General sparsity class. More...

#include <sparsity.hpp>

Detailed Description

The storage format is a compressed column storage (CCS) format.
In this format, the structural non-zero elements are stored in column-major order, starting from the upper left corner of the matrix and ending in the lower right corner.

In addition to the dimension (size1(), size2()), (i.e. the number of rows and the number of columns respectively), there are also two vectors of integers:

"colind" [length size2()+1], which contains the index to the first non-zero element on or after the corresponding column. All the non-zero elements of a particular column i are thus the elements with index el that fulfills: colind[i] <= el < colind[i+1].
"row" [same length as the number of non-zero elements, nnz()] The rows for each of the structural non-zeros.

Note that with this format, it is cheap to loop over all the non-zero elements of a particular column, at constant time per element, but expensive to jump to access a location (i, j).

If the matrix is dense, i.e. length(row) == size1()*size2(), the format reduces to standard dense column major format, which allows access to an arbitrary element in constant time.

Since the object is reference counted (it inherits from SharedObject), several matrices are allowed to share the same sparsity pattern.

The implementations of methods marked as such in this class has been taken from the CSparse package and modified to fit CasADi data structures and separation of sparsity pattern calculation and numerical evaluation. These functions are Copyright(c) Timothy A. Davis, 2006-2009 and licensed as a derivative work under the GNU LGPL

See also: Matrix

Author: Joel Andersson

Date: 2010-2015

Extra doc: https://github.com/casadi/casadi/wiki/L_b9

Definition at line 96 of file sparsity.hpp.

Inheritance diagram for casadi::Sparsity:

[legend]

Public Member Functions
	Sparsity (casadi_int dummy=0)
	Default constructor. More...

	Sparsity (casadi_int nrow, casadi_int ncol)
	Pattern with all structural zeros. More...

	Sparsity (casadi_int nrow, casadi_int ncol, const std::vector< casadi_int > &colind, const std::vector< casadi_int > &row, bool order_rows=false)
	Construct from sparsity pattern vectors given in compressed column storage format. More...

	Sparsity (const std::pair< casadi_int, casadi_int > &rc)
	Create a sparse matrix with all structural zeros. More...

const std::vector< casadi_int >	permutation_vector (bool invert=false) const
	Construct permutation vector from permutation matrix. More...

Sparsity	get_diag (std::vector< casadi_int > &mapping) const

std::vector< casadi_int >	compress () const
	Compress a sparsity pattern. More...

bool	operator!= (const Sparsity &y) const
	Check if two sparsity patterns are difference. More...

bool	is_stacked (const Sparsity &y, casadi_int n) const
	Check if pattern is horizontal repeat of another. More...

Dict	info () const

void	to_file (const std::string &filename, const std::string &format_hint="") const

std::string	serialize () const
	Serialize. More...

void	serialize (SerializingStream &s) const
	Serialize an object. More...

std::vector< casadi_int >	get_row () const
	Get the row for each non-zero entry. More...

std::vector< casadi_int >	get_colind () const
	Get the column index for each column. More...

casadi_int	colind (casadi_int cc) const
	Get a reference to the colindex of column cc (see class description) More...

casadi_int	row (casadi_int el) const
	Get the row of a non-zero element. More...

std::vector< casadi_int >	get_col () const
	Get the column for each non-zero entry. More...

void	resize (casadi_int nrow, casadi_int ncol)
	Resize. More...

casadi_int	add_nz (casadi_int rr, casadi_int cc)
	Get the index of a non-zero element. More...

casadi_int	get_nz (casadi_int rr, casadi_int cc) const
	Get the index of an existing non-zero element. More...

bool	has_nz (casadi_int rr, casadi_int cc) const
	Returns true if the pattern has a non-zero at location rr, cc. More...

std::vector< casadi_int >	get_nz (const std::vector< casadi_int > &rr, const std::vector< casadi_int > &cc) const
	Get a set of non-zero element. More...

void	get_nz (std::vector< casadi_int > &indices) const
	Get the nonzero index for a set of elements. More...

std::vector< casadi_int >	get_lower () const
	Get nonzeros in lower triangular part. More...

std::vector< casadi_int >	get_upper () const
	Get nonzeros in upper triangular part. More...

void	get_ccs (std::vector< casadi_int > &colind, std::vector< casadi_int > &row) const
	Get the sparsity in compressed column storage (CCS) format. More...

void	get_crs (std::vector< casadi_int > &rowind, std::vector< casadi_int > &col) const
	Get the sparsity in compressed row storage (CRS) format. More...

void	get_triplet (std::vector< casadi_int > &row, std::vector< casadi_int > &col) const
	Get the sparsity in sparse triplet format. More...

Sparsity	sub (const std::vector< casadi_int > &rr, const std::vector< casadi_int > &cc, std::vector< casadi_int > &mapping, bool ind1=false) const
	Get a submatrix. More...

Sparsity	sub (const std::vector< casadi_int > &rr, const Sparsity &sp, std::vector< casadi_int > &mapping, bool ind1=false) const
	Get a set of elements. More...

Sparsity	T () const
	Transpose the matrix. More...

Sparsity	transpose (std::vector< casadi_int > &mapping, bool invert_mapping=false) const
	Transpose the matrix and get the reordering of the non-zero entries. More...

bool	is_transpose (const Sparsity &y) const
	Check if the sparsity is the transpose of another. More...

bool	is_reshape (const Sparsity &y) const
	Check if the sparsity is a reshape of another. More...

bool	is_subset (const Sparsity &rhs) const
	Is subset? More...

Sparsity	sparsity_cast_mod (const Sparsity &X, const Sparsity &Y) const
	Propagates subset according to sparsity cast. More...

Sparsity	pattern_inverse () const
	Take the inverse of a sparsity pattern; flip zeros and non-zeros. More...

void	enlarge (casadi_int nrow, casadi_int ncol, const std::vector< casadi_int > &rr, const std::vector< casadi_int > &cc, bool ind1=false)
	Enlarge matrix. More...

void	enlargeRows (casadi_int nrow, const std::vector< casadi_int > &rr, bool ind1=false)
	Enlarge the matrix along the first dimension (i.e. insert rows) More...

void	enlargeColumns (casadi_int ncol, const std::vector< casadi_int > &cc, bool ind1=false)
	Enlarge the matrix along the second dimension (i.e. insert columns) More...

