End-user class encapsulating band square matrix of real numbers. More...

#include <cvm.h>

Inheritance diagram for basic_srbmatrix< TR >:

Collaboration diagram for basic_srbmatrix< TR >:

Public Member Functions
	basic_srbmatrix ()
	Default constructor.
	basic_srbmatrix (tint nDim)
	Diagonal band matrix constructor.
	basic_srbmatrix (tint nDim, tint nKL, tint nKU)
	Band matrix constructor.
	basic_srbmatrix (TR *pd, tint nDim, tint nKL, tint nKU)
	Constructor.
	basic_srbmatrix (const TR *pd, tint nDim, tint nKL, tint nKU)
	Constructor.
	basic_srbmatrix (const basic_srbmatrix &m)
	Copy constructor.
	basic_srbmatrix (basic_srbmatrix &&m) noexcept
	Move constructor.
	basic_srbmatrix (const BaseRMatrix &m, tint nKL, tint nKU)
	Constructor.
	basic_srbmatrix (const RVector &v)
	Constructor.
type_proxy< TR, TR >	operator() (tint nRow, tint nCol) throw (cvmexception)
	Reference to element (l-value)
TR	operator() (tint nRow, tint nCol) const throw (cvmexception)
	Value of element (not l-value)
const RVector	operator() (tint nCol) const throw (cvmexception)
	Column as not l-value.
const RVector	operator[] (tint nRow) const throw (cvmexception)
	Row as not l-value.
basic_srbmatrix &	operator= (const basic_srbmatrix &m) throw (cvmexception)
	Assignment operator.
basic_srbmatrix &	operator= (basic_srbmatrix &&m) throw (cvmexception)
	Move assignment operator.
basic_srbmatrix &	assign (const RVector &v) throw (cvmexception)
	Vector (as array) assignment.
basic_srbmatrix &	assign (const TR *pd)
	External array assignment.
basic_srbmatrix &	set (TR d)
	Sets all elements to one value.
basic_srbmatrix &	resize (tint nNewDim) throw (cvmexception)
	Changes dimension.
basic_srbmatrix &	resize_lu (tint nNewKL, tint nNewKU) throw (cvmexception)
	Changes number of sub- and super-diagonals.
bool	operator== (const basic_srbmatrix &m) const
	Band matrix comparison.
bool	operator!= (const basic_srbmatrix &m) const
	Band matrix comparison.
basic_srbmatrix &	operator<< (const basic_srbmatrix &m) throw (cvmexception)
	Matrix replacement.
basic_srbmatrix	operator+ (const basic_srbmatrix &m) const throw (cvmexception)
	Addition operator.
basic_srbmatrix	operator- (const basic_srbmatrix &m) const throw (cvmexception)
	Subtraction operator.
basic_srbmatrix &	sum (const basic_srbmatrix &m1, const basic_srbmatrix &m2) throw (cvmexception)
	Sum of matrices.
basic_srbmatrix &	diff (const basic_srbmatrix &m1, const basic_srbmatrix &m2) throw (cvmexception)
	Difference of matrices.
basic_srbmatrix &	operator+= (const basic_srbmatrix &m) throw (cvmexception)
	Increment operator.
basic_srbmatrix &	operator-= (const basic_srbmatrix &m) throw (cvmexception)
	Decrement operator.
basic_srbmatrix	operator- () const
	Unary minus operator.
basic_srbmatrix &	operator++ ()
	Plus identity, prefix.
basic_srbmatrix	operator++ (int)
	Plus identity, postfix.
basic_srbmatrix &	operator-- ()
	Minus identity, prefix.
basic_srbmatrix	operator-- (int)
	Minus identity, postfix.
basic_srbmatrix	operator* (TR dMult) const
	Multiply by number operator.
basic_srbmatrix	operator/ (TR dDiv) const throw (cvmexception)
	Divide by number operator.
basic_srbmatrix &	operator*= (TR dMult)
	Multiply by number and assign.
basic_srbmatrix &	operator/= (TR dDiv) throw (cvmexception)
	Divide by number and assign.
basic_srbmatrix &	normalize ()
	Matrix normalizer.
basic_srbmatrix	operator~ () const throw (cvmexception)
	Matrix transposition.
basic_srbmatrix &	transpose (const basic_srbmatrix &m) throw (cvmexception)
	Matrix transposition.
basic_srbmatrix &	transpose () throw (cvmexception)
	Matrix transposition (in-place)
RVector	operator* (const RVector &v) const throw (cvmexception)
	Matrix-vector product.
BaseRMatrix	operator* (const BaseRMatrix &m) const throw (cvmexception)
	Matrix-matrix product.
BaseSRMatrix	operator* (const BaseSRMatrix &m) const throw (cvmexception)
	Matrix-matrix product.
basic_srbmatrix	operator* (const basic_srbmatrix &m) const throw (cvmexception)
	Matrix-matrix product.
RVector	operator/ (const RVector &v) const throw (cvmexception)
	Linear solver operator.
basic_srbmatrix &	low_up (const basic_srbmatrix &m, tint *nPivots) throw (cvmexception)
	Low-up (LU) factorization.
basic_srbmatrix	low_up (tint *nPivots) const throw (cvmexception)
	Low-up (LU) factorization.
basic_srbmatrix &	identity ()
	Identity matrix.
basic_srbmatrix &	vanish ()
	Set matrix to zero.
basic_srbmatrix &	randomize (TR dFrom, TR dTo)
	Randomizer.
TR	norm () const override
	Euclidean norm.
TR	norm1 () const override
	1-norm
TR	norminf () const override
	Infinity norm.
basic_srbmatrix &	mult (const BaseRMatrix &m1, const BaseRMatrix &m2) throw (cvmexception)
Public Member Functions inherited from basic_srmatrix< TR >
	basic_srmatrix ()
	Default constructor.
	basic_srmatrix (tint nDim)
	Constructor.
	basic_srmatrix (TR *pd, tint nDim)
	Constructor.
	basic_srmatrix (const TR *pd, tint nDim)
	Constructor.
	basic_srmatrix (const basic_srmatrix &m)
	Copy constructor.
	basic_srmatrix (basic_srmatrix &&m) noexcept
	Move constructor.
	basic_srmatrix (const BaseRMatrix &m)
	Constructor.
	basic_srmatrix (const RVector &v)
	Constructor.
	basic_srmatrix (BaseRMatrix &m, tint nRow, tint nCol, tint nDim)
	Submatrix constructor.
RVector	operator() (tint nCol) throw (cvmexception)
	Column as l-value.
RVector	operator[] (tint nRow) throw (cvmexception)
	Row as l-value.
basic_srmatrix &	operator= (const basic_srmatrix &m) throw (cvmexception)
	Assignment operator.
basic_srmatrix &	operator= (basic_srmatrix &&m) throw (cvmexception)
	Move assignment operator.
basic_srmatrix &	assign (tint nRow, tint nCol, const BaseRMatrix &m) throw (cvmexception)
	Assignment to submatrix.
basic_srmatrix &	operator<< (const basic_srmatrix &m) throw (cvmexception)
	Matrix replacement.
basic_srmatrix	operator+ (const basic_srmatrix &m) const throw (cvmexception)
	Addition operator.
basic_srmatrix	operator- (const basic_srmatrix &m) const throw (cvmexception)
	Subtraction operator.
basic_srmatrix &	sum (const basic_srmatrix &m1, const basic_srmatrix &m2) throw (cvmexception)
	Sum of matrices.
basic_srmatrix &	diff (const basic_srmatrix &m1, const basic_srmatrix &m2) throw (cvmexception)
	Difference of matrices.
basic_srmatrix &	operator+= (const basic_srmatrix &m) throw (cvmexception)
	Increment operator.
basic_srmatrix &	operator-= (const basic_srmatrix &m) throw (cvmexception)
	Decrement operator.
basic_srmatrix &	transpose (const basic_srmatrix &m) throw (cvmexception)
	Matrix transposition.
basic_srmatrix	operator* (const basic_srmatrix &m) const throw (cvmexception)
	Matrix-matrix product.
basic_srmatrix &	operator*= (const basic_srmatrix &m) throw (cvmexception)
	Matrix-matrix product with assignment.
basic_srmatrix &	swap_rows (tint n1, tint n2) throw (cvmexception)
	Rows swap.
basic_srmatrix &	swap_cols (tint n1, tint n2) throw (cvmexception)
	Columns swap.
RVector	solve (const RVector &vB, TR &dErr) const throw (cvmexception)
	Linear solver.
RVector	solve_tran (const RVector &vB, TR &dErr) const throw (cvmexception)
	Linear solver (transposed)
RVector	solve (const RVector &vB) const throw (cvmexception)
	Linear solver.
RVector	solve_tran (const RVector &vB) const throw (cvmexception)
	Linear solver (transposed)
BaseRMatrix	solve (const BaseRMatrix &mB, TR &dErr) const throw (cvmexception)
	Linear solver.
BaseRMatrix	solve_tran (const BaseRMatrix &mB, TR &dErr) const throw (cvmexception)
	Linear solver (transposed)
BaseRMatrix	solve (const BaseRMatrix &mB) const throw (cvmexception)
	Linear solver.
BaseRMatrix	solve_tran (const BaseRMatrix &mB) const throw (cvmexception)
	Linear solver (transposed)
RVector	operator% (const RVector &vB) const throw (cvmexception)
	Linear solver operator (transposed)
RVector	solve_lu (const basic_srmatrix &mLU, const tint *pPivots, const RVector &vB, TR &dErr) const throw (cvmexception)
	LU factorization based linear solver.
RVector	solve_lu (const basic_srmatrix &mLU, const tint *pPivots, const RVector &vB) const throw (cvmexception)
	LU factorization based linear solver.
BaseRMatrix	solve_lu (const basic_srmatrix &mLU, const tint *pPivots, const BaseRMatrix &mB, TR &dErr) const throw (cvmexception)
	LU factorization based linear solver.
BaseRMatrix	solve_lu (const basic_srmatrix &mLU, const tint *pPivots, const BaseRMatrix &mB) const throw (cvmexception)
	LU factorization based linear solver.
TR	det () const throw (cvmexception)
	Matrix determinant.
basic_srmatrix &	low_up (const basic_srmatrix &m, tint *nPivots) throw (cvmexception)
	Low-up (LU) factorization.
TR	cond () const throw (cvmexception)
	Condition number reciprocal.
basic_srmatrix &	inv (const basic_srmatrix &m) throw (cvmexception)
	Matrix inversion.
basic_srmatrix	inv () const throw (cvmexception)
	Matrix inversion.
basic_srmatrix &	exp (const basic_srmatrix &m, TR tol=basic_cvmMachSp< TR >()) throw (cvmexception)
	Matrix exponent.
basic_srmatrix	exp (TR tol=basic_cvmMachSp< TR >()) const throw (cvmexception)
	Matrix exponent.
basic_srmatrix &	polynom (const basic_srmatrix &m, const RVector &v) throw (cvmexception)
	Matrix polynomial.
basic_srmatrix	polynom (const RVector &v) const
	Matrix polynomial.
CVector	eig (basic_scmatrix< TR, TC > &mEigVect, bool bRightVect=true) const throw (cvmexception)
	Eigenvalues and eigenvectors.
CVector	eig () const throw (cvmexception)
	Eigenvalues.
basic_srmatrix &	cholesky (const basic_srsmatrix< TR > &m) throw (cvmexception)
	Cholesky factorization.
basic_srmatrix &	bunch_kaufman (const basic_srsmatrix< TR > &m, tint *nPivots) throw (cvmexception)
	Bunch-Kaufman factorization.
void	qr (basic_srmatrix< TR > &mQ, basic_srmatrix< TR > &mR) const throw (cvmexception)
	QR factorization.
void	lq (basic_srmatrix< TR > &mL, basic_srmatrix< TR > &mQ) const throw (cvmexception)
	LQ factorization.
void	ql (basic_srmatrix< TR > &mQ, basic_srmatrix< TR > &mL) const throw (cvmexception)
	QL factorization.
void	rq (basic_srmatrix< TR > &mR, basic_srmatrix< TR > &mQ) const throw (cvmexception)
	RQ factorization.
Public Member Functions inherited from basic_rmatrix< TR >
	basic_rmatrix ()
	Default constructor.
	basic_rmatrix (tint nM, tint nN)
	Constructor.
	basic_rmatrix (TR *pd, tint nM, tint nN)
	Constructor.
	basic_rmatrix (const TR *pd, tint nM, tint nN)
	Constructor.
	basic_rmatrix (const basic_rmatrix &m)
	Copy constructor.
	basic_rmatrix (basic_rmatrix &&m) noexcept
	Move constructor.
	basic_rmatrix (const RVector &v, bool bBeColumn=true)
	Constructor.
	basic_rmatrix (basic_rmatrix &m, tint nRow, tint nCol, tint nHeight, tint nWidth)
