public static bool testri(bool silent)
{
bool result = new bool();
bool waserrors = new bool();
bool bcerrors = new bool();
bool nperrors = new bool();
bool fiterrors = new bool();
double threshold = 0;
double lipschitztol = 0;
int maxn = 0;
int passcount = 0;
ratint.barycentricinterpolant b1 = new ratint.barycentricinterpolant();
ratint.barycentricinterpolant b2 = new ratint.barycentricinterpolant();
double[] x = new double[0];
double[] x2 = new double[0];
double[] y = new double[0];
double[] y2 = new double[0];
double[] w = new double[0];
double[] w2 = new double[0];
double[] xc = new double[0];
double[] yc = new double[0];
int[] dc = new int[0];
double h = 0;
double s1 = 0;
double s2 = 0;
bool bsame = new bool();
int n = 0;
int m = 0;
int n2 = 0;
int i = 0;
int j = 0;
int k = 0;
int d = 0;
int pass = 0;
double err = 0;
double maxerr = 0;
double t = 0;
double a = 0;
double b = 0;
double s = 0;
double v = 0;
double v0 = 0;
double v1 = 0;
double v2 = 0;
double v3 = 0;
double d0 = 0;
double d1 = 0;
double d2 = 0;
int info = 0;
int info2 = 0;
double xmin = 0;
double xmax = 0;
double refrms = 0;
double refavg = 0;
double refavgrel = 0;
double refmax = 0;
double[] ra = new double[0];
double[] ra2 = new double[0];
int ralen = 0;
ratint.barycentricfitreport rep = new ratint.barycentricfitreport();
ratint.barycentricfitreport rep2 = new ratint.barycentricfitreport();
ratint.barycentricinterpolant b3 = new ratint.barycentricinterpolant();
ratint.barycentricinterpolant b4 = new ratint.barycentricinterpolant();
int i_ = 0;
nperrors = false;
bcerrors = false;
fiterrors = false;
waserrors = false;
//
// PassCount number of repeated passes
// Threshold error tolerance
// LipschitzTol Lipschitz constant increase allowed
// when calculating constant on a twice denser grid
//
passcount = 5;
maxn = 15;
threshold = 1000000*AP.Math.MachineEpsilon;
lipschitztol = 1.3;
//
// Basic barycentric functions
//
for(n=1; n<=10; n++)
{
//
// randomized tests
//
for(pass=1; pass<=passcount; pass++)
{
//
// generate weights from polynomial interpolation
//
v0 = 1+0.4*AP.Math.RandomReal()-0.2;
v1 = 2*AP.Math.RandomReal()-1;
v2 = 2*AP.Math.RandomReal()-1;
v3 = 2*AP.Math.RandomReal()-1;
x = new double[n];
y = new double[n];
w = new double[n];
for(i=0; i<=n-1; i++)
{
if( n==1 )
{
x[i] = 0;
}
else
{
x[i] = v0*Math.Cos(i*Math.PI/(n-1));
}
y[i] = Math.Sin(v1*x[i])+Math.Cos(v2*x[i])+Math.Exp(v3*x[i]);
}
for(j=0; j<=n-1; j++)
{
w[j] = 1;
for(k=0; k<=n-1; k++)
{
if( k!=j )
{
w[j] = w[j]/(x[j]-x[k]);
}
}
}
ratint.barycentricbuildxyw(ref x, ref y, ref w, n, ref b1);
//
// unpack, then pack again and compare
//
brcunset(ref b2);
ratint.barycentricunpack(ref b1, ref n2, ref x2, ref y2, ref w2);
bcerrors = bcerrors | n2!=n;
ratint.barycentricbuildxyw(ref x2, ref y2, ref w2, n2, ref b2);
t = 2*AP.Math.RandomReal()-1;
bcerrors = bcerrors | (double)(Math.Abs(ratint.barycentriccalc(ref b1, t)-ratint.barycentriccalc(ref b2, t)))>(double)(threshold);
//
// serialize, unserialize, compare
//
brcunset(ref b2);
ratint.barycentricserialize(ref b1, ref ra, ref ralen);
ra2 = new double[ralen];
for(i_=0; i_<=ralen-1;i_++)
{
ra2[i_] = ra[i_];
}
ratint.barycentricunserialize(ref ra2, ref b2);
t = 2*AP.Math.RandomReal()-1;
bcerrors = bcerrors | (double)(Math.Abs(ratint.barycentriccalc(ref b1, t)-ratint.barycentriccalc(ref b2, t)))>(double)(threshold);
//
// copy, compare
//
brcunset(ref b2);
ratint.barycentriccopy(ref b1, ref b2);
t = 2*AP.Math.RandomReal()-1;
bcerrors = bcerrors | (double)(Math.Abs(ratint.barycentriccalc(ref b1, t)-ratint.barycentriccalc(ref b2, t)))>(double)(threshold);
//
// test interpolation properties
//
for(i=0; i<=n-1; i++)
{
//
// test interpolation at nodes
//
bcerrors = bcerrors | (double)(Math.Abs(ratint.barycentriccalc(ref b1, x[i])-y[i]))>(double)(threshold*Math.Abs(y[i]));
//
