public static bool testsplineinterpolation(bool silent)
{
bool result = new bool();
bool waserrors = new bool();
bool crserrors = new bool();
bool cserrors = new bool();
bool hserrors = new bool();
bool aserrors = new bool();
bool lserrors = new bool();
bool dserrors = new bool();
bool uperrors = new bool();
bool cperrors = new bool();
bool lterrors = new bool();
bool ierrors = new bool();
bool fiterrors = new bool();
double nonstrictthreshold = 0;
double threshold = 0;
int passcount = 0;
double lstep = 0;
double h = 0;
int maxn = 0;
int bltype = 0;
int brtype = 0;
bool periodiccond = new bool();
int n = 0;
int m = 0;
int i = 0;
int k = 0;
int pass = 0;
int stype = 0;
double[] x = new double[0];
double[] y = new double[0];
double[] yp = new double[0];
double[] w = new double[0];
double[] w2 = new double[0];
double[] y2 = new double[0];
double[] d = new double[0];
double[] xc = new double[0];
double[] yc = new double[0];
int[] dc = new int[0];
spline1d.spline1dinterpolant c = new spline1d.spline1dinterpolant();
spline1d.spline1dinterpolant c2 = new spline1d.spline1dinterpolant();
int info = 0;
int info1 = 0;
int info2 = 0;
double a = 0;
double b = 0;
double bl = 0;
double br = 0;
double t = 0;
double sa = 0;
double sb = 0;
double v = 0;
double v1 = 0;
double v2 = 0;
double l10 = 0;
double l11 = 0;
double l12 = 0;
double l20 = 0;
double l21 = 0;
double l22 = 0;
double p0 = 0;
double p1 = 0;
double p2 = 0;
double s = 0;
double ds = 0;
double d2s = 0;
double s2 = 0;
double ds2 = 0;
double d2s2 = 0;
double vl = 0;
double vm = 0;
double vr = 0;
double err = 0;
double tension = 0;
double intab = 0;
spline1d.spline1dfitreport rep = new spline1d.spline1dfitreport();
spline1d.spline1dfitreport rep2 = new spline1d.spline1dfitreport();
double refrms = 0;
double refavg = 0;
double refavgrel = 0;
double refmax = 0;
int i_ = 0;
waserrors = false;
passcount = 20;
lstep = 0.005;
h = 0.00001;
maxn = 10;
threshold = 10000*AP.Math.MachineEpsilon;
nonstrictthreshold = 0.00001;
lserrors = false;
cserrors = false;
crserrors = false;
hserrors = false;
aserrors = false;
dserrors = false;
cperrors = false;
uperrors = false;
lterrors = false;
ierrors = false;
fiterrors = false;
//
// General test: linear, cubic, Hermite, Akima
//
for(n=2; n<=maxn; n++)
{
x = new double[n-1+1];
y = new double[n-1+1];
yp = new double[n-1+1];
d = new double[n-1+1];
for(pass=1; pass<=passcount; pass++)
{
//
// Prepare task:
// * X contains abscissas from [A,B]
// * Y contains function values
// * YP contains periodic function values
//
a = -1-AP.Math.RandomReal();
b = +1+AP.Math.RandomReal();
bl = 2*AP.Math.RandomReal()-1;
br = 2*AP.Math.RandomReal()-1;
for(i=0; i<=n-1; i++)
{
x[i] = 0.5*(b+a)+0.5*(b-a)*Math.Cos(Math.PI*(2*i+1)/(2*n));
if( i==0 )
{
x[i] = a;
}
if( i==n-1 )
{
x[i] = b;
}
y[i] = Math.Cos(1.3*Math.PI*x[i]+0.4);
yp[i] = y[i];
d[i] = -(1.3*Math.PI*Math.Sin(1.3*Math.PI*x[i]+0.4));
}
yp[n-1] = yp[0];
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 = yp[i];
yp[i] = yp[k];
yp[k] = t;
t = d[i];
d[i] = d[k];
d[k] = t;
}
}
//
// Build linear spline
// Test for general interpolation scheme properties:
// * values at nodes
// * continuous function
// Test for specific properties is implemented below.
//
spline1d.spline1dbuildlinear(x, y, n, ref c);
err = 0;
for(i=0; i<=n-1; i++)
{
err = Math.Max(err, Math.Abs(y[i]-spline1d.spline1dcalc(ref c, x[i])));
}
lserrors = lserrors | (double)(err)>(double)(threshold);
lconst(a, b, ref c, lstep, ref l10, ref l11, ref l12);
lconst(a, b, ref c, lstep/3, ref l20, ref l21, ref l22);
lserrors = lserrors | (double)(l20/l10)>(double)(1.2);
//
// Build cubic spline.
