I have a code that computes the max value. this code consists of four variables www is the function of a,b, and c labaled xx, yy, and zz respectively, so my question is how can i plot www against xx,yy, and zz? Thanks for helping
objfun file
function f=W4qubit(x,a,b,c,d)
c1=-cos(x(1))*(cos(x(5))*(cos(x(9))*(cos(x(13))-cos(x(15)))-cos(x(11))*(cos(x(13))+cos(x(15))))+...
cos(x(7))*(cos(x(11))*(cos(x(15))-cos(x(13)))-cos(x(9))*(cos(x(13))+cos(x(15)))))-...
cos(x(3))*(cos(x(5))*(cos(x(11))*(cos(x(15))-cos(x(13)))-cos(x(9))*(cos(x(13))+cos(x(15))))-...
cos(x(7))*(cos(x(9))*(cos(x(13))-cos(x(15)))-cos(x(11))*(cos(x(13))+cos(x(15)))));
c2=cos(x(1))*(cos(x(5))*(sin(x(9))*(sin(x(13))*cos(x(10)-x(14))-sin(x(15))*cos(x(10)-x(16)))-...
sin(x(11))*(sin(x(13))*cos(x(12)-x(14))+sin(x(15))*cos(x(12)-x(16))))+...
cos(x(7))*(sin(x(11))*(sin(x(15))*cos(x(12)-x(16))-sin(x(13))*cos(x(12)-x(14)))-...
sin(x(9))*(sin(x(13))*cos(x(10)-x(14))+sin(x(15))*cos(x(10)-x(16)))))+...
cos(x(3))*(cos(x(5))*(sin(x(11))*(sin(x(15))*cos(x(12)-x(16))-sin(x(13))*cos(x(12)-x(14)))-...
sin(x(9))*(sin(x(13))*cos(x(10)-x(14))+sin(x(15))*cos(x(10)-x(16))))-...
cos(x(7))*(sin(x(9))*(sin(x(13))*cos(x(10)-x(14))-sin(x(15))*cos(x(10)-x(16)))-...
sin(x(11))*(sin(x(13))*cos(x(12)-x(14))+sin(x(15))*cos(x(12)-x(16)))));
c3=cos(x(1))*(sin(x(5))*(cos(x(9))*(sin(x(13))*cos(x(6)-x(14))-sin(x(15))*cos(x(6)-x(16)))-...
cos(x(11))*(sin(x(13))*cos(x(6)-x(14))+sin(x(15))*cos(x(6)-x(16))))+...
sin(x(7))*(cos(x(11))*(sin(x(15))*cos(x(8)-x(16))-sin(x(13))*cos(x(8)-x(14)))-...
cos(x(9))*(sin(x(13))*cos(x(8)-x(14))+sin(x(15))*cos(x(8)-x(16)))))+...
cos(x(3))*(sin(x(5))*(cos(x(11))*(sin(x(15))*cos(x(6)-x(16))-sin(x(13))*cos(x(6)-x(14)))-...
cos(x(9))*(sin(x(13))*cos(x(6)-x(14))+sin(x(15))*cos(x(6)-x(16))))-...
sin(x(7))*(cos(x(9))*(sin(x(13))*cos(x(8)-x(14))-sin(x(15))*cos(x(8)-x(16)))-...
cos(x(11))*(sin(x(13))*cos(x(8)-x(14))+sin(x(15))*cos(x(8)-x(16)))));
c4=cos(x(1))*(sin(x(5))*(sin(x(9))*cos(x(6)-x(10))*(cos(x(13))-cos(x(15)))-sin(x(11))*cos(x(6)-x(12))*(cos(x(13))+cos(x(15))))+...
sin(x(7))*(sin(x(11))*cos(x(8)-x(12))*(cos(x(15))-cos(x(13)))-sin(x(9))*cos(x(8)-x(10))*(cos(x(13))+cos(x(15)))))+...
cos(x(3))*(sin(x(5))*(sin(x(11))*cos(x(6)-x(12))*(cos(x(15))-cos(x(13)))-sin(x(9))*cos(x(6)-x(10))*(cos(x(13))+cos(x(15))))-...
