casadi::Matrix< Scalar > Class Template Reference

Sparse matrix class. SX and DM are specializations. More...

#include <matrix_decl.hpp>

Detailed Description

template<typename Scalar>
class casadi::Matrix< Scalar >

General sparse matrix class that 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.
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.
Matrix<Scalar> is polymorphic with a std::vector<Scalar> that contain all non-identical-zero elements.
The sparsity can be accessed with Sparsity& sparsity()
SX holds symbolic scalar entries (SXElem), DM holds doubles. A structural zero prints as 00, a numerical zero as 0. The structural nonzeros are available as a flat column-major vector with nonzeros().

>>> A = DM([[1, 2], [3, 4]])
>>> A.sparsity().dim(), A.nonzeros()
('2x2', [1.0, 3.0, 2.0, 4.0])
>>> S = DM(Sparsity.diag(2))
>>> S
DM(
[[1, 00],
 [00, 1]])
>>> S.nnz(), S.numel()
(2, 4)

>> A = DM([1 2; 3 4]);
>> A.sparsity().dim(), A.nonzeros()
2x2
1 3 2 4
>> S = DM(Sparsity.diag(2));
>> S
[[1, 00],
 [00, 1]]
>> fprintf('%d %d\n', S.nnz(), S.numel())
2 4

julia> A = ca.DM([1 2; 3 4]);
julia> ca.dim(ca.sparsity(A)), ca.nonzeros(A)
("2x2", [1.0, 3.0, 2.0, 4.0])
julia> S = ca.DM(ca.Sparsity.diag(2))
DM(
[[1, 00],
 [00, 1]])
julia> ca.nnz(S), ca.numel(S)
(2, 4)

Author

Joel Andersson

Date

2010-2014

Extra doc: https://github.com/casadi/casadi/wiki/L_18e

Definition at line 143 of file matrix_decl.hpp.

Inheritance diagram for casadi::Matrix< Scalar >:

Public Member Functions
	Matrix ()
	Empty 0-by-0 matrix. More...
	Matrix (const Matrix< Scalar > &m)
	Copy constructor: the copy has its own sparsity pattern and nonzeros. More...
	Matrix (casadi_int nrow, casadi_int ncol)
	Create a matrix of the given shape with all structural zeros (no nonzeros) More...
	Matrix (const Sparsity &sp)
	Create a matrix with the given sparsity pattern and all nonzeros equal to one. More...
	Matrix (const Sparsity &sp, const Matrix< Scalar > &d)
	Create a matrix with a given sparsity pattern and given nonzeros. More...
	Matrix (double val)
	Dense 1-by-1 matrix holding a number; enables implicit conversion from a numeric type. More...
	Matrix (const std::vector< std::vector< double > > &m)
	Dense matrix from a list of rows. More...
template<typename A >
	Matrix (const std::vector< A > &x)
	Dense column vector from a flat list of numbers. More...
template<typename A >
	Matrix (const Matrix< A > &x)
	Create a matrix from another matrix with a different entry type. More...
bool	has_nz (casadi_int rr, casadi_int cc) const
	Check whether element (rr, cc) is a structural nonzero. More...
bool	__nonzero__ () const
	Truth value of a 1-by-1 matrix (Python: bool(x)) More...
Matrix< Scalar >	operator+ () const
Matrix< Scalar >	operator- () const
Matrix< Scalar >	printme (const Matrix< Scalar > &y) const
Matrix< Scalar >	T () const
	Transpose the matrix. More...
void	print_split (std::vector< std::string > &nz, std::vector< std::string > &inter) const
	String representation of each nonzero and of the shared subexpressions. More...
void	disp (std::ostream &stream, bool more=false) const
	Print a representation of the object to a stream. More...
std::string	get_str (bool more=false) const
	Get the string representation that disp prints. More...
void	print_scalar (std::ostream &stream) const
	Print a 1-by-1 matrix as a bare number or expression. More...
void	print_vector (std::ostream &stream, bool truncate=true) const
	Print a column vector as [a, b, ...], structural zeros as 00. More...
void	print_dense (std::ostream &stream, bool truncate=true) const
	Print as a dense matrix, one row per line, structural zeros as 00. More...
void	print_sparse (std::ostream &stream, bool truncate=true) const
	Print as a list of (row, col) -> value triplets, column-major order. More...
void	clear ()
	Reset to an empty 0-by-0 matrix, in place. More...
void	resize (casadi_int nrow, casadi_int ncol)
	Change the shape in place, keeping nonzeros that remain inside the new bounds. More...
void	reserve (casadi_int nnz)
	Reserve storage for the given number of nonzeros (performance hint, no visible effect) More...
void	reserve (casadi_int nnz, casadi_int ncol)
void	erase (const std::vector< casadi_int > &rr, const std::vector< casadi_int > &cc, bool ind1=false)
	Erase the block at the given rows and columns, leaving structural zeros. More...
void	erase (const std::vector< casadi_int > &rr, bool ind1=false)
	Erase the elements at the given linear indices, leaving structural zeros. More...
void	remove (const std::vector< casadi_int > &rr, const std::vector< casadi_int > &cc)
	Delete rows and columns, shrinking the matrix in place. More...
void	enlarge (casadi_int nrow, casadi_int ncol, const std::vector< casadi_int > &rr, const std::vector< casadi_int > &cc, bool ind1=false)
	Enlarge the matrix in place, moving the existing rows and columns to new positions. More...
Sparsity	get_sparsity () const
	Get the sparsity pattern (Python: sparsity()) More...
Matrix< Scalar >	get_output (casadi_int oind) const
	Get an output. More...
casadi_int	element_hash () const
	Hash of the node of a 1-by-1 SX expression. More...
bool	is_regular () const
	Check that no entry is nan, inf or -inf. More...
bool	is_smooth () const
	Check whether an SX expression contains only smooth operations. More...
bool	is_leaf () const
	Check if SX is a leaf of the SX graph. More...
bool	is_commutative () const
	Check whether a binary SX is commutative. More...
bool	is_symbolic () const
	Check if symbolic (Dense) More...
bool	is_valid_input () const
	Check if matrix can be used to define function inputs. More...
bool	is_constant () const
	Check if every entry is a numerical constant (no symbols) More...
bool	is_call () const
	Check if function call. More...
bool	is_output () const
	Check if evaluation output. More...
bool	has_output () const
	Check if a multiple output node. More...
casadi_int	which_output () const
	Get the index of evaluation output - only valid when is_output() is true. More...
Function	which_function () const
	Get function - only valid when is_call() is true. More...
bool	is_integer () const
	Check if the matrix is integer-valued. More...
bool	is_zero () const
	check if the matrix is 0 (note that false negative answers are possible) More...
bool	is_one () const
	check if the matrix is 1 (note that false negative answers are possible) More...
bool	is_minus_one () const
	check if the matrix is -1 (note that false negative answers are possible) More...
bool	is_half () const
	check if the matrix is 0.5 (note that false negative answers are possible) More...
bool	is_value (double val) const
	check if the matrix is value More...
bool	is_inf () const
	check if the matrix is inf (note that false negative answers are possible) More...
bool	is_minus_inf () const
	check if the matrix is -inf (note that false negative answers are possible) More...
bool	is_nonnegative () const
	check if the matrix is not negative More...
bool	is_eye () const
	check if the matrix is an identity matrix (note that false negative answers More...
casadi_int	op () const
	Get operation type. More...
bool	is_op (casadi_int op) const
	Is it a certain operation. More...
bool	has_zeros () const
	Check if any structural nonzero is known to be numerically zero. More...
std::vector< Scalar >	get_nonzeros () const
	Get all structural nonzeros as a flat list in column-major order (Python: nonzeros()) More...
std::vector< Scalar >	get_elements () const
	Get all elements as a flat list in column-major order (Python: elements()) More...
	operator double () const
	Conversion of a 1-by-1 matrix to a double (Python: float(x)) More...
	operator casadi_int () const
	Conversion of a 1-by-1 matrix to an integer (Python: int(x)), truncating. More...
std::string	name () const
	Name of a 1-by-1 symbolic SX primitive. More...
Matrix< Scalar >	dep (casadi_int ch=0) const
	Get operand ch of a 1-by-1 SX expression. More...
casadi_int	n_dep () const
	Number of operands of a 1-by-1 SX expression (0 for symbols and constants) More...
void	export_code (const std::string &lang, std::ostream &stream=casadi::uout(), const Dict &options=Dict()) const
	Export matrix in specific language. More...
Dict	info () const
	Dictionary with the sparsity pattern and the nonzeros (DM only) More...
std::string	serialize () const
	Serialize to a string. More...
void	serialize (SerializingStream &s) const
	Serialize an object. More...
void	to_file (const std::string &filename, const std::string &format="") const
	Write a numerical matrix to a text file (DM only) More...
template<typename Scalar >
	Matrix (const std::vector< Scalar > &x)
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...
void	get (Matrix< Scalar > &m, bool ind1, const Slice &rr) const
	Get elements by a single (linear) index. More...
void	get (Matrix< Scalar > &m, bool ind1, const Matrix< casadi_int > &rr) const
	Get elements by a single (linear) index. More...
void	get (Matrix< Scalar > &m, bool ind1, const Sparsity &sp) const
	Get elements by a single (linear) index. More...
void	get (Matrix< Scalar > &m, bool ind1, const Slice &rr, const Slice &cc) const
	Get a submatrix by row and column indices. More...
void	get (Matrix< Scalar > &m, bool ind1, const Slice &rr, const Matrix< casadi_int > &cc) const
	Get a submatrix by row and column indices. More...
void	get (Matrix< Scalar > &m, bool ind1, const Matrix< casadi_int > &rr, const Slice &cc) const
	Get a submatrix by row and column indices. More...
void	get (Matrix< Scalar > &m, bool ind1, const Matrix< casadi_int > &rr, const Matrix< casadi_int > &cc) const
	Get a submatrix by row and column indices. More...
void	set (const Matrix< Scalar > &m, bool ind1, const Slice &rr)
	Assign elements by a single (linear) index. More...
void	set (const Matrix< Scalar > &m, bool ind1, const Matrix< casadi_int > &rr)
	Assign elements by a single (linear) index. More...
void	set (const Matrix< Scalar > &m, bool ind1, const Sparsity &sp)
	Assign elements by a single (linear) index. More...
void	set (const Matrix< Scalar > &m, bool ind1, const Slice &rr, const Slice &cc)
	Assign a submatrix by row and column indices. More...
void	set (const Matrix< Scalar > &m, bool ind1, const Slice &rr, const Matrix< casadi_int > &cc)
	Assign a submatrix by row and column indices. More...
void	set (const Matrix< Scalar > &m, bool ind1, const Matrix< casadi_int > &rr, const Slice &cc)
	Assign a submatrix by row and column indices. More...
void	set (const Matrix< Scalar > &m, bool ind1, const Matrix< casadi_int > &rr, const Matrix< casadi_int > &cc)
	Assign a submatrix by row and column indices. More...
void	get_nz (Matrix< Scalar > &m, bool ind1, const Slice &k) const
	Get structural nonzeros by their position in the nonzero storage. More...
void	get_nz (Matrix< Scalar > &m, bool ind1, const Matrix< casadi_int > &k) const
	Get structural nonzeros by their position in the nonzero storage. More...
void	set_nz (const Matrix< Scalar > &m, bool ind1, const Slice &k)
	Assign structural nonzeros by their position in the nonzero storage. More...
void	set_nz (const Matrix< Scalar > &m, bool ind1, const Matrix< casadi_int > &k)
	Assign structural nonzeros by their position in the nonzero storage. 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...
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 void	set_max_depth (casadi_int eq_depth=1)
	Set the depth to which SX subexpressions are compared during simplification. More...
static casadi_int	get_max_depth ()
	Get the depth to which SX subexpressions are compared during simplification. More...
static std::vector< Matrix< Scalar > >	get_input (const Function &f)
	Get the symbolic input expressions of an SX Function. More...
static std::vector< Matrix< Scalar > >	get_free (const Function &f)
	Get the free symbols of an SX Function. More...
static std::string	type_name ()
	Name of the class: "DM" or "SX". More...
static Matrix< Scalar >	eye (casadi_int n)
	Create an n-by-n identity matrix. More...
static void	set_precision (casadi_int precision)
	Set the precision, field width and scientific flag used when printing nonzeros. More...
static void	set_width (casadi_int width)
static void	set_scientific (bool scientific)
static casadi_int	get_precision ()
	Get the precision, field width and scientific flag used when printing nonzeros. More...
static casadi_int	get_width ()
static bool	get_scientific ()
static void	rng (casadi_int seed)
	Seed the random number generator used by rand. More...
static Matrix< Scalar >	deserialize (std::istream &stream)
	Build a matrix from a serialization stream. More...
static Matrix< Scalar >	deserialize (const std::string &s)
	Build a matrix from a string produced by serialize. More...
static Matrix< Scalar >	deserialize (DeserializingStream &s)
static Matrix< double >	from_file (const std::string &filename, const std::string &format_hint="")
	Read a numerical matrix from a text file written by to_file (DM only) More...
static Matrix< Scalar >	logsumexp (const Matrix< Scalar > &x)
static Matrix< Scalar >	triplet (const std::vector< casadi_int > &row, const std::vector< casadi_int > &col, const Matrix< Scalar > &d)
	Construct a sparse matrix from triplet form (row indices, column indices, values) More...
static Matrix< Scalar >	triplet (const std::vector< casadi_int > &row, const std::vector< casadi_int > &col, const Matrix< Scalar > &d, casadi_int nrow, casadi_int ncol)
	Construct a sparse matrix from triplet form (row indices, column indices, values) More...
static Matrix< Scalar >	triplet (const std::vector< casadi_int > &row, const std::vector< casadi_int > &col, const Matrix< Scalar > &d, const std::pair< casadi_int, casadi_int > &rc)
	Construct a sparse matrix from triplet form (row indices, column indices, values) More...
static Matrix< Scalar >	inf (const Sparsity &sp)
	Create a matrix with every nonzero equal to +inf. More...
static Matrix< Scalar >	inf (casadi_int nrow=1, casadi_int ncol=1)
	Create a matrix with every nonzero equal to +inf. More...
static Matrix< Scalar >	inf (const std::pair< casadi_int, casadi_int > &rc)
	Create a matrix with every nonzero equal to +inf. More...
static Matrix< Scalar >	nan (const Sparsity &sp)
	Create a matrix with every nonzero equal to nan. More...
static Matrix< Scalar >	nan (casadi_int nrow=1, casadi_int ncol=1)
	Create a matrix with every nonzero equal to nan. More...
static Matrix< Scalar >	nan (const std::pair< casadi_int, casadi_int > &rc)
	Create a matrix with every nonzero equal to nan. More...
static Matrix< Scalar >	rand (casadi_int nrow=1, casadi_int ncol=1)
	Create a matrix with uniformly distributed random numbers in [0, 1) More...
static Matrix< Scalar >	rand (const Sparsity &sp)
	Create a matrix with uniformly distributed random numbers in [0, 1) More...
static Matrix< Scalar >	rand (const std::pair< casadi_int, casadi_int > &rc)
	Create a matrix with uniformly distributed random numbers in [0, 1) More...
static Matrix< Scalar >	mpower (const Matrix< Scalar > &x, const Matrix< Scalar > &y)
static Matrix< Scalar >	soc (const Matrix< Scalar > &x, const Matrix< Scalar > &y)
static Matrix< Scalar >	linearize (const Matrix< Scalar > &f, const Matrix< Scalar > &x, const Matrix< Scalar > &x0, const Dict &opts=Dict())
static Matrix< Scalar >	gradient (const Matrix< Scalar > &ex, const Matrix< Scalar > &arg, const Dict &opts=Dict())
static Matrix< Scalar >	tangent (const Matrix< Scalar > &ex, const Matrix< Scalar > &arg, const Dict &opts=Dict())
static Matrix< Scalar >	jtimes (const Matrix< Scalar > &ex, const Matrix< Scalar > &arg, const Matrix< Scalar > &v, bool tr=false, const Dict &opts=Dict())
static Matrix< Scalar >	bilin (const Matrix< Scalar > &A, const Matrix< Scalar > &x, const Matrix< Scalar > &y)
	Calculate bilinear/quadratic form x^T A y. More...
static Matrix< Scalar >	rank1 (const Matrix< Scalar > &A, const Matrix< Scalar > &alpha, const Matrix< Scalar > &x, const Matrix< Scalar > &y)
	Make a rank-1 update to a matrix A. More...
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 Matrix< Scalar >	sym (const std::string &name, casadi_int nrow=1, casadi_int ncol=1)
	Create an nrow-by-ncol symbolic primitive. More...
static Matrix< Scalar >	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 Matrix< Scalar >	sym (const std::string &name, const Sparsity &sp)
	Create symbolic primitive with a given sparsity pattern. More...
static std::vector< Matrix< Scalar > >	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< Matrix< Scalar > >	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< Matrix< Scalar > > >	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< Matrix< Scalar > > >	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 Matrix< Scalar >	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 Matrix< Scalar >	zeros (const Sparsity &sp)
	Create a dense matrix or a matrix with specified sparsity with all entries zero. More...
static Matrix< Scalar >	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 Matrix< Scalar >	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 Matrix< Scalar >	ones (const Sparsity &sp)
	Create a dense matrix or a matrix with specified sparsity with all entries one. More...
static Matrix< Scalar >	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
Matrix< Scalar >	adj (const Matrix< Scalar > &A)
	Adjugate (classical adjoint) of a square matrix. More...
Matrix< Scalar >	minor (const Matrix< Scalar > &x, casadi_int i, casadi_int j)
	Minor of a square matrix: determinant with one column and one row removed. More...
Matrix< Scalar >	cofactor (const Matrix< Scalar > &x, casadi_int i, casadi_int j)
	Cofactor of a square matrix: (-1)^(i+j) times minor(x, i, j) More...
void	qr (const Matrix< Scalar > &A, Matrix< Scalar > &Q, Matrix< Scalar > &R)
	Dense QR factorization using the modified Gram-Schmidt algorithm. More...
void	qr_sparse (const Matrix< Scalar > &A, Matrix< Scalar > &V, Matrix< Scalar > &R, Matrix< Scalar > &beta, std::vector< casadi_int > &prinv, std::vector< casadi_int > &pc, bool amd=true)
	Sparse direct QR factorization with Householder reflections. More...
Matrix< Scalar >	qr_solve (const Matrix< Scalar > &b, const Matrix< Scalar > &v, const Matrix< Scalar > &r, const Matrix< Scalar > &beta, const std::vector< casadi_int > &prinv, const std::vector< casadi_int > &pc, bool tr=false)
	Solve A*x = b (or A^T*x = b) with the factors returned by qr_sparse. More...
Matrix< Scalar >	chol (const Matrix< Scalar > &A)
	Cholesky factorization of a symmetric positive definite matrix. More...
void	ldl (const Matrix< Scalar > &A, Matrix< Scalar > &D, Matrix< Scalar > &LT, std::vector< casadi_int > &p, bool amd=true)
	Sparse LDL^T factorization of a symmetric matrix. More...
Matrix< Scalar >	ldl_solve (const Matrix< Scalar > &b, const Matrix< Scalar > &D, const Matrix< Scalar > &LT, const std::vector< casadi_int > &p)
	Solve A*x = b with the factors returned by ldl. More...
Matrix< Scalar >	any (const Matrix< Scalar > &x)
	True if any entry equals one. More...
Matrix< Scalar >	all (const Matrix< Scalar > &x)
	True if every entry equals one. More...
Matrix< Scalar >	norm_inf_mul (const Matrix< Scalar > &x, const Matrix< Scalar > &y)
	Infinity norm of a matrix product, without forming the product. More...
Matrix< Scalar >	sparsify (const Matrix< Scalar > &A, double tol=0)
	Make a matrix sparse by turning numerical zeros into structural zeros. More...
void	expand (const Matrix< Scalar > &ex, Matrix< Scalar > &weights, Matrix< Scalar > &terms)
	Expand a scalar SX expression as a weighted sum of terms with constant weights. More...
Matrix< Scalar >	pw_const (const Matrix< Scalar > &t, const Matrix< Scalar > &tval, const Matrix< Scalar > &val)
	Piecewise constant function of a scalar symbolic variable. More...
Matrix< Scalar >	pw_lin (const Matrix< Scalar > &t, const Matrix< Scalar > &tval, const Matrix< Scalar > &val)
	Piecewise linear function of a scalar symbolic variable. More...
Matrix< Scalar >	heaviside (const Matrix< Scalar > &x)
	Heaviside step function, elementwise. More...
Matrix< Scalar >	rectangle (const Matrix< Scalar > &x)
	Rectangle (gate, pulse, window) function, elementwise. More...
Matrix< Scalar >	triangle (const Matrix< Scalar > &x)
	Triangle (hat) function, elementwise. More...
Matrix< Scalar >	ramp (const Matrix< Scalar > &x)
	Ramp function, elementwise. More...
Matrix< Scalar >	mtaylor (const Matrix< Scalar > &ex, const Matrix< Scalar > &x, const Matrix< Scalar > &a, casadi_int order=1)
	Multivariate Taylor series expansion. More...
Matrix< Scalar >	mtaylor (const Matrix< Scalar > &ex, const Matrix< Scalar > &x, const Matrix< Scalar > &a, casadi_int order, const std::vector< casadi_int > &order_contributions)
	Multivariate Taylor series expansion with weighted degrees. More...
Matrix< Scalar >	poly_coeff (const Matrix< Scalar > &f, const Matrix< Scalar > &x)
	Extract the polynomial coefficients of a scalar expression in one symbol. More...
Matrix< Scalar >	poly_roots (const Matrix< Scalar > &p)
	Roots of a polynomial given by its coefficients, in closed form. More...
Matrix< Scalar >	eig_symbolic (const Matrix< Scalar > &m)
	Eigenvalues of a square SX matrix in closed form. More...
Matrix< double >	evalf (const Matrix< Scalar > &expr)
	Evaluate a constant expression numerically, returning a DM. More...
Matrix< Scalar >	gauss_quadrature (const Matrix< Scalar > &f, const Matrix< Scalar > &x, const Matrix< Scalar > &a, const Matrix< Scalar > &b, casadi_int order=5)
	Integrate a scalar SX expression over [a, b] with 5-point Gauss-Legendre quadrature. More...
Matrix< Scalar >	gauss_quadrature (const Matrix< Scalar > &f, const Matrix< Scalar > &x, const Matrix< Scalar > &a, const Matrix< Scalar > &b, casadi_int order, const Matrix< Scalar > &w)
	Integrate a scalar SX expression over [a, b] with 5-point Gauss-Legendre quadrature. More...
Matrix< Scalar >	taylor (const Matrix< Scalar > &ex, const Matrix< Scalar > &x, const Matrix< Scalar > &a, casadi_int order=1)
	Univariate Taylor series expansion. More...
Matrix< Scalar >	taylor (const Matrix< Scalar > &ex, const Matrix< Scalar > &x)
	Univariate Taylor series expansion. More...

