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]

Collaboration 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...

casadi_int	checkout () const
	Checkout a memory object. More...

void	release (int mem) const
	Release a memory object. More...

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

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

void	own (SharedObjectInternal *node)

void	assign (SharedObjectInternal *node)
	Assign the node to a node class pointer without reference counting. More...

SharedObjectInternal *	get () const
	Get a const pointer to the node. More...

casadi_int	getCount () const
	Get the reference count. More...

void	swap (GenericShared &other)
	Swap content with another instance. 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...

GenericWeakRef< SharedObject, SharedObjectInternal > *	weak ()
	Get a weak reference to the object. 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...


int	sfact (const double *A, int mem=0) const

int	nfact (const double *A, int mem=0) const

int	solve (const double A, double x, casadi_int nrhs=1, bool tr=false, int mem=0) const

double	det (const double *A, int mem=0) const

casadi_int	neig (const double *A, int mem=0) const

casadi_int	rank (const double *A, int mem=0) const

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

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

static Linsol	create (LinsolInternal *node)
	Create from node. 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...

static Linsol	deserialize (DeserializingStream &s)
	Deserialize with type disambiguation. More...

Protected Member Functions
void	count_up ()

void	count_down ()

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 ( )

Definition at line 32 of file linsol.cpp.

32 {

33 }

◆ 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

Definition at line 35 of file linsol.cpp.

                                                        {
     own(LinsolInternal::getPlugin(solver).creator(name, sp));
     (*this)->construct(opts);
   }

References casadi::PluginInterface< LinsolInternal >::getPlugin(), and casadi::GenericShared< SharedObject, SharedObjectInternal >::own().

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.

                                                              {
     return reinterpret_cast<casadi_int>(get());
   }

◆ assign()

void casadi::GenericShared< SharedObject , SharedObjectInternal >::assign ( Internal * node )

inherited

improper use will cause memory leaks!

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

Definition at line 96 of file generic_shared_impl.hpp.

                                                               {
     node = node_;
   }

◆ checkout()

casadi_int casadi::Linsol::checkout ( ) const

Definition at line 223 of file linsol.cpp.

                                     {
     return (*this)->checkout();
   }

Referenced by casadi::SundialsInterface::init_mem(), and casadi::Ipqp::solve().

◆ class_name()

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

inherited

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

Definition at line 31 of file shared_object.cpp.

                                            {
     return (*this)->class_name();
   }

Referenced by casadi::FmuFunction::check_mem_count(), casadi::MXFunction::export_code_body(), and casadi::BlazingSplineFunction::merge().

◆ count_down()

void casadi::GenericShared< SharedObject , SharedObjectInternal >::count_down

protectedinherited

Definition at line 133 of file generic_shared_impl.hpp.

                                                    {
 #ifdef WITH_EXTRA_CHECKS
     casadi_assert_dev(Function::call_depth_==0);
 #endif // WITH_EXTRA_CHECKS
     if (!node) return;
 #ifdef CASADI_WITH_THREADSAFE_SYMBOLICS
     GenericWeakRef<Shared, Internal>* weak_ref =
       node->weak_ref_.load(std::memory_order_acquire);
 #else
     GenericWeakRef<Shared, Internal>* weak_ref = node->weak_ref_;
 #endif // CASADI_WITH_THREADSAFE_SYMBOLICS
     if (weak_ref) {
 #ifdef CASADI_WITH_THREADSAFE_SYMBOLICS
       // get_mutex() returns a shared_ptr copy, so the mutex outlives this lock
       // even if delete node (below) destroys the WeakRefInternal holding it
       auto mutex = weak_ref->get_mutex();
       // Avoid triggering a delete while a weak_ref.shared_if_alive is being called
       std::lock_guard<std::mutex> lock(*mutex);
 #endif // CASADI_WITH_THREADSAFE_SYMBOLICS
  
       if (--static_cast<Internal*>(node)->count == 0) {
         delete node;
         node = nullptr;
       }
     } else {
       if (--static_cast<Internal*>(node)->count == 0) {
         delete node;
         node = nullptr;
       }
     }
   }

◆ count_up()

void casadi::GenericShared< SharedObject , SharedObjectInternal >::count_up

protectedinherited

Definition at line 132 of file generic_shared_impl.hpp.