sin(x(7))*(sin(x(9))*cos(x(8)-x(10))*(cos(x(13))-cos(x(15)))-sin(x(11))*cos(x(8)-x(12))*(cos(x(13))+cos(x(15)))));
c5=sin(x(1))*(cos(x(5))*(cos(x(9))*(sin(x(13))*cos(x(2)-x(14))-sin(x(15))*cos(x(2)-x(16)))-...
cos(x(11))*(sin(x(13))*cos(x(2)-x(14))+sin(x(15))*cos(x(2)-x(16))))+...
cos(x(7))*(cos(x(11))*(sin(x(15))*cos(x(2)-x(16))-sin(x(13))*cos(x(2)-x(14)))-...
cos(x(9))*(sin(x(13))*cos(x(2)-x(14))+sin(x(15))*cos(x(2)-x(16)))))+...
sin(x(3))*(cos(x(5))*(cos(x(11))*(sin(x(15))*cos(x(4)-x(16))-sin(x(13))*cos(x(4)-x(14)))-...
cos(x(9))*(sin(x(13))*cos(x(4)-x(14))+sin(x(15))*cos(x(4)-x(16))))-...
cos(x(7))*(cos(x(9))*(sin(x(13))*cos(x(4)-x(14))-sin(x(15))*cos(x(4)-x(16)))-...
cos(x(11))*(sin(x(13))*cos(x(4)-x(14))+sin(x(15))*cos(x(4)-x(16)))));
c6=sin(x(1))*(cos(x(5))*(sin(x(9))*cos(x(2)-x(10))*(cos(x(13))-cos(x(15)))-sin(x(11))*cos(x(2)-x(12))*(cos(x(13))+cos(x(15))))+...
cos(x(7))*(sin(x(11))*cos(x(2)-x(12))*(cos(x(15))-cos(x(13)))-sin(x(9))*cos(x(2)-x(10))*(cos(x(13))+cos(x(15)))))+...
sin(x(3))*(cos(x(5))*(sin(x(11))*cos(x(4)-x(12))*(cos(x(15))-cos(x(13)))-sin(x(9))*cos(x(4)-x(10))*(cos(x(13))+cos(x(15))))-...
cos(x(7))*(sin(x(9))*cos(x(4)-x(10))*(cos(x(13))-cos(x(15)))-sin(x(11))*cos(x(4)-x(12))*(cos(x(13))+cos(x(15)))));
c7=sin(x(1))*(sin(x(5))*cos(x(2)-x(6))*(cos(x(9))*(cos(x(13))-cos(x(15)))-cos(x(11))*(cos(x(13))+cos(x(15))))-...
sin(x(7))*cos(x(2)-x(8))*(cos(x(11))*(cos(x(15))-cos(x(13)))-cos(x(9))*(cos(x(13))+cos(x(15)))))+...
sin(x(3))*(sin(x(5))*cos(x(4)-x(6))*(cos(x(11))*(cos(x(15))-cos(x(13)))-cos(x(9))*(cos(x(13))+cos(x(15))))-...
sin(x(7))*cos(x(4)-x(8))*(cos(x(9))*(cos(x(13))-cos(x(15)))-cos(x(11))*(cos(x(13))+cos(x(15)))));
A2=2*a*b;
A3=2*a*c;
A4=2*b*c;
A5=2*a*d;
A6=2*b*d;
A7=2*c*d;
f1=c1+A2*c2+A3*c3+A4*c4+A5*c5+A6*c6+A7*c7;
f=-(f1^2);
my main file of the code
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),x(13),x(14),x(15),x(16)]; % angles;
lb=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0];
ub=[pi,2*pi,pi,2*pi,pi,2*pi,pi,2*pi,pi,2*pi,pi,2*pi,pi,2*pi,pi,2*pi];
options = optimoptions(#fmincon,'TolX',10^-12,'MaxIter',1500,'MaxFunEvals',10^8,'Algorithm','sqp','TolFun',10^-8);
a=0:0.1:1;
b=0:0.1:1;
c=0:0.1:1;
w=NaN(length(a),length(b),length(c));
ww=NaN(length(a),length(b),length(c));
www=NaN(length(a),length(c));
for k=1:100
x0=rand([1,16]).*ub*.9986;%7976
for i=1:length(a)
for j=1:length(b)
for l=1:length(c)
dhelp=1-(a(i)^2)-(b(j)^2)-(c(l)^2);
if (dhelp>0 || dhelp==0)
d=sqrt(dhelp);
[~,fval]=fmincon(#(x)W4qubit(x,a(i),b(j),c(l),d),x0,[],[],[],[],lb,ub,[],options);
w(i,j,l)=sqrt(-fval);
else
w(i,j,l)=nan;
end
ww=max(w,ww);
end
end
end
end
www=max(ww,[],3);
yy=b.^2;xx=a.^2;zz=c.^2;
meshc(xx,yy,www)
grid on
zlabel('\fontname{Times New Roman} M_{max}')
xlabel('\fontname{Times New Roman}\alpha^2')
ylabel('\fontname{Times New Roman}\gamma^2')
%title('fontname{Times New Roman} Maximum of the Svetlichny operator. Method 1 (alpha|0001>+beta|0010>+gamma|1000>)')
Not sure, but doesn't
plot(www,[xx;yy;zz]);
do the job for you? I do not have the optimization toolbox, so I can't test your script. But in principle, this should work.
