oct-norm.cc File Reference

#include <cassert>
#include <cfloat>
#include <cmath>
#include <iostream>
#include <vector>
#include "oct-cmplx.h"
#include "lo-error.h"
#include "lo-ieee.h"
#include "Array.h"
#include "Array-util.h"
#include "CMatrix.h"
#include "dMatrix.h"
#include "fCMatrix.h"
#include "fMatrix.h"
#include "CColVector.h"
#include "dColVector.h"
#include "CRowVector.h"
#include "dRowVector.h"
#include "fCColVector.h"
#include "fColVector.h"
#include "fCRowVector.h"
#include "fRowVector.h"
#include "CSparse.h"
#include "dSparse.h"
#include "dbleSVD.h"
#include "CmplxSVD.h"
#include "floatSVD.h"
#include "fCmplxSVD.h"

Include dependency graph for oct-norm.cc:

Go to the source code of this file.

Classes
class	norm_accumulator_0< R >
class	norm_accumulator_1< R >
class	norm_accumulator_2< R >
class	norm_accumulator_inf< R >
class	norm_accumulator_minf< R >
class	norm_accumulator_mp< R >
class	norm_accumulator_p< R >

Macros
#define	DEFINE_COLROW_NORM_FUNCS(PREFIX, RPREFIX, RTYPE)
#define	DEFINE_DISPATCHER(FUNC_NAME, ARG_TYPE, RES_TYPE)
#define	DEFINE_XNORM_FUNCS(PREFIX, RTYPE)
#define	DEFINE_XNORM_SPARSE_FUNCS(PREFIX, RTYPE)

Functions
template<class T , class R >
void	array_norm_2 (const T *v, octave_idx_type n, R &res)
template<class T , class R , class ACC >
void	column_norms (const MArray< T > &m, MArray< R > &res, ACC acc)
template<class T , class R , class ACC >
void	column_norms (const MSparse< T > &m, MArray< R > &res, ACC acc)
template<class T , class R >
MArray< R >	column_norms (const MArray< T > &v, R p)
template<class T , class R >
MArray< R >	column_norms (const MSparse< T > &v, R p)
template<class VectorT , class R >
VectorT	dual_p (const VectorT &x, R p, R q)
template<class T , class R >
T	elem_dual_p (T x, R p)
template<class MatrixT , class VectorT , class R >
R	higham (const MatrixT &m, R p, R tol, int maxiter, VectorT &x)
template<class ColVectorT , class R >
static void	higham_subp (const ColVectorT &y, const ColVectorT &col, octave_idx_type nsamp, R p, R &lambda, R &mu)
template<class ColVectorT , class R >
static void	higham_subp (const ColVectorT &y, const ColVectorT &col, octave_idx_type nsamp, R p, std::complex< R > &lambda, std::complex< R > &mu)
template<class MatrixT , class VectorT , class SVDT , class R >
R	matrix_norm (const MatrixT &m, R p, VectorT, SVDT)
template<class MatrixT , class VectorT , class R >
R	matrix_norm (const MatrixT &m, R p, VectorT)
template<class T , class R , class ACC >
void	row_norms (const MArray< T > &m, MArray< R > &res, ACC acc)
template<class T , class R , class ACC >
void	row_norms (const MSparse< T > &m, MArray< R > &res, ACC acc)
template<class T , class R >
MArray< R >	row_norms (const MArray< T > &v, R p)
template<class T , class R >
MArray< R >	row_norms (const MSparse< T > &v, R p)
template<class T , class R , class ACC >
void	vector_norm (const Array< T > &v, R &res, ACC acc)
template<class T , class R >
R	vector_norm (const MArray< T > &v, R p)
OCTAVE_API RowVector	xcolnorms (const Matrix &m, double p)
OCTAVE_API RowVector	xcolnorms (const ComplexMatrix &m, double p)
OCTAVE_API FloatRowVector	xcolnorms (const FloatMatrix &m, float p)
OCTAVE_API FloatRowVector	xcolnorms (const FloatComplexMatrix &m, float p)
OCTAVE_API RowVector	xcolnorms (const SparseMatrix &m, double p)
OCTAVE_API RowVector	xcolnorms (const SparseComplexMatrix &m, double p)
OCTAVE_API double	xfrobnorm (const Matrix &x)
OCTAVE_API double	xfrobnorm (const ComplexMatrix &x)
OCTAVE_API float	xfrobnorm (const FloatMatrix &x)
OCTAVE_API float	xfrobnorm (const FloatComplexMatrix &x)
OCTAVE_API double	xfrobnorm (const SparseMatrix &x)
OCTAVE_API double	xfrobnorm (const SparseComplexMatrix &x)
OCTAVE_API double	xnorm (const RowVector &x, double p)
OCTAVE_API double	xnorm (const ColumnVector &x, double p)
OCTAVE_API double	xnorm (const Matrix &x, double p)
OCTAVE_API double	xnorm (const ComplexMatrix &x, double p)
OCTAVE_API double	xnorm (const ComplexRowVector &x, double p)
OCTAVE_API double	xnorm (const ComplexColumnVector &x, double p)
OCTAVE_API float	xnorm (const FloatRowVector &x, float p)
OCTAVE_API float	xnorm (const FloatMatrix &x, float p)
OCTAVE_API float	xnorm (const FloatColumnVector &x, float p)
OCTAVE_API float	xnorm (const FloatComplexMatrix &x, float p)
OCTAVE_API float	xnorm (const FloatComplexRowVector &x, float p)
OCTAVE_API float	xnorm (const FloatComplexColumnVector &x, float p)
OCTAVE_API double	xnorm (const SparseMatrix &x, double p)
OCTAVE_API double	xnorm (const SparseComplexMatrix &x, double p)
OCTAVE_API ColumnVector	xrownorms (const Matrix &m, double p)
OCTAVE_API ColumnVector	xrownorms (const ComplexMatrix &m, double p)
OCTAVE_API FloatColumnVector	xrownorms (const FloatMatrix &m, float p)
OCTAVE_API FloatColumnVector	xrownorms (const FloatComplexMatrix &m, float p)
OCTAVE_API ColumnVector	xrownorms (const SparseMatrix &m, double p)
OCTAVE_API ColumnVector	xrownorms (const SparseComplexMatrix &m, double p)