// Test for interpolation scheme properties:
// * values at nodes
// * boundary conditions
// * continuous function
// * continuous first derivative
// * continuous second derivative
// * periodicity properties
//
for(bltype=-1; bltype<=2; bltype++)
{
for(brtype=-1; brtype<=2; brtype++)
{
//
// skip meaningless combination of boundary conditions
// (one condition is periodic, another is not)
//
periodiccond = bltype==-1 | brtype==-1;
if( periodiccond & bltype!=brtype )
{
continue;
}
//
// build
//
if( periodiccond )
{
spline1d.spline1dbuildcubic(x, yp, n, bltype, bl, brtype, br, ref c);
}
else
{
spline1d.spline1dbuildcubic(x, y, n, bltype, bl, brtype, br, ref c);
}
//
// interpolation properties
//
err = 0;
if( periodiccond )
{
//
// * check values at nodes; spline is periodic so
// we add random number of periods to nodes
// * we also test for periodicity of derivatives
//
for(i=0; i<=n-1; i++)
{
v = x[i];
vm = v+(b-a)*(AP.Math.RandomInteger(5)-2);
t = yp[i]-spline1d.spline1dcalc(ref c, vm);
err = Math.Max(err, Math.Abs(t));
spline1d.spline1ddiff(ref c, v, ref s, ref ds, ref d2s);
spline1d.spline1ddiff(ref c, vm, ref s2, ref ds2, ref d2s2);
err = Math.Max(err, Math.Abs(s-s2));
err = Math.Max(err, Math.Abs(ds-ds2));
err = Math.Max(err, Math.Abs(d2s-d2s2));
}
//
// periodicity between nodes
//
v = a+(b-a)*AP.Math.RandomReal();
vm = v+(b-a)*(AP.Math.RandomInteger(5)-2);
err = Math.Max(err, Math.Abs(spline1d.spline1dcalc(ref c, v)-spline1d.spline1dcalc(ref c, vm)));
spline1d.spline1ddiff(ref c, v, ref s, ref ds, ref d2s);
spline1d.spline1ddiff(ref c, vm, ref s2, ref ds2, ref d2s2);
err = Math.Max(err, Math.Abs(s-s2));
err = Math.Max(err, Math.Abs(ds-ds2));
err = Math.Max(err, Math.Abs(d2s-d2s2));
}
else
{
//
// * check values at nodes
//
for(i=0; i<=n-1; i++)
{
err = Math.Max(err, Math.Abs(y[i]-spline1d.spline1dcalc(ref c, x[i])));
}
}
cserrors = cserrors | (double)(err)>(double)(threshold);
//
// check boundary conditions
//
err = 0;
if( bltype==0 )
{
spline1d.spline1ddiff(ref c, a-h, ref s, ref ds, ref d2s);
spline1d.spline1ddiff(ref c, a+h, ref s2, ref ds2, ref d2s2);
t = (d2s2-d2s)/(2*h);
err = Math.Max(err, Math.Abs(t));
}
if( bltype==1 )
{
t = (spline1d.spline1dcalc(ref c, a+h)-spline1d.spline1dcalc(ref c, a-h))/(2*h);
err = Math.Max(err, Math.Abs(bl-t));
}
if( bltype==2 )
{
t = (spline1d.spline1dcalc(ref c, a+h)-2*spline1d.spline1dcalc(ref c, a)+spline1d.spline1dcalc(ref c, a-h))/AP.Math.Sqr(h);
err = Math.Max(err, Math.Abs(bl-t));
}
if( brtype==0 )
{
spline1d.spline1ddiff(ref c, b-h, ref s, ref ds, ref d2s);
spline1d.spline1ddiff(ref c, b+h, ref s2, ref ds2, ref d2s2);
t = (d2s2-d2s)/(2*h);
err = Math.Max(err, Math.Abs(t));
}
if( brtype==1 )
{
t = (spline1d.spline1dcalc(ref c, b+h)-spline1d.spline1dcalc(ref c, b-h))/(2*h);
err = Math.Max(err, Math.Abs(br-t));
}
if( brtype==2 )
{
t = (spline1d.spline1dcalc(ref c, b+h)-2*spline1d.spline1dcalc(ref c, b)+spline1d.spline1dcalc(ref c, b-h))/AP.Math.Sqr(h);
err = Math.Max(err, Math.Abs(br-t));
}
if( bltype==-1 | brtype==-1 )
{
spline1d.spline1ddiff(ref c, a+100*AP.Math.MachineEpsilon, ref s, ref ds, ref d2s);
spline1d.spline1ddiff(ref c, b-100*AP.Math.MachineEpsilon, ref s2, ref ds2, ref d2s2);
err = Math.Max(err, Math.Abs(s-s2));
err = Math.Max(err, Math.Abs(ds-ds2));
err = Math.Max(err, Math.Abs(d2s-d2s2));
}
cserrors = cserrors | (double)(err)>(double)(1.0E-3);
//
// Check Lipschitz continuity
//
lconst(a, b, ref c, lstep, ref l10, ref l11, ref l12);
lconst(a, b, ref c, lstep/3, ref l20, ref l21, ref l22);
if( (double)(l10)>(double)(1.0E-6) )
{
cserrors = cserrors | (double)(l20/l10)>(double)(1.2);
}
if( (double)(l11)>(double)(1.0E-6) )
{
cserrors = cserrors | (double)(l21/l11)>(double)(1.2);
}
if( (double)(l12)>(double)(1.0E-6) )
{
cserrors = cserrors | (double)(l22/l12)>(double)(1.2);
}
}
}
//
// Build Catmull-Rom spline.
