I am using a quiver plot in MATLAB to simulate a velocity field. Now I would like the vectors produced by the quiver plot to be all the same length, so that they just indicate the vectors direction. The value of the velocity in each point should be illustrated by different colors then.
Is there a possibility to have quiver plotting vectors of same length?
That's my current code:
%defining parameters:
age = 900;
vis= 15;
turbulences = zeros(9,3);
a = 0.01;
spacing = 1000;
[x,y] = meshgrid(-100000:spacing:100000);%, 0:spacing:10000);
u = a;
v = 0;
n = 0;
for i = 1:4
turbulences(i,1) = -80000 + n;
turbulences(i,2) = 15000;
n = 15000 * i;
end
n = 0;
for i = 5:9
turbulences(i,1) = -15000 + n*5000;
turbulences(i,2) = 4000;
n = n+1;
end
for i = 1:4
turbulences(i,3) = -1000;
end
for i = 5:9
turbulences(i,3) = 800;
end
%compute velocities in x and y direction
for k = 1:9
xc = turbulences(k,1);
yc = turbulences(k,2);
r1 = ((x-xc).^2 + (y-yc).^2);
r2 = ((x-xc).^2 + (y+yc).^2);
u = u + turbulences(k,3)/2*pi * (((y-yc)./r1).*(1-exp(-(r1./(4*vis*age)))) - ((y+yc)./r2).*(1-exp(-(r2./(4*vis*age)))));
v = v - turbulences(k,3)/2*pi* (((x-xc)./r1).*(1-exp(-(r1./(4*vis*age)))) - ((x-xc)./r2).*(1-exp(-(r2./(4*vis*age)))));
end
quiver(x,y,u,v);
grid on;
Thank you for your help!
One way to do this would be to normalize each component of your vectors to +- 1 just to keep their direction.
un = u./abs(u); % normalized u
vn = v./abs(v); % normalized v
quiver(x, y, un, vn)
Related
I want to determine the Steepest descent of the Rosenbruck function using Armijo steplength where x = [-1.2, 1]' (the initial column vector).
The problem is, that the code has been running for a long time. I think there will be an infinite loop created here. But I could not understand where the problem was.
Could anyone help me?
n=input('enter the number of variables n ');
% Armijo stepsize rule parameters
x = [-1.2 1]';
s = 10;
m = 0;
sigma = .1;
beta = .5;
obj=func(x);
g=grad(x);
k_max = 10^5;
k=0; % k = # iterations
nf=1; % nf = # function eval.
x_new = zeros([],1) ; % empty vector which can be filled if length is not known ;
[X,Y]=meshgrid(-2:0.5:2);
fx = 100*(X.^2 - Y).^2 + (X-1).^2;
contour(X, Y, fx, 20)
while (norm(g)>10^(-3)) && (k<k_max)
d = -g./abs(g); % steepest descent direction
s = 1;
newobj = func(x + beta.^m*s*d);
m = m+1;
if obj > newobj - (sigma*beta.^m*s*g'*d)
t = beta^m *s;
x = x + t*d;
m_new = m;
newobj = func(x + t*d);
nf = nf+1;
else
m = m+1;
end
obj=newobj;
g=grad(x);
k = k + 1;
x_new = [x_new, x];
end
% Output x and k
x_new, k, nf
fprintf('Optimal Solution x = [%f, %f]\n', x(1), x(2))
plot(x_new)
function y = func(x)
y = 100*(x(1)^2 - x(2))^2 + (x(1)-1)^2;
end
function y = grad(x)
y(1) = 100*(2*(x(1)^2-x(2))*2*x(1)) + 2*(x(1)-1);
end
I am in the process of writing a 2D non-linear Poisson's solver. One intermediate test I performed is using my non-linear solver to solve for a "linear" Poisson equation. Unfortunately, my non-linear solver is giving me incorrect results, unlike if I try to solve it directly in MATLAB using the backslash ""
