casadi::GenericMatrix< MatType > Class Template Reference

Matrix base class. More...

#include <generic_matrix.hpp>

Detailed Description

template<typename MatType>
class casadi::GenericMatrix< MatType >

This is a common base class for MX and Matrix<>, introducing a uniform syntax and implementing common functionality using the curiously recurring template pattern (CRTP) idiom.
The class is designed with the idea that "everything is a matrix", that is, also scalars and vectors.
This philosophy makes it easy to use and to interface in particularly with Python and Matlab/Octave.
The syntax tries to stay as close as possible to the ublas syntax when it comes to vector/matrix operations.
Index starts with 0.
Index vec happens as follows: (rr, cc) -> k = rr+cc*size1()
Vectors are column vectors.
The storage format is Compressed Column Storage (CCS), similar to that used for sparse matrices in Matlab,
but unlike this format, we do allow for elements to be structurally non-zero but numerically zero.
The sparsity pattern, which is reference counted and cached, can be accessed with Sparsity& sparsity()

Author

Joel Andersson

Date

2012

Extra doc: https://github.com/casadi/casadi/wiki/L_1am

Definition at line 75 of file generic_matrix.hpp.

Inheritance diagram for casadi::GenericMatrix< MatType >:

Collaboration diagram for casadi::GenericMatrix< MatType >:

Public Member Functions
casadi_int	nnz () const
	Get the number of structural nonzeros. More...
casadi_int	nnz_lower () const
	Get the number of structural nonzeros on or below the diagonal. More...
casadi_int	nnz_upper () const
	Get the number of structural nonzeros on or above the diagonal. More...
casadi_int	nnz_diag () const
	Get the number of structural nonzeros on the diagonal. More...
casadi_int	numel () const
	Get the number of elements, size1()*size2() More...
casadi_int	size1 () const
	Get the first dimension (i.e. number of rows) More...
casadi_int	rows () const
	Get the number of rows, Octave-style syntax (same as size1()) More...
casadi_int	size2 () const
	Get the second dimension (i.e. number of columns) More...
casadi_int	columns () const
	Get the number of columns, Octave-style syntax (same as size2()) More...
std::string	dim (bool with_nz=false) const
	Get string representation of dimensions. More...
std::pair< casadi_int, casadi_int >	size () const
	Get the shape as a pair (number of rows, number of columns) More...
casadi_int	size (casadi_int axis) const
	Get the size along a particular dimension. More...
bool	is_empty (bool both=false) const
	Check if the matrix is empty, i.e. if one of the dimensions is zero. More...
bool	is_dense () const
	Check if the matrix is dense, i.e. nnz() equals numel() More...
bool	is_scalar (bool scalar_and_dense=false) const
	Check if the matrix is scalar, i.e. 1-by-1. More...
bool	is_square () const
	Check if the matrix is square, i.e. size1() equals size2() More...
bool	is_vector () const
	Check if the matrix is a row or column vector. More...
bool	is_row () const
	Check if the matrix is a row vector (i.e. size1()==1) More...
bool	is_column () const
	Check if the matrix is a column vector (i.e. size2()==1) More...
bool	is_triu () const
	Check if the matrix is upper triangular. More...
bool	is_tril () const
	Check if the matrix is lower triangular. More...
Sparsity	sparsity () const
	Get the sparsity pattern. More...
template<typename K >
const MatType	nz (const K &k) const
	Get vector nonzero or slice of nonzeros. More...
template<typename K >
NonZeros< MatType, K >	nz (const K &k)
	Access vector nonzero or slice of nonzeros. More...
template<typename RR >
const MatType	operator() (const RR &rr) const
	Get vector element or slice. More...
template<typename RR , typename CC >
const MatType	operator() (const RR &rr, const CC &cc) const
	Get Matrix element or slice. More...
template<typename RR >
SubIndex< MatType, RR >	operator() (const RR &rr)
	Access Matrix elements (one argument) More...
template<typename RR , typename CC >
SubMatrix< MatType, RR, CC >	operator() (const RR &rr, const CC &cc)
	Access Matrix elements (two arguments) More...
std::vector< casadi_int >	get_row () const
	Get the sparsity pattern. See the Sparsity class for details. More...
std::vector< casadi_int >	get_colind () const
	Get the sparsity pattern. See the Sparsity class for details. More...
const casadi_int *	row () const
	Get the sparsity pattern. See the Sparsity class for details. More...
const casadi_int *	colind () const
	Get the sparsity pattern. See the Sparsity class for details. More...
casadi_int	row (casadi_int el) const
	Get the sparsity pattern. See the Sparsity class for details. More...
casadi_int	colind (casadi_int col) const
	Get the sparsity pattern. See the Sparsity class for details. More...

Static Public Member Functions
static MatType	logsumexp (const MatType &x)
static MatType	interp1d (const std::vector< double > &x, const MatType &v, const std::vector< double > &xq, const std::string &mode, bool equidistant)
	Functions called by friend functions defined here. More...
static casadi_int	sprank (const MatType &x)
	Functions called by friend functions defined here. More...
static casadi_int	norm_0_mul (const MatType &x, const MatType &y)
	Functions called by friend functions defined here. More...
static MatType	tril (const MatType &x, bool includeDiagonal=true)
	Functions called by friend functions defined here. More...
static MatType	triu (const MatType &x, bool includeDiagonal=true)
	Functions called by friend functions defined here. More...
static MatType	sumsqr (const MatType &x)
	Functions called by friend functions defined here. More...
static MatType	linspace (const MatType &a, const MatType &b, casadi_int nsteps)
	Functions called by friend functions defined here. More...
static MatType	cross (const MatType &a, const MatType &b, casadi_int dim=-1)
	Functions called by friend functions defined here. More...
static MatType	skew (const MatType &a)
	Functions called by friend functions defined here. More...
static MatType	inv_skew (const MatType &a)
	Functions called by friend functions defined here. More...
static MatType	tril2symm (const MatType &x)
	Functions called by friend functions defined here. More...
static MatType	triu2symm (const MatType &x)
	Functions called by friend functions defined here. More...
static MatType	repsum (const MatType &x, casadi_int n, casadi_int m=1)
	Functions called by friend functions defined here. More...
static MatType	diff (const MatType &x, casadi_int n=1, casadi_int axis=-1)
	Functions called by friend functions defined here. More...
static bool	is_linear (const MatType &expr, const MatType &var)
	Functions called by friend functions defined here. More...
static bool	is_quadratic (const MatType &expr, const MatType &var)
	Functions called by friend functions defined here. More...
static void	quadratic_coeff (const MatType &expr, const MatType &var, MatType &A, MatType &b, MatType &c, bool check)
	Functions called by friend functions defined here. More...
static void	linear_coeff (const MatType &expr, const MatType &var, MatType &A, MatType &b, bool check)
	Functions called by friend functions defined here. More...
static MatType	jtimes (const MatType &ex, const MatType &arg, const MatType &v, bool tr=false, const Dict &opts=Dict())
static MatType	gradient (const MatType &ex, const MatType &arg, const Dict &opts=Dict())
static MatType	tangent (const MatType &ex, const MatType &arg, const Dict &opts=Dict())
static MatType	linearize (const MatType &f, const MatType &x, const MatType &x0, const Dict &opts=Dict())
static MatType	mpower (const MatType &x, const MatType &y)
static MatType	soc (const MatType &x, const MatType &y)
Construct symbolic primitives
The "sym" function is intended to work in a similar way as "sym" used in the Symbolic Toolbox for Matlab but instead creating a CasADi symbolic primitive.
static MatType	sym (const std::string &name, casadi_int nrow=1, casadi_int ncol=1)
	Create an nrow-by-ncol symbolic primitive. More...
static MatType	sym (const std::string &name, const std::pair< casadi_int, casadi_int > &rc)
	Construct a symbolic primitive with given dimensions, as a pair (nrow, ncol) More...
static MatType	sym (const std::string &name, const Sparsity &sp)
	Create symbolic primitive with a given sparsity pattern. More...
static std::vector< MatType >	sym (const std::string &name, const Sparsity &sp, casadi_int p)
	Create a list of length p of symbolic primitives with a given sparsity. More...
static std::vector< MatType >	sym (const std::string &name, casadi_int nrow, casadi_int ncol, casadi_int p)
	Create a list of length p of nrow-by-ncol symbolic primitives. More...
static std::vector< std::vector< MatType > >	sym (const std::string &name, const Sparsity &sp, casadi_int p, casadi_int r)
	Create a list of length r of lists of length p of symbolic primitives. More...
static std::vector< std::vector< MatType > >	sym (const std::string &name, casadi_int nrow, casadi_int ncol, casadi_int p, casadi_int r)
	Create a list of length r of lists of length p of nrow-by-ncol symbolic primitives. More...
static MatType	zeros (casadi_int nrow=1, casadi_int ncol=1)
	Create a dense matrix or a matrix with specified sparsity with all entries zero. More...
static MatType	zeros (const Sparsity &sp)
	Create a dense matrix or a matrix with specified sparsity with all entries zero. More...
static MatType	zeros (const std::pair< casadi_int, casadi_int > &rc)
	Create a dense matrix or a matrix with specified sparsity with all entries zero. More...
static MatType	ones (casadi_int nrow=1, casadi_int ncol=1)
	Create a dense matrix or a matrix with specified sparsity with all entries one. More...
static MatType	ones (const Sparsity &sp)
	Create a dense matrix or a matrix with specified sparsity with all entries one. More...
static MatType	ones (const std::pair< casadi_int, casadi_int > &rc)
	Create a dense matrix or a matrix with specified sparsity with all entries one. More...

