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chol_inv_4.cpp
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chol_inv_4.cpp
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#include <stdio.h>
#include <math.h>
#define N 100
/*[H_i_re H_i_im]=chol_inv_4(real(H),imag(H));
这是一个基于改进型cholesky原理的矩阵求逆函数,只能分析正定hermite矩阵H;
real(H),imag(H)：分别为输入求逆矩阵的实部和虚部；
H_i_re，H_i_im：分别为输出逆矩阵的实部和虚部；
改进型cholesky原理：matrix=LDL',"'"表示共轭转置,matrix_i=L_i'*D_i*L_i;
作者: lyf
电子科技大学 通信与信息工程学院
School of Communication and Information Engineering,
University of Electronic Science and Technology of China, Chengdu, Sichuan, China
Email: 764778793@qq.com
2013-12-12
*/
typedef struct comp {
double re;
double im;
}COMPLEX;
void cdev(COMPLEX *x,COMPLEX *y,COMPLEX *res);
void cmult(COMPLEX *x,COMPLEX *y,COMPLEX *res){
double a,b;
//printf("\nin cmult\n");
//printf("%lf %lf %lf %lf\n",x->re,x->im,y->re,y->im );
a = x->re * y->re - x->im * y -> im;
b = x->re * y->im + x->im * y -> re;
res->re = a;
res->im = b;
}
void cadd(COMPLEX *x,COMPLEX *y,COMPLEX *res){
res->re = x->re + y->re;
res->im = x->im + y->im;
}
void mult(double x_re,double x_im,double y_re,double y_im,double *p1,double *p2)
{
double a,b;
a=x_re*y_re-x_im*y_im;
b=x_re*y_im+x_im*y_re;
*p1=a;
*p2=b;
}
void cinv22(COMPLEX *a,COMPLEX *b){
double tmp = 1/(a->re*(a+3)->im - (a+1)->im*(a+2)->re);
COMPLEX res1,res2,res3,res4,one;
cmult((a),(a+3),&res1);
cmult((a+1),(a+2),&res2);
res2.re *= -1;
res2.im *= -1;
cadd(&res1,&res2,&res3);
one.re = 1;
one.im = 0;
cdev(&one,&res3,&res4);
cmult(&res4,a+3,b);
cmult(&res4,a+1,b+1);
(b+1)->re *= -1;
(b+1)->im *= -1;
cmult(&res4,a+2,b+2);
(b+2)->re *= -1;
(b+2)->im *= -1;
cmult(&res4,a,b+3);
}
void cdev(COMPLEX *x,COMPLEX *y,COMPLEX *res){
double a,b;
a = x->re * y->re + x->im * y -> im;
a /= (y->re*y->re + y->im*y->im);
b = x->im * y->re - x->re * y->im;
b /= (y->re*y->re + y->im*y->im);
res->re = a;
res->im = b;
}
double soc(double x_re,double x_im)
{
double z;
z=x_re*x_re+x_im*x_im;
return(z);
}
void CMatMult(COMPLEX *p1,COMPLEX *p2,COMPLEX *p3,int m,int n,int p){//all the matrix in the multiplex must be allot the memory space
int i,j,k;
COMPLEX sum;
//printf("in cmatmult\n");
for( i = 0 ; i < m ; i++ ){
for( j = 0 ; j < p ; j++ ){
sum.re = 0;
sum.im = 0;
for( k = 0 ; k < n ; k++ ){
//printf("ijk:%d %d %d",i,j,k);
COMPLEX tmp;
COMPLEX ori = sum;
cmult((p1+i*n+k),(p2+k*p+j),&tmp);
cadd(&ori,&tmp,&sum);
}
*(p3+i*p+j)= sum; //sprintf(str,"\n%d %d %d %d sum : %lf \n",m,n,i,j,sum.re);qDebug() << str;
