Plot set of lines in Matlab - matlab

I have a matrix with a set points, divided in groups of 10 (example below). Each group of points corresponds to a line; how can I plot all lines?
Here is an example of how the matrix is organised:
y = [
109.41 110.55 111.69 112.83 113.96 115.10 116.24 117.37 118.51 119.65
56.87 56.21 55.55 54.89 54.23 53.57 52.91 52.25 51.5 50.92
-265.16 -263.07 -260.99 -258.90 -256.81 -254.73 -252.64 -250.55 -248.47 -246.38 ];
This is the code I am using to produce the matrix and try to plot all the lines:
for line = (1:n)
for point = (1:10)
y(line,point) = [Y(line)-point*sin(Omega(line))];
end
end
plot(0:1000,y,'linewidth',2)


I am not surprised you got the error you have with the code you are using. size(0:1000) is 1x1001. What size is your matrix y?
With the data you have provided, I would use the following:
y = [109.41 110.55 111.69 112.83 113.96 115.10 116.24 117.37 118.51 119.65; ...
56.87 56.21 55.55 54.89 54.23 53.57 52.91 52.25 51.5 50.92; ...
-265.16 -263.07 -260.99 -258.90 -256.81 -254.73 -252.64 -250.55 -248.47 -246.38];
plot(0:100:900,y,'linewidth',2) % size(0:100:900) is 1x10 and size(y) is 3x10 so we're good
This gives the following result (in Octave, should be exactly the same in MATLAB):


Assuming Y is of size 1-by-n, Omega is of size 1-by-n, then you can avoid the nested loop:
y = bsxfun( #minus, Y, bsxfun( #times, (1:10)', sin( Omega ) ) ); %'
plot( 1:n, y, 'LineWidth', 2 );

