/*************************************************************************
* Noisy test:
* F = x^2 + y^2 + z^2 + noise on [-1,+1]^3
* space is either R1=[-1,+1] (other dimensions are
* fixed at 0), R1^2 or R1^3.
* D = 1, 2
* 4096 points is used for function generation,
* 4096 points - for testing
* RMS error of "noisy" model on test set must be
* lower than RMS error of interpolation model.
*************************************************************************/
private static void testnoisy(ref bool idwerrors)
{
double noiselevel = 0;
int nq = 0;
int nw = 0;
int d = 0;
int nx = 0;
int ntrn = 0;
int ntst = 0;
int i = 0;
int j = 0;
double v = 0;
double t = 0;
double v1 = 0;
double v2 = 0;
double ve = 0;
double[,] xy = new double[0, 0];
double[] x = new double[0];
idwint.idwinterpolant z1 = new idwint.idwinterpolant();
idwint.idwinterpolant z2 = new idwint.idwinterpolant();
double rms1 = 0;
double rms2 = 0;
nq = 20;
nw = 40;
noiselevel = 0.2;
ntrn = 256;
ntst = 1024;
for (d = 1; d <= 2; d++)
{
for (nx = 1; nx <= 2; nx++)
{
//
// prepare dataset
//
xy = new double[ntrn, nx + 1];
for (i = 0; i <= ntrn - 1; i++)
{
v = noiselevel * (2 * AP.Math.RandomReal() - 1);
for (j = 0; j <= nx - 1; j++)
{
t = 2 * AP.Math.RandomReal() - 1;
v = v + AP.Math.Sqr(t);
xy[i, j] = t;
}
xy[i, nx] = v;
}
//
// build interpolants
//
idwint.idwbuildmodifiedshepard(ref xy, ntrn, nx, d, nq, nw, ref z1);
idwint.idwbuildnoisy(ref xy, ntrn, nx, d, nq, nw, ref z2);
//
// calculate RMS errors
//
x = new double[nx];
rms1 = 0;
rms2 = 0;
for (i = 0; i <= ntst - 1; i++)
{
ve = 0;
for (j = 0; j <= nx - 1; j++)
{
t = 2 * AP.Math.RandomReal() - 1;
x[j] = t;
ve = ve + AP.Math.Sqr(t);
}
v1 = idwint.idwcalc(ref z1, ref x);
v2 = idwint.idwcalc(ref z2, ref x);
rms1 = rms1 + AP.Math.Sqr(v1 - ve);
rms2 = rms2 + AP.Math.Sqr(v2 - ve);
}
idwerrors = idwerrors | (double)(rms2) > (double)(rms1);
}
}
}
/*************************************************************************
* Testing degree properties
*
* F is either:
* constant (DTask=0)
* linear (DTask=1)
* quadratic (DTask=2)
*
* Nodal functions are either
* constant (D=0)
* linear (D=1)
* quadratic (D=2)
*
* When DTask<=D, we can interpolate without errors.
* When DTask>D, we MUST have errors.
