/usr/include/linbox/blackbox/fibb.h is in liblinbox-dev 1.4.2-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 | /* linbox/blackbox/fibb.h
* Copyright (C) 2015 bds for LinBox Team. See linbox/COPYING.LESSER for License info.
*
* Written by bds
*/
#ifndef LB_FIBB_H
#define LB_FIBB_H
/*
FIBB: Fast Inverse BlackBox
The FIBB functions are those of a blackbox plus rank, det, and the solvers:
Solve, NullSpaceRandom, NullSpaceBasis.
The solvers have left and right forms.
THe FIBBs are Diagonal, Permutation, Triangular, and products of FIBBs in which one or both are nonsingular.
*/
#include "linbox/blackbox/bb.h"
namespace LinBox{
template <class Ring>
struct FIBB : public BB<Ring>
{
using Field = Ring;
using Element = typename Ring::Element;
using ResizableMatrix = DenseMatrix<Field>;
using Matrix = DenseMatrix<Field>;
// virtual const Field& field() const = 0;
virtual ~FIBB(){}
virtual size_t& rank(size_t& r) const
= 0;
virtual Element& det( Element& d) const
= 0;
// solveRight and solveLeft
/** @brief Y: AY = X, for this A.
Solve nonsingular or consistent singular system.
If it is consistent singular, an arbitrary solution is provided.
X and Y must have identical shape.
Note that Y+Z is a random sample of the solution space after
{solveRight(Y, X); nullspaceRandomRight(Z);}.
Behaviour is unspecified for inconsistent systems (see solveMP).
*/
virtual Matrix& solveRight(Matrix& Y, const Matrix& X) const
= 0;
/// Y: YA = X, for this A
virtual Matrix& solveLeft(Matrix& Y, const Matrix& X) const
= 0;
/// N: AN = 0, each col random.
virtual Matrix& nullspaceRandomRight(Matrix& N) const
= 0;
/// N: NA = 0, each row random.
virtual Matrix& nullspaceRandomLeft(Matrix& N) const
= 0;
// this generic is virtual so that it may be specialized for performance
// nullspaceBasisRight and nullspaceBasisLeft
/** B: columns are a right nullspace basis for this A.
B is resized and filled so that:
(1) AB = 0, (2) Ax = 0 => exists y: x = By, and (3) B has full rank.
*/
virtual ResizableMatrix& nullspaceBasisRight(ResizableMatrix& B) const
= 0;
/// BA= 0 and xA = 0 => exists y: x = yB and B full rank.
virtual ResizableMatrix& nullspaceBasisLeft(ResizableMatrix& B) const
= 0;
}; // class FIBB
/// N: AN = 0, each col random.
template<class Field>
DenseMatrix<Field>& genericNullspaceRandomRight(DenseMatrix<Field>& N, const FIBB<Field>& A)
//DenseMatrix<Field, std::vector<typename Field::Element> >& genericNullspaceRandomRight(DenseMatrix<Field, std::vector<typename Field::Element> >& N, const FIBB<Field>& A)
{ typedef DenseMatrix<Field> ResizableMatrix;
typedef DenseMatrix<Field> Matrix;
ResizableMatrix Xb(A.field(), N.rowdim(), N.coldim());
ResizableMatrix Yb(A.field(), A.rowdim(), N.coldim());
Matrix X(Xb); X.random();
Matrix Y(Yb);
A.applyRight(Y, X); // Y = AX
A.solveRight(N, Y); // AN = AX
BlasMatrixDomain<Field> MD(A.field());
return MD.subin(N, X);
}
/// N: NA = 0, each row random.
template<class Field>
DenseMatrix<Field>& genericNullspaceRandomLeft(DenseMatrix<Field>& N, const FIBB<Field>& A)
//DenseMatrix<Field, std::vector<typename Field::Element> >& genericNullspaceRandomLeft(DenseMatrix<Field, std::vector<typename Field::Element> >& N, const FIBB<Field>& A)
{ typedef DenseMatrix<Field> ResizableMatrix;
typedef DenseMatrix<Field> Matrix;
ResizableMatrix Xb(A.field(), N.rowdim(), N.coldim());
ResizableMatrix Yb(A.field(), N.rowdim(), A.coldim());
Matrix X(Xb); X.random();
Matrix Y(Yb);
A.applyLeft(Y, X); // Y = XA
A.solveLeft(N, Y); // NA = XA
BlasMatrixDomain<Field> MD(A.field());
return MD.subin(N, X);
}
} // namespace LinBox
#endif // LB_FIBB_H
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