Salve a tutti,
ho il seguente problema. Ho dei valori y[i] in funzione di una griglia x1[i], e devo interpolare questi y[i] in funzione di una nuova griglia x2[i].
In rete ho trovato questo codice, che interpola secondo il metodo di newton-lagrange:
Non sono riuscita ancora a capire se fa al caso mio, e se si, come eventualmte passare i miei valori x1[i], x2[i], y[i] per fare i calcoli. Inoltre non ho sinceramente capito cosa sia valueAt(double variabile), non lo capisco neppure guardando la documentazione!codice:package bbmath.numerical.interpolation; /** * Title: Polynomial Interpolation</p> * Description: Polynomial interpoaltion using Newton's and Lagrange's methods</p> * Copyright: Copyright Byrge Birkeland(c) 2002</p> * Company: Agder University College</p> * @author Byrge Birkeland * @version 1.0 */ import javax.swing.JOptionPane; import bbmath.functions.Function; public class Interpolation { /** * implements Horners-s method to compute the polynomial * a0+(t-x0)(a1+(t-x1)(a2+(t-x2)(a3+(...(an-1+(t-an))...)))))) * @param a the vector of coefficients * @param x the vector of x coordinates of noeds to be interpolated * @return the polynomial function * a0+(t-x0)(a1+(t-x1)(a2+(t-x2)(a3+(...(an-1+(t-an))...)))))) */ public static final Function horner(final double[] a,final double[] x) { return new Function() { public double valueAt(double t) { int n=a.length; double v=a[n-1]; for (int i=1; i<n;i++) v=v*(t-x[n-1-i]) + a[n-1-i]; return v; } }; } /** * finds the divided differences, i.e. the coefrficients i Newton's interpolation * polynomial intyerpolating the nodes (xi,yi) * @param x the x coordinates of the nodes to be interpolated * @param y the y coordinates of the nodes to be interpolated * @return the coefficients (divided differences) of the interpolating polynomial */ public static double[] divDif(double[] x, double[] y) { int N=x.length; double[][] M = new double[N][N]; for (int i=0; i<N; i++) M[i][0]=y[i]; for (int j=1; j<N; j++) for (int i=0;i<N-j;i++) M[i][j]=(M[i+1][j-1]-M[i][j-1])/(x[i+j]-x[i]); return M[0]; } public static final Function newtonInterp(final double[] x, final double[] y) { final double[] a=divDif(x,y); return new Function() { public double valueAt(double t) { return horner(a,x).valueAt(t); } }; } /** * finds the piecewice linear function whose graph interpolates the points (ti,xi) * @param t the argument values of the points to be interpolated * @param x the ordinate values if the points to bed interpolated * @return the linear function whose graph passes through the points (t0,x0) and */ public static final Function splineDegreeOne(final double[] t,final double[] x) { return new Function() { public double valueAt(double u) { double w=0; if(u<=t[0]) w = x[0]+(x[1]-x[0])*(u-t[0])/(t[1]-t[0]); if(u>t[0]) { int i=0; for (int k=1;k<x.length;k++) { if (u-t[i]>0) i++;} i--; w = x[i]+(x[i+1]-x[i])*(u-t[i])/(t[i+1]-t[i]); } return w; } }; } /** * gives the derivatives at the nodes of the quadratic spline functions that * interpolates the nodes (ti,xi) * @param t the argument values of the points to be interpolated * @param x the ordinate values of the points to be interpolated * @param z0 the value of the first derivative at the node with index 0 * @return the derivatives at the nodes of the quadratic spline functions that * interpolates the nodes (ti,xi) */ public static double[] quadSplineCoeff(double[] t, double [] x, double z0) { int n=t.length; double[] z=new double[n]; z[0]=z0; for(int i=1; i<n; i++) z[i]=-z[i-1]+2*(x[i]-x[i-1])/(t[i]-t[i-1]); return z; } /** * finds the piecewise second degree function that interpolates given nodes (xi,yi) * @param t the argument values of the nodes * @param x the ordinate values of the nodes * @param z the vector of derivatives at the nodes * @return the piecewise second degree function that interpolates given nodes (xi,yi) */ public static final Function quadSpline(final double[] t, final double[] x,final double[] z) { return new Function() { public double valueAt(double u) { double w=0.0; if (u<=t[0]) w=(z[1]-z[0])*(u-t[0])*(u-t[0])*0.5/(t[1]-t[0]) +z[0]*(u-t[0])+x[0]; if (u>t[0]) {int i=0; for (int k=1;k<t.length;k++) {if (u-t[i]>0) i++;} i--; w=(z[i+1]-z[i])*(u-t[i])*(u-t[i])*0.5/(t[i+1]-t[i])+z[i]*(u-t[i])+x[i]; } return w; } }; } /** * finds the natural cubic spline function that interpolates the noeds (xi,yi) * @param t the argument values of the points to be interpolated * @param x the ordinate values of the points to be interpolated * @param z0 the value of the second derivative at the node with index 0 * @param zn the value of the second derivative at the final node * @return the vector of second derivatives at the nodes */ public static double[] cubicSplineCoeff(double[] t, double[] x, double z0, double zn) { int n=t.length; double[] h=new double[n-1], b=new double[n-1], u=new double[n], v=new double[n],z=new double[n]; u[0]=0; v[0]=0; for(int i=0;i<n-1;i++) {h[i]=t[i+1]-t[i]; b[i]=(x[i+1]-x[i])/h[i];} u[1]=2*(h[0]+h[1]); v[1]=6*(b[1]-b[0]); for(int i=2;i<n-1;i++) { u[i]=2*(h[i]+h[i-1])-h[i-1]*h[i-1]/u[i-1]; v[i]=6*(b[i]-b[i-1])-h[i-1]*v[i-1]/u[i-1]; } z[n-1]=zn; for(int i=n-2;i>0;i--) z[i]=(v[i]-h[i]*z[i+1])/u[i]; z[0]=z0; return z;} /** * finds the cubic spline functions that interpolates the nodes (ti,xi) * @param t the argument values of the nodes * @param x the ordinate values of the nodes * @param z the vector of second derivatives at the nodes * @return the piecewise cubuc function that interpolates the nodes (xi,yi) and * has the given second derivatives at the noeds */ public static final Function cubicSpline(final double[] t,final double[] x, final double[] z) { return new Function() { public double valueAt(double u) { int n=t.length,i=0; if(u<=t[0]) i=0; else {i=0; for(int k=1;k<n;k++) if(u-t[i]>0) i++; i--; } double h=t[i+1]-t[i]; double tmp=0.5*z[i]+(u-t[i])*(z[i+1]-z[i])/6/h; tmp=-h*(z[i+1]+2*z[i])/6+(x[i+1]-x[i])/h+(u-t[i])*tmp; return x[i]+(u-t[i])*tmp; } }; } /** * converts a double[] array to a String object * @param x the array to be converted * @return the corresponding String object */ public static String toString(double[] x) { String s="["; for (int i=0; i<x.length;i++) s+=x[i]+" "; s+="]\n"; return s; } /** * converts a double[][] array to a String object * @param x the array to bed converted * @return the corresponding String object */ public static String toString(double[][] x) { String s="["; for (int r=0; r<x.length; r++) { s+="\n["; for(int c=0;c<x[r].length;c++) s+=x[r][c]+" "; s+="]"; } s+="\n]\n"; return s;} }
Invio una immagine per chiarire il problema.
Rispondi quotando