linbox

These matrix classes meet the simple interface needed for blackbox algorithms. More...
Files  
file  blackbox/archetype.h 
NO DOC.  
file  diagonalgf2.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  zeroone.inl 
NO DOC.  
file  zogf2.inl 
NO DOC.  
file  sparsetplmatrixomp.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 blockdecomposed zeroone 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...  
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 matrixvector 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
.
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.