GSLLinalg.h File Reference

#include <algorithm>
#include <cmath>
#include <vector>
#include "Utilities/GSLComplex.h"
#include "Utilities/GSLMatrix.h"

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Classes
struct	gsl_permutation
	Permutation vector for LU decomposition. More...

Functions
gsl_permutation *	gsl_permutation_alloc (size_t n)
	Allocate an identity permutation of size \(n\).
void	gsl_permutation_free (gsl_permutation *p)
	Free a permutation allocated by gsl_permutation_alloc.
int	gsl_linalg_LU_decomp (gsl_matrix *A, gsl_permutation *p, int *signum)
	In-place LU decomposition with partial pivoting (real).
double	gsl_linalg_LU_det (const gsl_matrix *LU, int signum)
	Determinant from LU decomposition (real).
int	gsl_linalg_LU_invert (const gsl_matrix *LU, const gsl_permutation *p, gsl_matrix *inverse)
	Invert a matrix from its LU decomposition (real).
int	gsl_linalg_complex_LU_decomp (gsl_matrix_complex *A, gsl_permutation *p, int *signum)
	In-place LU decomposition with partial pivoting (complex).
gsl_complex	gsl_linalg_complex_LU_det (const gsl_matrix_complex *LU, int signum)
	Determinant from LU decomposition (complex).
int	gsl_linalg_complex_LU_invert (const gsl_matrix_complex *LU, const gsl_permutation *p, gsl_matrix_complex *inverse)
	Invert a matrix from its LU decomposition (complex).
int	gsl_linalg_LU_decomp_complex (gsl_matrix_complex *A, gsl_permutation *p, int *signum)
	Alias for gsl_linalg_complex_LU_decomp.
gsl_complex	gsl_linalg_LU_det_complex (const gsl_matrix_complex *LU, int signum)
	Alias for gsl_linalg_complex_LU_det.
int	gsl_linalg_LU_invert_complex (const gsl_matrix_complex *LU, const gsl_permutation *p, gsl_matrix_complex *inverse)
	Alias for gsl_linalg_complex_LU_invert.

Function Documentation

gsl_linalg_complex_LU_decomp()

int gsl_linalg_complex_LU_decomp ( gsl_matrix_complex *  A, gsl_permutation *  p, int *  signum  )

inline

In-place LU decomposition with partial pivoting (complex).

Computes \(P A = L U\), storing \(L\) and \(U\) in A.

Parameters

A	Input/Output: matrix overwritten with LU factors.
p	Output: permutation encoding row swaps.
signum	Output: sign of the permutation ( \(\pm 1\)).

Returns

Output: 0 on success, -1 on failure (e.g. non-square or singular).

Definition at line 187 of file GSLLinalg.h.

References gsl_permutation::data, gsl_complex_abs(), gsl_complex_div(), gsl_complex_mul(), gsl_complex_sub(), gsl_matrix_complex_ptr(), gsl_matrix_complex::size1, and gsl_matrix_complex::size2.

Referenced by interpolation::MMatrix< Tmplt >::determinant(), gsl_linalg_LU_decomp_complex(), and interpolation::MMatrix< Tmplt >::invert().

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gsl_linalg_complex_LU_det()

gsl_complex gsl_linalg_complex_LU_det ( const gsl_matrix_complex *  LU, int  signum  )

inline

Determinant from LU decomposition (complex).

Computes \(\det(A) = \mathrm{signum} \prod_i U_{ii}\).

Parameters

LU	Input: LU-decomposed matrix.
signum	Input: sign from gsl_linalg_complex_LU_decomp.

Returns

Output: determinant value.

Definition at line 248 of file GSLLinalg.h.

References gsl_complex_mul(), gsl_matrix_complex_ptr(), and gsl_matrix_complex::size1.

Referenced by interpolation::MMatrix< Tmplt >::determinant(), and gsl_linalg_LU_det_complex().

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gsl_linalg_complex_LU_invert()

int gsl_linalg_complex_LU_invert ( const gsl_matrix_complex *  LU, const gsl_permutation *  p, gsl_matrix_complex *  inverse  )

inline

Invert a matrix from its LU decomposition (complex).

Computes \(A^{-1}\) using the stored \(L,U\) factors and permutation.

Parameters

LU	Input: LU-decomposed matrix.
p	Input: permutation from gsl_linalg_complex_LU_decomp.
inverse	Output: matrix to receive \(A^{-1}\).

Returns

Output: 0 on success, -1 on size mismatch.

Definition at line 263 of file GSLLinalg.h.

References gsl_permutation::data, gsl_complex_add(), gsl_complex_div(), gsl_complex_mul(), gsl_complex_sub(), gsl_matrix_complex_ptr(), gsl_matrix_complex::size1, and gsl_matrix_complex::size2.

Referenced by gsl_linalg_LU_invert_complex(), and interpolation::MMatrix< Tmplt >::invert().

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gsl_linalg_LU_decomp()

int gsl_linalg_LU_decomp ( gsl_matrix *  A, gsl_permutation *  p, int *  signum  )

inline

In-place LU decomposition with partial pivoting (real).