// Test for interpolation scheme properties:
// * values at nodes
// * boundary conditions
// * continuous function
// * continuous first derivative
// * periodicity properties
//
for(bltype=-1; bltype<=0; bltype++)
{
periodiccond = bltype==-1;
//
// select random tension value, then build
//
if( (double)(AP.Math.RandomReal())>(double)(0.5) )
{
if( (double)(AP.Math.RandomReal())>(double)(0.5) )
{
tension = 0;
}
else
{
tension = 1;
}
}
else
{
tension = AP.Math.RandomReal();
}
if( periodiccond )
{
spline1d.spline1dbuildcatmullrom(x, yp, n, bltype, tension, ref c);
}
else
{
spline1d.spline1dbuildcatmullrom(x, y, n, bltype, tension, ref c);
}
//
// interpolation properties
//
err = 0;
if( periodiccond )
{
//
// * check values at nodes; spline is periodic so
// we add random number of periods to nodes
// * we also test for periodicity of first derivative
//
for(i=0; i<=n-1; i++)
{
v = x[i];
vm = v+(b-a)*(AP.Math.RandomInteger(5)-2);
t = yp[i]-spline1d.spline1dcalc(ref c, vm);
err = Math.Max(err, Math.Abs(t));
spline1d.spline1ddiff(ref c, v, ref s, ref ds, ref d2s);
spline1d.spline1ddiff(ref c, vm, ref s2, ref ds2, ref d2s2);
err = Math.Max(err, Math.Abs(s-s2));
err = Math.Max(err, Math.Abs(ds-ds2));
}
//
// periodicity between nodes
//
v = a+(b-a)*AP.Math.RandomReal();
vm = v+(b-a)*(AP.Math.RandomInteger(5)-2);
err = Math.Max(err, Math.Abs(spline1d.spline1dcalc(ref c, v)-spline1d.spline1dcalc(ref c, vm)));
spline1d.spline1ddiff(ref c, v, ref s, ref ds, ref d2s);
spline1d.spline1ddiff(ref c, vm, ref s2, ref ds2, ref d2s2);
err = Math.Max(err, Math.Abs(s-s2));
err = Math.Max(err, Math.Abs(ds-ds2));
}
else
{
//
// * check values at nodes
//
for(i=0; i<=n-1; i++)
{
err = Math.Max(err, Math.Abs(y[i]-spline1d.spline1dcalc(ref c, x[i])));
}
}
crserrors = crserrors | (double)(err)>(double)(threshold);
//
// check boundary conditions
//
err = 0;
if( bltype==0 )
{
spline1d.spline1ddiff(ref c, a-h, ref s, ref ds, ref d2s);
spline1d.spline1ddiff(ref c, a+h, ref s2, ref ds2, ref d2s2);
t = (d2s2-d2s)/(2*h);
err = Math.Max(err, Math.Abs(t));
spline1d.spline1ddiff(ref c, b-h, ref s, ref ds, ref d2s);
spline1d.spline1ddiff(ref c, b+h, ref s2, ref ds2, ref d2s2);
t = (d2s2-d2s)/(2*h);
err = Math.Max(err, Math.Abs(t));
}
if( bltype==-1 )
{
spline1d.spline1ddiff(ref c, a+100*AP.Math.MachineEpsilon, ref s, ref ds, ref d2s);
spline1d.spline1ddiff(ref c, b-100*AP.Math.MachineEpsilon, ref s2, ref ds2, ref d2s2);
err = Math.Max(err, Math.Abs(s-s2));
err = Math.Max(err, Math.Abs(ds-ds2));
}
crserrors = crserrors | (double)(err)>(double)(1.0E-3);
//
// Check Lipschitz continuity
//
lconst(a, b, ref c, lstep, ref l10, ref l11, ref l12);
lconst(a, b, ref c, lstep/3, ref l20, ref l21, ref l22);
if( (double)(l10)>(double)(1.0E-6) )
{
crserrors = crserrors | (double)(l20/l10)>(double)(1.2);
}
if( (double)(l11)>(double)(1.0E-6) )
{
crserrors = crserrors | (double)(l21/l11)>(double)(1.2);
}
}
//
// Build Hermite spline.
// Test for interpolation scheme properties:
// * values and derivatives at nodes
// * continuous function
// * continuous first derivative
//
spline1d.spline1dbuildhermite(x, y, d, n, ref c);
err = 0;
for(i=0; i<=n-1; i++)
{
err = Math.Max(err, Math.Abs(y[i]-spline1d.spline1dcalc(ref c, x[i])));
}
hserrors = hserrors | (double)(err)>(double)(threshold);
err = 0;
for(i=0; i<=n-1; i++)
{
t = (spline1d.spline1dcalc(ref c, x[i]+h)-spline1d.spline1dcalc(ref c, x[i]-h))/(2*h);
err = Math.Max(err, Math.Abs(d[i]-t));
}
hserrors = hserrors | (double)(err)>(double)(1.0E-3);
lconst(a, b, ref c, lstep, ref l10, ref l11, ref l12);
lconst(a, b, ref c, lstep/3, ref l20, ref l21, ref l22);
hserrors = hserrors | (double)(l20/l10)>(double)(1.2);
hserrors = hserrors | (double)(l21/l11)>(double)(1.2);
//
// Build Akima spline
// Test for general interpolation scheme properties:
// * values at nodes
// * continuous function
// * continuous first derivative
// Test for specific properties is implemented below.
//
if( n>=5 )
{
spline1d.spline1dbuildakima(x, y, n, ref c);
err = 0;
for(i=0; i<=n-1; i++)
{
err = Math.Max(err, Math.Abs(y[i]-spline1d.spline1dcalc(ref c, x[i])));
}
aserrors = aserrors | (double)(err)>(double)(threshold);
lconst(a, b, ref c, lstep, ref l10, ref l11, ref l12);
lconst(a, b, ref c, lstep/3, ref l20, ref l21, ref l22);
hserrors = hserrors | (double)(l20/l10)>(double)(1.2);
hserrors = hserrors | (double)(l21/l11)>(double)(1.2);
}
}
}
//
// Special linear spline test:
// test for linearity between x[i] and x[i+1]
//
for(n=2; n<=maxn; n++)
{
x = new double[n-1+1];
y = new double[n-1+1];
//
// Prepare task
//
a = -1;
b = +1;
for(i=0; i<=n-1; i++)
{
x[i] = a+(b-a)*i/(n-1);
y[i] = 2*AP.Math.RandomReal()-1;
}
spline1d.spline1dbuildlinear(x, y, n, ref c);
//
// Test
//
err = 0;
for(k=0; k<=n-2; k++)
{
a = x[k];
b = x[k+1];
for(pass=1; pass<=passcount; pass++)
{
t = a+(b-a)*AP.Math.RandomReal();
v = y[k]+(t-a)/(b-a)*(y[k+1]-y[k]);
err = Math.Max(err, Math.Abs(spline1d.spline1dcalc(ref c, t)-v));
}
}
lserrors = lserrors | (double)(err)>(double)(threshold);
}
//
// Special Akima test: test outlier sensitivity
// Spline value at (x[i], x[i+1]) should depend from
// f[i-2], f[i-1], f[i], f[i+1], f[i+2], f[i+3] only.
