This class abstracts a decomposition choice for the quasi-range space Y and null space Z matrices for a linearly independent set of columns of Gc. More...

#include <ConstrainedOptPack_DecompositionSystem.hpp>

Inheritance diagram for ConstrainedOptPack::DecompositionSystem:

[legend]

Classes
class	InvalidMatrixType

class	SingularDecomposition

class	TestFailed

Public Member Functions
virtual	~DecompositionSystem ()

Public types
enum	EOutputLevel
	Enumeration for the amount of output to create from `update_decomp()`. More...

enum	ERunTests
	Enumeration for if to run internal tests or not. More...

enum	EMatRelations

typedef Teuchos::RCP< const Teuchos::AbstractFactory < MatrixOpNonsing > >	mat_nonsing_fcty_ptr_t

typedef Teuchos::RCP< const Teuchos::AbstractFactory < MatrixOp > >	mat_fcty_ptr_t

Dimensionality of the decomposition
virtual size_type	n () const
	Return the number of rows in `Gc`. More...

virtual size_type	m () const =0
	Return the number of columns in `Gc`. More...

virtual size_type	r () const
	Returns the rank of `Gc(:,equ_decomp())`. More...

virtual Range1D	equ_decomp () const
	Returns the range of the decomposed equalities. More...

virtual Range1D	equ_undecomp () const
	Returns the range of the undecomposed equalities. More...

Range and null vector spaces
virtual const VectorSpace::space_ptr_t	space_range () const =0
	Return a `VectorSpace` object for the range space. More...

virtual const VectorSpace::space_ptr_t	space_null () const =0
	Return a `VectorSpace` object for the range space. More...

Matrix factories
virtual const mat_fcty_ptr_t	factory_Z () const =0
	Return a matrix factory object for `Z` More...

virtual const mat_fcty_ptr_t	factory_Y () const =0
	Return a matrix factory object for `Y` More...

virtual const mat_nonsing_fcty_ptr_t	factory_R () const =0
	Return a matrix factory object for `R`. More...

virtual const mat_fcty_ptr_t	factory_Uz () const =0
	Return a matrix factory object for `Uz` More...

virtual const mat_fcty_ptr_t	factory_Uy () const =0
	Return a matrix factory object for `Uy` More...

Update range/null decomposition
virtual void	update_decomp (std::ostream out, EOutputLevel olevel, ERunTests test_what, const MatrixOp &Gc, MatrixOp Z, MatrixOp Y, MatrixOpNonsing R, MatrixOp Uz, MatrixOp Vy, EMatRelations mat_rel=MATRICES_INDEP_IMPS) const =0
	Creates the range/null decomposition for `Gc(:,equ_decomp)'`. More...

virtual void	print_update_decomp (std::ostream &out, const std::string &leading_str) const =0
	Print the sub-algorithm by which the decomposition is formed. More...

Detailed Description

This class abstracts a decomposition choice for the quasi-range space Y and null space Z matrices for a linearly independent set of columns of Gc.

Gc = [ Gc(:,equ_decomp), Gc(:,equ_undecomp) ]

where Gc is n x m, Gc(:,equ_decomp) is n x r and Gc(:,equ_undecomp) is n x (m - r).

Note that the columns in Gc(:,equ_undecomp) may be linearly dependent with the columns in Gc(:,equ_undecomp) or they may just be undecomposed linearly independent equality constraints.

The decomposition formed by subclasses must have the properties:

  Z s.t. Gc(:,equ_decomp)' * Z = 0
  Y s.t. [Z  Y] is nonsingular
  R = Gc(:,equ_decomp)' * Y is nonsingular
  Uz = Gc(:,equ_undecomp)' * Z
  Uy = Gc(:,equ_undecomp)' * Y

The matrix factory objects returned by ??? are ment to have a lifetime that is independent of this.

The decomposition matrices Z, Y, R, Uz and Uy which are updated in this->update_decomp() must be completely independent from this and from each other and Gc that they based on. For example, Once update_decomp() is called, this, Gc can be destroyed and the behaviors of the decomposition matrices must not be altered. In this respect the DecompositionSystem interface is really nothing more than a "Strategy" interface (with some state data of course) for computing range/null decompositions. This gives the client great flexibility in how the decomposition matrices are used.

ToDo: Finish documentation!

Definition at line 89 of file ConstrainedOptPack_DecompositionSystem.hpp.