Friends
MatType	interp1d (const std::vector< double > &x, const MatType &v, const std::vector< double > &xq, const std::string &mode, bool equidistant=false)
	Performs 1d linear interpolation. More...
MatType	mpower (const MatType &x, const MatType &n)
	Matrix power x^n. More...
MatType	soc (const MatType &x, const MatType &y)
	Construct second-order-cone matrix. More...
MatType	mrdivide (const MatType &x, const MatType &n)
	Matrix right divide, x/A (cf. slash '/' in MATLAB) More...
MatType	mldivide (const MatType &x, const MatType &n)
	Matrix left divide, A\b (cf. backslash '\' in MATLAB) More...
std::vector< MatType >	symvar (const MatType &x)
	Get all symbolic primitives present in an expression. More...
MatType	sumsqr (const MatType &x)
	Calculate sum of squares: sum_ij X_ij^2. More...
MatType	logsumexp (const MatType &x)
	x -> log(sum_i exp(x_i)) More...
MatType	logsumexp (const MatType &x, const MatType &margin)
	Scaled version of logsumexp. More...
MatType	linspace (const MatType &a, const MatType &b, casadi_int nsteps)
	Matlab's linspace command. More...
MatType	cross (const MatType &a, const MatType &b, casadi_int dim=-1)
	Matlab's cross command. More...
MatType	skew (const MatType &a)
	Generate a skew symmetric matrix from a 3-vector. More...
MatType	inv_skew (const MatType &a)
	Generate the 3-vector progenitor of a skew symmetric matrix. More...
MatType	det (const MatType &A)
	Matrix determinant (experimental) More...
MatType	det (const MatType &A, const std::string &lsolver, const Dict &dict=Dict())
	Matrix determinant through a linear solver factorization (experimental) More...
MatType	inv_minor (const MatType &A)
	Matrix inverse by the adjugate (experimental) More...
MatType	inv (const MatType &A)
	Matrix inverse. More...
MatType	inv (const MatType &A, const std::string &lsolver, const Dict &options=Dict())
	Matrix inverse using a linear solver plugin. More...
MatType	trace (const MatType &x)
	Matrix trace. More...
MatType	tril2symm (const MatType &a)
	Convert a lower triangular matrix to a symmetric one. More...
MatType	triu2symm (const MatType &a)
	Convert a upper triangular matrix to a symmetric one. More...
MatType	norm_fro (const MatType &x)
	Frobenius norm. More...
MatType	norm_2 (const MatType &x)
	2-norm More...
MatType	norm_1 (const MatType &x)
	1-norm More...
MatType	norm_inf (const MatType &x)
	Infinity-norm. More...
MatType	diff (const MatType &x, casadi_int n=1, casadi_int axis=-1)
	Returns difference (n-th order) along given axis (MATLAB convention) More...
MatType	cumsum (const MatType &x, casadi_int axis=-1)
	Returns cumulative sum along given axis (MATLAB convention) More...
MatType	dot (const MatType &x, const MatType &y)
	Inner product of two matrices. More...
MatType	nullspace (const MatType &A)
	Computes the nullspace of a matrix A. More...
MatType	polyval (const MatType &p, const MatType &x)
	Evaluate a polynomial with coefficients p in x. More...
MatType	diag (const MatType &A)
	Get the diagonal of a matrix or construct a diagonal. More...
MatType	unite (const MatType &A, const MatType &B)
	Unite two matrices with non-overlapping sparsity patterns. More...
MatType	densify (const MatType &x)
	Make the matrix dense if not already. More...
MatType	densify (const MatType &x, const MatType &val)
	Make the matrix dense and assign nonzeros to a value. More...
MatType	project (const MatType &A, const Sparsity &sp, bool intersect=false)
	Create a new matrix with a given sparsity pattern but with the. More...
MatType	if_else (const MatType &cond, const MatType &if_true, const MatType &if_false, bool short_circuit=false)
	Branching on MX nodes. More...
MatType	conditional (const MatType &ind, const std::vector< MatType > &x, const MatType &x_default, bool short_circuit=false)
	Create a switch. More...
bool	depends_on (const MatType &f, const MatType &arg)
	Check if expression depends on the argument. More...
MatType	substitute (const MatType &ex, const MatType &v, const MatType &vdef)
	Substitute variable v with expression vdef in an expression ex. More...
std::vector< MatType >	substitute (const std::vector< MatType > &ex, const std::vector< MatType > &v, const std::vector< MatType > &vdef)
	Substitute variables v with expressions vdef in multiple expressions ex. More...
void	substitute_inplace (const std::vector< MatType > &v, std::vector< MatType > &inout_vdef, std::vector< MatType > &inout_ex, bool reverse=false)
	Inplace substitution with piggyback expressions. More...
MatType	cse (const MatType &e)
	Common subexpression elimination. More...
std::vector< MatType >	cse (const std::vector< MatType > &e)
	Common subexpression elimination over a list of expressions. More...
MatType	solve (const MatType &A, const MatType &b)
	Solve a system of equations: A*x = b. More...
MatType	solve (const MatType &A, const MatType &b, const std::string &lsolver, const Dict &dict=Dict())
	Solve a system of equations: A*x = b, using a linear solver plugin. More...
MatType	linearize (const MatType &f, const MatType &x, const MatType &x0, const Dict &opts=Dict())
	Linearize an expression. More...
MatType	pinv (const MatType &A)
	Computes the Moore-Penrose pseudo-inverse. More...
MatType	pinv (const MatType &A, const std::string &lsolver, const Dict &dict=Dict())
	Computes the Moore-Penrose pseudo-inverse using a linear solver plugin. More...
MatType	expm_const (const MatType &A, const MatType &t)
	Calculate Matrix exponential. More...
MatType	expm (const MatType &A)
	Calculate Matrix exponential. More...
MatType	jacobian (const MatType &ex, const MatType &arg, const Dict &opts=Dict())
	Calculate Jacobian. More...
MatType	gradient (const MatType &ex, const MatType &arg, const Dict &opts=Dict())
	Calculate the gradient of an expression. More...
MatType	tangent (const MatType &ex, const MatType &arg, const Dict &opts=Dict())
	Calculate the tangent of an expression. More...
MatType	jtimes (const MatType &ex, const MatType &arg, const MatType &v, bool tr=false, const Dict &opts=Dict())
	Calculate the Jacobian and multiply by a vector from the right. More...
std::vector< std::vector< MatType > >	forward (const std::vector< MatType > &ex, const std::vector< MatType > &arg, const std::vector< std::vector< MatType > > &v, const Dict &opts=Dict())
	Forward directional derivative. More...
std::vector< std::vector< MatType > >	reverse (const std::vector< MatType > &ex, const std::vector< MatType > &arg, const std::vector< std::vector< MatType > > &v, const Dict &opts=Dict())
	Reverse directional derivative. More...
std::vector< bool >	which_depends (const MatType &expr, const MatType &var, casadi_int order, bool tr)
	Find out which variables enter with some order. More...
Sparsity	jacobian_sparsity (const MatType &f, const MatType &x)
	Get the sparsity pattern of a jacobian. More...
bool	is_linear (const MatType &expr, const MatType &var)
	Is expr linear in var? More...
bool	is_quadratic (const MatType &expr, const MatType &var)
	Is expr quadratic in var? More...
void	quadratic_coeff (const MatType &expr, const MatType &var, MatType &A, MatType &b, MatType &c, bool check=true)
	Recognizes quadratic form in scalar expression. More...
void	linear_coeff (const MatType &expr, const MatType &var, MatType &A, MatType &b, bool check=true)
	Recognizes linear form in vector expression. More...
void	extract_parametric (const MatType &expr, const MatType &par, MatType &expr_ret, std::vector< MatType > &symbols, std::vector< MatType > &parametric, const Dict &opts=Dict())
	Extract purely parametric parts from an expression graph. More...
void	extract_parametric (const std::vector< MatType > &expr, const MatType &par, std::vector< MatType > &expr_ret, std::vector< MatType > &symbols, std::vector< MatType > &parametric, const Dict &opts=Dict())
void	extract_parametric (const std::vector< MatType > &expr, const std::vector< MatType > &par, std::vector< MatType > &expr_ret, std::vector< MatType > &symbols, std::vector< MatType > &parametric, const Dict &opts=Dict())
void	extract_parametric (const MatType &expr, const std::vector< MatType > &par, MatType &expr_ret, std::vector< MatType > &symbols, std::vector< MatType > &parametric, const Dict &opts=Dict())
void	separate_linear (const MatType &expr, const MatType &sym_lin, const MatType &sym_const, MatType &expr_const, MatType &expr_lin, MatType &expr_nonlin)
	Separate an expression into subexpressions that are constant, linear and nonlinear. More...
void	separate_linear (const MatType &expr, const std::vector< MatType > &sym_lin, const std::vector< MatType > &sym_const, MatType &expr_const, MatType &expr_lin, MatType &expr_nonlin)
casadi_int	n_nodes (const MatType &A)
	Count the number of nodes in an expression graph. More...
MatType	simplify (const MatType &x)
	Simplify an expression. More...
std::string	print_operator (const MatType &xb, const std::vector< std::string > &args)
	Get a string representation for a binary MatType, using custom arguments. More...
void	extract (std::vector< MatType > &ex, std::vector< MatType > &v, std::vector< MatType > &vdef, const Dict &opts=Dict())
	Introduce intermediate variables for selected nodes in a graph. More...
void	shared (std::vector< MatType > &ex, std::vector< MatType > &v, std::vector< MatType > &vdef, const std::string &v_prefix="v_", const std::string &v_suffix="")
	Extract shared subexpressions from an set of expressions. More...
MatType	repsum (const MatType &A, casadi_int n, casadi_int m=1)
	Given a repeated matrix, computes the sum of repeated parts. More...
MatType	einstein (const MatType &A, const MatType &B, const MatType &C, const std::vector< casadi_int > &dim_a, const std::vector< casadi_int > &dim_b, const std::vector< casadi_int > &dim_c, const std::vector< casadi_int > &a, const std::vector< casadi_int > &b, const std::vector< casadi_int > &c)
	Compute any contraction of two dense tensors, using index/einstein notation. More...
MatType	einstein (const MatType &A, const MatType &B, const std::vector< casadi_int > &dim_a, const std::vector< casadi_int > &dim_b, const std::vector< casadi_int > &dim_c, const std::vector< casadi_int > &a, const std::vector< casadi_int > &b, const std::vector< casadi_int > &c)
	Compute any contraction of two dense tensors, using index/einstein notation. More...
bool	contains (const std::vector< MatType > &v, const MatType &n)
	Check if expression n is listed in v. More...
bool	contains_all (const std::vector< MatType > &v, const std::vector< MatType > &n)
	Check if expression n is listed in v. More...
bool	contains_any (const std::vector< MatType > &v, const std::vector< MatType > &n)
	Check if expression n is listed in v. More...
MatType	hessian (const MatType &ex, const MatType &arg, const Dict &opts=Dict())
	Hessian and (optionally) gradient. More...
MatType	hessian (const MatType &ex, const MatType &arg, MatType &output_g, const Dict &opts=Dict())
	Hessian and (optionally) gradient. More...
MatType	transform (const MatType &x, const Dict &opts=Dict())
	Apply transformation passes to an expression. More...
MatType	transform (const MatType &x, const std::vector< std::vector< GenericType > > &passes, const Dict &opts=Dict())
	Apply transformation passes to an expression. More...
std::vector< MatType >	transform (const std::vector< MatType > &x, const Dict &opts=Dict())
	Apply transformation passes to an expression. More...
std::vector< MatType >	transform (const std::vector< MatType > &x, const std::vector< std::vector< GenericType > > &passes, const Dict &opts=Dict())
	Apply transformation passes to an expression. More...
MatType	mmin (const MatType &x)
	Smallest element in a matrix. More...
MatType	mmax (const MatType &x)
	Largest element in a matrix. More...
static MatType	bilin (const MatType &A, const MatType &x, const MatType &y)
	Calculate bilinear/quadratic form x^T A y. More...
MatType	bilin (const MatType &A, const MatType &x, const MatType &y)
	Calculate bilinear/quadratic form x^T A y. More...
MatType	bilin (const MatType &A, const MatType &x)
	Calculate bilinear/quadratic form x^T A y. More...
static MatType	rank1 (const MatType &A, const MatType &alpha, const MatType &x, const MatType &y)
	Make a rank-1 update to a matrix A. More...
MatType	rank1 (const MatType &A, const MatType &alpha, const MatType &x, const MatType &y)
	Make a rank-1 update to a matrix A. More...

Member Function Documentation

colind() [1/2]

template<typename MatType >

const casadi_int* casadi::GenericMatrix< MatType >::colind ( ) const

inline

The pattern is stored in compressed column format: colind has size2()+1 entries, the nonzeros of column j are the entries colind(j) up to colind(j+1) (exclusive), and row(el) is the row index of nonzero el. Without argument, the full vectors are returned. Out-of-range indices raise an error.

>>> x = DM(Sparsity.diag(2), [5, 6])
>>> x.row(), x.colind()
([0, 1], [0, 1, 2])
>>> x.row(1), x.colind(2)
(1, 2)

>> x = DM(Sparsity.diag(2), [5; 6]);
>> x.row(), x.colind()
0 1
0 1 2
>> fprintf('%d %d\n', x.row(1), x.colind(2))
1 2

julia> x = ca.DM(ca.Sparsity.diag(2), [5, 6]);
julia> ca.row(x), ca.colind(x)
([0, 1], [0, 1, 2])
julia> ca.row(x, 1), ca.colind(x, 2)
(1, 2)

Extra doc: https://github.com/casadi/casadi/wiki/L_1b8

Definition at line 606 of file generic_matrix.hpp.

