# concepts::Constrained Class ReferenceLinear Solvers

Solves a linear system of equations subject to linear constraints. More...

`#include <constrained.hh>`

Inheritance diagram for concepts::Constrained:

## Public Types

typedef Cmplxtype< Real >::type c_type
Real type of data type. More...

typedef Realtype< Real >::type r_type
Real type of data type. More...

typedef Real type
Type of data, e.g. matrix entries. More...

## Public Member Functions

Constrained (SparseMatrix< Real > &S, SparseMatrix< Real > &C, const Vector< Real > &g, SolverFabric< Real > &fabric)
Constructor. More...

virtual const uint dimX () const
Returns the size of the image space of the operator (number of rows of the corresponding matrix) More...

virtual const uint dimY () const
Returns the size of the source space of the operator (number of columns of the corresponding matrix) More...

virtual void operator() ()
Application operator without argument. More...

virtual void operator() (const Function< c_type > &fncY, Function< c_type > &fncX)
Application operator for complex function `fncY`. More...

virtual void operator() (const Function< r_type > &fncY, Function< Real > &fncX)
Application operator for real function `fncY`. More...

virtual void operator() (const Function< Real > &fncY, Function< Real > &fncX)

virtual void show_messages ()

## Protected Member Functions

virtual std::ostream & info (std::ostream &os) const

## Protected Attributes

uint dimX_
Dimension of image space and the source space. More...

uint dimY_

## Private Attributes

SparseMatrix< Real > & C_

std::unique_ptr< SparseMatrix< Real > > CCt_

std::unique_ptr< Operator< Real > > CCtinv_

SparseMatrix< RealCt_

std::unique_ptr< concepts::Compose< Real > > CtC_

SolverFabric< Real > & fabric_

const Vector< Real > & g_

std::unique_ptr< LiCoI< Real > > Q_

std::unique_ptr< concepts::Compose< Real > > Qmin_

std::unique_ptr< concepts::Compose< Real > > QS_

std::unique_ptr< concepts::Compose< Real > > QSQ_

std::unique_ptr< concepts::Compose< Real > > R_

SparseMatrix< Real > & S_

std::unique_ptr< Operator< Real > > solver_

std::unique_ptr< LiCo< Real > > Sp_

Vector< RealSRg_

## Detailed Description

Solves a linear system of equations subject to linear constraints.

Ainsworth, Essential boundary conditions and multi-point constraints in finite element analysis, 2000, Comput. Methods Appl Mech. Engrg. 190 (2001) 6323-6339
Namespace constraints

Definition at line 31 of file constrained.hh.

## ◆ c_type

 typedef Cmplxtype::type concepts::Operator< Real >::c_type
inherited

Real type of data type.

Definition at line 49 of file compositions.hh.

## ◆ r_type

 typedef Realtype::type concepts::Operator< Real >::r_type
inherited

Real type of data type.

Definition at line 47 of file compositions.hh.

## ◆ type

 typedef Real concepts::Operator< Real >::type
inherited

Type of data, e.g. matrix entries.

Definition at line 45 of file compositions.hh.

## ◆ Constrained()

 concepts::Constrained::Constrained ( SparseMatrix< Real > & S, SparseMatrix< Real > & C, const Vector< Real > & g, SolverFabric< Real > & fabric )

Constructor.

Parameters
 S Stiffness matrix C Constraints matrix g Right hand side of the constraints

## ◆ dimX()

 virtual const uint concepts::Operator< Real >::dimX
inlinevirtualinherited

Returns the size of the image space of the operator (number of rows of the corresponding matrix)

Definition at line 93 of file compositions.hh.

## ◆ dimY()

 virtual const uint concepts::Operator< Real >::dimY
inlinevirtualinherited

Returns the size of the source space of the operator (number of columns of the corresponding matrix)

Definition at line 98 of file compositions.hh.

## ◆ info()

 virtual std::ostream& concepts::Constrained::info ( std::ostream & os ) const
protectedvirtual

Reimplemented from concepts::Operator< Real >.

## ◆ operator()() [1/4]

 virtual void concepts::Operator< Real >::operator()
virtualinherited

Application operator without argument.

Reimplemented in concepts::VecOperator< Real >.

