oct-norm.cc File Reference

#include <cmath>
#include <algorithm>
#include <iostream>
#include <limits>
#include <type_traits>
#include <vector>
#include "Array-oct.h"
#include "CColVector.h"
#include "CMatrix.h"
#include "CRowVector.h"
#include "CSparse.h"
#include "MArray.h"
#include "blas-proto.h"
#include "dColVector.h"
#include "dDiagMatrix.h"
#include "dMatrix.h"
#include "dRowVector.h"
#include "dSparse.h"
#include "f77-fcn.h"
#include "fCColVector.h"
#include "fCMatrix.h"
#include "fCRowVector.h"
#include "fColVector.h"
#include "fDiagMatrix.h"
#include "fMatrix.h"
#include "fRowVector.h"
#include "lapack-proto.h"
#include "lo-ieee.h"
#include "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-error.h"
#include "oct-norm.h"
#include "quit.h"
#include "svd.h"
#include "eigs-base.h"

Go to the source code of this file.

Macros
#define	DEFINE_COLROW_DISPATCHER(FCN_NAME, ARG_TYPE, RES_TYPE)
#define	DEFINE_COLROW_NORM_FCNS(PREFIX, RPREFIX, RTYPE)
#define	DEFINE_XNORM_FCNS(PREFIX, RTYPE)
#define	DEFINE_XNORM_SPARSE_FCNS(PREFIX, RTYPE)

Typedefs
template<typename R >
using	accum_type = std::conditional_t< std::is_same_v< R, float >, double, R >

Functions
template<typename T , typename R >
void	array_norm_2 (const T *v, octave_idx_type n, R &res)
double	blas_nrm2 (octave_idx_type n, const Complex *x, octave_idx_type incx)
double	blas_nrm2 (octave_idx_type n, const double *x, octave_idx_type incx)
float	blas_nrm2 (octave_idx_type n, const float *x, octave_idx_type incx)
float	blas_nrm2 (octave_idx_type n, const FloatComplex *x, octave_idx_type incx)
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)
double	lange (char norm_type, const ComplexMatrix &m)
float	lange (char norm_type, const FloatComplexMatrix &m)
float	lange (char norm_type, const FloatMatrix &m)
double	lange (char norm_type, const Matrix &m)
template<typename T , typename R >
R	lange_inf_fixup (R result, const T *data, octave_idx_type numel)
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 T >
constexpr T	safe_conj (T x)
template<typename MatrixT , typename VectorT , typename R >
R	sparse_2norm (const MatrixT &m, R tol, int maxiter, VectorT)
double	sparse_2norm_arpack (const SparseComplexMatrix &m, double tol, int maxiter)
double	sparse_2norm_arpack (const SparseMatrix &m, double tol, int maxiter)
template<typename MatrixT , typename VectorT , typename R >
R	sparse_2norm_power (const MatrixT &m, R tol, int maxiter, VectorT)
template<typename MatrixT , typename VectorT , typename R >
R	svd_matrix_norm (const MatrixT &m, R p, VectorT)
template<typename VectorT >
auto	vector_dot (const VectorT &x, const VectorT &y)
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)
template<typename T , typename R , typename ACC >
void	vector_norm (const MSparse< T > &v, R &res, ACC acc)
template<typename T , typename R >
R	vector_norm (const MSparse< T > &v, R p)
template<typename T , typename R >
R	vector_norm_2_blas (const MArray< T > &v)
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)

Variables
constexpr int	max_norm_iter = 256
constexpr const char *	p_less1_gripe = "xnorm: p must be >= 1"

Macro Definition Documentation

DEFINE_COLROW_DISPATCHER

#define DEFINE_COLROW_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 (math::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 598 of file oct-norm.cc.

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 1096 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 lange ('F', x);                                              \
}

Definition at line 1047 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 1081 of file oct-norm.cc.

Typedef Documentation

accum_type

template<typename R >

using accum_type = std::conditional_t<std::is_same_v<R, float>, double, R>

Definition at line 225 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 1072 of file oct-norm.cc.

blas_nrm2() [1/4]

double blas_nrm2 ( octave_idx_type  n, const Complex *  x, octave_idx_type  incx  )

inline

Definition at line 100 of file oct-norm.cc.

