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-rw-r--r--src/electronics/simulation/matrix.cpp546
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diff --git a/src/electronics/simulation/matrix.cpp b/src/electronics/simulation/matrix.cpp
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+/***************************************************************************
+ * Copyright (C) 2003-2004 by David Saxton *
+ * [email protected] *
+ * *
+ * 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. *
+ ***************************************************************************/
+
+#include "matrix.h"
+
+#include <kdebug.h>
+
+#include <assert.h>
+
+#include <cmath>
+#include <iostream>
+#include <vector>
+
+/// Minimum value before an entry is deemed "zero"
+const double epsilon = 1e-50;
+
+Matrix::Matrix( uint n, uint m )
+{
+ m_n = n;
+ m_m = m;
+ m_size = m_n+m_m;
+
+ m_mat = new matrix(m_size);
+ m_lu = new matrix(m_size);
+ m_y = new double[m_size];
+ m_inMap = new int[m_size];
+// m_outMap = new int[m_size];
+ m_map = new Map(m_size);
+ zero();
+}
+
+
+Matrix::~Matrix()
+{
+ delete m_map;
+ delete m_mat;
+ delete m_lu;
+ delete [] m_y;
+ delete [] m_inMap;
+// delete [] m_outMap;
+}
+
+
+void Matrix::zero()
+{
+ for ( uint i=0; i<m_size; i++ )
+ {
+ for ( uint j=0; j<m_size; j++ )
+ {
+ (*m_mat)[i][j] = 0.;
+ (*m_lu)[i][j] = 0.;
+ }
+ m_inMap[i] = i;
+// m_outMap[i] = i;
+ }
+
+ max_k = 0;
+}
+
+
+void Matrix::setUse( const uint i, const uint j, Map::e_type type, bool big )
+{
+ m_map->setUse( i, j, type, big );
+}
+
+
+void Matrix::createMap()
+{
+ int newMap[m_size];
+ m_map->createMap(newMap);
+ for ( uint i=0; i<m_size; i++ )
+ {
+ const int nu = newMap[i];
+ if ( nu != m_inMap[i] )
+ {
+ int old = -1;
+ for ( uint j=0; j<m_size && old == -1; j++ )
+ {
+ if ( m_inMap[j] == nu ) {
+ old = j;
+ }
+ }
+ assert( old != -1 );
+ swapRows( old, i );
+ }
+ }
+}
+
+
+void Matrix::swapRows( const uint a, const uint b )
+{
+ if ( a == b ) return;
+ m_mat->swapRows( a, b );
+
+ const int old = m_inMap[a];
+ m_inMap[a] = m_inMap[b];
+ m_inMap[b] = old;
+
+ max_k = 0;
+}
+
+
+/*void Matrix::genOutMap()
+{
+ for ( uint i=0; i<m_size; i++ )
+ {
+ m_outMap[ m_inMap[i] ] = i;
+ }
+}*/
+
+
+void Matrix::operator=( Matrix *const m )
+{
+ for ( uint _i=0; _i<m_size; _i++ )
+ {
+ uint i = m_inMap[_i];
+ for ( uint j=0; j<m_size; j++ )
+ {
+ (*m_mat)[i][j] = m->m(i,j);
+ }
+ }
+
+ max_k = 0;
+}
+
+void Matrix::operator+=( Matrix *const m )
+{
+ for ( uint _i=0; _i<m_size; _i++ )
+ {
+ uint i = m_inMap[_i];
+ for ( uint j=0; j<m_size; j++ )
+ {
+ (*m_mat)[i][j] += m->m(i,j);
+ }
+ }
+
+ max_k = 0;
+}
+
+void Matrix::performLU()
+{
+// max_k = 0;
+ uint n = m_size;
+ if ( n == 0 ) return;
+
+ // Copy the affected segment to LU
+ for ( uint i=max_k; i<n; i++ )
+ {
+ for ( uint j=max_k; j<n; j++ )
+ {
+ (*m_lu)[i][j] = (*m_mat)[i][j];
+ }
+ }
+
+ // LU decompose the matrix, and store result back in matrix
+ for ( uint k=0; k<n-1; k++ )
+ {
+ double * const lu_K_K = &(*m_lu)[k][k];
+ if ( std::abs(*lu_K_K) < 1e-10 )
+ {
+ if ( *lu_K_K < 0. ) *lu_K_K = -1e-10;
+ else *lu_K_K = 1e-10;
+ }
+ for ( uint i=std::max(k,max_k)+1; i<n; i++ )
+ {
+ (*m_lu)[i][k] /= *lu_K_K;
+ }
+ for ( uint i=std::max(k,max_k)+1; i<n; i++ )
+ {
+ const double lu_I_K = (*m_lu)[i][k];
+ if ( std::abs(lu_I_K) > 1e-12 )
+ {
+ for ( uint j=std::max(k,max_k)+1; j<n; j++ )
+ {
+ (*m_lu)[i][j] -= lu_I_K*(*m_lu)[k][j];
+ }
+ }
+ }
+ }
+