	Submatrix constructor.
RVector	diag (tint nDiag) throw (cvmexception)
	Diagonal as l-value.
const RVector	diag (tint nDiag) const throw (cvmexception)
	Diagonal (not l-value)
basic_rmatrix &	operator= (const basic_rmatrix &m) throw (cvmexception)
	Assignment operator.
basic_rmatrix &	operator= (basic_rmatrix &&m) throw (cvmexception)
	Move assignment operator.
basic_rmatrix &	assign (tint nRow, tint nCol, const basic_rmatrix &m) throw (cvmexception)
	Assignment to submatrix.
basic_rmatrix &	resize (tint nNewM, tint nNewN) throw (cvmexception)
	Changes dimensions.
bool	operator== (const basic_rmatrix &m) const
	Matrix comparison.
bool	operator!= (const basic_rmatrix &m) const
	Matrix comparison.
basic_rmatrix &	operator<< (const basic_rmatrix &m) throw (cvmexception)
	Matrix replacement.
basic_rmatrix	operator+ (const basic_rmatrix &m) const throw (cvmexception)
	Addition operator.
basic_rmatrix	operator- (const basic_rmatrix &m) const throw (cvmexception)
	Subtraction operator.
basic_rmatrix &	sum (const basic_rmatrix &m1, const basic_rmatrix &m2) throw (cvmexception)
	Sum of matrices.
basic_rmatrix &	diff (const basic_rmatrix &m1, const basic_rmatrix &m2) throw (cvmexception)
	Difference of matrices.
basic_rmatrix &	operator+= (const basic_rmatrix &m) throw (cvmexception)
	Increment operator.
basic_rmatrix &	operator-= (const basic_rmatrix &m) throw (cvmexception)
	Decrement operator.
basic_rmatrix &	transpose (const basic_rmatrix &m) throw (cvmexception)
	Matrix transposition.
basic_rmatrix	operator* (const basic_rmatrix &m) const throw (cvmexception)
	Matrix-matrix product.
basic_rmatrix &	mult (const basic_rmatrix &m1, const basic_rmatrix &m2) throw (cvmexception)
	Matrix-matrix product.
basic_rmatrix &	rank1update (const RVector &vCol, const RVector &vRow) throw (cvmexception)
	Rank-1 update.
basic_rmatrix &	solve (const basic_srmatrix< TR > &mA, const basic_rmatrix &mB, TR &dErr) throw (cvmexception)
	Linear solver.
basic_rmatrix &	solve_tran (const basic_srmatrix< TR > &mA, const basic_rmatrix &mB, TR &dErr) throw (cvmexception)
	Linear solver (transposed)
basic_rmatrix &	solve (const basic_srmatrix< TR > &mA, const basic_rmatrix &mB) throw (cvmexception)
	Linear solver.
basic_rmatrix &	solve_tran (const basic_srmatrix< TR > &mA, const basic_rmatrix &mB) throw (cvmexception)
	Linear solver (transposed)
basic_rmatrix &	solve_lu (const basic_srmatrix< TR > &mA, const basic_srmatrix< TR > &mLU, const tint *pPivots, const basic_rmatrix &mB, TR &dErr) throw (cvmexception)
	LU factorization based linear solver.
basic_rmatrix &	solve_lu (const basic_srmatrix< TR > &mA, const basic_srmatrix< TR > &mLU, const tint *pPivots, const basic_rmatrix &mB) throw (cvmexception)
	LU factorization based linear solver.
RVector	svd () const throw (cvmexception)
	Singular value decomposition.
RVector	svd (basic_srmatrix< TR > &mU, basic_srmatrix< TR > &mVH) const throw (cvmexception)
	Singular value decomposition.
basic_rmatrix	pinv (TR threshold=basic_cvmMachSp< TR >()) const throw (cvmexception)
	Pseudo (generalized) inversion.
basic_rmatrix &	pinv (const basic_rmatrix &mA, TR threshold=basic_cvmMachSp< TR >()) throw (cvmexception)
	Pseudo (generalized) inversion.
basic_rmatrix	gels (bool transpose, const basic_rmatrix &mB, basic_rvector< TR > &vErr) const throw (cvmexception)
	Overdetermined or underdetermined linear solver.
basic_rmatrix &	gels (bool transpose, const basic_rmatrix &mA, const basic_rmatrix &mB, basic_rvector< TR > &vErr) throw (cvmexception)
	Overdetermined or underdetermined linear solver.
basic_rvector< TR >	gels (bool transpose, const basic_rvector< TR > &vB, TR &dErr) const throw (cvmexception)
	Overdetermined or underdetermined linear solver.
basic_rmatrix	gelsy (const basic_rmatrix &mB, tint &rank, TR tol=basic_cvmMachSp< TR >()) const throw (cvmexception)
	Linear least squares problem.
basic_rmatrix &	gelsy (const basic_rmatrix &mA, const basic_rmatrix &mB, tint &rank, TR tol=basic_cvmMachSp< TR >()) throw (cvmexception)
	Linear least squares problem.
basic_rvector< TR >	gelsy (const basic_rvector< TR > &vB, tint &rank, TR tol=basic_cvmMachSp< TR >()) const throw (cvmexception)
	Linear least squares problem.
basic_rmatrix	gelss (const basic_rmatrix &mB, basic_rvector< TR > &sv, tint &rank, TR tol=basic_cvmMachSp< TR >()) const throw (cvmexception)
	Linear least squares problem.
basic_rmatrix &	gelss (const basic_rmatrix &mA, const basic_rmatrix &mB, basic_rvector< TR > &sv, tint &rank, TR tol=basic_cvmMachSp< TR >()) throw (cvmexception)
	Linear least squares problem.
basic_rvector< TR >	gelss (const basic_rvector< TR > &vB, basic_rvector< TR > &sv, tint &rank, TR tol=basic_cvmMachSp< TR >()) const throw (cvmexception)
	Linear least squares problem.
basic_rmatrix	gelsd (const basic_rmatrix &mB, basic_rvector< TR > &sv, tint &rank, TR tol=basic_cvmMachSp< TR >()) const throw (cvmexception)
	Linear least squares problem.
basic_rmatrix &	gelsd (const basic_rmatrix &mA, const basic_rmatrix &mB, basic_rvector< TR > &sv, tint &rank, TR tol=basic_cvmMachSp< TR >()) throw (cvmexception)
	Linear least squares problem.
basic_rvector< TR >	gelsd (const basic_rvector< TR > &vB, basic_rvector< TR > &sv, tint &rank, TR tol=basic_cvmMachSp< TR >()) const throw (cvmexception)
	Linear least squares problem.
tint	rank (TR tol=basic_cvmMachSp< TR >()) const throw (cvmexception)
	Matrix rank.
void	qr (basic_rmatrix< TR > &mQ, basic_srmatrix< TR > &mR) const throw (cvmexception)
	QR factorization ("economy" mode)
void	qr (basic_srmatrix< TR > &mQ, basic_rmatrix< TR > &mR) const throw (cvmexception)
	QR factorization ("full" mode)
void	lq (basic_srmatrix< TR > &mL, basic_rmatrix< TR > &mQ) const throw (cvmexception)
	LQ factorization ("economy" mode)
void	lq (basic_rmatrix< TR > &mL, basic_srmatrix< TR > &mQ) const throw (cvmexception)
	LQ factorization ("full" mode)
void	rq (basic_srmatrix< TR > &mR, basic_rmatrix< TR > &mQ) const throw (cvmexception)
	RQ factorization ("economy" mode)
void	rq (basic_rmatrix< TR > &mR, basic_srmatrix< TR > &mQ) const throw (cvmexception)
	RQ factorization ("full" mode)
void	ql (basic_rmatrix< TR > &mQ, basic_srmatrix< TR > &mL) const throw (cvmexception)
	QL factorization ("economy" mode)
void	ql (basic_srmatrix< TR > &mQ, basic_rmatrix< TR > &mL) const throw (cvmexception)
	QL factorization ("full" mode)
basic_rmatrix &	ger (TR alpha, const RVector &vCol, const RVector &vRow) throw (cvmexception)
	Rank-1 update matrix-vector operation.
basic_rmatrix &	gemm (const basic_rmatrix &m1, bool bTrans1, const basic_rmatrix &m2, bool bTrans2, TR dAlpha, TR dBeta) throw (cvmexception)
	Generic matrix-matrix operation.
basic_rmatrix &	symm (bool bLeft, const basic_srsmatrix< TR > &ms, const basic_rmatrix &m, TR dAlpha, TR dBeta) throw (cvmexception)
	Generic symmetric matrix-matrix operation.
TR	norm2 () const override
	2-norm
Public Member Functions inherited from Matrix< TR, TR >
tint	msize () const
	Number of rows.
tint	nsize () const
	Number of columns.
tint	ld () const
	Leading dimension.
tint	rowofmax () const
	Row with maximum element.
tint	rowofmin () const
	Row with minimum element.
tint	colofmax () const
	Column with maximum element.
tint	colofmin () const
	Column with minimum element.
Public Member Functions inherited from basic_array< TR, TR >
	basic_array ()
	Default constructor.
	basic_array (tint nSize, bool bZeroMemory=true)
	Constructor.
	basic_array (TR *pd, tint nSize, tint nIncr=1)
	Constructor.
	basic_array (const TR *pd, tint nSize, tint nIncr=1)
	Constructor.
	basic_array (const TR begin, const TR end)
	Constructor.
	basic_array (const basic_array &a)
	Copy constructor.
	basic_array (basic_array &&a) noexcept
	Move constructor.
basic_array &	operator= (const basic_array &a) throw (cvmexception)
	Assignment operator.
basic_array &	operator= (basic_array &&a) throw (cvmexception)
	Move assignment operator.
virtual	~basic_array ()
	Destructor.
tint	size () const
	Size (length) of array.
TR *	get ()
	Pointer to data.
const TR *	get () const
	Const pointer to data.
	operator TR * ()
	operator const TR * () const
void	assign (size_type n, const TR &val) throw (cvmexception)
	(STL) assigns given value to n-th element (0-based)
void	assign (const_iterator begin, const_iterator end) throw (cvmexception)
	(STL) assigns begin-end iteartor range to array
tint	incr () const
	Increment between elements.
tint	indofmax () const
	Index of element with maximum module.
tint	indofmin () const
	Index of element with minimum module.
iterator	begin ()
	(STL) iterator to begin
const_iterator	begin () const
	(STL) const iterator to begin
iterator	end ()
	(STL) iterator to end
const_iterator	end () const
	(STL) const iterator to end
reverse_iterator	rbegin ()
	(STL) iterator to begin reversed
const_reverse_iterator	rbegin () const
	(STL) const iterator to begin reversed
reverse_iterator	rend ()
	(STL) iterator to end reversed
const_reverse_iterator	rend () const
	(STL) const iterator to end reversed
size_type	max_size () const
	(STL) maximum possible size of array
size_type	capacity () const
	(STL) current capacity of array, equal to size()
bool	empty () const
	(STL) is array empty
reference	front ()
	(STL) reference to first element
const_reference	front () const
	(STL) const reference to first element
reference	back ()
	(STL) reference to last element
const_reference	back () const
	(STL) const reference to last element
void	clear ()
	(STL) clears array, dealocates memory and sets size() to zero
void	swap (basic_array &v) throw (cvmexception)
	(STL) swaps array values, throws cvmexception if sizes are different
reference	at (size_type n) throw (cvmexception)
	(STL) returns reference to n-th element of array (0-based), throws cvmexception if n is out of boundaries
const_reference	at (size_type n) const throw (cvmexception)
	(STL) returns const reference to n-th element of array (0-based), throws cvmexception if n is out of boundaries
void	push_back (const TR &x) throw (cvmexception)
	(STL) pushes new value to the end of array
void	pop_back () throw (cvmexception)
	(STL) removes last element from array
iterator	insert (iterator position, const TR &x) throw (cvmexception)
	(STL) inserts element to given position in array
iterator	erase (iterator position) throw (cvmexception)
	(STL) removes element from given position in array
Public Member Functions inherited from BandMatrix< TR, TR >
tint	lsize () const
	Number of lower sub-diagonals.
tint	usize () const
	Number of upper super-diagonals.

