calcBasisFunctionDerivatives static method

List<List<double>> calcBasisFunctionDerivatives(int span, num u, int p, int n, List<double> U,)

Implementation

static List<List<double>> calcBasisFunctionDerivatives(int span, num u, int p, int n, List<double> U ) {

  final List<double> zeroArr = [];
  for ( int i = 0; i <= p; ++ i ){
    zeroArr[ i ] = 0.0;
  }

  final List<List<double>> ders = [];

  for ( int i = 0; i <= n; ++ i ){
    ders[ i ] = zeroArr.sublist( 0 );
  }

  final ndu = [];

  for ( int i = 0; i <= p; ++ i ){
    ndu[ i ] = zeroArr.sublist( 0 );
  }

  ndu[ 0 ][ 0 ] = 1.0;

  final List<double> left = zeroArr.sublist( 0 );
  final List<double> right = zeroArr.sublist( 0 );

  for ( int j = 1; j <= p; ++ j ) {
    left[ j ] = u - U[ span + 1 - j ];
    right[ j ] = U[ span + j ] - u;

    double saved = 0.0;

    for ( int r = 0; r < j; ++ r ) {
      final rv = right[ r + 1 ];
      final lv = left[ j - r ];
      ndu[ j ][ r ] = rv + lv;

      final temp = ndu[ r ][ j - 1 ] / ndu[ j ][ r ];
      ndu[ r ][ j ] = saved + rv * temp;
      saved = lv * temp;
    }

    ndu[ j ][ j ] = saved;
  }

  for ( int j = 0; j <= p; ++ j ) {
    ders[ 0 ][ j ] = ndu[ j ][ p ];
  }

  for ( int r = 0; r <= p; ++ r ) {
    int s1 = 0;
    int s2 = 1;

    final a = [];
    for ( int i = 0; i <= p; ++ i ) {
      a[ i ] = zeroArr.sublist( 0 );
    }

    a[ 0 ][ 0 ] = 1.0;

    for ( int k = 1; k <= n; ++ k ) {
      double d = 0.0;
      final rk = r - k;
      final pk = p - k;

      if ( r >= k ) {
        a[ s2 ][ 0 ] = a[ s1 ][ 0 ] / ndu[ pk + 1 ][ rk ];
        d = a[ s2 ][ 0 ] * ndu[ rk ][ pk ];
      }

      final j1 = ( rk >= - 1 ) ? 1 : - rk;
      final j2 = ( r - 1 <= pk ) ? k - 1 : p - r;

      for ( int j = j1; j <= j2; ++ j ) {
        a[ s2 ][ j ] = ( a[ s1 ][ j ] - a[ s1 ][ j - 1 ] ) / ndu[ pk + 1 ][ rk + j ];
        d += a[ s2 ][ j ] * ndu[ rk + j ][ pk ];
      }

      if ( r <= pk ) {
        a[ s2 ][ k ] = - a[ s1 ][ k - 1 ] / ndu[ pk + 1 ][ r ];
        d += a[ s2 ][ k ] * ndu[ r ][ pk ];
      }

      ders[ k ][ r ] = d;

      final j = s1;
      s1 = s2;
      s2 = j;
    }
  }

  num r = p;

  for ( int k = 1; k <= n; ++ k ) {
    for ( int j = 0; j <= p; ++ j ) {
      ders[ k ][ j ] *= r;
    }
    r *= p - k;
  }

  return ders;
}