public static void FitNonlin(double[] x, double[] y, double[] sig, double[] a,
out double chisq, Funcs2 func)
{
MrqminFunc f = delegate(double x1, double[] a1, out double y1, double[] dyda, int na) {
y1 = func(x1, a1);
for (int i = 0; i < na; i++)
{
dyda[i] = Dyda(x1, a1, func, i, 1e-6);
}
};
FitNonlin(x, y, sig, a, out chisq, f);
}
public static void FitNonlin(double[] x, double[] y, double[] sig, double[] a,
out double chisq, MrqminFunc func)
{
int ndata = x.Length;
if (sig == null)
{
sig = new double[ndata];
for (int i = 0; i < sig.Length; i++)
{
sig[i] = 1;
}
}
int ma = a.Length;
double[,] covar = new double[ma, ma];
double[,] alpha = new double[ma, ma];
int[] ia = new int[ma];
for (int i = 0; i < ma; i++)
{
ia[i] = 1;
}
double alamda = -1;
double ochisq = 0;
double[,] oneda = null;
int mfit = 0;
double[] atry = null;
double[] beta = null;
double[] da = null;
NumericalRecipes.Mrqmin(x, y, sig, ndata, a, ia, ma, covar, alpha, out chisq, func, ref alamda, ref ochisq,
ref oneda, ref mfit, ref atry, ref beta, ref da);
int count1 = 0;
while (alamda > 1e-20 && alamda < 1e20 && count1 < 100)
{
NumericalRecipes.Mrqmin(x, y, sig, ndata, a, ia, ma, covar, alpha, out chisq, func, ref alamda, ref ochisq,
ref oneda, ref mfit, ref atry, ref beta, ref da);
count1++;
}
alamda = 0;
NumericalRecipes.Mrqmin(x, y, sig, ndata, a, ia, ma, covar, alpha, out chisq, func, ref alamda, ref ochisq,
ref oneda, ref mfit, ref atry, ref beta, ref da);
}
public static void Mrqcof(double[] x, double[] y, double[] sig, int ndata,
double[] a, double[,] alpha, double[] beta,
out double chisq, MrqminFunc func)
{
int ma = a.Length;
double[] dyda = new double[ma];
for (int j = 0; j < ma; 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 < ndata; i++)
{
double ymod;
func(x[i], a, out ymod, dyda, ma);
double sig2i = 1.0 / (sig[i] * sig[i]);
double dy = y[i] - ymod;
for (int j = 0, l = 0; l < ma; l++)
{
double wt = dyda[l] * sig2i;
for (int k = 0, m = 0; m <= l; m++)
{
alpha[j, k++] += wt * dyda[m];
}
beta[j] += dy * wt;
j++;
}
chisq += dy * dy * sig2i;
}
for (int j = 1; j < ma; j++)
{
for (int k = 0; k < j; k++)
{
alpha[k, j] = alpha[j, k];
}
}
}
public static void Mrqmin(double[] x, double[] y, double[] sig, int ndata, double[] a,
int[] ia, int ma, double[,] covar, double[,] alpha, out double chisq, MrqminFunc func,
ref double alamda, ref double ochisq, ref double[,] oneda, ref int mfit, ref double[] atry,
ref double[] beta, ref double[] da)
{
int j, k, l, m;
if (alamda < 0.0)
{
atry = new double[ma];
beta = new double[ma];
da = new double[ma];
mfit = ma;
oneda = new double[mfit, 1];
alamda = 0.001;
Mrqcof(x, y, sig, ndata, a, alpha, beta, out chisq, func);
ochisq = (chisq);
for (j = 0; j < ma; j++)
{
atry[j] = a[j];
}
}
for (j = 0, l = 0; l < ma; l++)
{
for (k = 0, m = 0; m < ma; m++)
{
covar[j, k] = alpha[j, k];
k++;
}
covar[j, j] = alpha[j, j] * (1.0 + (alamda));
oneda[j, 0] = beta[j];
j++;
}
