Linear solver. More...

#include <linsol.hpp>

Detailed Description

Solves the square linear system A*X = B or A'*X = B for X with a sparse direct solver plugin. A Linsol is created for a fixed sparsity pattern of A; the numerical values are given at every call. A matrix with another sparsity pattern is projected onto the fixed one (entries outside it are dropped). The solve is split in a symbolic factorization (sfact, pivot selection from the pattern), a numeric factorization (nfact) and the triangular solves (solve); solve(A, B) performs all three. A numerically singular matrix makes nfact (or solve) raise an error for most plugins; for a symbolic (MX) A, solve returns an expression node that is differentiable with respect to A and B.

Available plugins include "qr" and "ldl" (sparse direct QR and LDL, codegen support), "symbolicqr" (QR as a symbolic expression), "csparse", "csparsecholesky", "lapacklu", "lapackqr", "ma27", "mumps". neig and rank are only implemented by "ldl", det by "qr" and "csparse". The constructor raises an error for a non-square pattern only when the plugin checks it; otherwise the solve fails.

>>> A = DM([[3, 1], [1, 2]]); b = DM([4, 3])
>>> L = Linsol("L", "qr", A.sparsity())
>>> L.plugin_name(), L.sparsity()
('qr', Sparsity(2x2))
>>> L.solve(A, b), L.solve(DM([[1, 2], [0, 1]]), DM([1, 1]), True)
(DM([1, 1]), DM([1, -1]))
>>> L.solve(A, DM([[4, 1], [3, 0]]))
DM(
[[1, 0.4],
 [1, -0.2]])
>>> L.det(A)
5.0
>>> try:
...     L.solve(DM([[1, 1], [1, 1]]), b)
... except RuntimeError as e:
...     print("'nfact' failed" in str(e))
True
>>> Am = MX.sym("A", A.sparsity()); bm = MX.sym("b", 2)
>>> f = Function("f", [Am, bm], [L.solve(Am, bm), L.det(Am)])
>>> f(A, b)
(DM([1, 1]), DM(5))

>> A = DM([3 1; 1 2]); b = DM([4; 3]);
>> L = Linsol('L', 'qr', A.sparsity());
>> L.plugin_name(), L.sparsity()
qr
2x2
>> L.solve(A, b), L.solve(DM([1 2; 0 1]), DM([1; 1]), true)
[1, 1]
[1, -1]
>> L.solve(A, DM([4 1; 3 0]))
[[1, 0.4],
 [1, -0.2]]
>> L.det(A)
5
>> try, L.solve(DM([1 1; 1 1]), b); catch e, msg = e.message; end
>> contains(msg, '''nfact'' failed')
1
>> Am = MX.sym('A', A.sparsity()); bm = MX.sym('b', 2);
>> f = Function('f', {Am, bm}, {L.solve(Am, bm), L.det(Am)});
>> [xs, d] = f(A, b); disp(xs), disp(d)
[1, 1]
5

julia> A = ca.DM([3 1; 1 2]); b = ca.DM([4, 3]);
julia> L = ca.Linsol("L", "qr", ca.sparsity(A));
julia> ca.plugin_name(L), ca.sparsity(L)
("qr", 2x2)
julia> ca.solve(L, A, b)
DM([1, 1])
julia> ca.solve(L, ca.DM([1 2; 0 1]), ca.DM([1, 1]), true)
DM([1, -1])
julia> ca.solve(L, A, ca.DM([4 1; 3 0]))
DM(
[[1, 0.4],
 [1, -0.2]])
julia> L.det(A)
5.0
julia> try
           ca.solve(L, ca.DM([1 1; 1 1]), b, false)
       catch e
           println(occursin("'nfact' failed", sprint(showerror, e)))
       end
true
julia> Am = ca.MX.sym("A", ca.sparsity(A)); bm = ca.MX.sym("b", 2);
julia> f = ca.Function("f", [Am, bm], [ca.solve(L, Am, bm), L.det(Am)]);
julia> f(A, b)
([1, 1], 5)