Constructor & Destructor Documentation

Matrix() [1/10]

template<typename Scalar >

casadi::Matrix< Scalar >::Matrix

>>> DM().dim(), SX().is_empty()
('0x0', True)

>> fprintf('%s %d\n', DM().dim(), SX().is_empty())
0x0 1

julia> ca.dim(ca.DM()), ca.is_empty(ca.SX())
("0x0", true)

Extra doc: https://github.com/casadi/casadi/wiki/L_18f

Definition at line 586 of file matrix_impl.hpp.

Matrix() [2/10]

template<typename Scalar >

casadi::Matrix< Scalar >::Matrix

(

const Matrix< Scalar > &

m

)

Definition at line 590 of file matrix_impl.hpp.

Matrix() [3/10]

template<typename Scalar >

casadi::Matrix< Scalar >::Matrix	(	casadi_int	nrow,
		casadi_int	ncol
	)

The result has nnz()==0. Use zeros(nrow, ncol) for a dense matrix of numerical zeros. Structural zeros print as 00.

Parameters

nrow	Number of rows, nonnegative
ncol	Number of columns, nonnegative

>>> DM(2, 3)
DM(
[[00, 00, 00],
 [00, 00, 00]])
>>> DM(2, 3).nnz(), DM.zeros(2, 3).nnz()
(0, 6)
>>> SX(2, 0).dim()
'2x0'

>> DM(2, 3)
[[00, 00, 00],
 [00, 00, 00]]
>> fprintf('%d %d\n', DM(2, 3).nnz(), DM.zeros(2, 3).nnz())
0 6
>> SX(2, 0).dim()
2x0

julia> ca.DM(2, 3)
DM(
[[00, 00, 00],
 [00, 00, 00]])
julia> ca.nnz(ca.DM(2, 3)), ca.nnz(ca.DM.zeros(2, 3))
(0, 6)
julia> ca.dim(ca.SX(2, 0))
"2x0"

See also

zeros, ones

Extra doc: https://github.com/casadi/casadi/wiki/L_18g

Matrix() [4/10]

template<typename Scalar >

casadi::Matrix< Scalar >::Matrix ( const Sparsity &  sp )

explicit

Same as ones(sp).

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

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

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

Extra doc: https://github.com/casadi/casadi/wiki/L_18k

Matrix() [5/10]

template<typename Scalar >

casadi::Matrix< Scalar >::Matrix	(	const Sparsity &	sp,
		const Matrix< Scalar > &	d
	)

Parameters

sp	Sparsity pattern of the result
d	Either a scalar, which is used for every structural nonzero, or a dense vector (row or column) with exactly sp.nnz() entries, in column-major order of the pattern. Anything else raises an error.

>>> DM(Sparsity.diag(2), [5, 6])
DM(
[[5, 00],
 [00, 6]])
>>> DM(Sparsity.diag(2), 5)
DM(
[[5, 00],
 [00, 5]])
>>> SX(Sparsity.lower(2), SX.sym("v", 3))
SX(
[[v_0, 00],
 [v_1, v_2]])
>>> try: DM(Sparsity.diag(3), [1, 2])
... except Exception as e: print("error")
error

>> DM(Sparsity.diag(2), [5; 6])
[[5, 00],
 [00, 6]]
>> DM(Sparsity.diag(2), 5)
[[5, 00],
 [00, 5]]
>> SX(Sparsity.lower(2), SX.sym('v', 3))
[[v_0, 00],
 [v_1, v_2]]
>> try, DM(Sparsity.diag(3), [1; 2]); catch e, disp('error'); end
error

julia> ca.DM(ca.Sparsity.diag(2), [5, 6])
DM(
[[5, 00],
 [00, 6]])
julia> ca.DM(ca.Sparsity.diag(2), 5)
DM(
[[5, 00],
 [00, 5]])
julia> ca.SX(ca.Sparsity.lower(2), ca.SX.sym("v", 3))
SX(
[[v_0, 00],
 [v_1, v_2]])
julia> try ca.DM(ca.Sparsity.diag(3), [1, 2]); catch; println("error") end
error

Extra doc: https://github.com/casadi/casadi/wiki/L_18l

Matrix() [6/10]

template<typename Scalar >

casadi::Matrix< Scalar >::Matrix

(

double

val

)

Matrix() [7/10]

template<typename Scalar >

casadi::Matrix< Scalar >::Matrix ( const std::vector< std::vector< double > > &  m )

explicit

Every row must have the same length; a ragged input raises an error. An empty outer list gives a 0-by-1 matrix. At the Python level, 2-D NumPy arrays and SciPy sparse matrices are accepted as well; a sparse input keeps its sparsity pattern.

>>> DM([[1, 2], [3, 4]])
DM(
[[1, 2],
 [3, 4]])
>>> DM(np.array([[1, 2], [3, 4]])).dim()
'2x2'
>>> try: DM([[1, 2], [3]])
... except Exception as e: print("error")
error

julia> ca.DM([1 2; 3 4])
DM(
[[1, 2],
 [3, 4]])
julia> try ca.DM([[1, 2], [3]]); catch; println("error") end
error

Extra doc: https://github.com/casadi/casadi/wiki/L_2oo

Matrix() [8/10]

template<typename Scalar >

template<typename A >

casadi::Matrix< Scalar >::Matrix ( const std::vector< A > &  x )

inline

A 1-D NumPy array also gives a column vector.

>>> DM([1, 2, 3]).dim(), DM(np.array([1, 2, 3])).dim(), DM([]).dim()
('3x1', '3x1', '0x1')

julia> ca.dim(ca.DM([1, 2, 3])), ca.dim(ca.DM(Float64[]))
("3x1", "0x1")

Extra doc: https://github.com/casadi/casadi/wiki/L_18m

Definition at line 409 of file matrix_decl.hpp.

Matrix() [9/10]

template<typename Scalar >

template<typename A >

casadi::Matrix< Scalar >::Matrix ( const Matrix< A > &  x )

inline

The sparsity pattern is kept and every nonzero is converted. SX(DM) always works. DM(SX) requires constant entries: a symbolic entry is converted to nan without an error. Use evalf to get an error instead.

>>> SX(DM(Sparsity.diag(2))).dim()
'2x2'
>>> DM(SX([1, 2]))
DM([1, 2])
>>> DM(SX.sym("x"))
DM(nan)

>> SX(DM(Sparsity.diag(2))).dim()
2x2
>> DM(SX([1; 2]))
[1, 2]
>> DM(SX.sym('x'))
nan

julia> ca.dim(ca.SX(ca.DM(ca.Sparsity.diag(2))))
"2x2"
julia> ca.DM(ca.SX([1, 2]))
DM([1, 2])
julia> ca.DM(ca.SX.sym("x"))
DM(nan)

See also

evalf

Extra doc: https://github.com/casadi/casadi/wiki/L_18n

Definition at line 459 of file matrix_decl.hpp.

Matrix() [10/10]

template<typename Scalar >

template<typename Scalar >

casadi::Matrix< Scalar >::Matrix

(

const std::vector< Scalar > &

x

)

Definition at line 594 of file matrix_impl.hpp.

Member Function Documentation

__nonzero__()

bool casadi::SX::__nonzero__

(

)

const

Only defined for 1-by-1 matrices; other shapes raise an error. A structurally empty 1-by-1 matrix is false. A symbolic SX entry raises an error unless the on-the-fly simplifications already decided its value (x==x is true).

>>> bool(DM(2)), bool(DM(0)), bool(DM(1, 1))
(True, False, False)
>>> x = SX.sym("x")
>>> bool(x == x)
True
>>> try: bool(x > 0)
... except Exception as e: print("error")
error

julia> Bool(ca.DM(1)), Bool(ca.DM(0)), Bool(ca.DM(1, 1))
(true, false, false)
julia> x = ca.SX.sym("x");
julia> Bool(x == x)
true
julia> try Bool(x > 0); catch; println("error") end
error

Extra doc: https://github.com/casadi/casadi/wiki/L_2oq

Definition at line 80 of file matrix_impl.hpp.

bilin()

static Matrix< Scalar > casadi::GenericMatrix< Matrix< Scalar > >::bilin ( const Matrix< Scalar > &  A, const Matrix< Scalar > &  x, const Matrix< Scalar > &  y  )

staticinherited

x and y must be vectors (row vectors are transposed, sparse vectors densified) with x.numel() == A.size1() and y.numel() == A.size2(); otherwise an error is raised. The result is scalar. When y is omitted, the quadratic form x^T A x is calculated.

>>> A = DM([[1, 2], [3, 4]])
>>> bilin(A, DM([1, 1]), DM([1, 2]))
DM(16)
>>> bilin(A, DM([1, 1]))
DM(10)
>>> bilin(MX.sym("A", 2, 2), MX.sym("x", 2), MX.sym("y", 2))
MX(bilin(A, x, y))

>> A = DM([1 2; 3 4]);
>> bilin(A, DM([1; 1]), DM([1; 2]))
16
>> bilin(A, DM([1; 1]))
10
>> bilin(MX.sym('A', 2, 2), MX.sym('x', 2), MX.sym('y', 2))
bilin(A, x, y)

julia> A = ca.DM([1 2; 3 4]);
julia> ca.bilin(A, ca.DM([1, 1]), ca.DM([1, 2]))
DM(16)
julia> ca.bilin(A, ca.DM([1, 1]))
DM(10)
julia> ca.bilin(ca.MX.sym("A", 2, 2), ca.MX.sym("x", 2), ca.MX.sym("y", 2))
MX(bilin(A, x, y))

See also

rank1, dot, mtimes

Extra doc: https://github.com/casadi/casadi/wiki/L_1bo

clear()

template<typename Scalar >

void casadi::Matrix< Scalar >::clear

(

)

colind()

casadi_int casadi::GenericMatrix< Matrix< Scalar > >::colind ( casadi_int  col ) const

inlineinherited

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.

columns()

casadi_int casadi::GenericMatrix< Matrix< Scalar > >::columns ( ) const

inlineinherited

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

Definition at line 295 of file generic_matrix.hpp.

dep()

SX casadi::SX::dep

(

casadi_int

ch = 0

)

const

Only defined for a scalar SX that is the result of an operation; a symbol, a constant or a DM raises an error.

Parameters

ch	Operand index, 0 or 1

>>> x = SX.sym("x"); y = SX.sym("y")
>>> e = x * y
>>> e.dep(0), e.dep(1), e.n_dep()
(SX(x), SX(y), 2)

>> x = SX.sym('x'); y = SX.sym('y');
>> e = x * y;
>> e.dep(0), e.dep(1), e.n_dep()
x
y
2

julia> x = ca.SX.sym("x"); y = ca.SX.sym("y");
julia> e = x * y;
julia> ca.dep(e, 0), ca.dep(e, 1), ca.n_dep(e)
(x, y, 2)

See also

n_dep, op

Extra doc: https://github.com/casadi/casadi/wiki/L_1a9

deserialize() [1/3]

template<typename Scalar >

static Matrix<Scalar> casadi::Matrix< Scalar >::deserialize ( const std::string &  s )

static

A string that is not a CasADi serialization raises an error.

See also

serialize

Extra doc: https://github.com/casadi/casadi/wiki/L_1ag

deserialize() [2/3]

template<typename Scalar >

static Matrix<Scalar> casadi::Matrix< Scalar >::deserialize ( DeserializingStream &  s )

static

deserialize() [3/3]

template<typename Scalar >

static Matrix<Scalar> casadi::Matrix< Scalar >::deserialize ( std::istream &  stream )

static

Extra doc: https://github.com/casadi/casadi/wiki/L_1af

dim()

std::string casadi::GenericMatrix< Matrix< Scalar > >::dim ( bool  with_nz = false ) const

inherited

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

disp()

template<typename Scalar >

void casadi::Matrix< Scalar >::disp	(	std::ostream &	stream,
		bool	more = false
	)		const

Picks the layout automatically: scalar, vector, dense matrix (small or at least half full) or sparse coordinate list. This is what str() and print() use. more has no effect for matrices.

Extra doc: https://github.com/casadi/casadi/wiki/L_2oz

element_hash()

casadi_int casadi::SX::element_hash

(

)

const

Equal expressions (same node) have the same hash. Only defined for a scalar SX; a vector or a DM raises an error.

>>> x = SX.sym("x"); y = SX.sym("y")
>>> x.element_hash() == x.element_hash(), x.element_hash() == y.element_hash()
(True, False)

>> x = SX.sym('x'); y = SX.sym('y');
>> h = x.element_hash();
>> fprintf('%d %d\n', h == x.element_hash(), h == y.element_hash())
1 0

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

Extra doc: https://github.com/casadi/casadi/wiki/L_19n

enlarge()

template<typename Scalar >

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

The new shape is nrow-by-ncol. rr lists, for every existing row, its index in the enlarged matrix; cc does the same for the columns. Both must have exactly size1() and size2() entries. All other rows and columns are structurally zero.

