/*************************************************************************
LinTrans test
*************************************************************************/
private static bool testlintrans(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*math.randomreal()-1;
}
while( (double)(a1)==(double)(0) );
a1 = a1*xjob;
b1 = 2*math.randomreal()-1;
do
{
a2 = 2*math.randomreal()-1;
}
while( (double)(a2)==(double)(0) );
a2 = a2*yjob;
b2 = 2*math.randomreal()-1;
//
// Test XY
//
spline2d.spline2dcopy(c, c2);
spline2d.spline2dlintransxy(c2, a1, b1, a2, b2);
tx = ax+math.randomreal()*(bx-ax);
ty = ay+math.randomreal()*(by-ay);
if( xjob==0 )
{
tx = b1;
vx = ax+math.randomreal()*(bx-ax);
}
else
{
vx = (tx-b1)/a1;
}
if( yjob==0 )
{
ty = b2;
vy = ay+math.randomreal()*(by-ay);
}
else
{
vy = (ty-b2)/a2;
}
v1 = spline2d.spline2dcalc(c, tx, ty);
v2 = spline2d.spline2dcalc(c2, vx, vy);
err = Math.Max(err, Math.Abs(v1-v2));
//
// Test F
//
spline2d.spline2dcopy(c, c2);
spline2d.spline2dlintransf(c2, a1, b1);
tx = ax+math.randomreal()*(bx-ax);
ty = ay+math.randomreal()*(by-ay);
v1 = spline2d.spline2dcalc(c, tx, ty);
v2 = spline2d.spline2dcalc(c2, tx, ty);
err = Math.Max(err, Math.Abs(a1*v1+b1-v2));
}
}
}
result = (double)(err)<(double)(10000*math.machineepsilon);
return result;
}
public spline2dinterpolant(spline2d.spline2dinterpolant obj)
{
_innerobj = obj;
}
public static bool testspline2d(bool silent)
{
bool result = new bool();
bool waserrors = new bool();
bool blerrors = new bool();
bool bcerrors = new bool();
bool dserrors = new bool();
bool cperrors = new bool();
bool uperrors = new bool();
bool lterrors = new bool();
bool syerrors = new bool();
bool rlerrors = new bool();
bool rcerrors = new bool();
int pass = 0;
int passcount = 0;
int jobtype = 0;
double lstep = 0;
double h = 0;
double[] x = new double[0];
double[] y = new double[0];
spline2d.spline2dinterpolant c = new spline2d.spline2dinterpolant();
spline2d.spline2dinterpolant c2 = new spline2d.spline2dinterpolant();
double[] lx = new double[0];
double[] ly = new double[0];
double[,] f = new double[0,0];
double[,] fr = new double[0,0];
double[,] ft = new double[0,0];
double ax = 0;
double ay = 0;
double bx = 0;
double by = 0;
int i = 0;
int j = 0;
int k = 0;
int n = 0;
int m = 0;
int n2 = 0;
int m2 = 0;
double err = 0;
double t = 0;
double t1 = 0;
double t2 = 0;
double l1 = 0;
double l1x = 0;
double l1y = 0;
double l1xy = 0;
double l2 = 0;
double l2x = 0;
double l2y = 0;
double l2xy = 0;
double fm = 0;
double f1 = 0;
double f2 = 0;
double f3 = 0;
double f4 = 0;
double v1 = 0;
double v1x = 0;
double v1y = 0;
double v1xy = 0;
double v2 = 0;
double v2x = 0;
double v2y = 0;
double v2xy = 0;
double mf = 0;
waserrors = false;
passcount = 10;
h = 0.00001;
lstep = 0.001;
blerrors = false;
bcerrors = false;
dserrors = false;
cperrors = false;
uperrors = false;
lterrors = false;
syerrors = false;
rlerrors = false;
rcerrors = false;
//
// Test: bilinear, bicubic
//
for(n=2; n<=7; n++)