{ return sparsity().colind(); }

References casadi::Sparsity::colind(), and casadi::GenericMatrix< MatType >::sparsity().

Referenced by casadi::Matrix< Scalar >::densify(), casadi::SnoptInterface::init(), casadi::Conic::sdp_to_socp_init(), casadi::MX::set(), casadi::SnoptInterface::solve(), and casadi::SnoptInterface::userfun().

colind() [2/2]

template<typename MatType >

casadi_int casadi::GenericMatrix< MatType >::colind ( casadi_int  col ) const

inline

The pattern is stored in compressed column format: colind has size2()+1 entries, the nonzeros of column j are the entries colind(j) up to colind(j+1) (exclusive), and row(el) is the row index of nonzero el. Without argument, the full vectors are returned. Out-of-range indices raise an error.

>>> x = DM(Sparsity.diag(2), [5, 6])
>>> x.row(), x.colind()
([0, 1], [0, 1, 2])
>>> x.row(1), x.colind(2)
(1, 2)

>> x = DM(Sparsity.diag(2), [5; 6]);
>> x.row(), x.colind()
0 1
0 1 2
>> fprintf('%d %d\n', x.row(1), x.colind(2))
1 2

julia> x = ca.DM(ca.Sparsity.diag(2), [5, 6]);
julia> ca.row(x), ca.colind(x)
([0, 1], [0, 1, 2])
julia> ca.row(x, 1), ca.colind(x, 2)
(1, 2)

Extra doc: https://github.com/casadi/casadi/wiki/L_1b8

Definition at line 609 of file generic_matrix.hpp.

{ return sparsity().colind(col); }

References casadi::Sparsity::colind(), and casadi::GenericMatrix< MatType >::sparsity().

columns()

template<typename MatType >

casadi_int casadi::GenericMatrix< MatType >::columns ( ) const

inline

Extra doc: https://github.com/casadi/casadi/wiki/L_1av

Definition at line 295 of file generic_matrix.hpp.

{return size2();}

References casadi::GenericMatrix< MatType >::size2().

cross()

template<typename MatType >

MatType casadi::GenericMatrix< MatType >::cross ( const MatType &  a, const MatType &  b, casadi_int  dim = -1  )

static

Definition at line 5326 of file generic_matrix.hpp.

                                                                                          {
    casadi_assert(a.size1()==b.size1() && a.size2()==b.size2(),
      "cross(a, b): Inconsistent dimensions. Dimension of a ("
      + a.dim() + " ) must equal that of b (" + b.dim() + ").");
 
    casadi_assert(a.size1()==3 || a.size2()==3,
      "cross(a, b): One of the dimensions of a should have length 3, but got "
        + a.dim() + ".");
    casadi_assert(dim==-1 || dim==1 || dim==2,
      "cross(a, b, dim): Dim must be 1, 2 or -1 (automatic).");
 
    std::vector<MatType> ret(3);
 
    bool t = a.size1()==3;
 
    if (dim==1) t = true;
    if (dim==2) t = false;
 
    MatType a1 = t ? a(0, Slice()) : a(Slice(), 0);
    MatType a2 = t ? a(1, Slice()) : a(Slice(), 1);
    MatType a3 = t ? a(2, Slice()) : a(Slice(), 2);
 
    MatType b1 = t ? b(0, Slice()) : b(Slice(), 0);
    MatType b2 = t ? b(1, Slice()) : b(Slice(), 1);
    MatType b3 = t ? b(2, Slice()) : b(Slice(), 2);
 
    ret[0] = a2*b3-a3*b2;
    ret[1] = a3*b1-a1*b3;
    ret[2] = a1*b2-a2*b1;
 
    return t ? vertcat(ret) : horzcat(ret);
  }

diff()

template<typename MatType >

MatType casadi::GenericMatrix< MatType >::diff ( const MatType &  x, casadi_int  n = 1, casadi_int  axis = -1  )

static

Definition at line 5709 of file generic_matrix.hpp.

                                                                                      {
    casadi_assert(axis==-1 || axis==0 || axis==1, "Axis argument invalid");
    casadi_assert(n>=1, "n argument invalid");
 
    MatType ret = x;
    for (casadi_int i=0;i<n;++i) {
      // Matlab's special case
      if (axis==-1 && ret.is_scalar()) return MatType();
 
      casadi_int local_axis = (axis==-1) ? ret.is_row() : axis;
      if (local_axis==0) {
        if (ret.size1()<=1) {
          ret = MatType::zeros(0, ret.size2());
        } else {
          ret = ret(Slice(1, ret.size1()), Slice())-ret(Slice(0, ret.size1()-1), Slice());
        }
      } else {
        if (ret.size2()<=1) {
          ret = MatType::zeros(ret.size1(), 0);
        } else {
          ret = ret(Slice(), Slice(1, ret.size2()))-ret(Slice(), Slice(0, ret.size2()-1));
        }
      }
    }
    return ret;
  }

dim()

template<typename MatType >

std::string casadi::GenericMatrix< MatType >::dim

(

bool

with_nz = false

)

const

The representation is e.g. "4x5" or, with with_nz true, "4x5,10nz".

>>> DM.eye(3).dim(), DM.eye(3).dim(True), DM.ones(3, 3).dim(True)
('3x3', '3x3,3nz', '3x3,9nz')

>> fprintf('%s %s %s\n', DM.eye(3).dim(), DM.eye(3).dim(true), DM.ones(3, 3).dim(true))
3x3 3x3,3nz 3x3,9nz

julia> ca.dim(ca.DM.eye(3)), ca.dim(ca.DM.eye(3), true), ca.dim(ca.DM.ones(3, 3), true)
("3x3", "3x3,3nz", "3x3,9nz")

See also

size, nnz

Extra doc: https://github.com/casadi/casadi/wiki/L_1aw

Definition at line 5274 of file generic_matrix.hpp.

                                                          {
    return sparsity().dim(with_nz);
  }

Referenced by casadi::Assertion::Assertion(), casadi::MX::attachAssert(), casadi::MX::binary(), casadi::OptiNode::canon_expr(), casadi::BSplineParametric::create(), casadi::BSpline::create(), casadi::OptiNode::describe(), casadi::SymbolicQr::det(), casadi::Determinant::Determinant(), casadi::MXNode::get_find(), casadi::MXNode::get_mac(), casadi::MX::interpn_linear(), casadi::Inverse::Inverse(), casadi::Low::Low(), casadi::MX::mac(), casadi::OptiNode::minimize(), casadi::Multiplication::Multiplication(), casadi::MX::MX(), casadi::MX::project(), casadi::OptiNode::set_linear_scale(), casadi::Linsol::solve(), casadi::Solve< Tr >::Solve(), and casadi::OptiNode::subject_to().

get_colind()

template<typename MatType >

std::vector<casadi_int> casadi::GenericMatrix< MatType >::get_colind ( ) const

inline

The pattern is stored in compressed column format: colind has size2()+1 entries, the nonzeros of column j are the entries colind(j) up to colind(j+1) (exclusive), and row(el) is the row index of nonzero el. Without argument, the full vectors are returned. Out-of-range indices raise an error.

>>> x = DM(Sparsity.diag(2), [5, 6])
>>> x.row(), x.colind()
([0, 1], [0, 1, 2])
>>> x.row(1), x.colind(2)
(1, 2)

>> x = DM(Sparsity.diag(2), [5; 6]);
>> x.row(), x.colind()
0 1
0 1 2
>> fprintf('%d %d\n', x.row(1), x.colind(2))
1 2

julia> x = ca.DM(ca.Sparsity.diag(2), [5, 6]);
julia> ca.row(x), ca.colind(x)
([0, 1], [0, 1, 2])
julia> ca.row(x, 1), ca.colind(x, 2)
(1, 2)

Extra doc: https://github.com/casadi/casadi/wiki/L_1b8

Definition at line 603 of file generic_matrix.hpp.

{ return sparsity().get_colind(); }

References casadi::Sparsity::get_colind(), and casadi::GenericMatrix< MatType >::sparsity().

get_row()

template<typename MatType >

std::vector<casadi_int> casadi::GenericMatrix< MatType >::get_row ( ) const

inline

The pattern is stored in compressed column format: colind has size2()+1 entries, the nonzeros of column j are the entries colind(j) up to colind(j+1) (exclusive), and row(el) is the row index of nonzero el. Without argument, the full vectors are returned. Out-of-range indices raise an error.

>>> x = DM(Sparsity.diag(2), [5, 6])
>>> x.row(), x.colind()
([0, 1], [0, 1, 2])
>>> x.row(1), x.colind(2)
(1, 2)

>> x = DM(Sparsity.diag(2), [5; 6]);
>> x.row(), x.colind()
0 1
0 1 2
>> fprintf('%d %d\n', x.row(1), x.colind(2))
1 2

julia> x = ca.DM(ca.Sparsity.diag(2), [5, 6]);
julia> ca.row(x), ca.colind(x)
([0, 1], [0, 1, 2])
julia> ca.row(x, 1), ca.colind(x, 2)
(1, 2)

Extra doc: https://github.com/casadi/casadi/wiki/L_1b8

Definition at line 602 of file generic_matrix.hpp.

{ return sparsity().get_row(); }

References casadi::Sparsity::get_row(), and casadi::GenericMatrix< MatType >::sparsity().

interp1d()

template<typename MatType >

MatType casadi::GenericMatrix< MatType >::interp1d ( const std::vector< double > &  x, const MatType &  v, const std::vector< double > &  xq, const std::string &  mode, bool  equidistant  )

static

Definition at line 5363 of file generic_matrix.hpp.

                                                                            {
 
    bool mode_floor = false;
    bool mode_ceil = false;
    if (mode=="floor") {
      mode_floor = true;
    } else if (mode=="ceil") {
      mode_ceil = true;
    } else if (mode=="linear") {
      //
    } else {
      casadi_error("interp1d(x, v, xq, mode): "
        "Mode must be 'floor', 'ceil' or 'linear'. Got '" + mode + "' instead.");
    }
 
    casadi_assert(is_increasing(x), "interp1d(x, v, xq): x must be increasing.");
 
    casadi_assert(x.size()==v.size1(),
      "interp1d(x, v, xq): dimensions mismatch. v expected to have " + str(x.size()) + " rows,"
      " but got " + str(v.size1()) + " instead.");
 
    // Need at least two elements
    casadi_assert(x.size()>=2, "interp1d(x, v, xq): x must be at least length 2.");
 
    // Vectors to compose a sparse matrix
    std::vector<double> val;
    std::vector<casadi_int> colind(1, 0);
    std::vector<casadi_int> row;
 
    // Number of nonzeros in to-be composed matrix
    casadi_int nnz = 0;
    for (casadi_int i=0;i<xq.size();++i) {
      // Obtain index corresponding to xq[i]
      double ind = index_interp1d(x, xq[i], equidistant);
 
      if (mode_floor) ind = floor(ind);
      if (mode_ceil) ind = ceil(ind);
 
      // Split into integer and fractional part
      double int_partd;
      double frac_part = modf(ind, &int_partd);
      casadi_int int_part = static_cast<casadi_int>(int_partd);
 
      if (frac_part==0) {
         // Create a single entry
         val.push_back(1);
         row.push_back(int_part);
         nnz+=1;
         colind.push_back(nnz);
       } else {
         // Create a double entry
         val.push_back(1-frac_part);
         val.push_back(frac_part);
         row.push_back(int_part);
         row.push_back(int_part+1);
         nnz+=2;
         colind.push_back(nnz);
       }
     }
 
     // Construct sparsity for composed matrix
     Sparsity sp(x.size(), xq.size() , colind, row);
 
     return MatType::mtimes(MatType(sp, val).T(), v);
 
  }

References casadi::index_interp1d(), casadi::is_increasing(), casadi::str(), and casadi::T.

inv_skew()

template<typename MatType >

MatType casadi::GenericMatrix< MatType >::inv_skew ( const MatType &  a )

static

Definition at line 5443 of file generic_matrix.hpp.

