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 "oct-norm.h"
#include "quit.h"
#include "svd.h"

Go to the source code of this file.

Macros
#define	DEFINE_COLROW_NORM_FCNS(PREFIX, RPREFIX, RTYPE)
#define	DEFINE_DISPATCHER(FCN_NAME, ARG_TYPE, RES_TYPE)
#define	DEFINE_XNORM_FCNS(PREFIX, RTYPE)
#define	DEFINE_XNORM_SPARSE_FCNS(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 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)
RowVector	xcolnorms (const ComplexMatrix &m, double p)
FloatRowVector	xcolnorms (const FloatComplexMatrix &m, float p)
FloatRowVector	xcolnorms (const FloatMatrix &m, float p)
RowVector	xcolnorms (const Matrix &m, double p)
RowVector	xcolnorms (const SparseComplexMatrix &m, double p)
RowVector	xcolnorms (const SparseMatrix &m, double p)
double	xfrobnorm (const ComplexMatrix &x)
float	xfrobnorm (const FloatComplexMatrix &x)
float	xfrobnorm (const FloatMatrix &x)
double	xfrobnorm (const Matrix &x)
double	xfrobnorm (const SparseComplexMatrix &x)
double	xfrobnorm (const SparseMatrix &x)
double	xnorm (const ColumnVector &x, double p)
double	xnorm (const ComplexColumnVector &x, double p)
double	xnorm (const ComplexMatrix &x, double p)
double	xnorm (const ComplexRowVector &x, double p)
float	xnorm (const FloatColumnVector &x, float p)
float	xnorm (const FloatComplexColumnVector &x, float p)
float	xnorm (const FloatComplexMatrix &x, float p)
float	xnorm (const FloatComplexRowVector &x, float p)
float	xnorm (const FloatMatrix &x, float p)
float	xnorm (const FloatRowVector &x, float p)
double	xnorm (const Matrix &x, double p)
double	xnorm (const RowVector &x, double p)
double	xnorm (const SparseComplexMatrix &x, double p)
double	xnorm (const SparseMatrix &x, double p)
ColumnVector	xrownorms (const ComplexMatrix &m, double p)
FloatColumnVector	xrownorms (const FloatComplexMatrix &m, float p)
FloatColumnVector	xrownorms (const FloatMatrix &m, float p)
ColumnVector	xrownorms (const Matrix &m, double p)
ColumnVector	xrownorms (const SparseComplexMatrix &m, double p)
ColumnVector	xrownorms (const SparseMatrix &m, double p)

Macro Definition Documentation

DEFINE_COLROW_NORM_FCNS

#define DEFINE_COLROW_NORM_FCNS	(		PREFIX,
			RPREFIX,
			RTYPE
	)

Value:

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

Definition at line 641 of file oct-norm.cc.

DEFINE_DISPATCHER

#define DEFINE_DISPATCHER	(		FCN_NAME,
			ARG_TYPE,
			RES_TYPE
	)

Value:

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

Definition at line 351 of file oct-norm.cc.

DEFINE_XNORM_FCNS

#define DEFINE_XNORM_FCNS	(		PREFIX,
			RTYPE
	)

Value:

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

Definition at line 592 of file oct-norm.cc.

DEFINE_XNORM_SPARSE_FCNS

#define DEFINE_XNORM_SPARSE_FCNS	(		PREFIX,
			RTYPE
	)

Value:

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

Definition at line 626 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 617 of file oct-norm.cc.

References 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 289 of file oct-norm.cc.

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

column_norms() [2/4]

template<typename T , typename R >

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

Definition at line 377 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 321 of file oct-norm.cc.

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

column_norms() [4/4]

template<typename T , typename R >

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

Definition at line 379 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 472 of file oct-norm.cc.

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

elem_dual_p()

template<typename T , typename R >

T elem_dual_p ( T  x, R  p  )

inline

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

References pow(), 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 483 of file oct-norm.cc.

References m, and x.

Referenced by matrix_norm(), and svd_matrix_norm().

matrix_norm()

template<typename MatrixT , typename VectorT , typename R >

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

Definition at line 571 of file oct-norm.cc.

References higham(), lo_ieee_isinf, m, ColumnVector::max(), RowVector::max(), 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 304 of file oct-norm.cc.

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

row_norms() [2/4]

template<typename T , typename R >

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

Definition at line 378 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 336 of file oct-norm.cc.

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

row_norms() [4/4]

template<typename T , typename R >

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

Definition at line 380 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 544 of file oct-norm.cc.

References higham(), lo_ieee_isinf, m, ColumnVector::max(), RowVector::max(), 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 278 of file oct-norm.cc.

References Array< T, Alloc >::numel().

