oct-norm.cc File Reference

#include <cmath>
#include <algorithm>
#include <limits>
#include <vector>
#include "Array.h"
#include "CColVector.h"
#include "CMatrix.h"
#include "CRowVector.h"
#include "CSparse.h"
#include "MArray.h"
#include "dColVector.h"
#include "dDiagMatrix.h"
#include "dMatrix.h"
#include "dRowVector.h"
#include "dSparse.h"
#include "fCColVector.h"
#include "fCMatrix.h"
#include "fCRowVector.h"
#include "fColVector.h"
#include "fDiagMatrix.h"
#include "fMatrix.h"
#include "fRowVector.h"
#include "lo-error.h"
#include "lo-ieee.h"
#include "lo-mappers.h"
#include "mx-cm-s.h"
#include "mx-fcm-fs.h"
#include "mx-fs-fcm.h"
#include "mx-s-cm.h"
#include "oct-cmplx.h"
#include "quit.h"
#include "svd.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<typename T , typename R >
void	array_norm_2 (const T *v, octave_idx_type n, R &res)
template<typename T , typename R , typename ACC >
void	column_norms (const MArray< T > &m, MArray< R > &res, ACC acc)
template<typename T , typename R >
MArray< R >	column_norms (const MArray< T > &v, R p)
template<typename T , typename R , typename ACC >
void	column_norms (const MSparse< T > &m, MArray< R > &res, ACC acc)
template<typename T , typename R >
MArray< R >	column_norms (const MSparse< T > &v, R p)
template<typename VectorT , typename R >
VectorT	dual_p (const VectorT &x, R p, R q)
template<typename T , typename R >
T	elem_dual_p (T x, R p)
template<typename MatrixT , typename VectorT , typename R >
R	higham (const MatrixT &m, R p, R tol, int maxiter, VectorT &x)
template<typename ColVectorT , typename R >
static void	higham_subp (const ColVectorT &y, const ColVectorT &col, octave_idx_type nsamp, R p, R &lambda, R &mu)
template<typename ColVectorT , typename 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<typename MatrixT , typename VectorT , typename R >
R	matrix_norm (const MatrixT &m, R p, VectorT)
template<typename T , typename R , typename ACC >
void	row_norms (const MArray< T > &m, MArray< R > &res, ACC acc)
template<typename T , typename R >
MArray< R >	row_norms (const MArray< T > &v, R p)
template<typename T , typename R , typename ACC >
void	row_norms (const MSparse< T > &m, MArray< R > &res, ACC acc)
template<typename T , typename R >
MArray< R >	row_norms (const MSparse< T > &v, R p)
template<typename MatrixT , typename VectorT , typename R >
R	svd_matrix_norm (const MatrixT &m, R p, VectorT)
template<typename T , typename R , typename ACC >
void	vector_norm (const Array< T > &v, R &res, ACC acc)
template<typename T , typename R >
R	vector_norm (const MArray< T > &v, R p)
OCTAVE_API RowVector	xcolnorms (const ComplexMatrix &m, double p)
OCTAVE_API FloatRowVector	xcolnorms (const FloatComplexMatrix &m, float p)
OCTAVE_API FloatRowVector	xcolnorms (const FloatMatrix &m, float p)
OCTAVE_API RowVector	xcolnorms (const Matrix &m, double p)
OCTAVE_API RowVector	xcolnorms (const SparseComplexMatrix &m, double p)
OCTAVE_API RowVector	xcolnorms (const SparseMatrix &m, double p)
OCTAVE_API double	xfrobnorm (const ComplexMatrix &x)
OCTAVE_API float	xfrobnorm (const FloatComplexMatrix &x)
OCTAVE_API float	xfrobnorm (const FloatMatrix &x)
OCTAVE_API double	xfrobnorm (const Matrix &x)
OCTAVE_API double	xfrobnorm (const SparseComplexMatrix &x)
OCTAVE_API double	xfrobnorm (const SparseMatrix &x)
OCTAVE_API double	xnorm (const ColumnVector &x, double p)
OCTAVE_API double	xnorm (const ComplexColumnVector &x, double p)
OCTAVE_API double	xnorm (const ComplexMatrix &x, double p)
OCTAVE_API double	xnorm (const ComplexRowVector &x, double p)
OCTAVE_API float	xnorm (const FloatColumnVector &x, float p)
OCTAVE_API float	xnorm (const FloatComplexColumnVector &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 FloatMatrix &x, float p)
OCTAVE_API float	xnorm (const FloatRowVector &x, float p)
OCTAVE_API double	xnorm (const Matrix &x, double p)
OCTAVE_API double	xnorm (const RowVector &x, double p)
OCTAVE_API double	xnorm (const SparseComplexMatrix &x, double p)
OCTAVE_API double	xnorm (const SparseMatrix &x, double p)
OCTAVE_API ColumnVector	xrownorms (const ComplexMatrix &m, double p)
OCTAVE_API FloatColumnVector	xrownorms (const FloatComplexMatrix &m, float p)
OCTAVE_API FloatColumnVector	xrownorms (const FloatMatrix &m, float p)
OCTAVE_API ColumnVector	xrownorms (const Matrix &m, double p)
OCTAVE_API ColumnVector	xrownorms (const SparseComplexMatrix &m, double p)
OCTAVE_API ColumnVector	xrownorms (const SparseMatrix &m, double p)

