Best fit line for scatter data along y=x line

I have a scatter data point (file name PntP) and corresponding temperature values (file name uu) for different time levels. In the data file 'PntP' the PntP(:,1) is 'x' coordinate and PntP(:,2) is 'y' coordinate. In data file 'uu' each column represents the temperature values corresponding to given data points at time levels. Please give me idea how to find the temperature plot along the line y=mx pasing through coordinates (x1,y1) and (x2,y2) for a fix time stations.

Answer 1

[Star Strider]

What sort of regression would you want for the volume in the second figure?

LD1= load('uu.mat');
uu = LD1.uu;
uu_size = size(uu)

uu_size = 1x2

4381 51

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LD2 = load('PntP.mat');
x = LD2.PntP(:,1);
y = LD2.PntP(:,2)'

y = 1x4381

0.0155 0.0160 0.0140 0.0145 0.0150 0.0155 0.0160 0.0165 0.0170 0.0175 0.0180 0.0130 0.0135 0.0140 0.0145 0.0150 0.0155 0.0160 0.0165 0.0170 0.0175 0.0180 0.0185 0.0190 0.0125 0.0130 0.0135 0.0140 0.0145 0.0150

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figure
scatter(x, y, '.')
grid

figure
hold on
for k = 1:size(uu,2)
    scatter3(x, y, uu(:,k), '.')
end
hold off
grid on
xlabel('X')
ylabel('Y')
zlabel('UU')
view(-27,30)

The linear regressions themselves would likely not be difficult, however how would they be defined iin therms of ‘x’, ‘y’, and the columns of ‘uu’?

.

[Rohit]

I want temerature plot vs 'x' at fix time corresponding to data value interpolate the line y=mx+c.

[Star Strider]

I still do not understand.

See if this works —

LD1= load('uu.mat');
uu = LD1.uu;
uu_size = size(uu);

LD2 = load('PntP.mat');
x = LD2.PntP(:,1);
y = LD2.PntP(:,2);

DM = [x ones(size(x))];                         % Design Matrix
B = DM \ y;
RL = DM * B;                                    % Regreession Line

figure
scatter(x, y, '.', 'DisplayName','Data')
hold on
plot(x, RL, '-r', 'LineWidth',2, 'DisplayName','Linear Regression Line')
hold off
grid
legend('Location','best')
% text(max(x), max(RL), sprintf('$y = %.5f\\cdot x %+.5f$',B), 'Horiz','left', 'Interpreter','LaTeX')
text(0.03, 0.035, sprintf('$y = %.5f\\cdot x %+.5f$',B), 'Horiz','left', 'Interpreter','LaTeX')

xv = repmat(x, size(uu,2), 1);
RLv = repmat(RL, size(uu,2), 1);
UUfcn = scatteredInterpolant(xv, RLv, uu(:));

Warning: Duplicate data points have been detected and removed - corresponding values have been averaged.

uuv = UUfcn(x,RL);


figure
hold on
for k = 1:size(uu,2)
    hs3(k) = scatter3(x, y, uu(:,k), '.', 'DisplayName','Data');
end
hp3 = plot3(x, RL, uuv, '-r', 'LineWidth',5, 'DisplayName','Regression Line (Spatial)');
hold off
grid on
xlabel('X')
ylabel('Y')
zlabel('UU')
view(-27,30)
legend(hp3, 'Location','best')

figure
% hold on
% for k = 1:size(uu,2)
%     scatter3(x, y, uu(:,k), '.')
% end
plot3(x, RL, uuv, '-r', 'LineWidth',5, 'DisplayName','Regression Line (Spatial)')
% hold off
grid on
xlabel('X')
ylabel('Y')
zlabel('UU')
view(-27,30)
xlabel('X')
ylabel('Y')
zlabel('UU')
title('Isolated 3D Regression Line')

Result = table(x, y, uuv)

Result = 4381x3 table
      x         y        uuv  
    ______    ______    ______

    0.0035    0.0155    36.769
    0.0035     0.016    36.769
     0.004     0.014    35.236
     0.004    0.0145    35.236
     0.004     0.015    35.236
     0.004    0.0155    35.236
     0.004     0.016    35.236
     0.004    0.0165    35.236
     0.004     0.017    35.236
     0.004    0.0175    35.236
     0.004     0.018    35.236
    0.0045     0.013    33.829
    0.0045    0.0135    33.829
    0.0045     0.014    33.829
    0.0045    0.0145    33.829
    0.0045     0.015    33.829

The values for the regression line are in the ‘uuv’ variable.

.

[Rohit]

Not like this. I have to draw a line from a point (x1,y1) which should be paas through center (0.02,0.02) and another point (x2,y2). Both point (x1,y1) and (x2,y2) are in the opposite side of center. Points are diagonally but 'y' not equal 'x'. By using the interpolation we can get a best fit line from (x1,y1) and (x2,y2). So corresponding to this line data i have to calculate the temperature. And want to plot this temperature at 50 sec.

In 'uu.mat' each column like uu(:,1) are for 1 sec, uu(:,50) for 50 sec.

[Star Strider]

I stiill do not understand.

How do I get the ‘temperature at 50 sec’? I have no idea what that refers to.

I can’t get it to work regardless.

.

[Walter Roberson]

The code I posted should handle interpolation along (x1,y1) to (x2,y2) .

However, I do not understand how you would get the temperature at 50 seconds. Although the input matrix uu is described as having temperatures over time, there is no apparent information relating columns of uu to particular times.

[Star Strider]

I have no idea what (x1,y1) and (x2,y2) means, since they’re not specifically defined. (They should be.)

