public static int Main(string[] args) { int m = 0; int n = 0; double[] x = new double[0]; double[] y = new double[0]; double[] w = new double[0]; double[] xc = new double[0]; double[] yc = new double[0]; int[] dc = new int[0]; polint.polynomialfitreport rep = new polint.polynomialfitreport(); int info = 0; ratint.barycentricinterpolant p = new ratint.barycentricinterpolant(); int i = 0; int j = 0; double a = 0; double b = 0; double v = 0; double dv = 0; System.Console.WriteLine(); System.Console.WriteLine(); System.Console.Write("Fitting exp(2*x) at [-1,+1] by polinomial"); System.Console.WriteLine(); System.Console.WriteLine(); System.Console.Write("Fit type rms.err max.err p(0) dp(0)"); System.Console.WriteLine(); // // Prepare points // m = 5; a = -1; b = +1; n = 1000; x = new double[n]; y = new double[n]; w = new double[n]; for(i=0; i<=n-1; i++) { x[i] = a+(b-a)*i/(n-1); y[i] = Math.Exp(2*x[i]); w[i] = 1.0; } // // Fitting: // a) f(x)=exp(2*x) at [-1,+1] // b) by 5th degree polynomial // c) without constraints // polint.polynomialfit(ref x, ref y, n, m, ref info, ref p, ref rep); ratint.barycentricdiff1(ref p, 0.0, ref v, ref dv); System.Console.Write("Unconstrained "); System.Console.Write("{0,7:F4}",rep.rmserror); System.Console.Write(" "); System.Console.Write("{0,7:F4}",rep.maxerror); System.Console.Write(" "); System.Console.Write("{0,7:F4}",v); System.Console.Write(" "); System.Console.Write("{0,7:F4}",dv); System.Console.WriteLine(); // // Fitting: // a) f(x)=exp(2*x) at [-1,+1] // b) by 5th degree polynomial // c) constrained: p(0)=1 // xc = new double[1]; yc = new double[1]; dc = new int[1]; xc[0] = 0; yc[0] = 1; dc[0] = 0; polint.polynomialfitwc(x, y, ref w, n, xc, yc, ref dc, 1, m, ref info, ref p, ref rep); ratint.barycentricdiff1(ref p, 0.0, ref v, ref dv); System.Console.Write("Constrained, p(0)=1 "); System.Console.Write("{0,7:F4}",rep.rmserror); System.Console.Write(" "); System.Console.Write("{0,7:F4}",rep.maxerror); System.Console.Write(" "); System.Console.Write("{0,7:F4}",v); System.Console.Write(" "); System.Console.Write("{0,7:F4}",dv); System.Console.WriteLine(); // // Fitting: // a) f(x)=exp(2*x) at [-1,+1] // b) by 5th degree polynomial // c) constrained: dp(0)=2 // xc = new double[1]; yc = new double[1]; dc = new int[1]; xc[0] = 0; yc[0] = 2; dc[0] = 1; polint.polynomialfitwc(x, y, ref w, n, xc, yc, ref dc, 1, m, ref info, ref p, ref rep); ratint.barycentricdiff1(ref p, 0.0, ref v, ref dv); System.Console.Write("Constrained, dp(0)=2 "); System.Console.Write("{0,7:F4}",rep.rmserror); System.Console.Write(" "); System.Console.Write("{0,7:F4}",rep.maxerror); System.Console.Write(" "); System.Console.Write("{0,7:F4}",v); System.Console.Write(" "); System.Console.Write("{0,7:F4}",dv); System.Console.WriteLine(); // // Fitting: // a) f(x)=exp(2*x) at [-1,+1] // b) by 5th degree polynomial // c) constrained: p(0)=1, dp(0)=2 // xc = new double[2]; yc = new double[2]; dc = new int[2]; xc[0] = 0; yc[0] = 1; dc[0] = 0; xc[1] = 0; yc[1] = 2; dc[1] = 1; polint.polynomialfitwc(x, y, ref w, n, xc, yc, ref dc, 2, m, ref info, ref p, ref rep); ratint.barycentricdiff1(ref p, 0.0, ref v, ref dv); System.Console.Write("Constrained, both "); System.Console.Write("{0,7:F4}",rep.rmserror); System.Console.Write(" "); System.Console.Write("{0,7:F4}",rep.maxerror); System.Console.Write(" "); System.Console.Write("{0,7:F4}",v); System.Console.Write(" "); System.Console.Write("{0,7:F4}",dv); System.Console.WriteLine(); System.Console.WriteLine(); System.Console.WriteLine(); return 0; }
public polynomialfitreport(polint.polynomialfitreport obj) { _innerobj = obj; }