Related
I am trying to control motor torque and am using a workspace variable in Simulink and want to output similar variable to workspace.
I have size(T_u)=[3, 91] whereas the output I am getting from the simulation has size [91, 90]
I am unable to understand why this is so.
Code that I am using:
load('Motor_Param.mat')
t = 1:0.1:10;
T_o = [0.05*(10-t);0.04*(10-t);0.03*(10-t)];
T_d = zeros(size(T_o));
T_e = (T_d - T_o);
C_PD = pid(100,0,10,100);
T_u = zeros(size(T_e));
for k=1:size(T_e,1)
T_u(k,:) = lsim(C_PD,T_e(k,:),t);
%T_u(1,:)= -45.0450000000000 -44.5444552724092 -44.0439110892737 -43.5433674500493 -43.0428243541925 -42.5422818011600 -42.0417397904094 -41.5411983213986 -41.0406573935862 -40.5401170064312 -40.0395771593933 -39.5390378519326 -39.0384990835098 -38.5379608535861 -38.0374231616233 -37.5368860070837 -37.0363493894301 -36.5358133081260 -36.0352777626353 -35.5347427524223 -35.0342082769522 -34.5336743356904 -34.0331409281029 -33.5326080536564 -33.0320757118181 -32.5315439020554 -32.0310126238368 -31.5304818766308 -31.0299516599067 -30.5294219731343 -30.0288928157839 -29.5283641873264 -29.0278360872332 -28.5273085149760 -28.0267814700274 -27.5262549518604 -27.0257289599483 -26.5252034937652 -26.0246785527857 -25.5241541364848 -25.0236302443380 -24.5231068758215 -24.0225840304120 -23.5220617075865 -23.0215399068228 -22.5210186275990 -22.0204978693939 -21.5199776316868 -21.0194579139572 -20.5189387156857 -20.0184200363529 -19.5179018754402 -19.0173842324294 -18.5168671068029 -18.0163504980435 -17.5158344056347 -17.0153188290603 -16.5148037678048 -16.0142892213531 -15.5137751891906 -15.0132616708034 -14.5127486656779 -14.0122361733011 -13.5117241931606 -13.0112127247442 -12.5107017675407 -12.0101913210389 -11.5096813847285 -11.0091719580996 -10.5086630406426 -10.0081546318487 -9.50764673120954 -9.00713933821711 -8.50663245236405 -8.00612607314350 -7.50562020004906 -7.00511483257487 -6.50460997021554 -6.00410561246623 -5.50360175882257 -5.00309840878072 -4.50259556183731 -4.00209321748951 -3.50159137523496 -3.00109003457184 -2.50058919499879 -2.00008885601498 -1.49958901712007 -0.999089677814209 -0.498590837598075 0.00190750402718064
a = sim('Motor_Control','SimulationMode','normal');
out = a.get('T_l')
end
Link to .mat and .slx files is: https://drive.google.com/open?id=1kGeA4Cmt8mEeM3ku_C4NtXclVlHsssuw
If you set the Save format in the To Workspace block to Timeseries the output will have the dimensions of the signal times the number of timesteps.
In your case I activated the option Display->Signals & Ports->Signal dimensions and the signal dimensions in your model look like this:
So the signal that you output to the workspace has the size 90. Now if I print size(out.Data) I get
ans = 138 90
where 90 is the signal dimension and 138 is the number of timesteps in your Simulink model.
You could now use the last row of the data (which has the length 90) and add it to your array.
I edit your code, the code has [21,3] output size. "21" is coming from (t_final*1/sample_time+1)
In your code, time t should start from 0.
Motor_Control.slx model has 0.1 sample time if you run the model for a 9 second, the output file has 91 samples for each signal and that's why you have [91, 90] sized output. I download from your drive link and this Simulink model has 2 sec. simulation.
T_u is used as an input of the Simulink model, it is not constant so T_u must be time series.
The edited code is below;
load('Motor_Param.mat')
t = 0:0.1:10;
T_o = [0.05*(10-t);0.04*(10-t);0.03*(10-t)];
T_d = zeros(size(T_o));
T_e = (T_d - T_o);
C_PD = pid(100,0,10,100);
T_u = timeseries(zeros(size(T_e)),t);
for k=1:size(T_e,1)
T_u.Data(k,:) = lsim(C_PD,T_e(k,:),t);
a = sim('Motor_Control','SimulationMode','normal');
out = a.get('T_l')
end
I am trying to read from a file and display the data in rows 6, 11, 111 and 127 in Matlab. I could not figure out how to do it. I have been searching Matlab forums and this platform for an answer. I used fscanf, textscan and other functions but they did not work as intended. I also used a for loop but again the output was not what I wanted. I can now only read one row and display it. Simply I want to display all of them(data in rows given above) at the same time. How can I do that?
matlab code
n = [0 :1: 127];
%% Problem 1
figure
x1 = cos(0.17*pi*n)
%it creates file and writes content of x1 to the file
fileID = fopen('file.txt','w');
fprintf(fileID,'%d \n',x1);
fclose(fileID);
%line number can be changed in order to obtain wanted values.
fileID = fopen('file.txt');
line = 6;
C = textscan(fileID,'%s',1,'delimiter','\n', 'headerlines',line-1);
celldisp(C)
fclose(fileID);
and this is the file
1
8.607420e-01
4.817537e-01
-3.141076e-02
-5.358268e-01
-8.910065e-01
-9.980267e-01
-8.270806e-01
-4.257793e-01
9.410831e-02
5.877853e-01
9.177546e-01
9.921147e-01
7.901550e-01
3.681246e-01
-1.564345e-01
-6.374240e-01
-9.408808e-01
-9.822873e-01
-7.501111e-01
-3.090170e-01
2.181432e-01
6.845471e-01
9.602937e-01
9.685832e-01
7.071068e-01
2.486899e-01
-2.789911e-01
-7.289686e-01
-9.759168e-01
-9.510565e-01
-6.613119e-01
-1.873813e-01
3.387379e-01
7.705132e-01
9.876883e-01
9.297765e-01
6.129071e-01
1.253332e-01
-3.971479e-01
-8.090170e-01
-9.955620e-01
-9.048271e-01
-5.620834e-01
-6.279052e-02
4.539905e-01
8.443279e-01
9.995066e-01
8.763067e-01
5.090414e-01
-4.288121e-15
-5.090414e-01
-8.763067e-01
-9.995066e-01
-8.443279e-01
-4.539905e-01
6.279052e-02
5.620834e-01
9.048271e-01
9.955620e-01
8.090170e-01
3.971479e-01
-1.253332e-01
-6.129071e-01
-9.297765e-01
-9.876883e-01
-7.705132e-01
-3.387379e-01
1.873813e-01
6.613119e-01
9.510565e-01
9.759168e-01
7.289686e-01
2.789911e-01
-2.486899e-01
-7.071068e-01
-9.685832e-01
-9.602937e-01
-6.845471e-01
-2.181432e-01
3.090170e-01
7.501111e-01
9.822873e-01
9.408808e-01
6.374240e-01
1.564345e-01
-3.681246e-01
-7.901550e-01
-9.921147e-01
-9.177546e-01
-5.877853e-01
-9.410831e-02
4.257793e-01
8.270806e-01
9.980267e-01
8.910065e-01
5.358268e-01
3.141076e-02
-4.817537e-01
-8.607420e-01
-1
-8.607420e-01
-4.817537e-01
3.141076e-02
5.358268e-01
8.910065e-01
9.980267e-01
8.270806e-01
4.257793e-01
-9.410831e-02
-5.877853e-01
-9.177546e-01
-9.921147e-01
-7.901550e-01
-3.681246e-01
1.564345e-01
6.374240e-01
9.408808e-01
9.822873e-01
7.501111e-01
3.090170e-01
-2.181432e-01
-6.845471e-01
-9.602937e-01
-9.685832e-01
-7.071068e-01
-2.486899e-01
2.789911e-01
Assuming the file is not exceedingly large, the simplest way would probably be read the entire file & index the output to your desired lines.
