PolynomialFit3<Real>::PolynomialFit3 (int numXSamples, int numYSamples,
const Real* xSamples, const Real* ySamples, const Real* wSamples,
int numPowers, const Tuple<2,int>* powers)
{
InitializePowers(numPowers, powers);
// Repackage the input into samples of the form (x[i],y[i],w[i]).
int numSamples = numXSamples*numYSamples;
Real* xRepackage = new1<Real>(numSamples);
Real* yRepackage = new1<Real>(numSamples);
for (int y = 0, i = 0; y < numYSamples; ++y)
{
Real yInput = ySamples[y];
for (int x = 0; x < numXSamples; ++x, ++i)
{
xRepackage[i] = xSamples[x];
yRepackage[i] = yInput;
}
}
const Real* srcSamples[3] = { xRepackage, yRepackage, wSamples };
Real* trgSamples[3] = { 0, 0, 0 };
TransformToUnit(numSamples, srcSamples, trgSamples);
DoLeastSquaresFit(numSamples, trgSamples);
delete1(trgSamples[0]);
delete1(trgSamples[1]);
delete1(trgSamples[2]);
delete1(xRepackage);
delete1(yRepackage);
}
PolynomialFit3<Real>::PolynomialFit3 (int numSamples, const Real* xSamples,
const Real* ySamples, const Real* wSamples, int numPowers,
const Tuple<2,int>* powers)
{
InitializePowers(numPowers, powers);
const Real* srcSamples[3] = { xSamples, ySamples, wSamples };
Real* trgSamples[3] = { 0, 0, 0 };
TransformToUnit(numSamples, srcSamples, trgSamples);
DoLeastSquaresFit(numSamples, trgSamples);
delete1(trgSamples[0]);
delete1(trgSamples[1]);
delete1(trgSamples[2]);
}
PolynomialFit2<Real>::PolynomialFit2 ( int numSamples, const Real* xSamples,
const Real* wSamples, int numPowers, const int* powers )
:
mNumPowers( numPowers )
{
InitializePowers( numPowers, powers );
mPowers = new1<int>( mNumPowers );
memcpy( mPowers, powers, mNumPowers * sizeof( int ) );
mCoefficients = new1<Real>( mNumPowers );
GMatrix<Real> mat( mNumPowers, mNumPowers ); // initially zero
GVector<Real> rhs( mNumPowers ); // initially zero
GVector<Real> xPower( mNumPowers );
int i, row, col;
for ( i = 0; i < numSamples; ++i )
{
// Compute relevant powers of x. TODO: Build minimum tree for
// powers of x?
Real x = xSamples[i];
Real w = wSamples[i];
for ( int j = 0; j < mNumPowers; ++j )
{
xPower[j] = Math<Real>::Pow( x, ( Real )mPowers[j] );
}
for ( row = 0; row < mNumPowers; ++row )
{
// Update the upper-triangular portion of the symmetric matrix.
for ( col = row; col < mNumPowers; ++col )
{
mat[row][col] += xPower[mPowers[row] + mPowers[col]];
}
// Update the right-hand side of the system.
rhs[row] += w * xPower[mPowers[row]];
}
}
// Copy the upper-triangular portion of the symmetric matrix to the
// lower-triangular portion.
for ( row = 0; row < mNumPowers; ++row )
{
for ( col = 0; col < row; ++col )
{
mat[row][col] = mat[col][row];
}
}
// Precondition by normalizing the sums.
Real invNumSamples = ( ( Real )1 ) / ( Real )numSamples;
for ( row = 0; row < mNumPowers; ++row )
{
for ( col = 0; col < mNumPowers; ++col )
{
mat[row][col] *= invNumSamples;
}
rhs[row] *= invNumSamples;
}
if ( LinearSystem<Real>().Solve( mat, rhs, mCoefficients ) )
{
mSolved = true;
}
else
{
memset( mCoefficients, 0, mNumPowers * sizeof( Real ) );
mSolved = false;
}
}