                                                  {
 #ifdef WITH_EXTRA_CHECKS
     casadi_assert_dev(Function::call_depth_==0);
 #endif // WITH_EXTRA_CHECKS
  
     if (node) static_cast<Internal*>(node)->count++;
  
   }

◆ create()

Linsol casadi::Linsol::create ( LinsolInternal * node )

static

Extra doc: https://github.com/casadi/casadi/wiki/L_1kj

Definition at line 262 of file linsol.cpp.

                                             {
     Linsol ret;
     ret.own(node);
     return ret;
   }

References casadi::GenericShared< Shared, Internal >::own().

◆ debug_repr()

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

inherited

Definition at line 112 of file generic_shared_impl.hpp.

                                                               {
     if (node) {
         return node->debug_repr(node);
     } else {
         return "NULL";
     }
   }

◆ deserialize()

Linsol casadi::Linsol::deserialize ( DeserializingStream & s )

static

Extra doc: https://github.com/casadi/casadi/wiki/L_1kn

Definition at line 255 of file linsol.cpp.

                                                    {
     Linsol linsol;
     linsol.own(LinsolInternal::deserialize(s));
     linsol->finalize();
     return linsol;
   }

References casadi::LinsolInternal::deserialize(), casadi::ProtoFunction::finalize(), and casadi::GenericShared< Shared, Internal >::own().

◆ det() [1/3]

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

Definition at line 198 of file linsol.cpp.

                                       {
     if (A.sparsity()!=sparsity()) return det(project(A, sparsity()));
     scoped_checkout<Linsol> mem(*this);
     if (sfact(A.ptr(), mem)) casadi_error("Linsol::det: 'sfact' failed");
     if (nfact(A.ptr(), mem)) casadi_error("Linsol::det: 'nfact' failed");
     return det(A.ptr(), mem);
   }

References nfact(), casadi::Matrix< Scalar >::ptr(), sfact(), sparsity(), and casadi::Matrix< Scalar >::sparsity().

Referenced by casadi::MX::det(), casadi::Determinant::eval(), and casadi::Determinant::eval_mx().

◆ det() [2/3]

double casadi::Linsol::det	(	const double *	A,
		int	mem = `0`
	)		const

Low-level API

Definition at line 174 of file linsol.cpp.

                                                    {
     auto m = static_cast<LinsolMemory*>((*this)->memory(mem));
     casadi_assert(m->is_nfact, "Linear system has not been factorized");
     return (*this)->det(m, A);
   }

◆ det() [3/3]

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

Definition at line 206 of file linsol.cpp.

                                   {
     return A->get_det(*this);
   }

References casadi::MXNode::get_det().

◆ disp()

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

inherited

Definition at line 35 of file shared_object.cpp.

                                                              {
     if (is_null()) {
       stream << "NULL";
     } else {
       (*this)->disp(stream, more);
     }
   }

References casadi::GenericShared< SharedObject, SharedObjectInternal >::is_null().

Referenced by casadi::WeakRefInternal::disp(), casadi::Nlpsol::disp_more(), and casadi::CsparseInterface::nfact().

◆ doc()

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

Definition at line 61 of file linsol.cpp.

                                              {
     return LinsolInternal::getPlugin(name).doc;
   }

References casadi::PluginInterface< LinsolInternal >::getPlugin().

Referenced by casadi::doc_linsol().

◆ get()

SharedObjectInternal * casadi::GenericShared< SharedObject , SharedObjectInternal >::get

inherited

Definition at line 99 of file generic_shared_impl.hpp.

                                                        {
     return node;
   }

◆ get_str()

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

inlineinherited

Definition at line 91 of file shared_object.hpp.

                                                {
         std::stringstream ss;
         disp(ss, more);
         return ss.str();
       }

◆ getCount()

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

inherited

Definition at line 102 of file generic_shared_impl.hpp.

                                                              {
     return (*this)->getCount();
   }

◆ has_plugin()

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

Definition at line 53 of file linsol.cpp.

                                                {
     return LinsolInternal::has_plugin(name);
   }

References casadi::PluginInterface< LinsolInternal >::has_plugin().

Referenced by casadi::has_linsol().

◆ is_null()

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

inherited

Definition at line 116 of file generic_shared_impl.hpp.

