Class NumericalUtil

Class Documentation

class NumericalUtil

Utility class for various numerical operations including interpolation, regression, optimization, and variability estimation.

Public Static Functions

static inline std::vector<double> calculate_first_derivative(const std::vector<double> &x, const std::vector<double> &y)

Computes the first derivative (finite difference) of y with respect to x.

Parameters:

  • x – Vector of x-values.

  • y – Vector of y-values.

Returns:

Vector of approximate derivatives.

static inline std::string to_lower_case(const std::string &str)

Converts a string to lowercase.

Parameters:

str – Input string.

Returns:

Lowercase version of the string.

static int spline(const double *x, const double *y, int n, double yp1, double ypn, double *y2, double *u)

Computes the second derivatives (spline coefficients) for natural cubic spline.

Parameters:

  • x – Input x-values.

  • y – Input y-values.

  • n – Number of points.

  • yp1 – First derivative at first point.

  • ypn – First derivative at last point.

  • y2 – Output array for second derivatives.

  • u – Temporary array for intermediate results.

Returns:

Status code.

static int splint(const double *xa, const double *ya, double *y2a, int n, double x, double *y, int klo = -1, int khi = -1)

Evaluates cubic spline interpolation.

Parameters:

  • xa – x-values used in spline.

  • ya – y-values used in spline.

  • y2a – Second derivatives computed by spline().

  • n – Number of data points.

  • x – The point to evaluate the spline at.

  • y – Output interpolated value.

  • klo – Optional: lower index for interval search.

  • khi – Optional: upper index for interval search.

Returns:

Status code.

static void interpolate_values(int size, const double *x, const double *y, double *u, int size2, const double *x2, double *y2, double *y2a, bool truncate = false, bool extrapolate = false)

Interpolates a set of values onto another grid.

Parameters:

  • size – Size of original data.

  • x – Input x-values.

  • y – Input y-values.

  • u – Temporary buffer.

  • size2 – Size of output grid.

  • x2 – New x-values.

  • y2 – Output interpolated y-values.

  • y2a – Temporary buffer for spline coefficients.

  • truncate – Whether to truncate output range.

  • extrapolate – Whether to allow extrapolation.

static void gaussian_kernal2_d(const arma::mat &surface, arma::mat &output, double bwx, double bwy)

Applies a 2D Gaussian kernel smoother to a surface.

Parameters:

  • surface – Input matrix (data grid).

  • output – Smoothed output.

  • bwx – Bandwidth in x-direction.

  • bwy – Bandwidth in y-direction.

static void local_polynomial_regression(const arma::mat &xyw, arma::mat &xy2, double bw, unsigned int order)

Performs local polynomial regression on a dataset.

Parameters:

  • xyw – Input matrix of (x, y, weights).

  • xy2 – Output matrix of (x, smoothed y).

  • bw – Bandwidth for kernel.

  • order – Polynomial order.

static void gaussian_kernal1_d(const arma::mat &xyw, arma::mat &xy2, double bw)

Applies a 1D Gaussian kernel smoother to weighted data.

Parameters:

  • xyw – Input matrix of (x, y, weights).

  • xy2 – Output matrix of (x, smoothed y).

  • bw – Bandwidth for kernel.

static void local_regression(const arma::mat &xyw, arma::mat &xy2, double bw, unsigned int order)

Performs 1D local regression on a dataset.

Parameters:

  • xyw – Input matrix of (x, y, weights).

  • xy2 – Output matrix of (x, smoothed y).

  • bw – Bandwidth.

  • order – Polynomial order.

static int newton(double &x, double (&f)(double), double (&fdiv)(double), int max_loop, double accuracy)

Newton’s method to find a root of a function.

Parameters:

  • x – Input and output: initial guess and result.

  • f – Function whose root to find.

  • fdiv – Derivative of the function.

  • max_loop – Maximum number of iterations.

  • accuracy – Target accuracy.

Returns:

Status code.

static double zbrent(double (*func)(double, void *adata), double x1, double x2, double tol, double ftol, int ITMAX, void *adata)

Finds a root using Brent’s method.

Note

Using Brent’s method, find the root of a function func known to lie between x1 and x2. The root, returned as zbrent, will be refined until its accuracy is tol.

Parameters:

  • func – Function whose root to find.

  • x1 – Lower bound of root.

  • x2 – Upper bound of root.

  • tol – Tolerance for root location.

  • ftol – Tolerance for function value.

  • ITMAX – Maximum number of iterations.

  • adata – Additional data for the function.

Returns:

The computed root.

static double first_order_variability(const std::vector<double> &x, const std::vector<double> &y, const std::vector<double> &ye)

Computes first-order variability measure of a curve.

Parameters:

  • x – Vector of x-values.

  • y – Vector of y-values.

  • ye – Vector of y-errors or weights.

Returns:

First-order variability measure.

static double second_order_variability(const std::vector<double> &x, const std::vector<double> &y, const std::vector<double> &ye)

Computes second-order variability measure of a curve.

Parameters:

  • x – Vector of x-values.

  • y – Vector of y-values.

  • ye – Vector of y-errors or weights.

Returns:

Second-order variability measure.