/*T Math/CS 466/666 Midterm Solutions
\medskip\noindent
Problem 1(iii).  Write or modify a computer program to computer the
Frobenious norm
$$
    \|A\|_F = {\textstyle \sqrt{\sum_{i,j} |A_{ij}|^2}}
$$
of the $4\times 4$ matrix $A$ with entries given by the formula
$A_{ij}=\sqrt{\vphantom{|}i+2j}$. */

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

double normF(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);
}
void matprint(int n,double A[n][n]){
    for(int i=0;i<n;i++) for(int j=0;j<n;j++){
        printf("%8g%c",A[i][j],j==n-1?'\n':' ');
    }
}

#define N 4
double A[N][N];

int main(){
    printf("Math/CS 466/666 Midterm\nProblem 1(iii)\n\n");
    for(int i=1;i<=N;i++) for(int j=1;j<=N;j++){
        /*T Mathematical notation assumes $i$ and $j$ range
        from $1$ to $N$.  As C arrays always start at zero 
        we store the matrix as $A_{ij}=@A[i-1][j-j]@$ */
        A[i-1][j-1]=sqrt(i+2*j);
    }
    printf("A=\n");
    matprint(N,A);
    printf("\nnormF(A)=%.14e\n",normF(N,A));
    return 0;
}