Sparsity	makeDense (std::vector< casadi_int > &mapping) const
	Make a patten dense. More...

std::vector< casadi_int >	erase (const std::vector< casadi_int > &rr, const std::vector< casadi_int > &cc, bool ind1=false)
	Erase rows and/or columns of a matrix. More...

std::vector< casadi_int >	erase (const std::vector< casadi_int > &rr, bool ind1=false)
	Erase elements of a matrix. More...

void	append (const Sparsity &sp)
	Append another sparsity patten vertically (NOTE: only efficient if vector) More...

void	appendColumns (const Sparsity &sp)
	Append another sparsity patten horizontally. More...

bool	is_scalar (bool scalar_and_dense=false) const
	Is scalar? More...

bool	is_dense () const
	Is dense? More...

bool	is_row () const
	Check if the pattern is a row vector (i.e. size1()==1) More...

bool	is_column () const
	Check if the pattern is a column vector (i.e. size2()==1) More...

bool	is_vector () const
	Check if the pattern is a row or column vector. More...

bool	is_diag () const
	Is diagonal? More...

bool	is_square () const
	Is square? More...

bool	is_symmetric () const
	Is symmetric? More...

bool	is_triu (bool strictly=false) const
	Is upper triangular? More...

bool	is_tril (bool strictly=false) const
	Is lower triangular? More...

bool	is_singular () const
	Check whether the sparsity-pattern indicates structural singularity. More...

bool	is_permutation () const
	Is this a permutation matrix? More...

bool	is_selection (bool allow_empty=false) const
	Is this a selection matrix? More...

bool	is_orthonormal (bool allow_empty=false) const
	Are both rows and columns orthonormal ? More...

bool	is_orthonormal_rows (bool allow_empty=false) const
	Are the rows of the pattern orthonormal ? More...

bool	is_orthonormal_columns (bool allow_empty=false) const
	Are the columns of the pattern orthonormal ? More...

bool	rowsSequential (bool strictly=true) const
	Do the rows appear sequentially on each column. More...

void	removeDuplicates (std::vector< casadi_int > &mapping)
	Remove duplicate entries. More...

std::vector< casadi_int >	etree (bool ata=false) const
	Calculate the elimination tree. More...

Sparsity	ldl (std::vector< casadi_int > &p, bool amd=true) const
	Symbolic LDL factorization. More...

void	qr_sparse (Sparsity &V, Sparsity &R, std::vector< casadi_int > &prinv, std::vector< casadi_int > &pc, bool amd=true) const
	Symbolic QR factorization. More...

casadi_int	dfs (casadi_int j, casadi_int top, std::vector< casadi_int > &xi, std::vector< casadi_int > &pstack, const std::vector< casadi_int > &pinv, std::vector< bool > &marked) const
	Depth-first search on the adjacency graph of the sparsity. More...

casadi_int	scc (std::vector< casadi_int > &index, std::vector< casadi_int > &offset) const
	Find the strongly connected components of the bigraph defined by the sparsity pattern. More...

casadi_int	btf (std::vector< casadi_int > &rowperm, std::vector< casadi_int > &colperm, std::vector< casadi_int > &rowblock, std::vector< casadi_int > &colblock, std::vector< casadi_int > &coarse_rowblock, std::vector< casadi_int > &coarse_colblock) const
	Calculate the block triangular form (BTF) More...

std::vector< casadi_int >	amd () const
	Approximate minimal degree preordering. More...

std::vector< casadi_int >	find (bool ind1=SWIG_IND1) const
	Get the location of all non-zero elements as they would appear in a Dense matrix. More...

Sparsity	uni_coloring (const Sparsity &AT=Sparsity(), casadi_int cutoff=std::numeric_limits< casadi_int >::max()) const
	Perform a unidirectional coloring: A greedy distance-2 coloring algorithm. More...

Sparsity	star_coloring (casadi_int ordering=1, casadi_int cutoff=std::numeric_limits< casadi_int >::max()) const
	Perform a star coloring of a symmetric matrix: More...

Sparsity	star_coloring2 (casadi_int ordering=1, casadi_int cutoff=std::numeric_limits< casadi_int >::max()) const
	Perform a star coloring of a symmetric matrix: More...

std::vector< casadi_int >	largest_first () const
	Order the columns by decreasing degree. More...

Sparsity	pmult (const std::vector< casadi_int > &p, bool permute_rows=true, bool permute_columns=true, bool invert_permutation=false) const
	Permute rows and/or columns. More...

std::string	dim (bool with_nz=false) const
	Get the dimension as a string. More...

std::string	postfix_dim () const
	Dimension string as a postfix to a name. More...

std::string	repr_el (casadi_int k) const
	Describe the nonzero location k as a string. More...

void	spy (std::ostream &stream=casadi::uout()) const
	Print a textual representation of sparsity. More...

void	spy_matlab (const std::string &mfile) const
	Generate a script for Matlab or Octave which visualizes. More...

void	export_code (const std::string &lang, std::ostream &stream=casadi::uout(), const Dict &options=Dict()) const
	Export matrix in specific language. More...

std::size_t	hash () const

std::string	class_name () const
	Get class name. More...

void	disp (std::ostream &stream, bool more=false) const
	Print a description of the object. More...

std::string	get_str (bool more=false) const
	Get string representation. More...

bool	is_null () const
	Is a null pointer? More...

casadi_int	__hash__ () const
	Returns a number that is unique for a given Node. More...

Check if two sparsity patterns are identical
bool	is_equal (const Sparsity &y) const

bool	is_equal (casadi_int nrow, casadi_int ncol, const std::vector< casadi_int > &colind, const std::vector< casadi_int > &row) const

bool	operator== (const Sparsity &y) const

Size and element counting
casadi_int	size1 () const
	Get the number of rows. More...

casadi_int	rows () const
	Get the number of rows, Octave-style syntax. More...

casadi_int	size2 () const
	Get the number of columns. More...

casadi_int	columns () const
	Get the number of columns, Octave-style syntax. More...

casadi_int	numel () const
	The total number of elements, including structural zeros, i.e. size2()*size1() More...

double	density () const
	The percentage of nonzero. More...

bool	is_empty (bool both=false) const
	Check if the sparsity is empty. More...

casadi_int	nnz () const
	Get the number of (structural) non-zeros. More...

casadi_int	nnz_upper (bool strictly=false) const
	Number of non-zeros in the upper triangular half,. More...

casadi_int	nnz_lower (bool strictly=false) const
	Number of non-zeros in the lower triangular half,. More...

casadi_int	nnz_diag () const
	Number of non-zeros on the diagonal, i.e. the number of elements (i, j) with j==i. More...

casadi_int	bw_upper () const
	Upper half-bandwidth. More...

casadi_int	bw_lower () const
	Lower half-bandwidth. More...

std::pair< casadi_int, casadi_int >	size () const
	Get the shape. More...

casadi_int	size (casadi_int axis) const
	Get the size along a particular dimensions. More...