My interpretation is that Rohit wants to interpolate across all 300+ diameters, each goiing through the centroid. (This requires a loop.) I could get those regressions to work, however using scatteredInterpolant on those (x,y) ranges gave inconsistent results. (I usually get good results from it.)

The border is irregular, however the interpolations should be in some sense consistent, and they weren’t. I arbitrarily used ‘uu(:,50)’ for the ‘z’ value, however I’m not certain that’s correct.

There is too much missing information to answer this, at least for me. (I kept my code and downloaded the files to work on later, when I have more time.)

[Rohit]

I have used surfir(PntP(:,1),PntP(:,2),uu(:,50),0.9) to get the surface for the scatter data at time t= 50sec. But I want the temperature along the line y=mx.

[Star Strider]

What is ‘surfir’?

[Sam Chak]

Hi @Rohit,

Could you please create a sketch of the "expected" straight line () from Point A (x₁, y₁) to Point B (x₂, y₂) that passes through the point (0.02, 0.02)?

Your sketch will indicate the exact coordinates of (x₁, y₁) and (x₂, y₂).

[Rohit]

@Star Strider surfir - Surface plot from irregular data points

[Star Strider]

O.K. I never heard of it, and could not find it in a web search.

[Star Strider]

This took lonoger than I ever could have imagined.

To briefly describe how iit works, it first calculates the boundary and thee centroid, then uses them to find the midliine indices of the selected valuees of ‘y’ that define the boundary, and from them index vector, ‘idxv’. It then uses ‘idxv’ to select the ‘x’ values of tthe boundary and the corresponding ‘y’ values of the boundary to define the linear regression of all lines joining the opposite sides of the boundary and that pass through the centroid. It does this by defining a design matrix ‘DM’ and then performing the linear regression. (See the documentation on mldivide, \ to understand how that works.) It then stores the ‘x’ values used in the regressiono (as ‘xr’) and correspoiinding ‘y’ values (computed from the regression) as ‘yr’. (It also stores the regression coefficients ‘B’ for later reference, if needed.) When completed, it has computed 399 regressions, with their corresponding ‘x’ and ‘y’ values of the boundary.

It then calculates the interpolation funciton ‘UUfcn’ using the available ‘x’ and ‘y’ data and ‘uu(:50)’. The second loop creeates vectors ‘xq’ and ‘yq’ (arbitrarily 100 elements each) and stores them as ‘xp’ and ‘yp’ for later reference, and uses them to calculate the hypotenuse of the triangle they create to use as the independent variable vector for the trapz calculation of the area under the ‘z’ curve.. The ‘z’ curve is created by using ‘xq’ and ‘yq’ as arguments to ‘UUfcn’, to interpolate the ‘uu(:50)’ data along the line created by them. It then use the ‘profile’ cell array to store the necessary data, does some simple analyses (minimum, maximum, mean, RMS value, and area under the curve). You can do whatever additional analyses you want, using the information in the ‘profile’ array.

IIt then plots all the 399 regreession lines it calculates (the magenta lines), as well as selected regressionl lines from the calculatiion loop in red to demonstrate what it actually does. It plots the calculated centroid as a green pentagram.

And with that, I am finished with this!

LD1= load('uu.mat');
uu = LD1.uu;
uu_size = size(uu);

LD2 = load('PntP.mat');
x = LD2.PntP(:,1);
y = LD2.PntP(:,2);

kb = boundary(x, y, 0.965);
BndryLen = numel(kb);
[xl(1),xl(2)] = bounds(x(kb))

xl = 1x2

0.0034 0.0393

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xl = 1x2

0.0034 0.0393

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[yl(1),yl(2)] = bounds(y(kb))

yl = 1x2

0.0011 0.0371

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yl = 1x2

0.0011 0.0371

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ctrd = @(x,y) [trapz(x, x.*y) / trapz(x, y); trapz(y, x.*y) / trapz(y, x)];
cxcy = ctrd(x(kb), y(kb));                                  % Centroid Coordiates
cx = cxcy(1);
cy = cxcy(2);

Lvml = ismembertol(y(kb), cx, 1E-4);
mlidx = find(Lvml);                                         % Midline 'x' Indices
% CheckCoords = [x(kb(mlidx([1 2]))) y(kb(mlidx([1 2])))]
% CheckCoords2 = [x(kb(mlidx([1 2])+25)) y(kb(mlidx([1 2])+25))]

idxv = mlidx(1) : mlidx(2);

for k1 = 1:numel(idxv)
    % k1
    idxrng = mlidx([1 2])+k1;
    DM = [x(kb(idxrng)) ones(size(x(kb(idxrng))))];         % Design Matrix
    % Q3 = [x(kb(idxrng)) y(kb(idxrng))];
    B(:,k1) = DM \ y(kb(idxrng));
    xr(:,k1) = x(kb(idxrng));
    yr(:,k1) = DM * B(:,k1);                                % Regreession Line
end

B

B = 2x399

0.0079 0.0157 0.0236 0.0314 0.0393 0.0472 0.0550 0.0629 0.0708 0.0787 0.0866 0.0945 0.1025 0.1104 0.1184 0.1263 0.1343 0.1423 0.1503 0.1584 0.1664 0.1745 0.1826 0.1908 0.1989 0.2071 0.2153 0.2235 0.2318 0.2401 0.0198 0.0197 0.0195 0.0194 0.0192 0.0191 0.0189 0.0187 0.0186 0.0184 0.0183 0.0181 0.0180 0.0178 0.0176 0.0175 0.0173 0.0172 0.0170 0.0168 0.0167 0.0165 0.0163 0.0162 0.0160 0.0159 0.0157 0.0155 0.0154 0.0152

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Bref = [1:size(B,2); B];
disp(Bref)