Protected Attributes
BaseSRMatrix	mSM
	Temporary storage for square matrix enclosing band one (if needed)
Protected Attributes inherited from BandMatrix< TR, TR >
tint	mkl
	Number of sub-diagonals.
tint	mku
	Number of super-diagonals.

Friends
class	basic_scbmatrix< TR, TC >

Additional Inherited Members
Public Types inherited from basic_array< TR, TR >
typedef TR	value_type
	STL-specific value type definition.
typedef value_type *	pointer
	STL-specific value pointer definition.
typedef value_type *	iterator
	STL-specific iterator definition.
typedef const value_type *	const_iterator
	STL-specific const iterator definition.
typedef const value_type *	const_pointer
	STL-specific const pointer definition.
typedef value_type &	reference
	STL-specific reference definition.
typedef const value_type &	const_reference
	STL-specific const reference definition.
typedef size_t	size_type
	STL-specific size type definition.
typedef ptrdiff_t	difference_type
	STL-specific difference type definition.
typedef std::reverse_iterator < const_iterator >	const_reverse_iterator
	STL-specific const reverse iterator definition.
typedef std::reverse_iterator < iterator >	reverse_iterator
	STL-specific reverse iterator definition.
Protected Member Functions inherited from Matrix< TR, TR >
	Matrix ()
	Default constructor.
	Matrix (tint nM, tint nN, tint nLD, bool bZeroMemory)
	Constructor.
	Matrix (TR *pd, tint nM, tint nN, tint nLD, tint nSize)
	Constructor.
	Matrix (const TR *pd, tint nM, tint nN, tint nLD, tint nSize)
	Constructor.
	Matrix (const BaseArray &v, bool bBeColumn)
	Constructor.
	Matrix (Matrix &&m) noexcept
	Move constructor.
Matrix &	operator= (Matrix &&m) throw (cvmexception)
	Move assignment operator.
Protected Member Functions inherited from SqMatrix< TR, TR >
	SqMatrix ()
	internal constructor
virtual	~SqMatrix ()
Protected Member Functions inherited from BandMatrix< TR, TR >
	BandMatrix ()
	internal protected constructor
	BandMatrix (tint nKL, tint nKU)
	internal protected constructor
virtual	~BandMatrix ()
	Destructor.

Detailed Description

template<typename TR>
class basic_srbmatrix< TR >

End-user class encapsulating band square matrix of real numbers.

TR type stands for treal. Please use predefined srbmatrix class in your applications. Band storage can be described as follows (cited from MKL manual): an $m$ by $n$ band matrix with $k_l$ sub-diagonals and $k_u$ super-diagonals is stored compactly in a two-dimensional array with $k_l+k_u+1$ rows and $n$ columns. Columns of the matrix are stored in the corresponding columns of the array, and diagonals of the matrix are stored in rows of the array}. This way of storage can be illustrated as follows (referenced elements are shown as $*$ , not referenced as $-$ , zeros are not stored):

$\begin{aligned} m=n=3, k_l=0, k_u=0&:\ \begin{bmatrix} * & 0 & 0 \\ 0 & * & 0 \\ 0 & 0 & * \end{bmatrix}\\ m=n=4, k_l=1, k_u=0&:\ \begin{bmatrix} * & 0 & 0 & 0 \\ * & * & 0 & 0 \\ 0 & * & * & 0 \\ 0 & 0 & * & * \\ & & & - \end{bmatrix}\\ m=n=6, k_l=1, k_u=2&:\ \begin{bmatrix} - & & & & & \\ - & - & & & & \\ * & * & * & 0 & 0 & 0 \\ * & * & * & * & 0 & 0 \\ 0 & * & * & * & * & 0 \\ 0 & 0 & * & * & * & * \\ 0 & 0 & 0 & * & * & * \\ 0 & 0 & 0 & 0 & * & * \\ & & & & & - \end{bmatrix} \end{aligned}$

CVM library implements square band matrices only, therefore $m=n$ is satisfied for them.

See Also: BandMatrix

Definition at line 28309 of file cvm.h.

Constructor & Destructor Documentation

template<typename TR>

basic_srbmatrix< TR >::basic_srbmatrix ( )

inline

Default constructor.

Creates empty square band matrix. No memory gets allocated.

Example:: using namespace cvm;

srbmatrix m;

std::cout << m.msize() << " " << m.nsize() << " " << m.size();

std::cout << " " << m.lsize() << " " << m.usize() << std::endl;

m.resize (3);

m.resize_lu(1,0);

m.set(1.);

std::cout << m;

prints
0 0 0 0 0

1 0 0

1 1 0

0 1 1

Definition at line 28349 of file cvm.h.

template<typename TR>

basic_srbmatrix< TR >::basic_srbmatrix ( tint nDim )

inlineexplicit

Diagonal band matrix constructor.

Creates $n\times n$ srbmatrix object where dimension $n$ is passed in nDim parameter. The matrix created is diagonal, i.e. $k_l=k_u=0$ . Constructor throws cvmexception in case of non-positive size passed or memory allocation failure.

Example:: using namespace cvm;

srbmatrix m(4);

std::cout << m.msize() << " " << m.nsize() << " " << m.size();

std::cout << " " << m.lsize() << " " << m.usize() << std::endl;

m.set(1.);

std::cout << m;

prints
4 4 4 0 0

1 0 0 0

0 1 0 0

0 0 1 0

0 0 0 1

Parameters

[in] nDim Number of rows and columns.

Definition at line 28379 of file cvm.h.

template<typename TR>

basic_srbmatrix< TR >::basic_srbmatrix	(	tint	nDim,
		tint	nKL,
		tint	nKU
	)

inline

Band matrix constructor.

Creates srbmatrix object of dimension passed in nDim parameter. The matrix created has nKL sub-diagonals and nKU super-diagonals. Constructor throws cvmexception in case of non-positive size or negative number of sub-diagonals or super-diagonals passed or in case of memory allocation failure. Example:

using namespace cvm;
srbmatrix m(5,1,1);
m.set(1.);
std::cout << m << std::endl
          << m.msize() << " " << m.nsize() << " " << m.size()
          << " " << m.lsize() << " " << m.usize() << std::endl;

prints

Parameters

[in]	nDim	Number of rows and columns.
[in]	nKL	Number of lower sub-diagonals.
[in]	nKU	Number of upper super-diagonals.

Definition at line 28415 of file cvm.h.

template<typename TR>

basic_srbmatrix< TR >::basic_srbmatrix	(	TR *	pd,
		tint	nDim,
		tint	nKL,
		tint	nKU
	)

inline

Constructor.

Creates $n\times n$ srbmatrix object where $n$ is passed in nDim parameter. The matrix created has nKL sub-diagonals and nKU super-diagonals. Constructor throws cvmexception in case of non-positive size or negative number of sub-diagonals or super-diagonals passed or in case of memory allocation failure. Unlike others, this constructor does not allocate memory. It just shares memory with array pointed to by pd (for matrices nIncr=1 is always satisfied).

Example:: using namespace cvm;

double a[] = {1., 2., 3., 4., 5., 6., 7., 8.};

srbmatrix ml(a,4,1,0);

srbmatrix mu(a,4,0,1);

ml(2,1) = 9.;

std::cout << ml << std::endl << mu << std::endl;

std::cout << a[0] << " " << a[1] << " " << a[2] << " "

<< a[3] << " " << a[4] << " " << a[5] << " " << std::endl;

prints
1 0 0 0

9 3 0 0

0 4 5 0

0 0 6 7

9 3 0 0

0 4 5 0

0 0 6 7

0 0 0 8

1 9 3 4 5 6

See Also: http://cvmlib.com/faq.htm; basic_rmatrix::basic_rmatrix(TR*,tint,tint)

Parameters

[in]	pd	Pointer to array to share memory with.
[in]	nDim	Number of rows and columns.
[in]	nKL	Number of lower sub-diagonals.
[in]	nKU	Number of upper super-diagonals.