General information

List of plugins

- csparsecholesky

- csparse

- ma27

- lapacklu

- lapackqr

- mumps

- ldl

- qr

- tridiag

- symbolicqr

Note: some of the plugins in this list might not be available on your system. Also, there might be extra plugins available to you that are not listed here. You can obtain their documentation with Linsol.doc("myextraplugin")

csparsecholesky

Linsol with CSparseCholesky Interface

Extra doc: https://github.com/casadi/casadi/wiki/L_21u

csparse

Linsol with CSparse Interface

Extra doc: https://github.com/casadi/casadi/wiki/L_21t

ma27

Interface to the sparse direct linear solver MA27 Works for symmetric indefinite systems Partly adopted from qpOASES 3.2

Author: Joel Andersson

Date: 2016

Extra doc: https://github.com/casadi/casadi/wiki/L_229

lapacklu

This class solves the linear system A.x=b by making an LU factorization of A:
A = L.U, with L lower and U upper triangular

Extra doc: https://github.com/casadi/casadi/wiki/L_22h

List of available options
Id	Type	Description
allow_equilibration_failure	OT_BOOL	Non-fatal error when equilibration fails
equilibration	OT_BOOL	Equilibrate the matrix

lapackqr

This class solves the linear system A.x=b by making an QR factorization of A:
A = Q.R, with Q orthogonal and R upper triangular

Extra doc: https://github.com/casadi/casadi/wiki/L_22g

List of available options
Id	Type	Description
max_nrhs	OT_INT	Maximum number of right-hand-sides that get processed in a single pass [default:10].

mumps

Interface to the sparse direct linear solver MUMPS Works for symmetric indefinite systems

Author: Joel Andersson

Date: 2019

Extra doc: https://github.com/casadi/casadi/wiki/L_22t

List of available options
Id	Type	Description
posdef	OT_BOOL	Positive definite
symmetric	OT_BOOL	Symmetric matrix

ldl

Linear solver using sparse direct LDL factorization

Extra doc: https://github.com/casadi/casadi/wiki/L_233

List of available options
Id	Type	Description
incomplete	OT_BOOL	Incomplete factorization, without any fill-in
preordering	OT_BOOL	Approximate minimal degree (AMD) preordering

qr

Linear solver using sparse direct QR factorization

Extra doc: https://github.com/casadi/casadi/wiki/L_22z

List of available options
Id	Type	Description
cache	OT_DOUBLE	Amount of factorisations to remember (thread-local) [0]
eps	OT_DOUBLE	Minimum R entry before singularity is declared [1e-12]

tridiag

Linear solver for tridiagonal matrices

Extra doc: https://github.com/casadi/casadi/wiki/L_22v

symbolicqr

Linear solver for sparse least-squares problems Inspired from https://github.com/scipy/scipy/blob/v0.14.0/scipy/sparse/linalg/isolve/lsqr.py#L96

Extra doc: https://github.com/casadi/casadi/wiki/L_230

Linsol based on QR factorization with sparsity pattern based reordering without partial pivoting

Extra doc: https://github.com/casadi/casadi/wiki/L_231

List of available options
Id	Type	Description
fopts	OT_DICT	Options to be passed to generated function objects

Author: Joel Andersson

Date: 2011-2016

Extra doc: https://github.com/casadi/casadi/wiki/L_1kh

Definition at line 142 of file linsol.hpp.

Inheritance diagram for casadi::Linsol:

[legend]

Public Types
using	internal_base_type = SharedObjectInternal

using	base_type = SharedObject

Public Member Functions
	Linsol ()
	Default constructor (a null object) More...

	Linsol (const std::string &name, const std::string &solver, const Sparsity &sp, const Dict &opts=Dict())
	Create a linear solver. More...

LinsolInternal *	operator-> ()
	Access functions of the node. More...

const LinsolInternal *	operator-> () const

std::string	plugin_name () const
	Query plugin name. More...

const Sparsity &	sparsity () const
	Get the sparsity pattern of A fixed at construction. More...

void	sfact (const DM &A) const
	Symbolic factorization of the linear system, e.g. selecting pivots. More...

void	nfact (const DM &A) const
	Numeric factorization of the linear system. More...

casadi_int	neig (const DM &A) const
	Number of negative eigenvalues. More...

casadi_int	rank (const DM &A) const
	Matrix rank. More...

double	det (const DM &A) const
	Matrix determinant. More...

MX	det (const MX &A) const
	Matrix determinant as an MX graph node. More...

Dict	stats (int mem=1) const
	Get all statistics obtained at the end of the last evaluate call. More...

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

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

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

std::string	debug_repr () const

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

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


DM	solve (const DM &A, const DM &B, bool tr=false) const
	Solve the linear system AX = B (or A'X = B with `tr` true) More...

MX	solve (const MX &A, const MX &B, bool tr=false) const
	Solve the linear system AX = B (or A'X = B with `tr` true) More...

Static Public Member Functions
static std::string	type_name ()
	Get type name. More...

static bool	has_plugin (const std::string &name)
	Check if a plugin is available. More...

static void	load_plugin (const std::string &name)
	Explicitly load a plugin dynamically. More...

static std::string	doc (const std::string &name)
	Get solver specific documentation. More...

Member Typedef Documentation

◆ base_type

using casadi::SharedObject::base_type = SharedObject

inherited

Definition at line 103 of file shared_object.hpp.

◆ internal_base_type

using casadi::SharedObject::internal_base_type = SharedObjectInternal

inherited

Definition at line 102 of file shared_object.hpp.

Constructor & Destructor Documentation

◆ Linsol() [1/2]

casadi::Linsol::Linsol ( )

◆ Linsol() [2/2]

casadi::Linsol::Linsol	(	const std::string &	name,
		const std::string &	solver,
		const Sparsity &	sp,
		const Dict &	opts = `Dict()`
	)

explicit

Parameters

name	Name of the solver object
solver	Plugin name, e.g. "qr", "ldl", "csparse"; see has_linsol
sp	Sparsity pattern of A (square); the numerical values are given at every call
opts	Options; an unknown option raises an error

>>> L = Linsol("L", "ldl", Sparsity.dense(2, 2))
>>> L
Linsol(Linear solver LinsolLdl)
>>> try:
...     Linsol("L", "qr", Sparsity.dense(2, 2), {"no_such_option": 1})
... except RuntimeError as e:
...     print("Unknown option" in str(e))
True

>> L = Linsol('L', 'ldl', Sparsity.dense(2, 2)); disp(L)
Linear solver LinsolLdl
>> opts = struct('no_such_option', 1);
>> try, Linsol('L', 'qr', Sparsity.dense(2, 2), opts); catch e, msg = e.message; end
>> contains(msg, 'Unknown option')
1

julia> L = ca.Linsol("L", "ldl", ca.Sparsity.dense(2, 2));
julia> ca.str(L)
"Linear solver LinsolLdl"
julia> try
           ca.Linsol("L", "qr", ca.Sparsity.dense(2, 2), Dict("no_such_option" => 1))
       catch e
           println(occursin("Unknown option", sprint(showerror, e)))
       end
true

Extra doc: https://github.com/casadi/casadi/wiki/L_2pe

Member Function Documentation

◆ hash()

casadi_int casadi::GenericShared< SharedObject , SharedObjectInternal >::__hash__

inherited

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

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

Definition at line 123 of file generic_shared_impl.hpp.

◆ class_name()

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

inherited

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

◆ debug_repr()

std::string casadi::GenericShared< SharedObject , SharedObjectInternal >::debug_repr

inherited

Definition at line 112 of file generic_shared_impl.hpp.

◆ det() [1/2]

double casadi::Linsol::det ( const DM & A ) const

Not available for all solvers ("qr" and "csparse"); factorizes A first.

>>> A = DM([[3, 1], [1, 2]])
>>> Linsol("L", "qr", A.sparsity()).det(A)
5.0
>>> try:
...     Linsol("L", "ldl", A.sparsity()).det(A)
... except RuntimeError as e:
...     print("'det' not defined" in str(e))
True

>> A = DM([3 1; 1 2]); L = Linsol('L', 'qr', A.sparsity()); disp(L.det(A))
5
>> L = Linsol('L', 'ldl', A.sparsity());
>> try, L.det(A); catch e, disp(contains(e.message, '''det'' not defined')); end
1

julia> A = ca.DM([3 1; 1 2]);
julia> ca.Linsol("L", "qr", ca.sparsity(A)).det(A)
5.0
julia> try
           ca.Linsol("L", "ldl", ca.sparsity(A)).det(A)
       catch e
           println(occursin("'det' not defined", sprint(showerror, e)))
       end
true

Extra doc: https://github.com/casadi/casadi/wiki/L_2hw

◆ det() [2/2]

MX casadi::Linsol::det ( const MX & A ) const

◆ disp()

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

inherited

◆ doc()

static std::string casadi::Linsol::doc ( const std::string & name )

static

Same as doc_linsol.