                                                           {
    casadi_assert(a.size1()==3 && a.size2()==3,
      "inv_skew(a): Expecting 3-by-3 matrix, got " + a.dim() + ".");
 
    return 0.5*vertcat(std::vector<MatType>({a(2, 1)-a(1, 2), a(0, 2)-a(2, 0), a(1, 0)-a(0, 1)}));
  }

is_column()

template<typename MatType >

bool casadi::GenericMatrix< MatType >::is_column ( ) const

inline

Extra doc: https://github.com/casadi/casadi/wiki/L_1b5

Definition at line 517 of file generic_matrix.hpp.

{ return sparsity().is_column();}

References casadi::Sparsity::is_column(), and casadi::GenericMatrix< MatType >::sparsity().

Referenced by casadi::Bilin::Bilin(), casadi::DaeBuilderInternal::der(), casadi::DaeBuilderInternal::eq(), casadi::Find::Find(), casadi::MX::get(), casadi::MXNode::get_find(), casadi::MXNode::get_mac(), casadi::Matrix< Scalar >::get_nz(), casadi::MX::get_nz(), casadi::is_slice(), casadi::MX::MX(), casadi::MX::set(), and casadi::MX::vertsplit().

is_dense()

template<typename MatType >

bool casadi::GenericMatrix< MatType >::is_dense ( ) const

inline

Based on the sparsity pattern only: stored numerical zeros still count as nonzeros. Empty matrices are dense.

>>> DM.zeros(2, 2).is_dense(), DM(2, 2).is_dense(), DM(0, 3).is_dense()
(True, False, True)

>> Z = DM.zeros(2, 2);
>> fprintf('%d %d %d\n', Z.is_dense(), DM(2, 2).is_dense(), DM(0, 3).is_dense())
1 0 1

julia> ca.is_dense(ca.DM.zeros(2, 2)), ca.is_dense(ca.DM(2, 2)), ca.is_dense(ca.DM(0, 3))
(true, false, true)

See also

nnz, numel, densify

Extra doc: https://github.com/casadi/casadi/wiki/L_1b0

Definition at line 434 of file generic_matrix.hpp.

{ return sparsity().is_dense();}

References casadi::Sparsity::is_dense(), and casadi::GenericMatrix< MatType >::sparsity().

Referenced by casadi::MXNode::_get_binary(), casadi::GetNonzerosParam::create(), casadi::SetNonzerosParam< Add >::create(), casadi::Matrix< Scalar >::densify(), casadi::MX::densify(), casadi::DaeBuilderInternal::eq(), casadi::Function::generate_in(), casadi::Function::generate_out(), casadi::Matrix< Scalar >::get(), casadi::MX::get(), casadi::MXNode::get_mac(), casadi::is_slice(), casadi::Low::Low(), casadi::MX::MX(), casadi::MX::polyval(), casadi::Matrix< Scalar >::set(), casadi::MX::set(), casadi::MX::set_nz(), casadi::DenseKron::try_create(), casadi::DenseSparseKron::try_create(), casadi::SparseDenseKron::try_create(), casadi::DenseKronContract::try_create(), casadi::DenseSparseKronContract::try_create(), casadi::SparseDenseKronContract::try_create(), casadi::DenseMultiplication::try_create(), and casadi::DenseSparseMultiplication::try_create().

is_empty()

template<typename MatType >

bool casadi::GenericMatrix< MatType >::is_empty ( bool  both = false ) const

inline

With both true, only a 0-by-0 matrix counts as empty.

>>> DM(0, 3).is_empty(), DM(0, 3).is_empty(True), DM(0, 0).is_empty(True)
(True, False, True)
>>> DM(1, 1).is_empty()
False

>> E = DM(0, 3);
>> fprintf('%d %d %d\n', E.is_empty(), E.is_empty(true), DM(0, 0).is_empty(true))
1 0 1
>> DM(1, 1).is_empty()
0

julia> E = ca.DM(0, 3);
julia> ca.is_empty(E), ca.is_empty(E, true), ca.is_empty(ca.DM(0, 0), true)
(true, false, true)
julia> ca.is_empty(ca.DM(1, 1))
false

Extra doc: https://github.com/casadi/casadi/wiki/L_1az

Definition at line 402 of file generic_matrix.hpp.

{ return sparsity().is_empty(both);}

References casadi::Sparsity::is_empty(), and casadi::GenericMatrix< MatType >::sparsity().

Referenced by casadi::activation(), casadi::Call::ad_reverse(), casadi::OptiNode::assert_empty(), casadi::OptiNode::bake(), casadi::MX::binary(), casadi::Call::common_cond(), casadi::DaeBuilderInternal::create(), casadi::DaeBuilderInternal::disp(), casadi::Function::generate_in(), casadi::Function::generate_out(), casadi::MXNode::get_nzadd(), casadi::AmplInterface::init(), casadi::BSpline::jac_cached(), casadi::BSplineParametric::jac_cached(), casadi::MX::project(), casadi::Call::projectArg(), casadi::DaeBuilderInternal::set_init(), and casadi::OptiNode::subject_to().

is_linear()

template<typename MatType >

bool casadi::GenericMatrix< MatType >::is_linear ( const MatType &  expr, const MatType &  var  )

static

Definition at line 5678 of file generic_matrix.hpp.

                                                                                {
    return !any(MatType::which_depends(expr, var, 2, true));
  }

References casadi::any().

is_quadratic()

template<typename MatType >

bool casadi::GenericMatrix< MatType >::is_quadratic ( const MatType &  expr, const MatType &  var  )

static

Definition at line 5683 of file generic_matrix.hpp.

                                                                                   {
    return is_linear(gradient(expr, var), var);
  }

is_row()

template<typename MatType >

bool casadi::GenericMatrix< MatType >::is_row ( ) const

inline

Extra doc: https://github.com/casadi/casadi/wiki/L_1b4

Definition at line 512 of file generic_matrix.hpp.

{ return sparsity().is_row();}

References casadi::Sparsity::is_row(), and casadi::GenericMatrix< MatType >::sparsity().

Referenced by casadi::Matrix< Scalar >::cumsum(), casadi::MX::cumsum(), casadi::MX::get(), casadi::Matrix< Scalar >::get_nz(), and casadi::MX::get_nz().

is_scalar()

template<typename MatType >

bool casadi::GenericMatrix< MatType >::is_scalar

(

bool

scalar_and_dense = false

)

const

Parameters

scalar_and_dense

When true, a 1-by-1 matrix with a structural zero does not count

>>> x = SX.sym("x", Sparsity(1, 1))
>>> x.is_scalar(), x.is_scalar(True), SX.sym("y").is_scalar(True)
(True, False, True)

>> x = SX.sym('x', Sparsity(1, 1));
>> fprintf('%d %d %d\n', x.is_scalar(), x.is_scalar(true), SX.sym('y').is_scalar(true))
1 0 1

julia> x = ca.SX.sym("x", ca.Sparsity(1, 1));
julia> ca.is_scalar(x), ca.is_scalar(x, true), ca.is_scalar(ca.SX.sym("y"), true)
(true, false, true)

Extra doc: https://github.com/casadi/casadi/wiki/L_1b1

Definition at line 5279 of file generic_matrix.hpp.

                                                                    {
    return sparsity().is_scalar(scalar_and_dense);
  }

Referenced by casadi::MXNode::_get_binary(), casadi::BinaryMX< ScX, ScY >::ad_reverse(), casadi::Call::ad_reverse(), casadi::Assertion::Assertion(), casadi::MX::attachAssert(), casadi::MX::binary(), casadi::OptiNode::canon_expr(), casadi::ConstantMX::create(), casadi::Matrix< Scalar >::densify(), casadi::MX::densify(), casadi::MXFunction::export_code_body(), casadi::Matrix< Scalar >::get(), casadi::MXNode::get_binary(), casadi::Matrix< Scalar >::get_nz(), casadi::is_slice(), casadi::MX::mac(), casadi::OptiNode::minimize(), casadi::MX::mldivide(), casadi::MX::mrdivide(), casadi::MX::mtimes(), casadi::MX::MX(), casadi::Call::projectArg(), casadi::qr_block_det(), casadi::Matrix< Scalar >::set(), casadi::MX::set(), casadi::OptiNode::set_linear_scale(), casadi::Matrix< Scalar >::set_nz(), casadi::MX::set_nz(), and casadi::to_slice().

is_square()

template<typename MatType >

bool casadi::GenericMatrix< MatType >::is_square ( ) const

inline

Extra doc: https://github.com/casadi/casadi/wiki/L_1b2

Definition at line 470 of file generic_matrix.hpp.

{ return sparsity().is_square();}

References casadi::Sparsity::is_square(), and casadi::GenericMatrix< MatType >::sparsity().

Referenced by casadi::SymbolicQr::det(), casadi::Determinant::Determinant(), and casadi::MX::trace().

is_tril()

template<typename MatType >

bool casadi::GenericMatrix< MatType >::is_tril ( ) const

inline

Decided on the sparsity pattern alone, see is_triu.

See also

is_triu, tril, tril2symm

Extra doc: https://github.com/casadi/casadi/wiki/L_1b7

Definition at line 560 of file generic_matrix.hpp.

{ return sparsity().is_tril();}

References casadi::Sparsity::is_tril(), and casadi::GenericMatrix< MatType >::sparsity().

Referenced by casadi::MX::solve().

is_triu()

template<typename MatType >

bool casadi::GenericMatrix< MatType >::is_triu ( ) const

inline

Decided on the sparsity pattern alone: all structural nonzeros must lie on or above the diagonal. A dense matrix with numerical zeros below the diagonal is not upper triangular. Also defined for non-square matrices.

>>> DM(Sparsity.upper(3), 1).is_triu(), DM.zeros(2, 2).is_triu(), DM(2, 2).is_triu()
(True, False, True)

>> U = DM(Sparsity.upper(3), 1);
>> fprintf('%d %d %d\n', U.is_triu(), DM.zeros(2, 2).is_triu(), DM(2, 2).is_triu())
1 0 1

julia> U = ca.DM(ca.Sparsity.upper(3), 1);
julia> ca.is_triu(U), ca.is_triu(ca.DM.zeros(2, 2)), ca.is_triu(ca.DM(2, 2))
(true, false, true)

See also

is_tril, triu, triu2symm

Extra doc: https://github.com/casadi/casadi/wiki/L_1b6

Definition at line 551 of file generic_matrix.hpp.

{ return sparsity().is_triu();}

References casadi::Sparsity::is_triu(), and casadi::GenericMatrix< MatType >::sparsity().

Referenced by casadi::MX::solve().

is_vector()

template<typename MatType >

bool casadi::GenericMatrix< MatType >::is_vector ( ) const

inline

True when size1() or size2() is one, so scalars and n-by-1 or 1-by-n empties count. A 0-by-0 matrix does not.