+ max_k = n;
+}
+
+void Matrix::fbSub( Vector* b )
+{
+ if ( m_size == 0 ) return;
+
+ for ( uint i=0; i<m_size; i++ )
+ {
+ m_y[m_inMap[i]] = (*b)[i];
+ }
+
+ // Forward substitution
+ for ( uint i=1; i<m_size; i++ )
+ {
+ double sum = 0;
+ for ( uint j=0; j<i; j++ )
+ {
+ sum += (*m_lu)[i][j]*m_y[j];
+ }
+ m_y[i] -= sum;
+ }
+
+ // Back substitution
+ m_y[m_size-1] /= (*m_lu)[m_size-1][m_size-1];
+ for ( int i=m_size-2; i>=0; i-- )
+ {
+ double sum = 0;
+ for ( uint j=i+1; j<m_size; j++ )
+ {
+ sum += (*m_lu)[i][j]*m_y[j];
+ }
+ m_y[i] -= sum;
+ m_y[i] /= (*m_lu)[i][i];
+ }
+
+ for ( uint i=0; i<m_size; i++ )
+ (*b)[i] = m_y[i];
+}
+
+
+void Matrix::multiply( Vector *rhs, Vector *result )
+{
+ if ( !rhs || !result ) return;
+ result->reset();
+ for ( uint _i=0; _i<m_size; _i++ )
+ {
+ uint i = m_inMap[_i];
+ for ( uint j=0; j<m_size; j++ )
+ {
+ (*result)[_i] += (*m_mat)[i][j] * (*rhs)[j];
+ }
+ }
+}
+
+
+void Matrix::displayMatrix()
+{
+ uint n = m_size;
+ for ( uint _i=0; _i<n; _i++ )
+ {
+ uint i = m_inMap[_i];
+ for ( uint j=0; j<n; j++ )
+ {
+ if ( j > 0 && (*m_mat)[i][j] >= 0 ) kdDebug() << "+";
+ kdDebug() << (*m_mat)[i][j] << "("<<j<<")";
+ }
+ kdDebug() << endl;
+ }
+}
+
+void Matrix::displayLU()
+{
+ uint n = m_size;
+ for ( uint _i=0; _i<n; _i++ )
+ {
+ uint i = m_inMap[_i];
+// uint i = _i;
+ for ( uint j=0; j<n; j++ )
+ {
+ if ( j > 0 && (*m_lu)[i][j] >= 0 ) std::cout << "+";
+ std::cout << (*m_lu)[i][j] << "("<<j<<")";
+ }
+ std::cout << std::endl;
+ }
+ std::cout << "m_inMap: ";
+ for ( uint i=0; i<n; i++ )
+ {
+ std::cout << i<<"->"<<m_inMap[i]<<" ";
+ }
+ std::cout << std::endl;
+ /*cout << "m_outMap: ";
+ for ( uint i=0; i<n; i++ )
+ {
+ cout << i<<"->"<<m_outMap[i]<<" ";
+ }
+ cout << endl;*/
+}
+
+
+Map::Map( const uint size )
+{
+ m_size = size;
+ m_map = new ETMap( m_size );
+ reset();
+}
+
+
+Map::~Map()
+{
+ delete m_map;
+}
+
+
+void Map::reset()
+{
+ for ( uint i=0; i<m_size; i++ )
+ {
+ for ( uint j=0; j<m_size; j++ )
+ {
+ (*m_map)[i][j] = 0;
+ }
+ }
+}
+
+
+void Map::setUse( const uint i, const uint j, Map::e_type type, bool big )
+{
+ if ( type == Map::et_none ) {
+ (*m_map)[i][j] = Map::et_none;
+ } else {
+ (*m_map)[i][j] = type | (big)?Map::et_big:0;
+ }
+}
+
+
+void Map::createMap( int *map )
+{
+ assert(map);
+
+ // In this function, the passes through that we make want to be done from
+ // top left to bottom right, to minimise fill-in
+
+ // available[i] is true if an external-row can be mapped to internal-row "i"
+ // map[i] gives the internal-row for external-row i
+ bool available[m_size];
+ for ( uint i=0; i<m_size; i++ )
+ {
+ available[i] = true;
+ map[i] = -1;
+ }
+
+ // This loop looks through columns and rows to find any swaps that are necessary
+ // (e.g. only one matrix-element in that row/column), and if no necessary swaps
+ // were found, then it will swap two rows according to criteria given below
+ bool badMap = false;
+ bool changed;
+ do
+ {
+ changed = false;
+
+ // Pass through columns
+ int E,N;
+ uint highest = 0;
+ for ( uint j=0; j<m_size; j++ )
+ {
+ if ( map[j] == -1 ) // If we haven't mapped this column yet
+ {
+ int count = 0; // Number of "spare" elements
+ int element; // Last element that is "spare", only applicable if count=1
+ for ( uint i=0; i<m_size; i++ )
+ {
+ if ( available[i] && (*m_map)[i][j] )
+ {
+ count++;
+ element = i;
+ }
+ }
+ if ( count == 0 ) {
+ badMap = true;
+ }
+ else if ( count == 1 )
+ {