}
}
}
void Matrix_mult441(double a1_re[][4],double a1_im[][4],double b1_re[][1],double b1_im[][1],double c1_re[][1],double c1_im[][1])
{
int i,j,k;
double sum_re,sum_im;
double temp_re,temp_im;
double *p_re;
double *p_im;
p_re=&temp_re;
p_im=&temp_im;
for(i=0;i<4;i++)
{
for(j=0;j<1;j++)
{
sum_re=0;
sum_im=0;
for(k=0;k<4;k++)
{
mult(a1_re[i][k],a1_im[i][k],b1_re[k][j],b1_im[k][j],p_re,p_im);
sum_re=sum_re+temp_re;
sum_im=sum_im+temp_im;
}
c1_re[i][j]=sum_re;
c1_im[i][j]=sum_im;
}
}
/*
FILE *fp1,*fp2;
fp1 = fopen("data.txt","w");
for( int i = 0 ; i < 4 ; i++){
for( int j = 0 ; j < 4 ; j++ ){
fprintf(fp1,"%lf\t",c1_re[i][j]);
}fprintf(fp1,"\n");
}
fclose(fp1);
*/
}
void Matrix_mult484(double a1_re[][8],double a1_im[][8],double b1_re[][4],double b1_im[][4],double c1_re[][4],double c1_im[][4])
{
int i,j,k;
double sum_re,sum_im;
double temp_re,temp_im;
double *p_re;
double *p_im;
p_re=&temp_re;
p_im=&temp_im;
for(i=0;i<4;i++)
{
for(j=0;j<4;j++)
{
sum_re=0;
sum_im=0;
for(k=0;k<8;k++)
{
mult(a1_re[i][k],a1_im[i][k],b1_re[k][j],b1_im[k][j],p_re,p_im);
sum_re=sum_re+temp_re;
sum_im=sum_im+temp_im;
}
c1_re[i][j]=sum_re;
c1_im[i][j]=sum_im;
}
}
/*
FILE *fp1,*fp2;
fp1 = fopen("data.txt","w");
for( int i = 0 ; i < 4 ; i++){
for( int j = 0 ; j < 4 ; j++ ){
fprintf(fp1,"%lf\t",c1_re[i][j]);
}fprintf(fp1,"\n");
}
fclose(fp1);
*/
}
void Matrix_mult482(double a1_re[][8],double a1_im[][8],double b1_re[][2],double b1_im[][2],double c1_re[][2],double c1_im[][2])
{
int i,j,k;
double sum_re,sum_im;
double temp_re,temp_im;
double *p_re;
double *p_im;
p_re=&temp_re;
p_im=&temp_im;
for(i=0;i<4;i++)
{
for(j=0;j<2;j++)
{
sum_re=0;
sum_im=0;
for(k=0;k<8;k++)
{
mult(a1_re[i][k],a1_im[i][k],b1_re[k][j],b1_im[k][j],p_re,p_im);
sum_re=sum_re+temp_re;
sum_im=sum_im+temp_im;
}
c1_re[i][j]=sum_re;
c1_im[i][j]=sum_im;
}
}
/*
FILE *fp1,*fp2;
fp1 = fopen("data.txt","w");
for( int i = 0 ; i < 4 ; i++){
for( int j = 0 ; j < 4 ; j++ ){
fprintf(fp1,"%lf\t",c1_re[i][j]);
}fprintf(fp1,"\n");
}
fclose(fp1);
*/
}
void Matrix_mult844(double a1_re[][4],double a1_im[][4],double b1_re[][4],double b1_im[][4],double c1_re[][4],double c1_im[][4])
{
int i,j,k;
double sum_re,sum_im;
double temp_re,temp_im;
double *p_re;
double *p_im;
p_re=&temp_re;
p_im=&temp_im;
for(i=0;i<8;i++)
{
for(j=0;j<4;j++)
{
sum_re=0;
sum_im=0;
for(k=0;k<4;k++)
{
mult(a1_re[i][k],a1_im[i][k],b1_re[k][j],b1_im[k][j],p_re,p_im);
sum_re=sum_re+temp_re;
sum_im=sum_im+temp_im;
}
c1_re[i][j]=sum_re;
c1_im[i][j]=sum_im;