  Columns 1 through 18

    1.0000    2.0000    3.0000    4.0000    5.0000    6.0000    7.0000    8.0000    9.0000   10.0000   11.0000   12.0000   13.0000   14.0000   15.0000   16.0000   17.0000   18.0000
    0.0079    0.0157    0.0236    0.0314    0.0393    0.0472    0.0550    0.0629    0.0708    0.0787    0.0866    0.0945    0.1025    0.1104    0.1184    0.1263    0.1343    0.1423
    0.0198    0.0197    0.0195    0.0194    0.0192    0.0191    0.0189    0.0187    0.0186    0.0184    0.0183    0.0181    0.0180    0.0178    0.0176    0.0175    0.0173    0.0172

  Columns 19 through 36

   19.0000   20.0000   21.0000   22.0000   23.0000   24.0000   25.0000   26.0000   27.0000   28.0000   29.0000   30.0000   31.0000   32.0000   33.0000   34.0000   35.0000   36.0000
    0.1503    0.1584    0.1664    0.1745    0.1826    0.1908    0.1989    0.2071    0.2153    0.2235    0.2318    0.2401    0.2484    0.2568    0.2651    0.2736    0.2820    0.2905
    0.0170    0.0168    0.0167    0.0165    0.0163    0.0162    0.0160    0.0159    0.0157    0.0155    0.0154    0.0152    0.0150    0.0149    0.0147    0.0145    0.0144    0.0142

  Columns 37 through 54

   37.0000   38.0000   39.0000   40.0000   41.0000   42.0000   43.0000   44.0000   45.0000   46.0000   47.0000   48.0000   49.0000   50.0000   51.0000   52.0000   53.0000   54.0000
    0.2991    0.3076    0.3163    0.3249    0.3336    0.3424    0.3512    0.3600    0.3689    0.3779    0.3869    0.3959    0.4050    0.4142    0.4234    0.4327    0.4421    0.4515
    0.0140    0.0138    0.0137    0.0135    0.0133    0.0132    0.0130    0.0128    0.0126    0.0124    0.0123    0.0121    0.0119    0.0117    0.0115    0.0113    0.0112    0.0110

  Columns 55 through 72

   55.0000   56.0000   57.0000   58.0000   59.0000   60.0000   61.0000   62.0000   63.0000   64.0000   65.0000   66.0000   67.0000   68.0000   69.0000   70.0000   71.0000   72.0000
    0.4610    0.4706    0.4802    0.4899    0.4997    0.5095    0.5195    0.5295    0.5396    0.5498    0.5600    0.5704    0.5808    0.5914    0.6020    0.6128    0.6237    0.6346
    0.0108    0.0106    0.0104    0.0102    0.0100    0.0098    0.0096    0.0094    0.0092    0.0090    0.0088    0.0086    0.0084    0.0082    0.0080    0.0077    0.0075    0.0073

  Columns 73 through 90

   73.0000   74.0000   75.0000   76.0000   77.0000   78.0000   79.0000   80.0000   81.0000   82.0000   83.0000   84.0000   85.0000   86.0000   87.0000   88.0000   89.0000   90.0000
    0.6457    0.6569    0.6682    0.6796    0.6911    0.7028    0.7146    0.7265    0.7386    0.7508    0.7632    0.7757    0.7883    0.8012    0.8141    0.8273    0.8406    0.8541
    0.0071    0.0069    0.0066    0.0064    0.0062    0.0059    0.0057    0.0055    0.0052    0.0050    0.0047    0.0045    0.0042    0.0040    0.0037    0.0035    0.0032    0.0029

  Columns 91 through 108

   91.0000   92.0000   93.0000   94.0000   95.0000   96.0000   97.0000   98.0000   99.0000  100.0000  101.0000  102.0000  103.0000  104.0000  105.0000  106.0000  107.0000  108.0000
    0.8678    0.8816    0.8957    0.9099    0.9244    0.9391    0.9540    0.9691    0.9844    1.0000    1.0158    1.0319    1.0483    1.0649    1.0896    1.1069    1.1245    1.1425
    0.0026    0.0024    0.0021    0.0018    0.0015    0.0012    0.0009    0.0006    0.0003    0.0000   -0.0003   -0.0006   -0.0010   -0.0013   -0.0017   -0.0021   -0.0024   -0.0028

  Columns 109 through 126

  109.0000  110.0000  111.0000  112.0000  113.0000  114.0000  115.0000  116.0000  117.0000  118.0000  119.0000  120.0000  121.0000  122.0000  123.0000  124.0000  125.0000  126.0000
    1.1607    1.1793    1.1983    1.2176    1.2373    1.2573    1.2778    1.2987    1.3200    1.3417    1.3640    1.3867    1.4099    1.4336    1.4579    1.4827    1.5081    1.5341
   -0.0031   -0.0035   -0.0039   -0.0043   -0.0047   -0.0051   -0.0055   -0.0059   -0.0063   -0.0067   -0.0072   -0.0076   -0.0081   -0.0086   -0.0090   -0.0095   -0.0100   -0.0106

  Columns 127 through 144

  127.0000  128.0000  129.0000  130.0000  131.0000  132.0000  133.0000  134.0000  135.0000  136.0000  137.0000  138.0000  139.0000  140.0000  141.0000  142.0000  143.0000  144.0000
    1.5608    1.5881    1.6162    1.6449    1.6744    1.7047    1.7358    1.7677    1.8006    1.8344    1.8692    1.9050    1.9419    1.9800    2.0193    2.0598    2.1017    2.1450
   -0.0111   -0.0116   -0.0122   -0.0128   -0.0134   -0.0140   -0.0146   -0.0152   -0.0159   -0.0166   -0.0172   -0.0180   -0.0187   -0.0195   -0.0202   -0.0210   -0.0219   -0.0227