Variables
static int	max_norm_iter = 100
static const char *	p_less1_gripe = "xnorm: p must be at least 1"

Macro Definition Documentation

#define DEFINE_COLROW_NORM_FUNCS	(		PREFIX,
			RPREFIX,
			RTYPE
	)

Value:

extern OCTAVE_API RPREFIX##RowVector xcolnorms (const PREFIX##Matrix& m, RTYPE p) \
  { return column_norms (m, p); } \
  extern OCTAVE_API RPREFIX##ColumnVector xrownorms (const PREFIX##Matrix& m, RTYPE p) \
  { return row_norms (m, p); } \

Definition at line 556 of file oct-norm.cc.

#define DEFINE_DISPATCHER	(		FUNC_NAME,
			ARG_TYPE,
			RES_TYPE
	)

Value:

template <class T, class R> \
RES_TYPE FUNC_NAME (const ARG_TYPE& v, R p) \
{ \
  RES_TYPE res; \
  if (p == 2) \
    FUNC_NAME (v, res, norm_accumulator_2<R> ()); \
  else if (p == 1) \
    FUNC_NAME (v, res, norm_accumulator_1<R> ()); \
  else if (lo_ieee_isinf (p)) \
    { \
      if (p > 0) \
        FUNC_NAME (v, res, norm_accumulator_inf<R> ()); \
      else \
        FUNC_NAME (v, res, norm_accumulator_minf<R> ()); \
    } \
  else if (p == 0) \
    FUNC_NAME (v, res, norm_accumulator_0<R> ()); \
  else if (p > 0) \
    FUNC_NAME (v, res, norm_accumulator_p<R> (p)); \
  else \
    FUNC_NAME (v, res, norm_accumulator_mp<R> (p)); \
  return res; \
}

Definition at line 287 of file oct-norm.cc.