/************************************************************************* Unit test *************************************************************************/ public static bool testpolint(bool silent) { bool result = new bool(); bool waserrors = new bool(); bool interrors = new bool(); bool fiterrors = new bool(); double threshold = 0; double[] x = new double[0]; double[] y = new double[0]; double[] w = new double[0]; double[] x2 = new double[0]; double[] y2 = new double[0]; double[] w2 = new double[0]; double[] xfull = new double[0]; double[] yfull = new double[0]; double a = 0; double b = 0; double t = 0; int i = 0; int k = 0; double[] xc = new double[0]; double[] yc = new double[0]; int[] dc = new int[0]; int info = 0; int info2 = 0; double v = 0; double v0 = 0; double v1 = 0; double v2 = 0; double s = 0; double xmin = 0; double xmax = 0; double refrms = 0; double refavg = 0; double refavgrel = 0; double refmax = 0; ratint.barycentricinterpolant p = new ratint.barycentricinterpolant(); ratint.barycentricinterpolant p1 = new ratint.barycentricinterpolant(); ratint.barycentricinterpolant p2 = new ratint.barycentricinterpolant(); polint.polynomialfitreport rep = new polint.polynomialfitreport(); polint.polynomialfitreport rep2 = new polint.polynomialfitreport(); int n = 0; int m = 0; int maxn = 0; int pass = 0; int passcount = 0; waserrors = false; interrors = false; fiterrors = false; maxn = 5; passcount = 20; threshold = 1.0E8*math.machineepsilon; // // Test equidistant interpolation // for(pass=1; pass<=passcount; pass++) { for(n=1; n<=maxn; n++) { // // prepare task: // * equidistant points // * random Y // * T in [A,B] or near (within 10% of its width) // do { a = 2*math.randomreal()-1; b = 2*math.randomreal()-1; } while( (double)(Math.Abs(a-b))<=(double)(0.2) ); t = a+(1.2*math.randomreal()-0.1)*(b-a); apserv.taskgenint1dequidist(a, b, n, ref x, ref y); // // test "fast" equidistant interpolation (no barycentric model) // interrors = interrors | (double)(Math.Abs(polint.polynomialcalceqdist(a, b, y, n, t)-internalpolint(x, y, n, t)))>(double)(threshold); // // test "slow" equidistant interpolation (create barycentric model) // brcunset(p); polint.polynomialbuild(x, y, n, p); interrors = interrors | (double)(Math.Abs(ratint.barycentriccalc(p, t)-internalpolint(x, y, n, t)))>(double)(threshold); // // test "fast" interpolation (create "fast" barycentric model) // brcunset(p); polint.polynomialbuildeqdist(a, b, y, n, p); interrors = interrors | (double)(Math.Abs(ratint.barycentriccalc(p, t)-internalpolint(x, y, n, t)))>(double)(threshold); } } // // Test Chebyshev-1 interpolation // for(pass=1; pass<=passcount; pass++) { for(n=1; n<=maxn; n++) { // // prepare task: // * equidistant points // * random Y // * T in [A,B] or near (within 10% of its width) // do { a = 2*math.randomreal()-1; b = 2*math.randomreal()-1; } while( (double)(Math.Abs(a-b))<=(double)(0.2) ); t = a+(1.2*math.randomreal()-0.1)*(b-a); apserv.taskgenint1dcheb1(a, b, n, ref x, ref y); // // test "fast" interpolation (no barycentric model) // interrors = interrors | (double)(Math.Abs(polint.polynomialcalccheb1(a, b, y, n, t)-internalpolint(x, y, n, t)))>(double)(threshold); // // test "slow" interpolation (create barycentric model) // brcunset(p); polint.polynomialbuild(x, y, n, p); interrors = interrors | (double)(Math.Abs(ratint.barycentriccalc(p, t)-internalpolint(x, y, n, t)))>(double)(threshold); // // test "fast" interpolation (create "fast" barycentric model) // brcunset(p); polint.polynomialbuildcheb1(a, b, y, n, p); interrors = interrors | (double)(Math.Abs(ratint.barycentriccalc(p, t)-internalpolint(x, y, n, t)))>(double)(threshold); } } // // Test Chebyshev-2 interpolation // for(pass=1; pass<=passcount; pass++) { for(n=1; n<=maxn; n++) { // // prepare task: // * equidistant points // * random Y // * T in [A,B] or near (within 10% of its width) // do { a = 