>>> DM(3, 1).is_vector(), DM(1, 3).is_vector(), DM(1, 1).is_vector()
(True, True, True)
>>> DM(3, 3).is_vector(), DM(0, 1).is_vector(), DM(0, 0).is_vector()
(False, True, False)

>> fprintf('%d %d %d\n', DM(3, 1).is_vector(), DM(1, 3).is_vector(), DM(1, 1).is_vector())
1 1 1
>> fprintf('%d %d %d\n', DM(3, 3).is_vector(), DM(0, 1).is_vector(), DM(0, 0).is_vector())
0 1 0

julia> ca.is_vector(ca.DM(3, 1)), ca.is_vector(ca.DM(1, 3)), ca.is_vector(ca.DM(1, 1))
(true, true, true)
julia> ca.is_vector(ca.DM(3, 3)), ca.is_vector(ca.DM(0, 1)), ca.is_vector(ca.DM(0, 0))
(false, true, false)

See also

is_row, is_column

Extra doc: https://github.com/casadi/casadi/wiki/L_1b3

Definition at line 507 of file generic_matrix.hpp.

{ return sparsity().is_vector();}

References casadi::Sparsity::is_vector(), and casadi::GenericMatrix< MatType >::sparsity().

Referenced by casadi::OptiNode::canon_expr(), casadi::BSplineParametric::create(), casadi::GetNonzerosParam::create(), casadi::BSpline::create(), casadi::SetNonzerosParam< Add >::create(), casadi::Function::generate_in(), casadi::Function::generate_out(), casadi::Matrix< Scalar >::get(), casadi::MX::get(), casadi::MXNode::get_find(), casadi::MX::interpn_linear(), casadi::Low::Low(), casadi::MX::norm_2(), casadi::orient_vector(), and casadi::MX::polyval().

linear_coeff()

template<typename MatType >

void casadi::GenericMatrix< MatType >::linear_coeff ( const MatType &  expr, const MatType &  var, MatType &  A, MatType &  b, bool  check  )

static

Definition at line 5699 of file generic_matrix.hpp.

                                              {
    casadi_assert(expr.is_vector(), "'linear_coeff' only defined for vector expressions.");
    if (check)
      casadi_assert(is_linear(expr, var), "'linear_coeff' called on non-linear expression.");
    A = substitute(jacobian(expr, var), var, 0);
    b = vec(substitute(expr, var, 0));
  }

linspace()

template<typename MatType >

MatType casadi::GenericMatrix< MatType >::linspace ( const MatType &  a, const MatType &  b, casadi_int  nsteps  )

static

Definition at line 5312 of file generic_matrix.hpp.

                                                                                                {
    casadi_assert(nsteps>=1, "linspace: nsteps (" + str(nsteps) + ") must be at least 1");
    std::vector<MatType> ret(nsteps);
    ret[0] = a;
    MatType step = (b-a)/static_cast<MatType>(nsteps-1);
 
    for (casadi_int i=1; i<nsteps-1; ++i)
      ret[i] = a + i * step;
 
    ret[nsteps-1] = b;
    return vertcat(ret);
  }

References casadi::str().

nnz()

template<typename MatType >

casadi_int casadi::GenericMatrix< MatType >::nnz

Counts the entries present in the sparsity pattern. Entries that are stored but numerically zero still count; structural zeros (not stored) do not. For a dense matrix this equals numel().

>>> DM.eye(3).nnz(), DM.ones(3, 3).nnz(), DM(3, 3).nnz()
(3, 9, 0)
>>> DM([[1, 0], [0, 2]]).nnz()
4
>>> MX.sym("x", 2, 0).nnz()
0

>> fprintf('%d %d %d\n', DM.eye(3).nnz(), DM.ones(3, 3).nnz(), DM(3, 3).nnz())
3 9 0
>> DM([1 0; 0 2]).nnz()
4
>> MX.sym('x', 2, 0).nnz()
0

julia> ca.nnz(ca.DM.eye(3)), ca.nnz(ca.DM.ones(3, 3)), ca.nnz(ca.DM(3, 3))
(3, 9, 0)
julia> ca.nnz(ca.DM([1 0; 0 2]))
4
julia> ca.nnz(ca.MX.sym("x", 2, 0))
0

See also

numel, nnz_lower, nnz_upper, nnz_diag, sparsity

Extra doc: https://github.com/casadi/casadi/wiki/L_1an

Definition at line 5229 of file generic_matrix.hpp.

                                               {
    return sparsity().nnz();
  }

Referenced by casadi::Constant< Value >::_get_binary(), casadi::OptiNode::bake(), casadi::ConstantMX::create(), casadi::GetNonzerosParam::create(), casadi::SetNonzeros< Add >::create(), casadi::GetNonzeros::create(), casadi::MX::depends_on(), casadi::Diagsplit::Diagsplit(), casadi::Dump::Dump(), casadi::Find::eval(), casadi::Low::eval(), casadi::GetNonzerosParamVector::eval(), casadi::GetNonzerosSliceParam::eval(), casadi::GetNonzerosParamSlice::eval(), casadi::GetNonzerosParamParam::eval(), casadi::HorzRepmat::eval_gen(), casadi::Concat::eval_gen(), casadi::Transpose::eval_gen(), casadi::Find::generate(), casadi::Low::generate(), casadi::Concat::generate(), casadi::GetNonzerosParamVector::generate(), casadi::GetNonzerosSliceParam::generate(), casadi::GetNonzerosParamSlice::generate(), casadi::GetNonzerosParamParam::generate(), casadi::Output::generate(), casadi::HorzRepmat::generate(), casadi::MXNode::get_binary(), casadi::MXNode::get_kron_contract(), casadi::MX::get_nonzeros(), casadi::MX::get_nz(), casadi::Concat::get_nzref(), casadi::HorzRepmat::get_nzref(), casadi::AmplInterface::init(), casadi::SnoptInterface::init(), casadi::SuperscsInterface::init(), casadi::Scpgen::init(), casadi::CplexInterface::init_mem(), casadi::SnoptInterface::init_mem(), casadi::SymbolicQr::linsol_eval_sx(), casadi::Monitor::Monitor(), casadi::mtaylor_recursive(), casadi::MX::polyval(), casadi::MXFunction::print_arg(), casadi::Reshape::Reshape(), casadi::Matrix< Scalar >::set(), casadi::MX::set(), casadi::MX::set_nz(), casadi::SuperscsInterface::solve(), casadi::MX::solve(), casadi::SnoptInterface::solve(), casadi::MXNode::sp_forward(), casadi::Concat::sp_forward(), casadi::Dot::sp_forward(), casadi::MXNode::sp_reverse(), casadi::Concat::sp_reverse(), casadi::Dot::sp_reverse(), casadi::GetNonzerosParam::sp_reverse(), casadi::HorzRepmat::sp_reverse(), casadi::MX::sparsity_cast(), casadi::SparsityCast::SparsityCast(), casadi::OptiNode::subject_to(), casadi::GetNonzerosParamSlice::sz_iw(), casadi::GetNonzerosParamParam::sz_iw(), and casadi::PseudoDenseMultiplication::try_create().

nnz_diag()

template<typename MatType >

casadi_int casadi::GenericMatrix< MatType >::nnz_diag

Also defined for non-square matrices.

>>> DM.ones(3, 3).nnz_diag(), DM.eye(3).nnz_diag(), DM.ones(2, 3).nnz_diag()
(3, 3, 2)

>> A = DM.ones(3, 3); I = DM.eye(3); B = DM.ones(2, 3);
>> fprintf('%d %d %d\n', A.nnz_diag(), I.nnz_diag(), B.nnz_diag())
3 3 2

julia> A = ca.DM.ones(3, 3); I = ca.DM.eye(3); B = ca.DM.ones(2, 3);
julia> ca.nnz_diag(A), ca.nnz_diag(I), ca.nnz_diag(B)
(3, 3, 2)

See also

nnz, nnz_lower, nnz_upper

Extra doc: https://github.com/casadi/casadi/wiki/L_1aq

Definition at line 5244 of file generic_matrix.hpp.

                                                    {
    return sparsity().nnz_diag();
  }

nnz_lower()

template<typename MatType >

casadi_int casadi::GenericMatrix< MatType >::nnz_lower

>>> DM.ones(3, 3).nnz_lower(), DM.eye(3).nnz_lower(), DM.ones(2, 3).nnz_lower()
(6, 3, 3)

>> A = DM.ones(3, 3); I = DM.eye(3); B = DM.ones(2, 3);
>> fprintf('%d %d %d\n', A.nnz_lower(), I.nnz_lower(), B.nnz_lower())
6 3 3

julia> A = ca.DM.ones(3, 3); I = ca.DM.eye(3); B = ca.DM.ones(2, 3);
julia> ca.nnz_lower(A), ca.nnz_lower(I), ca.nnz_lower(B)
(6, 3, 3)

See also

nnz, nnz_upper, nnz_diag

Extra doc: https://github.com/casadi/casadi/wiki/L_1ao

Definition at line 5234 of file generic_matrix.hpp.

                                                     {
    return sparsity().nnz_lower();
  }

nnz_upper()

template<typename MatType >

casadi_int casadi::GenericMatrix< MatType >::nnz_upper

>>> DM.ones(3, 3).nnz_upper(), DM.eye(3).nnz_upper(), DM.ones(2, 3).nnz_upper()
(6, 3, 5)

>> A = DM.ones(3, 3); I = DM.eye(3); B = DM.ones(2, 3);
>> fprintf('%d %d %d\n', A.nnz_upper(), I.nnz_upper(), B.nnz_upper())
6 3 5

julia> A = ca.DM.ones(3, 3); I = ca.DM.eye(3); B = ca.DM.ones(2, 3);
julia> ca.nnz_upper(A), ca.nnz_upper(I), ca.nnz_upper(B)
(6, 3, 5)

See also

nnz, nnz_lower, nnz_diag

Extra doc: https://github.com/casadi/casadi/wiki/L_1ap

Definition at line 5239 of file generic_matrix.hpp.

                                                     {
    return sparsity().nnz_upper();
  }

norm_0_mul()

template<typename MatType >

static casadi_int casadi::GenericMatrix< MatType >::norm_0_mul ( const MatType &  x, const MatType &  y  )

inlinestatic

Definition at line 651 of file generic_matrix.hpp.

                                                                     {
      return Sparsity::norm_0_mul(x.sparsity(), y.sparsity());
    }

References casadi::Sparsity::norm_0_mul().

numel()

template<typename MatType >

casadi_int casadi::GenericMatrix< MatType >::numel

Counts all entries, structural zeros included.

>>> DM.eye(3).numel(), MX.sym("x", 2, 0).numel(), SX.sym("x").numel()
(9, 0, 1)

>> fprintf('%d %d %d\n', DM.eye(3).numel(), MX.sym('x', 2, 0).numel(), SX.sym('x').numel())
9 0 1

julia> ca.numel(ca.DM.eye(3)), ca.numel(ca.MX.sym("x", 2, 0)), ca.numel(ca.SX.sym("x"))
(9, 0, 1)
julia> length(ca.DM.eye(3))
9

See also

nnz, size

Extra doc: https://github.com/casadi/casadi/wiki/L_1ar

Definition at line 5249 of file generic_matrix.hpp.

                                                 {
    return sparsity().numel();
  }

Referenced by casadi::BSpline::BSpline(), casadi::constant_ints(), casadi::BSplineParametric::create(), casadi::GetNonzerosParam::create(), casadi::BSpline::create(), casadi::OptiNode::g_describe(), casadi::Function::generate_in(), casadi::Function::generate_out(), casadi::DaeBuilderInternal::hess_v_v_from_calls(), casadi::init_gen(), casadi::MX::interpn_linear(), casadi::DaeBuilderInternal::jac_vdef_v_from_calls(), casadi::Low::Low(), casadi::orient_vector(), and casadi::KronContract::sz_w().

nz() [1/2]

template<typename MatType >

template<typename K >

NonZeros<MatType, K> casadi::GenericMatrix< MatType >::nz ( const K &  k )

inline

Extra doc: https://github.com/casadi/casadi/wiki/L_1bc

Definition at line 693 of file generic_matrix.hpp.

