linbox
Public Member Functions
MatrixDomain< Field > Class Template Reference

Class of matrix arithmetic functions. More...

#include <matrix-domain.h>

+ Inheritance diagram for MatrixDomain< Field >:

Public Member Functions

 MatrixDomain (const Field &F)
 Constructor.
MatrixDomainoperator= (const MatrixDomain &MD)
 Copy operator.
template<class Matrix >
std::ostream & write (std::ostream &os, const Matrix &A) const
 Print matrix.
template<class Matrix >
std::istream & read (std::istream &is, Matrix &A) const
 Read matrix.
template<class Matrix1 , class Matrix2 >
Matrix1 & copy (Matrix1 &B, const Matrix2 &A) const
 Matrix copy B <- A.
template<class Matrix1 , class Matrix2 >
bool areEqual (const Matrix1 &A, const Matrix2 &B) const
 Matrix equality.
template<class Matrix >
bool isZero (const Matrix &A) const
 Matrix equality with zero.
template<class Matrix1 , class Matrix2 , class Matrix3 >
Matrix1 & add (Matrix1 &C, const Matrix2 &A, const Matrix3 &B) const
 Matrix-matrix addition C <- A + B.
template<class Matrix1 , class Matrix2 >
Matrix1 & addin (Matrix1 &A, const Matrix2 &B) const
 Matrix-matrix in-place addition A <- A + B.
template<class Matrix1 , class Matrix2 , class Matrix3 >
Matrix1 & sub (Matrix1 &C, const Matrix2 &A, const Matrix3 &B) const
 Matrix-matrix subtraction C <- A - B.
template<class Matrix1 , class Matrix2 >
Matrix1 & subin (Matrix1 &A, const Matrix2 &B) const
 Matrix-matrix in-place subtraction A <- A - B.
template<class Matrix1 , class Matrix2 >
Matrix1 & neg (Matrix1 &B, const Matrix2 &A) const
 Matrix negate B <- -A.
template<class Matrix >
Matrix & negin (Matrix &A) const
 Matrix in-place negate A <- -A.
template<class Matrix1 , class Matrix2 , class Matrix3 >
Matrix1 & mul (Matrix1 &C, const Matrix2 &A, const Matrix3 &B) const
 Matrix-matrix multiply C <- A * B.
template<class Matrix1 , class Matrix2 >
Matrix2 & leftMulin (const Matrix1 &A, Matrix2 &B) const
 Matrix-matrix in-place multiply on the left B <- A * B.
template<class Matrix1 , class Matrix2 >
Matrix1 & rightMulin (Matrix1 &A, const Matrix2 &B) const
 Matrix-matrix in-place multiply on the right A <- A * B.
template<class Matrix1 , class Matrix2 >
Matrix1 & mulin (Matrix1 &A, const Matrix2 &B) const
 Matrix-matrix in-place multiply A <- A * B.
template<class Matrix1 , class Matrix2 >
Matrix1 & mul (Matrix1 &C, const Matrix2 &B, const typename Field::Element &a) const
 Matrix-scalar multiply C <- B * a.
template<class Matrix >
Matrix & mulin (Matrix &B, const typename Field::Element &a) const
 Matrix-scalar in-place multiply B <- B * a.
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.
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$.
const Fieldfield () const
 Retrieve the underlying field.
Fieldfield ()
 Retrieve the underlying field.
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.
template<class Vector1 , class Matrix , class Vector2 >
Vector1 & vectorAxpyin (Vector1 &y, const Matrix &A, const Vector2 &x) const
 Matrix-vector in-place axpy $y \gets y + A x$.
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.
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.

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.
template<class Matrix , class Iterator >
Matrix & permuteRows (Matrix &A, Iterator P_start, Iterator P_end) const
 Permute the rows of the given matrix.
template<class Matrix , class Iterator >
Matrix & permuteColumns (Matrix &A, Iterator P_start, Iterator P_end) const
 Permute the columns of the given matrix.

Detailed Description

template<class Field>
class LinBox::MatrixDomain< Field >

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 DenseMatrix 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 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
Field& field ( ) [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
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: