void CubicSplineInterpolation::calCubicSplineCoeffs(
std::vector<double> &input_x,
std::vector<double> &input_y,
CubicSplineCoeffs *&cubicCoeffs,
CubicSplineMode splineMode /* = CUBIC_NATURAL */,
SplineFilterMode filterMode /*= CUBIC_MEDIAN_FILTER*/ )
{
int sizeOfx = input_x.size();
int sizeOfy = input_y.size();
if ( sizeOfx != sizeOfy )
{
std::cout << "Data input error!" << std::endl <<
"Location: CubicSplineInterpolation.cpp" <<
" -> calCubicSplineCoeffs()" << std::endl;
return;
}
/*
hi*mi + 2*(hi + hi+1)*mi+1 + hi+1*mi+2
= 6{ (yi+2 - yi+1)/hi+1 - (yi+1 - yi)/hi }
so, ignore the both ends:
| - - - 0 ... 0 | |m0 |
| h0 2(h0+h1) h1 0 ... 0 | |m1 |
| 0 h1 2(h1+h2) h2 0 ... | |m2 |
| ... ... 0 | |...|
| 0 ... 0 h(n-2) 2(h(n-2)+h(n-1)) h(n-1) | | |
| 0 ... ... - | |mn |
*/
std::vector<double> copy_y = input_y;
if ( filterMode == CUBIC_MEDIAN_FILTER )
{
cubicMedianFilter(copy_y, 5);
}
const int count = sizeOfx;
const int count1 = sizeOfx - 1;
const int count2 = sizeOfx - 2;
const int count3 = sizeOfx - 3;
cubicCoeffs = new CubicSplineCoeffs( count1 );
std::vector<double> step_h( count1, 0.0 );
// for m matrix
cv::Mat_<double> m_a(1, count2, 0.0);
cv::Mat_<double> m_b(1, count2, 0.0);
cv::Mat_<double> m_c(1, count2, 0.0);
cv::Mat_<double> m_d(1, count2, 0.0);
cv::Mat_<double> m_part(1, count2, 0.0);
cv::Mat_<double> m_all(1, count, 0.0);
// initial step hi
for ( int idx=0; idx < count1; idx ++ )
{
step_h[idx] = input_x[idx+1] - input_x[idx];
}
// initial coefficients
for ( int idx=0; idx < count3; idx ++ )
{
m_a(idx) = step_h[idx];
m_b(idx) = 2 * (step_h[idx] + step_h[idx+1]);
m_c(idx) = step_h[idx+1];
}
// initial d
for ( int idx =0; idx < count3; idx ++ )
{
m_d(idx) = 6 * (
(copy_y[idx+2] - copy_y[idx+1]) / step_h[idx+1] -
(copy_y[idx+1] - copy_y[idx]) / step_h[idx] );
}
//cv::Mat_<double> matOfm( count2, )
bool isSucceed = caltridiagonalMatrices(m_a, m_b, m_c, m_d, m_part);
if ( !isSucceed )
{
std::cout<<"Calculate tridiagonal matrices failed!"<<std::endl<<
"Location: CubicSplineInterpolation.cpp -> " <<
"caltridiagonalMatrices()"<<std::endl;
return;
}
if ( splineMode == CUBIC_NATURAL )
{
m_all(0) = 0.0;
m_all(count1) = 0.0;
for ( int i=1; i<count1; i++ )
{
m_all(i) = m_part(i-1);
}
for ( int i=0; i<count1; i++ )
{
cubicCoeffs->a[i] = copy_y[i];
cubicCoeffs->b[i] = ( copy_y[i+1] - copy_y[i] ) / step_h[i] -
step_h[i]*( 2*m_all(i) + m_all(i+1) ) / 6;
cubicCoeffs->c[i] = m_all(i) / 2.0;
cubicCoeffs->d[i] = ( m_all(i+1) - m_all(i) ) / ( 6.0 * step_h[i] );
}
}
else
{
std::cout<<"Not define the interpolation mode!"<<std::endl;
}
}
V m_setpart(const AtomList &ret) { m_part(ret.Count(),ret.Atoms()); }