{
for(m=2; m<=7; m++)
{
x = new double[n-1+1];
y = new double[m-1+1];
lx = new double[2*n-2+1];
ly = new double[2*m-2+1];
f = new double[m-1+1, n-1+1];
ft = new double[n-1+1, m-1+1];
for(pass=1; pass<=passcount; pass++)
{
//
// Prepare task:
// * X and Y stores grid
// * F stores function values
// * LX and LY stores twice dense grid (for Lipschitz testing)
//
ax = -1-math.randomreal();
bx = 1+math.randomreal();
ay = -1-math.randomreal();
by = 1+math.randomreal();
for(j=0; j<=n-1; j++)
{
x[j] = 0.5*(bx+ax)-0.5*(bx-ax)*Math.Cos(Math.PI*(2*j+1)/(2*n));
if( j==0 )
{
x[j] = ax;
}
if( j==n-1 )
{
x[j] = bx;
}
lx[2*j] = x[j];
if( j>0 )
{
lx[2*j-1] = 0.5*(x[j]+x[j-1]);
}
}
for(j=0; j<=n-1; j++)
{
k = math.randominteger(n);
if( k!=j )
{
t = x[j];
x[j] = x[k];
x[k] = t;
}
}
for(i=0; i<=m-1; i++)
{
y[i] = 0.5*(by+ay)-0.5*(by-ay)*Math.Cos(Math.PI*(2*i+1)/(2*m));
if( i==0 )
{
y[i] = ay;
}
if( i==m-1 )
{
y[i] = by;
}
ly[2*i] = y[i];
if( i>0 )
{
ly[2*i-1] = 0.5*(y[i]+y[i-1]);
}
}
for(i=0; i<=m-1; i++)
{
k = math.randominteger(m);
if( k!=i )
{
t = y[i];
y[i] = y[k];
y[k] = t;
}
}
for(i=0; i<=m-1; i++)
{
for(j=0; j<=n-1; j++)
{
f[i,j] = Math.Exp(0.6*x[j])-Math.Exp(-(0.3*y[i])+0.08*x[j])+2*Math.Cos(Math.PI*(x[j]+1.2*y[i]))+0.1*Math.Cos(20*x[j]+15*y[i]);
}
}
//
// Test bilinear interpolation:
// * interpolation at the nodes
// * linearity
// * continuity
// * differentiation in the inner points
//
spline2d.spline2dbuildbilinear(x, y, f, m, n, c);
err = 0;
for(i=0; i<=m-1; i++)
{
for(j=0; j<=n-1; j++)
{
err = Math.Max(err, Math.Abs(f[i,j]-spline2d.spline2dcalc(c, x[j], y[i])));
}
}
blerrors = blerrors | (double)(err)>(double)(10000*math.machineepsilon);
err = 0;
for(i=0; i<=m-2; i++)
{
for(j=0; j<=n-2; j++)
{
//
// Test for linearity between grid points
// (test point - geometric center of the cell)
//
fm = spline2d.spline2dcalc(c, lx[2*j+1], ly[2*i+1]);
f1 = spline2d.spline2dcalc(c, lx[2*j], ly[2*i]);
f2 = spline2d.spline2dcalc(c, lx[2*j+2], ly[2*i]);
f3 = spline2d.spline2dcalc(c, lx[2*j+2], ly[2*i+2]);
f4 = spline2d.spline2dcalc(c, lx[2*j], ly[2*i+2]);
err = Math.Max(err, Math.Abs(0.25*(f1+f2+f3+f4)-fm));
}
}
blerrors = blerrors | (double)(err)>(double)(10000*math.machineepsilon);
lconst(c, lx, ly, m, n, lstep, ref l1, ref l1x, ref l1y, ref l1xy);
lconst(c, lx, ly, m, n, lstep/3, ref l2, ref l2x, ref l2y, ref l2xy);
blerrors = blerrors | (double)(l2/l1)>(double)(1.2);
err = 0;
for(i=0; i<=m-2; i++)
{
for(j=0; j<=n-2; j++)
{
spline2d.spline2ddiff(c, lx[2*j+1], ly[2*i+1], ref v1, ref v1x, ref v1y, ref v1xy);
twodnumder(c, lx[2*j+1], ly[2*i+1], h, ref v2, ref v2x, ref v2y, ref v2xy);
err = Math.Max(err, Math.Abs(v1-v2));
err = Math.Max(err, Math.Abs(v1x-v2x));
err = Math.Max(err, Math.Abs(v1y-v2y));
err = Math.Max(err, Math.Abs(v1xy-v2xy));
}
}
dserrors = dserrors | (double)(err)>(double)(1.0E-3);
uperrors = uperrors | !testunpack(c, lx, ly);
lterrors = lterrors | !testlintrans(c, ax, bx, ay, by);
//
// Test bicubic interpolation.