Member Typedef Documentation

typedef Teuchos::RCP< const Teuchos::AbstractFactory<MatrixOpNonsing> > ConstrainedOptPack::DecompositionSystem::mat_nonsing_fcty_ptr_t

Definition at line 97 of file ConstrainedOptPack_DecompositionSystem.hpp.

typedef Teuchos::RCP< const Teuchos::AbstractFactory<MatrixOp> > ConstrainedOptPack::DecompositionSystem::mat_fcty_ptr_t

Definition at line 100 of file ConstrainedOptPack_DecompositionSystem.hpp.

Member Enumeration Documentation

enum ConstrainedOptPack::DecompositionSystem::EOutputLevel

Enumeration for the amount of output to create from update_decomp().

Definition at line 111 of file ConstrainedOptPack_DecompositionSystem.hpp.

enum ConstrainedOptPack::DecompositionSystem::ERunTests

Enumeration for if to run internal tests or not.

Definition at line 119 of file ConstrainedOptPack_DecompositionSystem.hpp.

enum ConstrainedOptPack::DecompositionSystem::EMatRelations

Definition at line 121 of file ConstrainedOptPack_DecompositionSystem.hpp.

Constructor & Destructor Documentation

virtual ConstrainedOptPack::DecompositionSystem::~DecompositionSystem ( )

inlinevirtual

Definition at line 126 of file ConstrainedOptPack_DecompositionSystem.hpp.

Member Function Documentation

size_type ConstrainedOptPack::DecompositionSystem::n ( ) const

virtual

Return the number of rows in Gc.

Postconditions:

n > m

The default implementation returns this->space_range()->dim() + this->space_null()->dim().

Reimplemented in ConstrainedOptPack::DecompositionSystemVarReductImp, and ConstrainedOptPack::DecompositionSystemVarReductPermStd.

Definition at line 46 of file ConstrainedOptPack_DecompositionSystem.cpp.

virtual size_type ConstrainedOptPack::DecompositionSystem::m ( ) const

pure virtual

Return the number of columns in Gc.

Postconditions:

m > 0

Implemented in ConstrainedOptPack::DecompositionSystemVarReductImp, and ConstrainedOptPack::DecompositionSystemVarReductPermStd.

size_type ConstrainedOptPack::DecompositionSystem::r ( ) const

virtual

Returns the rank of Gc(:,equ_decomp()).

Postconditions:

r =< m

The default implementation returns this->space_range()->dim().

Reimplemented in ConstrainedOptPack::DecompositionSystemVarReductImp, and ConstrainedOptPack::DecompositionSystemVarReductPermStd.

Definition at line 51 of file ConstrainedOptPack_DecompositionSystem.cpp.

Range1D ConstrainedOptPack::DecompositionSystem::equ_decomp ( ) const

virtual

Returns the range of the decomposed equalities.

The default implementation returns Range1D(1,this->r()).

Reimplemented in ConstrainedOptPack::DecompositionSystemVarReductPermStd.

Definition at line 56 of file ConstrainedOptPack_DecompositionSystem.cpp.

Range1D ConstrainedOptPack::DecompositionSystem::equ_undecomp ( ) const

virtual

Returns the range of the undecomposed equalities.

The default implementation returns Range1D(this->r()+1,this->m()) or Range1D::Invalid if this->r() == this->m()

Reimplemented in ConstrainedOptPack::DecompositionSystemVarReductPermStd.

Definition at line 63 of file ConstrainedOptPack_DecompositionSystem.cpp.

virtual const VectorSpace::space_ptr_t ConstrainedOptPack::DecompositionSystem::space_range ( ) const

pure virtual

Return a VectorSpace object for the range space.

Postconditions:

return.get() != NULL
return->dim() == this->r()

Implemented in ConstrainedOptPack::DecompositionSystemVarReductImp, and ConstrainedOptPack::DecompositionSystemVarReductPermStd.

virtual const VectorSpace::space_ptr_t ConstrainedOptPack::DecompositionSystem::space_null ( ) const

pure virtual

Return a VectorSpace object for the range space.

