# Phase portrait with vector field

**URL:** <https://discourse.julialang.org/t/phase-portrait-with-vector-field/98587>\
**Category:** New to Julia\
**Created:** [May 10, 2023, 1:57am UTC](https://discourse.julialang.org/t/phase-portrait-with-vector-field/98587 "2023-05-10T01:57:06Z")\
**Posts on this page:** 4\
**Page:** 1

<div class="post-metadata">

**Author:** ![moxeeeem](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/moxeeeem/32/47902_2.png) [@moxeeeem](https://discourse.julialang.org/u/moxeeeem)\
**Post date:** [May 10, 2023, 1:57am UTC](https://discourse.julialang.org/t/phase-portrait-with-vector-field/98587/1 "2023-05-10T01:57:07Z")

</div>

I’m trying to reformat a python code that plots a phase portrait with vector field. It seems that I did everything right, but the error is in the quiver () function. What did I write wrong?

Python code (working correctly):

```julia
# Phase portrait with vector field. Check two systems are the same.
import matplotlib.pyplot as plt
import numpy as np
from scipy.integrate import odeint
import pylab as pl

# The 2-dimensional linear system.
a, b, c, d = 2, 1, 1, 2
def dx_dt(x, t):
    return [a*x[0] + b*x[1], c*x[0] + d*x[1]]

# Trajectories in forward time.
ts = np.linspace(0, 4, 100)
ic = np.linspace(-1, 1, 5)
for r in ic:
    for s in ic:
        x0 = [r, s]
        xs = odeint(dx_dt, x0, ts)
        plt.plot(xs[:,0], xs[:,1], "r-")

# Trajectories in backward time.
ts = np.linspace(0, -4, 100)
ic = np.linspace(-1, 1, 5)
for r in ic:
    for s in ic:
        x0 = [r, s]
        xs = odeint(dx_dt, x0, ts)
        plt.plot(xs[:,0], xs[:,1], "r-")
        
# Label the axes and set fontsizes.
plt.xlabel("x", fontsize=15)
plt.ylabel("y", fontsize=15)
plt.tick_params(labelsize=15)
plt.xlim(-1, 1)
plt.ylim(-1, 1);

# Plot the vectorfield.

X,Y = np.mgrid[-1:1:10j, -1:1:10j]
u = a*X + b*Y
v = c*X + d*Y
pl.quiver(X, Y, u, v, color = "b")
plt.show()

```

Output which I want to get:  
 ![Снимок экрана 2023-05-10 045546](https://global.discourse-cdn.com/julialang/original/3X/5/d/5d45a91f27a370bbd4a87aadd5e062aeae7c766e.png)

My Julia code:

````julia
using Plots
using SciPy
using LinearAlgebra
using DifferentialEquations

# The 2-dimensional linear system.
a, b, c, d = 2, 1, 1, 2

function dx_dt(du, u, p, t)
    du[1] = a*u[1] + b*u[2]
    du[2] = c*u[1] + d*u[2]
end

# Trajectories in forward time.
ts = LinRange(0, 4, 100)
ic = LinRange(-1, 1, 5)
tspan = (0.0, 4.0)

for r in ic
    for s in ic
        x0 = [r, s]
        xs = solve(ODEProblem(dx_dt, x0, tspan))
        Plots.plot(xs, color="red", linestyle="-")
        
    end
end

# Trajectories in backward time.
ts = LinRange(0, -4, 100)
ic = LinRange(-1, 1, 5)
tspan = (-4.0, 0.0)  

for r in ic
    for s in ic
        x0 = [r, s]
        xs = solve(ODEProblem(dx_dt, x0, tspan))
        Plots.plot(xs, color="red", linestyle="-")
    end
end
        
# Label the axes and set fontsizes.
xlabel!("x")
ylabel!("y")
#fontfamily("sans-serif")
#fontsize!(15)
xlims!(-1, 1)
ylims!(-1, 1)

# Plot the vectorfield.
function meshgrid(x, y)
    X = repeat(x', length(y), 1)
    Y = repeat(y, 1, length(x))
    return (X, Y)
end

x = range(-1, 1, length=10)
y = range(-1, 1, length=10)

a, b, c, d = 1, 1, -1, 1

X, Y = meshgrid(x, y)

u = a .* X .+ b .* Y
v = c .* X .+ d .* Y

quiver(X, Y, u, v, color="blue", alpha=0.5, aspect_ratio=:equal, framestyle=:box)```

My error: 

````

Couldn’t process recipe args: (Matrix{Float64}, Matrix{Float64}, Matrix{Float64}, Matrix{Float64})

```julia

```

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<div class="post-metadata">

**Author:** ![tomerarnon](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tomerarnon/32/3170_2.png) [@tomerarnon](https://discourse.julialang.org/u/tomerarnon)\
**Post date:** [May 10, 2023, 5:09am UTC](https://discourse.julialang.org/t/phase-portrait-with-vector-field/98587/2 "2023-05-10T05:09:43Z")

</div>

It’s usually a mistake to make a “meshgrid” in julia…

`quiver` takes in 4 vectors, and has signature `quiver(x, y, quiver = (u, v))`. x and y are vectors of x-y coordinates. It will also accept a vector of 2-Tuples (each one being a point), or an Nx2 matrix. `u` and `v` must also be vectors, representing the x and y offset of each arrow in the quiver. You have all 4 being NxN matrices.

Given how you’ve set things up (with a `meshgrid`), you could recover the vectors you need by calling `vec` on x, y, u and v. In general though, it is better not to use a meshgrid in the first place and just iterate over the product of x and y with e.g. `iterators.product(x, y)`, or using a nested for loop, or something similar.

Using `vec`, I get what I assume you were looking for:  
`quiver(vec(X), vec(Y), quiver=(vec(u), vec(v)), color="blue", alpha=0.5, aspect_ratio=:equal, framestyle=:box)`

 ![Screen Shot 2023-05-09 at 10.08.38 PM](https://global.discourse-cdn.com/julialang/original/3X/9/9/99bb8444a6a00731b940044f5d8c1ceb97709053.png)

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<div class="post-metadata">

**Author:** ![moxeeeem](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/moxeeeem/32/47902_2.png) [@moxeeeem](https://discourse.julialang.org/u/moxeeeem)\
**Post date:** [May 10, 2023, 12:47pm UTC](https://discourse.julialang.org/t/phase-portrait-with-vector-field/98587/3 "2023-05-10T12:47:36Z")

</div>

Thank you very much, your answer saved me. Do you know why I don’t have the red lines of my plot displayed?

---

<div class="post-metadata">

**Author:** ![tomerarnon](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tomerarnon/32/3170_2.png) [@tomerarnon](https://discourse.julialang.org/u/tomerarnon)\
**Post date:** [May 10, 2023, 11:04pm UTC](https://discourse.julialang.org/t/phase-portrait-with-vector-field/98587/4 "2023-05-10T23:04:45Z")

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Not off the top of my head, because I haven’t gone over all of your code in detail. What I did notice is this:

- you use `Plots.plot` repeatedly. Each of these makes a new plot. To add things to an existing plot, you need to use the `plot!` form (or `quiver!`, etc)
- I don’t think `linestyle="-"` is something thats supported… not sure where you got that (I could be wrong about this though)

I suggest splitting this up and solving this one piece at a time. Make a plot with the red lines separately from the quiver, and combine once you figure out each piece.