/// linear interpolation of the function y = f(x) at point xi
/// assumes that x is strictly increasing
double interp(const Vector& x, const Vector& y, double xi, InterpMethod interpMethod, ExtrapMethod extrapMethod){
unsigned N = x.size();
double result = 0.0;
if (y.size() != N){
return result;
}
InterpInfo info = interpInfo(x, xi);
if (info.extrapolated){
switch(extrapMethod){
case NoneExtrap:
// set to zero
result = 0.0;
break;
case NearestExtrap:
// pick closest point
result = (info.wa > info.wb ? y(info.ia) : y(info.ib));
break;
}
}else{
switch(interpMethod){
case LinearInterp:
// linear interpolation
result = info.wa*y(info.ia) + info.wb*y(info.ib);
break;
case NearestInterp:
// pick closest point
result = (info.wa > info.wb ? y(info.ia) : y(info.ib));
break;
case HoldLastInterp:
// set to previous value
result = y(info.ia);
break;
case HoldNextInterp:
// set to next value
result = y(info.ib);
break;
}
}
return result;
}
/// linear interpolation of the function v = f(x, y) at point xi, yi
/// assumes that x and y are strictly increasing
double interp(const Vector& x, const Vector& y, const Matrix& v, double xi, double yi, InterpMethod interpMethod, ExtrapMethod extrapMethod)
{
double result = 0.0;
unsigned M = x.size();
unsigned N = y.size();
if ((M != v.size1()) || (N != v.size2())) {
return result;
}
InterpInfo xInfo = interpInfo(x, xi);
if (xInfo.extrapolated) {
switch(extrapMethod) {
case NoneExtrap:
// set all weights to zero
xInfo.wa = 0.0;
xInfo.wb = 0.0;
break;
case NearestExtrap:
// pick closest point
// no-op
break;
}
} else {
switch(interpMethod) {
case LinearInterp:
// linear interpolation
// no-op
break;
case NearestInterp:
// pick closest point
if(xInfo.wa > xInfo.wb) {
xInfo.wa = 1.0;
xInfo.wb = 0.0;
} else {
xInfo.wa = 0.0;
xInfo.wb = 1.0;
}
break;
case HoldLastInterp:
// set to previous value
xInfo.wa = 1.0;
xInfo.wb = 0.0;
break;
case HoldNextInterp:
// set to next value
xInfo.wa = 0.0;
xInfo.wb = 1.0;
break;
}
}
InterpInfo yInfo = interpInfo(y, yi);
if (yInfo.extrapolated) {
switch(extrapMethod) {
case NoneExtrap:
// set all weights to zero
yInfo.wa = 0.0;
yInfo.wb = 0.0;
break;
case NearestExtrap:
// pick closest point
// no-op
break;
}
} else {
switch(interpMethod) {
case LinearInterp:
// linear interpolation
// no-op
break;
case NearestInterp:
// pick closest point
if(yInfo.wa > yInfo.wb) {
yInfo.wa = 1.0;
yInfo.wb = 0.0;
} else {
yInfo.wa = 0.0;
yInfo.wb = 1.0;
}
break;
case HoldLastInterp:
// set to previous value
yInfo.wa = 1.0;
yInfo.wb = 0.0;
break;
case HoldNextInterp:
// set to next value
yInfo.wa = 0.0;
yInfo.wb = 1.0;
break;
}
}
// we have set weights appropriately so that here we can compute in the same way all the time
result = xInfo.wa*yInfo.wa*v(xInfo.ia, yInfo.ia) +
xInfo.wa*yInfo.wb*v(xInfo.ia, yInfo.ib) +
xInfo.wb*yInfo.wa*v(xInfo.ib, yInfo.ia) +
xInfo.wb*yInfo.wb*v(xInfo.ib, yInfo.ib);
return result;
}