Postconditions:

return.get() != NULL
return->dim() == this->n() - this->r()

Implemented in ConstrainedOptPack::DecompositionSystemVarReductImp, and ConstrainedOptPack::DecompositionSystemVarReductPermStd.

virtual const mat_fcty_ptr_t ConstrainedOptPack::DecompositionSystem::factory_Z ( ) const

pure virtual

Return a matrix factory object for Z

Implemented in ConstrainedOptPack::DecompositionSystemVarReductImp, and ConstrainedOptPack::DecompositionSystemVarReductPermStd.

virtual const mat_fcty_ptr_t ConstrainedOptPack::DecompositionSystem::factory_Y ( ) const

pure virtual

Return a matrix factory object for Y

Implemented in ConstrainedOptPack::DecompositionSystemVarReductPermStd, ConstrainedOptPack::DecompositionSystemOrthogonal, and ConstrainedOptPack::DecompositionSystemCoordinate.

virtual const mat_nonsing_fcty_ptr_t ConstrainedOptPack::DecompositionSystem::factory_R ( ) const

pure virtual

Return a matrix factory object for R.

Implemented in ConstrainedOptPack::DecompositionSystemVarReductPermStd, ConstrainedOptPack::DecompositionSystemOrthogonal, and ConstrainedOptPack::DecompositionSystemCoordinate.

virtual const mat_fcty_ptr_t ConstrainedOptPack::DecompositionSystem::factory_Uz ( ) const

pure virtual

Return a matrix factory object for Uz

Implemented in ConstrainedOptPack::DecompositionSystemVarReductImp, and ConstrainedOptPack::DecompositionSystemVarReductPermStd.

virtual const mat_fcty_ptr_t ConstrainedOptPack::DecompositionSystem::factory_Uy ( ) const

pure virtual

Return a matrix factory object for Uy

Implemented in ConstrainedOptPack::DecompositionSystemVarReductPermStd, ConstrainedOptPack::DecompositionSystemOrthogonal, and ConstrainedOptPack::DecompositionSystemCoordinate.

virtual void ConstrainedOptPack::DecompositionSystem::update_decomp	(	std::ostream *	out,
		EOutputLevel	olevel,
		ERunTests	test_what,
		const MatrixOp &	Gc,
		MatrixOp *	Z,
		MatrixOp *	Y,
		MatrixOpNonsing *	R,
		MatrixOp *	Uz,
		MatrixOp *	Vy,
		EMatRelations	mat_rel = `MATRICES_INDEP_IMPS`
	)		const

pure virtual

Creates the range/null decomposition for Gc(:,equ_decomp)'.

The decomposition is based on the linearly independent columns Gc(:,equ_decomp) of Gc

Gc = [ Gc(:,equ_decomp), Gc(:,equ_undecomp) ]

Specifically this operation finds the matrices:

Z s.t. Gc(:,equ_deomp)' * Z = 0
Y s.t. [Z  Y] is nonsingular
R = Gc(:,equ_decomp)' * Y is nonsingular
Uz = Gc(:,equ_undecomp)' * Z
Uy = Gc(:,equ_undecomp)' * Y

If there is some problem creating the decomposition then exceptions with the base class std::exception may be thrown. The meaning of these exceptions are more associated with the subclasses that implement this operation.

The concrete types for Gc, Z, Y, Uz and Uy must be compatable with the concrete implementation of this or an InvalidMatrixType exeption will be thrown..

Parameters

out	[out] If `out!=NULL` then output is printed to this stream depending on the value of `olevel`.
olevel	[in] Determines the amount of output to print to `out`. The exact type of output is determined by the implementing subclass but here is the sugguested behavior: `PRINT_NONE` : Don't print anything (same as `out==NULL`). `PRINT_BASIC_INFO` : Only print basic information about how the decomposition is formed. Amount of output = `O(1)`. `PRINT_VECTORS` : Prints out important vectors computed durring the computations (usually only durring testing). This level is only useful for debugging. Amount of output = `O(n)`. `PRINT_EVERY_THING` : Print out nearly every important quantity that is computed (except for the output matrices themselves, clients can do that) while the matrices are being formed or tests are being conducted. This level is only useful for debugging. Amount of output = `O(mn)`
test_what	[in] Determines if internal validation tests are performed. The post conditions for the output matrices are not checked internally. This is something that client can (and should) do independently (see `DecompositionSystemTester`). Values: `RUN_TESTS` : As many validation/consistency tests are performed internally as possible. If a test fails then a `TestFailed` execption will be thrown. The subclasses determine what the tests are and what failing a test means. `NO_TEST` : No tests are performed internally. This is to allow the fastest possible execution. If a test fails, then a `TestFailed` exception will be thrown with a helpful error message.
Gc	[in] The matrix for which the range/null decomposition is defined.
Z	[out] On output represents the `n x (n-r)` null space matrix such that `Gc(:,equ_decomp) * Z == 0`. This matrix object must have been created by `this->factory_Z()->create()`.
Y	[out] On output represents the `n x r` range space matrix such that `[ Y Z ]` is nonsingular. This matrix object must have been created by `this->factory_Y()->create()`.
R	[out] On output represents the nonsingular `r x r` matrix `Gc(:,equ_decomp) * Y`. This matrix object must have been created by `this->factory_R()->create()`.
Uz	[in/out] If `Uz != NULL` (`this->m() > this->r()` only) then on output `Uz` represents the `(m-r) x (n-r)` matrix `Gc(:,equ_undecomp) Z`. If `this->m() == this->r()` then `Uz == NULL` must be true. If `Uz!=NULL`, then this matrix object must have been created by `this->factory_Uz()->create()`.
Uy	[in/out] If `Uy != NULL` (`this->m() > this->r()` only) then on output `Uy` represents the `(m-r) x r` matrix `Gc(:,equ_undecomp) Y`. If `this->m() == this->r()` then `Uy == NULL` must be true. If `Uy!=NULL`, then this matrix object must have been created by `this->factory_Uy()->create()`.
mat_rel	[in] Determines if the ouput matrix objects must be completely independent or not. MATRICES_INDEP_IMPS: The matrix objects must have independent implementations (default). MATRICES_ALLOW_DEP_IMPS: The matrix objects can have implementation dependencies.

