271 lines
11 KiB
C++
271 lines
11 KiB
C++
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/*
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* Portable Agile C++ Classes (PACC)
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* Copyright (C) 2001-2004 by Marc Parizeau
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* http://manitou.gel.ulaval.ca/~parizeau/PACC
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*
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* This library is free software; you can redistribute it and/or
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* modify it under the terms of the GNU Lesser General Public
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* License as published by the Free Software Foundation; either
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* version 2.1 of the License, or (at your option) any later version.
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*
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* This library is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public
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* License along with this library; if not, write to the Free Software
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* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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*
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* Contact:
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* Laboratoire de Vision et Systemes Numeriques
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* Departement de genie electrique et de genie informatique
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* Universite Laval, Quebec, Canada, G1K 7P4
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* http://vision.gel.ulaval.ca
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*
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*/
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/*!
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* \file PACC/Math/Matrix.hpp
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* \brief Definition of class Matrix.
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* \author Christian Gagne
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* \author Marc Parizeau
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* $Revision: 1.8.2.1 $
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* $Date: 2007/09/10 18:24:08 $
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*/
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#ifndef PACC_Matrix_hpp
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#define PACC_Matrix_hpp
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#include "Util/Assert.hpp"
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#include "XML/Document.hpp"
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#include "XML/Streamer.hpp"
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#include <vector>
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namespace PACC {
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using namespace std;
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// Forward declarations
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class Vector;
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/*! \brief %Matrix of floating point numbers.
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\author Marc Parizeau and Christian Gagné, Laboratoire de vision et
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systèmes numériques, Université Laval
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\ingroup Math
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\ingroup MLP
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This class encapsulates a vector of floating point numbers (double) as a matrix.
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It contains operators and methods for sum, difference, and product of matrices,
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as well as product with a scalar. It also includes matrix transposition and
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inversion methods, as well as computation of eigenvalues and eigenvectors
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for symetric matrices. Matrices can read and write themselves in %XML.
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\attention Row and column indices start at 0.
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*/
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class Matrix : protected vector<double> {
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public:
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//! Construct an empty matrix with name \c inName.
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Matrix(const string& inName="") : mRows(0), mCols(0), mPrec(15), mName(inName) {}
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//! Construct a matrix of size \c inRows rows by \c inColumns columns, initialized with 0, and with name \c inName.
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explicit Matrix(unsigned int inRows, unsigned int inCols, const string& inName="")
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: vector<double>(inRows*inCols, 0), mRows(inRows), mCols(inCols), mPrec(15), mName(inName) {}
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//! Construct a matrix of size \c inRows rows by \c inColumns columns, initialized with value \c inValue, and with name \c inName.
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explicit Matrix(unsigned int inRows, unsigned int inCols, double inValue, const string& inName="")
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: vector<double>(inRows*inCols, inValue), mRows(inRows), mCols(inCols), mPrec(15), mName(inName) {}
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//! Delete this matrix.
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virtual ~Matrix() {mRows = mCols = 0;}
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//! Assign matrix \c inMatrix to this matrix but do not overwrite name unless it is undefined.
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Matrix& operator=(const Matrix& inMatrix) {
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if(&inMatrix != this) {
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// don't self assign!
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vector<double>::operator=(inMatrix);
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mRows = inMatrix.mRows; mCols = inMatrix.mCols;
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if(mName == "") mName = inMatrix.mName;
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}
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return *this;
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}
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//! Return const reference to element \c (inRow,inColumn).
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inline const double& operator()(unsigned int inRow, unsigned int inCol) const {
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PACC_AssertM(inRow < mRows && inCol < mCols, "invalid matrix indices!");
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return (*this)[(inRow*mCols)+inCol];
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}
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//! Return reference to element \c (inRow,inColumn).
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inline double& operator()(unsigned int inRow, unsigned int inCol) {
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PACC_AssertM(inRow < mRows && inCol < mCols, "invalid matrix indices!");
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return (*this)[(inRow*mCols)+inCol];
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}
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//! Add scalar \c inScalar to this matrix, and return new matrix.
