#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 >:

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Collaboration diagram for casadi::GenericMatrix< MatType >:

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Public Member Functions
casadi_int	nnz () const
	Get the number of (structural) non-zero elements. More...

casadi_int	nnz_lower () const
	Get the number of non-zeros in the lower triangular half. More...

casadi_int	nnz_upper () const
	Get the number of non-zeros in the upper triangular half. More...

casadi_int	nnz_diag () const
	Get get the number of non-zeros on the diagonal. More...

casadi_int	numel () const
	Get the number of elements. 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. 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. 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. More...

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

bool	is_empty (bool both=false) const
	Check if the sparsity is empty, i.e. if one of the dimensions is zero. More...

bool	is_dense () const
	Check if the matrix expression is dense. More...

bool	is_scalar (bool scalar_and_dense=false) const
	Check if the matrix expression is scalar. More...

bool	is_square () const
	Check if the matrix expression is square. 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. 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 vector of length p with with matrices. More...

static std::vector< MatType >	sym (const std::string &name, casadi_int nrow, casadi_int ncol, casadi_int p)
	Create a vector of length p with 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 vector of length r of vectors of length p with. 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 vector of length r of vectors of length p. 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-convex. More...

MatType	mrdivide (const MatType &x, const MatType &n)
	Matrix divide (cf. slash '/' in MATLAB) More...

MatType	mldivide (const MatType &x, const MatType &n)
	Matrix divide (cf. backslash '\' in MATLAB) More...

std::vector< MatType >	symvar (const MatType &x)
	Get all symbols contained in the supplied 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 (experimental) More...

MatType	inv_minor (const MatType &A)
	Matrix inverse (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. 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 no overlapping sparsity. 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 variable var with expression expr in multiple expressions. 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. 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. 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. 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)

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)

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())

MatType	transform (const MatType &x, const std::vector< std::vector< GenericType > > &passes, const Dict &opts=Dict())

std::vector< MatType >	transform (const std::vector< MatType > &x, const Dict &opts=Dict())

std::vector< MatType >	transform (const std::vector< MatType > &x, const std::vector< std::vector< GenericType > > &passes, const Dict &opts=Dict())


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

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

Definition at line 198 of file generic_matrix.hpp.

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

casadi::GenericMatrix::sparsity

Sparsity sparsity() const

Get the sparsity pattern.

Definition: generic_matrix.hpp:1320

casadi::Sparsity::colind

const casadi_int * colind() const

Get a reference to the colindex of all column element (see class description)

Definition: sparsity.cpp:168

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

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

Definition at line 201 of file generic_matrix.hpp.

201 { 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 124 of file generic_matrix.hpp.

124 {return size2();}

casadi::GenericMatrix::size2

casadi_int size2() const

Get the second dimension (i.e. number of columns)

Definition: generic_matrix.hpp:1355

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 1421 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 1801 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 "4x5,10nz"

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

Definition at line 1370 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::Inverse::Inverse(), casadi::MX::mac(), casadi::OptiNode::minimize(), casadi::Multiplication::Multiplication(), 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

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

Definition at line 195 of file generic_matrix.hpp.

195 { return sparsity().get_colind(); }

casadi::Sparsity::get_colind

std::vector< casadi_int > get_colind() const

Get the column index for each column.

Definition: sparsity.cpp:364

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

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

Definition at line 194 of file generic_matrix.hpp.

194 { return sparsity().get_row(); }

casadi::Sparsity::get_row

std::vector< casadi_int > get_row() const

Get the row for each non-zero entry.

Definition: sparsity.cpp:372

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 1458 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 1538 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 178 of file generic_matrix.hpp.

178 { return sparsity().is_column();}

casadi::Sparsity::is_column

bool is_column() const

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

Definition: sparsity.cpp:285

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::Matrix< Scalar >::get(), casadi::MX::get(), casadi::MXNode::get_find(), casadi::MXNode::get_mac(), casadi::MX::get_nz(), casadi::is_slice(), casadi::MX::MX(), casadi::MX::polyval(), casadi::MX::set(), and casadi::MX::vertsplit().

◆ is_dense()

template<typename MatType >

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

inline

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

Definition at line 153 of file generic_matrix.hpp.

153 { return sparsity().is_dense();}

casadi::Sparsity::is_dense

bool is_dense() const

Is dense?

