Math API

Collaboration diagram for Math API:

Functions
int	a4l_math_polyfit (unsigned r_dim, double *r, double orig, const unsigned dim, double *x, double *y)
	Calculate the polynomial fit. More...
void	a4l_math_mean (double *pmean, double *val, unsigned nr)
	Calculate the aritmetic mean of an array of values. More...
void	a4l_math_stddev (double *pstddev, double mean, double *val, unsigned nr)
	Calculate the standard deviation of an array of values. More...
void	a4l_math_stddev_of_mean (double *pstddevm, double mean, double *val, unsigned nr)
	Calculate the standard deviation of the mean. More...

Detailed Description

Function Documentation

a4l_math_mean()

void a4l_math_mean	(	double *	pmean,
		double *	val,
		unsigned	nr
	)

Calculate the aritmetic mean of an array of values.

Parameters

[out]	pmean	Pointer to the resulting value
[in]	val	Array of input values
[in]	nr	Number of array elements

a4l_math_polyfit()

int a4l_math_polyfit	(	unsigned	r_dim,
		double *	r,
		double	orig,
		const unsigned	dim,
		double *	x,
		double *	y
	)

Calculate the polynomial fit.

Parameters

[in]	r_dim	Number of elements of the resulting polynomial
[out]	r	Polynomial
[in]	orig
[in]	dim	Number of elements in the polynomials
[in]	x	Polynomial
[in]	y	Polynomial

Operation:

We are looking for Res such that A.Res = Y, with A the Vandermonde matrix made from the X vector.

Using the least square method, this means finding Res such that: A^t.A.Res = A^tY

If we write A = Q.R with Q^t.Q = 1, and R non singular, this can be reduced to: R.Res = Q^t.Y

mat_qr() gives us R and Q^t.Y from A and Y

We can then obtain Res by back substitution using mat_upper_triangular_backsub() with R upper triangular.

a4l_math_stddev()

void a4l_math_stddev	(	double *	pstddev,
		double	mean,
		double *	val,
		unsigned	nr
	)

Calculate the standard deviation of an array of values.

Parameters

[out]	pstddev	Pointer to the resulting value
[in]	mean	Mean value
[in]	val	Array of input values
[in]	nr	Number of array elements

Referenced by a4l_math_stddev_of_mean().

a4l_math_stddev_of_mean()

void a4l_math_stddev_of_mean	(	double *	pstddevm,
		double	mean,
		double *	val,
		unsigned	nr
	)

Calculate the standard deviation of the mean.

Parameters

[out]	pstddevm	Pointer to the resulting value
[in]	mean	Mean value
[in]	val	Array of input values
[in]	nr	Number of array elements

References a4l_math_stddev().