  Columns 145 through 162

  145.0000  146.0000  147.0000  148.0000  149.0000  150.0000  151.0000  152.0000  153.0000  154.0000  155.0000  156.0000  157.0000  158.0000  159.0000  160.0000  161.0000  162.0000
    2.1897    2.2361    2.2841    2.3338    2.3854    2.4390    2.4947    2.5526    2.6128    2.6756    2.7411    2.8095    2.8810    2.9558    3.0341    3.1163    3.2026    3.2933
   -0.0236   -0.0246   -0.0255   -0.0265   -0.0275   -0.0286   -0.0297   -0.0309   -0.0321   -0.0333   -0.0346   -0.0360   -0.0374   -0.0389   -0.0405   -0.0421   -0.0438   -0.0456

  Columns 163 through 180

  163.0000  164.0000  165.0000  166.0000  167.0000  168.0000  169.0000  170.0000  171.0000  172.0000  173.0000  174.0000  175.0000  176.0000  177.0000  178.0000  179.0000  180.0000
    3.3889    3.4897    3.5962    3.7089    3.8283    3.9552    4.0902    4.2342    4.3881    4.5530    4.7301    4.9210    5.1271    5.3506    5.5938    5.8593    6.1504    6.4712
   -0.0475   -0.0495   -0.0517   -0.0539   -0.0563   -0.0588   -0.0615   -0.0644   -0.0674   -0.0707   -0.0743   -0.0781   -0.0822   -0.0866   -0.0915   -0.0968   -0.1026   -0.1090

  Columns 181 through 198

  181.0000  182.0000  183.0000  184.0000  185.0000  186.0000  187.0000  188.0000  189.0000  190.0000  191.0000  192.0000  193.0000  194.0000  195.0000  196.0000  197.0000  198.0000
    6.8263    7.2217    7.6647    8.1645    8.7329    9.3851   10.1412   11.0283   12.0839   13.3612   14.9383   16.9353   19.5457   23.1043   28.2428   36.3152   50.8404   84.7139
   -0.1160   -0.1239   -0.1328   -0.1427   -0.1540   -0.1670   -0.1821   -0.1998   -0.2208   -0.2463   -0.2777   -0.3176   -0.3696   -0.4405   -0.5430   -0.7039   -0.9934   -1.6687

  Columns 199 through 216

  199.0000  200.0000  201.0000  202.0000  203.0000  204.0000  205.0000  206.0000  207.0000  208.0000  209.0000  210.0000  211.0000  212.0000  213.0000  214.0000  215.0000  216.0000
  253.7531 -254.9471  -84.8450  -50.8865  -36.3379  -28.2559  -23.1125  -19.5511  -16.9389  -14.9408  -13.3628  -12.0850  -11.0290  -10.1415   -9.3851   -8.7327   -8.1642   -7.6642
   -5.0384    5.1023    1.7114    1.0344    0.7444    0.5833    0.4808    0.4098    0.3577    0.3179    0.2864    0.2609    0.2399    0.2222    0.2071    0.1941    0.1828    0.1728

  Columns 217 through 234

  217.0000  218.0000  219.0000  220.0000  221.0000  222.0000  223.0000  224.0000  225.0000  226.0000  227.0000  228.0000  229.0000  230.0000  231.0000  232.0000  233.0000  234.0000
   -7.2211   -6.8256   -6.4705   -6.1497   -5.8585   -5.5930   -5.3498   -5.1263   -4.9201   -4.7292   -4.5521   -4.3872   -4.2333   -4.0893   -3.9543   -3.8275   -3.7080   -3.5954
    0.1640    0.1561    0.1490    0.1426    0.1368    0.1315    0.1267    0.1222    0.1181    0.1143    0.1108    0.1075    0.1044    0.1015    0.0988    0.0963    0.0939    0.0917

  Columns 235 through 252

  235.0000  236.0000  237.0000  238.0000  239.0000  240.0000  241.0000  242.0000  243.0000  244.0000  245.0000  246.0000  247.0000  248.0000  249.0000  250.0000  251.0000  252.0000
   -3.4889   -3.3881   -3.2925   -3.2018   -3.0777   -2.9974   -2.9208   -2.8476   -2.7776   -2.7106   -2.6464   -2.5848   -2.5257   -2.4689   -2.4142   -2.3616   -2.3109   -2.2620
    0.0896    0.0876    0.0856    0.0838    0.0816    0.0799    0.0784    0.0770    0.0756    0.0742    0.0729    0.0717    0.0705    0.0694    0.0683    0.0672    0.0662    0.0652

  Columns 253 through 270

  253.0000  254.0000  255.0000  256.0000  257.0000  258.0000  259.0000  260.0000  261.0000  262.0000  263.0000  264.0000  265.0000  266.0000  267.0000  268.0000  269.0000  270.0000
   -2.2148   -2.1692   -2.1251   -2.0825   -2.0413   -2.0013   -1.9626   -1.9251   -1.8887   -1.8533   -1.8190   -1.7856   -1.7532   -1.7216   -1.6909   -1.6610   -1.6319   -1.6034
    0.0643    0.0634    0.0625    0.0616    0.0608    0.0600    0.0593    0.0585    0.0578    0.0571    0.0564    0.0557    0.0551    0.0544    0.0538    0.0532    0.0526    0.0521

