#include <bits/stdc++.h>
using namespace std;
 
const double pi = M_PI;
 
double P[8][8] = {
    {187, 188, 189, 202, 209, 175, 66,  41},
    {191, 186, 193, 209, 193,  98, 40,  39},
    {188, 187, 202, 202, 144,  53, 35,  37},
    {189, 195, 206, 172, 58,  47,  43,  45},
    {197, 204, 194, 106, 50,  48,  42,  45},
    {208, 204, 151,  50, 41,  41,  41,  53},
    {209, 179,  68,  42, 35,  36,  40,  47},
    {200, 117,  53,  41, 34,  38,  39,  63}
};
 
int main(int argc, char *argv[]) {
    double T[8][8];
    for (int u = 0; u < 8; u++) {
        for (int v = 0; v < 8; v++) {
            double cU, cV;
            cU = sqrt((u == 0 ? 1 : 2) / 8.0);
            cV = sqrt((v == 0 ? 1 : 2) / 8.0);
            for (int x = 0; x < 8; x++) {
                for (int y = 0; y < 8; y++) {
                    T[u][v] += P[x][y] * cU * cV * cos((2 * x + 1) * u * pi / 16.0) * cos((2 * y + 1) * v * pi / 16.0);
                }
            }
        }
    }
 
    for (int i = 0; i < 8; i++) {
        for (int j = 0; j < 8; j++) {
            printf("%10.3f", T[i][j]);
        }
        printf("\n");
    }
}
 

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