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();
}