*************************************************************************/
private static void testdegree(int n,
int nx,
int d,
int dtask,
ref bool idwerrors)
{
double threshold = 0;
int nq = 0;
int nw = 0;
int i = 0;
int j = 0;
double v = 0;
double c0 = 0;
double[] c1 = new double[0];
double[,] c2 = new double[0, 0];
double[] x = new double[0];
double[,] xy = new double[0, 0];
idwint.idwinterpolant z1 = new idwint.idwinterpolant();
double v1 = 0;
double v2 = 0;
int i_ = 0;
threshold = 1.0E6 * AP.Math.MachineEpsilon;
nq = 2 * (nx * nx + nx + 1);
nw = 10;
System.Diagnostics.Debug.Assert(nq <= n, "TestDegree: internal error");
//
// prepare model
//
c0 = 2 * AP.Math.RandomReal() - 1;
c1 = new double[nx];
for (i = 0; i <= nx - 1; i++)
{
c1[i] = 2 * AP.Math.RandomReal() - 1;
}
c2 = new double[nx, nx];
for (i = 0; i <= nx - 1; i++)
{
for (j = i + 1; j <= nx - 1; j++)
{
c2[i, j] = 2 * AP.Math.RandomReal() - 1;
c2[j, i] = c2[i, j];
}
do
{
c2[i, i] = 2 * AP.Math.RandomReal() - 1;
}while((double)(Math.Abs(c2[i, i])) <= (double)(0.3));
}
//
// prepare points
//
xy = new double[n, nx + 1];
for (i = 0; i <= n - 1; i++)
{
for (j = 0; j <= nx - 1; j++)
{
xy[i, j] = 4 * AP.Math.RandomReal() - 2;
}
xy[i, nx] = c0;
if (dtask >= 1)
{
v = 0.0;
for (i_ = 0; i_ <= nx - 1; i_++)
{
v += c1[i_] * xy[i, i_];
}
xy[i, nx] = xy[i, nx] + v;
}
if (dtask == 2)
{
for (j = 0; j <= nx - 1; j++)
{
v = 0.0;
for (i_ = 0; i_ <= nx - 1; i_++)
{
v += c2[j, i_] * xy[i, i_];
}
xy[i, nx] = xy[i, nx] + xy[i, j] * v;
}
}
}
//
// build interpolant, calculate value at random point
//
idwint.idwbuildmodifiedshepard(ref xy, n, nx, d, nq, nw, ref z1);
x = new double[nx];
for (i = 0; i <= nx - 1; i++)
{
x[i] = 4 * AP.Math.RandomReal() - 2;
}
v1 = idwint.idwcalc(ref z1, ref x);
//
// calculate model value at the same point
//
v2 = c0;
if (dtask >= 1)
{
v = 0.0;
for (i_ = 0; i_ <= nx - 1; i_++)
{
v += c1[i_] * x[i_];
}
v2 = v2 + v;
}
if (dtask == 2)
{
for (j = 0; j <= nx - 1; j++)
{
v = 0.0;
for (i_ = 0; i_ <= nx - 1; i_++)
{
v += c2[j, i_] * x[i_];
}
v2 = v2 + x[j] * v;
}
}
//
// Compare
//
if (dtask <= d)
{
idwerrors = idwerrors | (double)(Math.Abs(v2 - v1)) > (double)(threshold);
}
else
{
idwerrors = idwerrors | (double)(Math.Abs(v2 - v1)) < (double)(threshold);
}
}
/*************************************************************************
* Testing IDW:
* generate model using R-based model
* test basic properties
*************************************************************************/
private static void testrxy(ref double[,] xy,
int n,
int nx,
double r,
ref bool idwerrors)
{
double threshold = 0;
double lipschitzstep = 0;
int i = 0;
int j = 0;
int i1 = 0;
int i2 = 0;
double v = 0;
double v1 = 0;
double v2 = 0;
double t = 0;
double l1 = 0;
double l2 = 0;
idwint.idwinterpolant z1 = new idwint.idwinterpolant();
double[] x = new double[0];
int i_ = 0;
threshold = 1000 * AP.Math.MachineEpsilon;
lipschitzstep = 0.001;
x = new double[nx];
//
// build
//
idwint.idwbuildmodifiedshepardr(ref xy, n, nx, r, ref z1);
//
// first, test interpolation properties at nodes
//
for (i = 0; i <= n - 1; i++)
{
for (i_ = 0; i_ <= nx - 1; i_++)
{
x[i_] = xy[i, i_];
}
idwerrors = idwerrors | (double)(idwint.idwcalc(ref z1, ref x)) != (double)(xy[i, nx]);
}
//
// test Lipschitz continuity
//
i1 = AP.Math.RandomInteger(n);