// compare with polynomial interpolation
//
t = 2*AP.Math.RandomReal()-1;
poldiff2(ref x, y, n, t, ref v0, ref v1, ref v2);
bcerrors = bcerrors | (double)(Math.Abs(ratint.barycentriccalc(ref b1, t)-v0))>(double)(threshold*Math.Max(Math.Abs(v0), 1));
//
// test continuity between nodes
// calculate Lipschitz constant on two grids -
// dense and even more dense. If Lipschitz constant
// on a denser grid is significantly increased,
// continuity test is failed
//
t = 3.0;
k = 100;
s1 = 0;
for(j=0; j<=k-1; j++)
{
v1 = x[i]+(t-x[i])*j/k;
v2 = x[i]+(t-x[i])*(j+1)/k;
s1 = Math.Max(s1, Math.Abs(ratint.barycentriccalc(ref b1, v2)-ratint.barycentriccalc(ref b1, v1))/Math.Abs(v2-v1));
}
k = 2*k;
s2 = 0;
for(j=0; j<=k-1; j++)
{
v1 = x[i]+(t-x[i])*j/k;
v2 = x[i]+(t-x[i])*(j+1)/k;
s2 = Math.Max(s2, Math.Abs(ratint.barycentriccalc(ref b1, v2)-ratint.barycentriccalc(ref b1, v1))/Math.Abs(v2-v1));
}
bcerrors = bcerrors | (double)(s2)>(double)(lipschitztol*s1) & (double)(s1)>(double)(threshold*k);
}
//
// test differentiation properties
//
for(i=0; i<=n-1; i++)
{
t = 2*AP.Math.RandomReal()-1;
poldiff2(ref x, y, n, t, ref v0, ref v1, ref v2);
d0 = 0;
d1 = 0;
d2 = 0;
ratint.barycentricdiff1(ref b1, t, ref d0, ref d1);
bcerrors = bcerrors | (double)(Math.Abs(v0-d0))>(double)(threshold*Math.Max(Math.Abs(v0), 1));
bcerrors = bcerrors | (double)(Math.Abs(v1-d1))>(double)(threshold*Math.Max(Math.Abs(v1), 1));
d0 = 0;
d1 = 0;
d2 = 0;
ratint.barycentricdiff2(ref b1, t, ref d0, ref d1, ref d2);
bcerrors = bcerrors | (double)(Math.Abs(v0-d0))>(double)(threshold*Math.Max(Math.Abs(v0), 1));
bcerrors = bcerrors | (double)(Math.Abs(v1-d1))>(double)(threshold*Math.Max(Math.Abs(v1), 1));
bcerrors = bcerrors | (double)(Math.Abs(v2-d2))>(double)(Math.Sqrt(threshold)*Math.Max(Math.Abs(v2), 1));
}
//
// test linear translation
//
t = 2*AP.Math.RandomReal()-1;
a = 2*AP.Math.RandomReal()-1;
b = 2*AP.Math.RandomReal()-1;
brcunset(ref b2);
ratint.barycentriccopy(ref b1, ref b2);
ratint.barycentriclintransx(ref b2, a, b);
bcerrors = bcerrors | (double)(Math.Abs(ratint.barycentriccalc(ref b1, a*t+b)-ratint.barycentriccalc(ref b2, t)))>(double)(threshold);
a = 0;
b = 2*AP.Math.RandomReal()-1;
brcunset(ref b2);
ratint.barycentriccopy(ref b1, ref b2);
ratint.barycentriclintransx(ref b2, a, b);
bcerrors = bcerrors | (double)(Math.Abs(ratint.barycentriccalc(ref b1, a*t+b)-ratint.barycentriccalc(ref b2, t)))>(double)(threshold);
a = 2*AP.Math.RandomReal()-1;
b = 2*AP.Math.RandomReal()-1;
brcunset(ref b2);
ratint.barycentriccopy(ref b1, ref b2);
ratint.barycentriclintransy(ref b2, a, b);
bcerrors = bcerrors | (double)(Math.Abs(a*ratint.barycentriccalc(ref b1, t)+b-ratint.barycentriccalc(ref b2, t)))>(double)(threshold);
}
}
for(pass=0; pass<=3; pass++)
{
//
// Crash-test: small numbers, large numbers
//
x = new double[4];
y = new double[4];
w = new double[4];
h = 1;
if( pass%2==0 )
{
h = 100*AP.Math.MinRealNumber;
}
if( pass%2==1 )
{
h = 0.01*AP.Math.MaxRealNumber;
}
x[0] = 0*h;
x[1] = 1*h;
x[2] = 2*h;
x[3] = 3*h;
y[0] = 0*h;
y[1] = 1*h;
y[2] = 2*h;
y[3] = 3*h;
w[0] = -(1/(x[1]-x[0]));
w[1] = +(1*(1/(x[1]-x[0])+1/(x[2]-x[1])));
w[2] = -(1*(1/(x[2]-x[1])+1/(x[3]-x[2])));
w[3] = +(1/(x[3]-x[2]));
if( pass/2==0 )
{
v0 = 0;
}
if( pass/2==1 )
{
v0 = 0.6*h;
}
ratint.barycentricbuildxyw(ref x, ref y, ref w, 4, ref b1);
t = ratint.barycentriccalc(ref b1, v0);
d0 = 0;
d1 = 0;
d2 = 0;
ratint.barycentricdiff1(ref b1, v0, ref d0, ref d1);
bcerrors = bcerrors | (double)(Math.Abs(t-v0))>(double)(threshold*v0);
bcerrors = bcerrors | (double)(Math.Abs(d0-v0))>(double)(threshold*v0);
bcerrors = bcerrors | (double)(Math.Abs(d1-1))>(double)(1000*threshold);
}
//
// crash test: large abscissas, small argument
//
// test for errors in D0 is not very strict
// because renormalization used in Diff1()
// destroys part of precision.