                                                       {
     return node==nullptr;
   }

◆ load_plugin()

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

Definition at line 57 of file linsol.cpp.

                                                 {
     LinsolInternal::load_plugin(name);
   }

References casadi::PluginInterface< LinsolInternal >::load_plugin().

Referenced by casadi::load_linsol().

◆ neig() [1/2]

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

Definition at line 180 of file linsol.cpp.

                                            {
     if (A.sparsity()!=sparsity()) return neig(project(A, sparsity()));
     casadi_int n = neig(A.ptr());
     casadi_assert(n>=0, "'neig' failed");
     return n;
   }

References casadi::Matrix< Scalar >::ptr(), sparsity(), and casadi::Matrix< Scalar >::sparsity().

Referenced by casadi::QpoasesInterface::qpoases_nfact().

◆ neig() [2/2]

casadi_int casadi::Linsol::neig	(	const double *	A,
		int	mem = `0`
	)		const

Low-level API

Definition at line 187 of file linsol.cpp.

                                                         {
     return (*this)->neig((*this)->memory(mem), A);
   }

◆ nfact() [1/2]

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

Definition at line 133 of file linsol.cpp.

                                       {
     if (A.sparsity()!=sparsity()) {
       nfact(project(A, sparsity()));
       return;
     }
     if (nfact(A.ptr())) casadi_error("'nfact' failed");
   }

References casadi::Matrix< Scalar >::ptr(), sparsity(), and casadi::Matrix< Scalar >::sparsity().

Referenced by det(), casadi::Determinant::eval(), casadi::SlicotDple::eval(), casadi::KinsolInterface::psetup(), casadi::QpoasesInterface::qpoases_nfact(), solve(), casadi::Ipqp::solve(), and casadi::Newton::solve().

◆ nfact() [2/2]

int casadi::Linsol::nfact	(	const double *	A,
		int	mem = `0`
	)		const

Low-level API

Definition at line 141 of file linsol.cpp.

                                                   {
     if (A==nullptr) return 1;
     auto *m = static_cast<LinsolMemory*>((*this)->memory(mem));
  
     // Perform pivoting, if required
     if (!m->is_sfact) {
       if (sfact(A, mem)) return 1;
     }
  
     m->is_nfact = false;
     if (m->t_total) m->fstats.at("nfact").tic();
     int flag = (*this)->nfact(m, A);
     if (m->t_total) m->fstats.at("nfact").toc();
     if (flag && (*this)->regularity_check_) {
       // Collect nonzeros
       std::vector<std::string> nonzeros(sparsity().nnz());
       for (size_t nz = 0; nz < nonzeros.size(); ++nz)
         nonzeros[nz] = std::to_string(A[nz]);
       // Create .m file
       std::string fname = (*this)->class_name() + "_" + (*this)->name_ + "_debug.m";
       auto mfile_ptr = Filesystem::ofstream_ptr(fname);
       std::ostream& mfile = *mfile_ptr;
       Dict opts;
       opts["name"] = "A";
       opts["nonzeros"] = nonzeros;
       sparsity().export_code("matlab", mfile, opts);
       casadi_error("Numerical factorization failed for " + (*this)->name_
         + "[" + (*this)->class_name() + "]. Linear system saved to '" + fname + "'");
     }
     m->is_nfact = true;
     return flag;
   }

References casadi::Sparsity::export_code(), casadi::LinsolMemory::is_nfact, casadi::Filesystem::ofstream_ptr(), sfact(), and sparsity().

◆ operator->() [1/2]

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

Definition at line 41 of file linsol.cpp.

                                      {
     return static_cast<LinsolInternal*>(SharedObject::operator->());
   }

References casadi::GenericShared< SharedObject, SharedObjectInternal >::operator->().

◆ operator->() [2/2]

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

Definition at line 45 of file linsol.cpp.

                                                  {
     return static_cast<const LinsolInternal*>(SharedObject::operator->());
   }

References casadi::GenericShared< SharedObject, SharedObjectInternal >::operator->().

◆ own()

void casadi::GenericShared< SharedObject , SharedObjectInternal >::own ( Internal * node )

inherited

Assign the node to a node class pointer (or null)

Definition at line 89 of file generic_shared_impl.hpp.

                                                            {
     count_down();
     node = node_;
     count_up();
   }

◆ plugin_name()

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

Definition at line 65 of file linsol.cpp.