+ const uint newType = (*m_map)[element][j];
+ if ( typeCmp( newType, highest) )
+ {
+ E=element;
+ N=j;
+ highest=newType;
+ }
+ }
+ }
+ }
+ // Pass through rows
+ for ( uint i=0; i<m_size; i++ )
+ {
+ if ( map[i] == -1 ) // If we haven't mapped this row yet
+ {
+ int count = 0; // Number of "spare" elements
+ int element; // Last element that is "spare", only applicable if count=1
+ for ( uint j=0; j<m_size; j++ )
+ {
+ if ( available[j] && (*m_map)[i][j] )
+ {
+ count++;
+ element = j;
+ }
+ }
+ if ( count == 0 ) {
+ badMap = true;
+ }
+ else if ( count == 1 )
+ {
+ const uint newType = (*m_map)[i][element];
+ if ( typeCmp( newType, highest) )
+ {
+ E=element;
+ N=i;
+ highest=newType;
+ }
+ }
+ }
+ }
+ if (highest)
+ {
+ available[E] = false;
+ map[N] = E;
+ changed = true;
+ }
+ if (!changed)
+ {
+ int next = -1; // next is the row to mapped to (interally)
+ uint j=0;
+
+ /// TODO We want to change this search to one that finds a swap, taking into acocunt the priorities given below
+ while ( next == -1 && j<m_size )
+ {
+ if ( available[j] ) next=j;
+ j++;
+ }
+ uint i=0;
+ while ( i<m_size && map[i] != -1 ) i++;
+ if ( next != -1 && i < m_size )
+ {
+ available[next] = false;
+ map[i] = next;
+ changed = true;
+ }
+ }
+ } while (changed);
+
+ if (badMap)
+ {
+// cerr << "Map::createMap: unable to create decent mapping; do not trust the matrix, Neo!"<<endl;
+ }
+
+ for ( int i = 0; i < int(m_size); ++i )
+ {
+ assert( map[i] >= 0 && map[i] < int(m_size) );
+ }
+
+ // Ignore this, for now:
+
+ // Now, we want to order the matrix, with the following priorities:
+ // (1) How often values change
+ // (2) How few values there are
+ // (3) How large the values are
+ // For each value in the column,
+}
+
+
+bool Map::typeCmp( const uint t1, const uint t2 )
+{
+ if (!t2) return true;
+ if (!t1) return false;
+
+ int t1_score = 1;
+ if ( t1 | Map::et_constant ) t1_score += 64;
+ else if ( t1 | Map::et_stable ) t1_score += 16;
+ else if ( t1 | Map::et_variable ) t1_score += 4;
+
+ int t2_score = 1;
+ if ( t2 | Map::et_constant ) t2_score += 64;
+ else if ( t2 | Map::et_stable ) t2_score += 16;
+ else if ( t2 | Map::et_variable ) t2_score += 4;
+
+ if ( t1 | Map::et_big ) t1_score *= 2;
+ if ( t2 | Map::et_big ) t2_score *= 2;
+
+ return ( t1_score >= t2_score );
+}
+
+
+Matrix22::Matrix22()
+{
+ reset();
+}
+
+bool Matrix22::solve()
+{
+ const double old_x1 = m_x1;
+ const double old_x2 = m_x2;
+
+ const bool e11 = std::abs((m_a11))<epsilon;
+ const bool e12 = std::abs((m_a12))<epsilon;
+ const bool e21 = std::abs((m_a21))<epsilon;
+ const bool e22 = std::abs((m_a22))<epsilon;
+
+ if (e11)
+ {
+ if ( e12||e21 )
+ return false;
+ m_x2 = m_b1/m_a12;
+ m_x1 = (m_b2-(m_a22*m_x2))/m_a21;
+ }
+ else if (e12)
+ {
+ if ( e11||e22 )
+ return false;
+ m_x1 = m_b1/m_a11;
+ m_x2 = (m_b2-(m_a21*m_x1))/m_a22;
+ }
+ else if (e21)
+ {
+ if ( e11||e22 )
+ return false;
+ m_x2 = m_b2/m_a22;
+ m_x1 = (m_b1-(m_a12*m_x2))/m_a11;
+ }
+ else if (e22)
+ {
+ if ( e12||e21 )
+ return false;
+ m_x1 = m_b2/m_a21;
+ m_x2 = (m_b1-(m_a11*m_x1))/m_a12;
+ }
+ else
+ {
+ m_x2 = (m_b2-(m_a21*m_b1/m_a11))/(m_a22-(m_a21*m_a12/m_a11));
+ m_x1 = (m_b1-(m_a12*m_x2))/m_a11;
+ }
+ if ( !std::isfinite(m_x1) || !std::isfinite(m_x2) )
+ {
+ m_x1 = old_x1;
+ m_x2 = old_x2;
+ return false;
+ }
+ return true;
+}
+
+void Matrix22::reset()
+{
+ m_a11=m_a12=m_a21=m_a22=0.;
+ m_b1=m_b2=0.;
+ m_x1=m_x2=0.;
+}
+
+
+
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