//
for(n=5; n<=maxn; n++)
{
x = new double[n-1+1];
y = new double[n-1+1];
y2 = new double[n-1+1];
//
// Prepare unperturbed Akima spline
//
a = -1;
b = +1;
for(i=0; i<=n-1; i++)
{
x[i] = a+(b-a)*i/(n-1);
y[i] = Math.Cos(1.3*Math.PI*x[i]+0.4);
}
spline1d.spline1dbuildakima(x, y, n, ref c);
//
// Process perturbed tasks
//
err = 0;
for(k=0; k<=n-1; k++)
{
for(i_=0; i_<=n-1;i_++)
{
y2[i_] = y[i_];
}
y2[k] = 5;
spline1d.spline1dbuildakima(x, y2, n, ref c2);
//
// Test left part independence
//
if( k-3>=1 )
{
a = -1;
b = x[k-3];
for(pass=1; pass<=passcount; pass++)
{
t = a+(b-a)*AP.Math.RandomReal();
err = Math.Max(err, Math.Abs(spline1d.spline1dcalc(ref c, t)-spline1d.spline1dcalc(ref c2, t)));
}
}
//
// Test right part independence
//
if( k+3<=n-2 )
{
a = x[k+3];
b = +1;
for(pass=1; pass<=passcount; pass++)
{
t = a+(b-a)*AP.Math.RandomReal();
err = Math.Max(err, Math.Abs(spline1d.spline1dcalc(ref c, t)-spline1d.spline1dcalc(ref c2, t)));
}
}
}
aserrors = aserrors | (double)(err)>(double)(threshold);
}
//
// Differentiation, copy/unpack test
//
for(n=2; n<=maxn; n++)
{
x = new double[n-1+1];
y = new double[n-1+1];
//
// Prepare cubic spline
//
a = -1-AP.Math.RandomReal();
b = +1+AP.Math.RandomReal();
for(i=0; i<=n-1; i++)
{
x[i] = a+(b-a)*i/(n-1);
y[i] = Math.Cos(1.3*Math.PI*x[i]+0.4);
}
spline1d.spline1dbuildcubic(x, y, n, 2, 0.0, 2, 0.0, ref c);
//
// Test diff
//
err = 0;
for(pass=1; pass<=passcount; pass++)
{
t = a+(b-a)*AP.Math.RandomReal();
spline1d.spline1ddiff(ref c, t, ref s, ref ds, ref d2s);
vl = spline1d.spline1dcalc(ref c, t-h);
vm = spline1d.spline1dcalc(ref c, t);
vr = spline1d.spline1dcalc(ref c, t+h);
err = Math.Max(err, Math.Abs(s-vm));
err = Math.Max(err, Math.Abs(ds-(vr-vl)/(2*h)));
err = Math.Max(err, Math.Abs(d2s-(vr-2*vm+vl)/AP.Math.Sqr(h)));
}
dserrors = dserrors | (double)(err)>(double)(0.001);
//
// Test copy
//
unsetspline1d(ref c2);
spline1d.spline1dcopy(ref c, ref c2);
err = 0;
for(pass=1; pass<=passcount; pass++)
{
t = a+(b-a)*AP.Math.RandomReal();
err = Math.Max(err, Math.Abs(spline1d.spline1dcalc(ref c, t)-spline1d.spline1dcalc(ref c2, t)));
}
cperrors = cperrors | (double)(err)>(double)(threshold);
//
// Test unpack
//
uperrors = uperrors | !testunpack(ref c, ref x);
//
// Test lin.trans.
//
err = 0;
for(pass=1; pass<=passcount; pass++)
{
//
// LinTransX, general A
//
sa = 4*AP.Math.RandomReal()-2;
sb = 2*AP.Math.RandomReal()-1;
t = a+(b-a)*AP.Math.RandomReal();
spline1d.spline1dcopy(ref c, ref c2);
spline1d.spline1dlintransx(ref c2, sa, sb);
err = Math.Max(err, Math.Abs(spline1d.spline1dcalc(ref c, t)-spline1d.spline1dcalc(ref c2, (t-sb)/sa)));
//
// LinTransX, special case: A=0
//
sb = 2*AP.Math.RandomReal()-1;
t = a+(b-a)*AP.Math.RandomReal();
spline1d.spline1dcopy(ref c, ref c2);
spline1d.spline1dlintransx(ref c2, 0, sb);
err = Math.Max(err, Math.Abs(spline1d.spline1dcalc(ref c, sb)-spline1d.spline1dcalc(ref c2, t)));
//
// LinTransY
//
sa = 2*AP.Math.RandomReal()-1;
sb = 2*AP.Math.RandomReal()-1;
t = a+(b-a)*AP.Math.RandomReal();
spline1d.spline1dcopy(ref c, ref c2);
spline1d.spline1dlintransy(ref c2, sa, sb);
err = Math.Max(err, Math.Abs(sa*spline1d.spline1dcalc(ref c, t)+sb-spline1d.spline1dcalc(ref c2, t)));
}
lterrors = lterrors | (double)(err)>(double)(threshold);
}
//
// Testing integration.