Sparsity	combine (const Sparsity &y, bool f0x_is_zero, bool function0_is_zero) const
	Combine two sparsity patterns. More...


Sparsity	unite (const Sparsity &y) const
	Union of two sparsity patterns. More...

Sparsity	operator+ (const Sparsity &b) const
	Union of two sparsity patterns. More...


Sparsity	intersect (const Sparsity &y) const
	Intersection of two sparsity patterns. More...

Sparsity	operator* (const Sparsity &b) const
	Intersection of two sparsity patterns. More...

Static Public Member Functions
static Sparsity	upper (casadi_int n)
	Create a upper triangular square sparsity pattern *. More...

static Sparsity	lower (casadi_int n)
	Create a lower triangular square sparsity pattern *. More...

static Sparsity	band (casadi_int n, casadi_int p)
	Create a single band in a square sparsity pattern. More...

static Sparsity	banded (casadi_int n, casadi_int p)
	Create banded square sparsity pattern. More...

static Sparsity	rowcol (const std::vector< casadi_int > &row, const std::vector< casadi_int > &col, casadi_int nrow, casadi_int ncol)
	Construct a block sparsity pattern from (row, col) vectors. More...

static Sparsity	nonzeros (casadi_int nrow, casadi_int ncol, const std::vector< casadi_int > &nz, bool ind1=SWIG_IND1)
	Create a sparsity from nonzeros. More...

static Sparsity	permutation (const std::vector< casadi_int > &p, bool invert=false)
	Construct a permutation matrix P from a permutation vector p. More...

static Sparsity	from_file (const std::string &filename, const std::string &format_hint="")

static Sparsity	deserialize (std::istream &stream)
	Build Sparsity from serialization. More...

static Sparsity	deserialize (const std::string &s)
	Build Sparsity from serialization. More...

static Sparsity	deserialize (DeserializingStream &s)
	Deserialize. More...

static std::string	type_name ()
	Readable name of the public class. More...

static bool	test_cast (const SharedObjectInternal *ptr)
	Check if a particular cast is allowed. More...

static Sparsity	kkt (const Sparsity &H, const Sparsity &J, bool with_x_diag=true, bool with_lam_g_diag=true)
	Get KKT system sparsity. More...


static Sparsity	scalar (bool dense_scalar=true)
	Create a scalar sparsity pattern *. More...


static Sparsity	dense (casadi_int nrow, casadi_int ncol=1)
	Create a dense rectangular sparsity pattern *. More...

static Sparsity	dense (const std::pair< casadi_int, casadi_int > &rc)
	Create a dense rectangular sparsity pattern *. More...


static Sparsity	unit (casadi_int n, casadi_int el)
	Create the sparsity pattern for a unit vector of length n and a nonzero on. More...


static Sparsity	diag (casadi_int nrow)
	Create diagonal sparsity pattern *. More...

static Sparsity	diag (casadi_int nrow, casadi_int ncol)
	Create diagonal sparsity pattern *. More...

static Sparsity	diag (const std::pair< casadi_int, casadi_int > &rc)
	Create diagonal sparsity pattern *. More...


static Sparsity	triplet (casadi_int nrow, casadi_int ncol, const std::vector< casadi_int > &row, const std::vector< casadi_int > &col, std::vector< casadi_int > &mapping, bool invert_mapping)
	Create a sparsity pattern given the nonzeros in sparse triplet form *. More...

static Sparsity	triplet (casadi_int nrow, casadi_int ncol, const std::vector< casadi_int > &row, const std::vector< casadi_int > &col)
	Create a sparsity pattern given the nonzeros in sparse triplet form *. More...


static Sparsity	compressed (const std::vector< casadi_int > &v, bool order_rows=false)

Constructor & Destructor Documentation

◆ Sparsity() [1/4]

casadi::Sparsity::Sparsity ( casadi_int dummy = 0 )

explicit

◆ Sparsity() [2/4]

casadi::Sparsity::Sparsity	(	casadi_int	nrow,
		casadi_int	ncol
	)

Extra doc: https://github.com/casadi/casadi/wiki/L_ba

◆ Sparsity() [3/4]

casadi::Sparsity::Sparsity	(	casadi_int	nrow,
		casadi_int	ncol,
		const std::vector< casadi_int > &	colind,
		const std::vector< casadi_int > &	row,
		bool	order_rows = `false`
	)

◆ Sparsity() [4/4]

casadi::Sparsity::Sparsity ( const std::pair< casadi_int, casadi_int > & rc )

explicit

Extra doc: https://github.com/casadi/casadi/wiki/L_bb

Member Function Documentation

◆ hash()

casadi_int casadi::SharedObject::__hash__ ( ) const

inherited

If the Object does not point to any node, "0" is returned.

Extra doc: https://github.com/casadi/casadi/wiki/L_av

◆ add_nz()

casadi_int casadi::Sparsity::add_nz	(	casadi_int	rr,
		casadi_int	cc
	)

Add the element if it does not exist and copy object if it's not unique

Extra doc: https://github.com/casadi/casadi/wiki/L_ce

◆ amd()

std::vector<casadi_int> casadi::Sparsity::amd ( ) const

Fill-reducing ordering applied to the sparsity pattern of a linear system prior to factorization. The system must be symmetric, for an unsymmetric matrix A, first form the square of the pattern, A'*A.

The implementation is a modified version of cs_amd in CSparse Copyright(c) Timothy A. Davis, 2006-2009 Licensed as a derivative work under the GNU LGPL

Extra doc: https://github.com/casadi/casadi/wiki/L_d8

◆ append()

void casadi::Sparsity::append ( const Sparsity & sp )

◆ appendColumns()

void casadi::Sparsity::appendColumns ( const Sparsity & sp )

◆ band()

static Sparsity casadi::Sparsity::band	(	casadi_int	n,
		casadi_int	p
	)

static

band(n, 0) is equivalent to diag(n)
band(n, -1) has a band below the diagonal

Parameters

p indicate

Extra doc: https://github.com/casadi/casadi/wiki/L_bj

◆ banded()

static Sparsity casadi::Sparsity::banded	(	casadi_int	n,
		casadi_int	p
	)

static

banded(n, 0) is equivalent to diag(n)
banded(n, 1) is tri-diagonal matrix
Extra doc: https://github.com/casadi/casadi/wiki/L_bk

◆ btf()

casadi_int casadi::Sparsity::btf	(	std::vector< casadi_int > &	rowperm,
		std::vector< casadi_int > &	colperm,
		std::vector< casadi_int > &	rowblock,
		std::vector< casadi_int > &	colblock,
		std::vector< casadi_int > &	coarse_rowblock,
		std::vector< casadi_int > &	coarse_colblock
	)		const

See Direct Methods for Sparse Linear Systems by Davis (2006).