Parameters

nrow	New number of rows
ncol	New number of columns
rr	New position of each existing row, length size1()
cc	New position of each existing column, length size2()
ind1	True for one-based indices

>>> A = DM([[1, 2], [3, 4]])
>>> A.enlarge(3, 4, [0, 2], [0, 1])
>>> A
DM(
[[1, 2, 00, 00],
 [00, 00, 00, 00],
 [3, 4, 00, 00]])
>>> try: A.enlarge(4, 4, [0, 1], [0, 1])
... except Exception as e: print("error")
error

>> A = DM([1 2; 3 4]);
>> A.enlarge(3, 4, [1 3], [1 2], true);
>> A
[[1, 2, 00, 00],
 [00, 00, 00, 00],
 [3, 4, 00, 00]]
>> try, A.enlarge(4, 4, [1 2], [1 2], true); catch e, disp('error'); end
error

julia> A = ca.DM([1 2; 3 4]);
julia> ca.enlarge(A, 3, 4, [0, 2], [0, 1])
julia> A
DM(
[[1, 2, 00, 00],
 [00, 00, 00, 00],
 [3, 4, 00, 00]])
julia> try ca.enlarge(A, 4, 4, [0, 1], [0, 1]); catch; println("error") end
error

See also

resize, Sparsity::enlarge

Extra doc: https://github.com/casadi/casadi/wiki/L_19i

erase() [1/2]

template<typename Scalar >

void casadi::Matrix< Scalar >::erase	(	const std::vector< casadi_int > &	rr,
		bool	ind1 = false
	)

Column-major linear indices, as in get. The shape is unchanged.

>>> A = DM([[1, 2, 3], [4, 5, 6]])
>>> A.erase([0, -1])
>>> A
DM(
[[00, 2, 3],
 [4, 5, 00]])

>> A = DM([1 2 3; 4 5 6]);
>> A.erase([1 6], true);
>> A
[[00, 2, 3],
 [4, 5, 00]]

julia> A = ca.DM([1 2 3; 4 5 6]);
julia> ca.erase(A, [0, 5])
julia> A
DM(
[[00, 2, 3],
 [4, 5, 00]])

Extra doc: https://github.com/casadi/casadi/wiki/L_19g

erase() [2/2]

template<typename Scalar >

void casadi::Matrix< Scalar >::erase	(	const std::vector< casadi_int > &	rr,
		const std::vector< casadi_int > &	cc,
		bool	ind1 = false
	)

The shape is unchanged; the entries of the submatrix rr x cc are removed from the sparsity pattern. Negative indices count from the end; out-of-range indices raise an error.

Parameters

rr	Row indices
cc	Column indices
ind1	True for one-based indices

>>> A = DM([[1, 2, 3], [4, 5, 6]])
>>> A.erase([0], [1])
>>> A
DM(
[[1, 00, 3],
 [4, 5, 6]])
>>> A.dim(), A.nnz()
('2x3', 5)

>> A = DM([1 2 3; 4 5 6]);
>> A.erase(1, 2, true);
>> A
[[1, 00, 3],
 [4, 5, 6]]
>> fprintf('%s %d\n', A.dim(), A.nnz())
2x3 5

julia> A = ca.DM([1 2 3; 4 5 6]);
julia> ca.erase(A, [0], [1])
julia> A
DM(
[[1, 00, 3],
 [4, 5, 6]])
julia> ca.dim(A), ca.nnz(A)
("2x3", 5)

See also

remove, sparsify

Extra doc: https://github.com/casadi/casadi/wiki/L_19f

export_code()

template<typename Scalar >

void casadi::Matrix< Scalar >::export_code	(	const std::string &	lang,
		std::ostream &	stream = casadi::uout(),
		const Dict &	options = Dict()
	)		const

lang: only 'matlab' supported for now

* options:
*   inline: Indicates if you want everything on a single line (default: False)
*   name: Name of exported variable (default: 'm')
*   indent_level: Level of indentation (default: 0)
*   spoof_zero: Replace numerical zero by a 1e-200 (default: false)
*               might be needed for matlab sparse construct,
*               which doesn't allow numerical zero
* 

Extra doc: https://github.com/casadi/casadi/wiki/L_1ac

eye()

template<typename Scalar >

static Matrix<Scalar> casadi::Matrix< Scalar >::eye ( casadi_int  n )

static

The result is sparse: only the n diagonal entries are structural nonzeros.

>>> DM.eye(2)
DM(
[[1, 00],
 [00, 1]])
>>> DM.eye(3).nnz(), DM.eye(0).dim()
(3, '0x0')

>> DM.eye(2)
[[1, 00],
 [00, 1]]
>> fprintf('%d %s\n', DM.eye(3).nnz(), DM.eye(0).dim())
3 0x0

julia> ca.DM.eye(2)
DM(
[[1, 00],
 [00, 1]])
julia> ca.nnz(ca.DM.eye(3)), ca.dim(ca.DM.eye(0))
(3, "0x0")

See also

is_eye, Sparsity::diag

Extra doc: https://github.com/casadi/casadi/wiki/L_19m

from_file()

template<typename Scalar >

static Matrix<double> casadi::Matrix< Scalar >::from_file ( const std::string &  filename, const std::string &  format_hint = ""  )

static

Same formats as to_file. In txt format, lines starting with #, % or / and empty lines are skipped, 00 marks a structural zero and a plain 0 a stored zero; every row must have the same number of columns, otherwise an error is raised. An empty file gives a 0-by-0 matrix. A missing file raises an error.

Parameters

filename	Input path
format_hint	"mtx" or "txt"; empty means deduce from the extension

>>> import os, tempfile
>>> fn = os.path.join(tempfile.mkdtemp(), "a.txt")
>>> with open(fn, "w") as f: n = f.write("# comment\n1 00\n0 2\n")
>>> A = DM.from_file(fn)
>>> A
DM(
[[1, 00],
 [0, 2]])
>>> A.nnz()
3
>>> os.remove(fn); os.rmdir(os.path.dirname(fn))

>> fn = [tempname '.txt'];
>> fid = fopen(fn, 'w'); fprintf(fid, '# comment\n1 00\n0 2\n'); fclose(fid);
>> A = DM.from_file(fn);
>> A
[[1, 00],
 [0, 2]]
>> A.nnz()
3
>> delete(fn);

julia> fn = joinpath(mktempdir(), "a.txt");
julia> write(fn, "# comment\n1 00\n0 2\n");
julia> A = ca.DM.from_file(fn)
DM(
[[1, 00],
 [0, 2]])
julia> ca.nnz(A)
3
julia> rm(dirname(fn), recursive=true)

See also

to_file

Extra doc: https://github.com/casadi/casadi/wiki/L_2pa

get() [1/7]

template<typename Scalar >

void casadi::Matrix< Scalar >::get	(	Matrix< Scalar > &	m,
		bool	ind1,
		const Matrix< casadi_int > &	rr
	)		const

Backs the Python expressions x[k] and x[sp]. The index addresses elements, not nonzeros, in column-major order: element (i, j) has linear index i + j*size1(). Negative indices count from the end; out-of-range indices raise an error.

• A scalar index returns a 1-by-1 matrix. If that element is a structural zero, the result is structurally empty (prints 00).
• A Slice (Python slice) or a list of indices returns a column vector, except that indexing a row vector gives a row vector.
• A matrix of indices (IM) returns a matrix of the same shape.
• A Sparsity pattern must have the same shape as the matrix; the result is the projection of the matrix onto that pattern (entries outside it are dropped).

Note that the result of a comparison such as A > 2 is a DM of zeros and ones, not a boolean mask: indexing with it uses those values as linear indices. Use a Sparsity pattern or the nz accessor for masking.

Parameters

ind1	True for one-based indices (MATLAB); Python always passes false
rr	Linear index, Slice or list/matrix of indices
sp	Sparsity pattern of the same shape as the matrix

>>> A = DM([[1, 2, 3], [4, 5, 6]])
>>> A[1], A[2], A[-1]
(DM(4), DM(2), DM(6))
>>> A[[0, 5]]
DM([1, 6])
>>> A[Sparsity.diag(2, 3)]
DM(
[[1, 00, 00],
 [00, 5, 00]])
>>> S = DM(Sparsity.diag(2))
>>> S[1]
DM(00)
>>> A.get(False, Slice(0, 2))
DM([1, 4])
>>> try: A[6]
... except Exception as e: print("error")
error

>> A = DM([1 2 3; 4 5 6]);
>> A(2), A(3), A(end)
4
2
6
>> A([1 6])
[[1, 6]]
>> A(Sparsity.diag(2, 3))
[[1, 00, 00],
 [00, 5, 00]]
>> S = DM(Sparsity.diag(2));
>> S(2)
00
>> A.get(true, [1; 2])
[1, 4]
>> try, A(7); catch e, disp('error'); end
error

julia> A = ca.DM([1 2 3; 4 5 6]);
julia> A[2], A[3], A[end]
(4, 2, 6)
julia> A[[1, 6]]
DM([1, 6])
julia> S = ca.DM(ca.Sparsity.diag(2));
julia> S[2]
DM(00)
julia> try A[7]; catch; println("error") end
error

See also

set, get_nz, Sparsity::sub

Extra doc: https://github.com/casadi/casadi/wiki/L_2or

Definition at line 162 of file matrix_impl.hpp.

get() [2/7]

template<typename Scalar >

void casadi::Matrix< Scalar >::get	(	Matrix< Scalar > &	m,
		bool	ind1,
		const Matrix< casadi_int > &	rr,
		const Matrix< casadi_int > &	cc
	)		const

Backs the Python expression x[i, j]. Each of rr and cc is a scalar, a Slice or a list/vector of indices (any order, repetitions allowed, negative counts from the end). The result has len(rr) rows and len(cc) columns and keeps the sparsity of the selected entries. Two scalar indices give a 1-by-1 matrix (structurally empty when the entry is a structural zero). Out-of-range indices raise an error.

Parameters

ind1	True for one-based indices (MATLAB); Python always passes false
rr	Row index, Slice or list/matrix of row indices
cc	Column index, Slice or list/matrix of column indices

>>> A = DM([[1, 2, 3], [4, 5, 6]])
>>> A[0, 1], A[1, -1]
(DM(2), DM(6))
>>> A[:, 1]
DM([2, 5])
>>> A[[1, 0], [0, 2]]
DM(
[[4, 6],
 [1, 3]])
>>> A[1:1, :].dim()
'0x3'
>>> x = SX.sym("x", 2, 2)
>>> x[0, :]
SX([[x_0, x_2]])
>>> DM(Sparsity.diag(2))[1, 0]
DM(00)
>>> try: A[2, 0]
... except Exception as e: print("error")
error

>> A = DM([1 2 3; 4 5 6]);
>> A(1, 2), A(2, end)
2
6
>> A(:, 2)
[2, 5]
>> A([2 1], [1 3])
[[4, 6],
 [1, 3]]
>> B = A(2:1, :); disp(B.dim())
0x3
>> x = SX.sym('x', 2, 2);
>> x(1, :)
[[x_0, x_2]]
>> S = DM(Sparsity.diag(2));
>> S(2, 1)
00
>> try, A(3, 1); catch e, disp('error'); end
error

julia> A = ca.DM([1 2 3; 4 5 6]);
julia> A[1, 2], A[2, end]
(2, 6)
julia> A[:, 2]
DM([2, 5])
julia> A[[2, 1], [1, 3]]
DM(
[[4, 6],
 [1, 3]])
julia> ca.dim(A[2:1, :])
"0x3"
julia> x = ca.SX.sym("x", 2, 2);
julia> x[1, :]
SX([[x_0, x_2]])
julia> ca.DM(ca.Sparsity.diag(2))[2, 1]
DM(00)
julia> try A[3, 1]; catch; println("error") end
error

See also

set

Extra doc: https://github.com/casadi/casadi/wiki/L_2os

Definition at line 121 of file matrix_impl.hpp.

get() [3/7]

template<typename Scalar >

void casadi::Matrix< Scalar >::get	(	Matrix< Scalar > &	m,
		bool	ind1,
		const Matrix< casadi_int > &	rr,
		const Slice &	cc
	)		const

Backs the Python expression x[i, j]. Each of rr and cc is a scalar, a Slice or a list/vector of indices (any order, repetitions allowed, negative counts from the end). The result has len(rr) rows and len(cc) columns and keeps the sparsity of the selected entries. Two scalar indices give a 1-by-1 matrix (structurally empty when the entry is a structural zero). Out-of-range indices raise an error.

Parameters

ind1	True for one-based indices (MATLAB); Python always passes false
rr	Row index, Slice or list/matrix of row indices
cc	Column index, Slice or list/matrix of column indices

>>> A = DM([[1, 2, 3], [4, 5, 6]])
>>> A[0, 1], A[1, -1]
(DM(2), DM(6))
>>> A[:, 1]
DM([2, 5])
>>> A[[1, 0], [0, 2]]
DM(
[[4, 6],
 [1, 3]])
>>> A[1:1, :].dim()
'0x3'
>>> x = SX.sym("x", 2, 2)
>>> x[0, :]
SX([[x_0, x_2]])
>>> DM(Sparsity.diag(2))[1, 0]
DM(00)
>>> try: A[2, 0]
... except Exception as e: print("error")
error

>> A = DM([1 2 3; 4 5 6]);
>> A(1, 2), A(2, end)
2
6
>> A(:, 2)
[2, 5]
>> A([2 1], [1 3])
[[4, 6],
 [1, 3]]
>> B = A(2:1, :); disp(B.dim())
0x3
>> x = SX.sym('x', 2, 2);
>> x(1, :)
[[x_0, x_2]]
>> S = DM(Sparsity.diag(2));
>> S(2, 1)
00
>> try, A(3, 1); catch e, disp('error'); end
error

julia> A = ca.DM([1 2 3; 4 5 6]);
julia> A[1, 2], A[2, end]
(2, 6)
julia> A[:, 2]
DM([2, 5])
julia> A[[2, 1], [1, 3]]
DM(
[[4, 6],
 [1, 3]])
julia> ca.dim(A[2:1, :])
"0x3"
julia> x = ca.SX.sym("x", 2, 2);
julia> x[1, :]
SX([[x_0, x_2]])
julia> ca.DM(ca.Sparsity.diag(2))[2, 1]
DM(00)
julia> try A[3, 1]; catch; println("error") end
error

See also

set

Extra doc: https://github.com/casadi/casadi/wiki/L_2os

Definition at line 114 of file matrix_impl.hpp.

get() [4/7]

template<typename Scalar >

void casadi::Matrix< Scalar >::get	(	Matrix< Scalar > &	m,
		bool	ind1,
		const Slice &	rr
	)		const

Backs the Python expressions x[k] and x[sp]. The index addresses elements, not nonzeros, in column-major order: element (i, j) has linear index i + j*size1(). Negative indices count from the end; out-of-range indices raise an error.

• A scalar index returns a 1-by-1 matrix. If that element is a structural zero, the result is structurally empty (prints 00).
• A Slice (Python slice) or a list of indices returns a column vector, except that indexing a row vector gives a row vector.
• A matrix of indices (IM) returns a matrix of the same shape.
• A Sparsity pattern must have the same shape as the matrix; the result is the projection of the matrix onto that pattern (entries outside it are dropped).

Note that the result of a comparison such as A > 2 is a DM of zeros and ones, not a boolean mask: indexing with it uses those values as linear indices. Use a Sparsity pattern or the nz accessor for masking.

Parameters

ind1	True for one-based indices (MATLAB); Python always passes false
rr	Linear index, Slice or list/matrix of indices
sp	Sparsity pattern of the same shape as the matrix

>>> A = DM([[1, 2, 3], [4, 5, 6]])
>>> A[1], A[2], A[-1]
(DM(4), DM(2), DM(6))
>>> A[[0, 5]]
DM([1, 6])
>>> A[Sparsity.diag(2, 3)]
DM(
[[1, 00, 00],
 [00, 5, 00]])
>>> S = DM(Sparsity.diag(2))
>>> S[1]
DM(00)
>>> A.get(False, Slice(0, 2))
DM([1, 4])
>>> try: A[6]
... except Exception as e: print("error")
error

>> A = DM([1 2 3; 4 5 6]);
>> A(2), A(3), A(end)
4
2
6
>> A([1 6])
[[1, 6]]
>> A(Sparsity.diag(2, 3))
[[1, 00, 00],
 [00, 5, 00]]
>> S = DM(Sparsity.diag(2));
>> S(2)
00
>> A.get(true, [1; 2])
[1, 4]
>> try, A(7); catch e, disp('error'); end
error

julia> A = ca.DM([1 2 3; 4 5 6]);
julia> A[2], A[3], A[end]
(4, 2, 6)
julia> A[[1, 6]]
DM([1, 6])
julia> S = ca.DM(ca.Sparsity.diag(2));
julia> S[2]
DM(00)
julia> try A[7]; catch; println("error") end
error

See also

set, get_nz, Sparsity::sub

Extra doc: https://github.com/casadi/casadi/wiki/L_2or

Definition at line 144 of file matrix_impl.hpp.

get() [5/7]

template<typename Scalar >

void casadi::Matrix< Scalar >::get	(	Matrix< Scalar > &	m,
		bool	ind1,
		const Slice &	rr,
		const Matrix< casadi_int > &	cc
	)		const

Backs the Python expression x[i, j]. Each of rr and cc is a scalar, a Slice or a list/vector of indices (any order, repetitions allowed, negative counts from the end). The result has len(rr) rows and len(cc) columns and keeps the sparsity of the selected entries. Two scalar indices give a 1-by-1 matrix (structurally empty when the entry is a structural zero). Out-of-range indices raise an error.

