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// GLKSparseMatrixDirectSolver.cpp: implementation of the GLKSparseMatrixDirectSolver class.
//
//////////////////////////////////////////////////////////////////////
#include <stdio.h>
#include <math.h>
#include "GLKMatrixLib.h"
#include "GLKSparseMatrix.h"
#include "GLKSparseMatrixDirectSolver.h"
//////////////////////////////////////////////////////////////////////
// Construction/Destruction
//////////////////////////////////////////////////////////////////////
GLKSparseMatrixDirectSolver::GLKSparseMatrixDirectSolver()
{
}
GLKSparseMatrixDirectSolver::~GLKSparseMatrixDirectSolver()
{
}
//////////////////////////////////////////////////////////////////////
// Implementation
//////////////////////////////////////////////////////////////////////
bool GLKSparseMatrixDirectSolver::BandGaussianElimination(GLKSparseMatrix *sparseMatrix, double *B)
{
unsigned long nRowNum,nColNum,i;
unsigned long rowIndex,colIndex;
GLKSparseMatrixNode** rowRoots;
unsigned long *permutation;
//---------------------------------------------------------------------------------------------
// Step 1: preparation
nRowNum=sparseMatrix->GetRowNumber(); nColNum=sparseMatrix->GetColNumber();
permutation=sparseMatrix->GetPermutationPointer();
rowRoots=sparseMatrix->GetRowRoots();
//---------------------------------------------------------------------------------------------
// Step 2: compute the max semi-bandwidth
unsigned long semiBandWidth=0,maxRow;
for(i=0;i<nRowNum;i++) {
unsigned long minIndex=nRowNum,maxIndex=0;
unsigned long rowIndex=permutation[i];
GLKSparseMatrixNode* currentNode=rowRoots[i];
for(;currentNode!=NULL;) {
GLKSparseMatrixNode* nextNode=currentNode->pNext;
if (permutation[currentNode->nColIndex]<minIndex)
minIndex=permutation[currentNode->nColIndex];
if (permutation[currentNode->nColIndex]>maxIndex)
maxIndex=permutation[currentNode->nColIndex];
currentNode=nextNode;
}
if ((maxIndex>rowIndex) && ((maxIndex-rowIndex)>semiBandWidth))
{semiBandWidth=maxIndex-rowIndex;maxRow=rowIndex;}
if ((minIndex<rowIndex) && ((rowIndex-minIndex)>semiBandWidth))
{semiBandWidth=rowIndex-minIndex;maxRow=rowIndex;}
// printf ("max=%ld min=%ld row=%ld band=%ld\n",maxIndex,minIndex,rowIndex,(maxIndex-minIndex));
}
// printf("Semi-Bandwidth=%ld maxRow=%ld rowNum=%ld\n",semiBandWidth,maxRow,nRowNum);
//---------------------------------------------------------------------------------------------
// Step 3: create the band matrix
double *AA; double *b;
AA=new double[nRowNum*(semiBandWidth*2+1)];
b=new double[nRowNum];
for(i=0;i<nRowNum*(semiBandWidth*2+1);i++) AA[i]=0.0;
for(i=0;i<nRowNum;i++) {
GLKSparseMatrixNode* currentNode=rowRoots[i];
rowIndex=permutation[i];
for(;currentNode!=NULL;) {
GLKSparseMatrixNode* nextNode=currentNode->pNext;
colIndex=permutation[currentNode->nColIndex];
if (rowIndex>semiBandWidth)
AA[rowIndex*(semiBandWidth*2+1)+colIndex-rowIndex+semiBandWidth]=currentNode->data;
else
AA[rowIndex*(semiBandWidth*2+1)+colIndex]=currentNode->data;
currentNode=nextNode;
}
b[rowIndex]=B[i];
}
//---------------------------------------------------------------------------------------------
// Step 4: Gaussian Elimination
int rc=aband(AA,b,nRowNum,semiBandWidth,semiBandWidth*2+1,1);
//---------------------------------------------------------------------------------------------
// Step 6: Re-order the solution
if (rc>0) {for(i=0;i<nRowNum;i++) B[i]=b[permutation[i]];}
//---------------------------------------------------------------------------------------------
// Step 5: free the memory
delete []AA; delete []b;
if (rc>0) return true;
return false;
}
bool GLKSparseMatrixDirectSolver::BandGaussianElimination(GLKSparseMatrix *sparseMatrix, int colNum, double **B)