#define DEFINE_XNORM_FUNCS	(		PREFIX,
			RTYPE
	)

Value:

OCTAVE_API RTYPE xnorm (const PREFIX##ColumnVector& x, RTYPE p) \
  { return vector_norm (x, p); } \
  OCTAVE_API RTYPE xnorm (const PREFIX##RowVector& x, RTYPE p) \
  { return vector_norm (x, p); } \
  OCTAVE_API RTYPE xnorm (const PREFIX##Matrix& x, RTYPE p) \
  { return matrix_norm (x, p, PREFIX##Matrix (), PREFIX##SVD ()); } \
  OCTAVE_API RTYPE xfrobnorm (const PREFIX##Matrix& x) \
  { return vector_norm (x, static_cast<RTYPE> (2)); }

Definition at line 517 of file oct-norm.cc.

#define DEFINE_XNORM_SPARSE_FUNCS	(		PREFIX,
			RTYPE
	)

Value:

OCTAVE_API RTYPE xnorm (const Sparse##PREFIX##Matrix& x, RTYPE p) \
  { return matrix_norm (x, p, PREFIX##Matrix ()); } \
  OCTAVE_API RTYPE xfrobnorm (const Sparse##PREFIX##Matrix& x) \
  { \
    RTYPE res; \
    array_norm_2 (x.data (), x.nnz (), res); \
    return res; \
  }

Definition at line 543 of file oct-norm.cc.

Function Documentation

template<class T , class R >

void array_norm_2 ( const T *  v, octave_idx_type  n, R &  res  )

inline

Definition at line 534 of file oct-norm.cc.

References norm_accumulator_2< R >::accum().

template<class T , class R , class ACC >

void column_norms	(	const MArray< T > &	m,
		MArray< R > &	res,
		ACC	acc
	)

Definition at line 228 of file oct-norm.cc.

References Array< T >::columns(), Array< T >::rows(), and Array< T >::xelem().

template<class T , class R , class ACC >

void column_norms	(	const MSparse< T > &	m,
		MArray< R > &	res,
		ACC	acc
	)

Definition at line 258 of file oct-norm.cc.

References Sparse< T >::cidx(), Sparse< T >::columns(), Sparse< T >::data(), and Array< T >::xelem().

template<class T , class R >

MArray<R> column_norms	(	const MArray< T > &	v,
		R	p
	)

Definition at line 313 of file oct-norm.cc.

template<class T , class R >

MArray<R> column_norms	(	const MSparse< T > &	v,
		R	p
	)

Definition at line 315 of file oct-norm.cc.

template<class VectorT , class R >

VectorT dual_p	(	const VectorT &	x,
		R	p,
		R	q
	)

Definition at line 401 of file oct-norm.cc.

References elem_dual_p(), vector_norm(), and x.

Referenced by higham().

template<class T , class R >

T elem_dual_p ( T  x, R  p  )

inline

Definition at line 391 of file oct-norm.cc.

References abs(), pow(), and signum().

Referenced by dual_p().

template<class MatrixT , class VectorT , class R >

R higham	(	const MatrixT &	m,
		R	p,
		R	tol,
		int	maxiter,
		VectorT &	x
	)

Definition at line 411 of file oct-norm.cc.

References dual_p(), gamma(), higham_subp(), vector_norm(), and x.

Referenced by matrix_norm().

template<class ColVectorT , class R >

static void higham_subp ( const ColVectorT &  y, const ColVectorT &  col, octave_idx_type  nsamp, R  p, R &  lambda, R &  mu  )

static

Definition at line 323 of file oct-norm.cc.

References abs(), fi, pow(), and vector_norm().

Referenced by higham().

template<class ColVectorT , class R >

static void higham_subp ( const ColVectorT &  y, const ColVectorT &  col, octave_idx_type  nsamp, R  p, std::complex< R > &  lambda, std::complex< R > &  mu  )

static

Definition at line 349 of file oct-norm.cc.

