Julia语言列主元求解线性方程组问题-技术交流区-MoHub

function Gaussliezhuyuan(A, B)
(m, n) = size(A);
z = [A B];
x = zeros(Float64, n);

for k = 1:n - 1
    max_val = abs(z[k, k]);
    max_row = k;
    for i = k + 1:m
        if abs(z[i, k]) > max_val
            max_val = abs(z[i, k]);
            max_row = i;
        end
    end
    if max_val == 0
        for i = k + 1:m
            if abs(z[i, k])!= 0
                max_row = i;
                break
            end
        end
        if max_row == k
            println("不能用高斯消去")
            return x
        end
    end

    if max_row!= k
        z[[k, max_row], :] = z[[max_row, k], :];
    end

    for i = k + 1:m
        m = -z[i, k] / z[k, k];
        z[i, :] = z[i, :] + m * z[k, :];
    end
end

b = z[:, n + 1];
x[n] = b[n] / z[n, n];
for k = (n - 1):-1:1
    s = 0;
    for t = k + 1:n
        s = s + z[k, t] * x[t];
    end
    x[k] = (b[k] - s) / z[k, k];
end

return x

end

A = [1.0 -1.0 3.0; 3.0 -3.0 1.0; 1.0 1.0 0.0]
B = [2.0; -1.0; 3.0]
solution = Gaussliezhuyuan(A, B)
println("the solution is")
for i in 1:length(solution)
println("x$i = ", solution[i])
end
这个代码与列主元高斯消去法的原理一致吗？为什么运行出x的解全为0.0？如何修改呢？

function Gaussliezhuyuan(A::Matrix{Float64}, b::Vector{Float64}) n = size(A, 1) x = zeros(n) # 进行列主元高斯消去法 for k = 1:n-1 # 寻找第k列绝对值最大的元素作为主元 max_row = k for i = k+1:n if abs(A[i, k]) > abs(A[max_row, k]) max_row = i end end # 交换行，将主元所在行置于对角线位置 if max_row != k A[[k, max_row], :] = A[[max_row, k], :] b[[k, max_row]] = b[[max_row, k]] end # 消元 for i = k+1:n factor = A[i, k] / A[k, k] A[i, k+1:n] .= A[i, k+1:n] - factor * A[k, k+1:n] b[i] = b[i] - factor * b[k] end end # 回代求解 x[n] = b[n] / A[n, n] for i = n-1:-1:1 x[i] = (b[i] - A[i, i+1:n][1] * x[i+1:n][1]) / A[i, i] end return x end A = [1.0 -1.0 3.0; 3.0 -3.0 1.0; 1.0 1.0 0.0] b = [2.0; -1.0; 3.0] solution = Gaussliezhuyuan(A, b)

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