Julia矩阵热力图可视化求助：区域曲线显示异常

我想用热力图可视化矩阵，将其按(x,y)值约束划分为多个子区域，但两次尝试均出现问题：

• 第一次生成的热力图不符合预期，但矩阵数据完整
• 第二次矩阵3/4区域无数据，无法正常绘图

目标是实现与参考折线图一致的区域划分效果，考虑用自定义函数替代Julia自动计算的条件，以下是两次尝试的代码：

第一次尝试（生成错误热力图） #

using Plots

function W(x, y, g, d, ϕ, c, α, s)
    if x <= c/ϕ && y <= c/ϕ
        p_1 = x + g * x * (1 - x) - d * (x - y) - α*x
        p_2 = y + g * y * (1 - y) - d * (y - x) - α*y
        return 1 - p_1 + 1 - p_2

    elseif x >= c/ϕ && y <= c/ϕ 
        p_1 = x + g * x * (1 - x) - d * (x - y) - ϕ*x - α*x
        p_2 = y + g * y * (1 - y) - d * (y - x) - α*y
        return 1 - p_1 - c  + 1 - p_2 
    
    elseif x <= c/ϕ && y >= c/ϕ 
        p_1 = x + g * x * (1 - x) - d * (x - y) - α*x
        p_2 = y + g * y * (1 - y) - d * (y - x) - ϕ*y - α*y
        return 1 - p_1 + 1 - p_2 - c
    
    elseif x >= c/ϕ && y >= c/ϕ && x<= 0.79 && y<= 0.79 ### 我替换了不等式的满足值
        p_1 = x + g * x * (1 - x) - d * (x - y) - ϕ*x - α*x
        p_2 = y + g * y * (1 - y) - d * (y - x) - ϕ*y - α*y
        return 1 - p_1 - c + 1 - p_2 - c
    
    elseif x >= 0.79 && y >= c/ϕ  
        p_1 = x + g * x * (1 - x) - d * (x - y) - ϕ*x - α*x
        p_2 = y + g * y * (1 - y) - d * (y - x) - ϕ*y - α*y
        return s + 1 - p_2 - c
    
    elseif x >= c/ϕ && y >= 0.79 
        p_1 = x + g * x * (1 - x) - d * (x - y) - ϕ*x - α*x
        p_2 = y + g * y * (1 - y) - d * (y - x) - ϕ*y - α*y
        return 1 - p_1 - c + s
    
    elseif x >= 0.79 && y >=0.79
        p_1 = x + g * x * (1 - x) - d * (x - y) - ϕ*x - α*x
        p_2 = y + g * y * (1 - y) - d * (y - x) - ϕ*y - α*y
        return ((1 - p_1 - c + s) + (s + 1 - p_2 - c))/2
    end
end

g = 0.5
d = 0.25
c = 0.2
ϕ = 0.4
α = 0.25
s = 0.3

x_vals = range(0, stop = 1, length = 100)
y_vals = range(0, stop = 1, length = 100)

z = [W(x, y, g, d, ϕ, c, α, s) for x in x_vals, y in y_vals]

pyplot()
fig = heatmap(x_vals, y_vals, z, xlabel = "P1", ylabel = "P2",
zlabel = "", title = "Total Payoff", color = :viridis, aspect_ratio=:equal)

第二次尝试（矩阵多数区域无数据） #

using Plots

function W(x, y, g, d, ϕ, c, α, s)
    condition_3 = (1/d)*(1 - s - c) - (1/d)*(1 + g - d - ϕ)*x - (g/d)x^2
    condition_4 = (1/d)*(1 - s - c) - (1/d)(1 + g - d - ϕ)*y - (g/d)y^2
    condition_31 = (1/d)*(1 - s - c) - (1/d)(1 + g - d - ϕ - (α/2))*x - (g/d)x^2
    condition_41 = (1/d)*(1 - s - c) - (1/d)(1 + g - d - ϕ - (α/2))*y - (g/d)*y^2

    if x <= c/ϕ && y <= c/ϕ 
        p_1 = x + g * x * (1 - x) - d * (x - y) 
        p_2 = y + g * y * (1 - y) - d * (y - x)
        return 1 - p_1 + 1 - p_2 
    
    elseif x >= c/ϕ && y >= c/ϕ && y <= condition_3 && x <= condition_4 #y <= f(x) && x <= f(y)
        p_1 = x + g * x * (1 - x) - d * (x - y) - ϕ*x
        p_2 = y + g * y * (1 - y) - d * (y - x) - ϕ*y
        return 1 - p_1 - c + 1 - p_2 - c
    
    elseif x <= c/ϕ && y >= c/ϕ && x <= condition_4
        p_1 = x + g * x * (1 - x) - d * (x - y)
        p_2 = y + g * y * (1 - y) - d * (y - x) - ϕ*y
        return 1 - p_1 + 1 - p_2 - c
    
    elseif x >= c/ϕ && y <= c/ϕ && y <= condition_3
        p_1 = x + g * x * (1 - x) - d * (x - y) - ϕ*x
        p_2 = y + g * y * (1 - y) - d * (y - x) 
        return 1 - p_1 - c  + 1 - p_2 
    
    elseif x >= c/ϕ && y >= c/ϕ && y >= condition_3 && x <= condition_41
        p_1 = x + g * x * (1 - x) - d * (x - y)
        p_2 = y + g * y * (1 - y) - d * (y - x) - ϕ*y
        return s + (1 - P_2 - c + ϕ*y + (α/2)*y)
    
    elseif x >= c/ϕ && y >= c/ϕ && y <= condition_31 && x >= condition_4
        p_1 = x + g * x * (1 - x) - d * (x - y) 
        p_2 = y + g * y * (1 - y) - d * (y - x) - ϕ*y
        return (1 - P_1 - c + ϕ*x + (α/2)*x) + s
    end
end

g = 0.5
d = 0.25
c = 0.2
ϕ = 0.4
α = 0.25
s = 0.3

x_vals = range(0, stop = 1, length = 100)
y_vals = range(0, stop = 1, length = 100)

z = [W(x, y, g, d, ϕ, c, α, s) for x in x_vals, y in y_vals]

fig = heatmap(x_vals, y_vals, z, xlabel = "Pi", ylabel = "Pj",
zlabel = "", title = "Total Payoff", color = :viridis)

内容的提问来源于stack exchange，提问作者Linh