pprz_matrix_decomp_float.h File Reference

Matrix decompositions in floating point. More...

#include "std.h"

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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...
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.h.

Function Documentation

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
[out]	parameters*	Parameters of the linear fit
[out]	fit_error*	Total error of the fit

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 526 of file pprz_matrix_decomp_float.c.

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

Referenced by RANSAC_linear_model().

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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 614 of file pprz_matrix_decomp_float.c.

References AA, 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, and n_samples.

Referenced by RANSAC_linear_model().

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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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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 columns of the input matrix

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 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(), Int32RMat::m, MAKE_MATRIX_PTR, z1, and z2.

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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]. *

• C++ Release 2.0 By J-P Moreau, Paris * (www.jpmoreau.fr) * http://jean-pierre.moreau.pagesperso-orange.fr ------------------------------------------------------------------— *

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

------------------------------------------------------------------— * 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 164 of file pprz_matrix_decomp_float.c.

References H, Int32RMat::m, pythag(), mesonh.mesonh_atmosphere::X, mesonh.mesonh_atmosphere::Y, and mesonh.mesonh_atmosphere::Z.

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

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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

Definition at line 491 of file pprz_matrix_decomp_float.c.

References Int32RMat::m, and s.

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

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