The function computes the Dulmage-Mendelsohn decomposition, which allows you to reorder the rows and columns of a matrix to bring it into block triangular form (BTF).

It will not consider the distance of off-diagonal elements to the diagonal: there is no guarantee you will get a block-diagonal matrix if you supply a randomly permuted block-diagonal matrix.

If your matrix is symmetrical, this method is of limited use; permutation can make it non-symmetric.

See also: scc

The implementation is a modified version of cs_dmperm in CSparse Copyright(c) Timothy A. Davis, 2006-2009 Licensed as a derivative work under the GNU LGPL

Extra doc: https://github.com/casadi/casadi/wiki/L_d7

Examples: matrix/btf.py.

◆ bw_lower()

casadi_int casadi::Sparsity::bw_lower ( ) const

Extra doc: https://github.com/casadi/casadi/wiki/L_by

◆ bw_upper()

casadi_int casadi::Sparsity::bw_upper ( ) const

Extra doc: https://github.com/casadi/casadi/wiki/L_bx

◆ class_name()

std::string casadi::SharedObject::class_name ( ) const

inherited

Extra doc: https://github.com/casadi/casadi/wiki/L_au

◆ colind()

casadi_int casadi::Sparsity::colind ( casadi_int cc ) const

Extra doc: https://github.com/casadi/casadi/wiki/L_cb

◆ columns()

casadi_int casadi::Sparsity::columns ( ) const

inline

Definition at line 333 of file sparsity.hpp.

◆ combine()

Sparsity casadi::Sparsity::combine	(	const Sparsity &	y,
		bool	f0x_is_zero,
		bool	function0_is_zero
	)		const

Returns the new sparsity pattern as well as a mapping with the same length as the number of non-zero elements The mapping matrix contains the arguments for each nonzero, the first bit indicates if the first argument is nonzero, the second bit indicates if the second argument is nonzero (note that none of, one of or both of the arguments can be nonzero)

Extra doc: https://github.com/casadi/casadi/wiki/L_cl

◆ compress()

std::vector<casadi_int> casadi::Sparsity::compress ( ) const

◆ compressed()

static Sparsity casadi::Sparsity::compressed	(	const std::vector< casadi_int > &	v,
		bool	order_rows = `false`
	)

static

Create from a single vector containing the pattern in compressed column storage format: The format: The first two entries are the number of rows (nrow) and columns (ncol) The next ncol+1 entries are the column offsets (colind). Note that the last element, colind[ncol], gives the number of nonzeros The last colind[ncol] entries are the row indices

◆ dense() [1/2]

static Sparsity casadi::Sparsity::dense	(	casadi_int	nrow,
		casadi_int	ncol = `1`
	)

static

Extra doc: https://github.com/casadi/casadi/wiki/L_be

◆ dense() [2/2]

static Sparsity casadi::Sparsity::dense ( const std::pair< casadi_int, casadi_int > & rc )

inlinestatic

Extra doc: https://github.com/casadi/casadi/wiki/L_be

Definition at line 155 of file sparsity.hpp.

◆ density()

double casadi::Sparsity::density ( ) const

Equivalent to (100.0 * nnz())/numel(), but avoids overflow

Extra doc: https://github.com/casadi/casadi/wiki/L_br

◆ deserialize() [1/3]

static Sparsity casadi::Sparsity::deserialize ( const std::string & s )

static

Extra doc: https://github.com/casadi/casadi/wiki/L_c4

◆ deserialize() [2/3]

static Sparsity casadi::Sparsity::deserialize ( DeserializingStream & s )

static

Extra doc: https://github.com/casadi/casadi/wiki/L_c6

◆ deserialize() [3/3]

static Sparsity casadi::Sparsity::deserialize ( std::istream & stream )

static

Extra doc: https://github.com/casadi/casadi/wiki/L_c3

◆ dfs()

casadi_int casadi::Sparsity::dfs	(	casadi_int	j,
		casadi_int	top,
		std::vector< casadi_int > &	xi,
		std::vector< casadi_int > &	pstack,
		const std::vector< casadi_int > &	pinv,
		std::vector< bool > &	marked
	)		const

See Direct Methods for Sparse Linear Systems by Davis (2006).

Extra doc: https://github.com/casadi/casadi/wiki/L_d5

◆ diag() [1/3]

static Sparsity casadi::Sparsity::diag ( casadi_int nrow )

inlinestatic

Extra doc: https://github.com/casadi/casadi/wiki/L_bi

Definition at line 183 of file sparsity.hpp.

◆ diag() [2/3]

static Sparsity casadi::Sparsity::diag	(	casadi_int	nrow,
		casadi_int	ncol
	)

static

Extra doc: https://github.com/casadi/casadi/wiki/L_bi

◆ diag() [3/3]

static Sparsity casadi::Sparsity::diag ( const std::pair< casadi_int, casadi_int > & rc )

inlinestatic

Extra doc: https://github.com/casadi/casadi/wiki/L_bi

Definition at line 185 of file sparsity.hpp.

◆ dim()

std::string casadi::Sparsity::dim ( bool with_nz = false ) const

◆ disp()

void casadi::SharedObject::disp	(	std::ostream &	stream,
		bool	more = `false`
	)		const

inherited

◆ enlarge()

void casadi::Sparsity::enlarge	(	casadi_int	nrow,
		casadi_int	ncol,
		const std::vector< casadi_int > &	rr,
		const std::vector< casadi_int > &	cc,
		bool	ind1 = `false`
	)

Make the matrix larger by inserting empty rows and columns, keeping the existing non-zeros

For the matrices A to B A(m, n) length(jj)=m , length(ii)=n B(nrow, ncol)

A=enlarge(m, n, ii, jj) makes sure that

B[jj, ii] == A

Extra doc: https://github.com/casadi/casadi/wiki/L_cr

◆ enlargeColumns()

void casadi::Sparsity::enlargeColumns	(	casadi_int	ncol,
		const std::vector< casadi_int > &	cc,
		bool	ind1 = `false`
	)

Extra doc: https://github.com/casadi/casadi/wiki/L_ct

◆ enlargeRows()

void casadi::Sparsity::enlargeRows	(	casadi_int	nrow,
		const std::vector< casadi_int > &	rr,
		bool	ind1 = `false`
	)

Extra doc: https://github.com/casadi/casadi/wiki/L_cs

◆ erase() [1/2]

std::vector<casadi_int> casadi::Sparsity::erase	(	const std::vector< casadi_int > &	rr,
		bool	ind1 = `false`
	)

Extra doc: https://github.com/casadi/casadi/wiki/L_cw

◆ erase() [2/2]

std::vector<casadi_int> casadi::Sparsity::erase	(	const std::vector< casadi_int > &	rr,
		const std::vector< casadi_int > &	cc,
		bool	ind1 = `false`
	)

Extra doc: https://github.com/casadi/casadi/wiki/L_cv

◆ etree()

std::vector<casadi_int> casadi::Sparsity::etree ( bool ata = false ) const

See Direct Methods for Sparse Linear Systems by Davis (2006). If the parameter ata is false, the algorithm is equivalent to MATLAB's etree(A), except that the indices are zero-based. If ata is true, the algorithm is equivalent to MATLAB's etree(A, 'col').

