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 *   Copyright (C) 2003-2004 by David Saxton                               *
 *   david@bluehaze.org                                                    *
 *                                                                         *
 *   This program is free software; you can redistribute it and/or modify  *
 *   it under the terms of the GNU General Public License as published by  *
 *   the Free Software Foundation; either version 2 of the License, or     *
 *   (at your option) any later version.                                   *

#ifndef MATRIX_H
#define MATRIX_H

#include <math/qmatrix.h>

This class performs matrix storage, lu decomposition, forward and backward
substitution, and a few other useful operations. Steps in using class:
(1) Create an instance of this class with the correct size
(2) Define the matrix pattern as neccessary:
      (1) Call zero (unnecessary after initial ceration) to reset the pattern
            & matrix
      (2) Call setUse to set the use of each element in the matrix
      (3) Call createMap to generate the row-wise permutation mapping for use
            in partial pivoting
(3) Add the values to the matrix
(4) Call performLU, and get the results with fbSub
(5) Repeat 2, 3, 4 or 5 as necessary.
@todo We need to allow createMap to work while the matrix has already been initalised
@short Matrix manipulation class tailored for circuit equations
@author David Saxton
00033 class Matrix
       * Creates a size x size square matrix m, with all values zero,
       * and a right side vector x of size m+n
      Matrix( CUI n, CUI m );
       * Sets all elements to zero
      void zero();

       * Returns true if the matrix is changed since last calling performLU()
       * - i.e. if we do need to call performLU again.
00051       inline bool isChanged() const { return max_k < m_mat->size_m(); }
       * Performs LU decomposition. Going along the rows,
       * the value of the decomposed LU matrix depends only on
       * the previous values.
      void performLU();
       * Applies the right side vector (x) to the decomposed matrix,
       * with the solution returned in x.
      void fbSub( QuickVector* x );
       * Prints the matrix to stdout
      void displayMatrix();
       * Prints the LU-decomposed matrix to stdout
      void displayLU();
       * Sets the element matrix at row i, col j to value x
00074       double& g( CUI i, CUI j )
            const unsigned int mapped_i = m_inMap[i];
            if ( mapped_i<max_k ) max_k=mapped_i;
            if ( j<max_k ) max_k=j;
            // I think I need the next line...
            if ( max_k>0 ) max_k--;
            return (*m_mat)[mapped_i][j];

      double g( CUI i, CUI j ) const { return (*m_mat)[m_inMap[i]][j]; }

      double& b( CUI i, CUI j ) { return g( i, j+m_n ); }
      double& c( CUI i, CUI j ) { return g( i+m_n, j ); }
      double& d( CUI i, CUI j ) { return g( i+m_n, j+m_n ); }

      double b( CUI i, CUI j ) const { return g( i, j+m_n ); }
      double c( CUI i, CUI j ) const { return g( i+m_n, j ); }
      double d( CUI i, CUI j ) const { return g( i+m_n, j+m_n ); }
       * Returns the value of matrix at row i, col j.
00098       double m( CUI i, CUI j ) const
            return (*m_mat)[m_inMap[i]][j];
       * Multiplies this matrix by the Vector rhs, and places the result
       * in the vector pointed to by result. Will fail if wrong size.
      void multiply(const QuickVector *rhs, QuickVector *result );

       * Swaps around the rows in the (a) the matrix; and (b) the mappings
      void swapRows( CUI a, CUI b );

      unsigned int m_n; // number of cnodes. 
      unsigned int max_k; // optimization variable, allows partial L_U re-do. 
      int *m_inMap; // Rowwise permutation mapping from external reference to internal storage

      QuickMatrix *m_mat;
      QuickMatrix *m_lu;
      double *m_y; // Avoids recreating it lots of times

This class provides a very simple, lightweight, 2x2 matrix solver.
It's fast and reliable. Set the values for the entries of A and b:

A x = b

call solve() (which returns true if successful - i.e. exactly one solution to the
matrix), and get the values of x with the appropriate functions.

@short 2x2 Matrix
@author David Saxton
00137 class Matrix22
      double &a11() { return m_a11; }
      double &a12() { return m_a12; }
      double &a21() { return m_a21; }
      double &a22() { return m_a22; }
      double &b1() { return m_b1; }
      double &b2() { return m_b2; }
       * Solve the matrix. Returns true if successful (i.e. non-singular), else
       * false. Get the solution with x1() and x2().
      bool solve();
       * Resets all entries to zero
      void reset();
      double x1() const { return m_x1; }
      double x2() const { return m_x2; }
      double m_a11, m_a12, m_a21, m_a22;
      double m_b1, m_b2;
      double m_x1, m_x2;


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