do
{
i2 = AP.Math.RandomInteger(n);
}while(i2 == i1);
l1 = 0;
t = 0;
while ((double)(t) < (double)(1))
{
v = 1 - t;
for (i_ = 0; i_ <= nx - 1; i_++)
{
x[i_] = v * xy[i1, i_];
}
v = t;
for (i_ = 0; i_ <= nx - 1; i_++)
{
x[i_] = x[i_] + v * xy[i2, i_];
}
v1 = idwint.idwcalc(ref z1, ref x);
v = 1 - (t + lipschitzstep);
for (i_ = 0; i_ <= nx - 1; i_++)
{
x[i_] = v * xy[i1, i_];
}
v = t + lipschitzstep;
for (i_ = 0; i_ <= nx - 1; i_++)
{
x[i_] = x[i_] + v * xy[i2, i_];
}
v2 = idwint.idwcalc(ref z1, ref x);
l1 = Math.Max(l1, Math.Abs(v2 - v1) / lipschitzstep);
t = t + lipschitzstep;
}
l2 = 0;
t = 0;
while ((double)(t) < (double)(1))
{
v = 1 - t;
for (i_ = 0; i_ <= nx - 1; i_++)
{
x[i_] = v * xy[i1, i_];
}
v = t;
for (i_ = 0; i_ <= nx - 1; i_++)
{
x[i_] = x[i_] + v * xy[i2, i_];
}
v1 = idwint.idwcalc(ref z1, ref x);
v = 1 - (t + lipschitzstep / 3);
for (i_ = 0; i_ <= nx - 1; i_++)
{
x[i_] = v * xy[i1, i_];
}
v = t + lipschitzstep / 3;
for (i_ = 0; i_ <= nx - 1; i_++)
{
x[i_] = x[i_] + v * xy[i2, i_];
}
v2 = idwint.idwcalc(ref z1, ref x);
l2 = Math.Max(l2, Math.Abs(v2 - v1) / (lipschitzstep / 3));
t = t + lipschitzstep / 3;
}
idwerrors = idwerrors | (double)(l2) > (double)(2.0 * l1);
}
/*************************************************************************
Noisy test:
* F = x^2 + y^2 + z^2 + noise on [-1,+1]^3
* space is either R1=[-1,+1] (other dimensions are
fixed at 0), R1^2 or R1^3.
* D = 1, 2
* 4096 points is used for function generation,
4096 points - for testing
* RMS error of "noisy" model on test set must be
lower than RMS error of interpolation model.
*************************************************************************/
private static void testnoisy(ref bool idwerrors)
{
double noiselevel = 0;
int nq = 0;
int nw = 0;
int d = 0;
int nx = 0;
int ntrn = 0;
int ntst = 0;
int i = 0;
int j = 0;
double v = 0;
double t = 0;
double v1 = 0;
double v2 = 0;
double ve = 0;
double[,] xy = new double[0,0];
double[] x = new double[0];
idwint.idwinterpolant z1 = new idwint.idwinterpolant();
idwint.idwinterpolant z2 = new idwint.idwinterpolant();
double rms1 = 0;
double rms2 = 0;
nq = 20;
nw = 40;
noiselevel = 0.2;
ntrn = 256;
ntst = 1024;
for(d=1; d<=2; d++)
{
for(nx=1; nx<=2; nx++)
{
//
// prepare dataset
//
xy = new double[ntrn, nx+1];
for(i=0; i<=ntrn-1; i++)
{
v = noiselevel*(2*AP.Math.RandomReal()-1);
for(j=0; j<=nx-1; j++)
{
t = 2*AP.Math.RandomReal()-1;
v = v+AP.Math.Sqr(t);
xy[i,j] = t;
}
xy[i,nx] = v;
}
//
// build interpolants
//
idwint.idwbuildmodifiedshepard(ref xy, ntrn, nx, d, nq, nw, ref z1);
idwint.idwbuildnoisy(ref xy, ntrn, nx, d, nq, nw, ref z2);
//
// calculate RMS errors
//
x = new double[nx];
rms1 = 0;
rms2 = 0;
for(i=0; i<=ntst-1; i++)
{
ve = 0;
for(j=0; j<=nx-1; j++)
{
t = 2*AP.Math.RandomReal()-1;
x[j] = t;
ve = ve+AP.Math.Sqr(t);
}
v1 = idwint.idwcalc(ref z1, ref x);
v2 = idwint.idwcalc(ref z2, ref x);
rms1 = rms1+AP.Math.Sqr(v1-ve);
rms2 = rms2+AP.Math.Sqr(v2-ve);
}
idwerrors = idwerrors | (double)(rms2)>(double)(rms1);
}
}
}
/*************************************************************************
Testing degree properties
F is either:
* constant (DTask=0)
* linear (DTask=1)
* quadratic (DTask=2)
Nodal functions are either
* constant (D=0)
* linear (D=1)
* quadratic (D=2)
When DTask<=D, we can interpolate without errors.