Related

3d Graphing Data in matlab and changing the axis values

I am trying to do a 3d graph of a excel file that is 343 by 81 cells, The first column needs to be the X and the first row needs to be the Y and the remaining matrix needs to be the Z. I have the data successfully imported from excel and I create a matrix of the first column called energy (343,1)(x-axis), while creating a row matrix (1, 81) called Time Delay(y-axis) and a (343,81) matrix where the first column and row is zero called Absorbance Change(Z-axis). I've got the proper 3d graph that I need but I need the axes shown in the graph to be that of the Energy and Time Delay instead of the indices of the Absorbance Change matrix. I am putting the relevant portion of the code below as well as a picture of the graph:
EnergyString = dataArray{:, 1};
EnergyString(1,1) = {'0'};
Energy = str2double(EnergyString);
%Energy = [ Energy, zeros(343, 80) ];
TimeDelay = [ z1(1,1), z2(1,1), z3(1,1), z4(1,1), z5(1,1), z6(1,1), z7(1,1), z8(1,1), z9(1,1), z10(1,1), z11(1,1), z12(1,1), z13(1,1), z14(1,1), z15(1,1), z16(1,1), z17(1,1), z18(1,1), z19(1,1), z20(1,1), z21(1,1), z22(1,1), z23(1,1), z24(1,1), z25(1,1), z26(1,1), z27(1,1), z28(1,1), z29(1,1), z30(1,1), z31(1,1), z32(1,1), z33(1,1), z34(1,1), z35(1,1), z36(1,1), z37(1,1), z38(1,1), z39(1,1), z40(1,1), z41(1,1), z42(1,1), z42(1,1), z43(1,1), z44(1,1), z45(1,1), z46(1,1), z47(1,1), z48(1,1), z49(1,1), z50(1,1), z51(1,1), z52(1,1), z53(1,1), z54(1,1), z55(1,1), z56(1,1), z57(1,1), z58(1,1), z59(1,1), z60(1,1), z61(1,1), z62(1,1), z63(1,1), z64(1,1), z65(1,1), z66(1,1), z67(1,1), z68(1,1), z69(1,1), z70(1,1), z71(1,1), z72(1,1), z73(1,1), z74(1,1), z75(1,1), z76(1,1), z77(1,1), z78(1,1), z79(1,1), z80(1,1) ];
%TimeDelay = [ TimeDelay; zeros(342, 81)];
startRow formatSpec filename fileID delimiter ans EnergyString Alpha Beta Gamma Delta Epsilon Zeta Eta Theta Iota Kappa Lambda Mu Nu Xi Omicron Pi Rho Sigma Tau Upsilon Phi Chi Psi Omega AlphaAlpha AlphaBeta AlphaGamma AlphaDelta AlphaEpsilon AlphaZeta AlphaEta AlphaTheta AlphaIota AlphaKappa AlphaLambda AlphaMu AlphaNu AlphaXi AlphaOmicron AlphaPi AlphaRho AlphaSigma AlphaTau AlphaUpsilon AlphaPhi AlphaChi AlphaPsi AlphaOmega BetaAlpha BetaBeta BetaGamma BetaDelta BetaEpsilon BetaZeta BetaEta BetaTheta BetaIota BetaKappa BetaLambda BetaMu BetaNu BetaXi BetaOmicron BetaPi BetaRho BetaSigma BetaTau BetaUpsilon BetaPhi BetaChi BetaPsi BetaOmega GammaAlpha GammaBeta GammaGamma GammaDelta GammaEpsilon GammaZeta GammaEta GammaTheta; %Delete Excess Varaible
AbsorbanceChange = [ zeros(343, 1), z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, z13, z14, z15, z16, z17, z18, z19, z20, z21, z22, z23, z24, z25, z26, z27, z28, z29, z30, z31, z32, z33, z34, z35, z36, z37, z38, z39, z40, z41, z42, z43, z44, z45, z46, z47, z48, z49, z50, z51, z52, z53, z54, z55, z56, z57, z58, z59, z60, z61, z62, z63, z64, z65, z66, z67, z68, z69, z70, z71, z72, z73, z74, z75, z76, z77, z78, z79, z80];
AbsorbanceChange(1,:) = 0;
clear z1 z2 z3 z4 z5 z6 z7 z8 z9 z10 z11 z12 z13 z14 z15 z16 z17 z18 z19 z20 z21 z22 z23 z24 z25 z26 z27 z28 z29 z30 z31 z32 z33 z34 z35 z36 z37 z38 z39 z40 z41 z42 z43 z44 z45 z46 z47 z48 z49 z50 z51 z52 z53 z54 z55 z56 z57 z58 z59 z60 z61 z62 z63 z64 z65 z66 z67 z68 z69 z70 z71 z72 z73 z74 z75 z76 z77 z78 z79 z80;
mesh(AbsorbanceChange)
colorbar
title('WS2-Perovskite-image')
xlabel('Energy') % x-axis label
ylabel('Time-delay') % y-axis label
zlabel('Absorbance Change')

When I type help mesh in MATLAB I see, among other thins, this:
mesh(x,y,Z) and mesh(x,y,Z,C), with two vector arguments replacing
the first two matrix arguments, must have length(x) = n and
length(y) = m where [m,n] = size(Z). In this case, the vertices
of the mesh lines are the triples (x(j), y(i), Z(i,j)).
Note that x corresponds to the columns of Z and y corresponds to
the rows.
Thus, you can do
mesh(Energy, TimeDelay, AbsorbanceChange);
I don't know how you read the data from file, but there is a better way than specifying each cell individually in your code.

plot interpolate a curve between 2 different types of curves in matlab

I have the following data that predicts a curve in the middle of the two curves which has different equation and datas.I also need to spline and smothen the curve of the middle curve
I've tried searching other codes here in stackoverflow but this is the most close to the right solution. So far the plot for the two curve is right but the interpolated point gives me wrong plot.
Im trying to find the plot for val=30 given that (a25,vel25)=25 and (a50,vel50)=50. Please help me troubleshoot and get a table of data (x,y) for the generated interpolated curve. Thanks for your help
generated plot using this program
a50=[1.05
0.931818182
0.931818182
0.968181818
1.045454545
1.136363636
1.354545455
1.568181818
1.718181818
1.945454545
2.159090909
2.454545455
2.772727273
];
vel50=[0.85
0.705555556
0.605555556
0.533333333
0.472222222
0.45
0.427777778
0.45
0.477777778
0.533333333
0.611111111
0.711111111
0.827777778
];
a25=[0.5
0.613636364
0.686363636
0.795454545
0.918181818
0.963636364
1.090909091
1.236363636
1.304545455
1.431818182
1.545454545
1.659090909
1.818181818
];
vel25=[0.425555556
0.354444444
0.302222222
0.266666667
0.233333333
0.226666667
0.211111111
0.222222222
0.237777778
0.266666667
0.311111111
0.35
0.402222222
];
plot(a25,vel25,'b-');
hold on
plot(a50,vel50,'g-');
minX = min([a25 a50]);
maxX = max([a25,a50]);
xx = linspace(minX,maxX,100);
vel25_inter = interp1(a25,vel25,xx);
vel50_inter = interp1(a50,vel50,xx);
val = 30; % The interpolated point
interpVel = vel25_inter + ((val-25).*(vel50_inter-vel25_inter))./(50-25);
plot(xx,interpVel,'r-');

