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cheboksarovv.cpp
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/
cheboksarovv.cpp
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#include "cheboksarovv.h"
/**
* Ìåòîä Ãàóññà
*/
void cheboksarovv::lab1()
{
double koefc=0;
for(int k=0;k<N;k++)
{
for(int i=k+1;i<N;i++)
{
koefc=A[i][k]/A[k][k];
for(int j=k;j<N;j++)
{
A[i][j]-=A[k][j]*koefc;
}
b[i]-=koefc*b[k];
}
}
double summa=0;
for(int i=N-1;i>=0;i--)
{
for(int j=i+1;j<N;j++){
summa=summa+A[i][j]*x[j];}
x[i]=(b[i]-summa)/A[i][i];
summa=0;
}
}
void cheboksarovv::lab2()
{
double max=A[0][0],m=0,summa=0,koefc=0;
int index=0;
for(int j=0;j<N;j++)
{
for(int i=j;i<N;i++){if (abs(A[i][j])>max) {max=abs(A[i][j]);index=i;}}
for(int g=0;g<N;g++) {m=A[j][g];A[j][g]=A[index][g];A[index][g]=m;m=b[j]; b[j]=b[index];b[index]=m;}
max=0;
}
for(int k=0;k<N;k++)
for(int i=k+1;i<N;i++)
{
koefc=A[i][k];
for(int j=k;j<N;j++) A[i][j]-=A[k][j]*koefc/A[k][k];
b[i]-=koefc*b[k]/A[k][k];
}
for(int i=N-1;i>=0;i--)
{
for(int j=i+1;j<N;j++){
summa=summa+A[i][j]*x[j];}
x[i]=(b[i]-summa)/A[i][i];
summa=0;
}
}
void cheboksarovv::lab3()
{
double** L = new double*[N];
for (int i=0; i<N; i++)
L[i] = new double[N];
double* y = new double[N];
for (int i=0; i<N; i++)
for (int j=0; j<N; j++)
{L[i][j]=0;}
for(int i=0;i<N;i++)
{
for(int k=0;k<=i-1;k++)
L[i][i]+=L[i][k]*L[i][k];
L[i][i]=sqrt(A[i][i]-L[i][i]);
for(int j=i+1;j<N;j++)
{
for(int k=0;k<=i-1;k++)
L[j][i]+=L[i][k]*L[j][k];
L[j][i]=(A[i][j]-L[j][i])/L[i][i];
}
}
double summa=0;
for(int i=0;i<N;i++)
{
for(int j=0;j<i;j++){
summa+=L[i][j]*y[j];}
y[i]=(b[i]-summa)/L[i][i];
summa=0;
}
for(int i=N-1;i>=0;i--)
{
for(int j=i+1;j<N;j++){
summa+=L[j][i]*x[j];}
x[i]=(y[i]-summa)/L[i][i];
summa=0;
}
delete[] y;
}
void cheboksarovv::lab4()
{
double* a2=new double[N];
double* b2=new double[N];
a2[0]=-A[0][1]/A[0][0];
b2[0]=b[0]/A[0][0];
for(int i=1;i<N;i++)
{
a2[i]=-A[i][i+1]/(A[i][i-1]*a2[i-1]+A[i][i]);
b2[i]=(b[i]-A[i][i-1]*b2[i-1])/(A[i][i-1]*a2[i-1]+A[i][i]);
}
x[N-1] = b2[N-1];
for(int i=N-2; i>=0; i--)
x[i] = a2[i]*x[i+1]+b2[i];
delete[] a2;
delete[] b2;
}
void cheboksarovv::lab5()
{
double* a1=new double[N];
double e=0.00000001;
double n=e;
while (n>=e)
{
for (int i=0;i<N;i++)
{
a1[i]=b[i];
for (int j=0;j<N;j++)
{
if (i!=j) a1[i]-=A[i][j]*x[j];
}
a1[i]/=A[i][i];
}
n=abs(x[0]-a1[0]);
for (int k=0;k<N;k++)
{
if (abs(x[k]-a1[k])>n) n=abs(x[k]-a1[k]);
x[k]=a1[k];
}
}
}
void cheboksarovv::lab6()
{