References abs(), fi, pow(), and vector_norm().

template<class MatrixT , class VectorT , class SVDT , class R >

R matrix_norm	(	const MatrixT &	m,
		R	p,
		VectorT	,
		SVDT
	)

Definition at line 470 of file oct-norm.cc.

References current_liboctave_error_handler, higham(), lo_ieee_isinf, RowVector::max(), ColumnVector::max(), p_less1_gripe, SVD::sigma_only, x, xcolnorms(), and xrownorms().

template<class MatrixT , class VectorT , class R >

R matrix_norm	(	const MatrixT &	m,
		R	p,
		VectorT
	)

Definition at line 496 of file oct-norm.cc.

References current_liboctave_error_handler, higham(), lo_ieee_isinf, RowVector::max(), ColumnVector::max(), p_less1_gripe, x, xcolnorms(), and xrownorms().

template<class T , class R , class ACC >

void row_norms	(	const MArray< T > &	m,
		MArray< R > &	res,
		ACC	acc
	)

Definition at line 242 of file oct-norm.cc.

References Array< T >::columns(), Array< T >::rows(), and Array< T >::xelem().

template<class T , class R , class ACC >

void row_norms	(	const MSparse< T > &	m,
		MArray< R > &	res,
		ACC	acc
	)

Definition at line 272 of file oct-norm.cc.

References Sparse< T >::cidx(), Sparse< T >::columns(), Sparse< T >::data(), Sparse< T >::ridx(), Sparse< T >::rows(), and Array< T >::xelem().

template<class T , class R >

MArray<R> row_norms	(	const MArray< T > &	v,
		R	p
	)

Definition at line 314 of file oct-norm.cc.

template<class T , class R >

MArray<R> row_norms	(	const MSparse< T > &	v,
		R	p
	)

Definition at line 316 of file oct-norm.cc.

template<class T , class R , class ACC >

void vector_norm ( const Array< T > &  v, R &  res, ACC  acc  )

inline

Definition at line 218 of file oct-norm.cc.

References Array< T >::numel().

Referenced by dual_p(), higham(), and higham_subp().

template<class T , class R >

R vector_norm	(	const MArray< T > &	v,
		R	p
	)

Definition at line 312 of file oct-norm.cc.

OCTAVE_API RowVector xcolnorms	(	const Matrix &	m,
		double	p
	)

Definition at line 562 of file oct-norm.cc.

Referenced by Fnorm(), matrix_norm(), and xcolnorms().

OCTAVE_API RowVector xcolnorms	(	const ComplexMatrix &	m,
		double	p
	)

Definition at line 563 of file oct-norm.cc.

OCTAVE_API FloatRowVector xcolnorms	(	const FloatMatrix &	m,
		float	p
	)

Definition at line 564 of file oct-norm.cc.

OCTAVE_API FloatRowVector xcolnorms	(	const FloatComplexMatrix &	m,
		float	p
	)

Definition at line 565 of file oct-norm.cc.

OCTAVE_API RowVector xcolnorms	(	const SparseMatrix &	m,
		double	p
	)

Definition at line 567 of file oct-norm.cc.

OCTAVE_API RowVector xcolnorms	(	const SparseComplexMatrix &	m,
		double	p
	)

Definition at line 568 of file oct-norm.cc.

OCTAVE_API double xfrobnorm

(

const Matrix &

x

)

Definition at line 527 of file oct-norm.cc.

Referenced by Fnorm(), Fsqrtm(), and xfrobnorm().

OCTAVE_API double xfrobnorm

(

const ComplexMatrix &

x

)

Definition at line 528 of file oct-norm.cc.

OCTAVE_API float xfrobnorm

(

const FloatMatrix &

x

)

Definition at line 529 of file oct-norm.cc.

OCTAVE_API float xfrobnorm

(

const FloatComplexMatrix &

x

)

Definition at line 530 of file oct-norm.cc.