// Three tests are performed:
//
// * approximate test (well behaved smooth function, many points,
// integration inside [a,b]), non-periodic spline
//
// * exact test (integration of parabola, outside of [a,b], non-periodic spline
//
// * approximate test for periodic splines. F(x)=cos(2*pi*x)+1.
// Period length is equals to 1.0, so all operations with
// multiples of period are done exactly. For each value of PERIOD
// we calculate and test integral at four points:
// - 0 < t0 < PERIOD
// - t1 = PERIOD-eps
// - t2 = PERIOD
// - t3 = PERIOD+eps
//
err = 0;
for(n=20; n<=35; n++)
{
x = new double[n-1+1];
y = new double[n-1+1];
for(pass=1; pass<=passcount; pass++)
{
//
// Prepare cubic spline
//
a = -1-0.2*AP.Math.RandomReal();
b = +1+0.2*AP.Math.RandomReal();
for(i=0; i<=n-1; i++)
{
x[i] = a+(b-a)*i/(n-1);
y[i] = Math.Sin(Math.PI*x[i]+0.4)+Math.Exp(x[i]);
}
bl = Math.PI*Math.Cos(Math.PI*a+0.4)+Math.Exp(a);
br = Math.PI*Math.Cos(Math.PI*b+0.4)+Math.Exp(b);
spline1d.spline1dbuildcubic(x, y, n, 1, bl, 1, br, ref c);
//
// Test
//
t = a+(b-a)*AP.Math.RandomReal();
v = -(Math.Cos(Math.PI*a+0.4)/Math.PI)+Math.Exp(a);
v = -(Math.Cos(Math.PI*t+0.4)/Math.PI)+Math.Exp(t)-v;
v = v-spline1d.spline1dintegrate(ref c, t);
err = Math.Max(err, Math.Abs(v));
}
}
ierrors = ierrors | (double)(err)>(double)(0.001);
p0 = 2*AP.Math.RandomReal()-1;
p1 = 2*AP.Math.RandomReal()-1;
p2 = 2*AP.Math.RandomReal()-1;
a = -AP.Math.RandomReal()-0.5;
b = +AP.Math.RandomReal()+0.5;
n = 2;
x = new double[n];
y = new double[n];
d = new double[n];
x[0] = a;
y[0] = p0+p1*a+p2*AP.Math.Sqr(a);
d[0] = p1+2*p2*a;
x[1] = b;
y[1] = p0+p1*b+p2*AP.Math.Sqr(b);
d[1] = p1+2*p2*b;
spline1d.spline1dbuildhermite(x, y, d, n, ref c);
bl = Math.Min(a, b)-Math.Abs(b-a);
br = Math.Min(a, b)+Math.Abs(b-a);
err = 0;
for(pass=1; pass<=100; pass++)
{
t = bl+(br-bl)*AP.Math.RandomReal();
v = p0*t+p1*AP.Math.Sqr(t)/2+p2*AP.Math.Sqr(t)*t/3-(p0*a+p1*AP.Math.Sqr(a)/2+p2*AP.Math.Sqr(a)*a/3);
v = v-spline1d.spline1dintegrate(ref c, t);
err = Math.Max(err, Math.Abs(v));
}
ierrors = ierrors | (double)(err)>(double)(threshold);
n = 100;
x = new double[n];
y = new double[n];
for(i=0; i<=n-1; i++)
{
x[i] = (double)(i)/((double)(n-1));
y[i] = Math.Cos(2*Math.PI*x[i])+1;
}
y[0] = 2;
y[n-1] = 2;
spline1d.spline1dbuildcubic(x, y, n, -1, 0.0, -1, 0.0, ref c);
intab = spline1d.spline1dintegrate(ref c, 1.0);
v = AP.Math.RandomReal();
vr = spline1d.spline1dintegrate(ref c, v);
ierrors = ierrors | (double)(Math.Abs(intab-1))>(double)(0.001);
for(i=-10; i<=10; i++)
{
ierrors = ierrors | (double)(Math.Abs(spline1d.spline1dintegrate(ref c, i+v)-(i*intab+vr)))>(double)(0.001);
ierrors = ierrors | (double)(Math.Abs(spline1d.spline1dintegrate(ref c, i-1000*AP.Math.MachineEpsilon)-i*intab))>(double)(0.001);
ierrors = ierrors | (double)(Math.Abs(spline1d.spline1dintegrate(ref c, i)-i*intab))>(double)(0.001);
ierrors = ierrors | (double)(Math.Abs(spline1d.spline1dintegrate(ref c, i+1000*AP.Math.MachineEpsilon)-i*intab))>(double)(0.001);
}
//
// Test fitting.
//
for(pass=1; pass<=passcount; pass++)
{
//
// Cubic splines
// Ability to handle boundary constraints (1-4 constraints on F, dF/dx).