Preconditions:

Gc.rows() == this->n() (throw std::invalid_argument)
Gc.cols() == this->m() (throw std::invalid_argument)
[this->m() == this->r()] Uz == NULL (throw std::invalid_argument)
[this->m() == this->r()] Uy == NULL (throw std::invalid_argument)
Z!=NULL || Y!=NULL || R!=NULL || Uz!=NULL || Uy!=NULL (throw std::invalid_argument)

Postconditions:

[Z != NULL] Z.space_cols().is_compatible(Gc.space_cols()) == true)
[Z != NULL] Z.space_rows().is_compatible(*space_null()) == true
[Z != NULL] Gc(:,equ_decomp())' * Z == 0
[Y != NULL] Y.space_cols().is_compatible(Gc.space_cols()) == true)
[Y != NULL] Y.cols() == this->r()
[Y != NULL] [ Y Z ] is nonsingular
[R != NULL] R->space_cols().is_compatible(*Gc.space_cols()->sub_space(equ_decomp())) == true
[R != NULL] R->space_rows().is_compatible(*space_range()) == true
[R != NULL] R == Gc(:,equ_decomp())'*Y
[Uz != NULL] Uz.space_cols().is_compatible(*Gc.space_rows()->sub_space(equ_undecomp())) == true
[Uz != NULL] Uz.space_rows().is_compatible(*space_null()) == true
[Uz != NULL] Uz == Gc(:,equ_undecomp())'*Z
[Uy != NULL] Uy.space_cols().is_compatible(*Gc.space_rows()->sub_space(equ_undecomp())) == true
[Uy != NULL] Uy.space_rows().is_compatible(*space_range()) == true
[Uy != NULL] Uy == Gc(:,equ_undecomp())'*Y
[mat_rel == MATRICES_INDEP_IMPS] The behaviors of all of the participating output matrix objects must not be altered by changes to other matrix objects.
[mat_rel == MATRICES_ALLOW_DEP_IMPS] The behaviors of all of the participating output matrix objects may change when other matrix objects or this is altered.

Note that this method requires that all of the output matrix objects Z, Y, R, Uz, Uy, Vz and Vy must be independent of this and of each other. For example, the behavior of R must be be altered if this is destroyed or if Z is modified of destroyed. This requirment constrains the implementations somewhat but makes things much easier for the client and gives the client much more power.

Implemented in ConstrainedOptPack::DecompositionSystemVarReductImp, and ConstrainedOptPack::DecompositionSystemVarReductPermStd.

virtual void ConstrainedOptPack::DecompositionSystem::print_update_decomp	(	std::ostream &	out,
		const std::string &	leading_str
	)		const

pure virtual

Print the sub-algorithm by which the decomposition is formed.

Implemented in ConstrainedOptPack::DecompositionSystemVarReductImp, and ConstrainedOptPack::DecompositionSystemVarReductPermStd.

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

Classes

Public Member Functions

Public types

Dimensionality of the decomposition

Range and null vector spaces

Matrix factories

Update range/null decomposition

Detailed Description

Member Typedef Documentation

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation