#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>
#include <strings.h>
#include <cilk/cilk.h>
#include "matrixlib.h"
#include "tictoc.h"
double vecnorm2(int n,double x[n]){
    double r=0;
    for(int i=0;i<n;i++){
        double t=fabs(x[i]);
        r+=t*t;
    }
    return sqrt(r);
}
double matnorm2(int n,double A[n][n]){
    double B[n][n],x[n],y[n],yk[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];
            }
        }
    }
    for(int k=0;k<n;k++){
        x[k]=2.0*random()/RAND_MAX-1.0;
    }
    multAx(n,n,B,x,y);
    double t,tk;
    for(int k=2;k<10;k++){
        multAx(n,n,B,y,yk);  // yk=B^k x
        t=vecnorm2(n,y);
        tk=vecnorm2(n,yk);
        printf("%g,%g tk/t=%g\n",t,tk,tk/t);
        memcpy(y,yk,sizeof(double)*n);
    }
    return(sqrt(tk/t));
}

double vecnorm1(int n,double x[n]){
    double r=0;
    for(int i=0;i<n;i++){
        r+=fabs(x[i]);
    }
    return r;
}
double matnorm1(int n,double A[n][n]){
    double r=0;
    for(int j=0;j<n;j++){
        double s=0;
        for(int i=0;i<n;i++){
            s+=fabs(A[i][j]);
        }
        if(s>r) r=s;
    }
    return r;
}

#define N 20
double A[N][N];
double B[N], X[N], XX[N];
double *P[N];
int main(){
    for(int i=0;i<N;i++){
        for(int j=0;j<N;j++){
            A[i][j]=2.0*random()/RAND_MAX-1.0;
        }
        X[i]=1;
    }
    printf("N=%d\n",N);
    printf("|A|_1=%g\n",matnorm1(N,A));
    printf("|A|_2=%g\n",matnorm2(N,A));
//    printf("A=\n"); matprint(N,N,A);
    tic();
    multAx(N,N,A,X,B);  // B=AX
//    printf("B=\n"); vecprint(N,B);
    plufact(N,A,P);     // now A is overwritten with LU
//    printf("LU=\n"); matprint(N,N,A);
    plusolve(N,A,P,XX,B);
    double t=toc();
    printf("It took %g seconds!\n",t);
//    printf("XX=\n"); vecprint(N,XX);
    double r=0;
    for(int i=0;i<N;i++){
        double dx=XX[i]-1;
        r+=dx*dx;
    }
    r=sqrt(r);
    printf("The error is %g.\n",r);
    printf("Speed of %g double-precision GFLOPS.\n",
        2.0*(N/3.0+1)*N*N/t/1e9);
    return 0;
}