Collaboration diagram for polynomial:

Functions
void	a_poly_swap (a_real *a, a_size n)
	swap between $\sum_{i = 0}^{n} a_{i} x^{i}$ and $\sum_{i = 0}^{n} a_{i} x^{n - i}$

void	a_poly_swap_ (a_real a, a_real b)

a_real	a_poly_eval (a_real const *a, a_size n, a_real x)
	horner function for polynomial $\sum_{i = 0}^{n} a_{i} x^{i}$

a_real	a_poly_eval_ (a_real const a, a_real const b, a_real x)

a_real	a_poly_evar (a_real const *a, a_size n, a_real x)
	horner function for polynomial $\sum_{i = 0}^{n} a_{i} x^{n - i}$

a_real	a_poly_evar_ (a_real const a, a_real const b, a_real x)

void	a_poly_xTx (a_uint m, a_real const x, a_uint n, a_real A)
	compute the matrix A^T * A for polynomial fitting.

void	a_poly_xTy (a_uint m, a_real const x, a_real const y, a_uint n, a_real *b)
	compute the vector A^T * y for polynomial fitting.

Detailed Description

Function Documentation

◆ a_poly_eval()

a_real a_poly_eval	(	a_real const *	a,
		a_size	n,
		a_real	x )

horner function for polynomial $\sum_{i = 0}^{n} a_{i} x^{i}$

${\begin{cases} S_{n} = a_{n} \\ S_{i} = x S_{i + 1} + a_{i}, (i = n - 1, n - 2, \dots, 1, 0) \\ P (x) = S_{0} \end{cases}$

◆ a_poly_evar()

a_real a_poly_evar	(	a_real const *	a,
		a_size	n,
		a_real	x )

horner function for polynomial $\sum_{i = 0}^{n} a_{i} x^{n - i}$

${\begin{cases} S_{0} = a_{0} \\ S_{i} = x S_{i - 1} + a_{i}, (i = 1, 2, \dots, n - 1, n) \\ P (x) = S_{n} \end{cases}$

◆ a_poly_xTx()

void a_poly_xTx	(	a_uint	m,
		a_real const *	x,
		a_uint	n,
		a_real *	A )

compute the matrix A^T * A for polynomial fitting.

This function computes the product of the transpose of a design matrix A with itself (A^T * A), which is used in the normal equations for polynomial fitting using least squares method. The matrix A is implicitly defined by the input vector x, where each element of x corresponds to a data point.

Parameters

[in]	m	number of data points (rows in matrix A).
[in]	x	points to an array of size m containing the data points.
[in]	n	degree of the polynomial plus one (columns in matrix A).
[out]	A	points to an array of size nn where the result A^T A will be stored.

◆ a_poly_xTy()

void a_poly_xTy	(	a_uint	m,
		a_real const *	x,
		a_real const *	y,
		a_uint	n,
		a_real *	b )

compute the vector A^T * y for polynomial fitting.

This function computes the product of the transpose of a design matrix A with a vector y (A^T * y), which is used in the normal equations for polynomial fitting using least squares method. The matrix A is implicitly defined by the input vector x, where each element of x corresponds to a data point.