/*************************************************************************
Unset spline, i.e. initialize it with random garbage
*************************************************************************/
private static void unsetspline2d(ref spline2d.spline2dinterpolant c)
{
double[] x = new double[0];
double[] y = new double[0];
double[,] f = new double[0,0];
x = new double[2];
y = new double[2];
f = new double[2, 2];
x[0] = -1;
x[1] = +1;
y[0] = -1;
y[1] = +1;
f[0,0] = 0;
f[0,1] = 0;
f[1,0] = 0;
f[1,1] = 0;
spline2d.spline2dbuildbilinear(x, y, f, 2, 2, ref c);
}
/*************************************************************************
LinTrans test
*************************************************************************/
private static bool testlintrans(ref spline2d.spline2dinterpolant c,
double ax,
double bx,
double ay,
double by)
{
bool result = new bool();
double err = 0;
double a1 = 0;
double a2 = 0;
double b1 = 0;
double b2 = 0;
double tx = 0;
double ty = 0;
double vx = 0;
double vy = 0;
double v1 = 0;
double v2 = 0;
int pass = 0;
int passcount = 0;
int xjob = 0;
int yjob = 0;
spline2d.spline2dinterpolant c2 = new spline2d.spline2dinterpolant();
passcount = 5;
err = 0;
for(xjob=0; xjob<=1; xjob++)
{
for(yjob=0; yjob<=1; yjob++)
{
for(pass=1; pass<=passcount; pass++)
{
//
// Prepare
//
do
{
a1 = 2*AP.Math.RandomReal()-1;
}
while( (double)(a1)==(double)(0) );
a1 = a1*xjob;
b1 = 2*AP.Math.RandomReal()-1;
do
{
a2 = 2*AP.Math.RandomReal()-1;
}
while( (double)(a2)==(double)(0) );
a2 = a2*yjob;
b2 = 2*AP.Math.RandomReal()-1;
//
// Test XY
//
spline2d.spline2dcopy(ref c, ref c2);
spline2d.spline2dlintransxy(ref c2, a1, b1, a2, b2);
tx = ax+AP.Math.RandomReal()*(bx-ax);
ty = ay+AP.Math.RandomReal()*(by-ay);
if( xjob==0 )
{
tx = b1;
vx = ax+AP.Math.RandomReal()*(bx-ax);
}
else
{
vx = (tx-b1)/a1;
}
if( yjob==0 )
{
ty = b2;
vy = ay+AP.Math.RandomReal()*(by-ay);
}
else
{
vy = (ty-b2)/a2;
}
v1 = spline2d.spline2dcalc(ref c, tx, ty);
v2 = spline2d.spline2dcalc(ref c2, vx, vy);
err = Math.Max(err, Math.Abs(v1-v2));
//
// Test F
//
spline2d.spline2dcopy(ref c, ref c2);
spline2d.spline2dlintransf(ref c2, a1, b1);
tx = ax+AP.Math.RandomReal()*(bx-ax);
ty = ay+AP.Math.RandomReal()*(by-ay);
v1 = spline2d.spline2dcalc(ref c, tx, ty);
v2 = spline2d.spline2dcalc(ref c2, tx, ty);
err = Math.Max(err, Math.Abs(a1*v1+b1-v2));
}
}
}
result = (double)(err)<(double)(10000*AP.Math.MachineEpsilon);
return result;
}
/*************************************************************************
Numerical differentiation.
*************************************************************************/
private static void twodnumder(ref spline2d.spline2dinterpolant c,
double x,
double y,
double h,
ref double f,
ref double fx,
ref double fy,
ref double fxy)
{
f = spline2d.spline2dcalc(ref c, x, y);
fx = (spline2d.spline2dcalc(ref c, x+h, y)-spline2d.spline2dcalc(ref c, x-h, y))/(2*h);
fy = (spline2d.spline2dcalc(ref c, x, y+h)-spline2d.spline2dcalc(ref c, x, y-h))/(2*h);
fxy = (spline2d.spline2dcalc(ref c, x+h, y+h)-spline2d.spline2dcalc(ref c, x-h, y+h)-spline2d.spline2dcalc(ref c, x+h, y-h)+spline2d.spline2dcalc(ref c, x-h, y-h))/AP.Math.Sqr(2*h);
}
/*************************************************************************
Unpack test
*************************************************************************/
private static bool testunpack(ref spline2d.spline2dinterpolant c,
ref double[] lx,
ref double[] ly)
{
bool result = new bool();
int i = 0;
int j = 0;
int n = 0;
int m = 0;
int ci = 0;
int cj = 0;
int p = 0;
double err = 0;
double tx = 0;
double ty = 0;
double v1 = 0;
double v2 = 0;
int pass = 0;
int passcount = 0;
double[,] tbl = new double[0,0];
passcount = 20;
err = 0;
spline2d.spline2dunpack(ref c, ref m, ref n, ref tbl);
for(i=0; i<=m-2; i++)
{
for(j=0; j<=n-2; j++)
{
for(pass=1; pass<=passcount; pass++)
{
p = (n-1)*i+j;
tx = (0.001+0.999*AP.Math.RandomReal())*(tbl[p,1]-tbl[p,0]);
ty = (0.001+0.999*AP.Math.RandomReal())*(tbl[p,3]-tbl[p,2]);
//
// Interpolation properties
//
v1 = 0;
for(ci=0; ci<=3; ci++)
{
for(cj=0; cj<=3; cj++)
{
v1 = v1+tbl[p,4+ci*4+cj]*Math.Pow(tx, ci)*Math.Pow(ty, cj);
}
}
v2 = spline2d.spline2dcalc(ref c, tbl[p,0]+tx, tbl[p,2]+ty);
err = Math.Max(err, Math.Abs(v1-v2));
//
// Grid correctness
//
err = Math.Max(err, Math.Abs(lx[2*j]-tbl[p,0]));
err = Math.Max(err, Math.Abs(lx[2*(j+1)]-tbl[p,1]));
err = Math.Max(err, Math.Abs(ly[2*i]-tbl[p,2]));
err = Math.Max(err, Math.Abs(ly[2*(i+1)]-tbl[p,3]));
}
}
}
result = (double)(err)<(double)(10000*AP.Math.MachineEpsilon);
return result;
}
/*************************************************************************
Lipschitz constants for spline inself, first and second derivatives.
