小数字代替零？ [英] Tiny numbers in place of zero?

问题描述

我一直在做一个矩阵类（作为一个学习练习），我在测试我的逆函数时遇到了问题。

I have been making a matrix class (as a learning exercise) and I have come across and issue whilst testing my inverse function.

我输入一个任意矩阵例如：

I input a arbitrary matrix as such:

2 1 1
1 2 1
1 1 2

得到它来计算逆，我得到正确的结果：

And got it to calculate the inverse and I got the correct result:

0.75 -0.25 -0.25
-0.25 0.75 -0.25
-0.25 -0.25 0.75

但是当我尝试将两者相乘以确保我得到单位矩阵时，我得到：

But when I tried multiplying the two together to make sure I got the identity matrix I get:

1 5.5111512e-017 0
0 1 0
-1.11022302e-0.16 0 1

为什么得到这些结果？我会理解，如果我是乘以奇怪的数字，我可以理解一些舍入误差，但它的总和是：

Why am I getting these results? I would understand if I was multiplying weird numbers where I could understand some rounding errors but the sum it's doing is:

2 * -0.25 + 1 * 0.75 + 1 * -0.25

这显然是0，而不是5.111512e-017

which is clearly 0, not 5.111512e-017

如果我手动得到它做计算;例如：

If I manually get it to do the calculation; eg:

std::cout << (2 * -0.25 + 1 * 0.75 + 1 * -0.25) << "\n";

我预期得到0？

所有数字都表示为双精度。
这是我的乘法重载：

All the numbers are represented as doubles. Here's my multiplcation overload:

Matrix operator*(const Matrix& A, const Matrix& B)
{
    if(A.get_cols() == B.get_rows())
    {
        Matrix temp(A.get_rows(), B.get_cols());
        for(unsigned m = 0; m < temp.get_rows(); ++m)
        {
            for(unsigned n = 0; n < temp.get_cols(); ++n)
            {
                for(unsigned i = 0; i < temp.get_cols(); ++i)
                {
                    temp(m, n) += A(m, i) * B(i, n);
                }
            }
        }

        return temp;
    }

    throw std::runtime_error("Bad Matrix Multiplication");
}

和访问功能：

double& Matrix::operator()(unsigned r, unsigned c)
{
    return data[cols * r + c];
}

double Matrix::operator()(unsigned r, unsigned c) const
{
    return data[cols * r + c];
}

这里是找到反函数的函数：

Here's the function to find the inverse:

Matrix Inverse(Matrix& M)
{
    if(M.rows != M.cols)
    {
        throw std::runtime_error("Matrix is not square");
    }

    int r = 0;
    int c = 0;
    Matrix augment(M.rows, M.cols*2);
    augment.copy(M);

    for(r = 0; r < M.rows; ++r)
    {
        for(c = M.cols; c < M.cols * 2; ++c)
        {
            augment(r, c) = (r == (c - M.cols) ? 1.0 : 0.0);
        }
    }

    for(int R = 0; R < augment.rows; ++R)
    {
        double n = augment(R, R);
        for(c = 0; c < augment.cols; ++c)
        {
            augment(R, c) /= n;
        }

        for(r = 0; r < augment.rows; ++r)
        {
            if(r == R) { continue; }
            double a = augment(r, R);

            for(c = 0; c < augment.cols; ++c)
            {
                augment(r, c) -= a * augment(R, c);
            }
        }
    }

    Matrix inverse(M.rows, M.cols);
    for(r = 0; r < M.rows; ++r)
    {
        for(c = M.cols; c < M.cols * 2; ++c)
        {
            inverse(r, c - M.cols) = augment(r, c);
        }
    }

    return inverse;
}

推荐答案

0.250000000000000005在你的倒置矩阵，他们只是四舍五入显示，所以你看到很好的小圆的数字，如0.25。

You've got numbers like 0.250000000000000005 in your inverted matrix, they're just rounded for display so you see nice little round numbers like 0.25.

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