Gaussj(covar, mfit, oneda, 1);
for (j = 0; j < mfit; j++)
{
da[j] = oneda[j, 0];
}
if (alamda == 0.0)
{
Covsrt(covar);
chisq = ochisq;
return;
}
for (j = 0, l = 0; l < ma; l++)
{
atry[l] = a[l] + da[j++];
}
Mrqcof(x, y, sig, ndata, atry, covar, da, out chisq, func);
if (chisq < ochisq)
{
alamda *= 0.1;
ochisq = (chisq);
for (j = 0, l = 0; l < ma; l++)
{
for (k = 0, m = 0; m < ma; m++)
{
alpha[j, k] = covar[j, k];
k++;
}
beta[j] = da[j];
a[l] = atry[l];
j++;
}
}
else
{
alamda *= 10.0;
chisq = ochisq;
}
}
public static void Mrqcof(double[] x, double[] y, double[] sig, int ndata, double[] a, double[,] alpha, double[] beta,
out double chisq, MrqminFunc func)
{
int ma = a.Length;
double[] dyda = new double[ma];
for (int j = 0; j < ma; 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 < ndata; i++){
double ymod;
func(x[i], a, out ymod, dyda, ma);
double sig2I = sig != null ? 1.0/(sig[i]*sig[i]) : 1.0;
double dy = y[i] - ymod;
for (int j = 0, l = 0; l < ma; l++){
double wt = dyda[l]*sig2I;
for (int k = 0, m = 0; m <= l; m++){
alpha[j, k++] += wt*dyda[m];
}
beta[j] += dy*wt;
j++;
}
chisq += dy*dy*sig2I;
}
for (int j = 1; j < ma; j++){
for (int k = 0; k < j; k++){
alpha[k, j] = alpha[j, k];
}
}
}
public static void Mrqmin(double[] x, double[] y, double[] sig, int ndata, double[] a, double[] amin, double[] amax,
double[,] covar, double[,] alpha, out double chisq, MrqminFunc func, ref double alamda, ref double ochisq,
ref double[,] oneda, ref int mfit, ref double[] atry, ref double[] beta, ref double[] da, int nthreads)
{
if (amin == null){
amin = new double[a.Length];
for (int i = 0; i < amin.Length; i++){
amin[i] = double.MinValue;
}
}
if (amax == null){
amax = new double[a.Length];
for (int i = 0; i < amax.Length; i++){
amax[i] = double.MaxValue;
}
}
int ma = a.Length;
if (alamda < 0.0){
atry = new double[ma];
beta = new double[ma];
da = new double[ma];
mfit = ma;
oneda = new double[mfit,1];
alamda = 0.001;
if (nthreads > 1){
MrqcofMulti(x, y, sig, ndata, a, alpha, beta, out chisq, func, nthreads);
} else{
Mrqcof(x, y, sig, ndata, a, alpha, beta, out chisq, func);
}
ochisq = (chisq);
for (int j = 0; j < ma; j++){
atry[j] = a[j];
}
}
for (int j = 0; j < ma; j++){
for (int k = 0; k < ma; k++){
covar[j, k] = alpha[j, k];
}
covar[j, j] = alpha[j, j]*(1.0 + (alamda));
oneda[j, 0] = beta[j];
}
NumUtils.Gaussj(covar, mfit, oneda, 1);
for (int j = 0; j < mfit; j++){
da[j] = oneda[j, 0];
}
if (alamda == 0.0){
NumUtils.Covsrt(covar);
chisq = ochisq;
return;
}
for (int j = 0; j < ma; j++){
double ax = a[j] + da[j];
if (ax >= amin[j] && ax <= amax[j]){
atry[j] = ax;
}
}
if (nthreads > 1){
MrqcofMulti(x, y, sig, ndata, atry, covar, da, out chisq, func, nthreads);
} else{
Mrqcof(x, y, sig, ndata, atry, covar, da, out chisq, func);
}
if (chisq < ochisq){
alamda *= 0.1;
ochisq = (chisq);
for (int j = 0; j < ma; j++){
for (int k = 0; k < ma; k++){
alpha[j, k] = covar[j, k];
}
beta[j] = da[j];