Definition: sparsity.cpp:273

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

Referenced by casadi::Matrix< double >::__nonzero__(), 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::Matrix< Scalar >::set_nz(), 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

(or optionally both dimensions)

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

Definition at line 148 of file generic_matrix.hpp.

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

casadi::Sparsity::is_empty

bool is_empty(bool both=false) const

Check if the sparsity is empty.

Definition: sparsity.cpp:144

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

Referenced by 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 1770 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 1775 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 173 of file generic_matrix.hpp.

173 { return sparsity().is_row();}

casadi::Sparsity::is_row

bool is_row() const

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

Definition: sparsity.cpp:281

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

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

◆ is_scalar()

template<typename MatType >

bool casadi::GenericMatrix< MatType >::is_scalar ( bool scalar_and_dense = false ) const

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

Definition at line 1375 of file generic_matrix.hpp.

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

Referenced by casadi::Matrix< double >::__nonzero__(), casadi::MXNode::_get_binary(), casadi::BinaryMX< ScX, ScY >::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::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 163 of file generic_matrix.hpp.

163 { return sparsity().is_square();}

casadi::Sparsity::is_square

bool is_square() const

Is square?

Definition: sparsity.cpp:293

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

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

Definition at line 188 of file generic_matrix.hpp.

188 { return sparsity().is_tril();}

casadi::Sparsity::is_tril

bool is_tril(bool strictly=false) const

Is lower triangular?

Definition: sparsity.cpp:321

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

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

Definition at line 183 of file generic_matrix.hpp.

183 { return sparsity().is_triu();}

casadi::Sparsity::is_triu

bool is_triu(bool strictly=false) const

Is upper triangular?

Definition: sparsity.cpp:325

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

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

Definition at line 168 of file generic_matrix.hpp.

168 { return sparsity().is_vector();}

casadi::Sparsity::is_vector

bool is_vector() const

Check if the pattern is a row or column vector.

Definition: sparsity.cpp:289

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(), and casadi::MX::norm_2().

◆ 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 1791 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 1408 of file generic_matrix.hpp.

                                                                                                 {
     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);
   }

◆ nnz()

template<typename MatType >

casadi_int casadi::GenericMatrix< MatType >::nnz

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

Definition at line 1325 of file generic_matrix.hpp.

                                                {
     return sparsity().nnz();
   }

◆ nnz_diag()

template<typename MatType >

casadi_int casadi::GenericMatrix< MatType >::nnz_diag

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

Definition at line 1340 of file generic_matrix.hpp.

                                                     {
     return sparsity().nnz_diag();
   }

◆ nnz_lower()

template<typename MatType >

casadi_int casadi::GenericMatrix< MatType >::nnz_lower

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

Definition at line 1330 of file generic_matrix.hpp.

                                                      {
     return sparsity().nnz_lower();
   }

◆ nnz_upper()

template<typename MatType >

casadi_int casadi::GenericMatrix< MatType >::nnz_upper

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

Definition at line 1335 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 216 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

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

Definition at line 1345 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::KronContract::sz_w(), and casadi::OptiNode::x_describe().

◆ 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 258 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 248 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

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

Definition at line 1302 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

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

Definition at line 1305 of file generic_matrix.hpp.

1305 { 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

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

Definition at line 1306 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 286 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 266 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 294 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 276 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 1780 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 1556 of file generic_matrix.hpp.

                                                                                      {
     casadi_assert_dev(x.size1() % n==0);
     casadi_assert_dev(x.size2() % m==0);
     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::sum().

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

◆ row() [1/2]

template<typename MatType >

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

inline

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

Definition at line 197 of file generic_matrix.hpp.

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

casadi::Sparsity::row

const casadi_int * row() const

Get a reference to row-vector,.

Definition: sparsity.cpp:164

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

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

Definition at line 200 of file generic_matrix.hpp.

200 { 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 114 of file generic_matrix.hpp.

114 {return size1();}

casadi::GenericMatrix::size1

casadi_int size1() const

Get the first dimension (i.e. number of rows)

Definition: generic_matrix.hpp:1350

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

◆ size() [1/2]

template<typename MatType >

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

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

Definition at line 1360 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::Matrix< Scalar >::set_nz(), 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

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

Definition at line 1365 of file generic_matrix.hpp.

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

◆ size1()

template<typename MatType >

casadi_int casadi::GenericMatrix< MatType >::size1

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

Definition at line 1350 of file generic_matrix.hpp.