Definition at line 28464 of file cvm.h.

template<typename TR>

basic_srbmatrix< TR >::basic_srbmatrix	(	const TR *	pd,
		tint	nDim,
		tint	nKL,
		tint	nKU
	)

inline

Constructor.

Creates $n\times n$ srbmatrix object where $n$ is passed in nDim parameter. The matrix created has nKL sub-diagonals and nKU super-diagonals. Constructor throws cvmexception in case of non-positive size or negative number of sub-diagonals or super-diagonals passed or in case of memory allocation failure. Then constructor copies $(k_l + k_u + 1)*n$ elements of array pd to the matrix according to band storage.

Example:: using namespace cvm;

const double a[] = {1., 2., 3., 4., 5., 6., 7., 8.};

srbmatrix ml(a,4,1,0);

srbmatrix mu(a,4,0,1);

ml(2,1) = 9.;

std::cout << ml << std::endl << mu << std::endl;

std::cout << a[0] << " " << a[1] << " " << a[2] << " "

<< a[3] << " " << a[4] << " " << a[5] << " " << std::endl;

prints
1 0 0 0

9 3 0 0

0 4 5 0

0 0 6 7

2 3 0 0

0 4 5 0

0 0 6 7

0 0 0 8

1 2 3 4 5 6

See Also: http://cvmlib.com/faq.htm; basic_rmatrix::basic_rmatrix(TR*,tint,tint)

Parameters

[in]	pd	Pointer to array to share memory with.
[in]	nDim	Number of rows and columns.
[in]	nKL	Number of lower sub-diagonals.
[in]	nKU	Number of upper super-diagonals.

Definition at line 28513 of file cvm.h.

template<typename TR>

basic_srbmatrix< TR >::basic_srbmatrix ( const basic_srbmatrix< TR > & m )

inline

Copy constructor.

Creates srbmatrix object as a copy of band matrix m. It throws cvmexception in case of memory allocation failure.

Example:: using namespace cvm;

double a[] = {1., 2., 3., 4., 5., 6., 7., 8.};

srbmatrix m(a,4,1,0);

srbmatrix mc(m);

m(1,1) = 7.77;

std::cout << m << std::endl << mc;

prints
7.77 0 0 0

2 3 0 0

0 4 5 0

0 0 6 7

1 0 0 0

2 3 0 0

0 4 5 0

0 0 6 7

Parameters

[in] m srbmatrix to copy from.

Definition at line 28548 of file cvm.h.

template<typename TR>

basic_srbmatrix< TR >::basic_srbmatrix ( basic_srbmatrix< TR > && m )

inline

Move constructor.

Implements move semantics introduced in new C++ standard. Moves data ownership from other matrix to newly created object. It's usually executed implicitly in cases like this:

rvector a(b + c);

or this

rvector a = b + c;

Here temporary result of calling b.operator+(c) will not be destroyed but rather moved to newly created object a.

Parameters

[in] m rvalue reference to other matrix.

Definition at line 28572 of file cvm.h.

template<typename TR>

basic_srbmatrix< TR >::basic_srbmatrix	(	const BaseRMatrix &	m,
		tint	nKL,
		tint	nKU
	)

inline

Constructor.

Creates srbmatrix object as a copy of sliced matrix m, i.e. it copies main diagonal, nKL sub-diagonals and nKU super-diagonals of matrix m. It's assumed that $m\times n$ matrix m must have equal sizes, i.e. $m = n$ is satisfied. Constructor throws cvmexception if this is not true or in case of memory allocation failure.

Example:: using namespace cvm;

double a[] = {1., 2., 3., 4., 5., 6., 7., 8., 9.,

10., 11., 12., 13., 14., 15., 16.};

srmatrix m(a,4);

srbmatrix mb(m,1,2);

std::cout << m << std::endl << mb;

prints
1 5 9 13

2 6 10 14

3 7 11 15

4 8 12 16

1 5 9 0

2 6 10 14

0 7 11 15

0 0 12 16

Parameters

[in]	m	rmatrix to copy diagonal and subdiagonals from.
[in]	nKL	Number of lower sub-diagonals.
[in]	nKU	Number of upper super-diagonals.

Definition at line 28611 of file cvm.h.

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template<typename TR>

basic_srbmatrix< TR >::basic_srbmatrix ( const RVector & v )

inlineexplicit

Constructor.

Creates srbmatrix object of size v.size() by v.size() and assigns vector v to its main diagonal. Constructor throws cvmexception in case of memory allocation failure.

Example:: using namespace cvm;

double a[] = {1., 2., 3., 4., 5.};

rvector v(a, 5);

srbmatrix m(v);

std::cout << m;

prints
1 0 0 0 0

0 2 0 0 0

0 0 3 0 0

0 0 0 4 0

0 0 0 0 5

Parameters

[in] v rvector to copy main diagonal from.

Definition at line 28643 of file cvm.h.

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Member Function Documentation

template<typename TR>

type_proxy<TR,TR> basic_srbmatrix< TR >::operator()	(	tint	nRow,
		tint	nCol
	)		throw (cvmexception)

inline

Reference to element (l-value)

Operator provides access to a particular element of calling matrix by its row and column index. Indexes passed are CVM0 based. It returns l-value in order to make possible write access to an element. Operator throws cvmexception if nRow or nCol is outside of boundaries.

Example:: using namespace cvm;

std::cout.setf (std::ios::scientific | std::ios::left);

std::cout.precision (2);

try {

double a[] = {1., 2., 3., 4., 5., 6.};

const rmatrix m (a, 2, 3);

rmatrix ms(m);

std::cout << m(1,1) << " " << m(2,3) << std::endl << std::endl;

ms(2,2) = 7.77;

std::cout << ms;

}

catch (std::exception& e) {

std::cout << "Exception " << e.what () << std::endl;

}

prints
1.00e+00 6.00e+00

1.00e+00 3.00e+00 5.00e+00

2.00e+00 7.77e+00 6.00e+00

See Also: http://cvmlib.com/faq.htm

Parameters

[in]	nRow	Row index (CVM0 based).
[in]	nCol	Column index (CVM0 based).

Returns: type_proxy Proxy to element (l-value).

Reimplemented from basic_srmatrix< TR >.

Definition at line 28650 of file cvm.h.

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template<typename TR>

TR basic_srbmatrix< TR >::operator()	(	tint	nRow,
		tint	nCol
	)		const throw (cvmexception)

inline

Value of element (not l-value)

Operator returns value of a particular element of calling matrix by its row and column index. Indexes passed are CVM0 based. Operator throws cvmexception if nRow or nCol is outside of boundaries.

Example:: using namespace cvm;

std::cout.setf (std::ios::scientific | std::ios::left);

std::cout.precision (2);

try {

double a[] = {1., 2., 3., 4., 5., 6.};

const rmatrix m (a, 2, 3);

std::cout << m(1,1) << " " << m(2,3) << std::endl;

}

catch (std::exception& e) {

std::cout << "Exception " << e.what () << std::endl;

}

prints
1.00e+00 6.00e+00

See Also: http://cvmlib.com/faq.htm

Parameters

[in]	nRow	Row index (CVM0 based).
[in]	nCol	Column index (CVM0 based).

Returns: TR treal value.

Reimplemented from basic_srmatrix< TR >.

Definition at line 28657 of file cvm.h.

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template<typename TR>

const RVector basic_srbmatrix< TR >::operator() ( tint nCol ) const throw (cvmexception)

inline

Column as not l-value.

Operator creates rvector object as a copy of nCol-th column (CVM0 based) of calling matrix. Operator throws cvmexception if nCol is outside of boundaries.

Example:: using namespace cvm;

std::cout.setf (std::ios::scientific | std::ios::left);

std::cout.precision (2);

try {

double a[] = {1., 2., 3., 4., 5., 6.};

const rmatrix m (a, 2, 3);

std::cout << m(2) << std::endl;

}

catch (std::exception& e) {

std::cout << "Exception " << e.what () << std::endl;

}

prints
3.00e+00 4.00e+00

Parameters

[in] nCol Index of column (CVM0 based).

Returns: rvector Column value.

Reimplemented from basic_srmatrix< TR >.

Definition at line 28665 of file cvm.h.

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template<typename TR>

const RVector basic_srbmatrix< TR >::operator[] ( tint nRow ) const throw (cvmexception)

inline

Row as not l-value.

Operator creates rvector object as a copy of nRow-th row (CVM0 based) of calling matrix. Operator throws cvmexception if nRow is outside of boundaries.

Example:: using namespace cvm;

std::cout.setf (std::ios::scientific | std::ios::left);

std::cout.precision (2);

try {

double a[] = {1., 2., 3., 4., 5., 6.};

const rmatrix m (a, 2, 3);

std::cout << m[1] << std::endl;

}

catch (std::exception& e) {

std::cout << "Exception " << e.what () << std::endl;

}

prints
1.00e+00 3.00e+00 5.00e+00

Parameters

[in] nRow Index of row (CVM0 based).

Returns: rvector Row value.

Reimplemented from basic_srmatrix< TR >.

Definition at line 28672 of file cvm.h.

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template<typename TR>

basic_srbmatrix& basic_srbmatrix< TR >::operator= ( const basic_srbmatrix< TR > & m ) throw (cvmexception)

inline

Assignment operator.

Sets every element of calling srbmatrix to be equal to appropriate element of matrix m and returns reference to the matrix changed. Operator throws cvmexception in case of different matrix dimensions.

Example:: using namespace cvm;

try {

double a[] = {1., 2., 3., 4., 5., 6., 7., 8.};

const srbmatrix m1(a,4,1,0);

srbmatrix m2(4,1,0);

m2 = m1;

std::cout << m2;

}

catch (std::exception& e) {

std::cout << "Exception: " << e.what () << std::endl;

}

prints
1 0 0 0

2 3 0 0

0 4 5 0

0 0 6 7

Parameters

[in] m srbmatrix to assign from.

Returns: Reference to changed calling matrix.

Definition at line 28710 of file cvm.h.

template<typename TR>

basic_srbmatrix& basic_srbmatrix< TR >::operator= ( basic_srbmatrix< TR > && m ) throw (cvmexception)

inline

Move assignment operator.

Implements move semantics introduced in new C++ standard. Moves data ownership from other matrix to calling object. It's usually executed implicitly in cases like this:

a = b + c;

Here temporary result of calling b.operator+(c) will not be destroyed but rather moved to calling object a.

Parameters

[in] m rvalue reference to other matrix.

Definition at line 28730 of file cvm.h.

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template<typename TR>

basic_srbmatrix& basic_srbmatrix< TR >::assign ( const RVector & v ) throw (cvmexception)

inline

Vector (as array) assignment.