The question and answer linked in comment still apply and can be a solution.
In your case, it is not so direct because your data are not on the same grid and some are not monotonic, but once they are packaged properly, the easiest solution is still to use griddata.
By packaged properly, I mean finding the maximum common interval (on x, or what you call a), so the data can be interpolated between curve without producing NaNs.
This seems to work:
The red dashed line is the values interpolated at val=30, all the other lines are interpolations for values between 25 to 50.
The code to get there:
% back up original data, just for final plot
bkp_a50 = a50 ; bkp_vel50 = vel50 ;
% make second x vector monotonic
istart = find( diff(a50)>0 , 1 , 'first') ;
a50(1:istart-1) = [] ;
vel50(1:istart-1) = [] ;
% prepare a 3rd dimension vector (from 25 to 50)
T = [repmat(25,size(a25)) ; repmat(50,size(a50)) ] ;
% merge all observations together
A = [ a25 ; a50] ;
V = [vel25 ; vel50] ;
% find the minimum domain on which data can be interpolated
% (anything outside of that will return NaN)
Astart = max( [min(a25) min(a50)] ) ;
Astop = min( [max(a25) max(a50)] ) ;
% use the function 'griddata'
[TI,AI] = meshgrid( 25:50 , linspace(Astart,Astop,10) ) ;
VI = griddata(T,A,V,TI,AI) ;
% plot all the intermediate curves
plot(AI,VI)
hold on
% the original curves
plot(a25,vel25,'--k','linewidth',2)
plot(bkp_a50,bkp_vel50,'--k','linewidth',2)
% Highlight the curve at T = 30 ;
c30 = find( TI(1,:) == 30 ) ;
plot(AI(:,c30),VI(:,c30),'--r','linewidth',2)

There were quite a few issues with your code that's why it was not executing properly. I have just made very little changes to your code and made it running,
clc
%13
a50=[1.05
0.931818182
0.932
0.968181818
1.045454545
1.136363636
1.354545455
1.568181818
1.718181818
1.945454545
2.159090909
2.454545455
2.772727273
];
%13
vel50=[0.85
0.705555556
0.605555556
0.533333333
0.472222222
0.45
0.427777778
0.45
0.477777778
0.533333333
0.611111111
0.711111111
0.827777778
];
%13
a25=[0.5
0.613636364
0.686363636
0.795454545
0.918181818
0.963636364
1.090909091
1.236363636
1.304545455
1.431818182
1.545454545
1.659090909
1.818181818
];
%13
vel25=[0.425555556
0.354444444
0.302222222
0.266666667
0.233333333
0.226666667
0.211111111
0.222222222
0.237777778
0.266666667
0.311111111
0.35
0.402222222
];
plot(a25,vel25,'b-');
hold on
plot(a50,vel50,'g-');
minX = min([a25 a50])
maxX = max([a25 a50])
%xx = linspace(minX,maxX);
xx = linspace(0.5,2.7727,100);
vel25_inter = interp1(a25,vel25,xx);
vel50_inter = interp1(a50,vel50,xx);
val = 30; % The interpolated point
interpVel = vel25_inter + ((val-25).*(vel50_inter-vel25_inter))./(50-25);
plot(xx,interpVel,'r-');
There issues were
The interval on which you wanted to interpolate is xx = linspace(minX,maxX); but it gives an error of the type,
Matrix dimensions must agree.
Because you were assigning two values for the starting point and two for the ending point. So I replace it with xx = linspace(0.5,2.7727,100); where the starting point is being the minimum of the two minimum minX and the same for maxX
There are values of a50 (0.931818182) that repeat which was producing the following error
The grid vectors are not strictly monotonic increasing.
I change one of the value and replaced it with 0.932
The output is not that promising but is suppose the one you want?

