blackbox

These matrix classes meet the simple interface needed for blackbox algorithms. More...

Collaboration diagram for blackbox:

Files
file	blackbox/archetype.h
	NO DOC.
file	diagonal-gf2.h
	Random diagonal matrices and diagonal matrices Class especially meant for diagonal precondtionners.
file	diagonal.h
	Random diagonal matrices and diagonal matrices Class especially meant for diagonal precondtionners.
file	frobenius.h
	NO DESC.
file	hilbert.h
	NO DESC.
file	zero-one.inl
	NO DOC.
file	zo-gf2.inl
	NO DOC.
file	sparse-tpl-matrix-omp.inl
	NO DOC.

Data Structures
class	BlackboxArchetype
	showing the member functions provided by all blackbox matrix classes. More...
class	BlockCompose< _Blackbox1, _Blackbox2 >
	Blackbox of a product: , i.e . More...
class	Butterfly< _Field, Switch >
	Switching Network based BlackBox Matrix. More...
struct	Companion< Field_ >
	Companion matrix of a monic polynomial. More...
class	Compose< _Blackbox1, _Blackbox2 >
	Blackbox of a product: , i.e . More...
class	ComposeOwner< _Blackbox1, _Blackbox2 >
	Blackbox of a product: , i.e . More...
class	CSF< _Field >
	Space efficient representation of sparse matrices. More...
class	Diagonal< Field, Trait >
	Random diagonal matrices are used heavily as preconditioners. More...
class	Dif< _Blackbox1, _Blackbox2 >
	Blackbox of a difference: C := A - B, i.e Cx = Ax - Bx. More...
class	DirectSum< _Blackbox1, _Blackbox2 >
	If C = DirectSum(A, B) and y = xA and z = wB, then (y,z) = (x,w)C. More...
class	Hilbert< _Field >
	Example of a blackbox that is space efficient, though not time efficient. More...
class	Inverse< Blackbox >
	A Blackbox for the inverse. More...
class	JIT_Matrix< _Field, JIT_EntryGenerator >
	example of a blackbox that is space efficient, though not time efficient. More...
class	MatrixBlackbox< _Field, _Matrix, _Vector >
	Matrix black box. More...
class	MoorePenrose< Blackbox >
	Generalized inverse of a blackbox. More...
class	Sylvester< _Field >
	This is a representation of the Sylvester matrix of two polynomials. More...
class	NullMatrix
	This is a representation of the 0 by 0 empty matrix which does not occupy memory. More...
class	PolynomialBB< Blackbox, Poly >
	represent the matrix P(A) where A is a blackbox and P a polynomial More...
class	PolynomialBBOwner< Blackbox, Poly >
	represent the matrix P(A) where A is a blackbox and P a polynomial More...
class	ZOQuad< _Field >
	A class of striped or block-decomposed zero-one matrices. More...
class	ScalarMatrix< Field_ >
	Blackbox for aI. More...
class	Squarize< Blackbox >
	transpose matrix without copying. More...
class	Submatrix< Blackbox, Trait >
	leading principal minor of existing matrix without copying. More...
class	Sum< _Blackbox1, _Blackbox2 >
	blackbox of a matrix sum without copying. More...
class	SumOwner< _Blackbox1, _Blackbox2 >
	blackbox of a matrix sum without copying. More...
class	Toeplitz< _CField, _PRing >
	This is the blackbox representation of a Toeplitz matrix. More...
class	Transpose< Blackbox >
	transpose matrix without copying. More...
class	TransposeOwner< Blackbox >
	transpose matrix without copying. More...
class	ZeroOne< _Field >
	Time and space efficient representation of sparse {0,1}-matrices. More...
class	ZeroOne< GF2 >
	Time and space efficient representation of sparse matrices over GF2. More...
class	SparseMatrix< Field_, SparseMatrixFormat::TPL_omp >
	Sparse matrix representation which stores nonzero entries by i,j,value triples. More...
class	SparseMatrix< Field_, SparseMatrixFormat::TPL >
	Sparse Matrix in Triples storage. More...

Detailed Description

These matrix classes meet the simple interface needed for blackbox algorithms.

Blackbox matrix algorithms require of the matrix only it's property of being a linear operator. Such algorithms exploit only the capacity to multiply the matrix with a vector or suitably shaped matrix (on right or left). The advantage is efficient generic methods particularly applicable to sparse and structured matrix classes in which matrix-vector product is fast. Importantly, these methods are also space efficient, typically, for an n by n matrix using only O(n) space beyond the matrix representation itself.

These classes all implement the simple black box interface as it is defined in the LinBox::BlackboxArchetype base class. Thus blackbox matrix algorithms may be used on objects of any of these classes. In contrast, classes representing matrices in such a way that elimination and other operations can be performed on them adhere to more extensive interfaces defined in the matrix directory.

Some of the classes are intended for general use, some are designed to support specific needs of algorithms, and some are primarily for testing purposes.

Users are most likely to be interested in the sparse matrix classes (SparseMatrix, TriplesBB), the class DenseMatrix, and structured matrix classes such as Toeplitz. Consult the constructors and/or read() member function documentation to see how to create them. To use a blackbox of class BB in a code:

Classes designed to be used as preconditioners in algorithms or for testing typically also provide functionality to generate random instances of the class. Examples are Diagonal and Butterfly for preconditioners, xxx for testing.

Some of the classes provide a rudimentary basis of blackbox operators for a "blackbox calculus." These include Compose, Sum, Dif, Submatrix, DirectSum, Inverse, MoorePenrose.

Note

Developers: All black box matrices should be derived from the BlackboxArchetype , so that they may be used as parameters to functions compiled with the blackbox archetype.

Blackboxes exist in 3 states: bare, shaped, and ready. A bare blackbox results from default construction. Only shaping functions may be used on bare blackboxes. Shaping functions establish the field of the elements and the row and column dimensions. Functions field(), rowdim(), coldim(), and initializing functions may be used on shaped matrices. initializing functions include read() and, in some cases, setEntry(). The ready() function converts to the ready state. For many blackbox classes it is optional, for others it is essential. Mathematical operations are valid on ready blackboxes (apply(), applyTranspose(), matrixHom()).

The mother model is used for the member field of a blackbox. The lifetime of the field must enclose the lifetime of a blackbox based on the field. The public field() function of a blackbox returns a "const Field &" and thus may only be called on a shaped blackbox. The protected field member is a "const Field *". This convention (1) allows bare blackboxes and (2) avoids proliferation of field copies. While most fields are tiny objects, a few have a large amount of data.