Sets every element of calling matrix to be equal to appropriate element of rvector v as an array. Assignment is performed according to matrix storage (by columns). It's assumed that vector passed is long enough to fill calling matrix. Function throws cvmexception otherwise.

Example:: try {

const double a[] = {1., 2., 3., 4., 5., 6., 7., 8.};

const rvector v(a,8);

rmatrix m(2,3);

std::cout << v << std::endl;

m.assign(v);

std::cout << m;

} catch (std::exception& e) {

std::cout << "Exception: " << e.what () << std::endl;

}

prints
1 2 3 4 5 6 7 8

1 3 5

2 4 6

Parameters

[in] v rvector to assign.

Returns: Reference to changed calling matrix.

Reimplemented from basic_srmatrix< TR >.

Definition at line 28738 of file cvm.h.

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template<typename TR>

basic_srbmatrix& basic_srbmatrix< TR >::assign ( const TR * pd )

inline

External array assignment.

Sets every element of calling matrix to be equal to appropriate element of array pointed to by parameter pd and returns reference to the matrix changed. Assignment is performed according to matrix storage (by columns). It's assumed that array passed is long enough to fill calling matrix.

Example:: using namespace cvm;

std::cout.setf (std::ios::scientific | std::ios::left);

std::cout.precision (2);

const double a[] = {1., 2., 3., 4., 5., 6.};

rmatrix m(2, 3);

m.assign(a);

std::cout << m;

prints
1.00e+000 3.00e+000 5.00e+000

2.00e+000 4.00e+000 6.00e+000

Parameters

[in] pd Const pointer to external array.

Returns: Reference to changed calling matrix.

Reimplemented from basic_srmatrix< TR >.

Definition at line 28746 of file cvm.h.

template<typename TR>

basic_srbmatrix& basic_srbmatrix< TR >::set ( TR d )

inline

Sets all elements to one value.

Sets every element of calling matrix to be equal to parameter d and returns reference to the matrix changed.

Example:: using namespace cvm;

std::cout.setf (std::ios::scientific | std::ios::left);

std::cout.precision (2);

rmatrix m(2, 3);

m.set(3.);

std::cout << m;

prints
3.00e+000 3.00e+000 3.00e+000

3.00e+000 3.00e+000 3.00e+000

Parameters

[in] d Value to set to.

Returns: Reference to changed calling matrix.

Reimplemented from basic_srmatrix< TR >.

Definition at line 28753 of file cvm.h.

template<typename TR>

basic_srbmatrix& basic_srbmatrix< TR >::resize ( tint nNewDim ) throw (cvmexception)

inline

Changes dimension.

Changes dimension of calling square matrix to nNewDim and returns reference to the matrix changed. In case of increasing of its size, the matrix is filled up with zeroes. Function throws cvmexception in case of negative dimension passed or memory allocation failure.

Example:: using namespace cvm;

try {

double a[] = {1., 2., 3., 4.};

srmatrix m(a, 2);

std::cout << m << std::endl;

m.resize (3);

std::cout << m;

}

catch (std::exception& e) {

std::cout << "Exception " << e.what () << std::endl;

}

prints
1 3

2 4

1 3 0

2 4 0

0 0 0

Parameters

[in] nNewDim New dimension.

Returns: Reference to changed calling matrix.

Reimplemented from basic_srmatrix< TR >.

Definition at line 28759 of file cvm.h.

template<typename TR>

basic_srbmatrix& basic_srbmatrix< TR >::resize_lu	(	tint	nNewKL,
		tint	nNewKU
	)		throw (cvmexception)

inline

Changes number of sub- and super-diagonals.

Changes number of sub- and super-diagonals of calling band matrix to nNewKL and nNewKU respectively and returns reference to the matrix changed. In case of increasing of the numbers, calling matrix is filled up with zeroes. Function throws cvmexception in case of negative number passed or memory allocation failure.

Example:: using namespace cvm;

try {

double a[] = {1., 2., 3., 4., 5., 6., 7., 8.};

srbmatrix m(a,4,1,0);

std::cout << m << std::endl;

m.resize_lu (0,1);

m.diag(1).set(9.);

std::cout << m;

}

catch (std::exception& e) {

std::cout << "Exception: " << e.what () << std::endl;

}

prints
1 0 0 0

2 3 0 0

0 4 5 0

0 0 6 7

1 9 0 0

0 3 9 0

0 0 5 9

0 0 0 7

Parameters

[in]	nNewKL	New number of lower sub-diagonals.
[in]	nNewKU	New number of upper super-diagonals.

Returns: Reference to changed calling matrix.

Definition at line 28803 of file cvm.h.

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template<typename TR>

bool basic_srbmatrix< TR >::operator== ( const basic_srbmatrix< TR > & m ) const

inline

Band matrix comparison.

Operator compares calling band matrix with band matrix m and returns true if they have same dimensions and their appropriate elements differ by not more than cvmMachMin() (the smallest normalized positive number). Returns false otherwise.

Example:: using namespace cvm;

double a[] = {1., 2., 3., 4.};

srbmatrix m1(a,2,1,0);

srbmatrix m2(2,1,0);

std::cout << m1 << std::endl;

m2(1,1) = 1.;

m2(2,1) = 2.; m2(2,2) = 3.;

std::cout << (m1 == m2) << std::endl;

prints
1 0

2 3

1

See Also: operator !=()

Parameters

[in] m srbmatrix to compare to.

Returns: bool Result of comparison.

Definition at line 28843 of file cvm.h.

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template<typename TR>

bool basic_srbmatrix< TR >::operator!= ( const basic_srbmatrix< TR > & m ) const

inline

Band matrix comparison.

Operator compares calling band matrix with band matrix m and returns true if they have different dimensions or at least one of their appropriate elements differs by more than cvmMachMin() (the smallest normalized positive number). Returns false otherwise.

Example:: using namespace cvm;

double a[] = {1., 2., 3., 4.};

srbmatrix m1(a,2,1,0);

srbmatrix m2(2,1,0);

std::cout << m1 << std::endl;

m2(1,1) = 1.;

m2(2,1) = 2.; m2(2,2) = 3.;

std::cout << (m1 == m2) << std::endl;

prints
1 0

2 3

0

See Also: operator ==()

Parameters

[in] m srbmatrix to compare to.

Returns: bool Result of comparison.

Definition at line 28880 of file cvm.h.

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template<typename TR>

basic_srbmatrix& basic_srbmatrix< TR >::operator<< ( const basic_srbmatrix< TR > & m ) throw (cvmexception)

inline

Matrix replacement.

Destroys calling band matrix, creates a new one as a copy of band matrix m and returns reference to the matrix changed. Operator throws cvmexception in case of memory allocation failure.

Example:: using namespace cvm;

try {

srbmatrix m(3,1,0);

srmatrix mc(1);

m(2,1) = 1.;

m(2,2) = 2.;

std::cout << m << std::endl << mc << std::endl;

mc << m;

std::cout << mc;

}

catch (std::exception& e) {

std::cout << "Exception: " << e.what () << std::endl;

}

prints
0 0 0

1 2 0

0 0 0

0

0 0 0

1 2 0

0 0 0

See Also: operator =()

Parameters

[in] m srbmatrix to replace by.

Returns: Reference to changed calling matrix.

Definition at line 28922 of file cvm.h.

template<typename TR>

basic_srbmatrix basic_srbmatrix< TR >::operator+ ( const basic_srbmatrix< TR > & m ) const throw (cvmexception)

inline

Addition operator.

Creates object of type srbmatrix as sum of calling matrix and matrix m. Operator throws cvmexception in case of different dimensions of the operands or memory allocation failure.

Example:: using namespace cvm;

std::cout.setf (std::ios::scientific | std::ios::left);

std::cout.precision (1);

try {

double a[] = {1., 2., 3., 4., 5., 6., 7., 8.};

double b[] = {10., 20., 30., 40., 50., 60., 70., 80.};

srbmatrix m1(a,4,1,0);

srbmatrix m2(b,4,1,0);

std::cout << m1 + m2 << std::endl << m1 + m1;

}

catch (std::exception& e) {

std::cout << "Exception: " << e.what () << std::endl;

}

prints
1.1e+01 0.0e+00 0.0e+00 0.0e+00

2.2e+01 3.3e+01 0.0e+00 0.0e+00

0.0e+00 4.4e+01 5.5e+01 0.0e+00

0.0e+00 0.0e+00 6.6e+01 7.7e+01

2.0e+00 0.0e+00 0.0e+00 0.0e+00

4.0e+00 6.0e+00 0.0e+00 0.0e+00

0.0e+00 8.0e+00 1.0e+01 0.0e+00

0.0e+00 0.0e+00 1.2e+01 1.4e+01

See Also: sum()

Parameters

[in] m srbmatrix to add to calling one.

Returns: Sum of matrices.

Definition at line 28973 of file cvm.h.

template<typename TR>

basic_srbmatrix basic_srbmatrix< TR >::operator- ( const basic_srbmatrix< TR > & m ) const throw (cvmexception)

inline

Subtraction operator.

Creates object of type srbmatrix as difference of calling band matrix and band matrix m. It throws cvmexception in case of different dimensions of the operands or memory allocation failure.

Example:: using namespace cvm;

std::cout.setf (std::ios::scientific | std::ios::left);

std::cout.precision (1);

try {

double a[] = {1., 2., 3., 4., 5., 6., 7., 8.};

double b[] = {10., 20., 30., 40., 50., 60., 70., 80.};

srbmatrix m1(a,4,1,0);

srbmatrix m2(b,4,1,0);

std::cout << m2 - m1 << std::endl << m1 - m1;

}

catch (std::exception& e) {

std::cout << "Exception: " << e.what () << std::endl;

}

prints
9.0e+00 0.0e+00 0.0e+00 0.0e+00

1.8e+01 2.7e+01 0.0e+00 0.0e+00

0.0e+00 3.6e+01 4.5e+01 0.0e+00

0.0e+00 0.0e+00 5.4e+01 6.3e+01

0.0e+00 0.0e+00 0.0e+00 0.0e+00

0.0e+00 0.0e+00 0.0e+00 0.0e+00

0.0e+00 0.0e+00 0.0e+00 0.0e+00

0.0e+00 0.0e+00 0.0e+00 0.0e+00

See Also: diff()

Parameters

[in] m srbmatrix to subtract from calling one.

Returns: Difference of matrices.

Definition at line 29020 of file cvm.h.

template<typename TR>

basic_srbmatrix& basic_srbmatrix< TR >::sum	(	const basic_srbmatrix< TR > &	m1,
		const basic_srbmatrix< TR > &	m2
	)		throw (cvmexception)

inline

Sum of matrices.

Assigns sum of square band matrices m1 and m2 to calling matrix and returns reference to the matrices changed. It throws cvmexception in case of different sizes of the operands.