//
x = new double[4];
y = new double[4];
w = new double[4];
h = 0.01*AP.Math.MaxRealNumber;
x[0] = 0*h;
x[1] = 1*h;
x[2] = 2*h;
x[3] = 3*h;
y[0] = 0*h;
y[1] = 1*h;
y[2] = 2*h;
y[3] = 3*h;
w[0] = -(1/(x[1]-x[0]));
w[1] = +(1*(1/(x[1]-x[0])+1/(x[2]-x[1])));
w[2] = -(1*(1/(x[2]-x[1])+1/(x[3]-x[2])));
w[3] = +(1/(x[3]-x[2]));
v0 = 100*AP.Math.MinRealNumber;
ratint.barycentricbuildxyw(ref x, ref y, ref w, 4, ref b1);
t = ratint.barycentriccalc(ref b1, v0);
d0 = 0;
d1 = 0;
d2 = 0;
ratint.barycentricdiff1(ref b1, v0, ref d0, ref d1);
bcerrors = bcerrors | (double)(Math.Abs(t))>(double)(v0*(1+threshold));
bcerrors = bcerrors | (double)(Math.Abs(d0))>(double)(v0*(1+threshold));
bcerrors = bcerrors | (double)(Math.Abs(d1-1))>(double)(1000*threshold);
//
// crash test: test safe barycentric formula
//
x = new double[4];
y = new double[4];
w = new double[4];
h = 2*AP.Math.MinRealNumber;
x[0] = 0*h;
x[1] = 1*h;
x[2] = 2*h;
x[3] = 3*h;
y[0] = 0*h;
y[1] = 1*h;
y[2] = 2*h;
y[3] = 3*h;
w[0] = -(1/(x[1]-x[0]));
w[1] = +(1*(1/(x[1]-x[0])+1/(x[2]-x[1])));
w[2] = -(1*(1/(x[2]-x[1])+1/(x[3]-x[2])));
w[3] = +(1/(x[3]-x[2]));
v0 = AP.Math.MinRealNumber;
ratint.barycentricbuildxyw(ref x, ref y, ref w, 4, ref b1);
t = ratint.barycentriccalc(ref b1, v0);
bcerrors = bcerrors | (double)(Math.Abs(t-v0)/v0)>(double)(threshold);
//
// Testing "No Poles" interpolation
//
maxerr = 0;
for(pass=1; pass<=passcount-1; pass++)
{
x = new double[1];
y = new double[1];
x[0] = 2*AP.Math.RandomReal()-1;
y[0] = 2*AP.Math.RandomReal()-1;
ratint.barycentricbuildfloaterhormann(ref x, ref y, 1, 1, ref b1);
maxerr = Math.Max(maxerr, Math.Abs(ratint.barycentriccalc(ref b1, 2*AP.Math.RandomReal()-1)-y[0]));
}
for(n=2; n<=10; n++)
{
//
// compare interpolant built by subroutine
// with interpolant built by hands
//
x = new double[n];
y = new double[n];
w = new double[n];
w2 = new double[n];
//
// D=1, non-equidistant nodes
//
for(pass=1; pass<=passcount; pass++)
{
//
// Initialize X, Y, W
//
a = -1-1*AP.Math.RandomReal();
b = +1+1*AP.Math.RandomReal();
for(i=0; i<=n-1; i++)
{
x[i] = Math.Atan((b-a)*i/(n-1)+a);
}
for(i=0; i<=n-1; i++)
{
y[i] = 2*AP.Math.RandomReal()-1;
}
w[0] = -(1/(x[1]-x[0]));
s = 1;
for(i=1; i<=n-2; i++)
{
w[i] = s*(1/(x[i]-x[i-1])+1/(x[i+1]-x[i]));
s = -s;
}
w[n-1] = s/(x[n-1]-x[n-2]);
for(i=0; i<=n-1; i++)
{
k = AP.Math.RandomInteger(n);
if( k!=i )
{
t = x[i];
x[i] = x[k];
x[k] = t;
t = y[i];
y[i] = y[k];
y[k] = t;
t = w[i];
w[i] = w[k];
w[k] = t;
}
}
//
// Build and test
//
ratint.barycentricbuildfloaterhormann(ref x, ref y, n, 1, ref b1);
ratint.barycentricbuildxyw(ref x, ref y, ref w, n, ref b2);
for(i=1; i<=2*n; i++)
{
t = a+(b-a)*AP.Math.RandomReal();
maxerr = Math.Max(maxerr, Math.Abs(ratint.barycentriccalc(ref b1, t)-ratint.barycentriccalc(ref b2, t)));
}
}
//
// D = 0, 1, 2. Equidistant nodes.
//
for(d=0; d<=2; d++)
{
for(pass=1; pass<=passcount; pass++)
{
//
// Skip incorrect (N,D) pairs
//
if( n<2*d )
{
continue;
}
//
// Initialize X, Y, W
//
a = -1-1*AP.Math.RandomReal();
b = +1+1*AP.Math.RandomReal();
for(i=0; i<=n-1; i++)
{
x[i] = (b-a)*i/(n-1)+a;
}
for(i=0; i<=n-1; i++)
{
y[i] = 2*AP.Math.RandomReal()-1;
}
s = 1;
if( d==0 )
{
for(i=0; i<=n-1; i++)
{
w[i] = s;
s = -s;
}
}
if( d==1 )
{
w[0] = -s;
for(i=1; i<=n-2; i++)
{
w[i] = 2*s;
s = -s;
}
w[n-1] = s;
}
if( d==2 )
{
w[0] = s;
w[1] = -(3*s);
for(i=2; i<=n-3; i++)
{
w[i] = 4*s;
s = -s;
}
w[n-2] = 3*s;
w[n-1] = -s;
}
//
// Mix
//
for(i=0; i<=n-1; i++)
{
k = AP.Math.RandomInteger(n);
if( k!=i )
{
t = x[i];
x[i] = x[k];
x[k] = t;
t = y[i];
y[i] = y[k];
y[k] = t;
t = w[i];
w[i] = w[k];
w[k] = t;
}
}
//
// Build and test
//
ratint.barycentricbuildfloaterhormann(ref x, ref y, n, d, ref b1);
ratint.barycentricbuildxyw(ref x, ref y, ref w, n, ref b2);
for(i=1; i<=2*n; i++)
{
t = a+(b-a)*AP.Math.RandomReal();
maxerr = Math.Max(maxerr, Math.Abs(ratint.barycentriccalc(ref b1, t)-ratint.barycentriccalc(ref b2, t)));
}
}
}
}
if( (double)(maxerr)>(double)(threshold) )
{
nperrors = true;
}
//
// Test rational fitting:
//
for(pass=1; pass<=passcount; pass++)
{
for(n=2; n<=maxn; n++)
{
//
// N=M+K fitting (i.e. interpolation)
//
for(k=0; k<=n-1; k++)
{
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] = (double)(i)/((double)(n-1));
y[i] = 2*AP.Math.RandomReal()-1;
w[i] = 1+AP.Math.RandomReal();
}
for(i=0; i<=k-1; i++)
{
xc[i] = ((double)(n-k+i))/((double)(n-1));
yc[i] = 2*AP.Math.RandomReal()-1;
dc[i] = 0;
}
ratint.barycentricfitfloaterhormannwc(ref x, ref y, ref w, n-k, ref xc, ref yc, ref dc, k, n, ref info, ref b1, ref rep);
if( info<=0 )
{
fiterrors = true;
}
else
{
for(i=0; i<=n-k-1; i++)
{
fiterrors = fiterrors | (double)(Math.Abs(ratint.barycentriccalc(ref b1, x[i])-y[i]))>(double)(threshold);
}
for(i=0; i<=k-1; i++)
{
fiterrors = fiterrors | (double)(Math.Abs(ratint.barycentriccalc(ref b1, xc[i])-yc[i]))>(double)(threshold);
}
}
}
//
// Testing constraints on derivatives:
// * several M's are tried
// * several K's are tried - 1, 2.