## ◆ operator()() [2/4]

 virtual void concepts::Operator< Real >::operator() ( const Function< c_type > & fncY, Function< c_type > & fncX )
virtualinherited

Application operator for complex function `fncY`.

Computes `fncX` = A(`fncY`) where A is this operator. `fncX` becomes complex.

In derived classes its enough to implement the operator() for complex Operator's. If a real counterpart is not implemented, the function `fncY` is splitted into real and imaginary part and the application operator for real functions is called for each. Then the result is combined.

If in a derived class the operator() for complex Operator's is not implemented, a exception is thrown from here.

Reimplemented in concepts::VecOperator< Real >.

## ◆ operator()() [3/4]

 virtual void concepts::Operator< Real >::operator() ( const Function< r_type > & fncY, Function< Real > & fncX )
virtualinherited

Application operator for real function `fncY`.

Computes `fncX` = A(`fncY`) where A is this operator.

`fncX` becomes the type of the operator, for real data it becomes real, for complex data it becomes complex.

In derived classes its enough to implement the operator() for real Operator's. If a complex counterpart is not implemented, the function `fncY` is transformed to a complex function and then the application operator for complex functions is called.

If in a derived class the operator() for real Operator's is not implemented, a exception is thrown from here.

Reimplemented in concepts::VecOperator< Real >.

## ◆ operator()() [4/4]

 virtual void concepts::Constrained::operator() ( const Function< Real > & fncY, Function< Real > & fncX )
virtual

## ◆ show_messages()

 virtual void concepts::Operator< Real >::show_messages
inlinevirtualinherited

Definition at line 100 of file compositions.hh.

## ◆ C_

 SparseMatrix& concepts::Constrained::C_
private

Definition at line 44 of file constrained.hh.

## ◆ CCt_

 std::unique_ptr > concepts::Constrained::CCt_
private

Definition at line 46 of file constrained.hh.

## ◆ CCtinv_

 std::unique_ptr > concepts::Constrained::CCtinv_
private

Definition at line 49 of file constrained.hh.

## ◆ Ct_

 SparseMatrix concepts::Constrained::Ct_
private

Definition at line 45 of file constrained.hh.

## ◆ CtC_

 std::unique_ptr > concepts::Constrained::CtC_
private

Definition at line 50 of file constrained.hh.

## ◆ dimX_

 uint concepts::Operator< Real >::dimX_
protectedinherited

Dimension of image space and the source space.

Definition at line 104 of file compositions.hh.

## ◆ dimY_

 uint concepts::Operator< Real >::dimY_
protectedinherited

Definition at line 104 of file compositions.hh.

## ◆ fabric_

 SolverFabric& concepts::Constrained::fabric_
private

Definition at line 53 of file constrained.hh.

## ◆ g_

 const Vector& concepts::Constrained::g_
private

Definition at line 47 of file constrained.hh.

## ◆ Q_

 std::unique_ptr > concepts::Constrained::Q_
private

Definition at line 51 of file constrained.hh.

## ◆ Qmin_

 std::unique_ptr > concepts::Constrained::Qmin_
private

Definition at line 50 of file constrained.hh.

## ◆ QS_

 std::unique_ptr > concepts::Constrained::QS_
private

Definition at line 50 of file constrained.hh.

## ◆ QSQ_

 std::unique_ptr > concepts::Constrained::QSQ_
private

Definition at line 50 of file constrained.hh.

## ◆ R_

 std::unique_ptr > concepts::Constrained::R_
private

Definition at line 50 of file constrained.hh.

## ◆ S_

 SparseMatrix & concepts::Constrained::S_
private

Definition at line 44 of file constrained.hh.

## ◆ solver_

 std::unique_ptr > concepts::Constrained::solver_
private

Definition at line 49 of file constrained.hh.

## ◆ Sp_

 std::unique_ptr > concepts::Constrained::Sp_
private

Definition at line 52 of file constrained.hh.

## ◆ SRg_

 Vector concepts::Constrained::SRg_
private

Definition at line 48 of file constrained.hh.

The documentation for this class was generated from the following file:
Page URL: http://wiki.math.ethz.ch/bin/view/Concepts/WebHome
21 August 2020
© 2020 Eidgenössische Technische Hochschule Zürich