>>> "LDL" in Linsol.doc("ldl")
True

>> contains(Linsol.doc('ldl'), 'LDL')
1

julia> occursin("LDL", ca.Linsol.doc("ldl"))
true

Extra doc: https://github.com/casadi/casadi/wiki/L_2ph

◆ get_str()

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

inlineinherited

Definition at line 91 of file shared_object.hpp.

◆ has_plugin()

static bool casadi::Linsol::has_plugin ( const std::string & name )

static

Same as has_linsol.

>>> Linsol.has_plugin("qr"), Linsol.has_plugin("no_such_plugin")
(True, False)

>> Linsol.has_plugin('qr'), Linsol.has_plugin('no_such_plugin')
1
0

julia> ca.Linsol.has_plugin("qr"), ca.Linsol.has_plugin("no_such_plugin")
(true, false)

Extra doc: https://github.com/casadi/casadi/wiki/L_2pf

◆ is_null()

bool casadi::GenericShared< SharedObject , SharedObjectInternal >::is_null

inherited

Definition at line 116 of file generic_shared_impl.hpp.

◆ load_plugin()

static void casadi::Linsol::load_plugin ( const std::string & name )

static

Same as load_linsol; raises an error when the plugin cannot be found.

>>> try:
...     Linsol.load_plugin("no_such_plugin")
... except RuntimeError as e:
...     print("no_such_plugin" in str(e))
True

>> try, Linsol.load_plugin('no_such_plugin'); catch e, msg = e.message; end
>> contains(msg, 'no_such_plugin')
1

julia> try
           ca.Linsol.load_plugin("no_such_plugin")
       catch e
           println(occursin("no_such_plugin", sprint(showerror, e)))
       end
true

Extra doc: https://github.com/casadi/casadi/wiki/L_2pg

◆ neig()

casadi_int casadi::Linsol::neig ( const DM & A ) const

Not available for all solvers (only "ldl"); uses the factorization of the most recent nfact call, which must have been made with the same matrix.

>>> A = DM([[-2, 0], [0, 1]])
>>> L = Linsol("L", "ldl", A.sparsity())
>>> L.nfact(A)
>>> L.neig(A)
1
>>> try:
...     Linsol("L", "qr", A.sparsity()).neig(A)
... except RuntimeError as e:
...     print("'neig' not defined" in str(e))
True

>> A = DM([-2 0; 0 1]); L = Linsol('L', 'ldl', A.sparsity());
>> L.nfact(A); disp(L.neig(A))
1
>> L = Linsol('L', 'qr', A.sparsity());
>> try, L.neig(A); catch e, disp(contains(e.message, '''neig'' not defined')); end
1

julia> A = ca.DM([-2 0; 0 1]);
julia> L = ca.Linsol("L", "ldl", ca.sparsity(A));
julia> ca.nfact(L, A)
julia> ca.neig(L, A)
1
julia> try
           ca.neig(ca.Linsol("L", "qr", ca.sparsity(A)), A)
       catch e
           println(occursin("'neig' not defined", sprint(showerror, e)))
       end
true

Extra doc: https://github.com/casadi/casadi/wiki/L_1kk

◆ nfact()

void casadi::Linsol::nfact ( const DM & A ) const

Factorizes the values of A (after sfact if not done yet), so that neig, rank and the low-level solve can use the factorization. Raises an error when the factorization fails with option "regularity_check" set; otherwise a failure is only reported by solve.

>>> A = DM([[3, 1], [1, 2]])
>>> L = Linsol("L", "ldl", A.sparsity())
>>> L.nfact(A)
>>> L.neig(A), L.rank(A)
(0, 2)
>>> L.nfact(DM([[-1, 0], [0, 1]]))
>>> L.neig(DM([[-1, 0], [0, 1]]))
1

>> A = DM([3 1; 1 2]); L = Linsol('L', 'ldl', A.sparsity());
>> L.nfact(A); fprintf('%d %d\n', L.neig(A), L.rank(A))
0 2
>> B = DM([-1 0; 0 1]); L.nfact(B); disp(L.neig(B))
1

julia> A = ca.DM([3 1; 1 2]);
julia> L = ca.Linsol("L", "ldl", ca.sparsity(A));
julia> ca.nfact(L, A)
julia> ca.neig(L, A), ca.rank(L, A)
(0, 2)
julia> ca.nfact(L, ca.DM([-1 0; 0 1]))
julia> ca.neig(L, ca.DM([-1 0; 0 1]))
1

Extra doc: https://github.com/casadi/casadi/wiki/L_2pj

◆ operator->() [1/2]

LinsolInternal* casadi::Linsol::operator-> ( )

◆ operator->() [2/2]

const LinsolInternal* casadi::Linsol::operator-> ( ) const

◆ plugin_name()

std::string casadi::Linsol::plugin_name ( ) const

◆ rank()

casadi_int casadi::Linsol::rank ( const DM & A ) const

Not available for all solvers (only "ldl"); uses the factorization of the most recent nfact call, which must have been made with the same matrix.

A rank-deficient matrix also triggers a warning in nfact.

>>> A = DM([[2, 1], [1, 3]])
>>> L = Linsol("L", "ldl", A.sparsity())
>>> L.nfact(A)
>>> L.rank(A)
2

>> A = DM([2 1; 1 3]); L = Linsol('L', 'ldl', A.sparsity());
>> L.nfact(A); disp(L.rank(A))
2

julia> A = ca.DM([2 1; 1 3]);
julia> L = ca.Linsol("L", "ldl", ca.sparsity(A));
julia> ca.nfact(L, A)
julia> ca.rank(L, A)
2

Extra doc: https://github.com/casadi/casadi/wiki/L_1kl

◆ sfact()

void casadi::Linsol::sfact ( const DM & A ) const

Only uses the sparsity pattern of A. Called automatically by nfact and solve when needed; raises an error when the plugin fails.

Extra doc: https://github.com/casadi/casadi/wiki/L_2pi

◆ solve() [1/2]

DM casadi::Linsol::solve	(	const DM &	A,
		const DM &	B,
		bool	tr = `false`
	)		const

For DM arguments, factorizes A and solves for all columns of B at once; the result is dense. For MX arguments, returns an expression node that is differentiable. The row count of A and B must match.

Parameters

A	Square matrix with the sparsity pattern given at construction (projected onto it otherwise)
B	Right-hand side, one column per system to solve
tr	Solve with the transpose of `A` instead

Returns: X with the shape of B

>>> L = Linsol("L", "qr", Sparsity.dense(2, 2))
>>> L.solve(DM([[3, 1], [1, 2]]), DM([4, 3]))
DM([1, 1])
>>> try:
...     L.solve(DM([[3, 1], [1, 2]]), DM([1, 2, 3]))
... except RuntimeError as e:
...     print("matching row count" in str(e))
True

>> L = Linsol('L', 'qr', Sparsity.dense(2, 2));
>> L.solve(DM([3 1; 1 2]), DM([4; 3]))
[1, 1]
>> try, L.solve(DM([3 1; 1 2]), DM([1; 2; 3])); catch e, msg = e.message; end
>> contains(msg, 'matching row count')
1

julia> L = ca.Linsol("L", "qr", ca.Sparsity.dense(2, 2));
julia> ca.solve(L, ca.DM([3 1; 1 2]), ca.DM([4, 3]))
DM([1, 1])
julia> try
           ca.solve(L, ca.DM([3 1; 1 2]), ca.DM([1, 2, 3]))
       catch e
           println(occursin("matching row count", sprint(showerror, e)))
       end
true

Extra doc: https://github.com/casadi/casadi/wiki/L_2pk

◆ solve() [2/2]

MX casadi::Linsol::solve	(	const MX &	A,
		const MX &	B,
		bool	tr = `false`
	)		const

For DM arguments, factorizes A and solves for all columns of B at once; the result is dense. For MX arguments, returns an expression node that is differentiable. The row count of A and B must match.

