238 lines
6.3 KiB
C
238 lines
6.3 KiB
C
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// Created by 顾涵彬 on 2019-08-30.
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//
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#ifndef MATRIX_MATRIXSOLVER_H
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#define MATRIX_MATRIXSOLVER_H
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#include <cmath>
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#include <complex>
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static bool Matrix_EigenValue(double *K1,int n,int LoopNumber,double Error1,double *Ret);
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namespace Ctain {
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class EigenSolver {
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public:
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EigenSolver(SMatrix<double> s) {
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_matrix = s;
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Matrix<double> tt(_matrix.rows(),2);
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Matrix_EigenValue(_matrix.addr(),_matrix.rows(),1000,1e-10,tt.addr());
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t=tt;
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}
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Matrix<double> eigenvalues() {
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return t;
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}
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private:
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SMatrix<double> _matrix;
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Matrix<double> t;
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};
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} //namespace Ctain end
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static void Matrix_Hessenberg(double *A1,int n,double *ret)
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{
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int i,j,k,MaxNumber;
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double temp,*A;
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A=new double[n*n];
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for (i=0;i<n;i++) {
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k=i*n;
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for (j=0;j<n;j++)
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{
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A[k+j]=A1[k+j];
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}
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}
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for (k=1;k<n-1;k++) {
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i=k-1;
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MaxNumber=k;
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temp=abs(A[k*n+i]);
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for (j=k+1;j<n;j++) {
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if (abs(A[j*n+i])>temp) {
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temp=abs(A[j*n+i]);
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MaxNumber=j;
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}
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}
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ret[0]=A[MaxNumber*n+i];
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i=MaxNumber;
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if (ret[0]!=0) {
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if (i!=k) {
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for(j=k-1;j<n;j++) {
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temp=A[i*n+j];
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A[i*n+j]=A[k*n+j];
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A[k*n+j]=temp;
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}
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for(j=0;j<n;j++) {
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temp=A[j*n+i];
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A[j*n+i]=A[j*n+k];
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A[j*n+k]=temp;
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}
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}
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for (i=k+1;i<n;i++) {
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temp=A[i*n+k-1]/ret[0];
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A[i*n+k-1]=0;
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for (j=k;j<n;j++) {
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A[i*n+j]-=temp*A[k*n+j];
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}
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for (j=0;j<n;j++) {
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A[j*n+k]+=temp*A[j*n+i];
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}
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}
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}
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}
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for (i=0;i<n;i++) {
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k=i*n;
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for (j=0;j<n;j++) {
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ret[k+j]=A[k+j];
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}
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}
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delete []A;
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}
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static bool Matrix_EigenValue(double *K1,int n,int LoopNumber,double Error1,double *Ret)
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{
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int i,j,k,t,m,Loop1;
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double b,c,d,g,xy,p,q,r,x,s,e,f,z,y,temp,*A;
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A=new double[n*n];
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Matrix_Hessenberg(K1,n,A);
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m=n;
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Loop1=LoopNumber;
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while(m!=0) {
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t=m-1;
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while(t>0) {
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temp=abs(A[(t-1)*n+t-1]);
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temp+=abs(A[t*n+t]);
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temp=temp*Error1;
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if (abs(A[t*n+t-1])>temp) {
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t--;
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}
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else {
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break;
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}
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}
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if (t==m-1) {
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Ret[(m-1)*2]=A[(m-1)*n+m-1];
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Ret[(m-1)*2+1]=0;
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m-=1;
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Loop1=LoopNumber;
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}
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else if(t==m-2) {
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b=-A[(m-1)*n+m-1]-A[(m-2)*n+m-2];
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c=A[(m-1)*n+m-1]*A[(m-2)*n+m-2]-A[(m-1)*n+m-2]*A[(m-2)*n+m-1];
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d=b*b-4*c;
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y=sqrt(abs(d));
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if (d>0) {
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xy=1;
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if (b<0) {
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xy=-1;
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}
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Ret[(m-1)*2]=-(b+xy*y)/2;
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Ret[(m-1)*2+1]=0;
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Ret[(m-2)*2]=c/Ret[(m-1)*2];
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Ret[(m-2)*2+1]=0;
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}
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else {
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Ret[(m-1)*2]=-b/2;
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Ret[(m-2)*2]=-b/2;
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Ret[(m-1)*2+1]=y/2;
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Ret[(m-2)*2+1]=-y/2;
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}
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m-=2;
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Loop1=LoopNumber;
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}
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else {
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if (Loop1<1) {
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return false;
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}
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Loop1--;
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j=t+2;
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while (j<m) {
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A[j*n+j-2]=0;
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j++;
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}
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j=t+3;
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while (j<m) {
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A[j*n+j-3]=0;
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j++;
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}
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k=t;
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while (k<m-1) {
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if (k!=t) {
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p=A[k*n+k-1];
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q=A[(k+1)*n+k-1];
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if (k!=m-2) {
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r=A[(k+2)*n+k-1];
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}
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else {
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r=0;
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}
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}
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else {
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b=A[(m-1)*n+m-1];
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c=A[(m-2)*n+m-2];
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x=b+c;
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y=b*c-A[(m-2)*n+m-1]*A[(m-1)*n+m-2];
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p=A[t*n+t]*(A[t*n+t]-x)+A[t*n+t+1]*A[(t+1)*n+t]+y;
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q=A[(t+1)*n+t]*(A[t*n+t]+A[(t+1)*n+t+1]-x);
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r=A[(t+1)*n+t]*A[(t+2)*n+t+1];
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}
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if (p!=0 || q!=0 || r!=0) {
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if (p<0) {
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xy=-1;
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}
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else {
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xy=1;
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}
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s=xy*sqrt(p*p+q*q+r*r);
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if (k!=t) {
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A[k*n+k-1]=-s;
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}
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e=-q/s;
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f=-r/s;
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x=-p/s;
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y=-x-f*r/(p+s);
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g=e*r/(p+s);
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z=-x-e*q/(p+s);
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for (j=k;j<m;j++) {
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b=A[k*n+j];
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c=A[(k+1)*n+j];
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p=x*b+e*c;
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q=e*b+y*c;
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r=f*b+g*c;
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if (k!=m-2) {
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b=A[(k+2)*n+j];
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p+=f*b;
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q+=g*b;
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r+=z*b;
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A[(k+2)*n+j]=r;
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}
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A[(k+1)*n+j]=q;
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A[k*n+j]=p;
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}
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j=k+3;
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if (j>m-2) {
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j=m-1;
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}
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for (i=t;i<j+1;i++) {
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b=A[i*n+k];
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c=A[i*n+k+1];
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p=x*b+e*c;
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q=e*b+y*c;
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r=f*b+g*c;
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if (k!=m-2) {
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b=A[i*n+k+2];
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p+=f*b;
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q+=g*b;
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r+=z*b;
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A[i*n+k+2]=r;
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}
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A[i*n+k+1]=q;
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A[i*n+k]=p;
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}
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}
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k++;
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}
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}
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}
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delete []A;
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return true;
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}
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#endif //MATRIX_MATRIXSOLVER_H
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