When DTask>D, we MUST have errors.
*************************************************************************/
private static void testdegree(int n,
int nx,
int d,
int dtask,
ref bool idwerrors)
{
double threshold = 0;
int nq = 0;
int nw = 0;
int i = 0;
int j = 0;
double v = 0;
double c0 = 0;
double[] c1 = new double[0];
double[,] c2 = new double[0,0];
double[] x = new double[0];
double[,] xy = new double[0,0];
idwint.idwinterpolant z1 = new idwint.idwinterpolant();
double v1 = 0;
double v2 = 0;
int i_ = 0;
threshold = 1.0E6*AP.Math.MachineEpsilon;
nq = 2*(nx*nx+nx+1);
nw = 10;
System.Diagnostics.Debug.Assert(nq<=n, "TestDegree: internal error");
//
// prepare model
//
c0 = 2*AP.Math.RandomReal()-1;
c1 = new double[nx];
for(i=0; i<=nx-1; i++)
{
c1[i] = 2*AP.Math.RandomReal()-1;
}
c2 = new double[nx, nx];
for(i=0; i<=nx-1; i++)
{
for(j=i+1; j<=nx-1; j++)
{
c2[i,j] = 2*AP.Math.RandomReal()-1;
c2[j,i] = c2[i,j];
}
do
{
c2[i,i] = 2*AP.Math.RandomReal()-1;
}
while( (double)(Math.Abs(c2[i,i]))<=(double)(0.3) );
}
//
// prepare points
//
xy = new double[n, nx+1];
for(i=0; i<=n-1; i++)
{
for(j=0; j<=nx-1; j++)
{
xy[i,j] = 4*AP.Math.RandomReal()-2;
}
xy[i,nx] = c0;
if( dtask>=1 )
{
v = 0.0;
for(i_=0; i_<=nx-1;i_++)
{
v += c1[i_]*xy[i,i_];
}
xy[i,nx] = xy[i,nx]+v;
}
if( dtask==2 )
{
for(j=0; j<=nx-1; j++)
{
v = 0.0;
for(i_=0; i_<=nx-1;i_++)
{
v += c2[j,i_]*xy[i,i_];
}
xy[i,nx] = xy[i,nx]+xy[i,j]*v;
}
}
}
//
// build interpolant, calculate value at random point
//
idwint.idwbuildmodifiedshepard(ref xy, n, nx, d, nq, nw, ref z1);
x = new double[nx];
for(i=0; i<=nx-1; i++)
{
x[i] = 4*AP.Math.RandomReal()-2;
}
v1 = idwint.idwcalc(ref z1, ref x);
//
// calculate model value at the same point
//
v2 = c0;
if( dtask>=1 )
{
v = 0.0;
for(i_=0; i_<=nx-1;i_++)
{
v += c1[i_]*x[i_];
}
v2 = v2+v;
}
if( dtask==2 )
{
for(j=0; j<=nx-1; j++)
{
v = 0.0;
for(i_=0; i_<=nx-1;i_++)
{
v += c2[j,i_]*x[i_];
}
v2 = v2+x[j]*v;
}
}
//
// Compare
//
if( dtask<=d )
{
idwerrors = idwerrors | (double)(Math.Abs(v2-v1))>(double)(threshold);
}
else
{
idwerrors = idwerrors | (double)(Math.Abs(v2-v1))<(double)(threshold);