// * interpolation at the nodes
// * smoothness
// * differentiation
//
spline2d.spline2dbuildbicubic(x, y, f, m, n, c);
err = 0;
for(i=0; i<=m-1; i++)
{
for(j=0; j<=n-1; j++)
{
err = Math.Max(err, Math.Abs(f[i,j]-spline2d.spline2dcalc(c, x[j], y[i])));
}
}
bcerrors = bcerrors | (double)(err)>(double)(10000*math.machineepsilon);
lconst(c, lx, ly, m, n, lstep, ref l1, ref l1x, ref l1y, ref l1xy);
lconst(c, lx, ly, m, n, lstep/3, ref l2, ref l2x, ref l2y, ref l2xy);
bcerrors = bcerrors | (double)(l2/l1)>(double)(1.2);
bcerrors = bcerrors | (double)(l2x/l1x)>(double)(1.2);
bcerrors = bcerrors | (double)(l2y/l1y)>(double)(1.2);
if( (double)(l2xy)>(double)(0.01) & (double)(l1xy)>(double)(0.01) )
{
//
// Cross-derivative continuity is tested only when
// bigger than 0.01. When the task size is too
// small, the d2F/dXdY is nearly zero and Lipschitz
// constant ratio is ill-conditioned.
//
bcerrors = bcerrors | (double)(l2xy/l1xy)>(double)(1.2);
}
err = 0;
for(i=0; i<=2*m-2; i++)
{
for(j=0; j<=2*n-2; j++)
{
spline2d.spline2ddiff(c, lx[j], ly[i], ref v1, ref v1x, ref v1y, ref v1xy);
twodnumder(c, lx[j], ly[i], h, ref v2, ref v2x, ref v2y, ref v2xy);
err = Math.Max(err, Math.Abs(v1-v2));
err = Math.Max(err, Math.Abs(v1x-v2x));
err = Math.Max(err, Math.Abs(v1y-v2y));
err = Math.Max(err, Math.Abs(v1xy-v2xy));
}
}
dserrors = dserrors | (double)(err)>(double)(1.0E-3);
uperrors = uperrors | !testunpack(c, lx, ly);
lterrors = lterrors | !testlintrans(c, ax, bx, ay, by);
//
// Copy/Serialise test
//
if( (double)(math.randomreal())>(double)(0.5) )
{
spline2d.spline2dbuildbicubic(x, y, f, m, n, c);
}
else
{
spline2d.spline2dbuildbilinear(x, y, f, m, n, c);
}
unsetspline2d(c2);
spline2d.spline2dcopy(c, c2);
err = 0;
for(i=1; i<=5; i++)
{
t1 = ax+(bx-ax)*math.randomreal();
t2 = ay+(by-ay)*math.randomreal();
err = Math.Max(err, Math.Abs(spline2d.spline2dcalc(c, t1, t2)-spline2d.spline2dcalc(c2, t1, t2)));
}
cperrors = cperrors | (double)(err)>(double)(10000*math.machineepsilon);
//
// Special symmetry test
//
err = 0;
for(jobtype=0; jobtype<=1; jobtype++)
{
//
// Prepare
//
for(i=0; i<=m-1; i++)
{
for(j=0; j<=n-1; j++)
{
ft[j,i] = f[i,j];
}
}
if( jobtype==0 )
{
spline2d.spline2dbuildbilinear(x, y, f, m, n, c);
spline2d.spline2dbuildbilinear(y, x, ft, n, m, c2);
}
else
{
spline2d.spline2dbuildbicubic(x, y, f, m, n, c);
spline2d.spline2dbuildbicubic(y, x, ft, n, m, c2);
}
//
// Test
//
for(i=1; i<=10; i++)
{
t1 = ax+(bx-ax)*math.randomreal();
t2 = ay+(by-ay)*math.randomreal();
err = Math.Max(err, Math.Abs(spline2d.spline2dcalc(c, t1, t2)-spline2d.spline2dcalc(c2, t2, t1)));
}
}
syerrors = syerrors | (double)(err)>(double)(10000*math.machineepsilon);
}
}
}
//
// Test resample
//
for(m=2; m<=6; m++)
{
for(n=2; n<=6; n++)
{
f = new double[m-1+1, n-1+1];
x = new double[n-1+1];
y = new double[m-1+1];
for(j=0; j<=n-1; j++)
{
x[j] = (double)j/(double)(n-1);
}
for(i=0; i<=m-1; i++)
{
y[i] = (double)i/(double)(m-1);
}
for(i=0; i<=m-1; i++)
{
for(j=0; j<=n-1; j++)
{