// * constraints at the ends of the interval
//
for(m=3; m<=5; m++)
{
for(k=1; k<=2; k++)
{
x = new double[n];
y = new double[n];
w = new double[n];
xc = new double[2];
yc = new double[2];
dc = new int[2];
for(i=0; i<=n-1; i++)
{
x[i] = 2*AP.Math.RandomReal()-1;
y[i] = 2*AP.Math.RandomReal()-1;
w[i] = 1+AP.Math.RandomReal();
}
xc[0] = -1;
yc[0] = 2*AP.Math.RandomReal()-1;
dc[0] = 0;
xc[1] = +1;
yc[1] = 2*AP.Math.RandomReal()-1;
dc[1] = 0;
ratint.barycentricfitfloaterhormannwc(ref x, ref y, ref w, n, ref xc, ref yc, ref dc, k, m, ref info, ref b1, ref rep);
if( info<=0 )
{
fiterrors = true;
}
else
{
for(i=0; i<=k-1; i++)
{
ratint.barycentricdiff1(ref b1, xc[i], ref v0, ref v1);
fiterrors = fiterrors | (double)(Math.Abs(v0-yc[i]))>(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 = AP.Math.MaxRealNumber;
xmax = -AP.Math.MaxRealNumber;
for(i=0; i<=n-1; i++)
{
x2[i] = 2*Math.PI*AP.Math.RandomReal();
y2[i] = Math.Sin(x2[i]);
w2[i] = 1;
xmin = Math.Min(xmin, x2[i]);
xmax = Math.Max(xmax, x2[i]);
}
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]);
}
ratint.barycentricbuildfloaterhormann(ref x, ref y, m, 3, ref b1);
ratint.barycentricfitfloaterhormannwc(ref x2, ref y2, ref w2, n, ref xc, ref yc, ref dc, 0, m, ref info, ref b2, ref rep);
if( info<=0 )
{
fiterrors = true;
}
else
{
//
// calculate B1 (interpolant) RMS error, compare with B2 error
//
v1 = 0;
v2 = 0;
for(i=0; i<=n-1; i++)
{
v1 = v1+AP.Math.Sqr(ratint.barycentriccalc(ref b1, x2[i])-y2[i]);
v2 = v2+AP.Math.Sqr(ratint.barycentriccalc(ref b2, 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*AP.Math.RandomReal()-1;
y[i] = 2*AP.Math.RandomReal()-1;
w[i] = 1;
}
ratint.barycentricfitfloaterhormannwc(ref x, ref y, ref w, n, ref xc, ref yc, ref dc, 0, m, ref info, ref b1, ref rep);
ratint.barycentricfitfloaterhormann(ref x, ref y, n, m, ref info2, ref b2, ref rep2);
if( info<=0 | info2<=0 )
{
fiterrors = true;
}
else
{
//
// calculate B1 (interpolant), compare with B2
// compare RMS errors
//
t = 2*AP.Math.RandomReal()-1;
v1 = ratint.barycentriccalc(ref b1, t);
v2 = ratint.barycentriccalc(ref b2, 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++)
{
System.Diagnostics.Debug.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 = AP.Math.RandomReal();
v2 = AP.Math.RandomReal();
v = 1+AP.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((AP.Math.Sqr(v1)+AP.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
//
ratint.barycentricfitfloaterhormann(ref x, ref y, 4, 2, ref info, ref b1, ref rep);
if( info<=0 )
{
fiterrors = true;
}
else
{
s = ratint.barycentriccalc(ref b1, 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 = bcerrors | nperrors | fiterrors;
if( !silent )
{
System.Console.Write("TESTING RATIONAL INTERPOLATION");
System.Console.WriteLine();
System.Console.Write("BASIC BARYCENTRIC FUNCTIONS: ");
if( bcerrors )
{
System.Console.Write("FAILED");
System.Console.WriteLine();
}
else
{
System.Console.Write("OK");
System.Console.WriteLine();
}
System.Console.Write("FLOATER-HORMANN: ");
if( nperrors )
{
System.Console.Write("FAILED");
System.Console.WriteLine();
}
else
{
System.Console.Write("OK");
System.Console.WriteLine();
}
System.Console.Write("RATIONAL FITTING: ");
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 static bool testri(bool silent)
{
bool result = new bool();
bool waserrors = new bool();
bool bcerrors = new bool();
bool nperrors = new bool();
bool fiterrors = new bool();
double threshold = 0;
double lipschitztol = 0;
int maxn = 0;
int passcount = 0;
ratint.barycentricinterpolant b1 = new ratint.barycentricinterpolant();
ratint.barycentricinterpolant b2 = new ratint.barycentricinterpolant();
double[] x = new double[0];
double[] x2 = new double[0];
double[] y = new double[0];
double[] y2 = new double[0];
