C#，数值计算——数据建模，非线性拟合列文伯格·马夸尔特算法（LM，Levenberg-Marquardt nonlinear fitting）的计算方法与源程序
1 文本格式
using System;
namespace Legalsoft.Truffer
{
///
/// Levenberg-Marquardt nonlinear fitting
///
public class Fitmrq
{
private const int NDONE = 4;
private const int ITMAX = 1000;
private int ndat { get; set; }
private int ma { get; set; }
private int mfit { get; set; }
private double[] x { get; set; }
private double[] y { get; set; }
private double[] sig { get; set; }
private double tol { get; set; }
private bool[] ia { get; set; }
private double[] a { get; set; }
private double[,] covar;
private double[,] alpha;
private double chisq { get; set; }
public MultiFuncd funcs;
public Fitmrq(double[] xx, double[] yy, double[] ssig, double[] aa, MultiFuncd funks, double TOL = 1.0e-3)
{
this.ndat = xx.Length;
this.ma = aa.Length;
this.x = xx;
this.y = yy;
this.sig = ssig;
this.tol = TOL;
this.funcs = funks;
this.ia = new bool[ma];
this.alpha = new double[ma, ma];
this.a = aa;
this.covar = new double[ma, ma];
for (int i = 0; i < ma; i++)
{
ia[i] = true;
}
}
public void hold(int i, double val)
{
ia[i] = false;
a[i] = val;
}
public void free(int i)
{
ia[i] = true;
}
public void fit()
{
int done = 0;
double alamda = .001;
double[] atry = new double[ma];
double[] beta = new double[ma];
double[] da = new double[ma];
mfit = 0;
for (int j = 0; j < ma; j++)
{
if (ia[j])
{
mfit++;
}
}
double[,] oneda = new double[mfit, 1];
double[,] temp = new double[mfit, mfit];
mrqcof(a, alpha, beta);
for (int j = 0; j < ma; j++)
{
atry[j] = a[j];
}
double ochisq = chisq;
for (int iter = 0; iter < ITMAX; iter++)
{
if (done == NDONE)
{
alamda = 0.0;
}
for (int j = 0; j < mfit; j++)
{
for (int k = 0; k < mfit; k++)
{
covar[j, k] = alpha[j, k];
}
covar[j, j] = alpha[j, j] * (1.0 + alamda);
for (int k = 0; k < mfit; k++)
{
temp[j, k] = covar[j, k];
}
oneda[j, 0] = beta[j];
}
GaussJordan.gaussj( temp, oneda);
for (int j = 0; j < mfit; j++)
{
for (int k = 0; k < mfit; k++)
{
covar[j, k] = temp[j, k];
}
da[j] = oneda[j, 0];
}
if (done == NDONE)
{
covsrt( covar);
covsrt( alpha);
return;
}
for (int j = 0, l = 0; l < ma; l++)
{
if (ia[l])
{
atry[l] = a[l] + da[j++];
}
}
mrqcof(atry, covar, da);
if (Math.Abs(chisq - ochisq) < Math.Max(tol, tol * chisq))
{
done++;
}
if (chisq < ochisq)
{
alamda *= 0.1;
ochisq = chisq;
for (int j = 0; j < mfit; j++)
{
for (int k = 0; k < mfit; k++)
{
alpha[j, k] = covar[j, k];
}
beta[j] = da[j];
}
for (int l = 0; l < ma; l++)
{
a[l] = atry[l];
}
}
else
{
alamda *= 10.0;
chisq = ochisq;
}
}
throw new Exception("Fitmrq too many iterations");
}
public void mrqcof(double[] a, double[,] alpha, double[] beta)
{
double ymod = 0.0;
double[] dyda = new double[ma];
for (int j = 0; j < mfit; j++)
{
for (int k = 0; k <= j; k++)
{
alpha[j, k] = 0.0;
}
beta[j] = 0.0;
}
chisq = 0.0;
for (int i = 0; i < ndat; i++)
{
funcs.funk(x[i], a, ref ymod, dyda);
double sig2i = 1.0 / (sig[i] * sig[i]);
double dy = y[i] - ymod;
for (int j = 0, l = 0; l < ma; l++)
{
if (ia[l])
{
double wt = dyda[l] * sig2i;
for (int k = 0, m = 0; m < l + 1; m++)
{
if (ia[m])
{
alpha[j, k++] += wt * dyda[m];
}
}
beta[j++] += dy * wt;
}
}
chisq += dy * dy * sig2i;
}
for (int j = 1; j < mfit; j++)
{
for (int k = 0; k < j; k++)
{
alpha[k, j] = alpha[j, k];
}
}
}
public void covsrt(double[,] covar)
{
for (int i = mfit; i < ma; i++)
{
for (int j = 0; j < i + 1; j++)
{
covar[i, j] = covar[j, i] = 0.0;
}
}
int k = mfit - 1;
for (int j = ma - 1; j >= 0; j--)
{
if (ia[j])
{
for (int i = 0; i < ma; i++)
{
Globals.SWAP(ref covar[i, k], ref covar[i, j]);
}
for (int i = 0; i < ma; i++)
{