double* a1=new double[N];
double e=0.000001;
double n=0,v=0;
for(int i=0;i<N;i++) {x[i]=0;}
do
{
for (int i=0;i<N;i++)
a1[i]=x[i];
for (int i=0;i<N;i++)
{
v=0;
for(int j=0;j<i;j++)
v+=(A[i][j]*x[j]);
for(int j=i+1;j<N;j++)
v+=(A[i][j]*a1[j]);
x[i]=(b[i]-v)/A[i][i];
n=0;
for (int k=0;k<N;k++)
{n+=pow((x[k]-a1[k]),2);}
}
} while (sqrt(n)>=e);
delete[] a1;
}
double* cheboksarovv::umc( double *x,double y)
{
double *z = new double [N];
for (int i=0; i<N; i++) z[i]=x[i]*y;
return z;
}
double cheboksarovv::uc(double *x, double *y)
{
double z=0;
for (int i=0;i<N;i++) z+=x[i]*y[i];
return z;
}
double* cheboksarovv::v(double *x, double *y)
{
double *z = new double [N];
for (int i=0; i<N; i++) z[i]=x[i]-y[i];
return z;
}
double* cheboksarovv::um(double **x,double *y)
{
double *z = new double [N];
double q=0;
for (int i=0; i<N; i++)
{for (int j=0; j<N; j++) q+=x[i][j]*y[j];
z[i]=q;
q=0;}
return z;
}
bool cheboksarovv::logik(double *x,double *y,double e)
{
double n=abs(x[0]-y[0]);
for(int j=0;j<N;j++)
{
if (abs(x[j]-y[j])>n) n=abs(x[j]-y[j]);
x[j]=y[j];
}
if (n>=e) return true;
else return false;
}
void cheboksarovv::lab7()
{ double* a1=new double[N];
double* a2=new double[N];
double e=0.00000001;
do{
a2=v(um(A,x),b);
a1=v(a1,umc(a2,uc(um(A,a2),a2)/uc(um(A,a2),um(A,a2))));
}while(logik(x,a1,e));
}
double** cheboksarovv::t(double **x)
{
double **z = new double *[N];
for(int i=0; i<N; i++) {z[i] = new double [N];}
for(int i=0; i<N; i++)
for(int j=0; j<N; j++) { z[i][j]=x[j][i];}
return z;
}
double** cheboksarovv::um1(double **x,double **y)
{
double q=0;
double **z = new double *[N];
for(int i=0; i<N; i++) {z[i] = new double [N];}
for(int i=0; i<N; i++) {
for(int j=0; j<N; j++) {
q=0;
for(int j1=0; j1<N; j1++) { q+=x[i][j1]*y[j1][j];}
z[i][j] = q;
}
}
int y1=0;
return z;
}
void cheboksarovv::lab8()
{
double e=0.01;
double m=0,s=0;
double **u = new double *[N];
for(int i=0; i<N; i++) {u[i] = new double [N];}
double fi=0;
int i1=0,j1=0;
do
{
m=0;
s=0;
for(int i=0;i<N;i++){
for(int j=0;j<N;j++) {if ((abs(A[i][j])>m)&&(i!=j)) {m=abs(A[i][j]);i1=i;j1=j;}}}
fi=0.5*(atan(2*m/(A[i1][i1]-A[j1][j1])));
if (A[i1][i1]==A[j1][j1]) fi=3.14/4;
for(int i=0;i<N;i++)
for(int j=0;j<N;j++)
{u[i][i]=1;if (i!=j) u[i][j]=0;}
u[j1][i1]=sin(fi);u[i1][i1]=cos(fi);u[j1][j1]=cos(fi);u[i1][j1]=-sin(fi);
A=um1(um1(t(u),A),u);
for(int i=0;i<N;i++)
for(int j=1;j<N;j++)
if ((i!=j)&&(j>i)) s+=A[i][j]*A[i][j];
s=sqrt(s);
} while (s>e);
for(int i=0;i<N;i++) x[i]=A[i][i];
}