//
for(m=4; m<=8; m++)
{
for(k=1; k<=4; k++)
{
if( k>=m )
{
continue;
}
n = 100;
x = new double[n];
y = new double[n];
w = new double[n];
xc = new double[4];
yc = new double[4];
dc = new int[4];
sa = 1+AP.Math.RandomReal();
sb = 2*AP.Math.RandomReal()-1;
for(i=0; i<=n-1; i++)
{
x[i] = sa*AP.Math.RandomReal()+sb;
y[i] = 2*AP.Math.RandomReal()-1;
w[i] = 1+AP.Math.RandomReal();
}
xc[0] = sb;
yc[0] = 2*AP.Math.RandomReal()-1;
dc[0] = 0;
xc[1] = sb;
yc[1] = 2*AP.Math.RandomReal()-1;
dc[1] = 1;
xc[2] = sa+sb;
yc[2] = 2*AP.Math.RandomReal()-1;
dc[2] = 0;
xc[3] = sa+sb;
yc[3] = 2*AP.Math.RandomReal()-1;
dc[3] = 1;
spline1d.spline1dfitcubicwc(ref x, ref y, ref w, n, ref xc, ref yc, ref dc, k, m, ref info, ref c, ref rep);
if( info<=0 )
{
fiterrors = true;
}
else
{
//
// Check that constraints are satisfied
//
for(i=0; i<=k-1; i++)
{
spline1d.spline1ddiff(ref c, xc[i], ref s, ref ds, ref d2s);
if( dc[i]==0 )
{
fiterrors = fiterrors | (double)(Math.Abs(s-yc[i]))>(double)(threshold);
}
if( dc[i]==1 )
{
fiterrors = fiterrors | (double)(Math.Abs(ds-yc[i]))>(double)(threshold);
}
if( dc[i]==2 )
{
fiterrors = fiterrors | (double)(Math.Abs(d2s-yc[i]))>(double)(threshold);
}
}
}
}
}
//
// Cubic splines
// Ability to handle one internal constraint
//
for(m=4; m<=8; m++)
{
n = 100;
x = new double[n];
y = new double[n];
w = new double[n];
xc = new double[1];
yc = new double[1];
dc = new int[1];
sa = 1+AP.Math.RandomReal();
sb = 2*AP.Math.RandomReal()-1;
for(i=0; i<=n-1; i++)
{
x[i] = sa*AP.Math.RandomReal()+sb;
y[i] = 2*AP.Math.RandomReal()-1;
w[i] = 1+AP.Math.RandomReal();
}
xc[0] = sa*AP.Math.RandomReal()+sb;
yc[0] = 2*AP.Math.RandomReal()-1;
dc[0] = AP.Math.RandomInteger(2);
spline1d.spline1dfitcubicwc(ref x, ref y, ref w, n, ref xc, ref yc, ref dc, 1, m, ref info, ref c, ref rep);
if( info<=0 )
{
fiterrors = true;
}
else
{
//
// Check that constraints are satisfied
//
spline1d.spline1ddiff(ref c, xc[0], ref s, ref ds, ref d2s);
if( dc[0]==0 )
{
fiterrors = fiterrors | (double)(Math.Abs(s-yc[0]))>(double)(threshold);
}
if( dc[0]==1 )
{
fiterrors = fiterrors | (double)(Math.Abs(ds-yc[0]))>(double)(threshold);
}
if( dc[0]==2 )
{
fiterrors = fiterrors | (double)(Math.Abs(d2s-yc[0]))>(double)(threshold);
}
}
}
//
// Hermite splines
// Ability to handle boundary constraints (1-4 constraints on F, dF/dx).
//
for(m=4; m<=8; m++)
{
for(k=1; k<=4; k++)
{
if( k>=m )
{
continue;
}
if( m%2!=0 )
{
continue;
}
n = 100;
x = new double[n];
y = new double[n];
w = new double[n];
xc = new double[4];
yc = new double[4];
dc = new int[4];
sa = 1+AP.Math.RandomReal();
sb = 2*AP.Math.RandomReal()-1;
for(i=0; i<=n-1; i++)
{
x[i] = sa*AP.Math.RandomReal()+sb;
y[i] = 2*AP.Math.RandomReal()-1;
w[i] = 1+AP.Math.RandomReal();
}
xc[0] = sb;
yc[0] = 2*AP.Math.RandomReal()-1;
dc[0] = 0;
xc[1] = sb;
yc[1] = 2*AP.Math.RandomReal()-1;
dc[1] = 1;
xc[2] = sa+sb;
yc[2] = 2*AP.Math.RandomReal()-1;
dc[2] = 0;
xc[3] = sa+sb;
yc[3] = 2*AP.Math.RandomReal()-1;
dc[3] = 1;
spline1d.spline1dfithermitewc(ref x, ref y, ref w, n, ref xc, ref yc, ref dc, k, m, ref info, ref c, ref rep);
if( info<=0 )
{
fiterrors = true;
}
else
{
//
// Check that constraints are satisfied
//
for(i=0; i<=k-1; i++)
{
spline1d.spline1ddiff(ref c, xc[i], ref s, ref ds, ref d2s);
if( dc[i]==0 )
{
fiterrors = fiterrors | (double)(Math.Abs(s-yc[i]))>(double)(threshold);
}
if( dc[i]==1 )
{
fiterrors = fiterrors | (double)(Math.Abs(ds-yc[i]))>(double)(threshold);
}
if( dc[i]==2 )
{
fiterrors = fiterrors | (double)(Math.Abs(d2s-yc[i]))>(double)(threshold);
}
}
}
}
}
//
// Hermite splines
// Ability to handle one internal constraint
//
for(m=4; m<=8; m++)
{
if( m%2!=0 )
{
continue;
}
n = 100;
x = new double[n];
y = new double[n];
w = new double[n];
xc = new double[1];
yc = new double[1];
dc = new int[1];
sa = 1+AP.Math.RandomReal();
sb = 2*AP.Math.RandomReal()-1;
for(i=0; i<=n-1; i++)
{
x[i] = sa*AP.Math.RandomReal()+sb;
y[i] = 2*AP.Math.RandomReal()-1;
w[i] = 1+AP.Math.RandomReal();
}
xc[0] = sa*AP.Math.RandomReal()+sb;
yc[0] = 2*AP.Math.RandomReal()-1;