                                        {
      return NonZeros<MatType, K>(self(), k);
    }

nz() [2/2]

template<typename MatType >

template<typename K >

const MatType casadi::GenericMatrix< MatType >::nz ( const K &  k ) const

inline

Extra doc: https://github.com/casadi/casadi/wiki/L_1bb

Definition at line 683 of file generic_matrix.hpp.

                                       {
      MatType ret;
      self().get_nz(ret, false, k);
      return ret;
    }

Referenced by casadi::SnoptInterface::init(), and casadi::MX::polyval().

ones() [1/3]

template<typename MatType >

static MatType casadi::GenericMatrix< MatType >::ones ( casadi_int  nrow = 1, casadi_int  ncol = 1  )

inlinestatic

ones(sp) sets every structural nonzero of sp to one; other entries stay structurally zero.

>>> DM.ones(2, 3)
DM(
[[1, 1, 1],
 [1, 1, 1]])
>>> DM.ones(Sparsity.diag(2))
DM(
[[1, 00],
 [00, 1]])

>> DM.ones(2, 3)
[[1, 1, 1],
 [1, 1, 1]]
>> DM.ones(Sparsity.diag(2))
[[1, 00],
 [00, 1]]

julia> ca.DM.ones(2, 3)
DM(
[[1, 1, 1],
 [1, 1, 1]])
julia> ca.DM.ones(ca.Sparsity.diag(2))
DM(
[[1, 00],
 [00, 1]])

See also

zeros, Sparsity

Extra doc: https://github.com/casadi/casadi/wiki/L_1di

Definition at line 5206 of file generic_matrix.hpp.

                                                              {
      return ones(Sparsity::dense(nrow, ncol));
    }

References casadi::Sparsity::dense().

Referenced by casadi::OptiNode::bake(), casadi::OptiNode::canon_expr(), casadi::GenericMatrix< MatType >::ones(), and casadi::OptiNode::variable().

ones() [2/3]

template<typename MatType >

static MatType casadi::GenericMatrix< MatType >::ones ( const Sparsity &  sp )

inlinestatic

ones(sp) sets every structural nonzero of sp to one; other entries stay structurally zero.

>>> DM.ones(2, 3)
DM(
[[1, 1, 1],
 [1, 1, 1]])
>>> DM.ones(Sparsity.diag(2))
DM(
[[1, 00],
 [00, 1]])

>> DM.ones(2, 3)
[[1, 1, 1],
 [1, 1, 1]]
>> DM.ones(Sparsity.diag(2))
[[1, 00],
 [00, 1]]

julia> ca.DM.ones(2, 3)
DM(
[[1, 1, 1],
 [1, 1, 1]])
julia> ca.DM.ones(ca.Sparsity.diag(2))
DM(
[[1, 00],
 [00, 1]])

See also

zeros, Sparsity

Extra doc: https://github.com/casadi/casadi/wiki/L_1di

Definition at line 5209 of file generic_matrix.hpp.

{ return MatType(sp, 1, false);}

ones() [3/3]

template<typename MatType >

static MatType casadi::GenericMatrix< MatType >::ones ( const std::pair< casadi_int, casadi_int > &  rc )

inlinestatic

ones(sp) sets every structural nonzero of sp to one; other entries stay structurally zero.

>>> DM.ones(2, 3)
DM(
[[1, 1, 1],
 [1, 1, 1]])
>>> DM.ones(Sparsity.diag(2))
DM(
[[1, 00],
 [00, 1]])

>> DM.ones(2, 3)
[[1, 1, 1],
 [1, 1, 1]]
>> DM.ones(Sparsity.diag(2))
[[1, 00],
 [00, 1]]

julia> ca.DM.ones(2, 3)
DM(
[[1, 1, 1],
 [1, 1, 1]])
julia> ca.DM.ones(ca.Sparsity.diag(2))
DM(
[[1, 00],
 [00, 1]])

See also

zeros, Sparsity

Extra doc: https://github.com/casadi/casadi/wiki/L_1di

Definition at line 5210 of file generic_matrix.hpp.

                                                                   {
      return ones(rc.first, rc.second);
    }

References casadi::GenericMatrix< MatType >::ones().

operator()() [1/4]

template<typename MatType >

template<typename RR >

SubIndex<MatType, RR> casadi::GenericMatrix< MatType >::operator() ( const RR &  rr )

inline

Extra doc: https://github.com/casadi/casadi/wiki/L_1bf

Definition at line 721 of file generic_matrix.hpp.

                                                   {
      return SubIndex<MatType, RR>(self(), rr);
    }

operator()() [2/4]

template<typename MatType >

template<typename RR >

const MatType casadi::GenericMatrix< MatType >::operator() ( const RR &  rr ) const

inline

Extra doc: https://github.com/casadi/casadi/wiki/L_1bd

Definition at line 701 of file generic_matrix.hpp.

                                                 {
      MatType ret;
      self().get(ret, false, rr);
      return ret;
    }

operator()() [3/4]

template<typename MatType >

template<typename RR , typename CC >

SubMatrix<MatType, RR, CC> casadi::GenericMatrix< MatType >::operator() ( const RR &  rr, const CC &  cc  )

inline

Extra doc: https://github.com/casadi/casadi/wiki/L_1bg

Definition at line 729 of file generic_matrix.hpp.

                                                                      {
      return SubMatrix<MatType, RR, CC>(self(), rr, cc);
    }

operator()() [4/4]

template<typename MatType >

template<typename RR , typename CC >

const MatType casadi::GenericMatrix< MatType >::operator() ( const RR &  rr, const CC &  cc  ) const

inline

Extra doc: https://github.com/casadi/casadi/wiki/L_1be

Definition at line 711 of file generic_matrix.hpp.

                                                               {
      MatType ret;
      self().get(ret, false, rr, cc);
      return ret;
    }

quadratic_coeff()

template<typename MatType >

void casadi::GenericMatrix< MatType >::quadratic_coeff ( const MatType &  expr, const MatType &  var, MatType &  A, MatType &  b, MatType &  c, bool  check  )

static

Definition at line 5688 of file generic_matrix.hpp.

                                                          {
    casadi_assert(expr.is_scalar(), "'quadratic_coeff' only defined for scalar expressions.");
    A = hessian(expr, var);
    b = substitute(jacobian(expr, var), var, 0).T();
    if (check)
      casadi_assert(!depends_on(A, var), "'quadratic_coeff' called on non-quadratic expression.");
    c = substitute(expr, var, 0);
  }

repsum()

template<typename MatType >

MatType casadi::GenericMatrix< MatType >::repsum ( const MatType &  x, casadi_int  n, casadi_int  m = 1  )

static

Definition at line 5461 of file generic_matrix.hpp.

                                                                                     {
    casadi_assert(n>0 && x.size1() % n==0,
      "repsum: x.size1() (" + str(x.size1()) + ") must be a multiple of n (" + str(n) + ")");
    casadi_assert(m>0 && x.size2() % m==0,
      "repsum: x.size2() (" + str(x.size2()) + ") must be a multiple of m (" + str(m) + ")");
    std::vector< std::vector< MatType> > s =
      blocksplit(x, x.size1()/n, x.size2()/m);
    MatType sum = 0;
    for (casadi_int i=0;i<s.size();++i) {
      for (casadi_int j=0;j<s[i].size();++j) {
        sum = sum + s[i][j];
      }
    }
    return sum;
  }

References casadi::str(), and casadi::sum().

Referenced by casadi::MXNode::get_repsum().

row() [1/2]

template<typename MatType >

const casadi_int* casadi::GenericMatrix< MatType >::row ( ) const

inline

The pattern is stored in compressed column format: colind has size2()+1 entries, the nonzeros of column j are the entries colind(j) up to colind(j+1) (exclusive), and row(el) is the row index of nonzero el. Without argument, the full vectors are returned. Out-of-range indices raise an error.

>>> x = DM(Sparsity.diag(2), [5, 6])
>>> x.row(), x.colind()
([0, 1], [0, 1, 2])
>>> x.row(1), x.colind(2)
(1, 2)

>> x = DM(Sparsity.diag(2), [5; 6]);
>> x.row(), x.colind()
0 1
0 1 2
>> fprintf('%d %d\n', x.row(1), x.colind(2))
1 2

julia> x = ca.DM(ca.Sparsity.diag(2), [5, 6]);
julia> ca.row(x), ca.colind(x)
([0, 1], [0, 1, 2])
julia> ca.row(x, 1), ca.colind(x, 2)
(1, 2)

Extra doc: https://github.com/casadi/casadi/wiki/L_1b8

Definition at line 605 of file generic_matrix.hpp.

{ return sparsity().row(); }

References casadi::Sparsity::row(), and casadi::GenericMatrix< MatType >::sparsity().

Referenced by casadi::Matrix< Scalar >::densify(), casadi::Transpose::eval_gen(), casadi::MX::set(), casadi::SnoptInterface::solve(), casadi::Transpose::sp_forward(), casadi::Transpose::sp_reverse(), and casadi::SnoptInterface::userfun().

row() [2/2]

template<typename MatType >

casadi_int casadi::GenericMatrix< MatType >::row ( casadi_int  el ) const

inline

The pattern is stored in compressed column format: colind has size2()+1 entries, the nonzeros of column j are the entries colind(j) up to colind(j+1) (exclusive), and row(el) is the row index of nonzero el. Without argument, the full vectors are returned. Out-of-range indices raise an error.

>>> x = DM(Sparsity.diag(2), [5, 6])
>>> x.row(), x.colind()
([0, 1], [0, 1, 2])
>>> x.row(1), x.colind(2)
(1, 2)

>> x = DM(Sparsity.diag(2), [5; 6]);
>> x.row(), x.colind()
0 1
0 1 2
>> fprintf('%d %d\n', x.row(1), x.colind(2))
1 2

julia> x = ca.DM(ca.Sparsity.diag(2), [5, 6]);
julia> ca.row(x), ca.colind(x)
([0, 1], [0, 1, 2])
julia> ca.row(x, 1), ca.colind(x, 2)
(1, 2)

Extra doc: https://github.com/casadi/casadi/wiki/L_1b8

Definition at line 608 of file generic_matrix.hpp.

{ return sparsity().row(el); }

References casadi::Sparsity::row(), and casadi::GenericMatrix< MatType >::sparsity().

rows()

template<typename MatType >

casadi_int casadi::GenericMatrix< MatType >::rows ( ) const

inline

Extra doc: https://github.com/casadi/casadi/wiki/L_1at

Definition at line 283 of file generic_matrix.hpp.

{return size1();}

References casadi::GenericMatrix< MatType >::size1().

size() [1/2]

template<typename MatType >

std::pair< casadi_int, casadi_int > casadi::GenericMatrix< MatType >::size

>>> x = MX.sym("x", 2, 3)
>>> x.size(), x.size(1), x.size(2)
((2, 3), 2, 3)

>> x = MX.sym('x', 2, 3);
>> size(x)
2 3
>> fprintf('%d %d\n', size(x, 1), size(x, 2))
2 3

julia> x = ca.MX.sym("x", 2, 3);
julia> size(x), size(x, 1), size(x, 2)
((2, 3), 2, 3)

See also

size1, size2, numel, dim

Extra doc: https://github.com/casadi/casadi/wiki/L_1ax

Definition at line 5264 of file generic_matrix.hpp.

