6-gradient-vector-fields

1. load pacages

using GLMakie,Symbolics

2.define symbolics variables

@variables x, y
Dx=Differential(x)
Dy=Differential(y)

(::Differential) (generic function with 3 methods)

3. make data

使用Symbolics.jl 方法构建求导函数.

• of 表示原函数
• fx 沿 x 轴的导函数
• fy 沿 y轴方向的导函数

f=x^2+2y^2
g=5-x^2-2y^2
h=x+2y+3
funcs=[f,g,h]
df=[]
for fun in funcs
    local of=build_function(fun, x,y)|>eval
    local fx=fun|>Dx|>expand_derivatives|>expr->build_function(expr, x,y)|>eval
    local fy=fun|>Dy|>expand_derivatives|>expr->build_function(expr, x,y)|>eval
    push!(df,[of,fx,fy])

end

4. plot

fig=Figure(resolution=(900,600))
xs=ys=range(-3,3,10)
for  i in 1:3
     local ax1=Axis(fig[1,i],title=L"%$(funcs[i])")
     local ax2=Axis(fig[2,i])
     local zs=[df[i][1](x,y) for x in xs, y in ys]
     local us=[df[i][2](x,y) for x in xs, y in ys]
     local vs=[df[i][3](x,y) for x in xs, y in ys]
     contour!(ax1,xs,ys,zs)
     arrows!( ax2,xs, ys, us, vs,lengthscale=i==3 ? 0.2 : 0.05,color=(:purple,0.8))

end
fig