                                       {
     return (*this)->plugin_name();
   }

◆ print_ptr()

void casadi::SharedObject::print_ptr ( std::ostream & stream = casadi::uout() ) const

inherited

Print the pointer to the internal class

Definition at line 43 of file shared_object.cpp.

                                                        {
     stream << get();
   }

References casadi::GenericShared< SharedObject, SharedObjectInternal >::get().

◆ rank() [1/2]

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

Definition at line 191 of file linsol.cpp.

                                            {
     if (A.sparsity()!=sparsity()) return rank(project(A, sparsity()));
     casadi_int n = rank(A.ptr());
     casadi_assert(n>=0, "'rank' failed");
     return n;
   }

References casadi::Matrix< Scalar >::ptr(), sparsity(), and casadi::Matrix< Scalar >::sparsity().

Referenced by casadi::QpoasesInterface::qpoases_nfact().

◆ rank() [2/2]

casadi_int casadi::Linsol::rank	(	const double *	A,
		int	mem = `0`
	)		const

Low-level API

Definition at line 210 of file linsol.cpp.

                                                         {
     return (*this)->rank((*this)->memory(mem), A);
   }

◆ release()

void casadi::Linsol::release ( int mem ) const

Definition at line 227 of file linsol.cpp.

                                     {
     (*this)->release(mem);
   }

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

◆ serialize()

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

Extra doc: https://github.com/casadi/casadi/wiki/L_1km

Definition at line 250 of file linsol.cpp.

                                                    {
     // TODO(jgillis): I don't get why LinsolInternal:: this is necessary
     (*this)->LinsolInternal::serialize(s);
   }

◆ sfact() [1/2]

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

Definition at line 108 of file linsol.cpp.

                                       {
     if (A.sparsity()!=sparsity()) {
       sfact(project(A, sparsity()));
       return;
     }
     if (sfact(A.ptr())) casadi_error("'sfact' failed");
   }

References casadi::Matrix< Scalar >::ptr(), sparsity(), and casadi::Matrix< Scalar >::sparsity().

Referenced by det(), casadi::Determinant::eval(), casadi::SlicotDple::eval(), nfact(), casadi::QpoasesInterface::qpoases_sfact(), and solve().

◆ sfact() [2/2]

int casadi::Linsol::sfact	(	const double *	A,
		int	mem = `0`
	)		const

Low-level API

Definition at line 116 of file linsol.cpp.

                                                   {
     if (A==nullptr) return 1;
     auto *m = static_cast<LinsolMemory*>((*this)->memory(mem));
  
     // Factorization will be needed after this step
     m->is_sfact = m->is_nfact = false;
  
     if (m->t_total) m->fstats.at("sfact").tic();
     // Perform pivoting
     if ((*this)->sfact(m, A)) return 1;
     if (m->t_total) m->fstats.at("sfact").toc();
  
     // Mark as (successfully) pivoted
     m->is_sfact = true;
     return 0;
   }

References casadi::LinsolMemory::is_sfact.

◆ solve() [1/3]

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

Definition at line 73 of file linsol.cpp.

                                                           {
     casadi_assert(A.size1()==B.size1(),
       "Linsol::solve: Dimension mismatch. A and b must have matching row count. "
       "Got " + A.dim() + " and " + B.dim() + ".");
  
     // Quick return if possible
     if (A.size1()==0) return densify(B);
  
     scoped_checkout<Linsol> mem(*this);
     auto *m = static_cast<LinsolMemory*>((*this)->memory(mem));
  
     // Reset statistics
     for (auto&& s : m->fstats) s.second.reset();
     if (m->t_total) m->t_total->tic();
     // Symbolic factorization
     if (sfact(A.ptr(), mem)) casadi_error("Linsol::solve: 'sfact' failed");
  
     // Numeric factorization
     if (nfact(A.ptr(), mem)) casadi_error("Linsol::solve: 'nfact' failed");
  
     // Solve
     DM x = densify(B);
     if (solve(A.ptr(), x.ptr(), x.size2(), tr, mem))
       casadi_error("Linsol::solve: 'solve' failed");
     // Show statistics
     if (m->t_total) m->t_total->toc();
  
     (*this)->print_time(m->fstats);
     return x;
   }

References casadi::GenericMatrix< MatType >::dim(), nfact(), casadi::Matrix< Scalar >::ptr(), sfact(), casadi::GenericMatrix< MatType >::size1(), casadi::GenericMatrix< MatType >::size2(), casadi::ProtoFunctionMemory::t_total, and casadi::FStats::tic().

