How i add a line in 2d plot

I'd like to add lines where the values of a(alpha) and b (beta) for which the max value is 4 and for which the max value is greater than 4 as shown by red dashed line and how i label them like in that box in the graph below.

My code

objfun file

function f = threestate2(x,a,b)
c1 =cos(x(1))*(cos(x(5))*(cos(x(9))+cos(x(11)))+cos(x(7))*(cos(x(9))-cos(x(11))))+ ...
    cos(x(3))*(cos(x(5))*(cos(x(9))-cos(x(11)))-cos(x(7))*(cos(x(9))+cos(x(11))));

c2=sin(x(1))*(sin(x(5))*(sin(x(9))*cos(x(2)+x(6)+x(10))+sin(x(11))*cos(x(2)+x(6)+x(12))) ...
+sin(x(7))*(sin(x(9))*cos(x(2)+x(8)+x(10))-sin(x(11))*cos(x(2)+x(8)+x(12))))+ ...
sin(x(3))*(sin(x(5))*(sin(x(9))*cos(x(4)+x(6)+x(10))-sin(x(11))*cos(x(4)+x(6)+x(12))) ...
-sin(x(7))*(sin(x(9))*cos(x(4)+x(8)+x(10))+sin(x(11))*cos(x(4)+x(8)+x(12))));

A1=a^2-b^2;
A2=2*a*b;
f1=A1*c1 +A2*c2;

f=-(f1^2);

my main file

clear 
close 
clc
%x=[x(1),x(2),x(3),x(4),x(5),x(6),x(7),x(8),x(9),x(10),x(11),x(12)]; % angles;

lb=[0,0,0,0,0,0,0,0,0,0,0,0];
ub=[pi,2*pi,pi,2*pi,pi,2*pi,pi,2*pi,pi,2*pi,pi,2*pi];
options = optimoptions(@fmincon,'TolX',10^-12,'MaxIter',1500,'MaxFunEvals',10^8,'Algorithm','sqp','TolFun',10^-8);
a=0:0.01:1;
% b=sqrt(1-a.^2);
w=NaN(size(a));
ww=NaN(size(a));

for k=1:30
    x0=rand([1,12]).*ub*.9986;%7976

for i=1:length(a)
bhelp=1-a(i)^2;
if (bhelp>0 || bhelp==0)
    b=sqrt(bhelp);
       [~,fval]=fmincon(@(x)threestate2(x,a(i),b),x0,[],[],[],[],lb,ub,[],options);
w(i)=sqrt(-fval);
else 
    w(i)=nan;
end 
ww=max(w,ww);
end
x=a.^2;
end
plot(x,ww)
grid on
ylabel('\fontname{Times New Roman} S_{max}(\Psi_{gs})')
xlabel('\fontname{Times New Roman}\alpha^2')

Answer 1

[Thorsten]

You can plot the horizontal line using

 line([min(xlim) max(xlim)], [4 4], 'Color', 'r', 'LineStyle', '--')

If you have computed a and b, you can add the vertical line analogously using

 for x = [a, b]; line([x x], [min(ylim) 4], 'Color', 'r', 'LineStyle', '--'); end

To add the text, use

 ypos = -diff(ylim)/12; % 1/12 of the y size of the plot; adapt if necessary
 for x = [a, b]; text(x, ypos, num2str(x), 'HorizontalAlignment', 'center'); end

[Raja Emlik]

Hello , Thanks for your respond. for the first one it works, but for the second and the third commands it did not work as you can see in the graph below. can you please help me.

[Raja Emlik]

in the second command you wrote , i want the values of a(alpha) and b (beta) which the max value is greater than 4

[Image Analyst]

Use the find() function:

leftIndex = find(ww > 4, 1, 'first');
minAlpha = x(leftIndex);
rightIndex = find(ww > 4, 1, 'last');
maxAlpha = x(rightIndex);

I don't see beta on your graph so I don't know what it is.

[Raja Emlik]

Hi thanks for helpig I tried that but it could not work no thing in the plot.

[Thorsten]

Unfortunately I cannot run your code because I don't have the optimization toolbox. Please provide ww as matfile along with the code you have done so far to do the plot. Otherwise I cannot help you.