References F77_CONST_DBLE_CMPLX_ARG, F77_FUNC(), x, and xdznrm2().

blas_nrm2() [2/4]

double blas_nrm2 ( octave_idx_type  n, const double *  x, octave_idx_type  incx  )

inline

Definition at line 80 of file oct-norm.cc.

References F77_FUNC(), x, and xdnrm2().

Referenced by vector_norm_2_blas().

blas_nrm2() [3/4]

float blas_nrm2 ( octave_idx_type  n, const float *  x, octave_idx_type  incx  )

inline

Definition at line 90 of file oct-norm.cc.

References F77_FUNC(), x, and xsnrm2().

blas_nrm2() [4/4]

float blas_nrm2 ( octave_idx_type  n, const FloatComplex *  x, octave_idx_type  incx  )

inline

Definition at line 110 of file oct-norm.cc.

References F77_CONST_CMPLX_ARG, F77_FUNC(), x, and xscnrm2().

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 476 of file oct-norm.cc.

References Array< T, Alloc >::columns(), Array< T, Alloc >::rows(), 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 623 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 508 of file oct-norm.cc.

References Sparse< T, Alloc >::cidx(), Sparse< T, Alloc >::columns(), Sparse< T, Alloc >::data(), 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 625 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 718 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 707 of file oct-norm.cc.

References 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 729 of file oct-norm.cc.

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

Referenced by matrix_norm(), and svd_matrix_norm().

lange() [1/4]

double lange ( char  norm_type, const ComplexMatrix &  m  )

inline

Definition at line 181 of file oct-norm.cc.

References Array< T, Alloc >::cols(), Array< T, Alloc >::data(), F77_CONST_DBLE_CMPLX_ARG, F77_FUNC(), lange_inf_fixup(), Array< T, Alloc >::numel(), OCTAVE_LOCAL_BUFFER, Array< T, Alloc >::rows(), and xzlange().

lange() [2/4]

float lange ( char  norm_type, const FloatComplexMatrix &  m  )

inline

Definition at line 198 of file oct-norm.cc.

References Array< T, Alloc >::cols(), Array< T, Alloc >::data(), F77_CONST_CMPLX_ARG, F77_FUNC(), lange_inf_fixup(), Array< T, Alloc >::numel(), OCTAVE_LOCAL_BUFFER, Array< T, Alloc >::rows(), and xclange().

lange() [3/4]

float lange ( char  norm_type, const FloatMatrix &  m  )

inline

Definition at line 165 of file oct-norm.cc.

References Array< T, Alloc >::cols(), Array< T, Alloc >::data(), F77_FUNC(), lange_inf_fixup(), Array< T, Alloc >::numel(), OCTAVE_LOCAL_BUFFER, Array< T, Alloc >::rows(), and xslange().

lange() [4/4]

double lange ( char  norm_type, const Matrix &  m  )

inline

Definition at line 149 of file oct-norm.cc.

References Array< T, Alloc >::cols(), Array< T, Alloc >::data(), F77_FUNC(), lange_inf_fixup(), Array< T, Alloc >::numel(), OCTAVE_LOCAL_BUFFER, Array< T, Alloc >::rows(), and xdlange().

Referenced by svd_matrix_norm().

lange_inf_fixup()

template<typename T , typename R >

R lange_inf_fixup ( R  result, const T *  data, octave_idx_type  numel  )

inline

Definition at line 127 of file oct-norm.cc.

References numel().

Referenced by lange(), lange(), lange(), and lange().

matrix_norm()

template<typename MatrixT , typename VectorT , typename R >

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

Definition at line 1020 of file oct-norm.cc.

References current_liboctave_error_handler, higham(), ColumnVector::max(), RowVector::max(), max_norm_iter, p_less1_gripe, sparse_2norm(), 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 491 of file oct-norm.cc.

References Array< T, Alloc >::columns(), Array< T, Alloc >::rows(), 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 624 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 523 of file oct-norm.cc.

References Sparse< T, Alloc >::cidx(), Sparse< T, Alloc >::columns(), Sparse< T, Alloc >::data(), Sparse< T, Alloc >::ridx(), Sparse< T, Alloc >::rows(), 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 626 of file oct-norm.cc.

References vector_norm().

safe_conj()

template<typename T >

constexpr T safe_conj ( T  x )

constexpr

Definition at line 816 of file oct-norm.cc.

References x.