How to interpolate random non monotonic increasing data

So I am working on my Thesis and I need to calculate geometric characteristics of an airfoil.
To do this, I need to interpolate the horizontal and vertical coordinates of an airfoil. This is used for a tool which will calculate the geometric characteristics automatically which come from random airfoil geometry files.
Sometime the Y values of the airfoil are non monotonic. Hence, the interp1 command gives an error since some values in the Y vector are repeated.
Therefore, my question is: How do I recognize and subsequently interpolate non monotonic increasing data automatically in Matlab.
Here is a sample data set:
0.999974 0.002176
0.994846 0.002555
0.984945 0.003283
0.973279 0.004131
0.960914 0.005022
0.948350 0.005919
0.935739 0.006810
0.923111 0.007691
0.910478 0.008564
0.897850 0.009428
0.885229 0.010282
0.872617 0.011125
0.860009 0.011960
0.847406 0.012783
0.834807 0.013598
0.822210 0.014402
0.809614 0.015199
0.797021 0.015985
0.784426 0.016764
0.771830 0.017536
0.759236 0.018297
0.746639 0.019053
0.734038 0.019797
0.721440 0.020531
0.708839 0.021256
0.696240 0.021971
0.683641 0.022674
0.671048 0.023367
0.658455 0.024048
0.645865 0.024721
0.633280 0.025378
0.620699 0.026029
0.608123 0.026670
0.595552 0.027299
0.582988 0.027919
0.570436 0.028523
0.557889 0.029115
0.545349 0.029697
0.532818 0.030265
0.520296 0.030820
0.507781 0.031365
0.495276 0.031894
0.482780 0.032414
0.470292 0.032920
0.457812 0.033415
0.445340 0.033898
0.432874 0.034369
0.420416 0.034829
0.407964 0.035275
0.395519 0.035708
0.383083 0.036126
0.370651 0.036530
0.358228 0.036916
0.345814 0.037284
0.333403 0.037629
0.320995 0.037950
0.308592 0.038244
0.296191 0.038506
0.283793 0.038733
0.271398 0.038920
0.259004 0.039061
0.246612 0.039153
0.234221 0.039188
0.221833 0.039162
0.209446 0.039064
0.197067 0.038889
0.184693 0.038628
0.172330 0.038271
0.159986 0.037809
0.147685 0.037231
0.135454 0.036526
0.123360 0.035684
0.111394 0.034690
0.099596 0.033528
0.088011 0.032181
0.076685 0.030635
0.065663 0.028864
0.055015 0.026849
0.044865 0.024579
0.035426 0.022076
0.027030 0.019427
0.019970 0.016771
0.014377 0.014268
0.010159 0.012029
0.007009 0.010051
0.004650 0.008292
0.002879 0.006696
0.001578 0.005207
0.000698 0.003785
0.000198 0.002434
0.000000 0.001190
0.000000 0.000000
0.000258 -0.001992
0.000832 -0.003348
0.001858 -0.004711
0.003426 -0.005982
0.005568 -0.007173
0.008409 -0.008303
0.012185 -0.009379
0.017243 -0.010404
0.023929 -0.011326
0.032338 -0.012056
0.042155 -0.012532
0.052898 -0.012742
0.064198 -0.012720
0.075846 -0.012533
0.087736 -0.012223
0.099803 -0.011837
0.111997 -0.011398
0.124285 -0.010925
0.136634 -0.010429
0.149040 -0.009918
0.161493 -0.009400
0.173985 -0.008878
0.186517 -0.008359
0.199087 -0.007845
0.211686 -0.007340
0.224315 -0.006846
0.236968 -0.006364
0.249641 -0.005898
0.262329 -0.005451
0.275030 -0.005022
0.287738 -0.004615
0.300450 -0.004231
0.313158 -0.003870
0.325864 -0.003534
0.338565 -0.003224
0.351261 -0.002939
0.363955 -0.002680
0.376646 -0.002447
0.389333 -0.002239
0.402018 -0.002057
0.414702 -0.001899
0.427381 -0.001766
0.440057 -0.001656
0.452730 -0.001566
0.465409 -0.001496
0.478092 -0.001443
0.490780 -0.001407
0.503470 -0.001381
0.516157 -0.001369
0.528844 -0.001364
0.541527 -0.001368
0.554213 -0.001376
0.566894 -0.001386
0.579575 -0.001398
0.592254 -0.001410
0.604934 -0.001424
0.617614 -0.001434
0.630291 -0.001437
0.642967 -0.001443
0.655644 -0.001442
0.668323 -0.001439
0.681003 -0.001437
0.693683 -0.001440
0.706365 -0.001442
0.719048 -0.001444
0.731731 -0.001446
0.744416 -0.001443
0.757102 -0.001445
0.769790 -0.001444
0.782480 -0.001445
0.795173 -0.001446
0.807870 -0.001446
0.820569 -0.001446
0.833273 -0.001446
0.845984 -0.001448
0.858698 -0.001448
0.871422 -0.001451
0.884148 -0.001448
0.896868 -0.001446
0.909585 -0.001443
0.922302 -0.001445
0.935019 -0.001446
0.947730 -0.001446
0.960405 -0.001439
0.972917 -0.001437
0.984788 -0.001441
0.994843 -0.001441
1.000019 -0.001441
First column is X and the second column is Y. Notice how the last values of Y are repeated.
Maybe someone can provide me with a piece of code to do this? Or any suggestions are welcome as well.
Remember I need to automate this process.
Thanks for your time and effort I really appreciate it!