2*math.randomreal()-1; b = 2*math.randomreal()-1; } while( (double)(Math.Abs(a-b))<=(double)(0.2) ); t = a+(1.2*math.randomreal()-0.1)*(b-a); apserv.taskgenint1dcheb2(a, b, n, ref x, ref y); // // test "fast" interpolation (no barycentric model) // interrors = interrors | (double)(Math.Abs(polint.polynomialcalccheb2(a, b, y, n, t)-internalpolint(x, y, n, t)))>(double)(threshold); // // test "slow" interpolation (create barycentric model) // brcunset(p); polint.polynomialbuild(x, y, n, p); interrors = interrors | (double)(Math.Abs(ratint.barycentriccalc(p, t)-internalpolint(x, y, n, t)))>(double)(threshold); // // test "fast" interpolation (create "fast" barycentric model) // brcunset(p); polint.polynomialbuildcheb2(a, b, y, n, p); interrors = interrors | (double)(Math.Abs(ratint.barycentriccalc(p, t)-internalpolint(x, y, n, t)))>(double)(threshold); } } // // crash-test: ability to solve tasks which will overflow/underflow // weights with straightforward implementation // for(n=1; n<=20; n++) { a = -(0.1*math.maxrealnumber); b = 0.1*math.maxrealnumber; apserv.taskgenint1dequidist(a, b, n, ref x, ref y); polint.polynomialbuild(x, y, n, p); for(i=0; i<=n-1; i++) { interrors = interrors | (double)(p.w[i])==(double)(0); } } // // Test rational fitting: // for(pass=1; pass<=passcount; pass++) { for(n=1; n<=maxn; n++) { // // N=M+K fitting (i.e. interpolation) // for(k=0; k<=n-1; k++) { apserv.taskgenint1d(-1, 1, n, ref xfull, ref yfull); x = new double[n-k]; y = new double[n-k]; w = new double[n-k]; if( k>0 ) { xc = new double[k]; yc = new double[k]; dc = new int[k]; } for(i=0; i<=n-k-1; i++) { x[i] = xfull[i]; y[i] = yfull[i]; w[i] = 1+math.randomreal(); } for(i=0; i<=k-1; i++) { xc[i] = xfull[n-k+i]; yc[i] = yfull[n-k+i]; dc[i] = 0; } polint.polynomialfitwc(x, y, w, n-k, xc, yc, dc, k, n, ref info, p1, rep); if( info<=0 ) { fiterrors = true; } else { for(i=0; i<=n-k-1; i++) { fiterrors = fiterrors | (double)(Math.Abs(ratint.barycentriccalc(p1, x[i])-y[i]))>(double)(threshold); } for(i=0; i<=k-1; i++) { fiterrors = fiterrors | (double)(Math.Abs(ratint.barycentriccalc(p1, xc[i])-yc[i]))>(double)(threshold); } } } // // Testing constraints on derivatives. // Special tasks which will always have solution: // 1. P(0)=YC[0] // 2. P(0)=YC[0], P'(0)=YC[1] // if( n>1 ) { for(m=3; m<=5; m++) { for(k=1; k<=2; k++) { apserv.taskgenint1d(-1, 1, n, ref x, ref y); w = new double[n]; xc = new double[2]; yc = new double[2]; dc = new int[2]; for(i=0; i<=n-1; i++) { w[i] = 1+math.randomreal(); } xc[0] = 0; yc[0] = 2*math.randomreal()-1; dc[0] = 0; xc[1] = 0; yc[1] = 2*math.randomreal()-1; dc[1] = 1; polint.polynomialfitwc(x, y, w, n, xc, yc, dc, k, m, ref info, p1, rep); if( info<=0 ) { fiterrors = true; } else { ratint.barycentricdiff1(p1, 0.0, ref v0, ref v1); fiterrors = fiterrors | (double)(Math.Abs(v0-yc[0]))>(double)(threshold); if( k==2 ) { fiterrors = fiterrors | (double)(Math.Abs(v1-yc[1]))>(double)(threshold); } } } } } } } for(m=2; m<=8; m++) { for(pass=1; pass<=passcount; pass++) { // // General fitting // // interpolating function through M nodes should have // greater RMS error than fitting it through the same M nodes // n = 100; x2 = new double[n]; y2 = new double[n]; w2 = new double[n]; xmin = 0; xmax = 2*Math.PI; for(i=0; i<=n-1; i++) { x2[i] = 2*Math.PI*math.randomreal(); y2[i] = Math.Sin(x2[i]); w2[i] = 1; } x = new double[m]; y = new double[m]; for(i=0; i<=m-1; i++) { x[i] = xmin+(xmax-xmin)*i/(m-1); y[i] = Math.Sin(x[i]); } polint.polynomialbuild(x, y, m, p1); polint.polynomialfitwc(x2, y2, w2, n, xc, yc, dc, 0, m, ref info, p2, rep); if( info<=0 ) { fiterrors = true; } else { // // calculate P1 (interpolant) RMS error, compare with P2 error // v1 = 0; v2 = 0; for(i=0; i<=n-1; i++) { v1 = v1+math.sqr(ratint.barycentriccalc(p1, x2[i])-y2[i]); v2 = v2+math.sqr(ratint.barycentriccalc(p2, x2[i])-y2[i]); } v1 = Math.Sqrt(v1/n); v2 = Math.Sqrt(v2/n); fiterrors = fiterrors | (double)(v2)>(double)(v1); fiterrors = fiterrors | (double)(Math.Abs(v2-rep.rmserror))>(double)(threshold); } // // compare weighted and non-weighted // n = 20; x = new double[n]; y = new double[n]; w = new double[n]; for(i=0; i<=n-1; i++) { x[i] = 2*math.randomreal()-1; y[i] = 2*math.randomreal()-1; w[i] = 1; } polint.polynomialfitwc(x, y, w, n, xc, yc, dc, 0, m, ref info, p1, rep); polint.polynomialfit(x, y, n, m, ref info2, p2, rep2); if( info<=0 | info2<=0 ) { fiterrors = true; } else { // // calculate P1 (interpolant), compare with P2 error // compare RMS errors // t = 2*math.randomreal()-1; v1 = ratint.barycentriccalc(p1, t); v2 = ratint.barycentriccalc(p2, t); fiterrors = fiterrors | (double)(v2)!=(double)(v1); fiterrors = fiterrors | (double)(rep.rmserror)!=(double)(rep2.rmserror); fiterrors = fiterrors | (double)(rep.avgerror)!=(double)(rep2.avgerror); fiterrors = fiterrors | (double)(rep.avgrelerror)!=(double)(rep2.avgrelerror); fiterrors = fiterrors | (double)(rep.maxerror)!=(double)(rep2.maxerror); } } } for(pass=1; pass<=passcount; pass++) { ap.assert(passcount>=2, "PassCount should be 2 or greater!"); // // solve simple task (all X[] are the same, Y[] are specially // calculated to ensure simple form of all types of errors) // and check correctness of the errors calculated by subroutines // // First pass is done with zero Y[], other passes - with random Y[]. // It should test both ability to correctly calculate errors and // ability to not fail while working with zeros :) // n = 4; if( pass==1 ) { v1 = 0; v2 = 0; v = 0; } else { v1 = math.randomreal(); v2 = math.randomreal(); v = 1+math.randomreal(); } x = new double[4]; y = new double[4]; w = new double[4]; x[0] = 0; y[0] = v-v2; w[0] = 1; x[1] = 0; y[1] = v-v1; w[1] = 1; x[2] = 0; y[2] = v+v1; w[2] = 1; x[3] = 0; y[3] = v+v2; w[3] = 1; refrms = Math.Sqrt((math.sqr(v1)+math.sqr(v2))/2); refavg = (Math.Abs(v1)+Math.Abs(v2))/2; if( pass==1 ) { refavgrel = 0; } else { refavgrel = 0.25*(Math.Abs(v2)/Math.Abs(v-v2)+Math.Abs(v1)/Math.Abs(v-v1)+Math.Abs(v1)/Math.Abs(v+v1)+Math.Abs(v2)/Math.Abs(v+v2)); } refmax = Math.Max(v1, v2); // // Test errors correctness // polint.polynomialfit(x, y, 4, 1, ref info, p, rep); if( info<=0 ) { fiterrors = true; } else { s = ratint.barycentriccalc(p, 0); fiterrors = fiterrors | (double)(Math.Abs(s-v))>(double)(threshold); fiterrors = fiterrors | (double)(Math.Abs(rep.rmserror-refrms))>(double)(threshold); fiterrors = fiterrors | (double)(Math.Abs(rep.avgerror-refavg))>(double)(threshold); fiterrors = fiterrors | (double)(Math.Abs(rep.avgrelerror-refavgrel))>(double)(threshold); fiterrors = fiterrors | (double)(Math.Abs(rep.maxerror-refmax))>(double)(threshold); } } // // report // waserrors = interrors | fiterrors; if( !silent ) { System.Console.Write("TESTING POLYNOMIAL INTERPOLATION AND FITTING"); System.Console.WriteLine(); // // Normal tests // System.Console.Write("INTERPOLATION TEST: "); if( interrors ) { System.Console.Write("FAILED"); System.Console.WriteLine(); } else { System.Console.Write("OK"); System.Console.WriteLine(); } System.Console.Write("FITTING TEST: "); if( fiterrors ) { System.Console.Write("FAILED"); System.Console.WriteLine(); } else { System.Console.Write("OK"); System.Console.WriteLine(); } if( waserrors ) { System.Console.Write("TEST FAILED"); System.Console.WriteLine(); } else { System.Console.Write("TEST PASSED"); System.Console.WriteLine(); } System.Console.WriteLine(); System.Console.WriteLine(); } // // end // result = !waserrors; return result; }
public polynomialfitreport() { _innerobj = new polint.polynomialfitreport(); }