[Raja Emlik]

Hello thanks this the ww matrix it is 1*101

ww =

    Columns 1 through 11

      4.0000    3.9992    3.9968    3.9928    3.9872    3.9800    3.9712    3.9608    3.9488    3.9352    3.9200

    Columns 12 through 22

      3.9032    3.8848    3.8648    3.8432    3.8200    3.7952    3.7688    3.7408    3.7112    3.6800    3.6472

    Columns 23 through 33

      3.6128    3.5768    3.5392    3.5000    3.4592    3.4168    3.3728    3.3272    3.2800    3.2312    3.4300

    Columns 34 through 44

      3.5244    3.6175    3.7093    3.7999    3.8890    3.9767    4.0630    4.1477    4.2308    4.3123    4.3922

    Columns 45 through 55

      4.4703    4.5466    4.6210    4.6935    4.7641    4.8326    4.8990    4.9632    5.0252    5.0848    5.1421

    Columns 56 through 66

      5.1968    5.2491    5.2986    5.3455    5.3895    5.4306    5.4686    5.5036    5.5353    5.5636    5.5885

    Columns 67 through 77

      5.6097    5.6272    5.6408    5.6504    5.6557    5.6567    5.6530    5.6446    5.6312    5.6125    5.5883

    Columns 78 through 88

      5.5584    5.5223    5.4798    5.4306    5.3741    5.3100    5.2376    5.1565    5.0659    4.9651    4.8531

    Columns 89 through 99

      4.7289    4.5912    4.4384    4.2686    4.0793    3.8674    3.6284    3.3561    3.3728    3.5272    3.6832

    Columns 100 through 101

      3.8408    4.0000

[Thorsten]

y = [4.0000    3.9992    3.9968    3.9928    3.9872    3.9800    3.9712    3.9608    3.9488    3.9352    3.9200...
      3.9032    3.8848    3.8648    3.8432    3.8200    3.7952    3.7688    3.7408    3.7112    3.6800    3.6472...
     3.6128    3.5768    3.5392    3.5000    3.4592    3.4168    3.3728    3.3272    3.2800    3.2312    3.4300...
    3.5244    3.6175    3.7093    3.7999    3.8890    3.9767    4.0630    4.1477    4.2308    4.3123    4.3922...
    4.4703    4.5466    4.6210    4.6935    4.7641    4.8326    4.8990    4.9632    5.0252    5.0848    5.1421...
 5.1968    5.2491    5.2986    5.3455    5.3895    5.4306    5.4686    5.5036    5.5353    5.5636    5.5885...
  5.6097    5.6272    5.6408    5.6504    5.6557    5.6567    5.6530    5.6446    5.6312    5.6125    5.5883...
   5.5584    5.5223    5.4798    5.4306    5.3741    5.3100    5.2376    5.1565    5.0659    4.9651    4.8531...
       4.7289    4.5912    4.4384    4.2686    4.0793    3.8674    3.6284    3.3561    3.3728    3.5272    3.6832...
       3.8408    4.0000];

x = linspace(0,1,numel(y));   

% find the zero crossings
yval = 4;    
x0 = findzeros(x, y-yval);
alpha = x0(2:3); % exclude zero crossings at the begin and end

% do the plot
plot(x, y)
line([min(xlim) max(xlim)], [yval yval], 'Color', 'r', 'LineStyle', '--')
ypos = min(ylim)-diff(ylim)/20; % 1/12 of the y size of the plot; adapt if necessary
for xi = alpha
  line([xi xi], [min(ylim) yval], 'Color', 'r', 'LineStyle', '--');
  text(xi, ypos, num2str(xi), 'HorizontalAlignment', 'center');
end

using my function findzeros

function x0 = findzeros(x, y)
%FINDZEROS find location of zero crossings with interpolation
%
%   X0 = FINDZEROS(X, Y) finds location X0 of zero crossings of function 
%       Y = f(X) given by vectors X and Y, with interpolation.
%
%   [e-mail]  2016-01-21

% solution adapted from 
% http://www.mathworks.com/matlabcentral/answers/118921-fast-location-of-zero-crossings-with-interpolation

% sample data
if nargin == 0
  x = 1:0.2:2e5;
  y = sin(x);
  %noise = -0.03 + (0.06).*rand(size(clean));
  %y = y + noise;
  x = x(1:100); y = y(1:100);
end

% find position of zero crossings
ind_y0 = find(diff(y>0) ~= 0);
% originall solution 
% ind_y0 = find(y .* circshift(y,[0 1]) < 0); % add - 1 to match my
% ind_y0 used above

N = numel(ind_y0); % number of zero crossings
x0 = nan(1,N); % preallocate for speed
% interpolate zeros
for i = 1:N
    %ixrng = y0(i)-2:y0(i)+2;% non-symmetric surround in original solution
    ind_y0i = ind_y0(i):ind_y0(i) + 1;
    X = x(ind_y0i);
    Y = y(ind_y0i);
    b = [ones(size(X)); X]'\Y';
    x0(i) = -b(1)/b(2);
end

% find zeros at the first and last position
if y(1) == 0, x0 = [x(1) x0]; end
if y(end) == 0, x0 = [x0 x(end)]; end  

if nargout == 0
  plot(x, y, 'o-')
  hline(0)
  vlines(x0, 'Color', 'r')
  clear x0
end