There is quick and dirty method if you do not know the exact function defining the foil profile. Split your data into 2 sets, top and bottom planes, so the 'x' data are monotonic increasing.
First I imported your data table in the variable A, then:
%// just reorganise your input in individual vectors. (this is optional but
%// if you do not do it you'll have to adjust the code below)
x = A(:,1) ;
y = A(:,2) ;
ipos = y > 0 ; %// indices of the top plane
ineg = y <= 0 ; %// indices of the bottom plane
xi = linspace(0,1,500) ; %// new Xi for interpolation
ypos = interp1( x(ipos) , y(ipos) , xi ) ; %// re-interp the top plane
yneg = interp1( x(ineg) , y(ineg) , xi ) ; %// re-interp the bottom plane
y_new = [fliplr(yneg) ypos] ; %// stiches the two half data set together
x_new = [fliplr(xi) xi] ;
%% // display
figure
plot(x,y,'o')
hold on
plot(x_new,y_new,'.r')
axis equal
As said on top, it is quick and dirty. As you can see from the detail figure, you can greatly improve the x resolution this way in the area where the profile is close to the horizontal direction, but you loose a bit of resolution at the noose of the foil where the profile is close to the vertical direction.
If it's acceptable then you're all set. If you really need the resolution at the nose, you could look at interpolating on x as above but do a very fine x grid near the noose (instead of the regular x grid I provided as example).
if your replace the xi definition above by:
xi = [linspace(0,0.01,50) linspace(0.01,1,500)] ;
You get the following near the nose:
adjust that to your needs.

To interpolate any function, there must be a function defined. When you define y=f(x), you cannot have the same x for two different values of y because then we are not talking about a function. In your example data, neither x nor y are monotonic, so anyway you slice it, you'll have two (or more) "y"s for the same "x". If you wish to interpolate, you need to divide this into two separate problems, top/bottom and define proper functions for interp1/2/n to work with, for example, slice it horizontally where x==0. In any case, you would have to provide additional info than just x or y alone, e.g.: x=0.5 and y is on top.
On the other hand, if all you want to do is to insert a few values between each x and y in your array, you can do this using finite differences:
%// transform your original xy into 3d array where x is in first slice and y in second
xy = permute(xy(85:95,:), [3,1,2]); %// 85:95 is near x=0 in your data
%// lets say you want to insert three additional points along each line between every two points on given airfoil
h = [0, 0.25, 0.5, 0.75].'; %// steps along each line - column vector
%// every interpolated h along the way between f(x(n)) and f(x(n+1)) can
%// be defined as: f(x(n) + h) = f(x(n)) + h*( f(x(n+1)) - f(x(n)) )
%// this is first order finite differences approximation in 1D. 2D is very
%// similar only with gradient (this should be common knowledge, look it up)
%// from here it's just fancy matrix play
%// 2D gradient of xy curve
gradxy = diff(xy, 1, 2); %// diff xy, first order, along the 2nd dimension, where x and y now run
h_times_gradxy = bsxfun(#times, h, gradxy); %// gradient times step size
xy_in_3d_array = bsxfun(#plus, xy(:,1:end-1,:), h_times_gradxy); %// addition of "f(x)" and there we have it, the new x and y for every step h
[x,y] = deal(xy_in_3d_array(:,:,1), xy_in_3d_array(:,:,2)); %// extract x and y from 3d matrix
xy_interp = [x(:), y(:)]; %// use Matlab's linear indexing to flatten x and y into columns
%// plot to check results
figure; ax = newplot; hold on;
plot(ax, xy(:,:,1), xy(:,:,2),'o-');
plot(ax, xy_interp(:,1), xy_interp(:,2),'+')
legend('Original','Interpolated',0);
axis tight;
grid;
%// The End
And these are the results, near x=0 for clarity of presentation:
Hope that helps.
Cheers.

finding absolute error of approximated function - matlab

During an experiment i registered several points. Thereafter I approximated them with 9th order polynomial. I need to find the absolute error of the measurements and the approximated function on y axis. Any idea?
*edit:
y = [0.006332 0.04056 0.11813 0.1776723 0.23840 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 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];
x2 = linspace (1,43,43);
x2 = x2';
y = y';
f = fit(x2,y,'poly9');
figure()
plot(f,x2,y)

This will do it:
y_fit = f(x2);
error = y - y_fit;
hold on
plot(x2, error)
% Several popular error norms:
norm(error, 1)
norm(error, 2)
norm(error, Inf)
Like y, the variable error is a vector. If you want to reduce this vector to a single number, you can use one the norms. See this for more on error norms.

Fitting an ellipse to a logical matrix

I have a logical matrix:
0,0,0,0,0,0,0,0,0,0,0
0,0,0,0,0,0,0,0,0,0,0
0,0,0,1,1,1,1,1,0,0,0
0,0,0,1,1,1,1,1,1,0,0
0,0,1,1,1,1,1,1,1,0,0
0,0,1,1,1,1,1,1,1,0,0
0,0,1,1,1,1,1,1,1,0,0
0,0,0,1,1,1,1,1,1,0,0
0,0,0,0,1,1,0,0,0,0,0
0,0,0,0,0,0,0,0,0,0,0
0,0,0,0,0,0,0,0,0,0,0
and I would like to fit an ellipse as best as possible and calculate the error. The error could be the elementwise difference between the original data and the best ellipse found.
I have seen the following method: MATLAB Curve Fitting (Ellipse-like)
but I am not sure that is the shortest way to do it.
How would you recommend to find the closest elliptical logical matrix?

Find the ellipse 6 DOF parameters:
%get edge locations
md = m-imerode(m,ones(3));
md = padarray(md,10);axis equal
%find edges x,y
[y,x] = find(md);
%fit to Q = a*x^2 + b*y^2 + 2*c*x*y + 2*d*x + 2*e*y + f
H=[x.*x y.*y 2*x.*y x y x*0+1];
[v,g]=eig(H'*H);
a = v(1,1);
b = v(2,1);
c = v(3,1);
d = v(4,1);
e = v(5,1);
f = v(6,1);
[xg, yg] = meshgrid(1:size(md,2),1:size(md,1));
ev = a*xg.^2+b*yg.^2+2*c*xg.*yg+d*xg+e*yg+f;
imagesc(ev);axis equal

I would fist extract the boundary of your logical ellipse. Iterate the following function from i=2 to n-1, j=2 to m-1, for [n,m]=size(M). It will give you the "boundary matrix", where the boundary is represented by 1 and 0 for others. Then use the method described in here to get the coefficients of the ellipse equation. Note that the matrix indices start from top-left. So you may need to modify the index ordering depending on where you want the origin to be.
function [ bd ] = logical_neighbor( loM, i, j )
bd=0;
if loM(i,j) == 0
return;
else
for ni=1:3
for nj=1:3
if loM(i-2+ni,j-2+nj) == 0
bd= 1;
return;
end
end
end
end
end