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matrix.cpp
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matrix.cpp
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void mdivide(float **a,int val,int m1,int n1){
if (val!=0) for(int i=0;i<m1;i++) for(int j=0;j<n1;j++) a[i][j]=a[i][j]/val;
}
void zero_m(float **a,int m1,int n1){
for(int i=0;i<m1;i++) for(int j=0;j<n1;j++) a[i][j]=0;
}
void madd(float **a,float **b,float **c,int m1,int n1){
for(int i=0;i<m1;i++){
for(int j=0;j<n1;j++){
c[i][j]=a[i][j]+b[i][j];
}
}
}
void msub(float **a,float **b,int m1,int n1){
for(int i=0;i<m1;i++){
for(int j=0;j<n1;j++){
a[i][j]=a[i][j]-b[i][j];
}
}
}
void mmultiply(float **a,float **b,float **c, int m1,int n1,int o, int p){
//m1 number of rows of A
//n1 number of coloumns of A
//o number of rows of B
//p number of coloumns of B
//float **c = new float *[m1];
//for (int i = 0; i<m1; i++) c[i] = new float [p];
if (n1==o){
for(int i=0;i<m1;i++){
for(int j=0;j<p;j++){
c[i][j]=0;
for( int k=0;k<n1;k++){
c[i][j]=c[i][j]+a[i][k]*b[k][j];
}
}
}
}
//else printf("Multiplication is not possible");
//return c;
}
void transp(float **m,float **transpose,int rows,int cols){
//òðàíñïîíèðóåì Ì è çàïèñûâàåì â transpose
// Allocate memory for transpose, and check if
// the memory was allocated with success.
//float **transpose = new float*[cols];
//for (int i = 0; i < cols; i++) transpose[i] = new float[rows];
// Build the transpose:
for (int i = 0; i < rows; i++)
for (int j = 0; j < cols; j++)
transpose[j][i] = m[i][j];
// Free memory
/*for (int i = 0; i < cols; i++)
{
delete transpose[i];
transpose[i] = NULL;
}
delete[] transpose;//*/
}
void LU(float** A,float** A1,float** L, float** U,int m1){
//ââîäåìî òèì÷àñîâèé ìàññèâ À1, ùîá íå çì³íþâàòè À;
int i,j,r;
int size=m1;
for (i=0; i<size; i++) for (j=0; j<m1; j++) A1[i][j]=A[i][j];
//Îáíóëþºìî Ó òà Ë
for (i=0; i<size; i++) for (j=0; j<m1; j++) U[i][j]=0;
for (i=0; i<size; i++) for (j=0; j<m1; j++) L[i][j]=0;
float d,e;
for (r=0;r<m1;r++){
d=1/A1[r][r];
for (i=(r+1);i<m1;i++){
e=d*A1[i][r];
A1[i][r]=e;
for (j=(r+1);j<m1;j++){
A1[i][j]=A1[i][j]-e*A1[r][j];
}
}
}
for (i=0; i<size; i++) for(j=i;j<m1;j++) U[i][j]=A1[i][j];
for (i=0; i<size; i++) for(j=0;j<i;j++) L[i][j]=A1[i][j];
for (i=0; i<size; i++) L[i][i]=1;
}
void invrsUp(float** U,int n1,float** U_1) {
float s;
for(int i=0;i<n1;i++){
for(int j=0;j<n1;j++){
U_1[i][j]=0;
}
}
for (int j=n1-1;j>=0;j--){
for (int i=j;i>=0;i--){
if (i==j) U_1[i][i]=1/U[i][i];
else{
s=0;
for (int k=j;k>i;k--) s+=U[i][k]*U_1[k][j];
U_1[i][j]=-s/U[i][i];
}
}
}
}
void invrsLw(float** L,int n1,float** L_1) {
float s;
for(int i=0;i<n1;i++){
for(int j=0;j<n1;j++){
L_1[i][j]=0;
}
}
for (int j=0;j<n1;j++){
for (int i=j;i<n1;i++){
if (i==j) L_1[i][i]=1/L[i][i];
else{
s=0;
s=0;
for (int k=j;k<i;k++) s+=L[i][k]*L_1[k][j];
L_1[i][j]=-s/L[i][i];
}
}
}
}
void minv(float ** in,float ** out,int m1){
/*inv(A) = inv((U)*inv(L)*I*/
float **eye= new float*[m1];
for(int i=0;i<m1;i++) eye[i] = new float[m1];
for(int i=0;i<m1;i++){
for(int j=0;j<m1;j++){
if (i!=j)eye[i][j]=0;
else eye[i][j]=1;
}
}
float **temp= new float*[m1];
for(int i=0;i<m1;i++) temp[i] = new float[m1];
float **L= new float*[m1];
for(int i=0;i<m1;i++) L[i] = new float[m1];
float **U= new float*[m1];
for(int i=0;i<m1;i++) U[i] = new float[m1];
float **inv_U= new float*[m1];
for(int i=0;i<m1;i++) inv_U[i] = new float[m1];
float **inv_L= new float*[m1];
for(int i=0;i<m1;i++) inv_L[i] = new float[m1];
float **inv_res= new float*[m1];
for(int i=0;i<m1;i++) inv_res[i] = new float[m1];
LU(in,temp,L, U,m1);
invrsUp(U,m1,inv_U);
invrsLw(L,m1,inv_L);
mmultiply(inv_U,inv_L,inv_res,m1,m1,m1,m1);
mmultiply(inv_res,eye,out,m1,m1,m1,m1);
for (int i = 0; i <m1; i++){
delete[] eye[i];
delete[] temp[i];
delete[] L[i];
delete[] U[i];
delete[] inv_U[i];
delete[] inv_L[i];
delete[] inv_res[i];
}
delete[] eye;
delete[] temp;
delete[] L;
delete[] U;
delete[] inv_U;
delete[] inv_L;
delete[] inv_res;
}
long double trace(float **a,int m1){
long double sum=0;
for(int i=0;i<m1;i++) sum+=a[i][i];
return sum;
}
long double trace_sum(float **a,int m1,int n1){
long double sum=0;
for(int i=0;i<m1;i++) for(int j=0;j<n1;j++) sum+=a[i][j]*a[i][j];
return sum;
}
long double trace_lin(float** a,float ** b,int m1,int n1){
long double c=0;
float **temp_mult= new float*[m1];
for(int i=0;i<m1;i++) temp_mult[i] = new float[m1];
float **temp_transp= new float*[n1];
for(int i=0;i<n1;i++) temp_transp[i] = new float[m1];
transp(b,temp_transp,m1,n1);
mmultiply(a,temp_transp,temp_mult,m1,n1,n1,m1);
c=trace(temp_mult,m1);
for(int i=0;i<n1;i++) delete temp_transp[i];
delete[] temp_transp;
for(int i=0;i<m1;i++) delete temp_mult[i];
delete[] temp_mult;
return c;
}