a[j] = atry[j];
}
} else{
alamda *= 10.0;
chisq = ochisq;
}
}
public static void MrqcofMulti(double[] x, double[] y, double[] sig, int ndata, double[] a, double[,] alpha,
double[] beta, out double chisq, MrqminFunc func, int nthreads)
{
int ma = a.Length;
for (int j = 0; j < ma; j++){
for (int k = 0; k <= j; k++){
alpha[j, k] = 0.0;
}
beta[j] = 0.0;
}
chisq = 0.0;
double[][] dyda = new double[ndata][];
double[] ymod = new double[ndata];
for (int i = 0; i < ndata; i++){
dyda[i] = new double[ma];
}
if (nthreads == 1){
for (int i = 0; i < ndata; i++){
func(x[i], a, out ymod[i], dyda[i], ma);
}
} else{
nthreads = Math.Min(nthreads, ndata);
int[] inds = new int[nthreads + 1];
for (int i = 0; i < nthreads + 1; i++){
inds[i] = (int) Math.Round(i/(double) (nthreads)*(ndata));
}
Thread[] t = new Thread[nthreads];
for (int i = 0; i < nthreads; i++){
int index0 = i;
t[i] = new Thread(new ThreadStart(delegate{
for (int i1 = inds[index0]; i1 < inds[index0 + 1]; i1++){
func(x[i1], a, out ymod[i1], dyda[i1], ma);
}
}));
t[i].Start();
}
for (int i = 0; i < nthreads; i++){
t[i].Join();
}
}
for (int i = 0; i < ndata; i++){
double sig2I = sig != null ? 1.0/(sig[i]*sig[i]) : 1.0;
double dy = y[i] - ymod[i];
for (int j = 0, l = 0; l < ma; l++){
double wt = dyda[i][l]*sig2I;
for (int k = 0, m = 0; m <= l; m++){
alpha[j, k++] += wt*dyda[i][m];
}
beta[j] += dy*wt;
j++;
}
chisq += dy*dy*sig2I;
}
for (int j = 1; j < ma; j++){
for (int k = 0; k < j; k++){
alpha[k, j] = alpha[j, k];
}
}
}
public static void FitNonlin(double[] x, double[] y, double[] sig, double[] a, double[] amin, double[] amax,
out double chisq, MrqminFunc func, int nthreads)
{
int ndata = x.Length;
if (sig == null){
sig = new double[ndata];
for (int i = 0; i < sig.Length; i++){
sig[i] = 1;
}
}
int ma = a.Length;
double[,] covar = new double[ma,ma];
double[,] alpha = new double[ma,ma];
double alamda = -1;
double ochisq = 0;
double[,] oneda = null;
int mfit = 0;
double[] atry = null;
double[] beta = null;
double[] da = null;
NumRecipes.Mrqmin(x, y, sig, ndata, a, amin, amax, covar, alpha, out chisq, func, ref alamda, ref ochisq, ref oneda,
ref mfit, ref atry, ref beta, ref da, nthreads);
int count1 = 0;
while (alamda > 1e-60 && alamda < 1e60 && count1 < 500){
NumRecipes.Mrqmin(x, y, sig, ndata, a, amin, amax, covar, alpha, out chisq, func, ref alamda, ref ochisq, ref oneda,
ref mfit, ref atry, ref beta, ref da, nthreads);
count1++;
}
alamda = 0;
NumRecipes.Mrqmin(x, y, sig, ndata, a, amin, amax, covar, alpha, out chisq, func, ref alamda, ref ochisq, ref oneda,
ref mfit, ref atry, ref beta, ref da, nthreads);
}
public static void Mrqmin(double[] x, double[] y, double[] sig, int ndata, double[] a, double[] amin, double[] amax,
double[,] covar, double[,] alpha, out double chisq, MrqminFunc func, ref double alamda, ref double ochisq,
ref double[,] oneda, ref int mfit, ref double[] atry, ref double[] beta, ref double[] da, int nthreads)
{