double[] w = new double[0];
double[] w2 = new double[0];
double[] xc = new double[0];
double[] yc = new double[0];
int[] dc = new int[0];
double h = 0;
double s1 = 0;
double s2 = 0;
bool bsame = new bool();
int n = 0;
int m = 0;
int n2 = 0;
int i = 0;
int j = 0;
int k = 0;
int d = 0;
int pass = 0;
double err = 0;
double maxerr = 0;
double t = 0;
double a = 0;
double b = 0;
double s = 0;
double v = 0;
double v0 = 0;
double v1 = 0;
double v2 = 0;
double v3 = 0;
double d0 = 0;
double d1 = 0;
double d2 = 0;
int info = 0;
int info2 = 0;
double xmin = 0;
double xmax = 0;
double refrms = 0;
double refavg = 0;
double refavgrel = 0;
double refmax = 0;
double[] ra = new double[0];
double[] ra2 = new double[0];
int ralen = 0;
ratint.barycentricfitreport rep = new ratint.barycentricfitreport();
ratint.barycentricfitreport rep2 = new ratint.barycentricfitreport();
ratint.barycentricinterpolant b3 = new ratint.barycentricinterpolant();
ratint.barycentricinterpolant b4 = new ratint.barycentricinterpolant();
int i_ = 0;
nperrors = false;
bcerrors = false;
fiterrors = false;
waserrors = false;
//
// PassCount number of repeated passes
// Threshold error tolerance
// LipschitzTol Lipschitz constant increase allowed
// when calculating constant on a twice denser grid
//
passcount = 5;
maxn = 15;
threshold = 1000000 * AP.Math.MachineEpsilon;
lipschitztol = 1.3;
//
// Basic barycentric functions
//
for (n = 1; n <= 10; n++)
{
//
// randomized tests
//
for (pass = 1; pass <= passcount; pass++)
{
//
// generate weights from polynomial interpolation
//
v0 = 1 + 0.4 * AP.Math.RandomReal() - 0.2;
v1 = 2 * AP.Math.RandomReal() - 1;
v2 = 2 * AP.Math.RandomReal() - 1;
v3 = 2 * AP.Math.RandomReal() - 1;
x = new double[n];
y = new double[n];
w = new double[n];
for (i = 0; i <= n - 1; i++)
{
if (n == 1)
{
x[i] = 0;
}
else
{
x[i] = v0 * Math.Cos(i * Math.PI / (n - 1));
}
y[i] = Math.Sin(v1 * x[i]) + Math.Cos(v2 * x[i]) + Math.Exp(v3 * x[i]);
}
for (j = 0; j <= n - 1; j++)
{
w[j] = 1;
for (k = 0; k <= n - 1; k++)
{
if (k != j)
{
w[j] = w[j] / (x[j] - x[k]);
}
}
}
ratint.barycentricbuildxyw(ref x, ref y, ref w, n, ref b1);
//
// unpack, then pack again and compare
//
brcunset(ref b2);
ratint.barycentricunpack(ref b1, ref n2, ref x2, ref y2, ref w2);
bcerrors = bcerrors | n2 != n;
ratint.barycentricbuildxyw(ref x2, ref y2, ref w2, n2, ref b2);
t = 2 * AP.Math.RandomReal() - 1;
bcerrors = bcerrors | (double)(Math.Abs(ratint.barycentriccalc(ref b1, t) - ratint.barycentriccalc(ref b2, t))) > (double)(threshold);
//
// serialize, unserialize, compare
//
brcunset(ref b2);
ratint.barycentricserialize(ref b1, ref ra, ref ralen);
ra2 = new double[ralen];
for (i_ = 0; i_ <= ralen - 1; i_++)
{
ra2[i_] = ra[i_];
}
ratint.barycentricunserialize(ref ra2, ref b2);
t = 2 * AP.Math.RandomReal() - 1;
bcerrors = bcerrors | (double)(Math.Abs(ratint.barycentriccalc(ref b1, t) - ratint.barycentriccalc(ref b2, t))) > (double)(threshold);
//
// copy, compare
//
brcunset(ref b2);
ratint.barycentriccopy(ref b1, ref b2);
t = 2 * AP.Math.RandomReal() - 1;
bcerrors = bcerrors | (double)(Math.Abs(ratint.barycentriccalc(ref b1, t) - ratint.barycentriccalc(ref b2, t))) > (double)(threshold);
//
// test interpolation properties
//
for (i = 0; i <= n - 1; i++)
{
//
// test interpolation at nodes
//
bcerrors = bcerrors | (double)(Math.Abs(ratint.barycentriccalc(ref b1, x[i]) - y[i])) > (double)(threshold * Math.Abs(y[i]));
//
// compare with polynomial interpolation
//
t = 2 * AP.Math.RandomReal() - 1;
poldiff2(ref x, y, n, t, ref v0, ref v1, ref v2);
bcerrors = bcerrors | (double)(Math.Abs(ratint.barycentriccalc(ref b1, t) - v0)) > (double)(threshold * Math.Max(Math.Abs(v0), 1));
//
// test continuity between nodes
// calculate Lipschitz constant on two grids -