Referenced by vector_dot().

sparse_2norm()

template<typename MatrixT , typename VectorT , typename R >

R sparse_2norm	(	const MatrixT &	m,
		R	tol,
		int	maxiter,
		VectorT
	)

Definition at line 1004 of file oct-norm.cc.

References sparse_2norm_arpack(), and sparse_2norm_power().

Referenced by matrix_norm().

sparse_2norm_arpack() [1/2]

double sparse_2norm_arpack	(	const SparseComplexMatrix &	m,
		double	tol,
		int	maxiter
	)

Definition at line 953 of file oct-norm.cc.

References B, Sparse< T, Alloc >::cols(), EigsComplexNonSymmetricMatrix(), SparseComplexMatrix::hermitian(), SparseComplexMatrix::insert(), Array< T, Alloc >::numel(), and Sparse< T, Alloc >::rows().

sparse_2norm_arpack() [2/2]

double sparse_2norm_arpack	(	const SparseMatrix &	m,
		double	tol,
		int	maxiter
	)

Definition at line 904 of file oct-norm.cc.

References B, Sparse< T, Alloc >::cols(), EigsRealSymmetricMatrix(), SparseMatrix::insert(), Array< T, Alloc >::numel(), Sparse< T, Alloc >::rows(), and SparseMatrix::transpose().

Referenced by sparse_2norm().

sparse_2norm_power()

template<typename MatrixT , typename VectorT , typename R >

R sparse_2norm_power	(	const MatrixT &	m,
		R	tol,
		int	maxiter,
		VectorT
	)

Definition at line 842 of file oct-norm.cc.

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

Referenced by sparse_2norm().

svd_matrix_norm()

template<typename MatrixT , typename VectorT , typename R >

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

Definition at line 790 of file oct-norm.cc.

References current_liboctave_error_handler, higham(), lange(), max_norm_iter, p_less1_gripe, and x.

vector_dot()

template<typename VectorT >

auto vector_dot	(	const VectorT &	x,
		const VectorT &	y
	)

Definition at line 827 of file oct-norm.cc.

References safe_conj(), and x.

Referenced by sparse_2norm_power().

vector_norm() [1/4]

template<typename T , typename R , typename ACC >

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

inline

Definition at line 453 of file oct-norm.cc.

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

Referenced by dual_p(), higham(), row_norms(), sparse_2norm_power(), vector_norm(), and vector_norm().

vector_norm() [2/4]

template<typename T , typename R >

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

Definition at line 548 of file oct-norm.cc.

References vector_norm().

vector_norm() [3/4]

template<typename T , typename R , typename ACC >

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

inline

Definition at line 464 of file oct-norm.cc.

References Sparse< T, Alloc >::data(), and Sparse< T, Alloc >::nnz().

vector_norm() [4/4]

template<typename T , typename R >

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

Definition at line 574 of file oct-norm.cc.

References vector_norm().

vector_norm_2_blas()

template<typename T , typename R >

R vector_norm_2_blas ( const MArray< T > &  v )

inline

Definition at line 540 of file oct-norm.cc.

References blas_nrm2(), Array< T, Alloc >::data(), and Array< T, Alloc >::numel().

xcolnorms() [1/6]

RowVector xcolnorms	(	const ComplexMatrix &	m,
		double	p
	)

Definition at line 1109 of file oct-norm.cc.

xcolnorms() [2/6]

FloatRowVector xcolnorms	(	const FloatComplexMatrix &	m,
		float	p
	)

Definition at line 1111 of file oct-norm.cc.

xcolnorms() [3/6]

FloatRowVector xcolnorms	(	const FloatMatrix &	m,
		float	p
	)

Definition at line 1110 of file oct-norm.cc.

xcolnorms() [4/6]

RowVector xcolnorms	(	const Matrix &	m,
		double	p
	)

Definition at line 1108 of file oct-norm.cc.

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

xcolnorms() [5/6]

RowVector xcolnorms	(	const SparseComplexMatrix &	m,
		double	p
	)

Definition at line 1114 of file oct-norm.cc.

xcolnorms() [6/6]

RowVector xcolnorms	(	const SparseMatrix &	m,
		double	p
	)

Definition at line 1113 of file oct-norm.cc.

xfrobnorm() [1/6]

double xfrobnorm

(

const ComplexMatrix &

x

)

Definition at line 1066 of file oct-norm.cc.

xfrobnorm() [2/6]

float xfrobnorm

(

const FloatComplexMatrix &

x

)

Definition at line 1068 of file oct-norm.cc.

xfrobnorm() [3/6]

float xfrobnorm

(

const FloatMatrix &

x

)

Definition at line 1067 of file oct-norm.cc.

xfrobnorm() [4/6]

double xfrobnorm

(

const Matrix &

x

)

Definition at line 1065 of file oct-norm.cc.