Parameters

ind1	True for one-based indices (MATLAB); Python always passes false
rr	Row index, Slice or list/matrix of row indices
cc	Column index, Slice or list/matrix of column indices

>>> A = DM([[1, 2, 3], [4, 5, 6]])
>>> A[0, 1], A[1, -1]
(DM(2), DM(6))
>>> A[:, 1]
DM([2, 5])
>>> A[[1, 0], [0, 2]]
DM(
[[4, 6],
 [1, 3]])
>>> A[1:1, :].dim()
'0x3'
>>> x = SX.sym("x", 2, 2)
>>> x[0, :]
SX([[x_0, x_2]])
>>> DM(Sparsity.diag(2))[1, 0]
DM(00)
>>> try: A[2, 0]
... except Exception as e: print("error")
error

>> A = DM([1 2 3; 4 5 6]);
>> A(1, 2), A(2, end)
2
6
>> A(:, 2)
[2, 5]
>> A([2 1], [1 3])
[[4, 6],
 [1, 3]]
>> B = A(2:1, :); disp(B.dim())
0x3
>> x = SX.sym('x', 2, 2);
>> x(1, :)
[[x_0, x_2]]
>> S = DM(Sparsity.diag(2));
>> S(2, 1)
00
>> try, A(3, 1); catch e, disp('error'); end
error

julia> A = ca.DM([1 2 3; 4 5 6]);
julia> A[1, 2], A[2, end]
(2, 6)
julia> A[:, 2]
DM([2, 5])
julia> A[[2, 1], [1, 3]]
DM(
[[4, 6],
 [1, 3]])
julia> ca.dim(A[2:1, :])
"0x3"
julia> x = ca.SX.sym("x", 2, 2);
julia> x[1, :]
SX([[x_0, x_2]])
julia> ca.DM(ca.Sparsity.diag(2))[2, 1]
DM(00)
julia> try A[3, 1]; catch; println("error") end
error

See also

set

Extra doc: https://github.com/casadi/casadi/wiki/L_2os

Definition at line 107 of file matrix_impl.hpp.

get() [6/7]

template<typename Scalar >

void casadi::Matrix< Scalar >::get	(	Matrix< Scalar > &	m,
		bool	ind1,
		const Slice &	rr,
		const Slice &	cc
	)		const

Backs the Python expression x[i, j]. Each of rr and cc is a scalar, a Slice or a list/vector of indices (any order, repetitions allowed, negative counts from the end). The result has len(rr) rows and len(cc) columns and keeps the sparsity of the selected entries. Two scalar indices give a 1-by-1 matrix (structurally empty when the entry is a structural zero). Out-of-range indices raise an error.

Parameters

ind1	True for one-based indices (MATLAB); Python always passes false
rr	Row index, Slice or list/matrix of row indices
cc	Column index, Slice or list/matrix of column indices

>>> A = DM([[1, 2, 3], [4, 5, 6]])
>>> A[0, 1], A[1, -1]
(DM(2), DM(6))
>>> A[:, 1]
DM([2, 5])
>>> A[[1, 0], [0, 2]]
DM(
[[4, 6],
 [1, 3]])
>>> A[1:1, :].dim()
'0x3'
>>> x = SX.sym("x", 2, 2)
>>> x[0, :]
SX([[x_0, x_2]])
>>> DM(Sparsity.diag(2))[1, 0]
DM(00)
>>> try: A[2, 0]
... except Exception as e: print("error")
error

>> A = DM([1 2 3; 4 5 6]);
>> A(1, 2), A(2, end)
2
6
>> A(:, 2)
[2, 5]
>> A([2 1], [1 3])
[[4, 6],
 [1, 3]]
>> B = A(2:1, :); disp(B.dim())
0x3
>> x = SX.sym('x', 2, 2);
>> x(1, :)
[[x_0, x_2]]
>> S = DM(Sparsity.diag(2));
>> S(2, 1)
00
>> try, A(3, 1); catch e, disp('error'); end
error

julia> A = ca.DM([1 2 3; 4 5 6]);
julia> A[1, 2], A[2, end]
(2, 6)
julia> A[:, 2]
DM([2, 5])
julia> A[[2, 1], [1, 3]]
DM(
[[4, 6],
 [1, 3]])
julia> ca.dim(A[2:1, :])
"0x3"
julia> x = ca.SX.sym("x", 2, 2);
julia> x[1, :]
SX([[x_0, x_2]])
julia> ca.DM(ca.Sparsity.diag(2))[2, 1]
DM(00)
julia> try A[3, 1]; catch; println("error") end
error

See also

set

Extra doc: https://github.com/casadi/casadi/wiki/L_2os

Definition at line 89 of file matrix_impl.hpp.

get() [7/7]

template<typename Scalar >

void casadi::Matrix< Scalar >::get	(	Matrix< Scalar > &	m,
		bool	ind1,
		const Sparsity &	sp
	)		const

Backs the Python expressions x[k] and x[sp]. The index addresses elements, not nonzeros, in column-major order: element (i, j) has linear index i + j*size1(). Negative indices count from the end; out-of-range indices raise an error.

• A scalar index returns a 1-by-1 matrix. If that element is a structural zero, the result is structurally empty (prints 00).
• A Slice (Python slice) or a list of indices returns a column vector, except that indexing a row vector gives a row vector.
• A matrix of indices (IM) returns a matrix of the same shape.
• A Sparsity pattern must have the same shape as the matrix; the result is the projection of the matrix onto that pattern (entries outside it are dropped).

Note that the result of a comparison such as A > 2 is a DM of zeros and ones, not a boolean mask: indexing with it uses those values as linear indices. Use a Sparsity pattern or the nz accessor for masking.

Parameters

ind1	True for one-based indices (MATLAB); Python always passes false
rr	Linear index, Slice or list/matrix of indices
sp	Sparsity pattern of the same shape as the matrix

>>> A = DM([[1, 2, 3], [4, 5, 6]])
>>> A[1], A[2], A[-1]
(DM(4), DM(2), DM(6))
>>> A[[0, 5]]
DM([1, 6])
>>> A[Sparsity.diag(2, 3)]
DM(
[[1, 00, 00],
 [00, 5, 00]])
>>> S = DM(Sparsity.diag(2))
>>> S[1]
DM(00)
>>> A.get(False, Slice(0, 2))
DM([1, 4])
>>> try: A[6]
... except Exception as e: print("error")
error

>> A = DM([1 2 3; 4 5 6]);
>> A(2), A(3), A(end)
4
2
6
>> A([1 6])
[[1, 6]]
>> A(Sparsity.diag(2, 3))
[[1, 00, 00],
 [00, 5, 00]]
>> S = DM(Sparsity.diag(2));
>> S(2)
00
>> A.get(true, [1; 2])
[1, 4]
>> try, A(7); catch e, disp('error'); end
error

julia> A = ca.DM([1 2 3; 4 5 6]);
julia> A[2], A[3], A[end]
(4, 2, 6)
julia> A[[1, 6]]
DM([1, 6])
julia> S = ca.DM(ca.Sparsity.diag(2));
julia> S[2]
DM(00)
julia> try A[7]; catch; println("error") end
error

See also

set, get_nz, Sparsity::sub

Extra doc: https://github.com/casadi/casadi/wiki/L_2or

Definition at line 186 of file matrix_impl.hpp.

get_colind()

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

inlineinherited

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.

get_elements()

template<typename Scalar >

std::vector<Scalar> casadi::Matrix< Scalar >::get_elements

(

)

const

Like nonzeros, but structural zeros are included as 0, so the list has numel() entries.

>>> DM(Sparsity.diag(2)).elements()
[1.0, 0.0, 0.0, 1.0]

>> DM(Sparsity.diag(2)).elements()
1 0 0 1

julia> ca.elements(ca.DM(ca.Sparsity.diag(2)))
4-element Vector{Float64}:
 1.0
 0.0
 0.0
 1.0

See also

nonzeros, densify

Extra doc: https://github.com/casadi/casadi/wiki/L_1a3

get_free()

std::vector< SX > casadi::SX::get_free ( const Function &  f )

static

Same as Function::free_sx. Only defined for SX.

>>> x = SX.sym("x"); y = SX.sym("y")
>>> SX.get_free(Function("f", [x], [x + y], {"allow_free": True}))
[SX(y)]

>> x = SX.sym('x'); y = SX.sym('y');
>> v = SX.get_free(Function('f', {x}, {x + y}, struct('allow_free', true)));
>> v{1}
y

julia> x = ca.SX.sym("x"); y = ca.SX.sym("y");
julia> ca.SX.get_free(ca.Function("f", [x], [x + y], Dict("allow_free" => true)))
1-element Vector{SX}:
 SX(y)

See also

Function::free_sx, get_input

Extra doc: https://github.com/casadi/casadi/wiki/L_19e

get_input()

std::vector< SX > casadi::SX::get_input ( const Function &  f )

static

Same as Function::sx_in. Only defined for SX.

>>> x = SX.sym("x")
>>> SX.get_input(Function("f", [x], [x + 1]))
[SX(x)]

>> x = SX.sym('x');
>> v = SX.get_input(Function('f', {x}, {x + 1}));
>> numel(v), v{1}
1
x

julia> x = ca.SX.sym("x");
julia> ca.SX.get_input(ca.Function("f", [x], [x + 1]))
1-element Vector{SX}:
 SX(x)

See also

Function::sx_in, get_free

Extra doc: https://github.com/casadi/casadi/wiki/L_19d

get_max_depth()

casadi_int casadi::SX::get_max_depth ( )

static

See also

set_max_depth

Extra doc: https://github.com/casadi/casadi/wiki/L_19c

get_nonzeros()

template<typename Scalar >

std::vector< A > casadi::Matrix< Scalar >::get_nonzeros

(

)

const

Implementation of Matrix::get_nonzeros (in public API)

Returns floats for DM and 1-by-1 SX objects for SX. Structural zeros are skipped.

>>> DM([[1, 2], [3, 4]]).nonzeros()
[1.0, 3.0, 2.0, 4.0]
>>> DM(Sparsity.diag(2)).nonzeros(), DM(2, 0).nonzeros()
([1.0, 1.0], [])
>>> SX.sym("x", 2).nonzeros()
[SX(x_0), SX(x_1)]

>> DM([1 2; 3 4]).nonzeros()
1 3 2 4
>> DM(Sparsity.diag(2)).nonzeros(), size(DM(2, 0).nonzeros())
1 1
1 0
>> v = SX.sym('x', 2).nonzeros();
>> class(v), v{2}
cell
x_1

julia> ca.nonzeros(ca.DM([1 2; 3 4]))
4-element Vector{Float64}:
 1.0
 3.0
 2.0
 4.0
julia> ca.nonzeros(ca.DM(ca.Sparsity.diag(2))), ca.nonzeros(ca.DM(2, 0))
([1.0, 1.0], Float64[])

See also

elements, get_nz

Extra doc: https://github.com/casadi/casadi/wiki/L_1a2

Definition at line 4699 of file matrix_decl.hpp.

get_nz() [1/2]

template<typename Scalar >

void casadi::Matrix< Scalar >::get_nz	(	Matrix< Scalar > &	m,
		bool	ind1,
		const Matrix< casadi_int > &	k
	)		const

Backs the Python expression x.nz[k]. Index k runs over the nonzeros in column-major order, 0 <= k < nnz(); negative values count from the end and out-of-range values raise an error. Structural zeros are skipped, so for a dense matrix this coincides with linear indexing. The result is a column vector shaped like the index (a row vector when indexing a row vector; a matrix for a matrix index). Iterating over x.nz in Python yields the nonzeros one by one.

Parameters

ind1	True for one-based indices (MATLAB); Python always passes false
k	Nonzero index, Slice or list/matrix of indices

>>> S = DM(Sparsity.diag(3)); S[0, 2] = 7
>>> S.nz[:]
DM([1, 1, 7, 1])
>>> S.nz[2], S.nz[-1], len(S.nz)
(DM(7), DM(1), 4)
>>> x = SX.sym("x", Sparsity.lower(2))
>>> x.nz[[0, 2]]
SX([x_0, x_2])
>>> SX.sym("e", 2, 0).nz[:].dim()
'0x1'
>>> try: S.nz[4]
... except Exception as e: print("error")
error

>> S = DM(Sparsity.diag(3)); S(1, 3) = 7;
>> S.get_nz(true, Slice())
[1, 1, 7, 1]
>> S.get_nz(true, 3), S.get_nz(true, [1; 3])
7
[1, 7]
>> x = SX.sym('x', Sparsity.lower(2));
>> x.get_nz(true, [1; 3])
[x_0, x_2]
>> SX.sym('e', 2, 0).get_nz(true, Slice()).dim()
0x1
>> try, S.get_nz(true, 5); catch e, disp('error'); end
error

julia> S = ca.DM(ca.Sparsity.diag(3)); S[1, 3] = 7;
julia> S.nz[:]
DM([1, 1, 7, 1])
julia> S.nz[3], S.nz[end], length(S.nz)
(7, 1, 4)
julia> x = ca.SX.sym("x", ca.Sparsity.lower(2));
julia> x.nz[[1, 3]]
SX([x_0, x_2])
julia> ca.dim(ca.SX.sym("e", 2, 0).nz[:])
"0x1"
julia> try S.nz[5]; catch e; println(typeof(e)) end
BoundsError

See also

set_nz, get, nonzeros

Extra doc: https://github.com/casadi/casadi/wiki/L_2ov

Definition at line 416 of file matrix_impl.hpp.

get_nz() [2/2]

template<typename Scalar >

void casadi::Matrix< Scalar >::get_nz	(	Matrix< Scalar > &	m,
		bool	ind1,
		const Slice &	k
	)		const

Backs the Python expression x.nz[k]. Index k runs over the nonzeros in column-major order, 0 <= k < nnz(); negative values count from the end and out-of-range values raise an error. Structural zeros are skipped, so for a dense matrix this coincides with linear indexing. The result is a column vector shaped like the index (a row vector when indexing a row vector; a matrix for a matrix index). Iterating over x.nz in Python yields the nonzeros one by one.

Parameters

ind1	True for one-based indices (MATLAB); Python always passes false
k	Nonzero index, Slice or list/matrix of indices

>>> S = DM(Sparsity.diag(3)); S[0, 2] = 7
>>> S.nz[:]
DM([1, 1, 7, 1])
>>> S.nz[2], S.nz[-1], len(S.nz)
(DM(7), DM(1), 4)
>>> x = SX.sym("x", Sparsity.lower(2))
>>> x.nz[[0, 2]]
SX([x_0, x_2])
>>> SX.sym("e", 2, 0).nz[:].dim()
'0x1'
>>> try: S.nz[4]
... except Exception as e: print("error")
error

>> S = DM(Sparsity.diag(3)); S(1, 3) = 7;
>> S.get_nz(true, Slice())
[1, 1, 7, 1]
>> S.get_nz(true, 3), S.get_nz(true, [1; 3])
7
[1, 7]
>> x = SX.sym('x', Sparsity.lower(2));
>> x.get_nz(true, [1; 3])
[x_0, x_2]
>> SX.sym('e', 2, 0).get_nz(true, Slice()).dim()
0x1
>> try, S.get_nz(true, 5); catch e, disp('error'); end
error

julia> S = ca.DM(ca.Sparsity.diag(3)); S[1, 3] = 7;
julia> S.nz[:]
DM([1, 1, 7, 1])
julia> S.nz[3], S.nz[end], length(S.nz)
(7, 1, 4)
julia> x = ca.SX.sym("x", ca.Sparsity.lower(2));
julia> x.nz[[1, 3]]
SX([x_0, x_2])
julia> ca.dim(ca.SX.sym("e", 2, 0).nz[:])
"0x1"
julia> try S.nz[5]; catch e; println(typeof(e)) end
BoundsError

See also

set_nz, get, nonzeros

Extra doc: https://github.com/casadi/casadi/wiki/L_2ov

Definition at line 404 of file matrix_impl.hpp.

get_output()

SX casadi::SX::get_output

(

casadi_int

oind

)

const

Extra doc: https://github.com/casadi/casadi/wiki/L_28i

get_precision()

template<typename Scalar >

casadi_int casadi::Matrix< Scalar >::get_precision

static

Definition at line 49 of file matrix_impl.hpp.

get_row()

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

inlineinherited

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.

get_scientific()

template<typename Scalar >

bool casadi::Matrix< Scalar >::get_scientific

static

Definition at line 55 of file matrix_impl.hpp.

get_sparsity()

template<typename Scalar >

Sparsity casadi::Matrix< Scalar >::get_sparsity

(

)

const

Returns a copy of the Sparsity object; patterns are reference counted, so this is cheap.

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

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

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

See also

nonzeros

Extra doc: https://github.com/casadi/casadi/wiki/L_19j

get_str()

template<typename Scalar >

std::string casadi::Matrix< Scalar >::get_str

(

bool

more = false

)

const

get_width()

template<typename Scalar >

casadi_int casadi::Matrix< Scalar >::get_width

static

Definition at line 52 of file matrix_impl.hpp.

gradient()

static Matrix< Scalar > casadi::GenericMatrix< Matrix< Scalar > >::gradient ( const Matrix< Scalar > &  ex, const Matrix< Scalar > &  arg, const Dict &  opts = Dict()  )

staticinherited

Functions called by friend functions defined here

has_nz()

template<typename Scalar >

bool casadi::Matrix< Scalar >::has_nz	(	casadi_int	rr,
		casadi_int	cc
	)		const

Looks only at the sparsity pattern; a stored numerical zero still counts as a nonzero. Negative indices count from the end. An index past the end raises an error.

>>> S = DM(Sparsity.diag(2))
>>> S.has_nz(0, 0), S.has_nz(0, 1), DM([0, 1]).has_nz(0, 0)
(True, False, True)

>> S = DM(Sparsity.diag(2));
>> fprintf('%d %d %d\n', S.has_nz(0, 0), S.has_nz(0, 1), DM([0; 1]).has_nz(0, 0))
1 0 1

julia> S = ca.DM(ca.Sparsity.diag(2));
julia> ca.has_nz(S, 0, 0), ca.has_nz(S, 0, 1), ca.has_nz(ca.DM([0, 1]), 0, 0)
(true, false, true)

See also

has_zeros, Sparsity::has_nz

Extra doc: https://github.com/casadi/casadi/wiki/L_2op

Definition at line 75 of file matrix_impl.hpp.

has_output()

bool casadi::SX::has_output

(

)

const

Extra doc: https://github.com/casadi/casadi/wiki/L_28l

has_zeros()

template<typename Scalar >

bool casadi::Matrix< Scalar >::has_zeros

(

)

const

For SX only entries that are the constant 0 count. Use sparsify to remove them.

