linbox
Public Types | Public Member Functions
MatrixDomain< Matrix > Class Template Reference

Class of matrix arithmetic functions. More...

#include <matrix-domain.h>

+ Inheritance diagram for MatrixDomain< Matrix >:

Public Types

typedef Vector< Field >::Dense Rep_
 

Public Member Functions

 MatrixDomain (const Field &F)
 Constructor. More...
 
MatrixDomainoperator= (const MatrixDomain &MD)
 Copy operator.
 
template<class Matrix_ >
std::ostream & write (std::ostream &os, const Matrix_ &A) const
 Print matrix. More...
 
template<class Matrix_ >
std::istream & read (std::istream &is, Matrix_ &A) const
 Read matrix. More...
 
template<class Matrix1 , class Matrix2 >
Matrix1 & copy (Matrix1 &B, const Matrix2 &A) const
 Matrix copy B <- A. More...
 
Matrixcopy (Matrix &B, const Matrix &A) const
 B <– A. They must already have the same shape.
 
Matrixswap (Matrix &B, Matrix &A) const
 Matrix swap B <–> A. More...
 
template<class Matrix1 , class Matrix2 >
bool areEqual (const Matrix1 &A, const Matrix2 &B) const
 Matrix equality. More...
 
template<class Matrix_ >
bool isZero (const Matrix_ &A) const
 Matrix equality with zero. More...
 
template<class Matrix1 , class Matrix2 , class Matrix3 >
Matrix1 & add (Matrix1 &C, const Matrix2 &A, const Matrix3 &B) const
 Matrix-matrix addition C <- A + B. More...
 
template<class Matrix1 , class Matrix2 >
Matrix1 & addin (Matrix1 &A, const Matrix2 &B) const
 Matrix-matrix in-place addition A <- A + B. More...
 
template<class Matrix1 , class Matrix2 , class Matrix3 >
Matrix1 & sub (Matrix1 &C, const Matrix2 &A, const Matrix3 &B) const
 Matrix-matrix subtraction C <- A - B. More...
 
template<class Matrix1 , class Matrix2 >
Matrix1 & subin (Matrix1 &A, const Matrix2 &B) const
 Matrix-matrix in-place subtraction A <- A - B. More...
 
template<class Matrix1 , class Matrix2 >
Matrix1 & neg (Matrix1 &B, const Matrix2 &A) const
 Matrix negate B <- -A. More...
 
template<class Matrix_ >
Matrix_ & negin (Matrix_ &A) const
 Matrix in-place negate A <- -A. More...
 
template<class Matrix1 , class Matrix2 , class Matrix3 >
Matrix1 & mul (Matrix1 &C, const Matrix2 &A, const Matrix3 &B) const
 Matrix-matrix multiply C <- A * B. More...
 
template<class Matrix1 , class Matrix2 >
Matrix2 & leftMulin (const Matrix1 &A, Matrix2 &B) const
 Matrix-matrix in-place multiply on the left B <- A * B. More...
 
template<class Matrix1 , class Matrix2 >
Matrix1 & rightMulin (Matrix1 &A, const Matrix2 &B) const
 Matrix-matrix in-place multiply on the right A <- A * B. More...
 
template<class Matrix1 , class Matrix2 >
Matrix1 & mulin (Matrix1 &A, const Matrix2 &B) const
 Matrix-matrix in-place multiply A <- A * B. More...
 
template<class Matrix1 , class Matrix2 >
Matrix1 & mul (Matrix1 &C, const Matrix2 &B, const typename Field::Element &a) const
 Matrix-scalar multiply C <- B * a. More...
 
template<class Matrix_ >
Matrix_ & mulin (Matrix_ &B, const typename Field::Element &a) const
 Matrix-scalar in-place multiply B <- B * a. More...
 
template<class Matrix1 , class Matrix2 , class Matrix3 >
Matrix1 & axpyin (Matrix1 &Y, const Matrix2 &A, const Matrix3 &X) const
 Matrix-matrix in-place axpy Y <- Y + A*X. More...
 
template<class Matrix1 , class Matrix2 , class Matrix3 >
Matrix1 & axmyin (Matrix1 &Y, const Matrix2 &A, const Matrix3 &X) const
 Y <- AX-Y.
 