The implementation is a modified version of cs_etree in CSparse Copyright(c) Timothy A. Davis, 2006-2009 Licensed as a derivative work under the GNU LGPL

Extra doc: https://github.com/casadi/casadi/wiki/L_d2

◆ export_code()

void casadi::Sparsity::export_code	(	const std::string &	lang,
		std::ostream &	stream = `casadi::uout()`,
		const Dict &	options = `Dict()`
	)		const

lang: only 'matlab' supported for now

 * options:
 *   inline: Indicates if you want everything on a single line (default: False)
 *   name: Name of exported variable (default: 'sp')
 *   as_matrix: Matlab does not have a sparsity object. (default: false)
*               With this option true, a numeric matrix will be constructed
 *

Extra doc: https://github.com/casadi/casadi/wiki/L_dj

◆ find()

std::vector<casadi_int> casadi::Sparsity::find ( bool ind1 = SWIG_IND1 ) const

A : DenseMatrix 4 x 3 B : SparseMatrix 4 x 3 , 5 structural non-zeros

k = A.find() A[k] will contain the elements of A that are non-zero in B

Inverse of nonzeros.

Extra doc: https://github.com/casadi/casadi/wiki/L_da

◆ from_file()

static Sparsity casadi::Sparsity::from_file	(	const std::string &	filename,
		const std::string &	format_hint = `""`
	)

static

◆ get_ccs()

void casadi::Sparsity::get_ccs	(	std::vector< casadi_int > &	colind,
		std::vector< casadi_int > &	row
	)		const

◆ get_col()

std::vector<casadi_int> casadi::Sparsity::get_col ( ) const

Together with the row-vector, this vector gives the sparsity of the matrix in sparse triplet format, i.e. the column and row for each non-zero elements

Extra doc: https://github.com/casadi/casadi/wiki/L_cd

◆ get_colind()

std::vector<casadi_int> casadi::Sparsity::get_colind ( ) const

Together with the row-vector, one obtains the sparsity pattern in the column compressed format.

Extra doc: https://github.com/casadi/casadi/wiki/L_ca

◆ get_crs()

void casadi::Sparsity::get_crs	(	std::vector< casadi_int > &	rowind,
		std::vector< casadi_int > &	col
	)		const

◆ get_diag()

Sparsity casadi::Sparsity::get_diag ( std::vector< casadi_int > & mapping ) const

Get the diagonal of the matrix/create a diagonal matrix (mapping will contain the nonzero mapping) When the input is square, the diagonal elements are returned. If the input is vector-like, a diagonal matrix is constructed with it.

◆ get_lower()

std::vector<casadi_int> casadi::Sparsity::get_lower ( ) const

◆ get_nz() [1/3]

casadi_int casadi::Sparsity::get_nz	(	casadi_int	rr,
		casadi_int	cc
	)		const

return -1 if the element does not exist

Extra doc: https://github.com/casadi/casadi/wiki/L_cf

◆ get_nz() [2/3]

std::vector<casadi_int> casadi::Sparsity::get_nz	(	const std::vector< casadi_int > &	rr,
		const std::vector< casadi_int > &	cc
	)		const

return -1 if the element does not exist

Extra doc: https://github.com/casadi/casadi/wiki/L_cg

◆ get_nz() [3/3]

void casadi::Sparsity::get_nz ( std::vector< casadi_int > & indices ) const

The index vector is used both for input and outputs and must be sorted by increasing nonzero index, i.e. column-wise. Elements not found in the sparsity pattern are set to -1.

Extra doc: https://github.com/casadi/casadi/wiki/L_ch

◆ get_row()

std::vector<casadi_int> casadi::Sparsity::get_row ( ) const

Together with the column-vector, this vector gives the sparsity of the matrix in sparse triplet format, and together with the colind vector, one obtains the sparsity in column compressed format.

Extra doc: https://github.com/casadi/casadi/wiki/L_c9

◆ get_str()

std::string casadi::SharedObject::get_str ( bool more = false ) const

inlineinherited

Definition at line 138 of file shared_object.hpp.

◆ get_triplet()

void casadi::Sparsity::get_triplet	(	std::vector< casadi_int > &	row,
		std::vector< casadi_int > &	col
	)		const

◆ get_upper()

std::vector<casadi_int> casadi::Sparsity::get_upper ( ) const

◆ has_nz()

bool casadi::Sparsity::has_nz	(	casadi_int	rr,
		casadi_int	cc
	)		const

◆ hash()

std::size_t casadi::Sparsity::hash ( ) const

◆ info()

Dict casadi::Sparsity::info ( ) const

Obtain information about sparsity

◆ intersect()

Sparsity casadi::Sparsity::intersect ( const Sparsity & y ) const

Returns the new sparsity pattern as well as a mapping with the same length as the number of non-zero elements The value is 1 if the non-zero comes from the first (i.e. this) object, 2 if it is from the second and 3 (i.e. 1 | 2) if from both

Extra doc: https://github.com/casadi/casadi/wiki/L_cn

◆ is_column()

bool casadi::Sparsity::is_column ( ) const

Extra doc: https://github.com/casadi/casadi/wiki/L_cy

◆ is_dense()

bool casadi::Sparsity::is_dense ( ) const

◆ is_diag()

bool casadi::Sparsity::is_diag ( ) const

Extra doc: https://github.com/casadi/casadi/wiki/L_247

◆ is_empty()

bool casadi::Sparsity::is_empty ( bool both = false ) const

A sparsity is considered empty if one of the dimensions is zero (or optionally both dimensions)

Extra doc: https://github.com/casadi/casadi/wiki/L_bs

◆ is_equal() [1/2]

bool casadi::Sparsity::is_equal	(	casadi_int	nrow,
		casadi_int	ncol,
		const std::vector< casadi_int > &	colind,
		const std::vector< casadi_int > &	row
	)		const