Example:: using namespace cvm;

try {

double a[] = {1., 2., 3., 4., 5., 6.};

const srbmatrix m1(a,3,1,0);

srbmatrix m2(3,1,0);

srbmatrix m(3,1,0);

m2.set(1.);

std::cout << m1 << std::endl << m2 << std::endl;

std::cout << m.sum(m1, m2) << std::endl;

std::cout << m.sum(m, m2);

}

catch (std::exception& e) {

std::cout << "Exception: " << e.what () << std::endl;

}

prints
1 0 0

2 3 0

0 4 5

1 0 0

1 1 0

0 1 1

2 0 0

3 4 0

0 5 6

3 0 0

4 5 0

0 6 7

See Also: operator +()

Parameters

[in]	m1	First srbmatrix summand.
[in]	m2	Second srbmatrix summand.

Returns: Reference to changed calling matrix.

Definition at line 29074 of file cvm.h.

template<typename TR>

basic_srbmatrix& basic_srbmatrix< TR >::diff	(	const basic_srbmatrix< TR > &	m1,
		const basic_srbmatrix< TR > &	m2
	)		throw (cvmexception)

inline

Difference of matrices.

Assigns difference of square band matrices m1 and m2 to calling matrix and returns reference to the matrix changed. It throws cvmexception in case of different sizes of the operands.

Example:: using namespace cvm;

try {

double a[] = {1., 2., 3., 4., 5., 6.};

const srbmatrix m1(a,3,1,0);

srbmatrix m2(3,1,0);

srbmatrix m(3,1,0);

m2.set(1.);

std::cout << m1 << std::endl << m2 << std::endl;

std::cout << m.diff(m1, m2) << std::endl;

std::cout << m.diff(m, m2);

}

catch (std::exception& e) {

std::cout << "Exception: " << e.what () << std::endl;

}

prints
1 0 0

2 3 0

0 4 5

1 0 0

1 1 0

0 1 1

0 0 0

1 2 0

0 3 4

-1 0 0

0 1 0

0 2 3

See Also: operator -()

Parameters

[in]	m1	First srbmatrix subtrahend.
[in]	m2	Second srbmatrix subtrahend.

Returns: Reference to changed calling matrix.

Definition at line 29128 of file cvm.h.

template<typename TR>

basic_srbmatrix& basic_srbmatrix< TR >::operator+= ( const basic_srbmatrix< TR > & m ) throw (cvmexception)

inline

Increment operator.

Adds srbmatrix m to calling matrix and returns reference to the matrix changed. It throws cvmexception in case of different sizes of the operands.

Example:: using namespace cvm;

try {

srbmatrix m1(4,0,1);

srbmatrix m2(4,0,1);

m1.set(1.);

m2.set(2.);

m1 += m2;

std::cout << m1 << std::endl;

// well, you can do this too, but temporary object would be created

m2 += m2;

std::cout << m2;

}

catch (std::exception& e) {

std::cout << "Exception: " << e.what () << std::endl;

}

prints
3 3 0 0

0 3 3 0

0 0 3 3

0 0 0 3

4 4 0 0

0 4 4 0

0 0 4 4

0 0 0 4

See Also: operator +(); sum()

Parameters

[in] m srbmatrix to increment by.

Returns: Reference to changed calling matrix.

Definition at line 29179 of file cvm.h.

template<typename TR>

basic_srbmatrix& basic_srbmatrix< TR >::operator-= ( const basic_srbmatrix< TR > & m ) throw (cvmexception)

inline

Decrement operator.

Subtracts srbmatrix m from calling matrix and returns reference to the matrix changed. It throws cvmexception in case of different sizes of the operands.

Example:: using namespace cvm;

try {

srbmatrix m1(4,0,1);

srbmatrix m2(4,0,1);

m1.set(1.);

m2.set(4.);

m2 -= m1;

std::cout << m2 << std::endl;

// well, you can do this too, but temporary object would be created

m2 -= m2;

std::cout << m2;

}

catch (std::exception& e) {

std::cout << "Exception: " << e.what () << std::endl;

}

prints
3 3 0 0

0 3 3 0

0 0 3 3

0 0 0 3

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

See Also: operator -(); diff()

Parameters

[in] m srbmatrix to decrement by.

Returns: Reference to changed calling matrix.

Definition at line 29229 of file cvm.h.

template<typename TR>

basic_srbmatrix basic_srbmatrix< TR >::operator- ( ) const

inline

Unary minus operator.

Creates object of type srbmatrix as calling matrix multiplied by -1. It throws cvmexception in case of memory allocation failure.

Example:: using namespace cvm;

std::cout.setf (std::ios::scientific |

std::ios::left |

std::ios::showpos);

std::cout.precision (1);

double a[] = {1., 2., 3., 4., 5., 6., 7., 8.};

srbmatrix m(a,4,1,0);

std::cout << -m;

prints
-1.0e+00 +0.0e+00 +0.0e+00 +0.0e+00

-2.0e+00 -3.0e+00 +0.0e+00 +0.0e+00

+0.0e+00 -4.0e+00 -5.0e+00 +0.0e+00

+0.0e+00 +0.0e+00 -6.0e+00 -7.0e+00

Returns: Result object.

Reimplemented from basic_srmatrix< TR >.

Definition at line 29262 of file cvm.h.

template<typename TR>

basic_srbmatrix& basic_srbmatrix< TR >::operator++ ( )

inline

Plus identity, prefix.

Adds identity matrix to calling square band matrix and returns reference to the matrix changed.

Example:: using namespace cvm;

double a[] = {1., 2., 3., 4., 5., 6., 7., 8.};

srbmatrix m (a,4,1,0);

m++;

std::cout << m << std::endl;

std::cout << ++m;

prints
2 0 0 0

2 4 0 0

0 4 6 0

0 0 6 8

3 0 0 0

2 5 0 0

0 4 7 0

0 0 6 9

Returns: Reference to changed calling matrix.

Reimplemented from basic_srmatrix< TR >.

Definition at line 29297 of file cvm.h.

template<typename TR>

basic_srbmatrix basic_srbmatrix< TR >::operator++ ( int )

inline

Plus identity, postfix.

Adds identity matrix to calling square band matrix and returns reference to the matrix changed.

Example:: using namespace cvm;

double a[] = {1., 2., 3., 4., 5., 6., 7., 8.};

srbmatrix m (a,4,1,0);

m++;

std::cout << m << std::endl;

std::cout << ++m;

prints
2 0 0 0

2 4 0 0

0 4 6 0

0 0 6 8

3 0 0 0

2 5 0 0

0 4 7 0

0 0 6 9

Returns: Reference to changed calling matrix.

Reimplemented from basic_srmatrix< TR >.

Definition at line 29330 of file cvm.h.

template<typename TR>

basic_srbmatrix& basic_srbmatrix< TR >::operator-- ( )

inline

Minus identity, prefix.

Subtracts identity matrix from calling square band matrix and returns reference to the matrix changed.

Example:: using namespace cvm;

double a[] = {1., 2., 3., 4., 5., 6., 7., 8.};

srbmatrix m (a,4,1,0);

m--;

std::cout << m << std::endl;

std::cout << --m;

prints
0 0 0 0

2 2 0 0

0 4 4 0

0 0 6 6

-1 0 0 0

2 1 0 0

0 4 3 0

0 0 6 5

Returns: Reference to changed calling matrix.

Reimplemented from basic_srmatrix< TR >.

Definition at line 29363 of file cvm.h.

template<typename TR>

basic_srbmatrix basic_srbmatrix< TR >::operator-- ( int )

inline

Minus identity, postfix.

Subtracts identity matrix from calling square band matrix and returns reference to the matrix changed.

Example:: using namespace cvm;

double a[] = {1., 2., 3., 4., 5., 6., 7., 8.};

srbmatrix m (a,4,1,0);

m--;

std::cout << m << std::endl;

std::cout << --m;

prints
0 0 0 0

2 2 0 0

0 4 4 0

0 0 6 6

-1 0 0 0

2 1 0 0

0 4 3 0

0 0 6 5

Returns: Reference to changed calling matrix.

Reimplemented from basic_srmatrix< TR >.

Definition at line 29396 of file cvm.h.

template<typename TR>

basic_srbmatrix basic_srbmatrix< TR >::operator* ( TR dMult ) const

inline

Multiply by number operator.

Creates object of type srmatrix as product of calling square matrix and number dMult. It throws cvmexception in case of memory allocation failure.

Example:: using namespace cvm;

double a[] = {1., 2., 3., 4., 5., 6., 7., 8., 9.};

srmatrix m(a, 3);

std::cout << m * 5.;

prints
5 20 35

10 25 40

15 30 45

See Also: operator *=()

Parameters

[in] dMult Number to multiply by.

Returns: Result object.

Reimplemented from basic_srmatrix< TR >.

Definition at line 29402 of file cvm.h.

template<typename TR>

basic_srbmatrix basic_srbmatrix< TR >::operator/ ( TR dDiv ) const throw (cvmexception)

inline

Divide by number operator.

Creates object of type srmatrix as quotient of calling square matrix and number dDiv. It throws cvmexception if dDiv has absolute value equal or less than cvmMachMin() (the smallest normalized positive number). It also throws exception in case of memory allocation failure.

Example:: using namespace cvm;

try {

double a[] = {1., 2., 3., 4., 5., 6., 7., 8., 9.};

srmatrix m(a, 3);

std::cout << m / 4.;

}

catch (std::exception& e) {

std::cout << "Exception " << e.what () << std::endl;

}

prints
0.25 1 1.75

0.5 1.25 2

0.75 1.5 2.25

See Also: operator /=()

Parameters

[in] dDiv Number to divide by.

Returns: Result object.

Reimplemented from basic_srmatrix< TR >.

Definition at line 29409 of file cvm.h.

template<typename TR>

basic_srbmatrix& basic_srbmatrix< TR >::operator*= ( TR dMult )

inline

Multiply by number and assign.

Multiplies calling matrix by number dMult and returns reference to the matrix changed.

Example:: using namespace cvm;

double a[] = {1., 2., 3., 4., 5., 6.};

rmatrix m(a, 2, 3);

m *= 2.;

std::cout << m;

prints
2 6 10

4 8 12

See Also: operator *(TR) const

Parameters

[in] dMult Number to multiply by.

Returns: Reference to changed calling matrix.

Reimplemented from basic_srmatrix< TR >.

Definition at line 29416 of file cvm.h.

template<typename TR>

basic_srbmatrix& basic_srbmatrix< TR >::operator/= ( TR dDiv ) throw (cvmexception)

inline

Divide by number and assign.

Divides calling matrix by number dDiv and returns reference to the matrix changed. It throws cvmexception if dDiv has absolute value equal or less than cvmMachMin() (the smallest normalized positive number).

Example:: using namespace cvm;

std::cout.setf (std::ios::scientific | std::ios::left);

std::cout.precision (2);

try {

double a[] = {1., 2., 3., 4., 5., 6.};

rmatrix m(a, 2, 3);

m /= 2.;

std::cout << m;

}

catch (std::exception& e) {

std::cout << "Exception " << e.what () << std::endl;

}

prints
5.00e-01 1.50e+00 2.50e+00

1.00e+00 2.00e+00 3.00e+00

See Also: operator /(TR) const

Parameters

[in] dDiv Number to divide by.

