptote/lmfit.asy +++ b/Master/texmf/asymptote/lmfit.asy @@ -22,6 +22,18 @@ SOFTWARE. */ +/* + Fitting $n$ data points $(x_1, y_1 \pm \Delta y_1), \dots, (x_n, y_n \pm \Delta y_n)$ + to a function $f$ that depends on $m$ parameters $a_1, \dots, a_m$ means minimizing + the least-squares sum + % + \begin{equation*} + \sum_{i = 1}^n \left( \frac{y_i - f(a_1, \dots, a_m; x_i)}{\Delta y_i} \right)^2 + \end{equation*} + % + with respect to the parameters $a_1, \dots, a_m$. +*/ + /* This module provides an implementation of the Levenberg--Marquardt (LM) algorithm, converted from the C lmfit routine by Joachim Wuttke @@ -747,16 +759,20 @@ void lm_minimize(int m_dat, int n_par, real[] par, lm_evaluate_ftype evaluate, l // convenience functions; wrappers of lm_minimize -struct FitControl { - real squareSumTolerance; - real approximationTolerance; - real desiredOrthogonality; - real epsilon; - real stepBound; - int maxIterations; - bool verbose; - void operator init(real squareSumTolerance, real approximationTolerance, real desiredOrthogonality, real epsilon, real stepBound, int maxIterations, bool verbose) { +/* + The structure FitControl specifies various control parameters. +*/ +struct FitControl { + real squareSumTolerance; // relative error desired in the sum of squares + real approximationTolerance; // relative error between last two approximations + real desiredOrthogonality; // orthogonality desired between the residue vector and its derivatives + real epsilon; // step used to calculate the jacobian + real stepBound; // initial bound to steps in the outer loop + int maxIterations; // maximum number of iterations + bool verbose; // whether to print detailed information about every iteration, or nothing + + void operator init(real squareSumTolerance=LM_USERTOL, real approximationTolerance=LM_USERTOL, real desiredOrthogonality=LM_USERTOL, real epsilon=LM_USERTOL, real stepBound=100, int maxIterations=100, bool verbose=false) { this.squareSumTolerance = squareSumTolerance; this.approximationTolerance = approximationTolerance; this.desiredOrthogonality = desiredOrthogonality; @@ -779,30 +795,44 @@ struct FitControl { } }; +FitControl operator init() { + return FitControl(); +} + FitControl defaultControl; -defaultControl.squareSumTolerance = LM_USERTOL; -defaultControl.approximationTolerance = LM_USERTOL; -defaultControl.desiredOrthogonality = LM_USERTOL; -defaultControl.epsilon = LM_USERTOL; -defaultControl.stepBound = 100; -defaultControl.maxIterations = 100; -defaultControl.verbose = false; +/* + Upon returning, this structure provides information about the fit. +*/ struct FitResult { - restricted real norm; - restricted int iterations; - restricted int status; + real norm; // norm of the residue vector + int iterations; // actual number of iterations + int status; // status of minimization - void operator init(real norm, int status, int iterations) { + void operator init(real norm, int iterations, int status) { this.norm = norm; - this.status = status; this.iterations = iterations; + this.status = status; } }; -// Fits data points (xdata, ydata ± errors) to the given function using the given parameters. +/* + Fits data points to a function that depends on some parameters. + + Parameters: + - xdata: Array of x values. + - ydata: Array of y values. + - errors: Array of experimental errors; each element must be strictly positive + - function: Fit function. + - parameters: Parameter array. Before calling fit(), this must contain the initial guesses for the parameters. + Upon return, it will contain the solution parameters. + - control: object of type FitControl that controls various aspects of the fitting procedure. + + Returns: + An object of type FitResult that conveys information about the fitting process. +*/ FitResult fit(real[] xdata, real[] ydata, real[] errors, real function(real[], real), real[] parameters, FitControl control=defaultControl) { int m_dat = min(xdata.length, ydata.length); int n_par = parameters.length; @@ -831,7 +861,20 @@ FitResult fit(real[] xdata, real[] ydata, real[] errors, real function(real[], r } -// Fits data points (xdata, ydata) to the given function using the given parameters. +/* + Fits data points to a function that depends on some parameters. + + Parameters: + - xdata: Array of x values. + - ydata: Array of y values. + - function: Fit function. + - parameters: Parameter array. Before calling fit(), this must contain the initial guesses for the parameters. + Upon return, it will contain the solution parameters. + - control: object of type FitControl that controls various aspects of the fitting procedure. + + Returns: + An object of type FitResult that conveys information about the fitting process. +*/ FitResult fit(real[] xdata, real[] ydata, real function(real[], real), real[] parameters, FitControl control=defaultControl) { return fit(xdata, ydata, array(min(xdata.length, ydata.length), 1.0), function, parameters, control); } -- cgit v1.2.3