Computes \(P A = L U\), storing \(L\) (unit lower) and \(U\) in A. The permutation p encodes \(P\).

Parameters

A	Input/Output: matrix overwritten with LU factors.
p	Output: permutation encoding row swaps.
signum	Output: sign of the permutation ( \(\pm 1\)).

Returns

Output: 0 on success, -1 on failure (e.g. non-square or singular).

Definition at line 66 of file GSLLinalg.h.

References gsl_permutation::data, gsl_matrix_ptr(), gsl_matrix::size1, and gsl_matrix::size2.

Referenced by interpolation::MMatrix< Tmplt >::determinant(), interpolation::MMatrix< Tmplt >::invert(), TEST_F(), TEST_F(), TEST_F(), and TEST_F().

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gsl_linalg_LU_decomp_complex()

int gsl_linalg_LU_decomp_complex ( gsl_matrix_complex *  A, gsl_permutation *  p, int *  signum  )

inline

Alias for gsl_linalg_complex_LU_decomp.

Parameters

A	Input/Output: matrix overwritten with LU factors.
p	Output: permutation encoding row swaps.
signum	Output: sign of the permutation ( \(\pm 1\)).

Returns

Output: 0 on success, -1 on failure.

Definition at line 319 of file GSLLinalg.h.

References gsl_linalg_complex_LU_decomp().

Referenced by TEST_F(), TEST_F(), and TEST_F().

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gsl_linalg_LU_det()

double gsl_linalg_LU_det ( const gsl_matrix *  LU, int  signum  )

inline

Determinant from LU decomposition (real).

Computes \(\det(A) = \mathrm{signum} \prod_i U_{ii}\).

Parameters

LU	Input: LU-decomposed matrix.
signum	Input: sign from gsl_linalg_LU_decomp.

Returns

Output: determinant value.

Definition at line 124 of file GSLLinalg.h.

References gsl_matrix_ptr(), and gsl_matrix::size1.

Referenced by interpolation::MMatrix< Tmplt >::determinant(), and TEST_F().

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gsl_linalg_LU_det_complex()

gsl_complex gsl_linalg_LU_det_complex ( const gsl_matrix_complex *  LU, int  signum  )

inline

Alias for gsl_linalg_complex_LU_det.

Parameters

LU	Input: LU-decomposed matrix.
signum	Input: sign from decomposition.

Returns

Output: determinant value.

Definition at line 327 of file GSLLinalg.h.

References gsl_linalg_complex_LU_det().

Referenced by TEST_F().

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gsl_linalg_LU_invert()

int gsl_linalg_LU_invert ( const gsl_matrix *  LU, const gsl_permutation *  p, gsl_matrix *  inverse  )

inline

Invert a matrix from its LU decomposition (real).

Computes \(A^{-1}\) using the stored \(L,U\) factors and permutation.

Parameters

LU	Input: LU-decomposed matrix.
p	Input: permutation from gsl_linalg_LU_decomp.
inverse	Output: matrix to receive \(A^{-1}\).

Returns

Output: 0 on success, -1 on size mismatch.

Definition at line 139 of file GSLLinalg.h.

References gsl_permutation::data, gsl_matrix_ptr(), gsl_matrix::size1, and gsl_matrix::size2.

Referenced by interpolation::MMatrix< Tmplt >::invert(), TEST_F(), and TEST_F().

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gsl_linalg_LU_invert_complex()

int gsl_linalg_LU_invert_complex ( const gsl_matrix_complex *  LU, const gsl_permutation *  p, gsl_matrix_complex *  inverse  )

inline

Alias for gsl_linalg_complex_LU_invert.

Parameters

LU	Input: LU-decomposed matrix.
p	Input: permutation from decomposition.
inverse	Output: matrix to receive \(A^{-1}\).

Returns

Output: 0 on success, -1 on size mismatch.

Definition at line 336 of file GSLLinalg.h.

References gsl_linalg_complex_LU_invert().

Referenced by TEST_F().

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gsl_permutation_alloc()

gsl_permutation * gsl_permutation_alloc ( size_t  n )

inline

Allocate an identity permutation of size \(n\).

Parameters

n	Input: permutation size.

Returns

Output: pointer to newly allocated permutation.

Definition at line 40 of file GSLLinalg.h.

References gsl_permutation::data, and gsl_permutation::size.

Referenced by interpolation::MMatrix< Tmplt >::determinant(), interpolation::MMatrix< Tmplt >::invert(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), and TEST_F().

gsl_permutation_free()

void gsl_permutation_free ( gsl_permutation *  p )

inline

Free a permutation allocated by gsl_permutation_alloc.

Parameters

p	Input: permutation to release (can be null).

Definition at line 52 of file GSLLinalg.h.

References gsl_permutation::data.

Referenced by interpolation::MMatrix< Tmplt >::determinant(), interpolation::MMatrix< Tmplt >::invert(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), and TEST_F().