我想在 JAVA 中实现 Levenberg Marquardt 拟合,并发现 apache commons math 是合适的。由于我想拟合一个函数,而我没有计算梯度或雅可比行列式的导数,因此我需要来自 GNU octave 的 dfdp.m 之类的东西来计算数值导数。有人已经这样做了吗?
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我自己做的,以防其他人需要,这是方法
dfdp.m 代码
m=size(x,1); if (m==1), m=size(x,2); end %# PAK: in case #cols > #rows
n=length(p); %dimensions
ps=p; prt=zeros(m,n);del=zeros(n,1); % initialise Jacobian to Zero
for j=1:n
del(j)=dp(j) .*p(j); %cal delx=fract(dp)*param value(p)
if p(j)==0
del(j)=dp(j); %if param=0 delx=fraction
end
p(j)=ps(j) + del(j);
if del(j)~=0, f1=feval(func,x,p); %FJ ~= not equal (!=) ...> p is now (p + dp*p)
if dp(j) < 0, prt(:,j)=(f1-f)./del(j);
else
p(j)=ps(j) - del(j); %FJ ...> p is now (p - dp*p)
prt(:,j)=(f1-feval(func,x,p))./(2 .*del(j)); %FJ 2 steps from (ps + del) to (ps - del)
end
end
p(j)=ps(j); %restore p(j)
end
JAVA代码
private static class GhoosProblem {
private double[][] data;
private double[] dp;
public GhoosProblem(double[][] datapoints, double[] delta_p) {
data = datapoints;
//dp= fractional increment of p for numerical derivatives
//dp(j)>0 central differences calculated
//dp(j)<0 one sided differences calculated
//dp(j)=0 sets corresponding partials to zero; i.e. holds p(j) fixed
dp = delta_p;
}
public MultivariateVectorFunction getModelFunction() {
return new MultivariateVectorFunction() {
public double[] value(double[] params) {
double[] values = new double[data.length];
for (int i = 0; i < values.length; ++i) {
final double t = data[i][0]; // get the double value
values[i] = params[0] *
Math.pow(t, params[2]) *
Math.exp(-params[1] * t); // Ghoos function
}
return values; // function values
}
};
}
public MultivariateMatrixFunction getModelFunctionJacobian2() {
return new MultivariateMatrixFunction() {
public double[][] value(double[] params) {
double[][] jacobian = new double[data.length][params.length];
final double a = params[0];
final double b = params[2];
final double c = params[1];
for (int i = 0; i < jacobian.length; ++i) {
final double t = data[i][0]; // get the double value
jacobian[i][0] = Math.pow(t, b) * Math.exp(-c*t);
jacobian[i][2] = a * Math.exp(-c*t) * Math.pow(t, b) * Math.log(t);
jacobian[i][1] = a * Math.pow(t, b) * (-t*Math.exp(-c*t));
}
//System.out.println("Jacobian= "+ Arrays.deepToString(jacobian));
return jacobian;
}
};
}
// compared to Ge2.m octave
public MultivariateMatrixFunction getModelFunctionJacobian() {
return new MultivariateMatrixFunction() {
public double[][] value(double[] params) {
int m = data.length; // cols
int n = params.length; // rows
double[] p = params;
double[] ps = params;
double[] del = new double[n];
double[] f = new double[n];
double[] f1 = new double[n];
BlockRealMatrix prt = new BlockRealMatrix(m, n); // initializes to zeros
f=feval(p);
for (int j=0; j<n; ++j) {
del[j]=dp[j] * p[j]; //delta_x=fractional(dp) * param value(p)
if (p[j]==0)
del[j]=dp[j]; //if param=0 delta_x=fractional(dp)
p[j]=ps[j] + del[j];
if (del[j]!=0) {
f1=feval(p); //p is now (p + dp*p)
if (dp[j]<0)
prt.setColumn(j,(new ArrayRealVector(f1)).subtract(new ArrayRealVector(f)).mapDivideToSelf(del[j]).toArray()); // one sided diff
else {
p[j]=ps[j] - del[j]; // p is now (p - dp*p)
prt.setColumn(j,(new ArrayRealVector(f1)).subtract(new ArrayRealVector(feval(p))).mapDivideToSelf(2*del[j]).toArray()); // central diff
}
}
p[j]=ps[j]; //restore p(j)
}//for
//System.out.println("Jacobian= "+ Arrays.deepToString(prt.getData()));
return prt.getData(); //jacobian, dimension is (m x n)
}
};
}
public double[] feval(double[] params) {
double[] values = new double[data.length];
for (int i = 0; i < values.length; ++i) {
final double t = data[i][0]; // get the double value
values[i] = params[0] *
Math.pow(t, params[2]) *
Math.exp(-params[1] * t); // Ghoos function
}
return values;
}
}//GhoosProblem
抱歉,如果代码的识别效果不好!