◆ is_equal() [2/2]

bool casadi::Sparsity::is_equal ( const Sparsity & y ) const

◆ is_null()

bool casadi::SharedObject::is_null ( ) const

inherited

◆ is_orthonormal()

bool casadi::Sparsity::is_orthonormal ( bool allow_empty = false ) const

Parameters

[in] allow_empty Disregard empty rows and columns in the analysis

Extra doc: https://github.com/casadi/casadi/wiki/L_24f

◆ is_orthonormal_columns()

bool casadi::Sparsity::is_orthonormal_columns ( bool allow_empty = false ) const

Parameters

[in] allow_empty Disregard empty columns in the analysis

Extra doc: https://github.com/casadi/casadi/wiki/L_24h

◆ is_orthonormal_rows()

bool casadi::Sparsity::is_orthonormal_rows ( bool allow_empty = false ) const

Parameters

[in] allow_empty Disregard empty rows in the analysis

Extra doc: https://github.com/casadi/casadi/wiki/L_24g

◆ is_permutation()

bool casadi::Sparsity::is_permutation ( ) const

A Matrix P is permutation matrix if right multiplication with a dense vector v leads to a vector with the same elements, but permuted.

Implies square

Equivalent to is_orthonormal(false)

Extra doc: https://github.com/casadi/casadi/wiki/L_24d

◆ is_reshape()

bool casadi::Sparsity::is_reshape ( const Sparsity & y ) const

◆ is_row()

bool casadi::Sparsity::is_row ( ) const

Extra doc: https://github.com/casadi/casadi/wiki/L_cx

◆ is_scalar()

bool casadi::Sparsity::is_scalar ( bool scalar_and_dense = false ) const

◆ is_selection()

bool casadi::Sparsity::is_selection ( bool allow_empty = false ) const

A Matrix S is selection matrix if right multiplication with a dense vector leads to a vector with a subset of the elements of the original vector

Parameters

[in] allow_empty Allow the resultant vector to have structural zeros

Equivalent to is_orthonormal_rows(allow_empty)

Extra doc: https://github.com/casadi/casadi/wiki/L_24e

◆ is_singular()

bool casadi::Sparsity::is_singular ( ) const

Extra doc: https://github.com/casadi/casadi/wiki/L_24c

◆ is_square()

bool casadi::Sparsity::is_square ( ) const

Extra doc: https://github.com/casadi/casadi/wiki/L_248

◆ is_stacked()

bool casadi::Sparsity::is_stacked	(	const Sparsity &	y,
		casadi_int	n
	)		const

◆ is_subset()

bool casadi::Sparsity::is_subset ( const Sparsity & rhs ) const

◆ is_symmetric()

bool casadi::Sparsity::is_symmetric ( ) const

Extra doc: https://github.com/casadi/casadi/wiki/L_249

◆ is_transpose()

bool casadi::Sparsity::is_transpose ( const Sparsity & y ) const

◆ is_tril()

bool casadi::Sparsity::is_tril ( bool strictly = false ) const

Extra doc: https://github.com/casadi/casadi/wiki/L_24b

◆ is_triu()

bool casadi::Sparsity::is_triu ( bool strictly = false ) const

Extra doc: https://github.com/casadi/casadi/wiki/L_24a

◆ is_vector()

bool casadi::Sparsity::is_vector ( ) const

Extra doc: https://github.com/casadi/casadi/wiki/L_cz

◆ kkt()

static Sparsity casadi::Sparsity::kkt	(	const Sparsity &	H,
		const Sparsity &	J,
		bool	with_x_diag = `true`,
		bool	with_lam_g_diag = `true`
	)

static

[H + I1, J'; J, I2] where I1 and I2 are optional

Extra doc: https://github.com/casadi/casadi/wiki/L_dk

◆ largest_first()

std::vector<casadi_int> casadi::Sparsity::largest_first ( ) const

Extra doc: https://github.com/casadi/casadi/wiki/L_de

◆ ldl()

Sparsity casadi::Sparsity::ldl	(	std::vector< casadi_int > &	p,
		bool	amd = `true`
	)		const

Returns the sparsity pattern of L^T

The implementation is a modified version of LDL Copyright(c) Timothy A. Davis, 2005-2013 Licensed as a derivative work under the GNU LGPL

Extra doc: https://github.com/casadi/casadi/wiki/L_d3

◆ lower()

static Sparsity casadi::Sparsity::lower ( casadi_int n )

static

Extra doc: https://github.com/casadi/casadi/wiki/L_bh

◆ makeDense()

Sparsity casadi::Sparsity::makeDense ( std::vector< casadi_int > & mapping ) const

Extra doc: https://github.com/casadi/casadi/wiki/L_cu

◆ nnz()

casadi_int casadi::Sparsity::nnz ( ) const

See also: numel()

Extra doc: https://github.com/casadi/casadi/wiki/L_bt

◆ nnz_diag()

casadi_int casadi::Sparsity::nnz_diag ( ) const

Extra doc: https://github.com/casadi/casadi/wiki/L_bw

◆ nnz_lower()

casadi_int casadi::Sparsity::nnz_lower ( bool strictly = false ) const

i.e. the number of elements (i, j) with j<=i

Extra doc: https://github.com/casadi/casadi/wiki/L_bv

◆ nnz_upper()

casadi_int casadi::Sparsity::nnz_upper ( bool strictly = false ) const

i.e. the number of elements (i, j) with j>=i

Extra doc: https://github.com/casadi/casadi/wiki/L_bu

◆ nonzeros()

static Sparsity casadi::Sparsity::nonzeros	(	casadi_int	nrow,
		casadi_int	ncol,
		const std::vector< casadi_int > &	nz,
		bool	ind1 = `SWIG_IND1`
	)

static

Inverse of find()

Extra doc: https://github.com/casadi/casadi/wiki/L_23g

◆ numel()

casadi_int casadi::Sparsity::numel ( ) const

Beware of overflow

See also: nnz()

Extra doc: https://github.com/casadi/casadi/wiki/L_bq

◆ operator!=()

bool casadi::Sparsity::operator!= ( const Sparsity & y ) const

inline

Definition at line 295 of file sparsity.hpp.

◆ operator*()

Sparsity casadi::Sparsity::operator* ( const Sparsity & b ) const

Returns the new sparsity pattern as well as a mapping with the same length as the number of non-zero elements The value is 1 if the non-zero comes from the first (i.e. this) object, 2 if it is from the second and 3 (i.e. 1 | 2) if from both

Extra doc: https://github.com/casadi/casadi/wiki/L_cn

◆ operator+()

Sparsity casadi::Sparsity::operator+ ( const Sparsity & b ) const

Extra doc: https://github.com/casadi/casadi/wiki/L_cm

◆ operator==()

bool casadi::Sparsity::operator== ( const Sparsity & y ) const

inline

Definition at line 291 of file sparsity.hpp.