}
}
/*
FILE *fp1,*fp2;
fp1 = fopen("data.txt","w");
for( int i = 0 ; i < 4 ; i++){
for( int j = 0 ; j < 4 ; j++ ){
fprintf(fp1,"%lf\t",c1_re[i][j]);
}fprintf(fp1,"\n");
}
fclose(fp1);
*/
}
void Matrix_mult444(double a1_re[][4],double a1_im[][4],double b1_re[][4],double b1_im[][4],double c1_re[][4],double c1_im[][4])
{
int i,j,k;
double sum_re,sum_im;
double temp_re,temp_im;
double *p_re;
double *p_im;
p_re=&temp_re;
p_im=&temp_im;
for(i=0;i<4;i++)
{
for(j=0;j<4;j++)
{
sum_re=0;
sum_im=0;
for(k=0;k<4;k++)
{
mult(a1_re[i][k],a1_im[i][k],b1_re[k][j],b1_im[k][j],p_re,p_im);
sum_re=sum_re+temp_re;
sum_im=sum_im+temp_im;
}
c1_re[i][j]=sum_re;
c1_im[i][j]=sum_im;
}
}
}
void chol_inv(double a1_re[][4],double a1_im[][4],double b1_re[][4],double b1_im[][4])
{
//初始化
double d[4]={0}, L_re[4][4]={0};
double L_im[4][4]={0},d_i[4]={0},L_i_re[4][4]={0},L_i_im[4][4]={0},L_i_re2[4][4]={0},L_i_im2[4][4]={0},D_i_re[4][4]={0},D_i_im[4][4]={0};
double c_re[4][4]={0},c_im[4][4]={0};
double *p_re,*p_im,temp_re,temp_im;
int i,j;
p_re=&temp_re;
p_im=&temp_im;
for(i=0;i<4;i++)
{
L_re[i][i]=1;
L_i_re[i][i]=1;
}
//cholesky decomposition，Solution of d and L and d_i
d[0]=a1_re[0][0];
d_i[0]=1/d[0];
L_re[1][0]=a1_re[1][0]/d[0];
L_im[1][0]=a1_im[1][0]/d[0];
L_re[2][0]=a1_re[2][0]/d[0];
L_im[2][0]=a1_im[2][0]/d[0];
L_re[3][0]=a1_re[3][0]/d[0];
L_im[3][0]=a1_im[3][0]/d[0];
d[1]=a1_re[1][1]-d[0]*soc(L_re[1][0],L_im[1][0]);
d_i[1]=1/d[1];
mult(L_re[2][0],L_im[2][0],L_re[1][0],-L_im[1][0],p_re,p_im);
L_re[2][1]=(a1_re[2][1]-d[0]*temp_re)/d[1];
L_im[2][1]=(a1_im[2][1]-d[0]*temp_im)/d[1];
mult(L_re[3][0],L_im[3][0],L_re[1][0],-L_im[1][0],p_re,p_im);
L_re[3][1]=(a1_re[3][1]-d[0]*temp_re)/d[1];
L_im[3][1]=(a1_im[3][1]-d[0]*temp_im)/d[1];
d[2]=a1_re[2][2]-d[0]*soc(L_re[2][0],L_im[2][0])-d[1]*soc(L_re[2][1],L_im[2][1]);
d_i[2]=1/d[2];
mult(L_re[3][0],L_im[3][0],L_re[2][0],-L_im[2][0],p_re,p_im);
L_re[3][2]=a1_re[3][2]-d[0]*temp_re;
L_im[3][2]=a1_im[3][2]-d[0]*temp_im;
mult(L_re[3][1],L_im[3][1],L_re[2][1],-L_im[2][1],p_re,p_im);
L_re[3][2]=(L_re[3][2]-d[1]*temp_re)/d[2];
L_im[3][2]=(L_im[3][2]-d[1]*temp_im)/d[2];
d[3]=a1_re[3][3]-d[0]*soc(L_re[3][0],L_im[3][0])-d[1]*soc(L_re[3][1],L_im[3][1])-d[2]*soc(L_re[3][2],L_im[3][2]);
d_i[3]=1/d[3];
//L_i
L_i_re[1][0]=-L_re[1][0];
L_i_im[1][0]=-L_im[1][0];
mult(L_re[2][1],L_im[2][1],L_i_re[1][0],L_i_im[1][0],p_re,p_im);
L_i_re[2][0]=-(temp_re+L_re[2][0]);
L_i_im[2][0]=-(temp_im+L_im[2][0]);
mult(L_re[3][1],L_im[3][1],L_i_re[1][0],L_i_im[1][0],p_re,p_im);