non-linear solver iteratively code: "incorrect results"
clearvars; clc; close all;
Nx = 20;
Ny = 20;
Lx = 2*pi;
x = (0:Nx-1)/Nx*2*pi; % x coordinate in Fourier, equally spaced grid
kx = fftshift(-Nx/2:Nx/2-1); % wave number vector
kx(kx==0) = 1; %helps with error: matrix ill scaled because of 0s
ygl = -cos(pi*(0:Ny)/Ny)'; %Gauss-Lobatto chebyshev points
%make mesh
[X,Y] = meshgrid(x,ygl);
%Chebyshev matrix:
VGL = cos(acos(ygl(:))*(0:Ny));
dVGL = diag(1./sqrt(1-ygl.^2))*sin(acos(ygl)*(0:Ny))*diag(0:Ny);
dVGL(1,:) = (-1).^(1:Ny+1).*(0:Ny).^2;
dVGL(Ny+1,:) = (0:Ny).^2;
%Diferentiation matrix for Gauss-Lobatto points
Dgl = dVGL/VGL;
D = Dgl; %first-order derivative matrix
D2 = Dgl*Dgl;
%linear Poisson solved iteratively
Igl = speye(Ny+1);
Ig = speye(Ny);
ZNy = diag([0 ones(1,Ny-1) 0]);
div_x_act_on_grad_x = -Igl; % must be multiplied with kx(m)^2 for each Fourier mode
div_y_act_on_grad_y = D * ZNy *D;
u = Y.^2 .* sin( (2*pi / Lx) * X);
uh = fft(u,[],2);
uold = ones(size(u));
uoldk = fft(uold,[],2);
max_iter = 500;
err_max = 1e-5; %change to 1e-8;
for iterations = 1:max_iter
for m = 1:length(kx)
L = div_x_act_on_grad_x * (kx(m)^2) + div_y_act_on_grad_y;
d2xk = div_x_act_on_grad_x * (kx(m)^2) * uoldk;
d2x = real(ifft(d2xk,[],2));
d2yk = div_y_act_on_grad_y *uoldk;
d2y = real(ifft(d2yk,[],2));
ffh = d2xk + d2yk;
phikmax_old = max(max(abs(uoldk)));
unewh(:,m) = L\(ffh(:,m));
end
phikmax = max(max(abs(unewh)));
if phikmax == 0 %norm(unewh,inf) == 0
it_error = err_max /2;
else
it_error = abs( phikmax - phikmax_old) / phikmax;
end
if it_error < err_max
break;
end
end
unew = real(ifft(unewh,[],2));
DEsol = unew - u;
figure
surf(X, Y, unew);
colorbar;
title('Numerical solution of \nabla^2 u = f');
figure
surf(X, Y, u);
colorbar;
title('Exact solution of \nabla^2 u = f');
Direct solver
ubar = Y.^2 .* sin( (2*pi / Lx) * X);
uh = fft(ubar,[],2);
for m = 1:length(kx)
L = div_x_act_on_grad_x * (kx(m)^2) + div_y_act_on_grad_y;
d2xk = div_x_act_on_grad_x * (kx(m)^2) * uh;
d2x = real(ifft(d2xk,[],2));
d2yk = div_y_act_on_grad_y *uh;
d2y = real(ifft(d2yk,[],2));
ffh = d2xk + d2yk;
%----------------
unewh(:,m) = L\(ffh(:,m));
end
How can I fix code 1 to get the same results as code 2?
I work to about missile routing. I calculated throuhout the flight x,y,z coordinates of missile . I have data set about missile x,y,z coordinates. My goal is to move the servo motor according to x, y, z coordinates.
My input is 3-dimensional(x,y,z). I want to simulate in two dimensions. And for this I use vectoral calculation. The servo motor can take values between 0-1. But the result larger than 1 . When the results are reduced at the same rate, result is smaller than 0. But I get still the error
Undefined function 'writePosition' for input arguments of type 'matlab.graphics.chart.primitive.Surface'.
I will be grateful if you could help me.