Globals.SWAP(ref covar[k, i], ref covar[j, i]);
}
k--;
}
}
}
}
}
2 代码格式
using System;
namespace Legalsoft.Truffer
{
///
/// Levenberg-Marquardt nonlinear fitting
///
public class Fitmrq
{
private const int NDONE = 4;
private const int ITMAX = 1000;
private int ndat { get; set; }
private int ma { get; set; }
private int mfit { get; set; }
private double[] x { get; set; }
private double[] y { get; set; }
private double[] sig { get; set; }
private double tol { get; set; }
private bool[] ia { get; set; }
private double[] a { get; set; }
private double[,] covar;
private double[,] alpha;
private double chisq { get; set; }
public MultiFuncd funcs;
public Fitmrq(double[] xx, double[] yy, double[] ssig, double[] aa, MultiFuncd funks, double TOL = 1.0e-3)
{
this.ndat = xx.Length;
this.ma = aa.Length;
this.x = xx;
this.y = yy;
this.sig = ssig;
this.tol = TOL;
this.funcs = funks;
this.ia = new bool[ma];
this.alpha = new double[ma, ma];
this.a = aa;
this.covar = new double[ma, ma];
for (int i = 0; i < ma; i++)
{
ia[i] = true;
}
}
public void hold(int i, double val)
{
ia[i] = false;
a[i] = val;
}
public void free(int i)
{
ia[i] = true;
}
public void fit()
{
int done = 0;
double alamda = .001;
double[] atry = new double[ma];
double[] beta = new double[ma];
double[] da = new double[ma];
mfit = 0;
for (int j = 0; j < ma; j++)
{
if (ia[j])
{
mfit++;
}
}
double[,] oneda = new double[mfit, 1];
double[,] temp = new double[mfit, mfit];
mrqcof(a, alpha, beta);
for (int j = 0; j < ma; j++)
{
atry[j] = a[j];
}
double ochisq = chisq;
for (int iter = 0; iter < ITMAX; iter++)
{
if (done == NDONE)
{
alamda = 0.0;
}
for (int j = 0; j < mfit; j++)
{
for (int k = 0; k < mfit; k++)
{
covar[j, k] = alpha[j, k];
}
covar[j, j] = alpha[j, j] * (1.0 + alamda);
for (int k = 0; k < mfit; k++)
{
temp[j, k] = covar[j, k];
}
oneda[j, 0] = beta[j];
}
GaussJordan.gaussj( temp, oneda);
for (int j = 0; j < mfit; j++)
{
for (int k = 0; k < mfit; k++)
{
covar[j, k] = temp[j, k];
}
da[j] = oneda[j, 0];
}
if (done == NDONE)
{
covsrt( covar);
covsrt( alpha);
return;
}
for (int j = 0, l = 0; l < ma; l++)
{
if (ia[l])
{
atry[l] = a[l] + da[j++];
}
}
mrqcof(atry, covar, da);
if (Math.Abs(chisq - ochisq) < Math.Max(tol, tol * chisq))
{
done++;
}
if (chisq < ochisq)
{
alamda *= 0.1;
ochisq = chisq;
for (int j = 0; j < mfit; j++)
{
for (int k = 0; k < mfit; k++)
{
alpha[j, k] = covar[j, k];
}
beta[j] = da[j];
}
for (int l = 0; l < ma; l++)
{
a[l] = atry[l];
}
}
else
{
alamda *= 10.0;
chisq = ochisq;
}
}
throw new Exception("Fitmrq too many iterations");
}
public void mrqcof(double[] a, double[,] alpha, double[] beta)
{
double ymod = 0.0;
double[] dyda = new double[ma];
for (int j = 0; j < mfit; j++)
{
for (int k = 0; k <= j; k++)
{
alpha[j, k] = 0.0;
}
beta[j] = 0.0;
}
chisq = 0.0;
for (int i = 0; i < ndat; i++)
{
funcs.funk(x[i], a, ref ymod, dyda);
double sig2i = 1.0 / (sig[i] * sig[i]);
double dy = y[i] - ymod;
for (int j = 0, l = 0; l < ma; l++)
{
if (ia[l])
{
double wt = dyda[l] * sig2i;
for (int k = 0, m = 0; m < l + 1; m++)
{
if (ia[m])
{
alpha[j, k++] += wt * dyda[m];
}
}
beta[j++] += dy * wt;
}
}
chisq += dy * dy * sig2i;
}
for (int j = 1; j < mfit; j++)
{
for (int k = 0; k < j; k++)
{
alpha[k, j] = alpha[j, k];
}
}
}
public void covsrt(double[,] covar)
{
for (int i = mfit; i < ma; i++)
{
for (int j = 0; j < i + 1; j++)
{
covar[i, j] = covar[j, i] = 0.0;
}
}
int k = mfit - 1;
for (int j = ma - 1; j >= 0; j--)
{
if (ia[j])
{
for (int i = 0; i < ma; i++)
{
Globals.SWAP(ref covar[i, k], ref covar[i, j]);
}
for (int i = 0; i < ma; i++)
{
Globals.SWAP(ref covar[k, i], ref covar[j, i]);
}
k--;
}
}
}
}
}