Returns: Reference to changed calling matrix.

Reimplemented from basic_srmatrix< TR >.

Definition at line 29422 of file cvm.h.

template<typename TR>

basic_srbmatrix& basic_srbmatrix< TR >::normalize ( )

inline

Matrix normalizer.

Normalizes calling matrix so its Euclidean norm() becomes equal to 1 if it was greater than cvmMachMin() (the smallest normalized positive number) before the call. Does nothing otherwise.

Example:: using namespace cvm;

std::cout.setf (std::ios::scientific | std::ios::left);

std::cout.precision (2);

double a[] = {1., 2., 3., 4., 5., 6.};

rmatrix m(a, 2, 3);

m.normalize();

std::cout << m << m.norm() << std::endl;

prints
1.05e-01 3.14e-01 5.24e-01

2.10e-01 4.19e-01 6.29e-01

1

Returns: Reference to changed calling matrix.

Reimplemented from basic_srmatrix< TR >.

Definition at line 29428 of file cvm.h.

template<typename TR>

basic_srbmatrix basic_srbmatrix< TR >::operator~ ( ) const throw (cvmexception)

inline

Matrix transposition.

Creates object of type srmatrix as transposed calling matrix.

Example:: using namespace cvm;

try {

double a[] = {1., 2., 3., 4., 5., 6., 7., 8., 9.};

srmatrix m(a,3);

srmatrix mt(3);

std::cout << ~m << std::endl ;

mt.transpose(m);

std::cout << mt << std::endl;

mt.transpose();

std::cout << mt;

}

catch (std::exception& e) {

std::cout << "Exception " << e.what () << std::endl;

}

prints
1 2 3

4 5 6

7 8 9

1 2 3

4 5 6

7 8 9

1 4 7

2 5 8

3 6 9

Returns: Result object.

Reimplemented from basic_srmatrix< TR >.

Definition at line 29435 of file cvm.h.

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template<typename TR>

basic_srbmatrix& basic_srbmatrix< TR >::transpose ( const basic_srbmatrix< TR > & m ) throw (cvmexception)

inline

Matrix transposition.

Sets calling square band matrix to be equal to square band matrix m transposed. Function throws cvmexception in case of not appropriate sizes of the operands.

Example:: using namespace cvm;

double a[] = {1., 2., 3., 4., 5., 6., 7., 8.};

srbmatrix m (a,4,1,0);

srbmatrix mt(4,0,1);

std::cout << ~m << std::endl ;

mt.transpose(m);

std::cout << mt << std::endl;

mt.transpose();

std::cout << mt;

prints
1 2 0 0

0 3 4 0

0 0 5 6

0 0 0 7

1 2 0 0

0 3 4 0

0 0 5 6

0 0 0 7

1 0 0 0

2 3 0 0

0 4 5 0

0 0 6 7

Parameters

[in] m srbmatrix to transpose.

Returns: Reference to changed calling matrix.

Definition at line 29478 of file cvm.h.

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template<typename TR>

basic_srbmatrix& basic_srbmatrix< TR >::transpose ( ) throw (cvmexception)

inline

Matrix transposition (in-place)

Makes calling matrix to be equal to transposed itself. Function throws cvmexception in case of memory allocation failure.

Example:: using namespace cvm;

try {

double a[] = {1., 2., 3., 4., 5., 6.};

rmatrix m(a,2,3);

std::cout << m << std::endl;

std::cout << m.transpose();

}

catch (std::exception& e) {

std::cout << "Exception " << e.what () << std::endl;

}

prints
1 3 5

2 4 6

1 2

3 4

5 6

Returns: Reference to changed calling matrix.

Reimplemented from basic_srmatrix< TR >.

Definition at line 29487 of file cvm.h.

template<typename TR>

RVector basic_srbmatrix< TR >::operator* ( const RVector & v ) const throw (cvmexception)

inline

Matrix-vector product.

Creates object of type rvector as product of calling matrix and vector v. Function throws cvmexception if the number of columns of the calling matrix differs from size of the vector v. Use basic_rvector::mult(const basic_rmatrix<TR>&,const basic_rvector<TR>&) to avoid new object creation.

Example:: using namespace cvm;

try {

rmatrix m(2, 3);

rvector v(3);

m.set(1.);

v.set(1.);

std::cout << m * v;

}

catch (std::exception& e) {

std::cout << "Exception " << e.what () << std::endl;

}

prints
3 3

See Also: basic_rvector::mult(const basic_rmatrix<TR>&,const basic_rvector<TR>&)

Parameters

[in] v rvector to compute product with.

Returns: Result object.

Reimplemented from basic_srmatrix< TR >.

Definition at line 29493 of file cvm.h.

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template<typename TR>

BaseRMatrix basic_srbmatrix< TR >::operator* ( const BaseRMatrix & m ) const throw (cvmexception)

inline

Matrix-matrix product.

Creates object of type rmatrix as product of calling square matrix and matrix m. Operator throws cvmexception if number of columns of calling matrix differs from number of rows of the matrix m. Use mult() to avoid new object creation.

Example:: using namespace cvm;

try {

srmatrix ms(3);

rmatrix m(3,2);

ms.set(1.);

m.set(1.);

std::cout << ms * m;

}

catch (std::exception& e) {

std::cout << "Exception " << e.what () << std::endl;

}

prints
3 3

3 3

3 3

Parameters

[in] m rmatrix to compute product with.

Returns: Result object.

Reimplemented from basic_srmatrix< TR >.

Definition at line 29502 of file cvm.h.

template<typename TR>

BaseSRMatrix basic_srbmatrix< TR >::operator* ( const BaseSRMatrix & m ) const throw (cvmexception)

inline

Matrix-matrix product.

Creates object of type srmatrix as product of calling square band matrix and square matrix m. Operator throws cvmexception if number of columns of calling matrix differs from number of rows of the matrix m. Use mult() to avoid new object creation.

Example:: using namespace cvm;

try {

srbmatrix mb(4,1,0);

srmatrix ms(4);

mb.set(1.);

ms.set(1.);

std::cout << mb * ms;

}

catch (std::exception& e) {

std::cout << "Exception " << e.what () << std::endl;

}

prints
1 1 1 1

2 2 2 2

2 2 2 2

2 2 2 2

Parameters

[in] m srmatrix to compute product with.

Returns: Result object.

Definition at line 29539 of file cvm.h.

template<typename TR>

basic_srbmatrix basic_srbmatrix< TR >::operator* ( const basic_srbmatrix< TR > & m ) const throw (cvmexception)

inline

Matrix-matrix product.

Creates object of type srbmatrix as product of calling square band matrix and square band matrix m. Operator throws cvmexception if number of columns of calling matrix differs from number of rows of the matrix m. Use mult() to avoid new object creation.

Example:: using namespace cvm;

try {

srbmatrix m1(7,1,0);

srbmatrix m2(7,1,1);

m1.set(1.);

m2.set(1.);

std::cout << m1 * m2;

}

catch (std::exception& e) {

std::cout << "Exception: " << e.what () << std::endl;

}

prints
1 1 0 0 0 0 0

2 2 1 0 0 0 0

1 2 2 1 0 0 0

0 1 2 2 1 0 0

0 0 1 2 2 1 0

0 0 0 1 2 2 1

0 0 0 0 1 2 2

Parameters

[in] m srbmatrix to compute product with.

Returns: Result object.

Definition at line 29579 of file cvm.h.

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template<typename TR>

RVector basic_srbmatrix< TR >::operator/ ( const RVector & vB ) const throw (cvmexception)

inline

Linear solver operator.

Creates rvector object as solution $x$ of linear equation $A*x=b$ where calling matrix is square matrix $A$ and parameter vB is vector $b$ . Operator throws cvmexception in case of inappropriate sizes of the operands or when matrix $A$ is close to singular.

Example:: using namespace cvm;

std::cout.setf (std::ios::scientific | std::ios::showpos);

std::cout.precision (12);

try {

double m[] = {1., -1., 1., 2., -2., 1., 3., -2., 1.};

double b[] = {1., 2., 3.};

srmatrix ma(m, 3);

rvector vb(b, 3);

rvector vx(3);

vx = ma / vb;

std::cout << ma * vx - vb;

}

catch (std::exception& e) {

std::cout << "Exception " << e.what () << std::endl;

}

prints
+0.000000000000e+000 +0.000000000000e+000 +0.000000000000e+000

Parameters

[in] vB rvector .

Returns: Result object.

Reimplemented from basic_srmatrix< TR >.

Definition at line 29590 of file cvm.h.

template<typename TR>

basic_srbmatrix& basic_srbmatrix< TR >::low_up	(	const basic_srbmatrix< TR > &	m,
		tint *	nPivots
	)		throw (cvmexception)

inline

Low-up (LU) factorization.

Compute LU factorization of square band matrix $A$ as

$A=PLU$

where $P$ is permutation matrix, $L$ is lower triangular matrix with unit diagonal elements and $U$ is upper triangular matrix. Function stores result as the matrix $L$ without main diagonal combined with $U$ . Function returns pivot indices as array of integers (it should support at least msize() elements) pointed to by nPivots so $i$ -th row was interchanged with nPivots[ $i$ ]-th row. This version sets calling matrix to be equal to matrix m's LU factorization. This version also changes number of super-diagonals to be equal to $k_l+k_u$ in order to keep the result of factorization. Function throws cvmexception in case of inappropriate sizes of the operands or when the matrix to be factorized is close to singular. It is recommended to use iarray for pivot values.

Example:: using namespace cvm;

std::cout.setf (std::ios::scientific | std::ios::left);

std::cout.precision (4);

try {

double a[] = {1., 2., 3., 4., 5., 6., 7., 8.};

srbmatrix ma(a,4,1,0);

srbmatrix mLU(4,1,0);

rmatrix mb1(4,2); rvector vb1(4);

rmatrix mb2(4,2); rvector vb2(4);

rmatrix mx1(4,2); rvector vx1(4);

rmatrix mx2(4,2); rvector vx2(4);

iarray nPivots(4);

double dErr = 0.;

mb1.randomize(-1.,3.); vb1.randomize(-2.,4.);

mb2.randomize(-2.,5.); vb2.randomize(-3.,1.);

mLU.low_up(ma, nPivots);

mx1 = ma.solve_lu (mLU, nPivots, mb1, dErr);

std::cout << mx1 << dErr << std::endl << std::endl;

mx2 = ma.solve_lu (mLU, nPivots, mb2);

std::cout << mx2 << std::endl;;

std::cout << ma * mx1 - mb1 << std::endl << ma * mx2 - mb2;

vx1 = ma.solve_lu (mLU, nPivots, vb1, dErr);

std::cout << vx1 << dErr << std::endl;

vx2 = ma.solve_lu (mLU, nPivots, vb2);

std::cout << vx2 << std::endl;;

std::cout << ma * vx1 - vb1 << std::endl << ma * vx2 - vb2;

}

catch (std::exception& e) {

std::cout << "Exception: " << e.what () << std::endl;

}

prints
7.6327e-02 -4.7386e-01

-2.9523e-01 9.7577e-01

1.7288e-01 -3.5093e-01

1.0595e-01 4.7363e-01

1.1832e-15

3.1963e+00 4.8622e+00

-4.9904e-01 -2.6575e+00

8.2183e-01 2.3294e+00

-6.1693e-01 -1.8015e+00

0.0000e+00 0.0000e+00

0.0000e+00 -2.2204e-16

0.0000e+00 -4.4409e-16

0.0000e+00 0.0000e+00

0.0000e+00 0.0000e+00

8.8818e-16 0.0000e+00

0.0000e+00 -4.4409e-16

-4.4409e-16 4.4409e-16

7.8933e-01 7.0543e-01 -1.6338e-02 -2.6206e-01

1.4832e-15

-1.5505e+00 5.8987e-01 -8.4977e-01 7.3059e-01

0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00

-2.2204e-16 0.0000e+00 0.0000e+00 4.4409e-16

Parameters

[in]	m	srbmatrix to compute LU factorization for.
[out]	nPivots	Array of pivot indices.