{
unsigned long nRowNum,nColNum,i;
unsigned long rowIndex,colIndex;
GLKSparseMatrixNode** rowRoots;
unsigned long *permutation;
//---------------------------------------------------------------------------------------------
// Step 1: preparation
nRowNum=sparseMatrix->GetRowNumber(); nColNum=sparseMatrix->GetColNumber();
permutation=sparseMatrix->GetPermutationPointer();
rowRoots=sparseMatrix->GetRowRoots();
//---------------------------------------------------------------------------------------------
// Step 2: compute the max semi-bandwidth
unsigned long semiBandWidth=0,maxRow;
for(i=0;i<nRowNum;i++) {
unsigned long minIndex=nRowNum,maxIndex=0;
unsigned long rowIndex=permutation[i];
GLKSparseMatrixNode* currentNode=rowRoots[i];
for(;currentNode!=NULL;) {
GLKSparseMatrixNode* nextNode=currentNode->pNext;
if (permutation[currentNode->nColIndex]<minIndex)
minIndex=permutation[currentNode->nColIndex];
if (permutation[currentNode->nColIndex]>maxIndex)
maxIndex=permutation[currentNode->nColIndex];
currentNode=nextNode;
}
if ((maxIndex>rowIndex) && ((maxIndex-rowIndex)>semiBandWidth))
{semiBandWidth=maxIndex-rowIndex;maxRow=rowIndex;}
if ((minIndex<rowIndex) && ((rowIndex-minIndex)>semiBandWidth))
{semiBandWidth=rowIndex-minIndex;maxRow=rowIndex;}
}
//---------------------------------------------------------------------------------------------
// Step 3: create the band matrix
double *AA; double *b;
AA=new double[nRowNum*(semiBandWidth*2+1)];
b=new double[nRowNum*colNum];
for(i=0;i<nRowNum*(semiBandWidth*2+1);i++) AA[i]=0.0;
for(i=0;i<nRowNum;i++) {
GLKSparseMatrixNode* currentNode=rowRoots[i];
rowIndex=permutation[i];
for(;currentNode!=NULL;) {
GLKSparseMatrixNode* nextNode=currentNode->pNext;
colIndex=permutation[currentNode->nColIndex];
if (rowIndex>semiBandWidth)
AA[rowIndex*(semiBandWidth*2+1)+colIndex-rowIndex+semiBandWidth]=currentNode->data;
else
AA[rowIndex*(semiBandWidth*2+1)+colIndex]=currentNode->data;
currentNode=nextNode;
}
for(int j=0;j<colNum;j++) b[rowIndex*colNum+j]=B[i][j];
}
//---------------------------------------------------------------------------------------------
// Step 4: Gaussian Elimination
int rc=aband(AA,b,nRowNum,semiBandWidth,semiBandWidth*2+1,colNum);
//---------------------------------------------------------------------------------------------
// Step 6: Re-order the solution
if (rc>0) {
for(i=0;i<nRowNum;i++) {
for(int j=0;j<colNum;j++) B[i][j]=b[permutation[i]*colNum+j];
}
}
//---------------------------------------------------------------------------------------------
// Step 5: free the memory
delete []AA; delete []b;
if (rc>0) return true;
return false;
}
int GLKSparseMatrixDirectSolver::aband(double* b, double* d, long n, long l, long il, long m)
{
long ls,k,i,j,is,u,v;
double p,t;
if (il!=(2*l+1))
{ printf("fail\n"); return(-2);}
ls=l;
for (k=0;k<=n-2;k++)
{ p=0.0;
for (i=k;i<=ls;i++)
{ t=fabs(b[i*il]);
if (t>p) {p=t; is=i;}
}
if (p+1.0==1.0)
{ printf("fail 1 %ld %lf\n",k,p); return(0);}
for (j=0;j<=m-1;j++)
{ u=k*m+j; v=is*m+j;
t=d[u]; d[u]=d[v]; d[v]=t;
}
for (j=0;j<=il-1;j++)
{ u=k*il+j; v=is*il+j;
t=b[u]; b[u]=b[v]; b[v]=t;
}
for (j=0;j<=m-1;j++)
{ u=k*m+j; d[u]=d[u]/b[k*il];}
for (j=1;j<=il-1;j++)
{ u=k*il+j; b[u]=b[u]/b[k*il];}
for (i=k+1;i<=ls;i++)
{ t=b[i*il];
for (j=0;j<=m-1;j++)
{ u=i*m+j; v=k*m+j;
d[u]=d[u]-t*d[v];
}
for (j=1;j<=il-1;j++)
{ u=i*il+j; v=k*il+j;
b[u-1]=b[u]-t*b[v];
}
u=i*il+il-1; b[u]=0.0;
}
if (ls!=(n-1)) ls=ls+1;
}
p=b[(n-1)*il];
if (fabs(p)+1.0==1.0)
{ printf("fail 2\n"); return(0);}
for (j=0;j<=m-1;j++)
{ u=(n-1)*m+j; d[u]=d[u]/p;}
ls=1;
for (i=n-2;i>=0;i--)
{ for (k=0;k<=m-1;k++)
{
u=i*m+k;
for (j=1;j<=ls;j++)
{ v=i*il+j; is=(i+j)*m+k;
d[u]=d[u]-b[v]*d[is];
}
}
if (ls!=(il-1)) ls=ls+1;
}
return(2);
}