>>> DM([1, 0]).has_zeros(), DM([1, 2]).has_zeros(), DM(2, 2).has_zeros()
(True, False, False)
>>> x = SX.sym("x")
>>> vertcat(x, 0).has_zeros(), vertcat(x, x * 0).has_zeros()
(True, True)

>> fprintf('%d %d\n', DM([1; 0]).has_zeros(), DM([1; 2]).has_zeros())
1 0
>> DM(2, 2).has_zeros()
0
>> x = SX.sym('x');
>> fprintf('%d %d\n', vertcat(x, 0).has_zeros(), vertcat(x, x * 0).has_zeros())
1 1

julia> ca.has_zeros(ca.DM([1, 0])), ca.has_zeros(ca.DM([1, 2])), ca.has_zeros(ca.DM(2, 2))
(true, false, false)
julia> x = ca.SX.sym("x");
julia> ca.has_zeros([x; 0]), ca.has_zeros([x; x * 0])
(true, true)

See also

sparsify, has_nz

Extra doc: https://github.com/casadi/casadi/wiki/L_1a1

inf() [1/3]

template<typename Scalar >

static Matrix<Scalar> casadi::Matrix< Scalar >::inf ( casadi_int  nrow = 1, casadi_int  ncol = 1  )

static

Takes a shape (dense result, default 1-by-1) or a sparsity pattern.

>>> DM.inf(), DM.inf(2, 1).is_inf()
(DM(inf), True)
>>> DM.inf(Sparsity.diag(2))
DM(
[[inf, 00],
 [00, inf]])

>> DM.inf(), DM.inf(2, 1).is_inf()
inf
1
>> DM.inf(Sparsity.diag(2))
[[inf, 00],
 [00, inf]]

julia> ca.DM.inf(), ca.is_inf(ca.DM.inf(2, 1))
(inf, true)
julia> ca.DM.inf(ca.Sparsity.diag(2))
DM(
[[inf, 00],
 [00, inf]])

See also

nan, is_inf

Extra doc: https://github.com/casadi/casadi/wiki/L_19k

inf() [2/3]

template<typename Scalar >

static Matrix<Scalar> casadi::Matrix< Scalar >::inf ( const Sparsity &  sp )

static

Takes a shape (dense result, default 1-by-1) or a sparsity pattern.

>>> DM.inf(), DM.inf(2, 1).is_inf()
(DM(inf), True)
>>> DM.inf(Sparsity.diag(2))
DM(
[[inf, 00],
 [00, inf]])

>> DM.inf(), DM.inf(2, 1).is_inf()
inf
1
>> DM.inf(Sparsity.diag(2))
[[inf, 00],
 [00, inf]]

julia> ca.DM.inf(), ca.is_inf(ca.DM.inf(2, 1))
(inf, true)
julia> ca.DM.inf(ca.Sparsity.diag(2))
DM(
[[inf, 00],
 [00, inf]])

See also

nan, is_inf

Extra doc: https://github.com/casadi/casadi/wiki/L_19k

inf() [3/3]

template<typename Scalar >

static Matrix<Scalar> casadi::Matrix< Scalar >::inf ( const std::pair< casadi_int, casadi_int > &  rc )

static

Takes a shape (dense result, default 1-by-1) or a sparsity pattern.

>>> DM.inf(), DM.inf(2, 1).is_inf()
(DM(inf), True)
>>> DM.inf(Sparsity.diag(2))
DM(
[[inf, 00],
 [00, inf]])

>> DM.inf(), DM.inf(2, 1).is_inf()
inf
1
>> DM.inf(Sparsity.diag(2))
[[inf, 00],
 [00, inf]]

julia> ca.DM.inf(), ca.is_inf(ca.DM.inf(2, 1))
(inf, true)
julia> ca.DM.inf(ca.Sparsity.diag(2))
DM(
[[inf, 00],
 [00, inf]])

See also

nan, is_inf

Extra doc: https://github.com/casadi/casadi/wiki/L_19k

info()

Dict CASADI_EXPORT casadi::SX::info

(

)

const

>>> sorted(DM([1, 2]).info().keys())
['data', 'sparsity']

>> s = DM([1; 2]).info();
>> strjoin(sort(fieldnames(s))', ' ')
data sparsity

julia> sort(collect(keys(ca.info(ca.DM([1, 2])))))
2-element Vector{String}:
 "data"
 "sparsity"

Extra doc: https://github.com/casadi/casadi/wiki/L_2p8

is_call()

bool casadi::SX::is_call

(

)

const

Extra doc: https://github.com/casadi/casadi/wiki/L_28j

is_column()

bool casadi::GenericMatrix< Matrix< Scalar > >::is_column ( ) const

inlineinherited

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

Definition at line 517 of file generic_matrix.hpp.

is_commutative()

bool casadi::SX::is_commutative

(

)

const

Only defined if symbolic scalar.

Extra doc: https://github.com/casadi/casadi/wiki/L_19q

is_constant()

template<typename Scalar >

bool casadi::Matrix< Scalar >::is_constant

(

)

const

Always true for DM. For SX, true when no entry depends on a symbol; the simplifications make x*0 and x-x constant. A false negative is possible for expressions that are constant only in value, e.g. x - x after other operations.

>>> x = SX.sym("x")
>>> SX([1, 2]).is_constant(), x.is_constant(), (x * 0).is_constant()
(True, False, True)
>>> vertcat(x, 1).is_constant(), SX.sym("e", 2, 0).is_constant()
(False, True)

>> x = SX.sym('x'); z = x * 0;
>> fprintf('%d %d %d\n', SX([1; 2]).is_constant(), x.is_constant(), z.is_constant())
1 0 1
>> fprintf('%d %d\n', vertcat(x, 1).is_constant(), SX.sym('e', 2, 0).is_constant())
0 1

julia> x = ca.SX.sym("x");
julia> ca.is_constant(ca.SX([1, 2])), ca.is_constant(x), ca.is_constant(x * 0)
(true, false, true)
julia> ca.is_constant([x; 1]), ca.is_constant(ca.SX.sym("e", 2, 0))
(false, true)

See also

is_symbolic, evalf

Extra doc: https://github.com/casadi/casadi/wiki/L_19v

is_dense()

bool casadi::GenericMatrix< Matrix< Scalar > >::is_dense ( ) const

inlineinherited

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.

is_empty()

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

inlineinherited

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.

is_eye()

template<typename Scalar >

bool casadi::Matrix< Scalar >::is_eye

(

)

const

are possible)

Extra doc: https://github.com/casadi/casadi/wiki/L_1a0

is_half()

template<typename Scalar >

bool casadi::Matrix< Scalar >::is_half

(

)

const

Extra doc: https://github.com/casadi/casadi/wiki/L_2en

is_inf()

template<typename Scalar >

bool casadi::Matrix< Scalar >::is_inf

(

)

const

Extra doc: https://github.com/casadi/casadi/wiki/L_2e9

is_integer()

template<typename Scalar >

bool casadi::Matrix< Scalar >::is_integer

(

)

const

(note that false negative answers are possible)

Extra doc: https://github.com/casadi/casadi/wiki/L_19w

is_leaf()

bool casadi::SX::is_leaf

(

)

const

Only defined if symbolic scalar.

Extra doc: https://github.com/casadi/casadi/wiki/L_19p

is_minus_inf()

template<typename Scalar >

bool casadi::Matrix< Scalar >::is_minus_inf

(

)

const

Extra doc: https://github.com/casadi/casadi/wiki/L_2ea

is_minus_one()

template<typename Scalar >

bool casadi::Matrix< Scalar >::is_minus_one

(

)

const

Extra doc: https://github.com/casadi/casadi/wiki/L_19z

is_nonnegative()

template<typename Scalar >

bool casadi::Matrix< Scalar >::is_nonnegative

(

)

const

(note that false negative answers are possible)

Extra doc: https://github.com/casadi/casadi/wiki/L_2eb

is_one()

template<typename Scalar >

bool casadi::Matrix< Scalar >::is_one

(

)

const

Extra doc: https://github.com/casadi/casadi/wiki/L_19y

is_op()

bool casadi::SX::is_op

(

casadi_int

op

)

const

is_output()

bool casadi::SX::is_output

(

)

const

Extra doc: https://github.com/casadi/casadi/wiki/L_28k

is_regular()

bool casadi::SX::is_regular

(

)

const

Structural zeros are ignored. For SX, every entry must be a constant: the check raises an error when it reaches a symbolic entry (an infinite constant found before it still gives false).

>>> DM([1, 2]).is_regular(), DM([1, inf]).is_regular(), DM.nan(2, 2).is_regular()
(True, False, False)
>>> DM(2, 2).is_regular(), SX([1, 2]).is_regular()
(True, True)
>>> try: SX.sym("x").is_regular()
... except Exception as e: print("error")
error

>> fprintf('%d %d\n', DM([1; 2]).is_regular(), DM([1; inf]).is_regular())
1 0
>> fprintf('%d %d\n', DM.nan(2, 2).is_regular(), DM(2, 2).is_regular())
0 1
>> SX([1; 2]).is_regular()
1
>> try, SX.sym('x').is_regular(); catch e, disp('error'); end
error

julia> ca.is_regular(ca.DM([1, 2])), ca.is_regular(ca.DM([1, Inf]))
(true, false)
julia> ca.is_regular(ca.DM.nan(2, 2))
false
julia> ca.is_regular(ca.DM(2, 2)), ca.is_regular(ca.SX([1, 2]))
(true, true)
julia> try ca.is_regular(ca.SX.sym("x")); catch; println("error") end
error

See also

nan, inf

Extra doc: https://github.com/casadi/casadi/wiki/L_2p5

is_row()

bool casadi::GenericMatrix< Matrix< Scalar > >::is_row ( ) const

inlineinherited

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

Definition at line 512 of file generic_matrix.hpp.

is_scalar()

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

inherited

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

is_smooth()

bool casadi::SX::is_smooth

(

)

const

False when any node is a non-smooth operation such as floor, ceil, sign, a comparison or if_else. Operations such as fabs, fmin and fmax count as smooth. Always true for DM.

>>> x = SX.sym("x")
>>> sin(x).is_smooth(), fabs(x).is_smooth(), floor(x).is_smooth()
(True, True, False)
>>> if_else(x > 0, x, 0).is_smooth(), (x > 0).is_smooth(), DM(1).is_smooth()
(False, False, True)

>> x = SX.sym('x');
>> fprintf('%d %d %d\n', sin(x).is_smooth(), abs(x).is_smooth(), floor(x).is_smooth())
1 1 0
>> c = x > 0; b = if_else(c, x, 0);
>> fprintf('%d %d %d\n', b.is_smooth(), c.is_smooth(), DM(1).is_smooth())
0 0 1

julia> x = ca.SX.sym("x");
julia> ca.is_smooth(sin(x)), ca.is_smooth(abs(x)), ca.is_smooth(floor(x))
(true, true, false)
julia> ca.is_smooth(ifelse(x > 0, x, 0)), ca.is_smooth(x > 0), ca.is_smooth(ca.DM(1))
(false, false, true)

Extra doc: https://github.com/casadi/casadi/wiki/L_19o

is_square()

bool casadi::GenericMatrix< Matrix< Scalar > >::is_square ( ) const

inlineinherited

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

Definition at line 470 of file generic_matrix.hpp.

is_symbolic()

bool casadi::SX::is_symbolic

(

)

const

Check if an expression is a pure symbol. Pure means that no operations should happen on the symbol (not even vec, transpose, index, concatenation, ...) By consequence, a slice of a vector-shaped MX symbol is not a symbol. However, the SX type is really a container format with scalar entries. Therefore, a slice of a vector-shaped SX symbol is still a symbol.

Sparse matrices invariable return false

\seealso is_valid_input

Extra doc: https://github.com/casadi/casadi/wiki/L_19r

is_tril()

bool casadi::GenericMatrix< Matrix< Scalar > >::is_tril ( ) const

inlineinherited

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.

is_triu()

bool casadi::GenericMatrix< Matrix< Scalar > >::is_triu ( ) const

inlineinherited

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.

is_valid_input()

bool casadi::SX::is_valid_input

(

)

const

is_valid_input is more forgiving than is_symbolic. Some compositions are allowed: vec, vertcat.

Sparse matrices can return true if all non-zero elements are symbolic

\seealso is_symbolic

Extra doc: https://github.com/casadi/casadi/wiki/L_19s

is_value()

template<typename Scalar >

bool casadi::Matrix< Scalar >::is_value

(

double

val

)

const

Extra doc: https://github.com/casadi/casadi/wiki/L_2eo

is_vector()

bool casadi::GenericMatrix< Matrix< Scalar > >::is_vector ( ) const

inlineinherited

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.

is_zero()

template<typename Scalar >

bool casadi::Matrix< Scalar >::is_zero

(

)

const

Extra doc: https://github.com/casadi/casadi/wiki/L_19x

jtimes()

static Matrix< Scalar > casadi::GenericMatrix< Matrix< Scalar > >::jtimes ( const Matrix< Scalar > &  ex, const Matrix< Scalar > &  arg, const Matrix< Scalar > &  v, bool  tr = false, const Dict &  opts = Dict()  )

staticinherited

Functions called by friend functions defined here

linearize()

static Matrix< Scalar > casadi::GenericMatrix< Matrix< Scalar > >::linearize ( const Matrix< Scalar > &  f, const Matrix< Scalar > &  x, const Matrix< Scalar > &  x0, const Dict &  opts = Dict()  )

staticinherited

Functions called by friend functions defined here

logsumexp()

static Matrix< Scalar > casadi::GenericMatrix< Matrix< Scalar > >::logsumexp ( const Matrix< Scalar > &  x )

staticinherited

mpower()

static Matrix< Scalar > casadi::GenericMatrix< Matrix< Scalar > >::mpower ( const Matrix< Scalar > &  x, const Matrix< Scalar > &  y  )

staticinherited

Functions called by friend functions defined here

n_dep()

casadi_int casadi::SX::n_dep

(

)

const

See also

dep

Extra doc: https://github.com/casadi/casadi/wiki/L_1aa

name()

std::string casadi::SX::name

(

)

const

Raises an error for a non-scalar, for an expression that is not a pure symbol, and for DM.

>>> SX.sym("x").name(), SX.sym("v", 2)[1].name()
('x', 'v_1')

>> v = SX.sym('v', 2); v2 = v(2);
>> fprintf('%s %s\n', SX.sym('x').name(), v2.name())
x v_1

julia> ca.name(ca.SX.sym("x")), ca.name(ca.SX.sym("v", 2)[2])
("x", "v_1")

See also

is_symbolic

Extra doc: https://github.com/casadi/casadi/wiki/L_1a8

nan() [1/3]

template<typename Scalar >

static Matrix<Scalar> casadi::Matrix< Scalar >::nan ( casadi_int  nrow = 1, casadi_int  ncol = 1  )

static

Takes a shape (dense result, default 1-by-1) or a sparsity pattern. Useful as a placeholder that is easy to detect with is_regular.

>>> DM.nan(), DM.nan((2, 1)).dim()
(DM(nan), '2x1')
>>> DM.nan(2, 2).is_regular()
False

>> DM.nan(), DM.nan([2 1]).dim()
nan
2x1
>> DM.nan(2, 2).is_regular()
0

julia> ca.DM.nan(), ca.dim(ca.DM.nan(2, 1))
(nan, "2x1")
julia> ca.is_regular(ca.DM.nan(2, 2))
false

See also

inf, is_regular

Extra doc: https://github.com/casadi/casadi/wiki/L_19l

nan() [2/3]

template<typename Scalar >

static Matrix<Scalar> casadi::Matrix< Scalar >::nan ( const Sparsity &  sp )

static

Takes a shape (dense result, default 1-by-1) or a sparsity pattern. Useful as a placeholder that is easy to detect with is_regular.

>>> DM.nan(), DM.nan((2, 1)).dim()
(DM(nan), '2x1')
>>> DM.nan(2, 2).is_regular()
False

>> DM.nan(), DM.nan([2 1]).dim()
nan
2x1
>> DM.nan(2, 2).is_regular()
0

julia> ca.DM.nan(), ca.dim(ca.DM.nan(2, 1))
(nan, "2x1")
julia> ca.is_regular(ca.DM.nan(2, 2))
false

See also

inf, is_regular

Extra doc: https://github.com/casadi/casadi/wiki/L_19l

nan() [3/3]

template<typename Scalar >

static Matrix<Scalar> casadi::Matrix< Scalar >::nan ( const std::pair< casadi_int, casadi_int > &  rc )

static

Takes a shape (dense result, default 1-by-1) or a sparsity pattern. Useful as a placeholder that is easy to detect with is_regular.