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

Macro Definition Documentation

DEFINE_COLROW_NORM_FUNCS

#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 582 of file oct-norm.cc.

DEFINE_DISPATCHER

#define DEFINE_DISPATCHER	(		FUNC_NAME,
			ARG_TYPE,
			RES_TYPE
	)

Value:

  template <typename T, typename 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 297 of file oct-norm.cc.

DEFINE_XNORM_FUNCS

#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 svd_matrix_norm (x, p, PREFIX##Matrix ());                   \
  }                                                                     \
  OCTAVE_API RTYPE xfrobnorm (const PREFIX##Matrix& x)                  \
  {                                                                     \
    return vector_norm (x, static_cast<RTYPE> (2));                     \
  }

Definition at line 533 of file oct-norm.cc.

DEFINE_XNORM_SPARSE_FUNCS

#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 567 of file oct-norm.cc.

Function Documentation

array_norm_2()

template<typename T , typename R >

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

inline

Definition at line 558 of file oct-norm.cc.

References norm_accumulator_2< R >::accum(), and n.

column_norms() [1/4]

template<typename T , typename R , typename ACC >

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

Definition at line 238 of file oct-norm.cc.

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

column_norms() [2/4]

template<typename T , typename R >

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

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

column_norms() [3/4]

template<typename T , typename R , typename ACC >

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

Definition at line 268 of file oct-norm.cc.

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

column_norms() [4/4]

template<typename T , typename R >

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

Definition at line 325 of file oct-norm.cc.

dual_p()

template<typename VectorT , typename R >

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

Definition at line 415 of file oct-norm.cc.

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

Referenced by higham().

elem_dual_p()

template<typename T , typename R >

T elem_dual_p ( T  x, R  p  )

inline

Definition at line 405 of file oct-norm.cc.

References abs(), pow(), octave::math::signum(), and x.

Referenced by dual_p().

higham()

template<typename MatrixT , typename VectorT , typename R >

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

Definition at line 425 of file oct-norm.cc.

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

Referenced by matrix_norm(), and svd_matrix_norm().

higham_subp() [1/2]

template<typename ColVectorT , typename 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 333 of file oct-norm.cc.

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

Referenced by higham().

higham_subp() [2/2]

template<typename ColVectorT , typename 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 361 of file oct-norm.cc.

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

matrix_norm()

template<typename MatrixT , typename VectorT , typename R >

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

Definition at line 512 of file oct-norm.cc.

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

row_norms() [1/4]

template<typename T , typename R , typename ACC >

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

Definition at line 252 of file oct-norm.cc.

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

row_norms() [2/4]

template<typename T , typename R >

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

Definition at line 324 of file oct-norm.cc.

row_norms() [3/4]

template<typename T , typename R , typename ACC >

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

Definition at line 282 of file oct-norm.cc.

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

row_norms() [4/4]

template<typename T , typename R >

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

Definition at line 326 of file oct-norm.cc.

svd_matrix_norm()

template<typename MatrixT , typename VectorT , typename R >

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

Definition at line 485 of file oct-norm.cc.