My data example:
missile_x = 0.015
missile_y = 0.054
missile_z = 0.254
missile_flight = 0.00018794
My flight rotation code:
missile_x = vpa(Xval{id}(k)/10,5)
missile_y = vpa(Yval{id}(k)/10,5)
missile_z = vpa(Zval{id}(k)/10,5)
missile_flight = vpa(0.00555556*(missile_x^2+missile_y^2+missile_z^2)^1/2,5)
writePosition(s, missile_flight);
current_pos = readPosition(s);
current_pos = current_pos*missile_flight;
fprintf('Current motor position is %d degrees\n', current_pos);
pause(2);
Missile X,Y,Z calculation code:
dt = 0.005; %time step
g = 9.81; %gravity
ro = 1.2; %air density
A = pi*(0.2)^2; % reference area
Vmag = 0; % missile velocity vectoral value [m/sn]
t = 0;
T(1) = t;
U(1) = 0; %the missile is initially at rest at t = 0; So the velocity is 0
V(1) = 0;
W(1) = 0;
X(1) = X0;
Y(1) = Y0;
Z(1) = Z0;
n = 1;
h = interp2(x_terrain, y_terrain, h_terrain,X(1), Y(1));
while (Z(n) >= h)
[Thx, Thy, Thz] = thrust(t, Thmag0, theta, phi, Tburn, U(n), V(n), W(n));
Vmag = (U(n)^2 + V(n)^2 + W(n)^2)^(1/2);
Thmag = (Thx^2 + Thy^2 + Thz^2)^(1/2);
m = mass(t, m0, mf, Tburn);
[rho,sound_speed] = atmosphere(Z(n));
Cd = drag_coeff(Vmag,sound_speed);
U(n+1) = U(n) + (Thx/m - (Cd*rho*A/(2*m))*(U(n)*(U(n)^2+V(n)^2+W(n)^2)^(1/2)))*dt;
V(n+1) = V(n) + (Thy/m - (Cd*rho*A/(2*m)*(V(n)*(U(n)^2+V(n)^2+W(n)^2)^(1/2))))*dt;
W(n+1) = W(n) + (Thz/m - (Cd*rho*A/(2*m))*(W(n)*(U(n)^2+V(n)^2+W(n)^2)^(1/2)) - g)*dt;
X(n+1) = X(n) + U(n+1)*dt;
Y(n+1) = Y(n) + V(n+1)*dt;
Z(n+1) = Z(n) + W(n+1)*dt;
h = interp2(x_terrain, y_terrain, h_terrain, ...
X(end), Y(end));
t = t + dt;
T(n+1) = t;
n = n+1 ;
end
Tval = T;
Xval = X;
Yval = Y;
Zval = Z;
I want to move a red star marker along the spiral trajectory with an equal distance of 5 units between the red star points on its circumference like in the below image.
vertspacing = 10;
horzspacing = 10;
thetamax = 10*pi;
% Calculation of (x,y) - underlying archimedean spiral.
b = vertspacing/2/pi;
theta = 0:0.01:thetamax;
x = b*theta.*cos(theta)+50;
y = b*theta.*sin(theta)+50;
% Calculation of equidistant (xi,yi) points on spiral.
smax = 0.5*b*thetamax.*thetamax;
s = 0:horzspacing:smax;
thetai = sqrt(2*s/b);
xi = b*thetai.*cos(thetai);
yi = b*thetai.*sin(thetai);
plot(x,y,'b-');
hold on
I want to get a figure that looks like the following:
This is my code for the circle trajectory:
% Initialization steps.
format long g;
format compact;
fontSize = 20;
r1 = 50;
r2 = 35;
r3= 20;
xc = 50;
yc = 50;
% Since arclength = radius * (angle in radians),
% (angle in radians) = arclength / radius = 5 / radius.
