Problems with quiver plot
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Hey!
I try to create a quiver plot with unequl axis length. I' like to have the arrows the same length, which somehow does not want to work.
Any ideas?
Thanks!
%% system paramters
eta = .1;
mu = .1;
nu = 1;
gamma = 2;
%% dependent variables
roi = 2;
s = linspace(max([(1-roi)*s_0,0]),(1+roi)*s_0,10);
p = linspace(max([(1-roi)*p_0,0]),(1+roi)*p_0,10);
[s,p] = meshgrid(s,p);
%% gradient flow
v = s.*p.^gamma ./ (1+(1+s).*p.^gamma);
ds = -v + eta;
dp = mu*(v - nu*p);
mag = sqrt(ds.^2 + dp.^2);
arrow_scale = 3E-1;
norm_ds = arrow_scale*ds./mag;
norm_dp = arrow_scale*dp./mag;
%% plot
q = quiver(s,p,norm_ds,norm_dp,'Autoscale','off', 'Color',.6*[1,1,1]);
q.ShowArrowHead = 'off';
q.Marker = '.';
6 个评论
David Goodmanson
2025-8-29
编辑:David Goodmanson
2025-8-31
Hi Sam, here's the best I could do trying to reproduce the wikipedia plot, including the aspect ratio. The arrows are all normalized to the same value, but at least as importantly the plottting points for quiver are not equally spaced meshgrid values. Rather every x,y quiver point is changed slightly from what meshgrid has. I didn't use 'axis equal' so I guess the vectors are not quite constant length visually.

xx = linspace(-5,5,22);
yy = linspace(-10,10,22);
[x0 y0] = meshgrid(xx,yy);
th = atan(x0.^2-x0-2);
sf = 1/2; % factor to visually reduce the arrow length on the plot
u = sf*cos(th);
v = sf*sin(th);
x = x0 - u/2; % move the center of the arrow to the constant-spaced points
y = y0 - v/2;
figure(1)
quiver(x,y,u,v,'showarrowhead','off','autoscale','off')
ylim([-10 10])
xlim([-10 10])
hold on
x1 = -5:.01:5
y1 = x1.^3/3 -x1.^2/2-2*x1+4;
y2 = x1.^3/3 -x1.^2/2-2*x1;
y3 = x1.^3/3 -x1.^2/2-2*x1-4;
plot(x1,y1,x1,y2,x1,y3)
hold off
Sam Chak
2025-8-30
Thank you for your input. It appears that there is no specific parameter to set a constant length for all quiver objects without altering the original magnitudes of the directional components specified by u and v. However, you are absolutely correct that "constant length" representations are visually meaningless if the aspect ratios of the x- and y-axes are not equal.
s_0 = 10; % estimated based on the original image posted by the OP (now removed)
p_0 = 0.1; % estimated based on the original image posted by the OP (now removed)
%% system paramters
eta = .1;
mu = .1;
nu = 1;
gamma = 2;
%% dependent variables
roi = 2;
numArrX = 19; % number of arrows per row
numArrY = 19; % number of arrows per column
s = linspace(max([(1-roi)*s_0,0]), (1+roi)*s_0, numArrX);
p = linspace(max([(1-roi)*p_0,0]), (1+roi)*p_0, numArrY);
[s,p] = meshgrid(s,p);
%% gradient flow
v = s.*p.^gamma./(1 + (1 + s).*p.^gamma);
ds = -v + eta;
dp = mu*(v - nu*p);
mag = sqrt(ds.^2 + dp.^2);
Xarrow_scale = 4E-1;
Yarrow_scale = 1E-1;
norm_ds = Xarrow_scale*ds./mag;
norm_dp = Yarrow_scale*dp./mag;
% Finding the equilibrium point
fun = @(x) [-(x(1).*x(2).^gamma./(1 + (1 + x(1)).*x(2).^gamma)) + eta;
mu*(x(1).*x(2).^gamma./(1 + (1 + x(1)).*x(2).^gamma) - nu*x(2))];
x0 = [11, 1]; % initial guess
eq = fsolve(fun, x0) % equilibrium point
%% plot
l = streamslice(s, p, norm_ds, norm_dp, 0.5, 'noarrows');
set(l, 'Color', "#F63C4C"); % Red Salsa
hold on
q = quiver(s, p, norm_ds, norm_dp, 'off', 'Color', .6*[1,1,1]); % automatic scaling is disabled
q.ShowArrowHead = 'off'; % no arrowheads
q.Marker = '.'; % for the tails
% adding the equilibrium point to the slope field
plot(eq(1), eq(2), 'o', 'markersize', 10, 'linewidth', 1.5, 'Color', "#2F2CE0") % Palatinate Blue
hold off
title('Gradient flow')
xlabel('s')
ylabel('p')
xlim([0 30])
ylim([0 .3])
采纳的回答
Matt J
2025-8-27
编辑:Matt J
2025-8-27
I think you just need axis equal.
%% system paramters
eta = .1;
mu = .1;
nu = 1;
gamma = 2;
%% dependent variables
roi = 2;
s_0=1; p_0=3; %<---- Matt J chose randomly
s = linspace(max([(1-roi)*s_0,0]),(1+roi)*s_0,10);
p = linspace(max([(1-roi)*p_0,0]),(1+roi)*p_0,10);
[s,p] = meshgrid(s,p);
%% gradient flow
v = s.*p.^gamma ./ (1+(1+s).*p.^gamma);
ds = -v + eta;
dp = mu*(v - nu*p);
mag = sqrt(ds.^2 + dp.^2);
arrow_scale = 3E-1;
norm_ds = arrow_scale*ds./mag;
norm_dp = arrow_scale*dp./mag;
%% plot
q = quiver(s,p,norm_ds,norm_dp,'Autoscale','off', 'Color',.6*[1,1,1]);
q.ShowArrowHead = 'off';
q.Marker = '.';
axis equal %<---- Matt J added
5 个评论
Matt J
2025-8-27
You're very welcome, but since it works, please Accept-click the answer to indicate so.
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