  Columns 271 through 288

  271.0000  272.0000  273.0000  274.0000  275.0000  276.0000  277.0000  278.0000  279.0000  280.0000  281.0000  282.0000  283.0000  284.0000  285.0000  286.0000  287.0000  288.0000
   -1.5757   -1.5487   -1.5224   -1.4966   -1.4715   -1.4469   -1.4229   -1.3994   -1.3764   -1.3539   -1.3319   -1.3103   -1.2892   -1.2685   -1.2482   -1.2283   -1.2088   -1.1896
    0.0515    0.0510    0.0504    0.0499    0.0494    0.0489    0.0485    0.0480    0.0475    0.0471    0.0466    0.0462    0.0458    0.0454    0.0450    0.0446    0.0442    0.0438

  Columns 289 through 306

  289.0000  290.0000  291.0000  292.0000  293.0000  294.0000  295.0000  296.0000  297.0000  298.0000  299.0000  300.0000  301.0000  302.0000  303.0000  304.0000  305.0000  306.0000
   -1.1708   -1.1524   -1.1343   -1.1165   -1.0990   -1.0818   -1.0649   -1.0483   -1.0319   -1.0158   -1.0000   -0.9844   -0.9691   -0.9540   -0.9391   -0.9244   -0.9099   -0.8957
    0.0434    0.0430    0.0427    0.0423    0.0420    0.0416    0.0413    0.0410    0.0406    0.0403    0.0400    0.0397    0.0394    0.0391    0.0388    0.0385    0.0382    0.0379

  Columns 307 through 324

  307.0000  308.0000  309.0000  310.0000  311.0000  312.0000  313.0000  314.0000  315.0000  316.0000  317.0000  318.0000  319.0000  320.0000  321.0000  322.0000  323.0000  324.0000
   -0.8816   -0.8678   -0.8541   -0.8406   -0.8273   -0.8141   -0.8012   -0.7883   -0.7757   -0.7632   -0.7508   -0.7386   -0.7265   -0.7146   -0.7028   -0.6911   -0.6796   -0.6682
    0.0376    0.0374    0.0371    0.0368    0.0365    0.0363    0.0360    0.0358    0.0355    0.0353    0.0350    0.0348    0.0345    0.0343    0.0341    0.0338    0.0336    0.0334

  Columns 325 through 342

  325.0000  326.0000  327.0000  328.0000  329.0000  330.0000  331.0000  332.0000  333.0000  334.0000  335.0000  336.0000  337.0000  338.0000  339.0000  340.0000  341.0000  342.0000
   -0.6569   -0.6457   -0.6346   -0.6237   -0.6128   -0.6020   -0.5914   -0.5808   -0.5704   -0.5600   -0.5498   -0.5396   -0.5295   -0.5195   -0.5095   -0.4997   -0.4899   -0.4802
    0.0331    0.0329    0.0327    0.0325    0.0323    0.0320    0.0318    0.0316    0.0314    0.0312    0.0310    0.0308    0.0306    0.0304    0.0302    0.0300    0.0298    0.0296

  Columns 343 through 360

  343.0000  344.0000  345.0000  346.0000  347.0000  348.0000  349.0000  350.0000  351.0000  352.0000  353.0000  354.0000  355.0000  356.0000  357.0000  358.0000  359.0000  360.0000
   -0.4706   -0.4610   -0.4515   -0.4421   -0.4327   -0.4234   -0.4142   -0.4050   -0.3959   -0.3869   -0.3779   -0.3689   -0.3600   -0.3512   -0.3424   -0.3336   -0.3249   -0.3163
    0.0294    0.0292    0.0290    0.0288    0.0287    0.0285    0.0283    0.0281    0.0279    0.0277    0.0276    0.0274    0.0272    0.0270    0.0268    0.0267    0.0265    0.0263

  Columns 361 through 378

  361.0000  362.0000  363.0000  364.0000  365.0000  366.0000  367.0000  368.0000  369.0000  370.0000  371.0000  372.0000  373.0000  374.0000  375.0000  376.0000  377.0000  378.0000
   -0.3076   -0.2991   -0.2905   -0.2820   -0.2736   -0.2651   -0.2568   -0.2484   -0.2401   -0.2318   -0.2198   -0.2116   -0.2034   -0.1952   -0.1871   -0.1790   -0.1709   -0.1628
    0.0262    0.0260    0.0258    0.0256    0.0255    0.0253    0.0251    0.0250    0.0248    0.0246    0.0243    0.0242    0.0240    0.0238    0.0237    0.0235    0.0234    0.0232

  Columns 379 through 396

  379.0000  380.0000  381.0000  382.0000  383.0000  384.0000  385.0000  386.0000  387.0000  388.0000  389.0000  390.0000  391.0000  392.0000  393.0000  394.0000  395.0000  396.0000
   -0.1547   -0.1467   -0.1387   -0.1307   -0.1227   -0.1148   -0.1068   -0.0989   -0.0910   -0.0830   -0.0751   -0.0673   -0.0594   -0.0515   -0.0436   -0.0357   -0.0279   -0.0200
    0.0230    0.0229    0.0227    0.0226    0.0224    0.0222    0.0221    0.0219    0.0218    0.0216    0.0214    0.0213    0.0211    0.0210    0.0208    0.0207    0.0205    0.0203

  Columns 397 through 399

  397.0000  398.0000  399.0000
   -0.0122   -0.0043    0.0035
    0.0202    0.0200    0.0199

xr

xr = 2x399

0.0384 0.0385 0.0386 0.0386 0.0387 0.0388 0.0388 0.0389 0.0389 0.0390 0.0390 0.0391 0.0391 0.0391 0.0392 0.0392 0.0392 0.0392 0.0393 0.0393 0.0393 0.0393 0.0392 0.0392 0.0392 0.0392 0.0392 0.0391 0.0391 0.0390 0.0049 0.0048 0.0048 0.0047 0.0046 0.0045 0.0045 0.0044 0.0043 0.0042 0.0042 0.0041 0.0040 0.0040 0.0039 0.0039 0.0038 0.0038 0.0037 0.0037 0.0036 0.0036 0.0036 0.0035 0.0035 0.0035 0.0035 0.0034 0.0034 0.0034