dc[0] = AP.Math.RandomInteger(2);
spline1d.spline1dfithermitewc(ref x, ref y, ref w, n, ref xc, ref yc, ref dc, 1, m, ref info, ref c, ref rep);
if( info<=0 )
{
fiterrors = true;
}
else
{
//
// Check that constraints are satisfied
//
spline1d.spline1ddiff(ref c, xc[0], ref s, ref ds, ref d2s);
if( dc[0]==0 )
{
fiterrors = fiterrors | (double)(Math.Abs(s-yc[0]))>(double)(threshold);
}
if( dc[0]==1 )
{
fiterrors = fiterrors | (double)(Math.Abs(ds-yc[0]))>(double)(threshold);
}
if( dc[0]==2 )
{
fiterrors = fiterrors | (double)(Math.Abs(d2s-yc[0]))>(double)(threshold);
}
}
}
}
for(m=4; m<=8; m++)
{
for(stype=0; stype<=1; stype++)
{
for(pass=1; pass<=passcount; pass++)
{
if( stype==1 & m%2!=0 )
{
continue;
}
//
// cubic/Hermite spline fitting:
// * generate "template spline" C2
// * generate 2*N points from C2, such that result of
// ideal fit should be equal to C2
// * fit, store in C
// * compare C and C2
//
sa = 1+AP.Math.RandomReal();
sb = 2*AP.Math.RandomReal()-1;
if( stype==0 )
{
x = new double[m-2];
y = new double[m-2];
for(i=0; i<=m-2-1; i++)
{
x[i] = sa*i/(m-2-1)+sb;
y[i] = 2*AP.Math.RandomReal()-1;
}
spline1d.spline1dbuildcubic(x, y, m-2, 1, 2*AP.Math.RandomReal()-1, 1, 2*AP.Math.RandomReal()-1, ref c2);
}
if( stype==1 )
{
x = new double[m/2];
y = new double[m/2];
d = new double[m/2];
for(i=0; i<=m/2-1; i++)
{
x[i] = sa*i/(m/2-1)+sb;
y[i] = 2*AP.Math.RandomReal()-1;
d[i] = 2*AP.Math.RandomReal()-1;
}
spline1d.spline1dbuildhermite(x, y, d, m/2, ref c2);
}
n = 50;
x = new double[2*n];
y = new double[2*n];
w = new double[2*n];
for(i=0; i<=n-1; i++)
{
//
// "if i=0" and "if i=1" are needed to
// synchronize interval size for C2 and
// spline being fitted (i.e. C).
//
t = AP.Math.RandomReal();
x[i] = sa*AP.Math.RandomReal()+sb;
if( i==0 )
{
x[i] = sb;
}
if( i==1 )
{
x[i] = sa+sb;
}
v = spline1d.spline1dcalc(ref c2, x[i]);
y[i] = v+t;
w[i] = 1+AP.Math.RandomReal();
x[n+i] = x[i];
y[n+i] = v-t;
w[n+i] = w[i];
}
if( stype==0 )
{
spline1d.spline1dfitcubicwc(ref x, ref y, ref w, 2*n, ref xc, ref yc, ref dc, 0, m, ref info, ref c, ref rep);
}
if( stype==1 )
{
spline1d.spline1dfithermitewc(ref x, ref y, ref w, 2*n, ref xc, ref yc, ref dc, 0, m, ref info, ref c, ref rep);
}
if( info<=0 )
{
fiterrors = true;
}
else
{
for(i=0; i<=n-1; i++)
{
v = sa*AP.Math.RandomReal()+sb;
fiterrors = fiterrors | (double)(Math.Abs(spline1d.spline1dcalc(ref c, v)-spline1d.spline1dcalc(ref c2, v)))>(double)(threshold);
}
}
}
}
}
for(m=4; m<=8; m++)
{
for(pass=1; pass<=passcount; pass++)
{
//
// prepare points/weights
//
sa = 1+AP.Math.RandomReal();
sb = 2*AP.Math.RandomReal()-1;
n = 10+AP.Math.RandomInteger(10);
x = new double[n];
y = new double[n];
w = new double[n];
for(i=0; i<=n-1; i++)
{
x[i] = sa*AP.Math.RandomReal()+sb;
y[i] = 2*AP.Math.RandomReal()-1;
w[i] = 1;
}
//
// Fit cubic with unity weights, without weights, then compare
//
if( m>=4 )
{
spline1d.spline1dfitcubicwc(ref x, ref y, ref w, n, ref xc, ref yc, ref dc, 0, m, ref info1, ref c, ref rep);
spline1d.spline1dfitcubic(ref x, ref y, n, m, ref info2, ref c2, ref rep2);
if( info1<=0 | info2<=0 )
{
fiterrors = true;
}
else
{
for(i=0; i<=n-1; i++)
{
v = sa*AP.Math.RandomReal()+sb;
fiterrors = fiterrors | (double)(spline1d.spline1dcalc(ref c, v))!=(double)(spline1d.spline1dcalc(ref c2, v));
fiterrors = fiterrors | (double)(rep.taskrcond)!=(double)(rep2.taskrcond);
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);
}
}
}
//
// Fit Hermite with unity weights, without weights, then compare
//
if( m>=4 & m%2==0 )
{
spline1d.spline1dfithermitewc(ref x, ref y, ref w, n, ref xc, ref yc, ref dc, 0, m, ref info1, ref c, ref rep);
spline1d.spline1dfithermite(ref x, ref y, n, m, ref info2, ref c2, ref rep2);
if( info1<=0 | info2<=0 )
{
fiterrors = true;
}
else
{
for(i=0; i<=n-1; i++)
{
v = sa*AP.Math.RandomReal()+sb;
fiterrors = fiterrors | (double)(spline1d.spline1dcalc(ref c, v))!=(double)(spline1d.spline1dcalc(ref c2, v));
fiterrors = fiterrors | (double)(rep.taskrcond)!=(double)(rep2.taskrcond);