if (amin == null)
{
amin = new double[a.Length];
for (int i = 0; i < amin.Length; i++)
{
amin[i] = double.MinValue;
}
}
if (amax == null)
{
amax = new double[a.Length];
for (int i = 0; i < amax.Length; i++)
{
amax[i] = double.MaxValue;
}
}
int ma = a.Length;
if (alamda < 0.0)
{
atry = new double[ma];
beta = new double[ma];
da = new double[ma];
mfit = ma;
oneda = new double[mfit, 1];
alamda = 0.001;
if (nthreads > 1)
{
MrqcofMulti(x, y, sig, ndata, a, alpha, beta, out chisq, func, nthreads);
}
else
{
Mrqcof(x, y, sig, ndata, a, alpha, beta, out chisq, func);
}
ochisq = (chisq);
for (int j = 0; j < ma; j++)
{
atry[j] = a[j];
}
}
for (int j = 0; j < ma; j++)
{
for (int k = 0; k < ma; k++)
{
covar[j, k] = alpha[j, k];
}
covar[j, j] = alpha[j, j] * (1.0 + (alamda));
oneda[j, 0] = beta[j];
}
NumUtils.Gaussj(covar, mfit, oneda, 1);
for (int j = 0; j < mfit; j++)
{
da[j] = oneda[j, 0];
}
if (alamda == 0.0)
{
NumUtils.Covsrt(covar);
chisq = ochisq;
return;
}
for (int j = 0; j < ma; j++)
{
double ax = a[j] + da[j];
if (ax >= amin[j] && ax <= amax[j])
{
atry[j] = ax;
}
}
if (nthreads > 1)
{
MrqcofMulti(x, y, sig, ndata, atry, covar, da, out chisq, func, nthreads);
}
else
{
Mrqcof(x, y, sig, ndata, atry, covar, da, out chisq, func);
}
if (chisq < ochisq)
{
alamda *= 0.1;
ochisq = (chisq);
for (int j = 0; j < ma; j++)
{
for (int k = 0; k < ma; k++)
{
alpha[j, k] = covar[j, k];
}
beta[j] = da[j];
a[j] = atry[j];
}
}
else
{
alamda *= 10.0;
chisq = ochisq;
}
}
public static void MrqcofMulti(double[] x, double[] y, double[] sig, int ndata, double[] a, double[,] alpha,
double[] beta, out double chisq, MrqminFunc func, int nthreads)
{
int ma = a.Length;
for (int j = 0; j < ma; j++)
{
for (int k = 0; k <= j; k++)
{
alpha[j, k] = 0.0;
}
beta[j] = 0.0;
}
chisq = 0.0;
double[][] dyda = new double[ndata][];
double[] ymod = new double[ndata];
for (int i = 0; i < ndata; i++)
{
dyda[i] = new double[ma];
}
if (nthreads == 1)
{
for (int i = 0; i < ndata; i++)
{
func(x[i], a, out ymod[i], dyda[i], ma);
}
}
else
{
nthreads = Math.Min(nthreads, ndata);
int[] inds = new int[nthreads + 1];
for (int i = 0; i < nthreads + 1; i++)
{
inds[i] = (int)Math.Round(i / (double)(nthreads) * (ndata));
}
Thread[] t = new Thread[nthreads];
for (int i = 0; i < nthreads; i++)
{
int index0 = i;
t[i] = new Thread(new ThreadStart(delegate {
for (int i1 = inds[index0]; i1 < inds[index0 + 1]; i1++)
{
func(x[i1], a, out ymod[i1], dyda[i1], ma);
}
}));
t[i].Start();
}
for (int i = 0; i < nthreads; i++)
{
t[i].Join();
}
}
for (int i = 0; i < ndata; i++)
{
double sig2I = sig != null ? 1.0 / (sig[i] * sig[i]) : 1.0;
double dy = y[i] - ymod[i];
for (int j = 0, l = 0; l < ma; l++)
{
double wt = dyda[i][l] * sig2I;
for (int k = 0, m = 0; m <= l; m++)
{
alpha[j, k++] += wt * dyda[i][m];
}
beta[j] += dy * wt;
j++;
}
chisq += dy * dy * sig2I;
}
for (int j = 1; j < ma; j++)
{
for (int k = 0; k < j; k++)
{
alpha[k, j] = alpha[j, k];
}
}
}