                                                  {
     return sparsity().size1();
   }

Referenced by casadi::Constant< Value >::_get_binary(), casadi::SXFunction::ad_reverse(), casadi::MX::binary(), 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::OptiNode::parameter(), casadi::MX::pinv(), casadi::Call::projectArg(), casadi::MX::repmat(), casadi::MX::reshape(), casadi::GenericMatrix< MatType >::rows(), casadi::Matrix< Scalar >::set(), casadi::MX::set(), casadi::Matrix< Scalar >::set_nz(), 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(), casadi::OptiNode::variable(), and casadi::MX::vertsplit().

◆ size2()

template<typename MatType >

casadi_int casadi::GenericMatrix< MatType >::size2

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

Definition at line 1355 of file generic_matrix.hpp.

                                                  {
     return sparsity().size2();
   }

Referenced by casadi::Constant< Value >::_get_binary(), casadi::SXFunction::ad_reverse(), casadi::MX::binary(), casadi::OptiNode::canon_expr(), casadi::GenericMatrix< MatType >::columns(), casadi::BSplineInterpolant::construct_graph(), casadi::Matrix< Scalar >::cumsum(), 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::OptiNode::parameter(), 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::Matrix< Scalar >::set_nz(), 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(), casadi::MX::trace(), and casadi::OptiNode::variable().

◆ skew()

template<typename MatType >

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

static

Definition at line 1527 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

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

Definition at line 1320 of file generic_matrix.hpp.

                                                          {
     return self().sparsity();
   }

◆ sprank()

template<typename MatType >

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

inlinestatic

Definition at line 215 of file generic_matrix.hpp.

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

casadi::Sparsity::sprank

static casadi_int sprank(const Sparsity &x)

Enlarge matrix.

Definition: sparsity.cpp:1728

References casadi::Sparsity::sprank().

◆ sumsqr()

template<typename MatType >

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

inlinestatic

Definition at line 225 of file generic_matrix.hpp.

225 { return dot(x, x);}

casadi::GenericMatrix::dot

friend MatType dot(const MatType &x, const MatType &y)

Inner product of two matrices.

Definition: generic_matrix.hpp:573

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

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

Definition at line 1261 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

with nrow-by-ncol symbolic primitives

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

Definition at line 1280 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

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

Definition at line 1233 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

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

Definition at line 1247 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

with symbolic primitives of given sparsity

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

Definition at line 1382 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

symbolic primitives with given sparsity

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

Definition at line 1395 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 1240 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 219 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 1547 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 222 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 1571 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

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

Examples: misc/all.cc.

Definition at line 1289 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

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

Definition at line 1292 of file generic_matrix.hpp.

1292 { 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

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

Definition at line 1293 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

Detailed Description

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

Public Member Functions

Static Public Member Functions

Friends

Member Function Documentation

◆ colind() [1/2]

◆ colind() [2/2]

◆ columns()

◆ cross()

◆ diff()

◆ dim()

◆ get_colind()

◆ get_row()

◆ interp1d()

◆ inv_skew()

◆ is_column()

◆ is_dense()

◆ is_empty()

◆ is_linear()

◆ is_quadratic()

◆ is_row()

◆ is_scalar()

◆ is_square()

◆ is_tril()

◆ is_triu()

◆ is_vector()

◆ linear_coeff()

◆ linspace()

◆ nnz()

◆ nnz_diag()

◆ nnz_lower()

◆ nnz_upper()

◆ norm_0_mul()

◆ numel()

◆ nz() [1/2]

◆ nz() [2/2]

◆ ones() [1/3]

◆ ones() [2/3]

◆ ones() [3/3]

◆ operator()() [1/4]

◆ operator()() [2/4]

◆ operator()() [3/4]

◆ operator()() [4/4]

◆ quadratic_coeff()

◆ repsum()

◆ row() [1/2]

◆ row() [2/2]

◆ rows()

◆ size() [1/2]

◆ size() [2/2]

◆ size1()

◆ size2()

◆ skew()

◆ sparsity()

◆ sprank()

◆ sumsqr()

◆ sym() [1/7]

◆ sym() [2/7]

◆ sym() [3/7]

◆ sym() [4/7]

◆ sym() [5/7]

◆ sym() [6/7]

◆ sym() [7/7]

◆ tril()

◆ tril2symm()

◆ triu()

◆ triu2symm()

◆ zeros() [1/3]

◆ zeros() [2/3]

◆ zeros() [3/3]

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