template<class Matrix1 , class Matrix2 , class Matrix3 >
Matrix1 & muladd (Matrix1 &D, const typename Field::Element &beta, const Matrix1 &C, const typename Field::Element &alpha, const Matrix2 &A, const Matrix3 &B) const
 General matrix multiply $ D \gets \alpha A B + \beta C$. More...
 
const Field & field () const
 Retrieve the underlying field. More...
 
template<class Matrix1 , class Matrix2 >
Matrix1 & pow_apply (Matrix1 &M1, const Matrix2 &M2, unsigned long int k) const
 
template<class Matrix1 , class Matrix2 >
Matrix1 & pow_horn (Matrix1 &M1, const Matrix2 &M2, unsigned long int k) const
 
Matrix-vector arithmetic operations

These operations take a matrix satisfying the DenseMatrix archetype and LinBox vectors as inputs.

They involve matrix-vector product and matrix-vector AXPY

template<class Vector1 , class Matrix_ , class Vector2 >
Vector1 & vectorMul (Vector1 &w, const Matrix_ &A, const Vector2 &v) const
 Matrix-vector multiply w <- A * v. More...
 
template<class Vector1 , class Matrix_ , class Vector2 >
Vector1 & vectorAxpyin (Vector1 &y, const Matrix_ &A, const Vector2 &x) const
 Matrix-vector in-place axpy $y \gets y + A x$. More...
 
Matrix-black box arithmetic operations

These operations mimic the matrix-matrix arithmetic operations above, but one of the parameters is a BlackboxArchetype.

template<class Matrix1 , class Blackbox , class Matrix2 >
Matrix1 & blackboxMulLeft (Matrix1 &C, const Blackbox &A, const Matrix2 &B) const
 Matrix-black box left-multiply C <- A * B. More...
 
template<class Matrix1 , class Matrix2 , class Blackbox >
Matrix1 & blackboxMulRight (Matrix1 &C, const Matrix2 &A, const Blackbox &B) const
 Matrix-black box right-multiply C <- A * B. More...
 

Matrix permutations

These operations permute the rows or columns of a matrix based on the given permutation.

They are intended for use with Gauss-Jordan elimination

typedef std::pair< unsigned
int, unsigned int > 
Transposition
 Transposition.
 
typedef std::vector
< Transposition
Permutation
 Permutation. More...
 
template<class Matrix_ , class Iterator >
Matrix_ & permuteRows (Matrix_ &A, Iterator P_start, Iterator P_end) const
 Permute the rows of the given matrix. More...
 
template<class Matrix_ , class Iterator >
Matrix_ & permuteColumns (Matrix_ &A, Iterator P_start, Iterator P_end) const
 Permute the columns of the given matrix. More...
 

Detailed Description

template<class Matrix>
class LinBox::MatrixDomain< Matrix >

Class of matrix arithmetic functions.

This class encapuslated matrix-matrix and matrix-vector operations, roughly equivalent to BLAS levels 2 and 3. The arithmetic methods are parameterized by matrix type so that they may be used the same way with sparse matrices, dense matrices, and dense submatrices. Except where otherwise noted, they require the matrix inputs to meet the BlasMatrix archetype.

These methods are specialized so that they can run efficiently with different matrix representations. If a matrix has an efficient row iterator, but not an efficient column iterator, a specialization that makes use of the former will be selected. This allows a great deal of flexibility when dealing with sparse matrix arithmetic.

For all of the arithmetic operations that output matrices, it is assumed that the output matrix has an efficient row iterator. In typical use, the output matrix will be a BlasMatrix or a BlasSubmatrix, which has efficient row and column iterators. In particular, one should not perform these arithmetic operations outputting to a SparseMatrixBase.

There are other restrictions. See the method-specific documentation for more details.

Member Typedef Documentation

typedef Vector<Field>::Dense Rep_
Bug:
should be BlasVector
typedef std::vector<Transposition> Permutation

Permutation.

A permutation is represented as a vector of pairs, each pair representing a transposition.

Constructor & Destructor Documentation

MatrixDomain ( const Field &  F)
inline

Constructor.

Parameters
Ffield for MatrixDomain operations.

Member Function Documentation

const Field& field ( ) const
inline

Retrieve the underlying field.