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inline Matrix operator+(double inScalar) const {Matrix lMatrix; return add(lMatrix, inScalar);}
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//! Add scalar \c inScalar to this matrix, and assign result to this matrix.
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inline Matrix& operator+=(double inScalar) {return add(*this, inScalar);}
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//! Add matrix \c inMatrix to this matrix, and return new matrix.
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inline Matrix operator+(const Matrix& inMatrix) const {Matrix lMatrix; return add(lMatrix, inMatrix);}
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//! Add matrix \c inMatrix to this matrix, and assign result to this matrix.
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inline Matrix& operator+=(const Matrix& inMatrix) {return add(*this, inMatrix);}
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//! Subtract scalar \c inScalar from this matrix, and return new matrix.
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inline Matrix operator-(double inScalar) const {Matrix lMatrix; return subtract(lMatrix, inScalar);}
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//! Subtract scalar \c inScalar from this matrix, and assign result to this matrix.
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inline Matrix& operator-=(double inScalar) {return subtract(*this, inScalar);}
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//! Subtract matrix \c inMatrix from this matrix, and return new matrix.
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inline Matrix operator-(const Matrix& inMatrix) const {Matrix lMatrix; return subtract(lMatrix, inMatrix);}
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//! Subtract matrix \c inMatrix from this matrix, and assign result to this matrix.
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inline Matrix& operator-=(const Matrix& inMatrix) {return subtract(*this, inMatrix);}
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//! Multiply scalar \c inScalar with this matrix, and return new matrix.
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inline Matrix operator*(double inScalar) const {Matrix lMatrix; return multiply(lMatrix, inScalar);}
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//! Multiply scalar \c inScalar with this matrix, and assign result to this matrix.
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inline Matrix& operator*=(double inScalar) {return multiply(*this, inScalar);}
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//! Multiply this matrix with matrix \c inMatrix, and return new matrix.
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inline Matrix operator*(const Matrix& inMatrix) const {Matrix lMatrix; return multiply(lMatrix, inMatrix);}
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//! Multiply this matrix with matrix \c inMatrix, and assign result to this matrix.
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inline Matrix operator*=(const Matrix& inMatrix) {return multiply(*this, inMatrix);}
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//! Return number of columns.
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inline unsigned int getCols(void) const {return mCols;}
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//! Return number of rows.
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inline unsigned int getRows(void) const {return mRows;}
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//! Add this matrix with scalar \c inScalar and return result through matrix \c outMatrix.
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Matrix& add(Matrix& outMatrix, double inScalar) const;
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//! Add this matrix with matrix \c inMatrix and return result through matrix \c outMatrix.
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Matrix& add(Matrix& outMatrix, const Matrix& inMatrix) const;
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//! Return determinant of this matrix.
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double computeDeterminant(void) const;
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//! Compute eigenvalues and eigenvectors of a symetric matrix using the Triagonal QL method (matrix must be symetric).
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void computeEigens(Vector& outValues, Matrix& outVectors) const;
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//! Extract from this matrix a sub-matrix defined by row range \c [inRow1,inRow2] and column range \c [inCol1,inCol2], return result through matrix \c outMatrix.
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Matrix& extract(Matrix& outMatrix, unsigned int inRow1, unsigned int inRow2, unsigned int inCol1, unsigned int inCol2) const;
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//! Extract column \c inCol from this matrix and return it through matrix \c outMatrix.
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Matrix& extractColumn(Matrix& outVector, unsigned int inCol) const;
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//! Extract row \c inRow from this matrix and return it through matrix \c outMatrix.
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Matrix& extractRow(Matrix& outVector, unsigned int inRow) const;
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//! Return the inverse of this matrix.
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Matrix invert(void) const;
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//! Invert this matrix and return result through matrix \c outMatrix.
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Matrix& invert(Matrix& outMatrix) const;
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//! Multiply this matrix with scalar \c inScalar and return result through matrix \c outMatrix.