line = [6 11 111 127];
fileID = fopen('file.txt');
C = textscan(fileID,'%s','delimiter','\n');
fclose(fileID);
disp(C{1}(line))
I have the following matrix which rows are points sampled from a function
f = [ -3.7850 -11.5240
-3.7753 -11.4822
-3.7680 -11.5427
-3.7592 -11.5607
-3.7576 -11.5461
-3.7454 -11.5887
-3.7386 -11.4070
-3.7358 -11.4450
-3.7289 -11.5511
-3.7254 -11.3713
-3.7122 -11.4515
-3.6820 -11.5582
-3.6758 -11.5946
-3.6732 -11.5823
-3.6679 -11.6365
-3.6487 -11.3525
-3.6424 -11.2745
-3.6322 -11.3478
-3.6235 -11.6379
-3.6159 -11.6308
-3.5619 -11.1980
-3.5550 -11.2284
-3.5544 -11.5925
-3.5147 -11.6578
-3.5041 -11.6756
-3.4860 -11.1550
-3.4654 -11.6341
-3.4550 -11.1329
-3.3802 -11.6701
-3.3691 -11.1083
-3.3541 -11.0790
-3.3485 -11.5887
-3.3006 -11.6384
-3.2481 -11.5570
-3.2459 -11.0268
-3.2441 -10.9314
-3.2301 -11.5225
-3.2270 -10.8832
-3.1543 -10.8612
-3.1528 -11.5490
-3.1167 -11.5021
-3.1102 -10.8255
-3.0645 -11.5618
-2.9967 -11.5420
-2.9898 -10.8136
-2.9645 -10.7107
-2.9211 -11.4197
-2.9175 -10.6389
-2.8558 -10.6015
-2.8327 -11.5108
-2.7768 -11.4501
-2.7392 -10.5492
-2.7217 -11.4230
-2.6988 -10.4724
-2.6235 -11.3226
-2.6196 -11.3806
-2.5772 -10.4518
-2.5458 -10.4317
-2.5014 -10.3176
-2.4832 -11.3822
-2.4778 -10.2456
-2.4029 -11.2907
-2.3723 -10.3002
-2.3590 -11.2911
-2.3491 -10.2110
-2.2756 -11.2318
-2.2554 -10.1204
-2.2542 -10.1411
-2.2181 -11.2300
-2.1982 -9.9584
-2.1645 -9.7938
-2.1541 -11.1682
-2.1476 -9.8235
-2.1451 -9.9205
-2.1280 -10.0064
-2.1269 -9.8947
-2.0898 -9.7926
-2.0781 -11.1293
-1.9985 -11.0985
-1.9249 -11.0443
-1.8220 -11.0419
-1.7359 -11.0043
-1.6924 -10.9775
-1.6049 -10.9579
-1.5275 -10.9339
-1.4757 -10.9113
-1.4122 -10.8854
-1.3245 -10.8908
-1.2936 -10.7893
-1.2091 -10.8121
-1.1575 -10.8064
-1.1237 -10.7105
-1.0571 -10.7724
-1.0217 -10.7096
-0.9717 -10.6984
-0.9447 -10.7103
-0.9120 -10.6687
-0.8908 -10.6670]
Plotting by plot(f(:,1),f(:,2),'+') it is clear that the function has a V-shape. However, I need to plot it continuously, but doing plot(f(:,1),f(:,2)) results in a zig-zag function. How can I plot the points as I want to? (beside sorting them manually)
You could try rotating your data, sorting it and rotating it back. e.g:
theta = -1;
R = [cos(theta) -sin(theta);sin(theta) cos(theta)];
f2 = f*R;
f3 = sortrows(f2);
f4 = f3*R';
plot(f4(:,1),f4(:,2),'-',f(:,1),f(:,2),'+')
You can tweak theta to change the angle, which affects the sort order, I just took a guess that -1 is about right.
In the first scenario link the solution provided was excellent and it did work. However I tried to make it work with another function and I ended up with nothing close to what is expected. My code so far:
yn = [-1.20449 -1.14398 -1.02273 -0.962285 -0.90203 -0.841474 -0.780881...
-0.720346 -0.659896 -0.579599 -0.539505 -0.478662 -0.418963 -0.35859...
-0.299039 -0.238886 -0.179108 -0.118999 -0.058841 -0.006249 -0.06189...
0.006332 0.04056 0.11813 0.1776723 0.238403 0.29827 0.358396...
0.418149 0.4786 0.478154 0.538114 0.53862 0.598954 0.659804...
0.720267 0.781026 0.8412 0.901548 0.962022 1.022567 1.083291...
1.143653];
xn = linspace(-22,22,43)';
yn = yn';
fn = fit(xn,yn,'poly1')
figure()
hold all
plot(fn,xn,yn)
yn_fit = f(xn);
error = yn - yn_fit;
figure()
plot(xn, error,'k')
I would appreciate any help.
Suppose that we have following array:
0.196238259763928
0.0886250228175519
0.417543614272817
0.182403230538167
0.136500793051860
0.389922187581014
0.0344012946153299
0.381603315802419
0.0997542838649466
0.274807632628596
0.601652859233616
0.209431489000677
0.396925294300794
0.0351587496999554
0.177321874549738
0.369200511917405
0.287108838007101
0.477076452316346
0.127558716868438
0.792431584110476
0.0459982776925879
0.612598437936600
0.228340227044324
0.190267907472804
0.564751537228850
0.00269368929400299
0.940538666131177
0.101588565140294
0.426175626669060
0.600215481734847
0.127859067121782
0.985881201195063
0.0945679498528667
0.950077461673118
0.415212985598547
0.467423473845033
1.24336273213410
0.0848695928658021
1.84522775800633
0.289288949281834
1.38792131632743
1.73186592736729
0.554254947026916
3.46075557122590
0.0872957577705428
4.93259798197976
2.03544238985229
3.71059303259615
8.47095716918618
0.422940369071662
25.2287636895831
4.14535369056670
63.7312173032838
152.080907190007
1422.19492782494
832.134744027851
0.0220089962114756
60.8238733887811
7.71053463387430
10.4151913932115
11.3141744831953
0.988978595613829
8.65598040591953
0.219820300144944
3.92785491164888
2.28370963778411
1.60232807621444
2.51086405960291
0.0181622519984990
2.27469230188760
0.487809730727909
0.961063613990814
1.90435488292485
0.515640996120482
1.25933693517960
0.0953200831348589
1.52851575480462
0.582109930768162
0.933543409438383
0.717947488528521
0.0445235241119612
1.21157308704582
0.0942421028083462
0.536069075206508
0.821400666720535
0.308956823975938
1.28706199713640
0.0339217632187507
1.19575886464231
0.0853733920496230
0.736744959694641
0.635218502184121
0.262305581223588
0.986899895695809
0.0398800891449550
0.758792061180657
0.134279188964854
0.442531129290843
0.542782326712391
0.377221037448628
0.704787750202814
0.224180325609783
0.998785634315287
0.408055416702400
0.329684702125840
0.522384453408780
0.154542718256493
0.602294251721841
0.240357912028348
0.359040779285709
0.525224294805813
0.427539247203335
0.624034405807298
0.298184846094056
0.498659616687732
0.0962076792277457
0.430092706132805
0.656212420735658
0.278310520474744
0.866037361133916
0.184971060800812
0.481149730712771
0.624405636807668
0.382388147099945
0.435350646037440
0.216499523971397
1.22960953802959
0.330841706900755
0.891793067878849
0.628241046456751
0.278687691121678
1.06358076764171
0.365652714373067
1.34921178081181
0.652888708375276
0.861138633227739
1.02878577330537
0.591174450919664
1.93594290806582
0.497631035062465
1.14486512201656
0.978067581547298
0.948931658572253
2.01004088022982
0.917415940349743
2.24124811810385
1.42691656876436
2.15636037453584
1.92812357585099
1.12786835077183
4.81721425534142
1.70055431306602
4.87939454466131
3.90293284926105
5.16542230018432
10.5783535493504
1.74023535081791
27.0572221453758
7.78813114379733
69.2528169436690
167.769806437531
1490.03057130613
869.247150795648
3.27543244752518
62.3527480644562
9.74192115073051
13.6074209231800
10.5686495478844
7.70239986387120
9.62850426896699
9.85304975304259
7.09026325332085
12.8782040428502
16.3163128995995
7.00070066635845
74.1532966917877
4.80506505312457
1042.52337489620
1510.37374385290
118.514435606795
80.7915675273571
2.96352221859211
27.7825124315786
1.55102367292252
8.66382951478539
5.02910503820560
1.25219344189599
7.72195587189507
0.356973215117373
6.06702456628919
1.01953617014621
2.76489896186652
3.35353608882459
0.793376336025486
4.90341095941571
0.00742857354167949
5.07665716731356
1.16863474789604
4.47635486149688
4.33050121578669
2.42974020115261
9.79494608790444
0.0568839453395247
22.9153086380666
4.48791386399205
59.6962194708933
97.8636220152072
1119.97978883924
806.144299041605
7.33252581243942
57.0699524267842
0.900104994068117
15.2791339483160
3.31266162202546
3.20809490583211
5.36617545130941
0.648122925703121
3.90480316969632
0.0338850542128927
2.58828964019220
0.543604662856673
1.16385064506181
1.01835324272839
0.172915006573539
1.55998411282069
0.00221570175453666
1.14803074836796
0.0769335878967426
0.421762398811163
0.468260146832541
0.203765185125597
0.467641715366303
0.00142988680149041
0.698088976126660
0.0413316717103625
0.190548157914037
0.504713663418641
0.325697764871308
0.375910057283262
0.123307135682793
0.331115262928959
0.00263961045860704
0.204555648718379
0.139008751575803
0.182936666944843
0.154943314848474
0.0840483576044629
0.293075999812128
0.00306911699543199
0.272993318570981
0.0864711337990886
0.280495615619829
0.0910123210559269
0.148399626645134
0.141945002415500
0.0512001531781583
0.0295283557338525
In MATLAB it is very easy to find peaks using findpeaks, like so:
[pxx_peaks,location] = findpeaks(Pxx);
If we plot pxx_peaks, we get
plot(pxx_peaks)
Of course, besides these peaks, there are smaller peaks which are not shown on the picture, but my goal is to find all peaks which are 95-96% above all other peaks.
I have tried like this:
>> average = mean(pxx_peaks);
>> stand = std(pxx_peaks);
>> final_peaks = pxx_peaks( pxx_peaks > average + 3*stand );
The result of this is
>> final_peaks
final_peaks =
1.0e+03 *
1.4222
1.4900
1.5104
1.1200
but how to return their corresponding locations? I want to write it as one m-file, so please help me
EDIT
also please help me in this question: can I parameterize the confidence interval? For instance instead of 95%, I want to find peaks that are 60% above then other peaks, is it possible?
Note that 3σ ≈ 99.73%
As for your first question, it's easy, you just have to keep track of the locations in the same way as you do for the peaks:
inds = pxx_peaks > mean(pxx_peaks) + 3*std(pxx_peaks);
final_peaks = pxx_peaks(inds);
final_locations = location(inds);
plot(Pxx), hold on
plot(final_locations, final_peaks, 'r.')
As for your second question, that's a little more complicated. If you want to formulate it like you say, you'll have to convert a desired percentage to the correct number of σ. That involves an integration of the standard normal, and a root finding:
%// Convert confidence interval percentage to number-of-sigmas
F = #(P) fzero(#(sig) quadgk(#(x) exp(-x.^2/2),-sig,+sig)/sqrt(2*pi) - P/100, 1);
% // Repeat with the desired percentage
inds = pxx_peaks > mean(pxx_peaks) + F(63)*std(pxx_peaks); %// 63%
final_peaks = pxx_peaks(inds);
final_locations = location(inds);
plot(final_locations, final_peaks, 'r.')