                                                                     {
    return sparsity().size();
  }

Referenced by casadi::MXNode::_get_binary(), casadi::BinaryMX< ScX, ScY >::ad_reverse(), casadi::OptiNode::bake(), casadi::MX::binary(), casadi::OptiNode::canon_expr(), casadi::Matrix< Scalar >::densify(), casadi::MX::densify(), casadi::MX::erase(), casadi::MXFunction::generate_lifted(), casadi::MXNode::get_binary(), casadi::DaeBuilderInternal::CallIO::hess(), casadi::MX::horzcat(), casadi::init_gen(), casadi::interpn_G(), casadi::MX::interpn_linear(), casadi::DaeBuilderInternal::CallIO::jac(), casadi::MX::project(), casadi::Call::projectArg(), casadi::Matrix< Scalar >::set(), casadi::MX::set(), casadi::OptiNode::set_linear_scale(), casadi::MX::set_nz(), casadi::MXNode::to_matrix(), casadi::MX::unite(), and casadi::MX::vertcat().

size() [2/2]

template<typename MatType >

casadi_int casadi::GenericMatrix< MatType >::size

(

casadi_int

axis

)

const

Parameters

axis	1 for the number of rows, 2 for the number of columns; any other value raises an error

Extra doc: https://github.com/casadi/casadi/wiki/L_1ay

Definition at line 5269 of file generic_matrix.hpp.

                                                               {
    return sparsity().size(axis);
  }

size1()

template<typename MatType >

casadi_int casadi::GenericMatrix< MatType >::size1

>>> x = MX.sym("x", 2, 3)
>>> x.size1(), x.size2()
(2, 3)

>> x = MX.sym('x', 2, 3);
>> fprintf('%d %d\n', x.size1(), x.size2())
2 3

julia> x = ca.MX.sym("x", 2, 3);
julia> ca.size1(x), ca.size2(x)
(2, 3)

See also

size2, size, rows

Extra doc: https://github.com/casadi/casadi/wiki/L_1as

Definition at line 5254 of file generic_matrix.hpp.

                                                 {
    return sparsity().size1();
  }

Referenced by casadi::Constant< Value >::_get_binary(), casadi::SXFunction::ad_reverse(), casadi::MX::binary(), casadi::broadcastable(), casadi::BSplineParametric::BSplineParametric(), casadi::OptiNode::canon_expr(), casadi::BSplineInterpolant::construct_graph(), casadi::Matrix< Scalar >::cumsum(), casadi::Matrix< Scalar >::densify(), casadi::derivative_coeff_mx(), casadi::MX::diagsplit(), casadi::do_inline(), casadi::dplesol(), casadi::DaeBuilderInternal::eq(), casadi::Find::eval(), casadi::DenseTranspose::eval_gen(), casadi::DenseKronContract::eval_kernel(), casadi::Find::generate(), casadi::DenseKron::generate(), casadi::DenseSparseKron::generate(), casadi::SparseDenseKron::generate(), casadi::DenseKronContract::generate(), casadi::SparseDenseKronContract::generate(), casadi::DenseTranspose::generate(), casadi::get_boor(), casadi::MXNode::get_dot(), casadi::MXNode::get_mac(), casadi::MXNode::get_vertsplit(), casadi::SuperscsInterface::init(), casadi::SuperscsInterface::init_mem(), casadi::MX::inv(), casadi::Inverse::Inverse(), casadi::knot_size(), casadi::KronContract::KronContract(), casadi::SymbolicQr::linsol_eval_sx(), casadi::Onnx::load(), casadi::MX::mac(), casadi::Multiplication::Multiplication(), casadi::MX::MX(), casadi::orient_vector(), casadi::MX::pinv(), casadi::Call::projectArg(), casadi::MX::repmat(), casadi::MX::reshape(), casadi::GenericMatrix< MatType >::rows(), casadi::Matrix< Scalar >::set(), casadi::MX::set(), casadi::MX::set_nz(), casadi::simpleIRK(), casadi::Linsol::solve(), casadi::SuperscsInterface::solve(), casadi::Solve< Tr >::Solve(), casadi::DenseTranspose::sp_forward(), casadi::DenseTranspose::sp_reverse(), casadi::MX::sum1(), and casadi::MX::vertsplit().

size2()

template<typename MatType >

casadi_int casadi::GenericMatrix< MatType >::size2

See also

size1, size, columns

Extra doc: https://github.com/casadi/casadi/wiki/L_1au

Definition at line 5259 of file generic_matrix.hpp.

                                                 {
    return sparsity().size2();
  }

Referenced by casadi::Constant< Value >::_get_binary(), casadi::SXFunction::ad_reverse(), casadi::MX::binary(), casadi::broadcastable(), casadi::OptiNode::canon_expr(), casadi::GenericMatrix< MatType >::columns(), casadi::BSplineInterpolant::construct_graph(), casadi::MX::cumsum(), casadi::Matrix< Scalar >::densify(), casadi::MX::diagsplit(), casadi::do_inline(), casadi::DenseTranspose::eval_gen(), casadi::DenseKronContract::eval_kernel(), casadi::DenseKron::generate(), casadi::DenseSparseKron::generate(), casadi::SparseDenseKron::generate(), casadi::DenseKronContract::generate(), casadi::SparseDenseKronContract::generate(), casadi::DenseTranspose::generate(), casadi::get_boor(), casadi::MXNode::get_dot(), casadi::MXNode::get_horzsplit(), casadi::MXNode::get_mac(), casadi::HorzRepsum::HorzRepsum(), casadi::MX::horzsplit(), casadi::CplexInterface::init_mem(), casadi::SnoptInterface::init_mem(), casadi::SuperscsInterface::init_mem(), casadi::Inverse::Inverse(), casadi::KronContract::KronContract(), casadi::Onnx::load(), casadi::MX::mac(), casadi::Multiplication::Multiplication(), casadi::CsparseInterface::nfact(), casadi::orient_vector(), casadi::MX::pinv(), casadi::Call::projectArg(), casadi::MX::repmat(), casadi::MX::reshape(), casadi::Conic::sdp_to_socp_init(), casadi::Matrix< Scalar >::set(), casadi::MX::set(), casadi::MX::set_nz(), casadi::Linsol::solve(), casadi::SuperscsInterface::solve(), casadi::Solve< Tr >::Solve(), casadi::DenseTranspose::sp_forward(), casadi::DenseTranspose::sp_reverse(), casadi::MX::sum2(), and casadi::MX::trace().

skew()

template<typename MatType >

MatType casadi::GenericMatrix< MatType >::skew ( const MatType &  a )

static

Definition at line 5432 of file generic_matrix.hpp.

                                                       {
    casadi_assert(a.is_vector() && (a.size1()==3 || a.size2()==3),
      "skew(a): Expecting 3-vector, got " + a.dim() + ".");
 
    MatType x = a(0);
    MatType y = a(1);
    MatType z = a(2);
    return blockcat(std::vector< std::vector<MatType> >({{0, -z, y}, {z, 0, -x}, {-y, x, 0}}));
  }

sparsity()

template<typename MatType >

const Sparsity & casadi::GenericMatrix< MatType >::sparsity

>>> DM.eye(2).sparsity()
Sparsity(2x2,2nz)
>>> DM.eye(2).sparsity() == Sparsity.diag(2)
True

>> DM.eye(2).sparsity()
2x2,2nz
>> DM.eye(2).sparsity() == Sparsity.diag(2)
1

julia> ca.sparsity(ca.DM.eye(2))
Sparsity(2x2,2nz)
julia> ca.is_equal(ca.sparsity(ca.DM.eye(2)), ca.Sparsity.diag(2))
true

Extra doc: https://github.com/casadi/casadi/wiki/L_1b9

Definition at line 5224 of file generic_matrix.hpp.

                                                         {
    return self().sparsity();
  }

Referenced by casadi::GenericMatrix< MatType >::colind(), casadi::GenericMatrix< MatType >::get_colind(), casadi::GenericMatrix< MatType >::get_row(), casadi::GenericMatrix< MatType >::is_column(), casadi::GenericMatrix< MatType >::is_dense(), casadi::GenericMatrix< MatType >::is_empty(), casadi::GenericMatrix< MatType >::is_row(), casadi::GenericMatrix< MatType >::is_square(), casadi::GenericMatrix< MatType >::is_tril(), casadi::GenericMatrix< MatType >::is_triu(), casadi::GenericMatrix< MatType >::is_vector(), casadi::GenericMatrix< MatType >::row(), and casadi::MX::unite().

sprank()

template<typename MatType >

static casadi_int casadi::GenericMatrix< MatType >::sprank ( const MatType &  x )

inlinestatic

Definition at line 650 of file generic_matrix.hpp.

{ return Sparsity::sprank(x.sparsity());}

References casadi::Sparsity::sprank().

sumsqr()

template<typename MatType >

static MatType casadi::GenericMatrix< MatType >::sumsqr ( const MatType &  x )

inlinestatic

Definition at line 660 of file generic_matrix.hpp.

{ return dot(x, x);}

References casadi::GenericMatrix< MatType >::dot.

sym() [1/7]

template<typename MatType >

static std::vector<MatType > casadi::GenericMatrix< MatType >::sym ( const std::string &  name, casadi_int  nrow, casadi_int  ncol, casadi_int  p  )

inlinestatic

>>> SX.sym("x", 1, 1, 2)
[SX(x0), SX(x1)]

>> v = SX.sym('x', 1, 1, 2);
>> v{1}, v{2}
x0
x1

julia> ca.SX.sym("x", 1, 1, 2)
2-element Vector{SX}:
 SX(x0)
 SX(x1)

Extra doc: https://github.com/casadi/casadi/wiki/L_1de

Definition at line 5063 of file generic_matrix.hpp.

                                       {
      return sym(name, Sparsity::dense(nrow, ncol), p);
    }

References casadi::Sparsity::dense(), and casadi::GenericMatrix< MatType >::sym().

sym() [2/7]

template<typename MatType >

static std::vector<std::vector<MatType> > casadi::GenericMatrix< MatType >::sym ( const std::string &  name, casadi_int  nrow, casadi_int  ncol, casadi_int  p, casadi_int  r  )

inlinestatic

>>> MX.sym("x", 1, 1, 2, 2)
[[MX(x_00), MX(x_01)], [MX(x_10), MX(x_11)]]

>> v = MX.sym('x', 1, 1, 2, 2);
>> numel(v), v{1}{2}, v{2}{1}
2
x_01
x_10

julia> ca.MX.sym("x", 1, 1, 2, 2)
2-element Vector{Vector{MX}}:
 MX[x_00, x_01]
 MX[x_10, x_11]

Extra doc: https://github.com/casadi/casadi/wiki/L_1dg

Definition at line 5107 of file generic_matrix.hpp.

                                                                                               {
      return sym(name, Sparsity::dense(nrow, ncol), p, r);
    }

References casadi::Sparsity::dense(), and casadi::GenericMatrix< MatType >::sym().

sym() [3/7]

template<typename MatType >

static MatType casadi::GenericMatrix< MatType >::sym ( const std::string &  name, casadi_int  nrow = 1, casadi_int  ncol = 1  )

inlinestatic

Creates a new, dense symbol; two symbols with the same name are still different symbols. For SX each entry is a separate scalar symbol named name_k (k the column-major index), while an MX symbol is a single node with the given name. Only SX and MX have symbols; DM.sym raises an error.