deltaAngle1 = 5 / r1;
deltaAngle2 = 5 / r2;
deltaAngle3 = 5 / r3;
theta1 = 0 : deltaAngle1 : (2 * pi);
theta2 = 0 : deltaAngle2 : (2 * pi);
theta3 = 0 : deltaAngle3 : (2 * pi);
x1 = r1*cos(theta1) + xc;
y1 = r1*sin(theta1) + yc;
x2 = r2*cos(theta2) + xc;
y2 = r2*sin(theta2) + yc;
x3 = r3*cos(theta3) + xc;
y3 = r3*sin(theta3) + yc;
plot(x1,y1,'color',[1 0.5 0])
hold on
plot(x2,y2,'color',[1 0.5 0])
hold on
plot(x3,y3,'color',[1 0.5 0])
hold on
% Connecting Line:
plot([70 100], [50 50],'color',[1 0.5 0])
% Set up figure properties:
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0, 0, 1, 1]);
drawnow;
axis square;
for i = 1 : length(theta1)
plot(x1(i),y1(i),'r*')
pause(0.1)
end
for i = 1 : length(theta2)
plot(x2(i),y2(i),'r*')
pause(0.1)
end
for i = 1 : length(theta3)
plot(x3(i),y3(i),'r*')
pause(0.1)
end
I can't think of a way to compute distance along a spiral, so I'm approximating it with circles, in hopes that it will still be useful.
My solution relies on the InterX function from FEX, to find the intersection of circles with the spiral. I am providing an animation so it is easier to understand.
The code (tested on R2017a):
function [x,y,xi,yi] = q44916610(doPlot)
%% Input handling:
if nargin < 1 || isempty(doPlot)
doPlot = false;
end
%% Initialization:
origin = [50,50];
vertspacing = 10;
thetamax = 5*(2*pi);
%% Calculation of (x,y) - underlying archimedean spiral.
b = vertspacing/(2*pi);
theta = 0:0.01:thetamax;
x = b*theta.*cos(theta) + origin(1);
y = b*theta.*sin(theta) + origin(2);
%% Calculation of equidistant (xi,yi) points on spiral.
DST = 5; cRes = 360;
numPts = ceil(vertspacing*thetamax); % Preallocation
[xi,yi] = deal(NaN(numPts,1));
if doPlot && isHG2() % Plots are only enabled if the MATLAB version is new enough.
figure(); plot(x,y,'b-'); hold on; axis equal; grid on; grid minor;
hAx = gca; hAx.XLim = [-5 105]; hAx.YLim = [-5 105];
hP = plot(xi,yi,'r*');
else
hP = struct('XData',xi,'YData',yi);
end
hP.XData(1) = origin(1); hP.YData(1) = origin(2);
for ind = 2:numPts
P = InterX([x;y], makeCircle([hP.XData(ind-1),hP.YData(ind-1)],DST/2,cRes));
[~,I] = max(abs(P(1,:)-origin(1)+1i*(P(2,:)-origin(2))));
if doPlot, pause(0.1); end
hP.XData(ind) = P(1,I); hP.YData(ind) = P(2,I);
if doPlot, pause(0.1); delete(hAx.Children(1)); end
end
xi = hP.XData(~isnan(hP.XData)); yi = hP.YData(~isnan(hP.YData));
%% Nested function(s):
function [XY] = makeCircle(cnt, R, nPts)
P = (cnt(1)+1i*cnt(2))+R*exp(linspace(0,1,nPts)*pi*2i);
if doPlot, plot(P,'Color',lines(1)); end
XY = [real(P); imag(P)];
end
end
%% Local function(s):
function tf = isHG2()
try
tf = ~verLessThan('MATLAB', '8.4');
catch
tf = false;
end
end
function P = InterX(L1,varargin)
% DOCUMENTATION REMOVED. For a full version go to:
% https://www.mathworks.com/matlabcentral/fileexchange/22441-curve-intersections
narginchk(1,2);
if nargin == 1
L2 = L1; hF = #lt; %...Avoid the inclusion of common points
else
L2 = varargin{1}; hF = #le;
end
%...Preliminary stuff
x1 = L1(1,:)'; x2 = L2(1,:);
y1 = L1(2,:)'; y2 = L2(2,:);
dx1 = diff(x1); dy1 = diff(y1);
dx2 = diff(x2); dy2 = diff(y2);
%...Determine 'signed distances'
S1 = dx1.*y1(1:end-1) - dy1.*x1(1:end-1);
S2 = dx2.*y2(1:end-1) - dy2.*x2(1:end-1);
C1 = feval(hF,D(bsxfun(#times,dx1,y2)-bsxfun(#times,dy1,x2),S1),0);
C2 = feval(hF,D((bsxfun(#times,y1,dx2)-bsxfun(#times,x1,dy2))',S2'),0)';
%...Obtain the segments where an intersection is expected
[i,j] = find(C1 & C2);
if isempty(i), P = zeros(2,0); return; end
%...Transpose and prepare for output
i=i'; dx2=dx2'; dy2=dy2'; S2 = S2';
L = dy2(j).*dx1(i) - dy1(i).*dx2(j);
i = i(L~=0); j=j(L~=0); L=L(L~=0); %...Avoid divisions by 0
%...Solve system of eqs to get the common points
P = unique([dx2(j).*S1(i) - dx1(i).*S2(j), ...
