#include <stdio.h>
#include <stdlib.h>
#include <strings.h>
#include <math.h>

void pmatrix(int n,double A[n][n]){
    for(int i=0;i<n;i++){
        for(int j=0;j<n;j++){
            printf("%6g%c",A[i][j],
                j==n-1?';':',');
        }
        printf("\n");
    }
}
void mkA(int n,double A[n][n],int s){
    srand(s);
    for(int i=0;i<n;i++) for(int j=0;j<n;j++){
        A[i][j]=2.0*rand()/RAND_MAX-1.0;
    }
}
void AtA(int n,double B[n][n],double A[n][n]){
    bzero(B,sizeof(double)*n*n);
    for(int k=0;k<n;k++){
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){    
                B[i][j]+=A[k][i]*A[k][j];
            }
        }
    }
}
void Ax(int n,double y[n],
        double A[n][n],double x[n]){
    bzero(y,sizeof(double)*n);
    for(int i=0;i<n;i++){
        for(int k=0;k<n;k++){
            y[i]+=A[i][k]*x[k];
        }
    }
}
double dotprod(int n,double x[n],double y[n]){
    double r=0.0;
    for(int k=0;k<n;k++) r+=x[k]*y[k];
    return r;
}
double fnorm(int n,double A[n][n]){
    double r=0;
    for(int i=0;i<n;i++){
        for(int j=0;j<n;j++){
            r+=A[i][j]*A[i][j];
        }
    }
    return sqrt(r);
}