Parameters

name	Name used for printing. For SX, a name of the form "[a,b,c]" assigns individual names to the numel() entries.
nrow	Number of rows, default 1
ncol	Number of columns, default 1

>>> SX.sym("x"), MX.sym("x", 2, 3).dim()
(SX(x), '2x3')
>>> SX.sym("x", 2, 2)
SX(
[[x_0, x_2],
 [x_1, x_3]])
>>> SX.sym("[a,b,c]", 3)
SX([a, b, c])
>>> is_equal(SX.sym("x"), SX.sym("x"))
False

>> SX.sym('x'), MX.sym('x', 2, 3).dim()
x
2x3
>> SX.sym('x', 2, 2)
[[x_0, x_2],
 [x_1, x_3]]
>> SX.sym('[a,b,c]', 3)
[a, b, c]
>> is_equal(SX.sym('x'), SX.sym('x'))
0

julia> ca.SX.sym("x"), ca.dim(ca.MX.sym("x", 2, 3))
(x, "2x3")
julia> ca.SX.sym("x", 2, 2)
SX(
[[x_0, x_2],
 [x_1, x_3]])
julia> ca.SX.sym("[a,b,c]", 3)
SX([a, b, c])
julia> isequal(ca.SX.sym("x"), ca.SX.sym("x"))
false

See also

symvar, zeros, ones

Extra doc: https://github.com/casadi/casadi/wiki/L_1da

Definition at line 4948 of file generic_matrix.hpp.

                                                                                    {
      return sym(name, Sparsity::dense(nrow, ncol));
    }

References casadi::Sparsity::dense().

Referenced by casadi::GenericMatrix< MatType >::sym().

sym() [4/7]

template<typename MatType >

static MatType casadi::GenericMatrix< MatType >::sym ( const std::string &  name, const Sparsity &  sp  )

inlinestatic

Only the structural nonzeros of sp become symbolic entries; for SX they are numbered by nonzero index.

>>> SX.sym("p", Sparsity.diag(2))
SX(
[[p_0, 00],
 [00, p_1]])
>>> MX.sym("p", Sparsity.diag(2)).dim(True)
'2x2,2nz'

>> SX.sym('p', Sparsity.diag(2))
[[p_0, 00],
 [00, p_1]]
>> MX.sym('p', Sparsity.diag(2)).dim(true)
2x2,2nz

julia> ca.SX.sym("p", ca.Sparsity.diag(2))
SX(
[[p_0, 00],
 [00, p_1]])
julia> ca.dim(ca.MX.sym("p", ca.Sparsity.diag(2)), true)
"2x2,2nz"

Extra doc: https://github.com/casadi/casadi/wiki/L_1dc

Definition at line 4997 of file generic_matrix.hpp.

                                                                  {
      return MatType::_sym(name, sp);
    }

sym() [5/7]

template<typename MatType >

std::vector< MatType > casadi::GenericMatrix< MatType >::sym ( const std::string &  name, const Sparsity &  sp, casadi_int  p  )

static

The k-th symbol is named name followed by k (no separator).

>>> MX.sym("x", Sparsity.dense(2, 1), 3)
[MX(x0), MX(x1), MX(x2)]

>> v = MX.sym('x', Sparsity.dense(2, 1), 3);
>> numel(v), v{1}, v{3}
3
x0
x2

julia> ca.MX.sym("x", ca.Sparsity.dense(2, 1), 3)
3-element Vector{MX}:
 MX(x0)
 MX(x1)
 MX(x2)

Extra doc: https://github.com/casadi/casadi/wiki/L_1dd

Definition at line 5286 of file generic_matrix.hpp.

                                                                                     {
    std::vector<MatType> ret(p);
    std::stringstream ss;
    for (casadi_int k=0; k<p; ++k) {
      ss.str("");
      ss << name << k;
      ret[k] = sym(ss.str(), sp);
    }
    return ret;
  }

sym() [6/7]

template<typename MatType >

std::vector< std::vector< MatType > > casadi::GenericMatrix< MatType >::sym ( const std::string &  name, const Sparsity &  sp, casadi_int  p, casadi_int  r  )

static

with given sparsity. The symbol at outer index i and inner index k is named name_ik.

Extra doc: https://github.com/casadi/casadi/wiki/L_1df

Definition at line 5299 of file generic_matrix.hpp.

                                                                                {
    std::vector<std::vector<MatType> > ret(r);
    for (casadi_int k=0; k<r; ++k) {
      std::stringstream ss;
      ss << name << "_" << k;
      ret[k] = sym(ss.str(), sp, p);
    }
    return ret;
  }

sym() [7/7]

template<typename MatType >

static MatType casadi::GenericMatrix< MatType >::sym ( const std::string &  name, const std::pair< casadi_int, casadi_int > &  rc  )

inlinestatic

Extra doc: https://github.com/casadi/casadi/wiki/L_1db

Definition at line 4955 of file generic_matrix.hpp.

                                                                                         {
      return sym(name, rc.first, rc.second);
    }

References casadi::GenericMatrix< MatType >::sym().

tril()

template<typename MatType >

static MatType casadi::GenericMatrix< MatType >::tril ( const MatType &  x, bool  includeDiagonal = true  )

inlinestatic

Definition at line 654 of file generic_matrix.hpp.

                                                                     {
      return project(x, Sparsity::tril(x.sparsity(), includeDiagonal));
    }

References casadi::GenericMatrix< MatType >::project, and casadi::Sparsity::tril().

tril2symm()

template<typename MatType >

MatType casadi::GenericMatrix< MatType >::tril2symm ( const MatType &  x )

static

Definition at line 5452 of file generic_matrix.hpp.

                                                            {
    casadi_assert(x.is_square(),
      "Shape error in tril2symm. Expecting square shape but got " + x.dim());
    casadi_assert(x.nnz_upper()-x.nnz_diag()==0,
      "Sparsity error in tril2symm. Found above-diagonal entries in argument: " + x.dim());
    return x +  x.T() - diag(diag(x));
  }

triu()

template<typename MatType >

static MatType casadi::GenericMatrix< MatType >::triu ( const MatType &  x, bool  includeDiagonal = true  )

inlinestatic

Definition at line 657 of file generic_matrix.hpp.

                                                                     {
      return project(x, Sparsity::triu(x.sparsity(), includeDiagonal));
    }

References casadi::GenericMatrix< MatType >::project, and casadi::Sparsity::triu().

triu2symm()

template<typename MatType >

MatType casadi::GenericMatrix< MatType >::triu2symm ( const MatType &  x )

static

Definition at line 5478 of file generic_matrix.hpp.

                                                            {
    casadi_assert(x.is_square(),
      "Shape error in triu2symm. Expecting square shape but got " + x.dim());
    casadi_assert(x.nnz_lower()-x.nnz_diag()==0,
      "Sparsity error in triu2symm. Found below-diagonal entries in argument: " + x.dim());
    return x + x.T() - diag(diag(x));
  }

zeros() [1/3]

template<typename MatType >

static MatType casadi::GenericMatrix< MatType >::zeros ( casadi_int  nrow = 1, casadi_int  ncol = 1  )

inlinestatic

zeros(nrow, ncol) stores nrow*ncol numerical zeros; zeros(sp) stores a zero at every structural nonzero of sp. To get structural zeros instead, construct from a shape, e.g. DM(2, 2).

>>> DM.zeros(2, 2).nnz(), DM.zeros(Sparsity.diag(2)).nnz(), DM(2, 2).nnz()
(4, 2, 0)
>>> MX.zeros(2, 3)
MX(zeros(2x3))

>> Z = DM.zeros(Sparsity.diag(2));
>> fprintf('%d %d %d\n', DM.zeros(2, 2).nnz(), Z.nnz(), DM(2, 2).nnz())
4 2 0
>> MX.zeros(2, 3)
zeros(2x3)

julia> Z = ca.DM.zeros(ca.Sparsity.diag(2));
julia> ca.nnz(ca.DM.zeros(2, 2)), ca.nnz(Z), ca.nnz(ca.DM(2, 2))
(4, 2, 0)
julia> ca.MX.zeros(2, 3)
MX(zeros(2x3))

See also

ones, Sparsity

Extra doc: https://github.com/casadi/casadi/wiki/L_1dh

Examples

misc/all.cc.

Definition at line 5151 of file generic_matrix.hpp.

                                                               {
      return zeros(Sparsity::dense(nrow, ncol));
    }

References casadi::Sparsity::dense().

Referenced by casadi::GetNonzeros::ad_reverse(), casadi::GetNonzerosParamVector::ad_reverse(), casadi::GetNonzerosSliceParam::ad_reverse(), casadi::GetNonzerosParamSlice::ad_reverse(), casadi::GetNonzerosParamParam::ad_reverse(), casadi::HpmpcInterface::blocksparsity(), casadi::HpipmInterface::blocksparsity(), casadi::FatropConicInterface::blocksparsity(), casadi::OptiNode::canon_expr(), casadi::Sparsity::diagsplit(), casadi::FunctionInternal::dm_in(), casadi::FunctionInternal::dm_out(), casadi::Blocksqp::feasibilityRestorationPhase(), casadi::get_boor(), casadi::Expm::get_forward(), casadi::Expm::get_reverse(), casadi::init_gen(), casadi::MX::set(), casadi::OptiNode::variable(), and casadi::GenericMatrix< MatType >::zeros().

zeros() [2/3]

template<typename MatType >

static MatType casadi::GenericMatrix< MatType >::zeros ( const Sparsity &  sp )

inlinestatic

zeros(nrow, ncol) stores nrow*ncol numerical zeros; zeros(sp) stores a zero at every structural nonzero of sp. To get structural zeros instead, construct from a shape, e.g. DM(2, 2).

>>> DM.zeros(2, 2).nnz(), DM.zeros(Sparsity.diag(2)).nnz(), DM(2, 2).nnz()
(4, 2, 0)
>>> MX.zeros(2, 3)
MX(zeros(2x3))

>> Z = DM.zeros(Sparsity.diag(2));
>> fprintf('%d %d %d\n', DM.zeros(2, 2).nnz(), Z.nnz(), DM(2, 2).nnz())
4 2 0
>> MX.zeros(2, 3)
zeros(2x3)

julia> Z = ca.DM.zeros(ca.Sparsity.diag(2));
julia> ca.nnz(ca.DM.zeros(2, 2)), ca.nnz(Z), ca.nnz(ca.DM(2, 2))
(4, 2, 0)
julia> ca.MX.zeros(2, 3)
MX(zeros(2x3))

See also

ones, Sparsity

Extra doc: https://github.com/casadi/casadi/wiki/L_1dh

Definition at line 5154 of file generic_matrix.hpp.

{ return MatType(sp, 0, false);}

zeros() [3/3]

template<typename MatType >

static MatType casadi::GenericMatrix< MatType >::zeros ( const std::pair< casadi_int, casadi_int > &  rc )

inlinestatic

zeros(nrow, ncol) stores nrow*ncol numerical zeros; zeros(sp) stores a zero at every structural nonzero of sp. To get structural zeros instead, construct from a shape, e.g. DM(2, 2).

>>> DM.zeros(2, 2).nnz(), DM.zeros(Sparsity.diag(2)).nnz(), DM(2, 2).nnz()
(4, 2, 0)
>>> MX.zeros(2, 3)
MX(zeros(2x3))

>> Z = DM.zeros(Sparsity.diag(2));
>> fprintf('%d %d %d\n', DM.zeros(2, 2).nnz(), Z.nnz(), DM(2, 2).nnz())
4 2 0
>> MX.zeros(2, 3)
zeros(2x3)

julia> Z = ca.DM.zeros(ca.Sparsity.diag(2));
julia> ca.nnz(ca.DM.zeros(2, 2)), ca.nnz(Z), ca.nnz(ca.DM(2, 2))
(4, 2, 0)
julia> ca.MX.zeros(2, 3)
MX(zeros(2x3))

See also

ones, Sparsity

Extra doc: https://github.com/casadi/casadi/wiki/L_1dh

Definition at line 5155 of file generic_matrix.hpp.

                                                                    {
      return zeros(rc.first, rc.second);
    }

References casadi::GenericMatrix< MatType >::zeros().

---

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

• generic_matrix.hpp