Return a reference to the field that this matrix domain object uses

Returns
reference to field
std::ostream& write ( std::ostream &  os,
const Matrix_ &  A 
) const
inline

Print matrix.

Parameters
osOutput stream to which matrix is written.
AMatrix.
Returns
reference to os.
std::istream& read ( std::istream &  is,
Matrix_ &  A 
) const
inline

Read matrix.

Parameters
isInput stream from which matrix is read.
AMatrix.
Returns
reference to is.
Matrix1& copy ( Matrix1 &  B,
const Matrix2 &  A 
) const
inline

Matrix copy B <- A.

Copy the contents of the matrix B to the matrix A

Both matrices must support the same iterators, row or column.

Parameters
BMatrix B
AMatrix A
Returns
Reference to B
Matrix& swap ( Matrix B,
Matrix A 
) const
inline

Matrix swap B <–> A.

They must already have the same shape.

Returns
Reference to B
bool areEqual ( const Matrix1 &  A,
const Matrix2 &  B 
) const
inline

Matrix equality.

Test whether the matrices A and B are equal

Parameters
AInput vector
BInput vector
Returns
true if and only if the matrices A and B are equal
bool isZero ( const Matrix_ &  A) const
inline

Matrix equality with zero.

Parameters
AInput matrix
Returns
true if and only if the matrix A is zero
Matrix1& add ( Matrix1 &  C,
const Matrix2 &  A,
const Matrix3 &  B 
) const
inline

Matrix-matrix addition C <- A + B.

Each of A, B, and C must support the same iterator, either row or column

Parameters
COutput matrix C
AInput matrix A
BInput matrix B
Returns
Reference to C
Matrix1& addin ( Matrix1 &  A,
const Matrix2 &  B 
) const
inline

Matrix-matrix in-place addition A <- A + B.

Each of A and B must support the same iterator, either row or column

Parameters
AInput matrix A
BInput matrix B
Returns
Reference to A
Matrix1& sub ( Matrix1 &  C,
const Matrix2 &  A,
const Matrix3 &  B 
) const
inline

Matrix-matrix subtraction C <- A - B.

Each of A, B, and C must support the same iterator, either row or column

Parameters
COutput matrix C
AInput matrix A
BInput matrix B
Returns
Reference to C
Matrix1& subin ( Matrix1 &  A,
const Matrix2 &  B 
) const
inline

Matrix-matrix in-place subtraction A <- A - B.

Each of A and B must support the same iterator, either row or column

Parameters
AInput matrix A
BInput matrix B
Returns
Reference to A
Matrix1& neg ( Matrix1 &  B,
const Matrix2 &  A 
) const
inline

Matrix negate B <- -A.

Each of A and B must support the same iterator, either row or column

Parameters
BOutput matrix B
AInput matrix A
Returns
reference to B
Matrix_& negin ( Matrix_ &  A) const
inline

Matrix in-place negate A <- -A.

Parameters
AInput matrix A; result is stored here
Matrix1& mul ( Matrix1 &  C,
const Matrix2 &  A,
const Matrix3 &  B 
) const
inline

Matrix-matrix multiply C <- A * B.

C must support both row and column iterators, and the vector representations must be dense. Examples of supported matrices are BlasMatrix and BlasSubmatrix.

Either A or B, or both, may have limited iterators. However, either A must support row iterators or B must support column iterators. If both A and B lack support for an iterator (either row or column), then C must support the same type of iterator as A and B.

Parameters
COutput matrix C
AInput matrix A
BInput matrix B
Returns
Reference to C
Matrix2 & leftMulin ( const Matrix1 &  A,
Matrix2 &  B 
) const
inline

Matrix-matrix in-place multiply on the left B <- A * B.

B should support both row and column iterators, and must be dense. A must support row iterators.

Parameters
AInput matrix A
BInput matrix B
Returns
Reference to B
Matrix1 & rightMulin ( Matrix1 &  A,
const Matrix2 &  B 
) const
inline

Matrix-matrix in-place multiply on the right A <- A * B.

A should support both row and column iterators, and must be dense. B must support column iterators.

Parameters
AInput matrix A
BInput matrix B
Returns
Reference to A
Matrix1& mulin ( Matrix1 &  A,
const Matrix2 &  B 
) const
inline

Matrix-matrix in-place multiply A <- A * B.