// dense and even more dense. If Lipschitz constant
// on a denser grid is significantly increased,
// continuity test is failed
//
t = 3.0;
k = 100;
s1 = 0;
for (j = 0; j <= k - 1; j++)
{
v1 = x[i] + (t - x[i]) * j / k;
v2 = x[i] + (t - x[i]) * (j + 1) / k;
s1 = Math.Max(s1, Math.Abs(ratint.barycentriccalc(ref b1, v2) - ratint.barycentriccalc(ref b1, v1)) / Math.Abs(v2 - v1));
}
k = 2 * k;
s2 = 0;
for (j = 0; j <= k - 1; j++)
{
v1 = x[i] + (t - x[i]) * j / k;
v2 = x[i] + (t - x[i]) * (j + 1) / k;
s2 = Math.Max(s2, Math.Abs(ratint.barycentriccalc(ref b1, v2) - ratint.barycentriccalc(ref b1, v1)) / Math.Abs(v2 - v1));
}
bcerrors = bcerrors | (double)(s2) > (double)(lipschitztol * s1) & (double)(s1) > (double)(threshold * k);
}
//
// test differentiation properties
//
for (i = 0; i <= n - 1; i++)
{
t = 2 * AP.Math.RandomReal() - 1;
poldiff2(ref x, y, n, t, ref v0, ref v1, ref v2);
d0 = 0;
d1 = 0;
d2 = 0;
ratint.barycentricdiff1(ref b1, t, ref d0, ref d1);
bcerrors = bcerrors | (double)(Math.Abs(v0 - d0)) > (double)(threshold * Math.Max(Math.Abs(v0), 1));
bcerrors = bcerrors | (double)(Math.Abs(v1 - d1)) > (double)(threshold * Math.Max(Math.Abs(v1), 1));
d0 = 0;
d1 = 0;
d2 = 0;
ratint.barycentricdiff2(ref b1, t, ref d0, ref d1, ref d2);
bcerrors = bcerrors | (double)(Math.Abs(v0 - d0)) > (double)(threshold * Math.Max(Math.Abs(v0), 1));
bcerrors = bcerrors | (double)(Math.Abs(v1 - d1)) > (double)(threshold * Math.Max(Math.Abs(v1), 1));
bcerrors = bcerrors | (double)(Math.Abs(v2 - d2)) > (double)(Math.Sqrt(threshold) * Math.Max(Math.Abs(v2), 1));
}
//
// test linear translation
//
t = 2 * AP.Math.RandomReal() - 1;
a = 2 * AP.Math.RandomReal() - 1;
b = 2 * AP.Math.RandomReal() - 1;
brcunset(ref b2);
ratint.barycentriccopy(ref b1, ref b2);
ratint.barycentriclintransx(ref b2, a, b);
bcerrors = bcerrors | (double)(Math.Abs(ratint.barycentriccalc(ref b1, a * t + b) - ratint.barycentriccalc(ref b2, t))) > (double)(threshold);
a = 0;
b = 2 * AP.Math.RandomReal() - 1;
brcunset(ref b2);
ratint.barycentriccopy(ref b1, ref b2);
ratint.barycentriclintransx(ref b2, a, b);
bcerrors = bcerrors | (double)(Math.Abs(ratint.barycentriccalc(ref b1, a * t + b) - ratint.barycentriccalc(ref b2, t))) > (double)(threshold);
a = 2 * AP.Math.RandomReal() - 1;
b = 2 * AP.Math.RandomReal() - 1;
brcunset(ref b2);
ratint.barycentriccopy(ref b1, ref b2);
ratint.barycentriclintransy(ref b2, a, b);
bcerrors = bcerrors | (double)(Math.Abs(a * ratint.barycentriccalc(ref b1, t) + b - ratint.barycentriccalc(ref b2, t))) > (double)(threshold);
}
}
for (pass = 0; pass <= 3; pass++)
{
//
// Crash-test: small numbers, large numbers
//
x = new double[4];
y = new double[4];
w = new double[4];
h = 1;
if (pass % 2 == 0)
{
h = 100 * AP.Math.MinRealNumber;
}
if (pass % 2 == 1)
{
h = 0.01 * AP.Math.MaxRealNumber;
}
x[0] = 0 * h;
x[1] = 1 * h;
x[2] = 2 * h;
x[3] = 3 * h;
y[0] = 0 * h;
y[1] = 1 * h;
y[2] = 2 * h;
y[3] = 3 * h;
w[0] = -(1 / (x[1] - x[0]));
w[1] = +(1 * (1 / (x[1] - x[0]) + 1 / (x[2] - x[1])));
w[2] = -(1 * (1 / (x[2] - x[1]) + 1 / (x[3] - x[2])));
w[3] = +(1 / (x[3] - x[2]));
if (pass / 2 == 0)
{
v0 = 0;
}
if (pass / 2 == 1)
{
v0 = 0.6 * h;
}
ratint.barycentricbuildxyw(ref x, ref y, ref w, 4, ref b1);
t = ratint.barycentriccalc(ref b1, v0);
d0 = 0;
d1 = 0;
d2 = 0;
ratint.barycentricdiff1(ref b1, v0, ref d0, ref d1);
bcerrors = bcerrors | (double)(Math.Abs(t - v0)) > (double)(threshold * v0);
bcerrors = bcerrors | (double)(Math.Abs(d0 - v0)) > (double)(threshold * v0);
bcerrors = bcerrors | (double)(Math.Abs(d1 - 1)) > (double)(1000 * threshold);
}
//
// crash test: large abscissas, small argument
//
// test for errors in D0 is not very strict
// because renormalization used in Diff1()
// destroys part of precision.