dy2(j).*S1(i) - dy1(i).*S2(j)]./[L L],'rows')';
function u = D(x,y)
u = bsxfun(#minus,x(:,1:end-1),y).*bsxfun(#minus,x(:,2:end),y);
end
end
Result:
Note that in the animation above, the diameter of the circle (and hence the distance between the red points) is 10 and not 5.
I'm trying to build make a code where an equation is not calculated for some certain values. I have a meshgrid with several values for x and y and I want to include a for loop that will calculate some values for most of the points in the meshgrid but I'm trying to include in that loop a condition that if the points have a specified index, the value will not be calculated. In my second group of for/if loops, I want to say that for all values of i and k (row and column), the value for z and phi are calculated with the exception of the specified i and k values (in the if loop). What I'm doing at the moment is not working...
The error I'm getting is:
The expression to the left of the equals sign is not a valid target for an assignment.
Here is my code at the moment. I'd really appreciate any advice on this! Thanks in advance
U_i = 20;
a = 4;
c = -a*5;
b = a*10;
d = -20;
e = 20;
n = a*10;
[x,y] = meshgrid([c:(b-c)/n:b],[d:(e-d)/n:e]');
for i = 1:length(x)
for k = 1:length(x)
% Zeroing values where cylinder is
if sqrt(x(i,k).^2 + y(i,k).^2) < a
x(i,k) = 0;
y(i,k) = 0;
end
end
end
r = sqrt(x.^2 + y.^2);
theta = atan2(y,x);
z = zeros(length(x));
phi = zeros(length(x));
for i = 1:length(x)
for k = 1:length(x)
if (i > 16 && i < 24 && k > 16 && k <= length(x))
z = 0;
phi = 0;
else
z = U_i.*r.*(1-a^2./r.^2).*sin(theta); % Stream function
phi = U_i*r.*(1+a^2./r.^2).*cos(theta); % Velocity potential
end
end
end
The original code in the question can be rewritten as seen below. Pay attention in the line with ind(17:24,:) since your edit now excludes 24 and you original question included 24.
U_i = 20;
a = 4;
c = -a*5;
b = a*10;
d = -20;
e = 20;
n = a*10;
[x,y] = meshgrid([c:(b-c)/n:b],[d:(e-d)/n:e]');
ind = find(sqrt(x.^2 + y.^2) < a);
x(ind) = 0;
y(ind) = 0;
r = sqrt(x.^2 + y.^2);
theta = atan2(y,x);
ind = true(size(x));
ind(17:24,17:length(x)) = false;
z = zeros(size(x));
phi = zeros(size(x));
z(ind) = U_i.*r(ind).*(1-a^2./r(ind).^2).*sin(theta(ind)); % Stream function
phi(ind) = U_i.*r(ind).*(1+a^2./r(ind).^2).*cos(theta(ind)); % Velocity potential