Returns: Reference to changed calling matrix.

Definition at line 29686 of file cvm.h.

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template<typename TR>

basic_srbmatrix basic_srbmatrix< TR >::low_up ( tint * nPivots ) const throw (cvmexception)

inline

Low-up (LU) factorization.

Compute LU factorization of square matrix $A$ as

$A=PLU$

where $P$ is permutation matrix, $L$ is lower triangular matrix with unit diagonal elements and $U$ is upper triangular matrix. Function stores result as the matrix $L$ without main diagonal combined with $U$ . Function returns pivot indices as array of integers (it should support at least msize() elements) pointed to by nPivots so $i$ -th row was interchanged with nPivots[ $i$ ]-th row. This version creates object of type srmatrix as calling matrix LU factorization. Function throws cvmexception in case of inappropriate sizes of the operands or when the matrix to be factorized is close to singular. It is recommended to use iarray for pivot values.

Example:: using namespace cvm;

std::cout.setf (std::ios::scientific | std::ios::showpos);

std::cout.precision (3);

try {

double a[] = {1., 2., 3., 4., 5., 6., 7., 8., 10.};

srmatrix m(a, 3);

srmatrix mLU(3), mLo(3), mUp(3);

iarray naPivots(3);

mLU = m.low_up (naPivots);

mLo.identity ();

mLo.diag(-2) = mLU.diag(-2);

mLo.diag(-1) = mLU.diag(-1);

mUp.diag(0) = mLU.diag(0);

mUp.diag(1) = mLU.diag(1);

mUp.diag(2) = mLU.diag(2);

std::cout << mLo << std::endl << mUp

<< std::endl << naPivots << std::endl;

mLU = mLo * mUp;

for (int i = 3; i >= 1; i--) {

mLU.swap_rows (i, naPivots[i]);

}

std::cout << mLU;

}

catch (std::exception& e) {

std::cout << "Exception " << e.what () << std::endl;

}

prints
+1.000e+000 +0.000e+000 +0.000e+000

+3.333e-001 +1.000e+000 +0.000e+000

+6.667e-001 +5.000e-001 +1.000e+000

+3.000e+000 +6.000e+000 +1.000e+001

+0.000e+000 +2.000e+000 +3.667e+000

+0.000e+000 +0.000e+000 -5.000e-001

+3 +3 +3

+1.000e+000 +4.000e+000 +7.000e+000

+2.000e+000 +5.000e+000 +8.000e+000

+3.000e+000 +6.000e+000 +1.000e+001

Parameters

[out] nPivots Array of pivot indices.

Returns: Result object.

Reimplemented from basic_srmatrix< TR >.

Definition at line 29693 of file cvm.h.

template<typename TR>

basic_srbmatrix& basic_srbmatrix< TR >::identity ( )

inline

Identity matrix.

Sets calling matrix to be equal to identity matrix and returns reference to the matrix changed.

Example:: using namespace cvm;

std::cout.setf (std::ios::scientific | std::ios::left);

std::cout.precision (3);

srmatrix m(3);

m.randomize(0.,1.);

std::cout << m << std::endl;

std::cout << m.identity();

prints
9.423e-01 2.950e-01 8.429e-01

2.013e-01 3.250e-01 2.904e-01

7.920e-01 2.405e-02 7.801e-01

1.000e+00 0.000e+00 0.000e+00

0.000e+00 1.000e+00 0.000e+00

0.000e+00 0.000e+00 1.000e+00

Returns: Reference to changed calling matrix.

Reimplemented from basic_srmatrix< TR >.

Definition at line 29700 of file cvm.h.

template<typename TR>

basic_srbmatrix& basic_srbmatrix< TR >::vanish ( )

inline

Set matrix to zero.

Sets every element of calling square matrix to be equal to zero and returns reference to the matrix changed. This function is faster than, for example, set(TR) with zero parameter passed.

Example:: using namespace cvm;

std::cout.setf (std::ios::scientific | std::ios::left);

std::cout.precision (3);

srmatrix m(3);

m.randomize(0.,1.);

std::cout << m << std::endl;

std::cout << m.vanish ();

prints
1.747e-01 7.563e-01 5.163e-01

9.657e-01 6.619e-01 8.036e-01

6.392e-01 6.658e-01 6.495e-01

0.000e+00 0.000e+00 0.000e+00

0.000e+00 0.000e+00 0.000e+00

0.000e+00 0.000e+00 0.000e+00

Returns: Reference to changed calling matrix.

Reimplemented from basic_srmatrix< TR >.

Definition at line 29707 of file cvm.h.

template<typename TR>

basic_srbmatrix& basic_srbmatrix< TR >::randomize	(	TR	dFrom,
		TR	dTo
	)

inline

Randomizer.

Fills calling matrix with pseudo-random numbers distributed between dFrom and dTo. Function returns reference to the matrix changed.

Example:: using namespace cvm;

std::cout.setf (std::ios::scientific | std::ios::left);

std::cout.precision (7);

rmatrix m(3,4);

m.randomize(-2.,3.);

std::cout << m;

prints
9.6853542e-01 2.7761467e+00 2.3791009e+00 -3.4452345e-01

2.9029511e+00 -9.5519883e-01 -4.9131748e-01 -1.2561113e+00

1.5219886e+00 -1.4494461e+00 2.8193304e+00 4.8817408e-01

Parameters

[in]	dFrom	First limit.
[in]	dTo	Second limit.

Returns: Reference to changed calling matrix.

Reimplemented from basic_srmatrix< TR >.

Definition at line 29713 of file cvm.h.

template<typename TR>

TR basic_srbmatrix< TR >::norm ( ) const

inlineoverridevirtual

Euclidean norm.

Euclidean norm of calling array that for vectors is defined as

${\|x\|}_E=\left(\sum_{i=1}^{n} |x_i|^2\right)^{1/2}$

and for matrices as

${\|A\|}_E=\left(\sum_{i=1}^{m}\sum_{j=1}^{n} |a_{ij}|^2\right)^{1/2},$

Example:: using namespace cvm;

std::cout.setf (ios::scientific | ios::showpos);

std::cout.precision (12);

double a[] = {1., 2., 3., -4., 5., -6.};

const rvector v (a, 3);

const rmatrix m (a, 2, 3);

std::cout << v << v.norm () << std::endl << std::endl;

std::cout << m << m.norm () << std::endl;

prints
+1.000000000000e+000 +2.000000000000e+000 +3.000000000000e+000

+3.741657386774e+000

+1.000000000000e+000 +3.000000000000e+000 +5.000000000000e+000

+2.000000000000e+000 -4.000000000000e+000 -6.000000000000e+000

+9.539392014169e+000

Returns: treal Norm value

Reimplemented from basic_array< TR, TR >.

Definition at line 29720 of file cvm.h.

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template<typename TR>

TR basic_srbmatrix< TR >::norm1 ( ) const

inlineoverridevirtual

1-norm

1-norm of calling array that for vectors is defined as

${\|x\|}_1=\sum_{i=1}^{n} |x_i|$

and for matrices as

${\|A\|}_{1}=\max_{j=1,\dots,n} \sum_{i=1}^{m} |a_{ij}|,$

Example:: using namespace cvm;

std::cout.setf (std::ios::scientific | std::ios::showpos);

std::cout.precision (12);

double a[] = {1., 2., 3., -4., 5., -6.};

const rvector v (a, 3);

const rmatrix m (a, 2, 3);

std::cout << v << v.norm1 () << std::endl << std::endl;

std::cout << m << m.norm1 () << std::endl;

prints
+1.000000000000e+000 +2.000000000000e+000 +3.000000000000e+000

+6.000000000000e+000

+1.000000000000e+000 +3.000000000000e+000 +5.000000000000e+000

+2.000000000000e+000 -4.000000000000e+000 -6.000000000000e+000

+1.100000000000e+001

Returns: treal Norm value

Reimplemented from Matrix< TR, TR >.

Definition at line 29739 of file cvm.h.

template<typename TR>

TR basic_srbmatrix< TR >::norminf ( ) const

inlineoverridevirtual

Infinity norm.

Infinity norm of calling array that for vectors is defined as

${\|x\|}_\infty=\max_{i=1,\dots,n} |x_i|$

and for matrices as

${\|A\|}_\infty=\max_{i=1,\dots,m} \sum_{j=1}^{n} |a_{ij}|,$

Example:: using namespace cvm;

double a[] = {1., 2., 3., -4., 5., -6.};

const rvector v (a, 3);

const rmatrix m (a, 2, 3);

std::cout << v << v.norminf () << std::endl;

std::cout << m << m.norminf () << std::endl;

prints
1 2 3

3

1 3 5

2 -4 -6

12

Returns: treal Norm value

Reimplemented from Matrix< TR, TR >.

Definition at line 29744 of file cvm.h.

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template<typename TR>

basic_srbmatrix& basic_srbmatrix< TR >::mult	(	const BaseRMatrix &	m1,
		const BaseRMatrix &	m2
	)		throw (cvmexception)

inline

Definition at line 29752 of file cvm.h.

Friends And Related Function Documentation

template<typename TR>

friend class basic_scbmatrix< TR, TC >

friend

Definition at line 28320 of file cvm.h.

Member Data Documentation

template<typename TR>

BaseSRMatrix basic_srbmatrix< TR >::mSM

mutableprotected

Temporary storage for square matrix enclosing band one (if needed)

Definition at line 28323 of file cvm.h.

The documentation for this class was generated from the following file:

src/cvm.h

Public Member Functions

Protected Attributes

Friends

Additional Inherited Members

Detailed Description

template<typename TR> class basic_srbmatrix< TR >

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation

template<typename TR>
class basic_srbmatrix< TR >