//
x = new double[4];
y = new double[4];
w = new double[4];
h = 0.01 * AP.Math.MaxRealNumber;
x[0] = 0 * h;
x[1] = 1 * h;
x[2] = 2 * h;
x[3] = 3 * h;
y[0] = 0 * h;
y[1] = 1 * h;
y[2] = 2 * h;
y[3] = 3 * h;
w[0] = -(1 / (x[1] - x[0]));
w[1] = +(1 * (1 / (x[1] - x[0]) + 1 / (x[2] - x[1])));
w[2] = -(1 * (1 / (x[2] - x[1]) + 1 / (x[3] - x[2])));
w[3] = +(1 / (x[3] - x[2]));
v0 = 100 * AP.Math.MinRealNumber;
ratint.barycentricbuildxyw(ref x, ref y, ref w, 4, ref b1);
t = ratint.barycentriccalc(ref b1, v0);
d0 = 0;
d1 = 0;
d2 = 0;
ratint.barycentricdiff1(ref b1, v0, ref d0, ref d1);
bcerrors = bcerrors | (double)(Math.Abs(t)) > (double)(v0 * (1 + threshold));
bcerrors = bcerrors | (double)(Math.Abs(d0)) > (double)(v0 * (1 + threshold));
bcerrors = bcerrors | (double)(Math.Abs(d1 - 1)) > (double)(1000 * threshold);
//
// crash test: test safe barycentric formula
//
x = new double[4];
y = new double[4];
w = new double[4];
h = 2 * AP.Math.MinRealNumber;
x[0] = 0 * h;
x[1] = 1 * h;
x[2] = 2 * h;
x[3] = 3 * h;
y[0] = 0 * h;
y[1] = 1 * h;
y[2] = 2 * h;
y[3] = 3 * h;
w[0] = -(1 / (x[1] - x[0]));
w[1] = +(1 * (1 / (x[1] - x[0]) + 1 / (x[2] - x[1])));
w[2] = -(1 * (1 / (x[2] - x[1]) + 1 / (x[3] - x[2])));
w[3] = +(1 / (x[3] - x[2]));
v0 = AP.Math.MinRealNumber;
ratint.barycentricbuildxyw(ref x, ref y, ref w, 4, ref b1);
t = ratint.barycentriccalc(ref b1, v0);
bcerrors = bcerrors | (double)(Math.Abs(t - v0) / v0) > (double)(threshold);
//
// Testing "No Poles" interpolation
//
maxerr = 0;
for (pass = 1; pass <= passcount - 1; pass++)
{
x = new double[1];
y = new double[1];
x[0] = 2 * AP.Math.RandomReal() - 1;
y[0] = 2 * AP.Math.RandomReal() - 1;
ratint.barycentricbuildfloaterhormann(ref x, ref y, 1, 1, ref b1);
maxerr = Math.Max(maxerr, Math.Abs(ratint.barycentriccalc(ref b1, 2 * AP.Math.RandomReal() - 1) - y[0]));
}
for (n = 2; n <= 10; n++)
{
//
// compare interpolant built by subroutine
// with interpolant built by hands
//
x = new double[n];
y = new double[n];
w = new double[n];
w2 = new double[n];
//
// D=1, non-equidistant nodes
//
for (pass = 1; pass <= passcount; pass++)
{
//
// Initialize X, Y, W
//
a = -1 - 1 * AP.Math.RandomReal();
b = +1 + 1 * AP.Math.RandomReal();
for (i = 0; i <= n - 1; i++)
{
x[i] = Math.Atan((b - a) * i / (n - 1) + a);
}
for (i = 0; i <= n - 1; i++)
{
y[i] = 2 * AP.Math.RandomReal() - 1;
}
w[0] = -(1 / (x[1] - x[0]));
s = 1;
for (i = 1; i <= n - 2; i++)
{
w[i] = s * (1 / (x[i] - x[i - 1]) + 1 / (x[i + 1] - x[i]));
s = -s;
}
w[n - 1] = s / (x[n - 1] - x[n - 2]);
for (i = 0; i <= n - 1; i++)
{
k = AP.Math.RandomInteger(n);
if (k != i)
{
t = x[i];
x[i] = x[k];
x[k] = t;
t = y[i];
y[i] = y[k];
y[k] = t;
t = w[i];
w[i] = w[k];
w[k] = t;
}
}
//
// Build and test
//
ratint.barycentricbuildfloaterhormann(ref x, ref y, n, 1, ref b1);
ratint.barycentricbuildxyw(ref x, ref y, ref w, n, ref b2);
for (i = 1; i <= 2 * n; i++)
{
t = a + (b - a) * AP.Math.RandomReal();
maxerr = Math.Max(maxerr, Math.Abs(ratint.barycentriccalc(ref b1, t) - ratint.barycentriccalc(ref b2, t)));
}
}
//
// D = 0, 1, 2. Equidistant nodes.
//
for (d = 0; d <= 2; d++)
{
for (pass = 1; pass <= passcount; pass++)
{
//
// Skip incorrect (N,D) pairs
//
if (n < 2 * d)
{
continue;
}
//
// Initialize X, Y, W
//
a = -1 - 1 * AP.Math.RandomReal();
b = +1 + 1 * AP.Math.RandomReal();
for (i = 0; i <= n - 1; i++)
{
x[i] = (b - a) * i / (n - 1) + a;
}
for (i = 0; i <= n - 1; i++)
{
y[i] = 2 * AP.Math.RandomReal() - 1;
}
s = 1;
if (d == 0)
{
for (i = 0; i <= n - 1; i++)
{
w[i] = s;
s = -s;
}
}
if (d == 1)
{
w[0] = -s;
for (i = 1; i <= n - 2; i++)
{
w[i] = 2 * s;
s = -s;
}
w[n - 1] = s;
}
if (d == 2)
{
w[0] = s;
w[1] = -(3 * s);
for (i = 2; i <= n - 3; i++)
{
w[i] = 4 * s;
s = -s;
}
w[n - 2] = 3 * s;
w[n - 1] = -s;
}
//
// Mix
//
for (i = 0; i <= n - 1; i++)
{
k = AP.Math.RandomInteger(n);
if (k != i)
{
t = x[i];
x[i] = x[k];
x[k] = t;
t = y[i];
y[i] = y[k];
y[k] = t;
t = w[i];
w[i] = w[k];
w[k] = t;
}
}
//
// Build and test
//
ratint.barycentricbuildfloaterhormann(ref x, ref y, n, d, ref b1);
ratint.barycentricbuildxyw(ref x, ref y, ref w, n, ref b2);
for (i = 1; i <= 2 * n; i++)
{
t = a + (b - a) * AP.Math.RandomReal();
maxerr = Math.Max(maxerr, Math.Abs(ratint.barycentriccalc(ref b1, t) - ratint.barycentriccalc(ref b2, t)));
}
}
}
}
if ((double)(maxerr) > (double)(threshold))
{
nperrors = true;
}
//
// Test rational fitting:
//
for (pass = 1; pass <= passcount; pass++)
{
for (n = 2; n <= maxn; n++)
{
//
// N=M+K fitting (i.e. interpolation)
//
for (k = 0; k <= n - 1; k++)
{
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] = (double)(i) / ((double)(n - 1));
y[i] = 2 * AP.Math.RandomReal() - 1;
w[i] = 1 + AP.Math.RandomReal();
}
for (i = 0; i <= k - 1; i++)
{
xc[i] = ((double)(n - k + i)) / ((double)(n - 1));
yc[i] = 2 * AP.Math.RandomReal() - 1;
dc[i] = 0;
}
ratint.barycentricfitfloaterhormannwc(ref x, ref y, ref w, n - k, ref xc, ref yc, ref dc, k, n, ref info, ref b1, ref rep);
if (info <= 0)
{
fiterrors = true;
}
else
{
for (i = 0; i <= n - k - 1; i++)
{
fiterrors = fiterrors | (double)(Math.Abs(ratint.barycentriccalc(ref b1, x[i]) - y[i])) > (double)(threshold);
}
for (i = 0; i <= k - 1; i++)
{
fiterrors = fiterrors | (double)(Math.Abs(ratint.barycentriccalc(ref b1, xc[i]) - yc[i])) > (double)(threshold);
}
}
}
//
// Testing constraints on derivatives:
// * several M's are tried
// * several K's are tried - 1, 2.
