PROSAGA码农传奇-量子算法-Gram-Schmidt函数不能正常使用C ++

<div class =“post-text”itemprop =“text”>
  <P>
    首先，我的建议是利用矢量操作包，因为它会使你的程序更清洁，其次，由于浮点错误，不推荐使用正常的Gram-Schmidt方法进行数值评估（参考文献1）。
    <a href="https://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process#Numerical_stability" rel="nofollow noreferrer">
      维基百科
    </A>
    ）。
  </p>
   <pre>
    <code>
      void gramSchmidt()
{
double a[3][3] = {
    {1.0, -1.0, 1.0},
    {1.0, 0.0, 1.0},
    {1.0, 1.0, 2.0}
};

double Result[3][3];
double u1[3],u2[3],u3[3],v1[3],v2[3],v3[3];

for (int i =0; i<3; i++) // Set Result Array to 0 and set the values for u vectors
    for(int j= 0; j<3; j++)
    {
        Result[i][j] = 0.0;

if (i == 0)
        {
            u1[j] = a[i][j];
        } else if (i == 1)
        {
            u2[j] = a[i][j];
           // std::cout << "u2:" << j << u2[j] << '\n';
        } else if (i == 2)
        {
            u3[j] = a[i][j];
        }
    }

// Solve v1
for (int i=0; i < 3; i++)
{
    v1[i] = u1[i];

}

// Solve v2
for (int i=0; i< 3; i++)
{
    v2[i] = u2[i] - func(u2,v1)*v1[i];
}

// Solve v3
for (int i=0; i<3; i++)
{
    v3[i] = u3[i] - func(u3, v1)*v1[i] - func(u3, v2)*v2[i];
}

// Normalise 3 vectors and store to Results
for (int i=0; i<3; i++)
    Result[0][i] = v1[i]*(1/normalise3d(v1));

for (int i=0; i<3; i++)
{
    Result[1][i] = v2[i]*(1/normalise3d(v2));
}

for (int i=0; i<3; i++)
{
    Result[2][i] = v3[i]*(1/normalise3d(v3));
}

for (int i = 0; i<3; i++)
{
    std::cout << '\n';
    for(int j = 0; j<3; j++)
        std::cout << Result[i][j] << ' ';
}
return;
}

double normalise3d (double a[3])
{
double normal = 0.0;

for (int i = 0; i< 3; i++)
    normal+= a[i]*a[i];

normal = sqrt(normal);

return normal;
}

double func (double a[3], double b[3]) // To solve proj(w)
{
double ans = 0.0;
double norm = normalise3d(b);

double vecProduct = 0.0;

for (int i= 0; i < 3; i++)
    vecProduct += a[i] * b[i];

ans = vecProduct/(norm * norm);

std::cout << "ans: " << ans << '\n';

return ans;

}

</code>
  </pre>
</DIV>