gm_to_dirac_short_standard_normal_deviation

Gaussian-to-Dirac approximation (standard normal deviation variant).

Overview

gm_to_dirac_short_standard_normal_deviation<T> approximates a multivariate Gaussian distribution by a Dirac mixture with L components in N dimensions.

This implementation assumes a standardized Gaussian structure (standard normal deviation scaling) and performs gradient-based optimization using a GSL minimizer backend.

It is a single-threaded implementation.

Interface

Inherits:

• gm_to_dirac_approx_standard_normal_distribution_i<T>

Template parameter:

• T ∈ {float, double}

Provides overloads of:

• approximate(...)
• modified_van_mises_distance_sq(...)
• modified_van_mises_distance_sq_derivative(...)

Parameters

Common parameters:

• L → number of Dirac components
• N → dimension
• bMax → integration bound
• x → initial guess and output locations (L × N)
• wX → weights of the Dirac mixture (optional)

If wX is nullptr:

• Uniform weights are assumed

Supported Input Formats

Three overload families are available:

• Raw pointer interface (T*)
• GSL vector interface (gsl_vector / gsl_vector_float)
• GSL matrix interface (gsl_matrix / gsl_matrix_float)

Memory layout:

• x represents L × N Dirac locations

Example (Raw Pointer)

gm_to_dirac_short_standard_normal_deviation<double> approx;
 
bool ok = approx.approximate(
    L,
    N,
    bMax,
    x,        // initial guess / output (L × N)
    wX,       // weights (optional)
    &result,
    options
);

Example (GSL Vector)

gm_to_dirac_short_standard_normal_deviation<double> approx;
 
bool ok = approx.approximate(
    L,
    N,
    bMax,
    xVector,
    wXVector,
    &result,
    options
);

Example (GSL Matrix)

gm_to_dirac_short_standard_normal_deviation<double> approx;
 
bool ok = approx.approximate(
    L,
    N,
    bMax,
    xMatrix,
    wXVector,
    &result,
    options
);

Notes

• Single-threaded implementation
• Uses analytical gradient evaluation
• Specialized for standardized Gaussian structures
• Interface-compatible with other Gaussian-to-Dirac variants