Matrix decompositions in floating point. More...

#include "math/pprz_simple_matrix.h"
#include "math/pprz_matrix_decomp_float.h"
#include "math/pprz_algebra_float.h"
#include <math.h>
#include <string.h>

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Macros
#define	DEBUG_PRINT(...)

#define	DEBUG_MAT_PRINT(...)

Functions
void	pprz_cholesky_float (float out, float in, int n)
	Cholesky decomposition. More...

void	pprz_qr_float (float Q, float R, float **in, int m, int n)
	QR decomposition. More...

static float	pythag (float a, float b)
	Some SVD decomposition utility macros and functions. More...

static int	imin (int num1, int num2)

int	pprz_svd_float (float *a, float w, float **v, int m, int n)
	SVD decomposition. More...

void	pprz_svd_solve_float (float x, float u, float w, float v, float *b, int m, int n, int l)
	SVD based linear solver. More...

void	fit_linear_model (float targets, int D, float(samples)[D], uint16_t count, bool use_bias, float params, float fit_error)
	Fit a linear model from samples to target values. More...

void	fit_linear_model_prior (float targets, int D, float(samples)[D], uint16_t count, bool use_bias, float priors, float params, float *fit_error)
	Fit a linear model from samples to target values with a prior. More...

Detailed Description

Matrix decompositions in floating point.

Definition in file pprz_matrix_decomp_float.c.

Macro Definition Documentation

◆ DEBUG_MAT_PRINT

#define DEBUG_MAT_PRINT ( ... )

Definition at line 39 of file pprz_matrix_decomp_float.c.

◆ DEBUG_PRINT

#define DEBUG_PRINT ( ... )

Definition at line 38 of file pprz_matrix_decomp_float.c.

Function Documentation

◆ fit_linear_model()

void fit_linear_model	(	float *	targets,
		int	D,
		float(*)	samples[D],
		uint16_t	count,
		bool	use_bias,
		float *	params,
		float *	fit_error
	)

Fit a linear model from samples to target values.

Effectively a wrapper for the pprz_svd_float and pprz_svd_solve_float functions.

Parameters

[in]	targets	The target values
[in]	samples	The samples / feature vectors
[in]	D	The dimensionality of the samples
[in]	count	The number of samples
[in]	use_bias	Whether to use the bias. Please note that params should always be of size D+1, but in case of no bias, the bias value is set to 0.
[out]	parameters*	Parameters of the linear fit
[out]	fit_error*	Total error of the fit

Definition at line 529 of file pprz_matrix_decomp_float.c.

References D, MAKE_MATRIX_PTR, MAT_MUL, MAT_SUB, n_samples, parameters, pprz_svd_float(), and pprz_svd_solve_float().

Referenced by RANSAC_linear_model().

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◆ fit_linear_model_prior()

void fit_linear_model_prior	(	float *	targets,
		int	D,
		float(*)	samples[D],
		uint16_t	count,
		bool	use_bias,
		float *	priors,
		float *	params,
		float *	fit_error
	)

Fit a linear model from samples to target values with a prior.

Effectively a wrapper for the pprz_svd_float and pprz_svd_solve_float functions.

Parameters

[in]	targets	The target values
[in]	samples	The samples / feature vectors
[in]	D	The dimensionality of the samples
[in]	count	The number of samples
[in]	use_bias	Whether to use the bias. Please note that params should always be of size D+1, but in case of no bias, the bias value is set to 0.
[in]	priors	Prior per dimension. If use_bias, also for the dimension D+1.
[out]	parameters*	Parameters of the linear fit
[out]	fit_error*	Total error of the fit

Definition at line 617 of file pprz_matrix_decomp_float.c.

References D, DEBUG_MAT_PRINT, DEBUG_PRINT, float_mat_invert(), float_mat_mul(), float_mat_sum(), float_mat_transpose(), MAKE_MATRIX_PTR, MAT_MUL, MAT_SUB, n_samples, and parameters.

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◆ imin()

static int imin	(	int	num1,
		int	num2
	)

static

Definition at line 144 of file pprz_matrix_decomp_float.c.

Referenced by pprz_svd_float().

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◆ pprz_cholesky_float()

void pprz_cholesky_float	(	float **	out,
		float **	in,
		int	n
	)

Cholesky decomposition.

http://rosettacode.org/wiki/Cholesky_decomposition#C

Parameters

out	pointer to the output array [n x n]
in	pointer to the input array [n x n]
n	dimension of the matrix

Definition at line 50 of file pprz_matrix_decomp_float.c.

References float_mat_copy(), float_mat_zero(), MAKE_MATRIX_PTR, and s.

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◆ pprz_qr_float()

void pprz_qr_float	(	float **	Q,
		float **	R,
		float **	in,
		int	m,
		int	n
	)

QR decomposition.

using Householder method

http://rosettacode.org/wiki/QR_decomposition#C

Parameters

Q	square orthogonal matrix Q [m x m]
R	upper triangular matrix R [m x n]
in	pointer to the input array [m x n]
m	number of rows of the input matrix
n	number of column of the input matrix

Definition at line 89 of file pprz_matrix_decomp_float.c.

References b, float_mat_col(), float_mat_copy(), float_mat_minor(), float_mat_mul(), float_mat_transpose_square(), float_mat_vmul(), float_vect_norm(), float_vect_sdiv(), simple_quad_sim::m, MAKE_MATRIX_PTR, z1, and z2.

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◆ pprz_svd_float()

int pprz_svd_float	(	float **	a,
		float *	w,
		float **	v,
		int	m,
		int	n
	)

SVD decomposition.

------------------------------------------------------------------— * Reference: "Numerical Recipes By W.H. Press, B. P. Flannery, * S.A. Teukolsky and W.T. Vetterling, Cambridge * University Press, 1986" [BIBLI 08]. * ------------------------------------------------------------------— *

Given a matrix a(m,n), this routine computes its singular value decomposition, A = U · W · Vt. The matrix U replaces a on output. The diagonal matrix of singular values W is output as a vector w(n). The matrix V (not the transpose Vt) is output as v(n,n).

Parameters

a	input matrix [m x n] and output matrix U [m x n]
w	output diagonal vector of matrix W [n]
v	output square matrix V [n x n]
m	number of rows of input the matrix
n	number of columns of the input matrix

Returns: 0 (false) if convergence failed, 1 (true) if decomposition succed

Definition at line 167 of file pprz_matrix_decomp_float.c.

References H, imin(), simple_quad_sim::m, pythag(), mesonh.mesonh_atmosphere::X, mesonh.mesonh_atmosphere::Y, and mesonh.mesonh_atmosphere::Z.

Referenced by fit_linear_flow_field(), fit_linear_model(), fit_linear_model_OF(), and pprz_polyfit_float().

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◆ pprz_svd_solve_float()

void pprz_svd_solve_float	(	float **	x,
		float **	u,
		float *	w,
		float **	v,
		float **	b,
		int	m,
		int	n,
		int	l
	)

SVD based linear solver.

Solves A · X = B for a vector X, where A is specified by the arrays u, w, v as returned by pprz_svd_float. m and n are the dimensions of a. b(m) is the input right-hand side. x(n) is the output solution vector. No input quantities are destroyed, so the routine may be called sequentially with different b's.

Parameters

x	solution of the system ([n x l] matrix)
u	U matrix from SVD decomposition
w	diagonal of the W matrix from the SVD decomposition
v	V matrrix from SVD decomposition
b	right-hand side input matrix from system to solve (column vector [m x l])
m	number of rows of the matrix A
n	number of columns of the matrix A
l	number of columns of the matrix B