Referenced by Fnorm(), and Fsqrtm().

xfrobnorm() [5/6]

double xfrobnorm

(

const SparseComplexMatrix &

x

)

Definition at line 1094 of file oct-norm.cc.

xfrobnorm() [6/6]

double xfrobnorm

(

const SparseMatrix &

x

)

Definition at line 1093 of file oct-norm.cc.

xnorm() [1/14]

double xnorm	(	const ColumnVector &	x,
		double	p
	)

Definition at line 1065 of file oct-norm.cc.

Referenced by Fnorm().

xnorm() [2/14]

double xnorm	(	const ComplexColumnVector &	x,
		double	p
	)

Definition at line 1066 of file oct-norm.cc.

xnorm() [3/14]

double xnorm	(	const ComplexMatrix &	x,
		double	p
	)

Definition at line 1066 of file oct-norm.cc.

xnorm() [4/14]

double xnorm	(	const ComplexRowVector &	x,
		double	p
	)

Definition at line 1066 of file oct-norm.cc.

xnorm() [5/14]

float xnorm	(	const FloatColumnVector &	x,
		float	p
	)

Definition at line 1067 of file oct-norm.cc.

xnorm() [6/14]

float xnorm	(	const FloatComplexColumnVector &	x,
		float	p
	)

Definition at line 1068 of file oct-norm.cc.

xnorm() [7/14]

float xnorm	(	const FloatComplexMatrix &	x,
		float	p
	)

Definition at line 1068 of file oct-norm.cc.

xnorm() [8/14]

float xnorm	(	const FloatComplexRowVector &	x,
		float	p
	)

Definition at line 1068 of file oct-norm.cc.

xnorm() [9/14]

float xnorm	(	const FloatMatrix &	x,
		float	p
	)

Definition at line 1067 of file oct-norm.cc.

xnorm() [10/14]

float xnorm	(	const FloatRowVector &	x,
		float	p
	)

Definition at line 1067 of file oct-norm.cc.

xnorm() [11/14]

double xnorm	(	const Matrix &	x,
		double	p
	)

Definition at line 1065 of file oct-norm.cc.

xnorm() [12/14]

double xnorm	(	const RowVector &	x,
		double	p
	)

Definition at line 1065 of file oct-norm.cc.

xnorm() [13/14]

double xnorm	(	const SparseComplexMatrix &	x,
		double	p
	)

Definition at line 1094 of file oct-norm.cc.

xnorm() [14/14]

double xnorm	(	const SparseMatrix &	x,
		double	p
	)

Definition at line 1093 of file oct-norm.cc.

xrownorms() [1/6]

ColumnVector xrownorms	(	const ComplexMatrix &	m,
		double	p
	)

Definition at line 1109 of file oct-norm.cc.

xrownorms() [2/6]

FloatColumnVector xrownorms	(	const FloatComplexMatrix &	m,
		float	p
	)

Definition at line 1111 of file oct-norm.cc.

xrownorms() [3/6]

FloatColumnVector xrownorms	(	const FloatMatrix &	m,
		float	p
	)

Definition at line 1110 of file oct-norm.cc.

xrownorms() [4/6]

ColumnVector xrownorms	(	const Matrix &	m,
		double	p
	)

Definition at line 1108 of file oct-norm.cc.

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

xrownorms() [5/6]

ColumnVector xrownorms	(	const SparseComplexMatrix &	m,
		double	p
	)

Definition at line 1114 of file oct-norm.cc.

xrownorms() [6/6]

ColumnVector xrownorms	(	const SparseMatrix &	m,
		double	p
	)

Definition at line 1113 of file oct-norm.cc.

Variable Documentation

max_norm_iter

constexpr int max_norm_iter = 256

constexpr

Definition at line 785 of file oct-norm.cc.

Referenced by matrix_norm(), and svd_matrix_norm().

p_less1_gripe

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

constexpr

Definition at line 780 of file oct-norm.cc.

Referenced by matrix_norm(), and svd_matrix_norm().