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>

yr

yr = 2x399

0.0201 0.0203 0.0204 0.0206 0.0207 0.0209 0.0210 0.0212 0.0213 0.0215 0.0216 0.0218 0.0220 0.0221 0.0223 0.0224 0.0226 0.0227 0.0229 0.0231 0.0232 0.0234 0.0235 0.0237 0.0238 0.0240 0.0241 0.0243 0.0244 0.0246 0.0199 0.0198 0.0196 0.0195 0.0194 0.0193 0.0191 0.0190 0.0189 0.0188 0.0186 0.0185 0.0184 0.0182 0.0181 0.0180 0.0178 0.0177 0.0176 0.0174 0.0173 0.0171 0.0170 0.0169 0.0167 0.0166 0.0164 0.0163 0.0162 0.0160

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>

xv = x;
yv = y;
UUfcn = scatteredInterpolant(xv, yv, uu(:,50));

for k1 = 1:size(xr,2)
    col = k1;
    xq = linspace(xr(1,k1), xr(2,k1)).';
    yq = linspace(yr(1,k1), yr(2,k1)).';
    xp{k1} = xq;
    yp{k1} = yq;
    bl = hypot(xq, yq);
    z = UUfcn(xq, yq);
    blz = rmmissing([bl z]);
    AUC = trapz(blz(:,1), blz(:,2));
    profile{k1} = {xq, yq, z};
    zstats(:,k1) = [min(z); max(z); mean(z,'omitmissing'); sqrt(mean(z.^2,'omitmissing')); AUC];
end

profile{1}{1}                                               % Get The Information From The 'profile' Array

ans = 100x1

0.0384 0.0381 0.0377 0.0374 0.0371 0.0367 0.0364 0.0360 0.0357 0.0354

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>

profile{1}{2}

ans = 100x1

0.0201 0.0201 0.0201 0.0201 0.0201 0.0201 0.0201 0.0201 0.0201 0.0201

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>

profile{1}{3}

ans = 100x1

37.0000 34.8113 32.5516 30.4859 28.7377 27.6519 26.8135 26.1216 25.3872 24.3834

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>

Result = array2table(zstats, 'VariableNames',compose('Col %3d',1:size(xr,2)), 'RowNames',{'Min','Max','Mean','RMS','AUC'})

Result = 5x399 table
            Col   1    Col   2    Col   3    Col   4    Col   5    Col   6    Col   7    Col   8    Col   9    Col  10    Col  11    Col  12    Col  13    Col  14    Col  15    Col  16    Col  17    Col  18    Col  19    Col  20    Col  21    Col  22    Col  23    Col  24    Col  25    Col  26    Col  27    Col  28    Col  29    Col  30    Col  31    Col  32    Col  33    Col  34    Col  35    Col  36    Col  37    Col  38    Col  39    Col  40    Col  41    Col  42    Col  43    Col  44    Col  45    Col  46    Col  47    Col  48    Col  49    Col  50    Col  51    Col  52    Col  53    Col  54    Col  55    Col  56    Col  57    Col  58    Col  59    Col  60    Col  61    Col  62    Col  63    Col  64    Col  65    Col  66    Col  67    Col  68    Col  69    Col  70    Col  71    Col  72    Col  73    Col  74    Col  75    Col  76    Col  77    Col  78    Col  79    Col  80    Col  81    Col  82    Col  83    Col  84    Col  85    Col  86    Col  87    Col  88    Col  89    Col  90    Col  91    Col  92    Col  93    Col  94    Col  95    Col  96    Col  97    Col  98    Col  99    Col 100    Col 101    Col 102    Col 103    Col 104    Col 105    Col 106    Col 107    Col 108    Col 109    Col 110    Col 111    Col 112    Col 113    Col 114    Col 115    Col 116    Col 117    Col 118    Col 119    Col 120    Col 121    Col 122    Col 123    Col 124    Col 125    Col 126    Col 127    Col 128    Col 129    Col 130    Col 131    Col 132    Col 133    Col 134    Col 135    Col 136    Col 137    Col 138    Col 139    Col 140    Col 141    Col 142    Col 143    Col 144    Col 145    Col 146    Col 147    Col 148    Col 149    Col 150    Col 151    Col 152    Col 153    Col 154    Col 155    Col 156    Col 157    Col 158    Col 159    Col 160    Col 161    Col 162    Col 163    Col 164    Col 165    Col 166    Col 167    Col 168    Col 169    Col 170    Col 171    Col 172    Col 173    Col 174    Col 175    Col 176    Col 177    Col 178    Col 179    Col 180    Col 181    Col 182    Col 183    Col 184    Col 185    Col 186    Col 187    Col 188    Col 189    Col 190    Col 191    Col 192    Col 193    Col 194    Col 195    Col 196    Col 197    Col 198    Col 199    Col 200    Col 201    Col 202    Col 203    Col 204    Col 205    Col 206    Col 207    Col 208    Col 209    Col 210    Col 211    Col 212    Col 213    Col 214    Col 215    Col 216    Col 217    Col 218    Col 219    Col 220    Col 221    Col 222    Col 223    Col 224    Col 225    Col 226    Col 227    Col 228    Col 229    Col 230    Col 231    Col 232    Col 233    Col 234    Col 235    Col 236    Col 237    Col 238    Col 239    Col 240    Col 241    Col 242    Col 243    Col 244    Col 245    Col 246    Col 247    Col 248    Col 249    Col 250    Col 251    Col 252    Col 253    Col 254    Col 255    Col 256    Col 257    Col 258    Col 259    Col 260    Col 261    Col 262    Col 263    Col 264    Col 265    Col 266    Col 267    Col 268    Col 269    Col 270    Col 271    Col 272    Col 273    Col 274    Col 275    Col 276    Col 277    Col 278    Col 279    Col 280    Col 281    Col 282    Col 283    Col 284    Col 285    Col 286    Col 287    Col 288    Col 289    Col 290     Col 291     Col 292     Col 293     Col 294     Col 295      Col 296      Col 297       Col 298      Col 299      Col 300      Col 301      Col 302      Col 303     Col 304    Col 305     Col 306     Col 307     Col 308     Col 309     Col 310     Col 311     Col 312     Col 313    Col 314     Col 315     Col 316     Col 317    Col 318     Col 319     Col 320     Col 321     Col 322     Col 323     Col 324     Col 325     Col 326     Col 327     Col 328     Col 329     Col 330     Col 331     Col 332     Col 333     Col 334     Col 335     Col 336     Col 337     Col 338     Col 339     Col 340     Col 341     Col 342     Col 343     Col 344     Col 345     Col 346     Col 347     Col 348     Col 349     Col 350    Col 351     Col 352     Col 353    Col 354     Col 355     Col 356     Col 357     Col 358     Col 359     Col 360     Col 361    Col 362     Col 363     Col 364     Col 365     Col 366     Col 367    Col 368    Col 369    Col 370    Col 371    Col 372    Col 373    Col 374    Col 375    Col 376    Col 377    Col 378    Col 379    Col 380    Col 381    Col 382    Col 383    Col 384    Col 385    Col 386    Col 387    Col 388    Col 389    Col 390    Col 391    Col 392    Col 393    Col 394    Col 395    Col 396    Col 397    Col 398    Col 399
            _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    ________    ________    ________    ________    ________    ________    _________    __________    _________    _________    _________    _________    _________    _________    _______    ________    ________    ________    ________    ________    ________    ________    ________    _______    ________    ________    ________    _______    ________    ________    ________    ________    ________    ________    ________    ________    ________    ________    ________    ________    ________    ________    ________    ________    ________    ________    ________    ________    ________    ________    ________    ________    ________    ________    ________    ________    ________    ________    ________    ________    _______    ________    ________    _______    ________    ________    ________    ________    ________    ________    ________    _______    ________    ________    ________    ________    ________    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______    _______

