初等代数

一元函数绘图

绘制\(\sin(x)\)和\(\cos(x)\)函数在\(x \in [0,2\pi] \)的图像。

base

二元函数绘图

给定二元函数\(peaks(x,y)\)如下：

\[ peaks(x,y) = 3(1-x)^2e^{-x^2-(y+1)^2}-10(\frac{x}{5}-x^3-y^5)e^{-x^2-y^2}-\frac{1}{3}e^{-(x+1)^2-y^2} \]

试绘制它在\(x,y\in [-3,3]\)的图像。

base

local plt = require('package.plot')
local image = require('package.image')
local mol = libminoptlab


local imgs = {}

local title1 = '$\\sin(x)$和$\\cos(x)$'
local funs=  {math.sin,math.cos}
local labels = {'$\\sin(x)$','$\\cos(x)$'}
local lb = {0,0}
local ub = {2*math.pi,2*math.pi}

local img1 = plt.fplot(funs,lb,ub,labels)
local fw1 = plt.framework(111,title1,{'x','y'})
plt.show({{fw1,{img1}}},'images/base1.png',false)
table.insert(imgs,{'images/base1.png',121,'一元函数绘图'})


local title2 = 'peaks函数'
local peaks = function(xx)
    local x, y = xx[1], xx[2]
    return
        3 * (1 - x) ^ 2 * math.exp(-(x ^ 2) - (y + 1) ^ 2) - 10 * (x / 5 - x ^ 3 - y ^ 5) * math.exp(-x ^ 2 - y ^ 2) - 1 /
            3 * math.exp(-(x + 1) ^ 2 - y ^ 2)
end
local lb = {-3, -3}
local ub = {3, 3}
local n = 80

local img2 = plt.fplot3d({peaks}, {lb}, {ub}, n, {{
    cmap = 'cool'
}})
local fw2 = plt.framework3d(111, title2, {'x', 'y', 'z'})
plt.show({{fw2,{img2}}},'images/base2.png',false)
table.insert(imgs,{'images/base2.png',122,'二元函数绘图'})

image.show(imgs)