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 \( \sum_{i=0}^{n}a_{i}x^{i} \)

\[ \left\{\begin{array}{l} S_n = a_n\\ S_i = xS_{i+1} + a_i,\quad(i=n-1,n-2,\cdots,1,0)\\ P(x) = S_0 \end{array}\right. \]

◆ a_poly_evar()

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

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

\[ \left\{\begin{array}{l} S_0 = a_0\\ S_i = xS_{i-1} + a_i,\quad(i=1,2,\cdots,n-1,n)\\ P(x) = S_n \end{array}\right. \]

◆ 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.