References current_liboctave_error_handler, higham(), lo_ieee_isinf, m, ColumnVector::max(), RowVector::max(), max_norm_iter, p_less1_gripe, octave::math::svd< T >::singular_values(), x, xcolnorms(), and xrownorms().

vector_norm() [1/2]

template<typename T , typename R , typename ACC >

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

inline

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

References Array< T >::numel().

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

vector_norm() [2/2]

template<typename T , typename R >

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

Definition at line 322 of file oct-norm.cc.

xcolnorms() [1/6]

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

Definition at line 595 of file oct-norm.cc.

xcolnorms() [2/6]

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

Definition at line 597 of file oct-norm.cc.

xcolnorms() [3/6]

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

Definition at line 596 of file oct-norm.cc.

xcolnorms() [4/6]

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

Definition at line 594 of file oct-norm.cc.

Referenced by F__icholt__(), F__iluc__(), F__ilutp__(), Fnorm(), matrix_norm(), and svd_matrix_norm().

xcolnorms() [5/6]

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

Definition at line 600 of file oct-norm.cc.

xcolnorms() [6/6]

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

Definition at line 599 of file oct-norm.cc.

xfrobnorm() [1/6]

OCTAVE_API double xfrobnorm

(

const ComplexMatrix &

x

)

Definition at line 552 of file oct-norm.cc.

xfrobnorm() [2/6]

OCTAVE_API float xfrobnorm

(

const FloatComplexMatrix &

x

)

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

xfrobnorm() [3/6]

OCTAVE_API float xfrobnorm

(

const FloatMatrix &

x

)

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

xfrobnorm() [4/6]

OCTAVE_API double xfrobnorm

(

const Matrix &

x

)

Definition at line 551 of file oct-norm.cc.

Referenced by Fnorm(), and Fsqrtm().

xfrobnorm() [5/6]

OCTAVE_API double xfrobnorm

(

const SparseComplexMatrix &

x

)

Definition at line 580 of file oct-norm.cc.

xfrobnorm() [6/6]

OCTAVE_API double xfrobnorm

(

const SparseMatrix &

x

)

Definition at line 579 of file oct-norm.cc.

xnorm() [1/14]

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

Definition at line 551 of file oct-norm.cc.

Referenced by do_mgorth(), do_sqrtm(), Fnorm(), and chol< T >::init().

xnorm() [2/14]

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

Definition at line 552 of file oct-norm.cc.

xnorm() [3/14]

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

Definition at line 552 of file oct-norm.cc.

xnorm() [4/14]

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

Definition at line 552 of file oct-norm.cc.

xnorm() [5/14]

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

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

xnorm() [6/14]

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

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

xnorm() [7/14]

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

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

xnorm() [8/14]

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

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

xnorm() [9/14]

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

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

xnorm() [10/14]

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

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

xnorm() [11/14]

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

Definition at line 551 of file oct-norm.cc.

xnorm() [12/14]

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

Definition at line 551 of file oct-norm.cc.

xnorm() [13/14]

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

Definition at line 580 of file oct-norm.cc.

xnorm() [14/14]

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

Definition at line 579 of file oct-norm.cc.

xrownorms() [1/6]

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

Definition at line 595 of file oct-norm.cc.

xrownorms() [2/6]

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

Definition at line 597 of file oct-norm.cc.

xrownorms() [3/6]

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

Definition at line 596 of file oct-norm.cc.

xrownorms() [4/6]

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

Definition at line 594 of file oct-norm.cc.

Referenced by F__iluc__(), F__ilutp__(), Fnorm(), matrix_norm(), and svd_matrix_norm().

xrownorms() [5/6]

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

Definition at line 600 of file oct-norm.cc.

xrownorms() [6/6]

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

Definition at line 599 of file oct-norm.cc.

Variable Documentation

max_norm_iter

int max_norm_iter = 100

static

Definition at line 481 of file oct-norm.cc.

Referenced by matrix_norm(), and svd_matrix_norm().

p_less1_gripe

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

static

Definition at line 476 of file oct-norm.cc.

Referenced by matrix_norm(), and svd_matrix_norm().