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#ifndef _global_h
# include "global.h"
#endif
#include <stdarg.h>
#ifndef _matrix_h
# include "matrix.h"
#endif
Matrix MatrixZero;
Matrix::Matrix( int n, int m, ... )
{
va_list argptr;
va_start(argptr,m);
dim = n;
if (dim) {
data = new Vector [n];
for (int i=0;i<n;i++) {
data[i].Resize(m);
for (int j=0;j<m;j++) {
data[i][j] = Real( va_arg(argptr,double) );
}
}
}
va_end(argptr);
}
Matrix::Matrix( const Matrix &m ) {
dim = m.dim;
data = new Vector[dim];
for (int i=0;i<dim;i++) data[i] = m.data[i];
}
void Matrix::show(const char *str) const {
putchar( '[' );
for (int i=0;i<dim;i++) {
if (i) printf( ", " );
data[i].show();
}
putchar(']');
if (str) printf(str);
}
int Matrix::Cols() const {
int max=0;
for (int i=0;i<dim;i++) if (data[i].dim>max) max=data[i].dim;
return max;
}
int Matrix::IsZero() const {
for (int i=0;i<dim;i++) {
if (data[i]!=VectorZero) return 0;
}
return -1;
}
void Matrix::Resize(int n) {
if (n>dim) {
Vector *new_data;
new_data = new Vector[n]; // allocate new array
for (int i=0;i<dim;i++) new_data[i] = data[i]; // copy old data
// for ( ;i<n;i++) new_data[i] = VectorZero; // reset new data
delete [] data; // free old array
data = new_data;
dim = n;
}
}
void Matrix::Resize(int n,int m) {
Resize(n);
for (int i=0;i<dim;i++) data[i].Resize(m);
}
Vector &Matrix::GetRef(int n) {
static Vector error=VectorZero;
if (n<0) {
fprintf(stderr,"illegal index: Matrix::GetRef(%d)\n",n);
return error; // return at least something to play with ...
}
if (n>=dim) Resize(n+1);
return data[n];
}
const Matrix &Matrix::operator=(const Matrix &m) {
if (dim<m.dim) {
if (dim) delete [] data;
data = new Vector[m.dim];
}
dim = m.dim;
for (int i=0;i<dim;i++) data[i] = m.data[i];
return *this;
}
int operator==(const Matrix& z1, const Matrix& z2)
{
if (z1.dim<z2.dim) {
for (int i=0;i<z1.dim;i++)
if (z1.data[i]!=z2.data[i]) return 0;
for ( ;i<z2.dim;i++)
if (z2.data[i]!=VectorZero) return 0;
return -1;
}
else {
for (int i=0;i<z2.dim;i++)
if (z1.data[i]!=z2.data[i]) return 0;
for ( ;i<z1.dim;i++)
if (z1.data[i]!=VectorZero) return 0;
return -1;
}
}
const Matrix& Matrix::operator+=(const Matrix& z2)
{
if (z2.dim>dim) Resize(z2.dim);
for (int i=0;i<dim;i++) data[i]+=z2.data[i];
return *this;
}
const Matrix& Matrix::operator-=(const Matrix& z2)
{
if (z2.dim>dim) Resize(z2.dim);
for (int i=0;i<dim;i++) data[i]-=z2.data[i];
return *this;
}
const Matrix& Matrix::operator*=(const Real& r)
{
for (int i=0;i<dim;i++) data[i]*=r;
return *this;
}
const Matrix& Matrix::operator/=(const Real& r)
{
for (int i=0;i<dim;i++) data[i]/=r;
return *this;
}
Vector operator*(const Vector& v, const Matrix& m) {
Vector erg;
erg.Resize(m.Cols());
for (int i=0;i<erg.dim;i++) {
Real sum = RealZero;
for (int j=0;j<v.dim;j++) sum += v(j)*m(j)(i);
erg[i] = sum;
}
return erg;
}
Vector operator*(const Matrix& m, const Vector& v) {
Vector erg;
erg.Resize(m.dim);
for (int i=0;i<m.dim;i++) erg[i] = m(i)*v;
return erg;
}
const Matrix &Matrix::operator<<=(Matrix &m2) {
if (dim) delete [] data;
dim = m2.dim;
data = m2.data;
m2.dim = 0;
return *this;
}
const Matrix &Matrix::operator*=(const Matrix &m2) {
Matrix help;
help <<= *this;
int cols = m2.Cols();
Resize(help.dim,cols);
for (int i=0;i<dim;i++) {
for (int j=0;j<cols;j++) {
Real sum = RealZero;
for (int k=0;k<m2.dim;k++) sum += help(i)(k)*m2(k)(j);
(*this)[i][j] = sum;
}
}
return *this;
}
Matrix operator*(const Matrix& m1, const Matrix& m2) {
Matrix erg;
int cols = m2.Cols();
erg.Resize(m1.dim,cols);
for (int i=0;i<erg.dim;i++) {
for (int j=0;j<cols;j++) {
Real sum = RealZero;
for (int k=0;k<m2.dim;k++) sum += m1(i)(k)*m2(k)(j);
erg[i][j] = sum;
}
}
return erg;
}
Vector operator/(const Vector &b, const Matrix &a) {
Matrix a_tmp = a;
Vector b_tmp = b;
Vector x;
if (system_calc(a_tmp,&x,b_tmp)) return VectorZero;
else return x;
}
int system_calc(Matrix &a, Vector *x, Vector &b) {
int n; // Dimension
int *v; // Vertauschungsvektor
int i,j,k,help;
// berprfung der Vektorgren
n = b.dim;
if (n!=a.Rows()||n!=a.Cols()) {
fprintf(stderr,"Ax=b: Fehler in Dimension A[%d][%d], b[%d]\n", a.Rows(), a.Cols(), n );
return -1;
}
// Initialisierung des Vertauschungsvektors
v = new int[n];
for (i=0;i<n;i++) v[i]=i;
for (j=0;j<n-1;j++) {
Real pvt = RealZero;
int j2 = j;
// skalierte Pivotsuche
for (i=j;i<n;i++) {
Real a2;
Real d = RealZero;
// Zeilenmaximum fr Skalierung bestimmen
for (k=j;k<n;k++) {
if (Real(fabs(a(v[i])(k)))>d) d=fabs(a(v[i])(k));
}
if (d<EPS) {
fprintf(stderr,"Ax=b: Matrix singulr\n");
delete v;
return -2;
}
// skaliertes Pivotelement berechnen und mit bisher grtem vergleichen
a2 = a(v[i])(j)/d;
if (Real(fabs(a2))>pvt) {
pvt = fabs(a2);
j2 = i; // Pivotzeile merken
}
}
// Pivotisierung und fiktiever Zeilentausch
help = v[j];
v[j] = v[j2];
v[j2] = help;
if (fabs(a(v[j])(j))<EPS) {
fprintf(stderr,"Ax=b: Matrix singulr\n" );
delete v;
return -3;
}
// v[j] ist Pivotzeile
for (i=j+1;i<n;i++) {
Real q = a(v[i])(j)/a(v[j])(j);
for (k=j+1;k<n;k++) {
a[v[i]][k] -= q*a(v[j])(k);
}
b[v[i]] -= q*b(v[j]);
}
}
x->Resize(n);
for (i=n-1;i>=0;i--) {
(*x)[v[i]] = b(v[i]);
for (k=i+1;k<n;k++) {
(*x)[v[i]] -= a(v[i])(k) * (*x)(v[k]);
}
(*x)[v[i]] /= a(v[i])(i);
}
delete v;
return 0;
}
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