// the function CanSplitRangeFast()
// makes decision whether a given range should be split or not ;
//
// a given range is not subdivided if the specified accuracy of
// linear regression has been achieved, otherwise,
// the function selects for the best split the position of
// the greatest local maximum of absolute differences
// between original and smoothed values in a given range ;
//
static public bool CanSplitRangeFast
(
// original dataset
List <double> data_x,
List <double> data_y,
// absolute differences between original and smoothed values
List <double> vec_devns_in,
// positions (indices) of local maxima in vec_devns_in
List <int> vec_max_ind_in,
// the limit for maximum allowed approximation error (tolerance)
double devn_max_user,
// input range to be split if linear regression is not acceptable
RangeIndex idx_range_in,
// the position of a split point, when the function returns <true>
ref int idx_split_out,
// the parameters of linear regression for the given range,
// when the function returns <false>
LinearRegressionParams lr_params_out
)
{
idx_split_out = -1;
if (vec_devns_in.Count != data_x.Count)
{
Console.WriteLine("SLR: size error");
return(false);
}
int end_offset = RangeLengthMin();
int range_len = idx_range_in.Length();
if (range_len < end_offset)
{
Console.WriteLine("SLR: input range is too small");
return(false);
}
// compute linear regression and approximation error for input range
double err_range_in = double.MaxValue;
ComputeLinearRegression(data_x, data_y, idx_range_in, lr_params_out, ref err_range_in);
// if the approximation is acceptable, input range is not subdivided
if (err_range_in < devn_max_user)
{
return(false);
}
// check for indivisible range
if (range_len < 2 * RangeLengthMin())
{
return(false);
}
if (vec_devns_in.Count == 0)
{
return(false);
}
// for the main criterion of splitting here we use
// the greatest local maximum of deviations inside the given range
int idx_split_local_max = -1;
double devn_max = 0.0;
double devn_cur = 0.0;
int sz_loc_max = vec_max_ind_in.Count;
// find inside given range local maximum with the largest deviation
for (int k_max = 0; k_max < sz_loc_max; ++k_max)
{
int idx_max_cur = vec_max_ind_in[k_max];
// check if the current index is inside the given range and that
// potential split will not create segment with 1 data point only
if ((idx_max_cur < idx_range_in.idx_a + end_offset) ||
(idx_max_cur >= idx_range_in.idx_b - end_offset))
{
continue;
}
devn_cur = vec_devns_in[idx_max_cur];
if (devn_cur > devn_max)
{
devn_max = devn_cur;
idx_split_local_max = idx_max_cur;
}
}
// the case of no one local maximum inside the given range
if (idx_split_local_max < 0)
{
return(false);
}
// the case (idx_split_local_max==0) is not possible here due to (end_offset==RANGE_LENGTH_MIN),
// this is a valid result ( idx_split_local_max > 0 )
idx_split_out = idx_split_local_max;
return(true);
}
// the function ComputeLinearRegression() computes parameters of
// linear regression and approximation error
// for a given range of a given dataset ;
static public void ComputeLinearRegression
(
// original dataset
List <double> data_x,
List <double> data_y,
// semi-open range [ a , b )
RangeIndex idx_range,
// coefficients of linear regression in the given range
LinearRegressionParams lin_regr_out,
// approximation error
ref double err_appr_out
)
{
if (idx_range.Length() < RangeLengthMin())
{
Console.WriteLine("SLR error: input range is too small");
return;
}
int idx_a = idx_range.idx_a;
int idx_b = idx_range.idx_b;
double n_vals = idx_range.Length();
double sum_x = 0.0;
double sum_y = 0.0;
double sum_xx = 0.0;
double sum_xy = 0.0;
// compute the required sums:
for (int it = idx_a; it < idx_b; ++it)
{
double xi = data_x[it];
double yi = data_y[it];
sum_x += xi;
sum_y += yi;
sum_xx += xi * xi;
sum_xy += xi * yi;
}
// compute parameters of linear regression in the given range
if (!LinearRegressionParameters(n_vals, sum_x, sum_y, sum_xx, sum_xy, lin_regr_out))
{
// this is a very unusual case for real data
//Console.WriteLine("SLR: special case error");
return;
}
double coef_a = lin_regr_out.coef_a;
double coef_b = lin_regr_out.coef_b;
// use linear regression obtained to measure approximation error in the given range,
// the error is the maximum of absolute differences between original and approximation values
double diff_max = 0.0;
for (int it = idx_a; it < idx_b; ++it)
{
double xi = data_x[it];
double yi_orig = data_y[it];
double yi_appr = coef_a + coef_b * xi;
double diff_i = Math.Abs(yi_orig - yi_appr);
if (diff_i > diff_max)
{
diff_max = diff_i;
}
}
err_appr_out = diff_max;
}