>>> DM.nan(), DM.nan((2, 1)).dim()
(DM(nan), '2x1')
>>> DM.nan(2, 2).is_regular()
False

>> DM.nan(), DM.nan([2 1]).dim()
nan
2x1
>> DM.nan(2, 2).is_regular()
0

julia> ca.DM.nan(), ca.dim(ca.DM.nan(2, 1))
(nan, "2x1")
julia> ca.is_regular(ca.DM.nan(2, 2))
false

See also

inf, is_regular

Extra doc: https://github.com/casadi/casadi/wiki/L_19l

nnz()

casadi_int casadi::GenericMatrix< Matrix< Scalar > >::nnz ( ) const

inherited

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

nnz_diag()

casadi_int casadi::GenericMatrix< Matrix< Scalar > >::nnz_diag ( ) const

inherited

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

nnz_lower()

casadi_int casadi::GenericMatrix< Matrix< Scalar > >::nnz_lower ( ) const

inherited

>>> 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

nnz_upper()

casadi_int casadi::GenericMatrix< Matrix< Scalar > >::nnz_upper ( ) const

inherited

>>> 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

numel()

casadi_int casadi::GenericMatrix< Matrix< Scalar > >::numel ( ) const

inherited

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

ones() [1/3]

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

inlinestaticinherited

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.

ones() [2/3]

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

inlinestaticinherited

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.

ones() [3/3]

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

inlinestaticinherited

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.

op()

casadi_int casadi::SX::op

(

)

const

operator casadi_int()

template<typename Scalar >

casadi::Matrix< Scalar >::operator casadi_int ( ) const

explicit

>>> int(DM(3.7))
3

>> DM(3.7).to_int()
3

julia> ca.to_int(ca.DM(3.7))
3

Extra doc: https://github.com/casadi/casadi/wiki/L_1a6

operator double()

template<typename Scalar >

casadi::Matrix< Scalar >::operator double ( ) const

explicit

Other shapes raise an error. A symbolic SX entry converts to nan without an error.

>>> float(DM(2.5)), float(SX(3))
(2.5, 3.0)
>>> try: float(DM([1, 2]))
... except Exception as e: print("error")
error

>> fprintf('%g %g\n', full(DM(2.5)), SX(3).to_double())
2.5 3
>> try, DM([1; 2]).to_double(); catch e, disp('error'); end
error

julia> Float64(ca.DM(2.5)), Float64(ca.SX(3))
(2.5, 3.0)
julia> try Float64(ca.DM([1, 2])); catch; println("error") end
error

Extra doc: https://github.com/casadi/casadi/wiki/L_1a5

operator+()

template<typename Scalar >

Matrix<Scalar> casadi::Matrix< Scalar >::operator+

(

)

const

Examples

SX/SXaddition.cc.

operator-()

template<typename Scalar >

Matrix<Scalar> casadi::Matrix< Scalar >::operator-

(

)

const

print_dense()

template<typename Scalar >

void casadi::Matrix< Scalar >::print_dense	(	std::ostream &	stream,
		bool	truncate = true
	)		const

Shared SX subexpressions are printed first as @1=..., @2=....

Parameters

truncate

Print only 3 leading and trailing rows and columns when the matrix has more than 1000 elements and at least 7 rows or columns

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

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

See also

print_sparse

Extra doc: https://github.com/casadi/casadi/wiki/L_2p2

Definition at line 691 of file matrix_impl.hpp.

print_scalar()

template<typename Scalar >

void casadi::Matrix< Scalar >::print_scalar

(

std::ostream &

stream

)

const

A structurally empty 1-by-1 matrix prints as 00; other shapes raise an error.

>>> DM(3).print_scalar()
3
>>> DM(1, 1).print_scalar()
00

julia> ca.print_scalar(ca.DM(3))
3
julia> ca.print_scalar(ca.DM(1, 1))
00

Extra doc: https://github.com/casadi/casadi/wiki/L_2p0

Definition at line 619 of file matrix_impl.hpp.

print_sparse()

template<typename Scalar >

void casadi::Matrix< Scalar >::print_sparse	(	std::ostream &	stream,
		bool	truncate = true
	)		const

Parameters

truncate

Print only the first and last 3 nonzeros when there are more than 1000

>>> DM(Sparsity.diag(2)).print_sparse()
sparse: 2-by-2, 2 nnz
 (0, 0) -> 1
 (1, 1) -> 1
>>> DM(2, 2).print_sparse()
all zero sparse: 2-by-2

julia> ca.print_sparse(ca.DM(ca.Sparsity.diag(2)))
sparse: 2-by-2, 2 nnz
 (0, 0) -> 1
 (1, 1) -> 1
julia> ca.print_sparse(ca.DM(2, 2))
all zero sparse: 2-by-2

See also

print_dense

Extra doc: https://github.com/casadi/casadi/wiki/L_2p3

Definition at line 696 of file matrix_impl.hpp.

print_split()

template<typename Scalar >

void casadi::Matrix< Scalar >::print_split	(	std::vector< std::string > &	nz,
		std::vector< std::string > &	inter
	)		const

Returns two lists: one string per nonzero (in storage order) and the definitions of the intermediate expressions "@1", "@2", ... that the nonzero strings refer to (always empty for DM).

>>> DM([[1, 2], [3, 4]]).print_split()
(['1', '3', '2', '4'], [])
>>> x = SX.sym("x"); y = SX.sym("y")
>>> e = x * y
>>> vertcat(e + 1, e - 1).print_split()
(['(@1+@2)', '(@1-@2)'], ['(x*y)', '1'])

>> [nz, inter] = DM([1 2; 3 4]).print_split();
>> disp(strjoin(cellstr(nz)', ' ')), disp(isempty(inter))
1 3 2 4
1
>> x = SX.sym('x'); y = SX.sym('y');
>> e = x * y;
>> [nz, inter] = vertcat(e + 1, e - 1).print_split();
>> disp(strjoin(cellstr(nz)', ' ')), disp(strjoin(cellstr(inter)', ' '))
(@1+@2) (@1-@2)
(x*y) 1

julia> ca.print_split(ca.DM([1 2; 3 4]))
(["1", "3", "2", "4"], String[])
julia> x = ca.SX.sym("x"); y = ca.SX.sym("y");
julia> e = x * y;
julia> ca.print_split([e + 1; e - 1])
(["(@1+@2)", "(@1-@2)"], ["(x*y)", "1"])

Extra doc: https://github.com/casadi/casadi/wiki/L_2oy

Definition at line 701 of file matrix_impl.hpp.

print_vector()

template<typename Scalar >

void casadi::Matrix< Scalar >::print_vector	(	std::ostream &	stream,
		bool	truncate = true
	)		const

Only column vectors are accepted; a row vector raises an error.

Parameters

truncate

Print only the first and last 3 entries of vectors longer than 1000

>>> DM(Sparsity.unit(3, 1)).print_vector()
[00, 1, 00]

julia> ca.print_vector(ca.DM(ca.Sparsity.unit(3, 1)))
[00, 1, 00]

Extra doc: https://github.com/casadi/casadi/wiki/L_2p1

Definition at line 641 of file matrix_impl.hpp.

printme()

template<typename Scalar >

Matrix<Scalar> casadi::Matrix< Scalar >::printme

(

const Matrix< Scalar > &

y

)

const

rand() [1/3]

template<typename Scalar >

static Matrix<Scalar> casadi::Matrix< Scalar >::rand ( casadi_int  nrow = 1, casadi_int  ncol = 1  )

static

Takes a shape (dense result, default 1-by-1) or a sparsity pattern, in which case only the structural nonzeros get a random value. Only available for DM.

>>> DM.rand(2, 3).dim(), DM.rand().dim(), DM.rand(Sparsity.diag(3)).nnz()
('2x3', '1x1', 3)
>>> try: SX.rand(2)
... except Exception as e: print("error")
error

>> fprintf('%s %s\n', DM.rand(2, 3).dim(), DM.rand().dim())
2x3 1x1
>> DM.rand(Sparsity.diag(3)).nnz()
3
>> try, SX.rand(2); catch e, disp('error'); end
error

julia> ca.dim(ca.DM.rand(2, 3)), ca.dim(ca.DM.rand())
("2x3", "1x1")
julia> ca.nnz(ca.DM.rand(ca.Sparsity.diag(3)))
3
julia> try ca.SX.rand(2); catch; println("error") end
error

See also

rng

Extra doc: https://github.com/casadi/casadi/wiki/L_1ab

rand() [2/3]

template<typename Scalar >

static Matrix<Scalar> casadi::Matrix< Scalar >::rand ( const Sparsity &  sp )

static

Takes a shape (dense result, default 1-by-1) or a sparsity pattern, in which case only the structural nonzeros get a random value. Only available for DM.

>>> DM.rand(2, 3).dim(), DM.rand().dim(), DM.rand(Sparsity.diag(3)).nnz()
('2x3', '1x1', 3)
>>> try: SX.rand(2)
... except Exception as e: print("error")
error

>> fprintf('%s %s\n', DM.rand(2, 3).dim(), DM.rand().dim())
2x3 1x1
>> DM.rand(Sparsity.diag(3)).nnz()
3
>> try, SX.rand(2); catch e, disp('error'); end
error

julia> ca.dim(ca.DM.rand(2, 3)), ca.dim(ca.DM.rand())
("2x3", "1x1")
julia> ca.nnz(ca.DM.rand(ca.Sparsity.diag(3)))
3
julia> try ca.SX.rand(2); catch; println("error") end
error

See also

rng

Extra doc: https://github.com/casadi/casadi/wiki/L_1ab

rand() [3/3]

template<typename Scalar >

static Matrix<Scalar> casadi::Matrix< Scalar >::rand ( const std::pair< casadi_int, casadi_int > &  rc )

static

Takes a shape (dense result, default 1-by-1) or a sparsity pattern, in which case only the structural nonzeros get a random value. Only available for DM.

>>> DM.rand(2, 3).dim(), DM.rand().dim(), DM.rand(Sparsity.diag(3)).nnz()
('2x3', '1x1', 3)
>>> try: SX.rand(2)
... except Exception as e: print("error")
error

>> fprintf('%s %s\n', DM.rand(2, 3).dim(), DM.rand().dim())
2x3 1x1
>> DM.rand(Sparsity.diag(3)).nnz()
3
>> try, SX.rand(2); catch e, disp('error'); end
error

julia> ca.dim(ca.DM.rand(2, 3)), ca.dim(ca.DM.rand())
("2x3", "1x1")
julia> ca.nnz(ca.DM.rand(ca.Sparsity.diag(3)))
3
julia> try ca.SX.rand(2); catch; println("error") end
error

See also

rng

Extra doc: https://github.com/casadi/casadi/wiki/L_1ab

rank1()

static Matrix< Scalar > casadi::GenericMatrix< Matrix< Scalar > >::rank1 ( const Matrix< Scalar > &  A, const Matrix< Scalar > &  alpha, const Matrix< Scalar > &  x, const Matrix< Scalar > &  y  )

staticinherited

Calculates A + alpha * x*y'

Parameters

alpha	Scalar; if it is a structural zero, A is returned unchanged
x	Vector with x.numel() == A.size1() (row vectors are transposed)
y	Vector with y.numel() == A.size2()

>>> A = DM([[1, 2], [3, 4]])
>>> rank1(A, 2, DM([1, 0]), DM([0, 1]))
DM(
[[1, 4],
 [3, 4]])
>>> rank1(MX.sym("A", 2, 2), MX.sym("a"), MX.sym("x", 2), MX.sym("y", 2))
MX(rank1(A, a, x, y))

>> A = DM([1 2; 3 4]);
>> rank1(A, 2, DM([1; 0]), DM([0; 1]))
[[1, 4],
 [3, 4]]
>> rank1(MX.sym('A', 2, 2), MX.sym('a'), MX.sym('x', 2), MX.sym('y', 2))
rank1(A, a, x, y)

julia> A = ca.DM([1 2; 3 4]);
julia> ca.rank1(A, 2, ca.DM([1, 0]), ca.DM([0, 1]))
DM(
[[1, 4],
 [3, 4]])
julia> ca.rank1(ca.MX.sym("A", 2, 2), ca.MX.sym("a"), ca.MX.sym("x", 2), ca.MX.sym("y", 2))
MX(rank1(A, a, x, y))

See also

bilin, mtimes

Extra doc: https://github.com/casadi/casadi/wiki/L_1bp

remove()

template<typename Scalar >

void casadi::Matrix< Scalar >::remove	(	const std::vector< casadi_int > &	rr,
		const std::vector< casadi_int > &	cc
	)

Both lists may be empty; duplicates are ignored, out-of-range indices raise an error.

>>> A = DM([[1, 2, 3], [4, 5, 6]])
>>> A.remove([0], [1])
>>> A
DM([[4, 6]])

>> A = DM([1 2 3; 4 5 6]);
>> A.remove(0, 1);
>> A
[[4, 6]]

julia> A = ca.DM([1 2 3; 4 5 6]);
julia> ca.remove(A, [0], [1])
julia> A
DM([[4, 6]])

See also

erase

Extra doc: https://github.com/casadi/casadi/wiki/L_19h

reserve() [1/2]

template<typename Scalar >

void casadi::Matrix< Scalar >::reserve

(

casadi_int

nnz

)

reserve() [2/2]

template<typename Scalar >

void casadi::Matrix< Scalar >::reserve	(	casadi_int	nnz,
		casadi_int	ncol
	)

resize()

template<typename Scalar >

void casadi::Matrix< Scalar >::resize	(	casadi_int	nrow,
		casadi_int	ncol
	)

Growing appends structural zeros; shrinking drops the entries outside the new shape.

>>> A = DM([[1, 2], [3, 4]])
>>> A.resize(3, 3)
>>> A
DM(
[[1, 2, 00],
 [3, 4, 00],
 [00, 00, 00]])
>>> A.resize(1, 1)
>>> A
DM(1)

>> A = DM([1 2; 3 4]);
>> A.resize(3, 3);
>> A
[[1, 2, 00],
 [3, 4, 00],
 [00, 00, 00]]
>> A.resize(1, 1);
>> A
1

julia> A = ca.DM([1 2; 3 4]);
julia> ca.resize(A, 3, 3)
julia> A
DM(
[[1, 2, 00],
 [3, 4, 00],
 [00, 00, 00]])
julia> ca.resize(A, 1, 1)
julia> A
DM(1)

See also

enlarge, reshape

Extra doc: https://github.com/casadi/casadi/wiki/L_2p4

rng()

template<typename Scalar >

void casadi::Matrix< Scalar >::rng ( casadi_int  seed )

static

The generator is global to the class and is seeded from the clock at startup; seeding it makes subsequent rand calls reproducible.

>>> DM.rng(1); a = DM.rand(2, 2)
>>> DM.rng(1); b = DM.rand(2, 2)
>>> norm_inf(a - b)
DM(0)

>> DM.rng(1); a = DM.rand(2, 2);
>> DM.rng(1); b = DM.rand(2, 2);
>> norm_inf(a - b)
0

julia> ca.DM.rng(1); a = ca.DM.rand(2, 2);
julia> ca.DM.rng(1); b = ca.DM.rand(2, 2);
julia> ca.norm_inf(a - b)
DM(0)

See also

rand

Extra doc: https://github.com/casadi/casadi/wiki/L_2p7

Definition at line 70 of file matrix_impl.hpp.

row()

casadi_int casadi::GenericMatrix< Matrix< Scalar > >::row ( casadi_int  el ) const

inlineinherited

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.

rows()

casadi_int casadi::GenericMatrix< Matrix< Scalar > >::rows ( ) const

inlineinherited

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

Definition at line 283 of file generic_matrix.hpp.

serialize() [1/2]

template<typename Scalar >

std::string casadi::Matrix< Scalar >::serialize

(

)

const

The string can be restored with deserialize of the same class (DM or SX). For SX the whole expression graph is stored, symbols included.

>>> s = DM([[1, 2], [3, 4]]).serialize()
>>> DM.deserialize(s)
DM(
[[1, 2],
 [3, 4]])
>>> x = SX.sym("x")
>>> SX.deserialize((sin(x) + x).serialize())
SX((sin(x)+x))

>> s = DM([1 2; 3 4]).serialize();
>> DM.deserialize(s)
[[1, 2],
 [3, 4]]
>> x = SX.sym('x'); e = sin(x) + x;
>> SX.deserialize(e.serialize())
(sin(x)+x)

julia> s = ca.serialize(ca.DM([1 2; 3 4]));
julia> ca.DM.deserialize(s)
DM(
[[1, 2],
 [3, 4]])
julia> x = ca.SX.sym("x");
julia> ca.SX.deserialize(ca.serialize(sin(x) + x))
SX((sin(x)+x))

See also

deserialize, StringSerializer

Extra doc: https://github.com/casadi/casadi/wiki/L_1ae

serialize() [2/2]

template<typename Scalar >

void casadi::Matrix< Scalar >::serialize

(

SerializingStream &

s

)

const

Extra doc: https://github.com/casadi/casadi/wiki/L_1ah

set() [1/7]

template<typename Scalar >

void casadi::Matrix< Scalar >::set	(	const Matrix< Scalar > &	m,
		bool	ind1,
		const Matrix< casadi_int > &	rr
	)

Backs the Python statements x[k] = v and x[sp] = v. Indices are linear, column-major and zero-based (see get). The matrix is modified in place.

• m must be a scalar (assigned to every selected element) or have as many entries as there are indices (a vector of the other orientation is transposed). Any other shape raises an error.
• Assigning to a structural zero inserts a new nonzero; the sparsity pattern grows. Assigning a structurally empty value (e.g. DM(1, 1)) removes the entry instead.
• With a Sparsity index of the same shape, the entries at the pattern's positions receive m (a scalar) or the corresponding entries of m (a matrix).