// * constraints at the ends of the interval
//
for (m = 3; m <= 5; m++)
{
for (k = 1; k <= 2; k++)
{
x = new double[n];
y = new double[n];
w = new double[n];
xc = new double[2];
yc = new double[2];
dc = new int[2];
for (i = 0; i <= n - 1; i++)
{
x[i] = 2 * AP.Math.RandomReal() - 1;
y[i] = 2 * AP.Math.RandomReal() - 1;
w[i] = 1 + AP.Math.RandomReal();
}
xc[0] = -1;
yc[0] = 2 * AP.Math.RandomReal() - 1;
dc[0] = 0;
xc[1] = +1;
yc[1] = 2 * AP.Math.RandomReal() - 1;
dc[1] = 0;
ratint.barycentricfitfloaterhormannwc(ref x, ref y, ref w, n, ref xc, ref yc, ref dc, k, m, ref info, ref b1, ref rep);
if (info <= 0)
{
fiterrors = true;
}
else
{
for (i = 0; i <= k - 1; i++)
{
ratint.barycentricdiff1(ref b1, xc[i], ref v0, ref v1);
fiterrors = fiterrors | (double)(Math.Abs(v0 - yc[i])) > (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 = AP.Math.MaxRealNumber;
xmax = -AP.Math.MaxRealNumber;
for (i = 0; i <= n - 1; i++)
{
x2[i] = 2 * Math.PI * AP.Math.RandomReal();
y2[i] = Math.Sin(x2[i]);
w2[i] = 1;
xmin = Math.Min(xmin, x2[i]);
xmax = Math.Max(xmax, x2[i]);
}
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]);
}
ratint.barycentricbuildfloaterhormann(ref x, ref y, m, 3, ref b1);
ratint.barycentricfitfloaterhormannwc(ref x2, ref y2, ref w2, n, ref xc, ref yc, ref dc, 0, m, ref info, ref b2, ref rep);
if (info <= 0)
{
fiterrors = true;
}
else
{
//
// calculate B1 (interpolant) RMS error, compare with B2 error
//
v1 = 0;
v2 = 0;
for (i = 0; i <= n - 1; i++)
{
v1 = v1 + AP.Math.Sqr(ratint.barycentriccalc(ref b1, x2[i]) - y2[i]);
v2 = v2 + AP.Math.Sqr(ratint.barycentriccalc(ref b2, 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 * AP.Math.RandomReal() - 1;
y[i] = 2 * AP.Math.RandomReal() - 1;
w[i] = 1;
}
ratint.barycentricfitfloaterhormannwc(ref x, ref y, ref w, n, ref xc, ref yc, ref dc, 0, m, ref info, ref b1, ref rep);
ratint.barycentricfitfloaterhormann(ref x, ref y, n, m, ref info2, ref b2, ref rep2);
if (info <= 0 | info2 <= 0)
{
fiterrors = true;
}
else
{
//
// calculate B1 (interpolant), compare with B2
// compare RMS errors
//
t = 2 * AP.Math.RandomReal() - 1;
v1 = ratint.barycentriccalc(ref b1, t);
v2 = ratint.barycentriccalc(ref b2, 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++)
{
System.Diagnostics.Debug.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 = AP.Math.RandomReal();
v2 = AP.Math.RandomReal();
v = 1 + AP.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((AP.Math.Sqr(v1) + AP.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
//
ratint.barycentricfitfloaterhormann(ref x, ref y, 4, 2, ref info, ref b1, ref rep);
if (info <= 0)
{
fiterrors = true;
}
else
{
s = ratint.barycentriccalc(ref b1, 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 = bcerrors | nperrors | fiterrors;
if (!silent)
{
System.Console.Write("TESTING RATIONAL INTERPOLATION");
System.Console.WriteLine();
System.Console.Write("BASIC BARYCENTRIC FUNCTIONS: ");
if (bcerrors)
{
System.Console.Write("FAILED");
System.Console.WriteLine();
}
else
{
System.Console.Write("OK");
System.Console.WriteLine();
}
System.Console.Write("FLOATER-HORMANN: ");
if (nperrors)
{
System.Console.Write("FAILED");
System.Console.WriteLine();
}
else
{
System.Console.Write("OK");
System.Console.WriteLine();
}
System.Console.Write("RATIONAL FITTING: ");
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);
}
