L1 Trend Filter

This section provides methods for computing the L1 trend (L1 filtering) of vector data. This approach is used to extract a smooth trend from time series while preserving sharp changes (breakpoints), making it useful for financial and signal analysis.-тренда (L1-фильтрации) данных вектора. Этот подход используется для выделения сглаженного тренда во временных рядах с сохранением резких изменений (изломов), что делает его полезным при анализе финансовых и других сигналов.

The section includes the functions:

• L1TrendFilterLambdaMax – computes the maximum value of the regularization parameter λmax for a given vector. This value can be used as a reference when choosing λ.
• L1TrendFilter – performs L1 filtering (trend extraction) using a specified regularization parameter λ.

The parameter λ controls the degree of smoothing:

• small values produce a trend closer to the original data;
• large values result in a smoother trend.

The value of λ can be specified:

• in absolute units;
• relative to λmax, computed in advance using L1TrendFilterLambdaMax.

All methods operate on vector<double> and vector<float> types, and memory usage grows linearly with the size of the input data.