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 cubic fitting
//
spline1d.spline1dfitcubic(ref x, ref y, 4, 4, ref info, ref c, ref rep);
if( info<=0 )
{
fiterrors = true;
}
else
{
s = spline1d.spline1dcalc(ref c, 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);
}
//
// Test cubic fitting
//
spline1d.spline1dfithermite(ref x, ref y, 4, 4, ref info, ref c, ref rep);
if( info<=0 )
{
fiterrors = true;
}
else
{
s = spline1d.spline1dcalc(ref c, 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 = lserrors | cserrors | crserrors | hserrors | aserrors | dserrors | cperrors | uperrors | lterrors | ierrors | fiterrors;
if( !silent )
{
System.Console.Write("TESTING SPLINE INTERPOLATION");
System.Console.WriteLine();
//
// Normal tests
//
System.Console.Write("LINEAR SPLINE TEST: ");
if( lserrors )
{
System.Console.Write("FAILED");
System.Console.WriteLine();
}
else
{
System.Console.Write("OK");
System.Console.WriteLine();
}
System.Console.Write("CUBIC SPLINE TEST: ");
if( cserrors )
{
System.Console.Write("FAILED");
System.Console.WriteLine();
}
else
{
System.Console.Write("OK");
System.Console.WriteLine();
}
System.Console.Write("CATMULL-ROM SPLINE TEST: ");
if( crserrors )
{
System.Console.Write("FAILED");
System.Console.WriteLine();
}
else
{
System.Console.Write("OK");
System.Console.WriteLine();
}
System.Console.Write("HERMITE SPLINE TEST: ");
if( hserrors )
{
System.Console.Write("FAILED");
System.Console.WriteLine();
}
else
{
System.Console.Write("OK");
System.Console.WriteLine();
}
System.Console.Write("AKIMA SPLINE TEST: ");
if( aserrors )
{
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/SERIALIZATION 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("INTEGRATION TEST: ");
if( ierrors )
{
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;
}
/*************************************************************************
Bicubic spline resampling
Input parameters:
A - function values at the old grid,
array[0..OldHeight-1, 0..OldWidth-1]
OldHeight - old grid height, OldHeight>1
OldWidth - old grid width, OldWidth>1
NewHeight - new grid height, NewHeight>1
NewWidth - new grid width, NewWidth>1
Output parameters:
B - function values at the new grid,
array[0..NewHeight-1, 0..NewWidth-1]
-- ALGLIB routine --
15 May, 2007
Copyright by Bochkanov Sergey
*************************************************************************/
public static void spline2dresamplebicubic(ref double[,] a,
int oldheight,
int oldwidth,
ref double[,] b,
int newheight,
int newwidth)
{
double[,] buf = new double[0,0];
double[] x = new double[0];
double[] y = new double[0];
spline1d.spline1dinterpolant c = new spline1d.spline1dinterpolant();
int i = 0;
int j = 0;
int mw = 0;
int mh = 0;
System.Diagnostics.Debug.Assert(oldwidth>1 & oldheight>1, "Spline2DResampleBicubic: width/height less than 1");
System.Diagnostics.Debug.Assert(newwidth>1 & newheight>1, "Spline2DResampleBicubic: width/height less than 1");
//
// Prepare
//
mw = Math.Max(oldwidth, newwidth);
mh = Math.Max(oldheight, newheight);
b = new double[newheight-1+1, newwidth-1+1];
buf = new double[oldheight-1+1, newwidth-1+1];
x = new double[Math.Max(mw, mh)-1+1];
y = new double[Math.Max(mw, mh)-1+1];
//
// Horizontal interpolation
//
for(i=0; i<=oldheight-1; i++)
{
//
// Fill X, Y
//
for(j=0; j<=oldwidth-1; j++)
{
x[j] = (double)(j)/((double)(oldwidth-1));
y[j] = a[i,j];
}
//
// Interpolate and place result into temporary matrix
//
spline1d.spline1dbuildcubic(x, y, oldwidth, 0, 0.0, 0, 0.0, ref c);
for(j=0; j<=newwidth-1; j++)
{
buf[i,j] = spline1d.spline1dcalc(ref c, (double)(j)/((double)(newwidth-1)));
}
}
//
// Vertical interpolation
//
for(j=0; j<=newwidth-1; j++)
{
//
// Fill X, Y
//
for(i=0; i<=oldheight-1; i++)
{
x[i] = (double)(i)/((double)(oldheight-1));
y[i] = buf[i,j];
}
//
// Interpolate and place result into B
//
spline1d.spline1dbuildcubic(x, y, oldheight, 0, 0.0, 0, 0.0, ref c);
for(i=0; i<=newheight-1; i++)
{
b[i,j] = spline1d.spline1dcalc(ref c, (double)(i)/((double)(newheight-1)));
}
}
}