Referenced by casadi::SlicotDple::eval(), casadi::KinsolInterface::psolve(), casadi::QpoasesInterface::qpoases_solve(), casadi::Ipqp::solve(), casadi::LinsolCall< Tr >::solve(), casadi::MX::solve(), casadi::Newton::solve(), and casadi::IdasInterface::solve_transposed().

◆ solve() [2/3]

int casadi::Linsol::solve	(	const double *	A,
		double *	x,
		casadi_int	nrhs = `1`,
		bool	tr = `false`,
		int	mem = `0`
	)		const

Low-level API

Definition at line 214 of file linsol.cpp.

                                                                                        {
     auto *m = static_cast<LinsolMemory*>((*this)->memory(mem));
     casadi_assert(m->is_nfact, "Linear system has not been factorized");
     if (m->t_total) m->fstats.at("solve").tic();
     int ret = (*this)->solve(m, A, x, nrhs, tr);
     if (m->t_total) m->fstats.at("solve").toc();
     return ret;
   }

◆ solve() [3/3]

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

Definition at line 104 of file linsol.cpp.

                                                           {
     return A->get_solve(B, tr, *this);
   }

References casadi::MXNode::get_solve().

◆ sparsity()

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

Definition at line 69 of file linsol.cpp.

                                          {
     return (*this)->sp_;
   }

Referenced by det(), casadi::SundialsInterface::init(), neig(), nfact(), rank(), casadi::SundialsInterface::set_work(), and sfact().

◆ 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

Definition at line 244 of file linsol.cpp.

                                   {
     casadi_assert((*this)->has_memory(mem),
       "No stats available since Linsol did not solve a problem yet.");
     return (*this)->get_stats((*this)->memory(mem));
   }

◆ swap()

void casadi::GenericShared< SharedObject , SharedObjectInternal >::swap ( GenericShared< SharedObject, SharedObjectInternal > & other )

inherited

Definition at line 105 of file generic_shared_impl.hpp.

                                                                  {
     GenericShared<Shared, Internal> temp = *this;
     *this = other;
     other = temp;
   }

◆ test_cast()

bool casadi::Linsol::test_cast ( const SharedObjectInternal * ptr )

static

Definition at line 49 of file linsol.cpp.

                                                         {
     return dynamic_cast<const LinsolInternal*>(ptr)!=nullptr;
   }

◆ 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.

149 {return "Linsol";}

◆ weak()

GenericWeakRef< SharedObject , SharedObjectInternal > * casadi::GenericShared< SharedObject , SharedObjectInternal >::weak

inherited

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

Definition at line 130 of file generic_shared_impl.hpp.

                                                                           {
     return (*this)->weak();
   }

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

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

Protected Member Functions

Member Typedef Documentation

◆ base_type

◆ internal_base_type

Constructor & Destructor Documentation

◆ Linsol() [1/2]

◆ Linsol() [2/2]

Member Function Documentation

◆ __hash__()

◆ assign()

◆ checkout()

◆ class_name()

◆ count_down()

◆ count_up()

◆ create()

◆ debug_repr()

◆ deserialize()

◆ det() [1/3]

◆ det() [2/3]

◆ det() [3/3]

◆ disp()

◆ doc()

◆ get()

◆ get_str()

◆ getCount()

◆ has_plugin()

◆ is_null()

◆ load_plugin()

◆ neig() [1/2]

◆ neig() [2/2]

◆ nfact() [1/2]

◆ nfact() [2/2]

◆ operator->() [1/2]

◆ operator->() [2/2]

◆ own()

◆ plugin_name()

◆ print_ptr()

◆ rank() [1/2]

◆ rank() [2/2]

◆ release()

◆ serialize()

◆ sfact() [1/2]

◆ sfact() [2/2]

◆ solve() [1/3]

◆ solve() [2/3]

◆ solve() [3/3]

◆ sparsity()

◆ stats()

◆ swap()

◆ test_cast()

◆ type_name()

◆ weak()

◆ hash()