}
}
/*************************************************************************
Testing IDW:
* generate model using R-based model
* test basic properties
*************************************************************************/
private static void testrxy(ref double[,] xy,
int n,
int nx,
double r,
ref bool idwerrors)
{
double threshold = 0;
double lipschitzstep = 0;
int i = 0;
int j = 0;
int i1 = 0;
int i2 = 0;
double v = 0;
double v1 = 0;
double v2 = 0;
double t = 0;
double l1 = 0;
double l2 = 0;
idwint.idwinterpolant z1 = new idwint.idwinterpolant();
double[] x = new double[0];
int i_ = 0;
threshold = 1000*AP.Math.MachineEpsilon;
lipschitzstep = 0.001;
x = new double[nx];
//
// build
//
idwint.idwbuildmodifiedshepardr(ref xy, n, nx, r, ref z1);
//
// first, test interpolation properties at nodes
//
for(i=0; i<=n-1; i++)
{
for(i_=0; i_<=nx-1;i_++)
{
x[i_] = xy[i,i_];
}
idwerrors = idwerrors | (double)(idwint.idwcalc(ref z1, ref x))!=(double)(xy[i,nx]);
}
//
// test Lipschitz continuity
//
i1 = AP.Math.RandomInteger(n);
do
{
i2 = AP.Math.RandomInteger(n);
}
while( i2==i1 );
l1 = 0;
t = 0;
while( (double)(t)<(double)(1) )
{
v = 1-t;
for(i_=0; i_<=nx-1;i_++)
{
x[i_] = v*xy[i1,i_];
}
v = t;
for(i_=0; i_<=nx-1;i_++)
{
x[i_] = x[i_] + v*xy[i2,i_];
}
v1 = idwint.idwcalc(ref z1, ref x);
v = 1-(t+lipschitzstep);
for(i_=0; i_<=nx-1;i_++)
{
x[i_] = v*xy[i1,i_];
}
v = t+lipschitzstep;
for(i_=0; i_<=nx-1;i_++)
{
x[i_] = x[i_] + v*xy[i2,i_];
}
v2 = idwint.idwcalc(ref z1, ref x);
l1 = Math.Max(l1, Math.Abs(v2-v1)/lipschitzstep);
t = t+lipschitzstep;
}
l2 = 0;
t = 0;
while( (double)(t)<(double)(1) )
{
v = 1-t;
for(i_=0; i_<=nx-1;i_++)
{
x[i_] = v*xy[i1,i_];
}
v = t;
for(i_=0; i_<=nx-1;i_++)
{
x[i_] = x[i_] + v*xy[i2,i_];
}
v1 = idwint.idwcalc(ref z1, ref x);
v = 1-(t+lipschitzstep/3);
for(i_=0; i_<=nx-1;i_++)
{
x[i_] = v*xy[i1,i_];
}
v = t+lipschitzstep/3;
for(i_=0; i_<=nx-1;i_++)
{
x[i_] = x[i_] + v*xy[i2,i_];
}
v2 = idwint.idwcalc(ref z1, ref x);
l2 = Math.Max(l2, Math.Abs(v2-v1)/(lipschitzstep/3));
t = t+lipschitzstep/3;
}
idwerrors = idwerrors | (double)(l2)>(double)(2.0*l1);
}