◆ pattern_inverse()

Sparsity casadi::Sparsity::pattern_inverse ( ) const

◆ permutation()

static Sparsity casadi::Sparsity::permutation	(	const std::vector< casadi_int > &	p,
		bool	invert = `false`
	)

static

Right multiplication of P with a vector leads to the same results as indexing that vector with p

P @ v = v[p]

The inverse of a permutation matrix is equal to its transpose (property of orthonormality)

Extra doc: https://github.com/casadi/casadi/wiki/L_244

◆ permutation_vector()

const std::vector<casadi_int> casadi::Sparsity::permutation_vector ( bool invert = false ) const

Extra doc: https://github.com/casadi/casadi/wiki/L_245

◆ pmult()

Sparsity casadi::Sparsity::pmult	(	const std::vector< casadi_int > &	p,
		bool	permute_rows = `true`,
		bool	permute_columns = `true`,
		bool	invert_permutation = `false`
	)		const

Multiply the sparsity with a permutation matrix from the left and/or from the right P * A * trans(P), A * trans(P) or A * trans(P) with P defined by an index vector containing the row for each col. As an alternative, P can be transposed (inverted).

Extra doc: https://github.com/casadi/casadi/wiki/L_df

◆ postfix_dim()

std::string casadi::Sparsity::postfix_dim ( ) const

Rules:

Dense and scalar: ""
0-by-0: "[]"
Dense column vector: "[5]"
Dense matrix: "[5x10]"
Otherwise: "[5x10,3nz]"

Extra doc: https://github.com/casadi/casadi/wiki/L_dg

◆ qr_sparse()

void casadi::Sparsity::qr_sparse	(	Sparsity &	V,
		Sparsity &	R,
		std::vector< casadi_int > &	prinv,
		std::vector< casadi_int > &	pc,
		bool	amd = `true`
	)		const

Returns the sparsity pattern of V (compact representation of Q) and R as well as vectors needed for the numerical factorization and solution. The implementation is a modified version of CSparse Copyright(c) Timothy A. Davis, 2006-2009 Licensed as a derivative work under the GNU LGPL

Extra doc: https://github.com/casadi/casadi/wiki/L_d4

◆ removeDuplicates()

void casadi::Sparsity::removeDuplicates ( std::vector< casadi_int > & mapping )

The same indices will be removed from the mapping vector, which must have the same length as the number of nonzeros

Extra doc: https://github.com/casadi/casadi/wiki/L_d1

◆ repr_el()

std::string casadi::Sparsity::repr_el ( casadi_int k ) const

◆ resize()

void casadi::Sparsity::resize	(	casadi_int	nrow,
		casadi_int	ncol
	)

◆ row()

casadi_int casadi::Sparsity::row ( casadi_int el ) const

Extra doc: https://github.com/casadi/casadi/wiki/L_cc

◆ rowcol()

static Sparsity casadi::Sparsity::rowcol	(	const std::vector< casadi_int > &	row,
		const std::vector< casadi_int > &	col,
		casadi_int	nrow,
		casadi_int	ncol
	)

static

Extra doc: https://github.com/casadi/casadi/wiki/L_bl

◆ rows()

casadi_int casadi::Sparsity::rows ( ) const

inline

Definition at line 327 of file sparsity.hpp.

◆ rowsSequential()

bool casadi::Sparsity::rowsSequential ( bool strictly = true ) const

Parameters

[in] strictly if true, then do not allow multiple entries

Extra doc: https://github.com/casadi/casadi/wiki/L_d0

◆ scalar()

static Sparsity casadi::Sparsity::scalar ( bool dense_scalar = true )

inlinestatic

Extra doc: https://github.com/casadi/casadi/wiki/L_bd

Definition at line 146 of file sparsity.hpp.

◆ scc()

casadi_int casadi::Sparsity::scc	(	std::vector< casadi_int > &	index,
		std::vector< casadi_int > &	offset
	)		const

of a square matrix

See Direct Methods for Sparse Linear Systems by Davis (2006). Returns:

Number of components
Offset for each components (length: 1 + number of components)
Indices for each components, component i has indices index[offset[i]], ..., index[offset[i+1]]

In the case that the matrix is symmetric, the result has a particular interpretation: Given a symmetric matrix A and n = A.scc(p, r)

=> A[p, p] will appear block-diagonal with n blocks and with the indices of the block boundaries to be found in r.

The implementation is a modified version of cs_scc in CSparse Copyright(c) Timothy A. Davis, 2006-2009 Licensed as a derivative work under the GNU LGPL

Extra doc: https://github.com/casadi/casadi/wiki/L_d6

Examples: matrix/scc.py.

◆ serialize() [1/2]

std::string casadi::Sparsity::serialize ( ) const

Extra doc: https://github.com/casadi/casadi/wiki/L_c2

◆ serialize() [2/2]

void casadi::Sparsity::serialize ( SerializingStream & s ) const

Extra doc: https://github.com/casadi/casadi/wiki/L_c5

◆ size() [1/2]

std::pair<casadi_int, casadi_int> casadi::Sparsity::size ( ) const

Extra doc: https://github.com/casadi/casadi/wiki/L_bz

◆ size() [2/2]

casadi_int casadi::Sparsity::size ( casadi_int axis ) const

Extra doc: https://github.com/casadi/casadi/wiki/L_c0

◆ size1()

casadi_int casadi::Sparsity::size1 ( ) const

◆ size2()

casadi_int casadi::Sparsity::size2 ( ) const

◆ sparsity_cast_mod()

Sparsity casadi::Sparsity::sparsity_cast_mod	(	const Sparsity &	X,
		const Sparsity &	Y
	)		const

Assumption: 'this' is a subset of X.