Referenced by dual_p().

vector_norm() [2/2]

template<typename T , typename R >

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

Definition at line 376 of file oct-norm.cc.

xcolnorms() [1/6]

RowVector xcolnorms	(	const ComplexMatrix &	m,
		double	p
	)

Definition at line 654 of file oct-norm.cc.

xcolnorms() [2/6]

FloatRowVector xcolnorms	(	const FloatComplexMatrix &	m,
		float	p
	)

Definition at line 656 of file oct-norm.cc.

xcolnorms() [3/6]

FloatRowVector xcolnorms	(	const FloatMatrix &	m,
		float	p
	)

Definition at line 655 of file oct-norm.cc.

xcolnorms() [4/6]

RowVector xcolnorms	(	const Matrix &	m,
		double	p
	)

Definition at line 653 of file oct-norm.cc.

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

xcolnorms() [5/6]

RowVector xcolnorms	(	const SparseComplexMatrix &	m,
		double	p
	)

Definition at line 659 of file oct-norm.cc.

xcolnorms() [6/6]

RowVector xcolnorms	(	const SparseMatrix &	m,
		double	p
	)

Definition at line 658 of file oct-norm.cc.

xfrobnorm() [1/6]

double xfrobnorm

(

const ComplexMatrix &

x

)

Definition at line 611 of file oct-norm.cc.

xfrobnorm() [2/6]

float xfrobnorm

(

const FloatComplexMatrix &

x

)

Definition at line 613 of file oct-norm.cc.

xfrobnorm() [3/6]

float xfrobnorm

(

const FloatMatrix &

x

)

Definition at line 612 of file oct-norm.cc.

xfrobnorm() [4/6]

double xfrobnorm

(

const Matrix &

x

)

Definition at line 610 of file oct-norm.cc.

Referenced by Fnorm().

xfrobnorm() [5/6]

double xfrobnorm

(

const SparseComplexMatrix &

x

)

Definition at line 639 of file oct-norm.cc.

xfrobnorm() [6/6]

double xfrobnorm

(

const SparseMatrix &

x

)

Definition at line 638 of file oct-norm.cc.

xnorm() [1/14]

double xnorm	(	const ColumnVector &	x,
		double	p
	)

Definition at line 610 of file oct-norm.cc.

Referenced by Fnorm().

xnorm() [2/14]

double xnorm	(	const ComplexColumnVector &	x,
		double	p
	)

Definition at line 611 of file oct-norm.cc.

xnorm() [3/14]

double xnorm	(	const ComplexMatrix &	x,
		double	p
	)

Definition at line 611 of file oct-norm.cc.

xnorm() [4/14]

double xnorm	(	const ComplexRowVector &	x,
		double	p
	)

Definition at line 611 of file oct-norm.cc.

xnorm() [5/14]

float xnorm	(	const FloatColumnVector &	x,
		float	p
	)

Definition at line 612 of file oct-norm.cc.

xnorm() [6/14]

float xnorm	(	const FloatComplexColumnVector &	x,
		float	p
	)

Definition at line 613 of file oct-norm.cc.

xnorm() [7/14]

float xnorm	(	const FloatComplexMatrix &	x,
		float	p
	)

Definition at line 613 of file oct-norm.cc.

xnorm() [8/14]

float xnorm	(	const FloatComplexRowVector &	x,
		float	p
	)

Definition at line 613 of file oct-norm.cc.

xnorm() [9/14]

float xnorm	(	const FloatMatrix &	x,
		float	p
	)

Definition at line 612 of file oct-norm.cc.

xnorm() [10/14]

float xnorm	(	const FloatRowVector &	x,
		float	p
	)

Definition at line 612 of file oct-norm.cc.

xnorm() [11/14]

double xnorm	(	const Matrix &	x,
		double	p
	)

Definition at line 610 of file oct-norm.cc.

xnorm() [12/14]

double xnorm	(	const RowVector &	x,
		double	p
	)

Definition at line 610 of file oct-norm.cc.

xnorm() [13/14]

double xnorm	(	const SparseComplexMatrix &	x,
		double	p
	)

Definition at line 639 of file oct-norm.cc.

xnorm() [14/14]

double xnorm	(	const SparseMatrix &	x,
		double	p
	)

Definition at line 638 of file oct-norm.cc.

xrownorms() [1/6]

ColumnVector xrownorms	(	const ComplexMatrix &	m,
		double	p
	)

Definition at line 654 of file oct-norm.cc.

xrownorms() [2/6]

FloatColumnVector xrownorms	(	const FloatComplexMatrix &	m,
		float	p
	)

Definition at line 656 of file oct-norm.cc.

xrownorms() [3/6]

FloatColumnVector xrownorms	(	const FloatMatrix &	m,
		float	p
	)

Definition at line 655 of file oct-norm.cc.

xrownorms() [4/6]

ColumnVector xrownorms	(	const Matrix &	m,
		double	p
	)

Definition at line 653 of file oct-norm.cc.

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

xrownorms() [5/6]

ColumnVector xrownorms	(	const SparseComplexMatrix &	m,
		double	p
	)

Definition at line 659 of file oct-norm.cc.

xrownorms() [6/6]

ColumnVector xrownorms	(	const SparseMatrix &	m,
		double	p
	)

Definition at line 658 of file oct-norm.cc.