OCTAVE_API double xfrobnorm

(

const SparseMatrix &

x

)

Definition at line 553 of file oct-norm.cc.

OCTAVE_API double xfrobnorm

(

const SparseComplexMatrix &

x

)

Definition at line 554 of file oct-norm.cc.

OCTAVE_API double xnorm	(	const RowVector &	x,
		double	p
	)

Definition at line 527 of file oct-norm.cc.

OCTAVE_API double xnorm	(	const ColumnVector &	x,
		double	p
	)

Definition at line 527 of file oct-norm.cc.

Referenced by Matrix::determinant(), FloatMatrix::determinant(), ComplexMatrix::determinant(), FloatComplexMatrix::determinant(), do_mgorth(), do_sqrtm(), Fnorm(), CHOL::init(), FloatCHOL::init(), ComplexCHOL::init(), FloatComplexCHOL::init(), and xnorm().

OCTAVE_API double xnorm	(	const Matrix &	x,
		double	p
	)

Definition at line 527 of file oct-norm.cc.

OCTAVE_API double xnorm	(	const ComplexMatrix &	x,
		double	p
	)

Definition at line 528 of file oct-norm.cc.

OCTAVE_API double xnorm	(	const ComplexRowVector &	x,
		double	p
	)

Definition at line 528 of file oct-norm.cc.

OCTAVE_API double xnorm	(	const ComplexColumnVector &	x,
		double	p
	)

Definition at line 528 of file oct-norm.cc.

OCTAVE_API float xnorm	(	const FloatRowVector &	x,
		float	p
	)

Definition at line 529 of file oct-norm.cc.

OCTAVE_API float xnorm	(	const FloatMatrix &	x,
		float	p
	)

Definition at line 529 of file oct-norm.cc.

OCTAVE_API float xnorm	(	const FloatColumnVector &	x,
		float	p
	)

Definition at line 529 of file oct-norm.cc.

OCTAVE_API float xnorm	(	const FloatComplexMatrix &	x,
		float	p
	)

Definition at line 530 of file oct-norm.cc.

OCTAVE_API float xnorm	(	const FloatComplexRowVector &	x,
		float	p
	)

Definition at line 530 of file oct-norm.cc.

OCTAVE_API float xnorm	(	const FloatComplexColumnVector &	x,
		float	p
	)

Definition at line 530 of file oct-norm.cc.

OCTAVE_API double xnorm	(	const SparseMatrix &	x,
		double	p
	)

Definition at line 553 of file oct-norm.cc.

OCTAVE_API double xnorm	(	const SparseComplexMatrix &	x,
		double	p
	)

Definition at line 554 of file oct-norm.cc.

OCTAVE_API ColumnVector xrownorms	(	const Matrix &	m,
		double	p
	)

Definition at line 562 of file oct-norm.cc.

Referenced by Fnorm(), matrix_norm(), and xrownorms().

OCTAVE_API ColumnVector xrownorms	(	const ComplexMatrix &	m,
		double	p
	)

Definition at line 563 of file oct-norm.cc.

OCTAVE_API FloatColumnVector xrownorms	(	const FloatMatrix &	m,
		float	p
	)

Definition at line 564 of file oct-norm.cc.

OCTAVE_API FloatColumnVector xrownorms	(	const FloatComplexMatrix &	m,
		float	p
	)

Definition at line 565 of file oct-norm.cc.

OCTAVE_API ColumnVector xrownorms	(	const SparseMatrix &	m,
		double	p
	)

Definition at line 567 of file oct-norm.cc.

OCTAVE_API ColumnVector xrownorms	(	const SparseComplexMatrix &	m,
		double	p
	)

Definition at line 568 of file oct-norm.cc.

Variable Documentation

int max_norm_iter = 100

static

Definition at line 466 of file oct-norm.cc.

const char* p_less1_gripe = "xnorm: p must be at least 1"

static

Definition at line 461 of file oct-norm.cc.

Referenced by matrix_norm().