    Min     -188.62    -188.56    -188.54    -188.57    -188.64    -188.71    -195.71    -194.74     -193.7    -192.65    -191.57    -190.47     -190.5    -190.94    -191.43    -191.96    -192.54    -193.14    -193.76    -194.42    -195.79    -194.62    -193.45    -192.27    -191.06    -189.84    -188.62     -187.4    -186.26    -187.25     -188.3    -189.38    -190.51    -191.69    -194.75    -194.17    -192.27    -191.02    -189.76    -188.52    -187.28    -186.35    -187.89    -189.44    -191.03    -192.65    -194.31    -194.68    -193.42    -192.15     -190.9    -189.65    -189.03    -190.91    -192.81    -194.74    -183.3     -182.98    -185.03    -187.11    -193.67    -192.37    -193.45    -189.6     -188.22    -186.84     -186.6    -188.85    -191.14    -193.43    -180.39    -193.91     -192.5    -191.09    -189.73    -191.97     -194.2    -185.49    -184.11    -186.28    -188.47     -194.3    -192.86    -191.44    -190.03    -188.63    -187.19    -188.67    -190.59    -192.48    -194.31    -194.25    -192.87     -191.5    -190.08    -188.68    -190.14    -191.63    -193.06    -194.44    -182.04    -182.61    -193.91    -192.72     -191.3    -190.26    -189.24    -188.55    -189.17    -189.71    -190.15    -190.53    -190.85    -191.11    -191.31    -191.43    -191.47    -194.67    -194.09    -193.54    -193.04    -192.57    -192.15    -191.72    -191.34       -191     -190.7    -190.44     -190.2    -189.96    -189.77    -189.62    -189.51    -189.46    -189.47    -189.52    -189.62    -195.72    -194.85    -193.96    -193.02    -192.06    -191.13    -191.42    -191.75    -192.12    -192.53    -192.98    -193.47    -193.96    -194.49    -195.06    -195.86     -194.8    -193.77    -192.76    -191.75    -190.74    -189.73    -188.73    -187.73    -187.36    -188.35    -189.37    -190.44    -191.54    -192.67    -195.16    -194.81    -195.93    -192.21    -191.19    -190.18    -189.18    -188.18    -189.05    -190.38    -191.74    -193.14    -194.56    -195.98    -195.22    -194.23    -193.23    -192.25    -191.26    -191.41    -193.08    -194.76    -187.37     -186.4    -186.51    -188.34    -190.16    -195.14    -194.09    -195.47    -191.96    -190.9     -189.84    -190.22    -192.05    -193.88     -195.7    -185.47    -195.37    -194.21    -193.05    -192.85    -194.67    -189.38    -188.16    -188.21    -190.06    -191.88    -195.38    -195.42    -192.89    -191.66    -190.44    -190.43    -192.11    -193.73    -195.33    -185.11     -194.8    -193.59    -192.35    -191.12    -192.24     -193.5    -194.72    -195.88    -185.21    -195.96    -194.79    -193.61    -192.45    -191.44    -190.39    -190.78    -191.34    -191.84    -192.28    -192.66    -192.98    -193.25    -193.41    -195.59    -194.89    -194.24    -193.63    -193.39    -193.23    -192.97    -192.66     -192.3    -191.89    -191.44    -190.89    -190.21    -189.47     -188.7    -188.32    -188.09     -187.9    -187.76    -187.67    -187.63    -187.64    -187.72    -187.85    -194.99     -193.9    -192.79    -191.66    -190.51    -189.47    -189.88    -190.32    -190.79    -191.31    -191.87    -192.49    -193.15    -193.86    -194.64    -193.34    -192.04     -190.74     -189.43     -188.06     -186.68     -185.31     -184.86      -185.98       -187.16      -188.38      -189.65      -190.97      -193.41      -193.74      -190.78    -189.48     -188.18     -186.89     -185.62     -185.66     -187.35     -189.03     -190.75     -192.49    -194.23     -193.59     -192.32     -191.05    -189.79     -188.54     -189.02     -190.99        -193     -183.45     -182.13     -183.03     -185.19     -194.34     -193.01     -191.78     -194.01     -188.97     -187.67     -186.36     -187.42     -189.75     -192.08     -194.38     -181.55     -193.66     -192.32     -190.99     -190.92     -193.15     -187.05     -185.76     -185.58     -187.77     -189.89     -194.38     -194.05    -191.72     -190.41     -189.06    -188.35     -190.24     -192.09      -193.9     -182.47     -194.62     -193.33     -192.03    -190.75     -190.32     -191.77     -193.15     -194.48     -184.68     -183.7    -195.59    -194.47    -193.38    -192.17    -191.22    -190.28     -189.9    -190.42    -190.87    -191.25    -191.55    -191.78    -191.96    -192.08    -192.15    -195.81    -195.23    -194.68    -194.15    -193.62    -193.13    -192.68    -192.27    -191.89    -191.56    -191.27    -191.01     -190.8    -190.63    -190.49    -190.35    -190.25