This is an alias for rightMulin

Parameters
AInput matrix A
BInput matrix B
Returns
Reference to A
Matrix1& mul ( Matrix1 &  C,
const Matrix2 &  B,
const typename Field::Element &  a 
) const
inline

Matrix-scalar multiply C <- B * a.

Multiply B by the scalar element a and store the result in C. B and C must support the same iterators.

Parameters
COutput matrix C
BInput matrix B
aInput scalar a
Returns
Reference to C
Matrix_& mulin ( Matrix_ &  B,
const typename Field::Element &  a 
) const
inline

Matrix-scalar in-place multiply B <- B * a.

Multiply B by the scalar element a in-place.

Parameters
BInput matrix B
aInput scalar a
Returns
Reference to B
Matrix1& axpyin ( Matrix1 &  Y,
const Matrix2 &  A,
const Matrix3 &  X 
) const
inline

Matrix-matrix in-place axpy Y <- Y + A*X.

This function combines mul and add, eliminating the need for an additional temporary in expressions of the form $Y = Y + AX$. Only one row of additional storage is required. Y may have either efficient row iterators or efficient column iterators, and the same restrictions on A and X apply as in mul.

Note that no out-of-place axpy is provided, since it gives no benefit. One may just as easily multiply into the result and call addin.

Parameters
YInput matrix Y; result is stored here
AInput matrix A
XInput matrix X
Matrix1& muladd ( Matrix1 &  D,
const typename Field::Element &  beta,
const Matrix1 &  C,
const typename Field::Element &  alpha,
const Matrix2 &  A,
const Matrix3 &  B 
) const
inline

General matrix multiply $ D \gets \alpha A B + \beta C$.

Todo:
not efficient...
Matrix1& pow_apply ( Matrix1 &  M1,
const Matrix2 &  M2,
unsigned long int  k 
) const
Todo:
Need documentation of these methods
Matrix1& pow_horn ( Matrix1 &  M1,
const Matrix2 &  M2,
unsigned long int  k 
) const
Todo:
Need documentation of these methods
Vector1& vectorMul ( Vector1 &  w,
const Matrix_ &  A,
const Vector2 &  v 
) const
inline

Matrix-vector multiply w <- A * v.

The vectors v and w must be of the same representation (dense, sparse sequence, sparse associative, or sparse parallel), but they may be of different types. The matrix A may have any representation.

Parameters
wOutput vector w
AInput matrix A
vInput vector v
Returns
Reference to w
Vector1& vectorAxpyin ( Vector1 &  y,
const Matrix_ &  A,
const Vector2 &  x 
) const
inline

Matrix-vector in-place axpy $y \gets y + A x$.

This function eliminates the requirement for temporary storage when one is computing an expression of the form given above.

The vectors y and x must be of the same representation (dense, sparse sequence, sparse associative, or sparse parallel), but they may be of different types. The matrix A may have any representation.

Note that out-of-place axpy is not provided since it provides no benefit – one can use mul and then addin to exactly the same effect, with no additional storage or performance cost.

Parameters
yInput vector y; result is stored here
AInput matrix A
xInput vector x
Matrix1 & blackboxMulLeft ( Matrix1 &  C,
const Blackbox &  A,
const Matrix2 &  B 
) const
inline

Matrix-black box left-multiply C <- A * B.

Both C and B must support column iterators

Parameters
COutput matrix
ABlack box for A
BMatrix B
Matrix1 & blackboxMulRight ( Matrix1 &  C,
const Matrix2 &  A,
const Blackbox &  B 
) const
inline

Matrix-black box right-multiply C <- A * B.

Both C and A must support row iterators

Parameters
COutput matrix
AMatrix A
BBlack box for B
Matrix_& permuteRows ( Matrix_ &  A,
Iterator  P_start,
Iterator  P_end 
) const
inline

Permute the rows of the given matrix.

Parameters
AOutput matrix
P_startStart of permutation
P_endEnd of permutation
Returns
Reference to A
Matrix_& permuteColumns ( Matrix_ &  A,
Iterator  P_start,
Iterator  P_end 
) const
inline

Permute the columns of the given matrix.

Parameters
AOutput matrix
P_startStart of permutation
P_endEnd of permutation
Returns
Reference to A

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