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Matrix& multiply(Matrix& outMatrix, double inScalar) const;
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//! Multiply this matrix with matrix \c inMatrix and return result through matrix \c outMatrix.
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Matrix& multiply(Matrix& outMatrix, const Matrix& inMatrix) const;
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//! Subtract this matrix with scalar \c inScalar and return result through matrix \c outMatrix.
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Matrix& subtract(Matrix& outMatrix, double inScalar) const;
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//! Subtract this matrix with matrix \c inMatrix and return result through matrix \c outMatrix.
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Matrix& subtract(Matrix& outMatrix, const Matrix& inMatrix) const;
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//! Return the transpose of this matrix.
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Matrix transpose(void) const;
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//! Transpose this matrix and return result through matrix \c outMatrix.
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Matrix& transpose(Matrix& outMatrix) const;
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//! Resize matrix to \c inRows rows and \c inCols columns, while filing blanks with null values.
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void resize(unsigned int inRows, unsigned int inCols);
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//! Set this matrix to an identity matrix of size \c inSize.
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void setIdentity(unsigned int inSize);
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//! Return matrix name.
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inline const string& getName(void) const {return mName;}
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//! Set matrix name.
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inline void setName(string& inName) {mName = inName;};
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//! Read this matrix from parse tree node \c inNode.
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string read(const XML::Iterator& inNode);
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//! Write this matrix into streamer \c outStream using tag name \c inTag.
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void write(XML::Streamer& outStream, const string& inTag="Matrix") const;
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//! Set output write precision to \c inPrecision number of digits.
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void setPrecision(unsigned int inPrecision) {mPrec = inPrecision;}
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protected:
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unsigned int mRows; //!< Number of rows.
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unsigned int mCols; //!< Number of columns.
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unsigned int mPrec; //!< Output precision.
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string mName; //!< Name of matrix.
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//! Compute back substitution for the L-U decomposition.
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void computeBackSubLU(const vector<unsigned int>& inIndexes, Matrix& ioMatrixB) const;
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//! Compute L-U decomposition.
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void decomposeLU(vector<unsigned int>& outIndexes, int& outD);
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//! Return sqrt(a^2 + b^2) without under/overflow (used internally by method tql2).
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double hypot(double a, double b) const;
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//! Return in vector \c outScales the scaling values for the L-U decomposition.
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void scaleLU(vector<double>& outScales) const;
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//! Triagonalize matrix for computing eigensystem using QL method.
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void tql2(Vector& d, Vector& e, Matrix& V) const;
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//! Diagonalize matrix for computing eigensystem using QL method.
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void tred2(Vector& d, Vector& e, Matrix& V) const;
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//! Set matrix size to \c inRows rows and \c inCols columns; matrix content is lost.
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inline void setRowsCols(unsigned int inRows, unsigned int inCols) {
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mRows = inRows; mCols = inCols;
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vector<double>::resize(mRows*mCols);
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}
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//! Throw runtime error with message \c inMessage using parse tree node \c inNode.
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void throwError(const string& inMessage, const XML::Iterator& inNode) const;
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private:
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// disabled methods
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Matrix& add(Vector&, double) const;
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Matrix& add(Vector&, const Matrix&) const;
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void computeEigens(Vector&, Vector&) const;
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Matrix& extract(Vector&, unsigned int, unsigned int, unsigned int, unsigned int) const;
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Matrix& extractRow(Vector&, unsigned int) const;
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Matrix& invert(Vector&) const;
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Matrix& subtract(Vector&, double) const;
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Matrix& subtract(Vector&, const Matrix&) const;
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Matrix& multiply(Vector&, double) const;
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Matrix& multiply(Vector&, const Matrix&) const;
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Matrix& transpose(Vector&) const;
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};
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//! Insert matrix \c inMatrix into output stream \c outStream.
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ostream& operator<<(ostream& outStream, const Matrix& inMatrix);
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//! Extract matrix \c outMatrix from %XML document \c inDocument.
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XML::Document& operator>>(XML::Document& inDocument, Matrix& outMatrix);
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}
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#endif // PACC_Matrix_hpp
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