相关部分是 getModelFunctionJacobian() -Function
我已将分析导数部分重命名为 getModelFunctionJacobian2(),并在此处发布以供比较
完成这里是使用 GhoosFunction 的 levenberg marquardt 设置
public void fit() {
final double[][] dataPoints = { // x, y
//{0.0/60, 0.0}, // never use {0, 0} => org.apache.commons.math3.exception.ConvergenceException: illegal state: unable to perform Q.R decomposition on the 17x3 jacobian matrix
{15.0/60, 8.891104},
{30.0/60, 13.21852},
{45.0/60, 28.09051},
{60.0/60, 43.0011},
{75.0/60, 57.43561},
{90.0/60, 67.06862},
{105.0/60, 82.60239},
{120.0/60, 72.4649},
{135.0/60, 61.4},
{150.0/60, 43.97924},
{165.0/60, 30.6},
{180.0/60, 20.77112},
{195.0/60, 15.5},
{210.0/60, 10.85442},
{225.0/60, 9.33},
{240.0/60, 7.260234},
};
final double[] initialGuess = { 1.0, 1.0, 1.0 }; // p
final double[] fract_change = { 1E-4, 1E-4, 1E-4 }; // dp should be below 0.0001
final GhoosProblem problem = new GhoosProblem(dataPoints, fract_change);
final int len = dataPoints.length;
final double[] weights = new double[len];
final double[] target = new double[len];
for (int i = 0; i < len; i++){
weights[i] = 1.0;// / dataPoints[i][1];
target[i] = dataPoints[i][1];
}
final LevenbergMarquardtOptimizer optimizer = new LevenbergMarquardtOptimizer()
.withCostRelativeTolerance(1E-4) // stol in octave
.withParameterRelativeTolerance(1E-4); // dp should be below 0.0001
final Optimum optimum = optimizer.optimize(
builder(problem)
.weight(new DiagonalMatrix(weights))
.target(target)
.start(initialGuess)
.maxIterations(100)
.build()
);
final RealVector solution = optimum.getPoint();
solution.setEntry(0, solution.getEntry(0) / 60.0); // go back to minutes
System.out.println("solution= " + solution);
System.out.println("CostRelativeTolerance= " + optimizer.getCostRelativeTolerance());
System.out.println("ParameterRelativeTolerance= " + optimizer.getParameterRelativeTolerance());
System.out.println("evaluations= " + optimum.getEvaluations());
System.out.println("iterations= " + optimum.getIterations());
//System.out.println("residuals= " + optimum.getResiduals());
System.out.println("RMS= " + optimum.getRMS());
System.out.println("sigma= " + optimum.getSigma(1E-10));
}//fit
public LeastSquaresBuilder builder(GhoosProblem problem){
return new LeastSquaresBuilder()
.checkerPair(new SimpleVectorValueChecker(1e-6, 1e-6)) // The SimpleVectorValueChecker Class (Simple implementation of the ConvergenceChecker) contains a method that uses the value of the function between two successive iterations of the optimisation algorithm to check if convergence has occured
.maxEvaluations(Integer.MAX_VALUE)
.maxIterations(Integer.MAX_VALUE)
//.lazyEvaluation(true)
.model(problem.getModelFunction(), problem.getModelFunctionJacobian());
}
于 2015-07-07T12:00:22.233 回答