Example:

X = [ * . . .; . * . .; . . * .; . . . *] Y = [* *; . . ; * *] x = [ * . . .; . . . .; . . * .; . . . *] returns [* *; . . ; . *]

Extra doc: https://github.com/casadi/casadi/wiki/L_246

◆ spy()

void casadi::Sparsity::spy ( std::ostream & stream = casadi::uout() ) const

Extra doc: https://github.com/casadi/casadi/wiki/L_dh

◆ spy_matlab()

void casadi::Sparsity::spy_matlab ( const std::string & mfile ) const

the sparsity using the spy command

Extra doc: https://github.com/casadi/casadi/wiki/L_di

◆ star_coloring()

Sparsity casadi::Sparsity::star_coloring	(	casadi_int	ordering = `1`,
		casadi_int	cutoff = `std::numeric_limits< casadi_int >::max()`
	)		const

A greedy distance-2 coloring algorithm Algorithm 4.1 in What Color Is Your Jacobian? Graph Coloring for Computing Derivatives A. H. GEBREMEDHIN, F. MANNE, A. POTHEN SIAM Rev., 47(4), 629–705 (2006)

Ordering options: None (0), largest first (1)

Extra doc: https://github.com/casadi/casadi/wiki/L_dc

◆ star_coloring2()

Sparsity casadi::Sparsity::star_coloring2	(	casadi_int	ordering = `1`,
		casadi_int	cutoff = `std::numeric_limits< casadi_int >::max()`
	)		const

A new greedy distance-2 coloring algorithm Algorithm 4.1 in NEW ACYCLIC AND STAR COLORING ALGORITHMS WITH APPLICATION TO COMPUTING HESSIANS A. H. GEBREMEDHIN, A. TARAFDAR, F. MANNE, A. POTHEN SIAM J. SCI. COMPUT. Vol. 29, No. 3, pp. 1042–1072 (2007)

Ordering options: None (0), largest first (1)

Extra doc: https://github.com/casadi/casadi/wiki/L_dd

◆ sub() [1/2]

Sparsity casadi::Sparsity::sub	(	const std::vector< casadi_int > &	rr,
		const Sparsity &	sp,
		std::vector< casadi_int > &	mapping,
		bool	ind1 = `false`
	)		const

Returns the sparsity of the corresponding elements, with a mapping such that submatrix[k] = originalmatrix[mapping[k]]

Extra doc: https://github.com/casadi/casadi/wiki/L_cj

◆ sub() [2/2]

Sparsity casadi::Sparsity::sub	(	const std::vector< casadi_int > &	rr,
		const std::vector< casadi_int > &	cc,
		std::vector< casadi_int > &	mapping,
		bool	ind1 = `false`
	)		const

Returns the sparsity of the submatrix, with a mapping such that submatrix[k] = originalmatrix[mapping[k]]

Extra doc: https://github.com/casadi/casadi/wiki/L_ci

◆ T()

Sparsity casadi::Sparsity::T ( ) const

◆ test_cast()

static bool casadi::Sparsity::test_cast ( const SharedObjectInternal * ptr )

static

◆ to_file()

void casadi::Sparsity::to_file	(	const std::string &	filename,
		const std::string &	format_hint = `""`
	)		const

Export sparsity pattern to file

Supported formats:

.mtx Matrix Market

◆ transpose()

Sparsity casadi::Sparsity::transpose	(	std::vector< casadi_int > &	mapping,
		bool	invert_mapping = `false`
	)		const

Parameters

[out] mapping the non-zeros of the original matrix for each non-zero of the new matrix

Extra doc: https://github.com/casadi/casadi/wiki/L_ck

◆ triplet() [1/2]

static Sparsity casadi::Sparsity::triplet	(	casadi_int	nrow,
		casadi_int	ncol,
		const std::vector< casadi_int > &	row,
		const std::vector< casadi_int > &	col
	)

static

Extra doc: https://github.com/casadi/casadi/wiki/L_bm

◆ triplet() [2/2]

static Sparsity casadi::Sparsity::triplet	(	casadi_int	nrow,
		casadi_int	ncol,
		const std::vector< casadi_int > &	row,
		const std::vector< casadi_int > &	col,
		std::vector< casadi_int > &	mapping,
		bool	invert_mapping
	)

static

Extra doc: https://github.com/casadi/casadi/wiki/L_bm

◆ type_name()

static std::string casadi::Sparsity::type_name ( )

inlinestatic

Definition at line 1128 of file sparsity.hpp.

◆ uni_coloring()

Sparsity casadi::Sparsity::uni_coloring	(	const Sparsity &	AT = `Sparsity()`,
		casadi_int	cutoff = `std::numeric_limits< casadi_int >::max()`
	)		const

(Algorithm 3.1 in A. H. GEBREMEDHIN, F. MANNE, A. POTHEN)

Extra doc: https://github.com/casadi/casadi/wiki/L_db

Examples: matrix/coloring.py.

◆ unit()

static Sparsity casadi::Sparsity::unit	(	casadi_int	n,
		casadi_int	el
	)

static

position el *

Extra doc: https://github.com/casadi/casadi/wiki/L_bf

◆ unite()

Sparsity casadi::Sparsity::unite ( const Sparsity & y ) const

Extra doc: https://github.com/casadi/casadi/wiki/L_cm

◆ upper()

static Sparsity casadi::Sparsity::upper ( casadi_int n )

static

Extra doc: https://github.com/casadi/casadi/wiki/L_bg

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

sparsity.hpp

Detailed Description

Public Member Functions

Static Public Member Functions

Constructor & Destructor Documentation

◆ Sparsity() [1/4]

◆ Sparsity() [2/4]

◆ Sparsity() [3/4]

◆ Sparsity() [4/4]

Member Function Documentation

◆ __hash__()

◆ add_nz()

◆ amd()

◆ append()

◆ appendColumns()

◆ band()

◆ banded()

◆ btf()

◆ bw_lower()

◆ bw_upper()

◆ class_name()

◆ colind()

◆ columns()

◆ combine()

◆ compress()

◆ compressed()

◆ dense() [1/2]

◆ dense() [2/2]

◆ density()

◆ deserialize() [1/3]

◆ deserialize() [2/3]

◆ deserialize() [3/3]

◆ dfs()

◆ diag() [1/3]

◆ diag() [2/3]

◆ diag() [3/3]

◆ dim()

◆ disp()

◆ enlarge()

◆ enlargeColumns()

◆ enlargeRows()

◆ erase() [1/2]

◆ erase() [2/2]

◆ etree()

◆ export_code()

◆ find()

◆ from_file()

◆ get_ccs()

◆ get_col()

◆ get_colind()

◆ get_crs()

◆ get_diag()

◆ get_lower()

◆ get_nz() [1/3]

◆ get_nz() [2/3]

◆ get_nz() [3/3]

◆ get_row()

◆ get_str()

◆ get_triplet()

◆ get_upper()

◆ has_nz()

◆ hash()

◆ info()

◆ intersect()

◆ is_column()

◆ is_dense()

◆ is_diag()

◆ is_empty()

◆ is_equal() [1/2]

◆ is_equal() [2/2]

◆ is_null()

◆ is_orthonormal()

◆ is_orthonormal_columns()

◆ is_orthonormal_rows()

◆ is_permutation()

◆ is_reshape()

◆ is_row()

◆ is_scalar()

◆ is_selection()

◆ is_singular()

◆ is_square()

◆ hash()