*************************************************************************/
private static void lconst(ref spline2d.spline2dinterpolant c,
ref double[] lx,
ref double[] ly,
int m,
int n,
double lstep,
ref double lc,
ref double lcx,
ref double lcy,
ref double lcxy)
{
int i = 0;
int j = 0;
double f1 = 0;
double f2 = 0;
double f3 = 0;
double f4 = 0;
double fx1 = 0;
double fx2 = 0;
double fx3 = 0;
double fx4 = 0;
double fy1 = 0;
double fy2 = 0;
double fy3 = 0;
double fy4 = 0;
double fxy1 = 0;
double fxy2 = 0;
double fxy3 = 0;
double fxy4 = 0;
double s2lstep = 0;
lc = 0;
lcx = 0;
lcy = 0;
lcxy = 0;
s2lstep = Math.Sqrt(2)*lstep;
for(i=0; i<=m-1; i++)
{
for(j=0; j<=n-1; j++)
{
//
// Calculate
//
twodnumder(ref c, lx[j]-lstep/2, ly[i]-lstep/2, lstep/4, ref f1, ref fx1, ref fy1, ref fxy1);
twodnumder(ref c, lx[j]+lstep/2, ly[i]-lstep/2, lstep/4, ref f2, ref fx2, ref fy2, ref fxy2);
twodnumder(ref c, lx[j]+lstep/2, ly[i]+lstep/2, lstep/4, ref f3, ref fx3, ref fy3, ref fxy3);
twodnumder(ref c, lx[j]-lstep/2, ly[i]+lstep/2, lstep/4, ref f4, ref fx4, ref fy4, ref fxy4);
//
// Lipschitz constant for the function itself
//
lc = Math.Max(lc, Math.Abs((f1-f2)/lstep));
lc = Math.Max(lc, Math.Abs((f2-f3)/lstep));
lc = Math.Max(lc, Math.Abs((f3-f4)/lstep));
lc = Math.Max(lc, Math.Abs((f4-f1)/lstep));
lc = Math.Max(lc, Math.Abs((f1-f3)/s2lstep));
lc = Math.Max(lc, Math.Abs((f2-f4)/s2lstep));
//
// Lipschitz constant for the first derivative
//
lcx = Math.Max(lcx, Math.Abs((fx1-fx2)/lstep));
lcx = Math.Max(lcx, Math.Abs((fx2-fx3)/lstep));
lcx = Math.Max(lcx, Math.Abs((fx3-fx4)/lstep));
lcx = Math.Max(lcx, Math.Abs((fx4-fx1)/lstep));
lcx = Math.Max(lcx, Math.Abs((fx1-fx3)/s2lstep));
lcx = Math.Max(lcx, Math.Abs((fx2-fx4)/s2lstep));
//
// Lipschitz constant for the first derivative
//
lcy = Math.Max(lcy, Math.Abs((fy1-fy2)/lstep));
lcy = Math.Max(lcy, Math.Abs((fy2-fy3)/lstep));
lcy = Math.Max(lcy, Math.Abs((fy3-fy4)/lstep));
lcy = Math.Max(lcy, Math.Abs((fy4-fy1)/lstep));
lcy = Math.Max(lcy, Math.Abs((fy1-fy3)/s2lstep));
lcy = Math.Max(lcy, Math.Abs((fy2-fy4)/s2lstep));
//
// Lipschitz constant for the cross-derivative
//
lcxy = Math.Max(lcxy, Math.Abs((fxy1-fxy2)/lstep));
lcxy = Math.Max(lcxy, Math.Abs((fxy2-fxy3)/lstep));
lcxy = Math.Max(lcxy, Math.Abs((fxy3-fxy4)/lstep));
lcxy = Math.Max(lcxy, Math.Abs((fxy4-fxy1)/lstep));
lcxy = Math.Max(lcxy, Math.Abs((fxy1-fxy3)/s2lstep));
lcxy = Math.Max(lcxy, Math.Abs((fxy2-fxy4)/s2lstep));
}
}
}