Parameters

m	Value(s) to assign
ind1	True for one-based indices (MATLAB); Python always passes false
rr	Linear index, Slice or list/matrix of indices
sp	Sparsity pattern of the same shape as the matrix

>>> A = DM([[1, 2], [3, 4]])
>>> A[1] = 10; A[[0, 3]] = [7, 8]
>>> A
DM(
[[7, 2],
 [10, 8]])
>>> A[Sparsity.diag(2)] = 0
>>> A
DM(
[[0, 2],
 [10, 0]])
>>> S = DM(Sparsity.diag(2))
>>> S[1] = 5
>>> S.nnz(), S[0, 1]
(3, DM(00))
>>> try: A[[0, 1]] = [1, 2, 3]
... except Exception as e: print("error")
error

>> A = DM([1 2; 3 4]);
>> A(2) = 10; A([1 4]) = [7 8];
>> A
[[7, 2],
 [10, 8]]
>> A(Sparsity.diag(2)) = 0;
>> A
[[0, 2],
 [10, 0]]
>> S = DM(Sparsity.diag(2));
>> S(2) = 5;
>> S.nnz(), S(1, 2)
3
00
>> try, A([1 2]) = [1 2 3]; catch e, disp('error'); end
error

julia> A = ca.DM([1 2; 3 4]);
julia> A[2] = 10; A[[1, 4]] = [7, 8];
julia> A
DM(
[[7, 2],
 [10, 8]])
julia> S = ca.DM(ca.Sparsity.diag(2));
julia> S[2] = 5;
julia> ca.nnz(S), S[1, 2]
(3, 00)
julia> try A[[1, 2]] = [1, 2, 3]; catch; println("error") end
error

See also

get, set_nz, erase

Extra doc: https://github.com/casadi/casadi/wiki/L_2ot

Definition at line 314 of file matrix_impl.hpp.

set() [2/7]

template<typename Scalar >

void casadi::Matrix< Scalar >::set	(	const Matrix< Scalar > &	m,
		bool	ind1,
		const Matrix< casadi_int > &	rr,
		const Matrix< casadi_int > &	cc
	)

Backs the Python statement x[i, j] = v. The matrix is modified in place. m must be len(rr)-by-len(cc), a scalar (broadcast to all selected entries) or a vector of the transposed orientation (transposed automatically); other shapes raise an error. Assigning into structural zeros inserts nonzeros; assigning a sparse m first erases the selected block, so its structural zeros become structural zeros.

Parameters

m	Value(s) to assign
ind1	True for one-based indices (MATLAB); Python always passes false
rr	Row index, Slice or list/matrix of row indices
cc	Column index, Slice or list/matrix of column indices

>>> A = DM([[1, 2, 3], [4, 5, 6]])
>>> A[0, 1] = 9; A[1, :] = 0
>>> A
DM(
[[1, 9, 3],
 [0, 0, 0]])
>>> A[0, :] = DM([7, 8, 9])
>>> A[0, :]
DM([[7, 8, 9]])
>>> A[:, 0] = DM(2, 1)
>>> A.nnz()
4
>>> x = SX.sym("x", 2, 2)
>>> x[0, 0] = 0
>>> x
SX(
[[0, x_2],
 [x_1, x_3]])
>>> try: A[0, :] = [1, 2]
... except Exception as e: print("error")
error

>> A = DM([1 2 3; 4 5 6]);
>> A(1, 2) = 9; A(2, :) = 0;
>> A
[[1, 9, 3],
 [0, 0, 0]]
>> A(1, :) = DM([7; 8; 9]);
>> A(1, :)
[[7, 8, 9]]
>> A(:, 1) = DM(2, 1);
>> A.nnz()
4
>> x = SX.sym('x', 2, 2);
>> x(1, 1) = 0;
>> x
[[0, x_2],
 [x_1, x_3]]
>> try, A(1, :) = [1 2]; catch e, disp('error'); end
error

julia> A = ca.DM([1 2 3; 4 5 6]);
julia> A[1, 2] = 9; A[2, :] = 0;
julia> A
DM(
[[1, 9, 3],
 [0, 0, 0]])
julia> A[1, :] = ca.DM([7, 8, 9]);
julia> A[1, :]
DM([[7, 8, 9]])
julia> A[:, 1] = ca.DM(2, 1);
julia> ca.nnz(A)
4
julia> x = ca.SX.sym("x", 2, 2);
julia> x[1, 1] = 0;
julia> x
SX(
[[0, x_2],
 [x_1, x_3]])
julia> try A[1, :] = [1, 2]; catch; println("error") end
error

See also

get

Extra doc: https://github.com/casadi/casadi/wiki/L_2ou

Definition at line 228 of file matrix_impl.hpp.

set() [3/7]

template<typename Scalar >

void casadi::Matrix< Scalar >::set	(	const Matrix< Scalar > &	m,
		bool	ind1,
		const Matrix< casadi_int > &	rr,
		const Slice &	cc
	)

Backs the Python statement x[i, j] = v. The matrix is modified in place. m must be len(rr)-by-len(cc), a scalar (broadcast to all selected entries) or a vector of the transposed orientation (transposed automatically); other shapes raise an error. Assigning into structural zeros inserts nonzeros; assigning a sparse m first erases the selected block, so its structural zeros become structural zeros.

Parameters

m	Value(s) to assign
ind1	True for one-based indices (MATLAB); Python always passes false
rr	Row index, Slice or list/matrix of row indices
cc	Column index, Slice or list/matrix of column indices

>>> A = DM([[1, 2, 3], [4, 5, 6]])
>>> A[0, 1] = 9; A[1, :] = 0
>>> A
DM(
[[1, 9, 3],
 [0, 0, 0]])
>>> A[0, :] = DM([7, 8, 9])
>>> A[0, :]
DM([[7, 8, 9]])
>>> A[:, 0] = DM(2, 1)
>>> A.nnz()
4
>>> x = SX.sym("x", 2, 2)
>>> x[0, 0] = 0
>>> x
SX(
[[0, x_2],
 [x_1, x_3]])
>>> try: A[0, :] = [1, 2]
... except Exception as e: print("error")
error

>> A = DM([1 2 3; 4 5 6]);
>> A(1, 2) = 9; A(2, :) = 0;
>> A
[[1, 9, 3],
 [0, 0, 0]]
>> A(1, :) = DM([7; 8; 9]);
>> A(1, :)
[[7, 8, 9]]
>> A(:, 1) = DM(2, 1);
>> A.nnz()
4
>> x = SX.sym('x', 2, 2);
>> x(1, 1) = 0;
>> x
[[0, x_2],
 [x_1, x_3]]
>> try, A(1, :) = [1 2]; catch e, disp('error'); end
error

julia> A = ca.DM([1 2 3; 4 5 6]);
julia> A[1, 2] = 9; A[2, :] = 0;
julia> A
DM(
[[1, 9, 3],
 [0, 0, 0]])
julia> A[1, :] = ca.DM([7, 8, 9]);
julia> A[1, :]
DM([[7, 8, 9]])
julia> A[:, 1] = ca.DM(2, 1);
julia> ca.nnz(A)
4
julia> x = ca.SX.sym("x", 2, 2);
julia> x[1, 1] = 0;
julia> x
SX(
[[0, x_2],
 [x_1, x_3]])
julia> try A[1, :] = [1, 2]; catch; println("error") end
error

See also

get

Extra doc: https://github.com/casadi/casadi/wiki/L_2ou

Definition at line 221 of file matrix_impl.hpp.

set() [4/7]

template<typename Scalar >

void casadi::Matrix< Scalar >::set	(	const Matrix< Scalar > &	m,
		bool	ind1,
		const Slice &	rr
	)

Backs the Python statements x[k] = v and x[sp] = v. Indices are linear, column-major and zero-based (see get). The matrix is modified in place.

• m must be a scalar (assigned to every selected element) or have as many entries as there are indices (a vector of the other orientation is transposed). Any other shape raises an error.
• Assigning to a structural zero inserts a new nonzero; the sparsity pattern grows. Assigning a structurally empty value (e.g. DM(1, 1)) removes the entry instead.
• With a Sparsity index of the same shape, the entries at the pattern's positions receive m (a scalar) or the corresponding entries of m (a matrix).

Parameters

m	Value(s) to assign
ind1	True for one-based indices (MATLAB); Python always passes false
rr	Linear index, Slice or list/matrix of indices
sp	Sparsity pattern of the same shape as the matrix

>>> A = DM([[1, 2], [3, 4]])
>>> A[1] = 10; A[[0, 3]] = [7, 8]
>>> A
DM(
[[7, 2],
 [10, 8]])
>>> A[Sparsity.diag(2)] = 0
>>> A
DM(
[[0, 2],
 [10, 0]])
>>> S = DM(Sparsity.diag(2))
>>> S[1] = 5
>>> S.nnz(), S[0, 1]
(3, DM(00))
>>> try: A[[0, 1]] = [1, 2, 3]
... except Exception as e: print("error")
error

>> A = DM([1 2; 3 4]);
>> A(2) = 10; A([1 4]) = [7 8];
>> A
[[7, 2],
 [10, 8]]
>> A(Sparsity.diag(2)) = 0;
>> A
[[0, 2],
 [10, 0]]
>> S = DM(Sparsity.diag(2));
>> S(2) = 5;
>> S.nnz(), S(1, 2)
3
00
>> try, A([1 2]) = [1 2 3]; catch e, disp('error'); end
error

julia> A = ca.DM([1 2; 3 4]);
julia> A[2] = 10; A[[1, 4]] = [7, 8];
julia> A
DM(
[[7, 2],
 [10, 8]])
julia> S = ca.DM(ca.Sparsity.diag(2));
julia> S[2] = 5;
julia> ca.nnz(S), S[1, 2]
(3, 00)
julia> try A[[1, 2]] = [1, 2, 3]; catch; println("error") end
error

See also

get, set_nz, erase

Extra doc: https://github.com/casadi/casadi/wiki/L_2ot

Definition at line 295 of file matrix_impl.hpp.

set() [5/7]

template<typename Scalar >

void casadi::Matrix< Scalar >::set	(	const Matrix< Scalar > &	m,
		bool	ind1,
		const Slice &	rr,
		const Matrix< casadi_int > &	cc
	)

Backs the Python statement x[i, j] = v. The matrix is modified in place. m must be len(rr)-by-len(cc), a scalar (broadcast to all selected entries) or a vector of the transposed orientation (transposed automatically); other shapes raise an error. Assigning into structural zeros inserts nonzeros; assigning a sparse m first erases the selected block, so its structural zeros become structural zeros.

Parameters

m	Value(s) to assign
ind1	True for one-based indices (MATLAB); Python always passes false
rr	Row index, Slice or list/matrix of row indices
cc	Column index, Slice or list/matrix of column indices

>>> A = DM([[1, 2, 3], [4, 5, 6]])
>>> A[0, 1] = 9; A[1, :] = 0
>>> A
DM(
[[1, 9, 3],
 [0, 0, 0]])
>>> A[0, :] = DM([7, 8, 9])
>>> A[0, :]
DM([[7, 8, 9]])
>>> A[:, 0] = DM(2, 1)
>>> A.nnz()
4
>>> x = SX.sym("x", 2, 2)
>>> x[0, 0] = 0
>>> x
SX(
[[0, x_2],
 [x_1, x_3]])
>>> try: A[0, :] = [1, 2]
... except Exception as e: print("error")
error

>> A = DM([1 2 3; 4 5 6]);
>> A(1, 2) = 9; A(2, :) = 0;
>> A
[[1, 9, 3],
 [0, 0, 0]]
>> A(1, :) = DM([7; 8; 9]);
>> A(1, :)
[[7, 8, 9]]
>> A(:, 1) = DM(2, 1);
>> A.nnz()
4
>> x = SX.sym('x', 2, 2);
>> x(1, 1) = 0;
>> x
[[0, x_2],
 [x_1, x_3]]
>> try, A(1, :) = [1 2]; catch e, disp('error'); end
error

julia> A = ca.DM([1 2 3; 4 5 6]);
julia> A[1, 2] = 9; A[2, :] = 0;
julia> A
DM(
[[1, 9, 3],
 [0, 0, 0]])
julia> A[1, :] = ca.DM([7, 8, 9]);
julia> A[1, :]
DM([[7, 8, 9]])
julia> A[:, 1] = ca.DM(2, 1);
julia> ca.nnz(A)
4
julia> x = ca.SX.sym("x", 2, 2);
julia> x[1, 1] = 0;
julia> x
SX(
[[0, x_2],
 [x_1, x_3]])
julia> try A[1, :] = [1, 2]; catch; println("error") end
error

See also

get

Extra doc: https://github.com/casadi/casadi/wiki/L_2ou

Definition at line 214 of file matrix_impl.hpp.

set() [6/7]

template<typename Scalar >

void casadi::Matrix< Scalar >::set	(	const Matrix< Scalar > &	m,
		bool	ind1,
		const Slice &	rr,
		const Slice &	cc
	)

Backs the Python statement x[i, j] = v. The matrix is modified in place. m must be len(rr)-by-len(cc), a scalar (broadcast to all selected entries) or a vector of the transposed orientation (transposed automatically); other shapes raise an error. Assigning into structural zeros inserts nonzeros; assigning a sparse m first erases the selected block, so its structural zeros become structural zeros.

Parameters

m	Value(s) to assign
ind1	True for one-based indices (MATLAB); Python always passes false
rr	Row index, Slice or list/matrix of row indices
cc	Column index, Slice or list/matrix of column indices

>>> A = DM([[1, 2, 3], [4, 5, 6]])
>>> A[0, 1] = 9; A[1, :] = 0
>>> A
DM(
[[1, 9, 3],
 [0, 0, 0]])
>>> A[0, :] = DM([7, 8, 9])
>>> A[0, :]
DM([[7, 8, 9]])
>>> A[:, 0] = DM(2, 1)
>>> A.nnz()
4
>>> x = SX.sym("x", 2, 2)
>>> x[0, 0] = 0
>>> x
SX(
[[0, x_2],
 [x_1, x_3]])
>>> try: A[0, :] = [1, 2]
... except Exception as e: print("error")
error

>> A = DM([1 2 3; 4 5 6]);
>> A(1, 2) = 9; A(2, :) = 0;
>> A
[[1, 9, 3],
 [0, 0, 0]]
>> A(1, :) = DM([7; 8; 9]);
>> A(1, :)
[[7, 8, 9]]
>> A(:, 1) = DM(2, 1);
>> A.nnz()
4
>> x = SX.sym('x', 2, 2);
>> x(1, 1) = 0;
>> x
[[0, x_2],
 [x_1, x_3]]
>> try, A(1, :) = [1 2]; catch e, disp('error'); end
error

julia> A = ca.DM([1 2 3; 4 5 6]);
julia> A[1, 2] = 9; A[2, :] = 0;
julia> A
DM(
[[1, 9, 3],
 [0, 0, 0]])
julia> A[1, :] = ca.DM([7, 8, 9]);
julia> A[1, :]
DM([[7, 8, 9]])
julia> A[:, 1] = ca.DM(2, 1);
julia> ca.nnz(A)
4
julia> x = ca.SX.sym("x", 2, 2);
julia> x[1, 1] = 0;
julia> x
SX(
[[0, x_2],
 [x_1, x_3]])
julia> try A[1, :] = [1, 2]; catch; println("error") end
error

See also

get

Extra doc: https://github.com/casadi/casadi/wiki/L_2ou

Definition at line 195 of file matrix_impl.hpp.

set() [7/7]

template<typename Scalar >

void casadi::Matrix< Scalar >::set	(	const Matrix< Scalar > &	m,
		bool	ind1,
		const Sparsity &	sp
	)

Backs the Python statements x[k] = v and x[sp] = v. Indices are linear, column-major and zero-based (see get). The matrix is modified in place.

• m must be a scalar (assigned to every selected element) or have as many entries as there are indices (a vector of the other orientation is transposed). Any other shape raises an error.
• Assigning to a structural zero inserts a new nonzero; the sparsity pattern grows. Assigning a structurally empty value (e.g. DM(1, 1)) removes the entry instead.
• With a Sparsity index of the same shape, the entries at the pattern's positions receive m (a scalar) or the corresponding entries of m (a matrix).

Parameters

m	Value(s) to assign
ind1	True for one-based indices (MATLAB); Python always passes false
rr	Linear index, Slice or list/matrix of indices
sp	Sparsity pattern of the same shape as the matrix

>>> A = DM([[1, 2], [3, 4]])
>>> A[1] = 10; A[[0, 3]] = [7, 8]
>>> A
DM(
[[7, 2],
 [10, 8]])
>>> A[Sparsity.diag(2)] = 0
>>> A
DM(
[[0, 2],
 [10, 0]])
>>> S = DM(Sparsity.diag(2))
>>> S[1] = 5
>>> S.nnz(), S[0, 1]
(3, DM(00))
>>> try: A[[0, 1]] = [1, 2, 3]
... except Exception as e: print("error")
error

>> A = DM([1 2; 3 4]);
>> A(2) = 10; A([1 4]) = [7 8];
>> A
[[7, 2],
 [10, 8]]
>> A(Sparsity.diag(2)) = 0;
>> A
[[0, 2],
 [10, 0]]
>> S = DM(Sparsity.diag(2));
>> S(2) = 5;
>> S.nnz(), S(1, 2)
3
00
>> try, A([1 2]) = [1 2 3]; catch e, disp('error'); end
error

julia> A = ca.DM([1 2; 3 4]);
julia> A[2] = 10; A[[1, 4]] = [7, 8];
julia> A
DM(
[[7, 2],
 [10, 8]])
julia> S = ca.DM(ca.Sparsity.diag(2));
julia> S[2] = 5;
julia> ca.nnz(S), S[1, 2]
(3, 00)
julia> try A[[1, 2]] = [1, 2, 3]; catch; println("error") end
error

See also

get, set_nz, erase

Extra doc: https://github.com/casadi/casadi/wiki/L_2ot

Definition at line 390 of file matrix_impl.hpp.

set_max_depth()

void casadi::SX::set_max_depth ( casadi_int  eq_depth = 1 )

static

The on-the-fly simplifications (x - x -> 0, x/x -> 1, x == x -> 1, ...) recognise two operands as equal when they are the same node, or, up to this depth, when they are the same operation applied to equal operands. Depth 1 (the default) recognises (x+y) - (x+y); depth 2 also sin(x+y) - sin(x+y). Depth 0 compares nodes only. Global setting, SX only; calling without an argument restores the default.