L_i_re[3][0]=L_re[3][0]+temp_re;
L_i_im[3][0]=L_im[3][0]+temp_im;
mult(L_re[3][2],L_im[3][2],L_i_re[2][0],L_i_im[2][0],p_re,p_im);
L_i_re[3][0]=-(L_i_re[3][0]+temp_re);
L_i_im[3][0]=-(L_i_im[3][0]+temp_im);
L_i_re[2][1]=-L_re[2][1];
L_i_im[2][1]=-L_im[2][1];
mult(L_re[3][2],L_im[3][2],L_i_re[2][1],L_i_im[2][1],p_re,p_im);
L_i_re[3][1]=-(temp_re+L_re[3][1]);
L_i_im[3][1]=-(temp_im+L_im[3][1]);
L_i_re[3][2]=-L_re[3][2];
L_i_im[3][2]=-L_im[3][2];
//D_i
for(i=0;i<4;i++)
{
D_i_re[i][i]=d_i[i];
}
//(L_i)'
for(i=0;i<4;i++)
{
for(j=0;j<4;j++)
{
L_i_re2[i][j]=L_i_re[j][i];
L_i_im2[i][j]=-L_i_im[j][i];
}
}
//inverse matrix:(L_i)'*D_i*L_i
Matrix_mult444(L_i_re2,L_i_im2,D_i_re,D_i_im,c_re,c_im);
Matrix_mult444(c_re,c_im,L_i_re,L_i_im,b1_re,b1_im);
/*
FILE *fp1,*fp2;
fp1 = fopen("data.txt","w");
for( int i = 0 ; i < 4 ; i++){
for( int j = 0 ; j < 4 ; j++ ){
fprintf(fp1,"%lf\t",b1_re[i][j]);
}fprintf(fp1,"\n");
}
for( int i = 0 ; i < 4 ; i++){
for( int j = 0 ; j < 4 ; j++ ){
fprintf(fp1,"%lf\t",b1_im[i][j]);
}fprintf(fp1,"\n");
}
fclose(fp1);
*/
}
void chermitian( int m,int n,COMPLEX *mat48,COMPLEX *mat84_tmp){
// transform and conj
//m == 4 n == 8
for( int i = 0 ; i < m ; i++){
for( int j = 0 ; j < n ; j++ ){
(mat84_tmp+j*m+i) ->re = (mat48+i*n+j)->re;
(mat84_tmp+j*m+i)->im = -1 *( (mat48+i*n+j)->im);
char str[1000];
sprintf(str,"%d %d re : %lf\n",i,j,(mat84_tmp+j*m+i) ->re);
// qDebug() << str;
}
}
}
void hermitian( int m,int n, double mat48_1_re[][8],double mat48_1_im[][8],
double mat84_tmp_re[][4],double mat84_tmp_im[][4] ){
// transform and conj
//m == 4 n == 8
for( int i = 0 ; i < m ; i++){
for( int j = 0 ; j < n ; j++ ){
mat84_tmp_re[j][i] = mat48_1_re[i][j];
mat84_tmp_im[j][i] = -1 * mat48_1_im[i][j];
}
}
/*
FILE *fp1,*fp2;
fp1 = fopen("data.txt","w");
for( int i = 0 ; i < 8 ; i++){
for( int j = 0 ; j < 4 ; j++ ){
fprintf(fp1,"%lf\t",mat84_tmp_re[i][j]);
}fprintf(fp1,"\n");
}
fclose(fp1);
*/
}
/*
void mexFunction(int nlhs,mxArray *plhs[],int nrhs,const mxArray *prhs[])
{
int i,j;
double *p_re,*p_im;
double a_re[4][4],a_im[4][4],b_re[4][4],b_im[4][4];
plhs[0]=mxCreateDoubleMatrix(4,4,mxREAL);
plhs[1]=mxCreateDoubleMatrix(4,4,mxREAL);
p_re=mxGetPr(prhs[0]);
p_im=mxGetPr(prhs[1]);
for(i=0;i<4;i++)
{
for(j=0;j<4;j++)
{
a_re[i][j]=p_re[j*4+i];
a_im[i][j]=p_im[j*4+i];
}
}
chol_inv(a_re,a_im,b_re,b_im);
p_re=mxGetPr(plhs[0]);
p_im=mxGetPr(plhs[1]);
for(i=0;i<4;i++)
{
for(j=0;j<4;j++)
{
p_re[j*4+i]=b_re[i][j];
p_im[j*4+i]=b_im[i][j];
}
}
}
*/