Parameters

A	Square matrix with the sparsity pattern given at construction (projected onto it otherwise)
B	Right-hand side, one column per system to solve
tr	Solve with the transpose of `A` instead

Returns: X with the shape of B

>>> L = Linsol("L", "qr", Sparsity.dense(2, 2))
>>> L.solve(DM([[3, 1], [1, 2]]), DM([4, 3]))
DM([1, 1])
>>> try:
...     L.solve(DM([[3, 1], [1, 2]]), DM([1, 2, 3]))
... except RuntimeError as e:
...     print("matching row count" in str(e))
True

>> L = Linsol('L', 'qr', Sparsity.dense(2, 2));
>> L.solve(DM([3 1; 1 2]), DM([4; 3]))
[1, 1]
>> try, L.solve(DM([3 1; 1 2]), DM([1; 2; 3])); catch e, msg = e.message; end
>> contains(msg, 'matching row count')
1

julia> L = ca.Linsol("L", "qr", ca.Sparsity.dense(2, 2));
julia> ca.solve(L, ca.DM([3 1; 1 2]), ca.DM([4, 3]))
DM([1, 1])
julia> try
           ca.solve(L, ca.DM([3 1; 1 2]), ca.DM([1, 2, 3]))
       catch e
           println(occursin("matching row count", sprint(showerror, e)))
       end
true

Extra doc: https://github.com/casadi/casadi/wiki/L_2pk

◆ sparsity()

const Sparsity& casadi::Linsol::sparsity ( ) const

◆ stats()

Dict casadi::Linsol::stats ( int mem = 1 ) const

Plugin-specific; empty for most plugins. Raises an error before the first solve. With the option "record_time" set, it holds call counts and timings (n_call_*, t_proc_*, t_wall_*) of sfact, nfact and solve.

>>> L = Linsol("L", "qr", Sparsity.dense(1, 1))
>>> try:
...     L.stats()
... except RuntimeError as e:
...     print("did not solve a problem yet" in str(e))
True
>>> L.solve(DM(2), DM(4)), L.stats()
(DM(2), {})
>>> L = Linsol("L", "qr", Sparsity.dense(1, 1), {"record_time": True})
>>> L.solve(DM(2), DM(4)); L.stats()["n_call_solve"]
DM(2)
1

>> L = Linsol('L', 'qr', Sparsity.dense(1, 1));
>> try, L.stats(); catch e, disp(contains(e.message, 'did not solve a problem yet')); end
1
>> L.solve(DM(2), DM(4)), isempty(fieldnames(L.stats()))
2
1

julia> L = ca.Linsol("L", "qr", ca.Sparsity.dense(1, 1));
julia> try
           ca.stats(L)
       catch e
           println(occursin("did not solve a problem yet", sprint(showerror, e)))
       end
true
julia> ca.solve(L, ca.DM(2), ca.DM(4)), ca.stats(L)
(2, Dict{String, Any}())
julia> L = ca.Linsol("L", "qr", ca.Sparsity.dense(1, 1), Dict("record_time" => true));
julia> ca.solve(L, ca.DM(2), ca.DM(4)); ca.stats(L)["n_call_solve"]
1

Extra doc: https://github.com/casadi/casadi/wiki/L_2pl

◆ type_name()

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

inlinestatic

Extra doc: https://github.com/casadi/casadi/wiki/L_1ki

Definition at line 149 of file linsol.hpp.

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

linsol.hpp

Detailed Description

General information

List of plugins

csparsecholesky

csparse

ma27

lapacklu

lapackqr

mumps

ldl

qr

tridiag

symbolicqr

Public Types

Public Member Functions

Static Public Member Functions

Member Typedef Documentation

◆ base_type

◆ internal_base_type

Constructor & Destructor Documentation

◆ Linsol() [1/2]

◆ Linsol() [2/2]

Member Function Documentation

◆ __hash__()

◆ class_name()

◆ debug_repr()

◆ det() [1/2]

◆ det() [2/2]

◆ disp()

◆ doc()

◆ get_str()

◆ has_plugin()

◆ is_null()

◆ load_plugin()

◆ neig()

◆ nfact()

◆ operator->() [1/2]

◆ operator->() [2/2]

◆ plugin_name()

◆ rank()

◆ sfact()

◆ solve() [1/2]

◆ solve() [2/2]

◆ sparsity()

◆ stats()

◆ type_name()

◆ hash()