Parameters

eq_depth

Comparison depth, default 1

>>> x = SX.sym("x"); y = SX.sym("y")
>>> sin(x + y) - sin(x + y)
SX((sin((x+y))-sin((x+y))))
>>> SX.set_max_depth(2)
>>> sin(x + y) - sin(x + y)
SX(0)
>>> SX.set_max_depth()
>>> SX.get_max_depth()
1

>> x = SX.sym('x'); y = SX.sym('y');
>> sin(x + y) - sin(x + y)
(sin((x+y))-sin((x+y)))
>> SX.set_max_depth(2);
>> sin(x + y) - sin(x + y)
0
>> SX.set_max_depth();
>> SX.get_max_depth()
1

julia> x = ca.SX.sym("x"); y = ca.SX.sym("y");
julia> sin(x + y) - sin(x + y)
SX((sin((x+y))-sin((x+y))))
julia> ca.SX.set_max_depth(2)
julia> sin(x + y) - sin(x + y)
SX(0)
julia> ca.SX.set_max_depth()
julia> ca.SX.get_max_depth()
1

See also

get_max_depth, is_equal

Extra doc: https://github.com/casadi/casadi/wiki/L_19b

set_nz() [1/2]

template<typename Scalar >

void casadi::Matrix< Scalar >::set_nz	(	const Matrix< Scalar > &	m,
		bool	ind1,
		const Matrix< casadi_int > &	k
	)

Backs the Python statement x.nz[k] = v. The sparsity pattern never changes: only stored values are overwritten (writing 0 keeps the entry as a structural nonzero). m must be a scalar (assigned to every selected nonzero) or have as many entries as there are indices; a mismatch raises an error.

Parameters

m	Value(s) to assign
ind1	True for one-based indices (MATLAB); Python always passes false
k	Nonzero index, Slice or list/matrix of indices

>>> S = DM(Sparsity.diag(3))
>>> S.nz[:] = [4, 5, 6]; S.nz[0] = 0
>>> S
DM(
[[0, 00, 00],
 [00, 5, 00],
 [00, 00, 6]])
>>> S.nnz()
3
>>> try: S.nz[[0, 1]] = [1, 2, 3]
... except Exception as e: print("error")
error

>> S = DM(Sparsity.diag(3));
>> S.set_nz([4 5 6], true, 1:3); S.set_nz(0, true, 1);
>> S
[[0, 00, 00],
 [00, 5, 00],
 [00, 00, 6]]
>> S.nnz()
3
>> try, S.set_nz([1 2 3], true, [1 2]); catch e, disp('error'); end
error

julia> S = ca.DM(ca.Sparsity.diag(3));
julia> S.nz[:] = [4, 5, 6]; S.nz[1] = 0;
julia> S
DM(
[[0, 00, 00],
 [00, 5, 00],
 [00, 00, 6]])
julia> ca.nnz(S)
3
julia> try S.nz[[1, 2]] = [1, 2, 3]; catch; println("error") end
error

See also

get_nz, set

Extra doc: https://github.com/casadi/casadi/wiki/L_2ow

Definition at line 457 of file matrix_impl.hpp.

set_nz() [2/2]

template<typename Scalar >

void casadi::Matrix< Scalar >::set_nz	(	const Matrix< Scalar > &	m,
		bool	ind1,
		const Slice &	k
	)

Backs the Python statement x.nz[k] = v. The sparsity pattern never changes: only stored values are overwritten (writing 0 keeps the entry as a structural nonzero). m must be a scalar (assigned to every selected nonzero) or have as many entries as there are indices; a mismatch raises an error.

Parameters

m	Value(s) to assign
ind1	True for one-based indices (MATLAB); Python always passes false
k	Nonzero index, Slice or list/matrix of indices

>>> S = DM(Sparsity.diag(3))
>>> S.nz[:] = [4, 5, 6]; S.nz[0] = 0
>>> S
DM(
[[0, 00, 00],
 [00, 5, 00],
 [00, 00, 6]])
>>> S.nnz()
3
>>> try: S.nz[[0, 1]] = [1, 2, 3]
... except Exception as e: print("error")
error

>> S = DM(Sparsity.diag(3));
>> S.set_nz([4 5 6], true, 1:3); S.set_nz(0, true, 1);
>> S
[[0, 00, 00],
 [00, 5, 00],
 [00, 00, 6]]
>> S.nnz()
3
>> try, S.set_nz([1 2 3], true, [1 2]); catch e, disp('error'); end
error

julia> S = ca.DM(ca.Sparsity.diag(3));
julia> S.nz[:] = [4, 5, 6]; S.nz[1] = 0;
julia> S
DM(
[[0, 00, 00],
 [00, 5, 00],
 [00, 00, 6]])
julia> ca.nnz(S)
3
julia> try S.nz[[1, 2]] = [1, 2, 3]; catch; println("error") end
error

See also

get_nz, set

Extra doc: https://github.com/casadi/casadi/wiki/L_2ow

Definition at line 445 of file matrix_impl.hpp.

set_precision()

template<typename Scalar >

void casadi::Matrix< Scalar >::set_precision ( casadi_int  precision )

static

Global settings per class (DM and SX each keep their own), applied by str(), print() and the print_* methods. Defaults: precision 6, width 0, scientific false.

>>> DM.set_precision(3)
>>> DM(1/3)
DM(0.333)
>>> DM.set_precision(6)
>>> DM(1/3)
DM(0.333333)

>> DM.set_precision(3);
>> DM(1/3)
0.333
>> DM.set_precision(6);
>> DM(1/3)
0.333333

julia> ca.DM.set_precision(3)
julia> ca.DM(1/3)
DM(0.333)
julia> ca.DM.set_precision(6)
julia> ca.DM(1/3)
DM(0.333333)

See also

get_precision

Extra doc: https://github.com/casadi/casadi/wiki/L_2p6

Definition at line 40 of file matrix_impl.hpp.

set_scientific()

template<typename Scalar >

void casadi::Matrix< Scalar >::set_scientific ( bool  scientific )

static

Definition at line 46 of file matrix_impl.hpp.

set_width()

template<typename Scalar >

void casadi::Matrix< Scalar >::set_width ( casadi_int  width )

static

Definition at line 43 of file matrix_impl.hpp.

size() [1/2]

std::pair<casadi_int, casadi_int> casadi::GenericMatrix< Matrix< Scalar > >::size ( ) const

inherited

>>> 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

size() [2/2]

casadi_int casadi::GenericMatrix< Matrix< Scalar > >::size ( casadi_int  axis ) const

inherited

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

size1()

casadi_int casadi::GenericMatrix< Matrix< Scalar > >::size1 ( ) const

inherited

>>> 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

size2()

casadi_int casadi::GenericMatrix< Matrix< Scalar > >::size2 ( ) const

inherited

See also

size1, size, columns

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

soc()

static Matrix< Scalar > casadi::GenericMatrix< Matrix< Scalar > >::soc ( const Matrix< Scalar > &  x, const Matrix< Scalar > &  y  )

staticinherited

Functions called by friend functions defined here

sparsity()

Sparsity casadi::GenericMatrix< Matrix< Scalar > >::sparsity ( ) const

inherited

>>> 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

sym() [1/7]

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

inlinestaticinherited

>>> 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.

sym() [2/7]

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

inlinestaticinherited

>>> 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.

sym() [3/7]

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

inlinestaticinherited

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

Examples

SX/SXaddition.cc, and SX/ssym.py.

Definition at line 4948 of file generic_matrix.hpp.

sym() [4/7]

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

inlinestaticinherited

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.

sym() [5/7]

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

staticinherited

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 5033 of file generic_matrix.hpp.

sym() [6/7]

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

staticinherited

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 5075 of file generic_matrix.hpp.

sym() [7/7]

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

inlinestaticinherited

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

Definition at line 4955 of file generic_matrix.hpp.

T()

template<typename Scalar >

Matrix<Scalar> casadi::Matrix< Scalar >::T

(

)

const

tangent()

static Matrix< Scalar > casadi::GenericMatrix< Matrix< Scalar > >::tangent ( const Matrix< Scalar > &  ex, const Matrix< Scalar > &  arg, const Dict &  opts = Dict()  )

staticinherited

Functions called by friend functions defined here

to_file()

template<typename Scalar >

void casadi::Matrix< Scalar >::to_file	(	const std::string &	filename,
		const std::string &	format = ""
	)		const

Supported formats, selected by the file extension unless format is given:

• mtx: Matrix Market coordinate format (sparse, one-based row/col/value triplets)
• txt: one line per row, whitespace separated, aligned columns, full precision, structural zeros written as 00. Does not scale to large sparse matrices. Values are written with the C locale; nan and inf round-trip. An unknown extension or format raises an error. SX is not supported.

Parameters

filename	Output path
format	"mtx" or "txt"; empty means deduce from the extension

>>> import os, tempfile
>>> fn = os.path.join(tempfile.mkdtemp(), "a.txt")
>>> A = DM(Sparsity.diag(2)) * 2.5
>>> A.to_file(fn)
>>> DM.from_file(fn)
DM(
[[2.5, 00],
 [00, 2.5]])
>>> os.remove(fn); os.rmdir(os.path.dirname(fn))

>> fn = [tempname '.txt'];
>> A = DM(Sparsity.diag(2)) * 2.5;
>> A.to_file(fn);
>> DM.from_file(fn)
[[2.5, 00],
 [00, 2.5]]
>> delete(fn);

julia> fn = joinpath(mktempdir(), "a.txt");
julia> A = ca.DM(ca.Sparsity.diag(2)) * 2.5;
julia> ca.to_file(A, fn)
julia> ca.DM.from_file(fn)
DM(
[[2.5, 00],
 [00, 2.5]])
julia> rm(dirname(fn), recursive=true)

See also

from_file, Sparsity::to_file

Extra doc: https://github.com/casadi/casadi/wiki/L_2p9

triplet() [1/3]

template<typename Scalar >

static Matrix<Scalar> casadi::Matrix< Scalar >::triplet ( const std::vector< casadi_int > &  row, const std::vector< casadi_int > &  col, const Matrix< Scalar > &  d  )

static

Entry k of the result is at (row[k], col[k]) with value d[k]. The three lists must have the same length; indices are zero-based and must be within the matrix bounds. The nonzeros are reordered into column-major order. When the same (row, col) pair appears more than once, only the first value is kept; duplicates are not summed.

Parameters

row	Row index of each entry
col	Column index of each entry
d	Dense vector of values, one per entry
nrow	Number of rows of the result [default: largest row index plus one]
ncol	Number of columns of the result [default: largest column index plus one]

>>> DM.triplet([0, 1], [1, 0], [5, 6], 3, 3)
DM(
[[00, 5, 00],
 [6, 00, 00],
 [00, 00, 00]])
>>> DM.triplet([0, 1], [1, 0], [5, 6], (3, 3)).nonzeros()
[6.0, 5.0]
>>> SX.triplet([0, 1], [0, 1], SX.sym("v", 2), 2, 2)
SX(
[[v_0, 00],
 [00, v_1]])
>>> DM.triplet([], [], [], 2, 2).nnz()
0
>>> try: DM.triplet([0, 1], [1, 0], [5], 3, 3)
... except Exception as e: print("error")
error

>> DM.triplet([0 1], [1 0], [5 6], 3, 3)
[[00, 5, 00],
 [6, 00, 00],
 [00, 00, 00]]
>> DM.triplet([0 1], [1 0], [5 6], [3 3]).nonzeros()
6 5
>> SX.triplet([0 1], [0 1], SX.sym('v', 2), 2, 2)
[[v_0, 00],
 [00, v_1]]
>> DM.triplet([], [], [], 2, 2).nnz()
0
>> try, DM.triplet([0 1], [1 0], 5, 3, 3); catch e, disp('error'); end
error

julia> ca.DM.triplet([0, 1], [1, 0], [5, 6], 3, 3)
DM(
[[00, 5, 00],
 [6, 00, 00],
 [00, 00, 00]])
julia> ca.SX.triplet([0, 1], [0, 1], ca.SX.sym("v", 2), 2, 2)
SX(
[[v_0, 00],
 [00, v_1]])
julia> ca.nnz(ca.DM.triplet([], [], [], 2, 2))
0
julia> try ca.DM.triplet([0, 1], [1, 0], [5], 3, 3); catch; println("error") end
error

See also

Sparsity::triplet

Extra doc: https://github.com/casadi/casadi/wiki/L_23t

triplet() [2/3]

template<typename Scalar >

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

static

Entry k of the result is at (row[k], col[k]) with value d[k]. The three lists must have the same length; indices are zero-based and must be within the matrix bounds. The nonzeros are reordered into column-major order. When the same (row, col) pair appears more than once, only the first value is kept; duplicates are not summed.

Parameters

row	Row index of each entry
col	Column index of each entry
d	Dense vector of values, one per entry
nrow	Number of rows of the result [default: largest row index plus one]
ncol	Number of columns of the result [default: largest column index plus one]

>>> DM.triplet([0, 1], [1, 0], [5, 6], 3, 3)
DM(
[[00, 5, 00],
 [6, 00, 00],
 [00, 00, 00]])
>>> DM.triplet([0, 1], [1, 0], [5, 6], (3, 3)).nonzeros()
[6.0, 5.0]
>>> SX.triplet([0, 1], [0, 1], SX.sym("v", 2), 2, 2)
SX(
[[v_0, 00],
 [00, v_1]])
>>> DM.triplet([], [], [], 2, 2).nnz()
0
>>> try: DM.triplet([0, 1], [1, 0], [5], 3, 3)
... except Exception as e: print("error")
error

>> DM.triplet([0 1], [1 0], [5 6], 3, 3)
[[00, 5, 00],
 [6, 00, 00],
 [00, 00, 00]]
>> DM.triplet([0 1], [1 0], [5 6], [3 3]).nonzeros()
6 5
>> SX.triplet([0 1], [0 1], SX.sym('v', 2), 2, 2)
[[v_0, 00],
 [00, v_1]]
>> DM.triplet([], [], [], 2, 2).nnz()
0
>> try, DM.triplet([0 1], [1 0], 5, 3, 3); catch e, disp('error'); end
error

julia> ca.DM.triplet([0, 1], [1, 0], [5, 6], 3, 3)
DM(
[[00, 5, 00],
 [6, 00, 00],
 [00, 00, 00]])
julia> ca.SX.triplet([0, 1], [0, 1], ca.SX.sym("v", 2), 2, 2)
SX(
[[v_0, 00],
 [00, v_1]])
julia> ca.nnz(ca.DM.triplet([], [], [], 2, 2))
0
julia> try ca.DM.triplet([0, 1], [1, 0], [5], 3, 3); catch; println("error") end
error

See also

Sparsity::triplet

Extra doc: https://github.com/casadi/casadi/wiki/L_23t

triplet() [3/3]

template<typename Scalar >

static Matrix<Scalar> casadi::Matrix< Scalar >::triplet ( const std::vector< casadi_int > &  row, const std::vector< casadi_int > &  col, const Matrix< Scalar > &  d, const std::pair< casadi_int, casadi_int > &  rc  )

static

Entry k of the result is at (row[k], col[k]) with value d[k]. The three lists must have the same length; indices are zero-based and must be within the matrix bounds. The nonzeros are reordered into column-major order. When the same (row, col) pair appears more than once, only the first value is kept; duplicates are not summed.

Parameters

row	Row index of each entry
col	Column index of each entry
d	Dense vector of values, one per entry
nrow	Number of rows of the result [default: largest row index plus one]
ncol	Number of columns of the result [default: largest column index plus one]

>>> DM.triplet([0, 1], [1, 0], [5, 6], 3, 3)
DM(
[[00, 5, 00],
 [6, 00, 00],
 [00, 00, 00]])
>>> DM.triplet([0, 1], [1, 0], [5, 6], (3, 3)).nonzeros()
[6.0, 5.0]
>>> SX.triplet([0, 1], [0, 1], SX.sym("v", 2), 2, 2)
SX(
[[v_0, 00],
 [00, v_1]])
>>> DM.triplet([], [], [], 2, 2).nnz()
0
>>> try: DM.triplet([0, 1], [1, 0], [5], 3, 3)
... except Exception as e: print("error")
error

>> DM.triplet([0 1], [1 0], [5 6], 3, 3)
[[00, 5, 00],
 [6, 00, 00],
 [00, 00, 00]]
>> DM.triplet([0 1], [1 0], [5 6], [3 3]).nonzeros()
6 5
>> SX.triplet([0 1], [0 1], SX.sym('v', 2), 2, 2)
[[v_0, 00],
 [00, v_1]]
>> DM.triplet([], [], [], 2, 2).nnz()
0
>> try, DM.triplet([0 1], [1 0], 5, 3, 3); catch e, disp('error'); end
error

julia> ca.DM.triplet([0, 1], [1, 0], [5, 6], 3, 3)
DM(
[[00, 5, 00],
 [6, 00, 00],
 [00, 00, 00]])
julia> ca.SX.triplet([0, 1], [0, 1], ca.SX.sym("v", 2), 2, 2)
SX(
[[v_0, 00],
 [00, v_1]])
julia> ca.nnz(ca.DM.triplet([], [], [], 2, 2))
0
julia> try ca.DM.triplet([0, 1], [1, 0], [5], 3, 3); catch; println("error") end
error

See also

Sparsity::triplet

Extra doc: https://github.com/casadi/casadi/wiki/L_23t

type_name()

template<typename Scalar >

std::string casadi::Matrix< Scalar >::type_name

static

>>> DM.type_name(), SX.type_name()
('DM', 'SX')

>> fprintf('%s %s\n', DM.type_name(), SX.type_name())
DM SX

julia> ca.DM.type_name(), ca.SX.type_name()
("DM", "SX")

Extra doc: https://github.com/casadi/casadi/wiki/L_2ox

Definition at line 616 of file matrix_impl.hpp.

which_function()

Function casadi::SX::which_function

(

)

const

Extra doc: https://github.com/casadi/casadi/wiki/L_28n

which_output()

casadi_int casadi::SX::which_output

(

)

const

Extra doc: https://github.com/casadi/casadi/wiki/L_28m

zeros() [1/3]

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

inlinestaticinherited

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 5151 of file generic_matrix.hpp.

zeros() [2/3]

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

inlinestaticinherited

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.

zeros() [3/3]

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

inlinestaticinherited

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.

---

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

• casadi_common.hpp
• matrix_decl.hpp
• im.hpp
• matrix_impl.hpp
• sx.hpp