f[i,j] = Math.Exp(0.6*x[j])-Math.Exp(-(0.3*y[i])+0.08*x[j])+2*Math.Cos(Math.PI*(x[j]+1.2*y[i]))+0.1*Math.Cos(20*x[j]+15*y[i]);
}
}
for(m2=2; m2<=6; m2++)
{
for(n2=2; n2<=6; n2++)
{
for(pass=1; pass<=passcount; pass++)
{
for(jobtype=0; jobtype<=1; jobtype++)
{
if( jobtype==0 )
{
spline2d.spline2dresamplebilinear(f, m, n, ref fr, m2, n2);
spline2d.spline2dbuildbilinear(x, y, f, m, n, c);
}
if( jobtype==1 )
{
spline2d.spline2dresamplebicubic(f, m, n, ref fr, m2, n2);
spline2d.spline2dbuildbicubic(x, y, f, m, n, c);
}
err = 0;
mf = 0;
for(i=0; i<=m2-1; i++)
{
for(j=0; j<=n2-1; j++)
{
v1 = spline2d.spline2dcalc(c, (double)j/(double)(n2-1), (double)i/(double)(m2-1));
v2 = fr[i,j];
err = Math.Max(err, Math.Abs(v1-v2));
mf = Math.Max(mf, Math.Abs(v1));
}
}
if( jobtype==0 )
{
rlerrors = rlerrors | (double)(err/mf)>(double)(10000*math.machineepsilon);
}
if( jobtype==1 )
{
rcerrors = rcerrors | (double)(err/mf)>(double)(10000*math.machineepsilon);
}
}
}
}
}
}
}
//
// report
//
waserrors = (((((((blerrors | bcerrors) | dserrors) | cperrors) | uperrors) | lterrors) | syerrors) | rlerrors) | rcerrors;
if( !silent )
{
System.Console.Write("TESTING 2D INTERPOLATION");
System.Console.WriteLine();
//
// Normal tests
//
System.Console.Write("BILINEAR TEST: ");
if( blerrors )
{
System.Console.Write("FAILED");
System.Console.WriteLine();
}
else
{
System.Console.Write("OK");
System.Console.WriteLine();
}
System.Console.Write("BICUBIC TEST: ");
if( bcerrors )
{
System.Console.Write("FAILED");
System.Console.WriteLine();
}
else
{
System.Console.Write("OK");
System.Console.WriteLine();
}
System.Console.Write("DIFFERENTIATION TEST: ");
if( dserrors )
{
System.Console.Write("FAILED");
System.Console.WriteLine();
}
else
{
System.Console.Write("OK");
System.Console.WriteLine();
}
System.Console.Write("COPY/SERIALIZE TEST: ");
if( cperrors )
{
System.Console.Write("FAILED");
System.Console.WriteLine();
}
else
{
System.Console.Write("OK");
System.Console.WriteLine();
}
System.Console.Write("UNPACK TEST: ");
if( uperrors )
{
System.Console.Write("FAILED");
System.Console.WriteLine();
}
else
{
System.Console.Write("OK");
System.Console.WriteLine();
}
System.Console.Write("LIN.TRANS. TEST: ");
if( lterrors )
{
System.Console.Write("FAILED");
System.Console.WriteLine();
}
else
{
System.Console.Write("OK");
System.Console.WriteLine();
}
System.Console.Write("SPECIAL SYMMETRY TEST: ");
if( syerrors )
{
System.Console.Write("FAILED");
System.Console.WriteLine();
}
else
{
System.Console.Write("OK");
System.Console.WriteLine();
}
System.Console.Write("BILINEAR RESAMPLING TEST: ");
if( rlerrors )
{
System.Console.Write("FAILED");
System.Console.WriteLine();
}
else
{
System.Console.Write("OK");
System.Console.WriteLine();
}
System.Console.Write("BICUBIC RESAMPLING TEST: ");
if( rcerrors )
{
System.Console.Write("FAILED");
System.Console.WriteLine();
}
else
{
System.Console.Write("OK");
System.Console.WriteLine();
}
//
// Summary
//
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 declarations
//
public spline2dinterpolant()
{
_innerobj = new spline2d.spline2dinterpolant();
}