    Max          37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37        37          37         37         37         37         37         37        37          37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37        37          37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37          37          37          37          37          37          37           37            37           37           37           37           37           37           37         37          37          37          37          37          37          37          37          37         37          37          37          37         37          37          37          37          37          37          37          37          37          37          37          37          37          37          37          37          37          37          37          37          37          37          37          37          37          37          37          37          37          37          37          37          37         37          37          37         37          37          37          37          37          37          37          37         37          37          37          37          37          37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37         37
    Mean    -37.011    -36.584    -36.176    -35.781    -35.391    -35.006    -36.448    -36.078    -35.719    -35.369    -35.029      -34.7    -34.386    -34.084    -33.793    -33.521    -33.266    -33.024      -32.8    -32.595    -34.224    -32.227    -32.059    -31.908    -31.773    -31.657    -31.562    -31.481    -31.418    -31.369    -31.337    -31.319    -31.313    -31.321    -33.154    -33.169    -31.372    -31.396    -31.433    -31.485    -31.554     -31.64    -31.744    -31.867    -32.008    -32.174    -32.362    -32.561    -32.766    -32.994    -33.247    -33.522    -33.817    -34.131    -34.461    -34.806    -33.33     -33.688     -34.06    -34.443    -36.615     -36.99    -37.374    -35.97     -36.342    -36.728    -37.122    -37.515    -37.913    -38.317    -36.925    -39.106    -39.493    -39.888    -40.283    -40.679    -41.079    -39.698    -40.077    -40.458    -40.838    -42.944    -43.286    -41.884     -42.19    -42.482    -42.762    -43.029    -43.281    -43.516    -43.734    -43.911    -44.059    -44.187    -44.295    -44.383     -44.45    -44.498    -44.527    -44.539    -42.771     -42.73    -44.409    -44.319    -44.231    -44.096    -43.949    -43.781    -43.598    -43.399    -43.185    -42.954    -42.714    -42.458    -42.188    -41.902    -41.597    -43.023    -42.688    -42.336    -41.972    -41.592    -41.203      -40.8    -40.381    -39.952    -39.516    -39.072    -38.623    -38.169    -37.717    -37.265    -36.817    -36.374    -35.942    -35.525    -35.122     -36.54     -36.16      -35.8    -35.456    -35.128    -34.817    -34.524    -34.249    -33.993     -33.75    -33.522    -33.308    -33.109    -32.924     -32.75    -34.405    -32.428    -32.278    -32.134    -32.005    -31.891    -31.788    -31.693    -31.613    -31.549    -31.502     -31.47    -31.454    -31.459    -31.482    -33.343    -33.394    -33.459    -31.709    -31.803    -31.914    -32.045    -32.194    -32.359    -32.542     -32.74    -32.953    -33.182    -33.426    -33.661    -33.905    -34.166    -34.443    -34.731    -35.033     -35.35    -35.683    -34.206    -34.549    -34.909    -35.281    -35.671    -37.857     -38.25    -38.654    -37.272    -37.68     -38.093    -38.499    -38.913    -39.329    -39.754    -38.374    -40.562    -40.963    -41.372     -41.78     -42.18    -40.808    -41.195    -41.579    -41.952    -42.315    -44.408    -44.742    -43.319    -43.616    -43.898    -44.166    -44.418    -44.652    -44.873    -43.315    -45.223    -45.354    -45.463    -45.559    -45.633    -45.684    -45.711    -45.717    -43.942     -45.64    -45.554    -45.445    -45.315    -45.164    -44.979    -44.771    -44.541    -44.294    -44.027    -43.742    -43.438    -43.118    -42.781    -44.164    -43.787    -43.402    -43.005    -42.595    -42.173    -41.741    -41.302    -40.857    -40.407    -39.954    -39.496    -39.035    -38.574    -38.116    -37.661    -37.208    -36.761    -36.322    -35.892    -35.468    -35.055    -34.649    -34.254    -35.681    -35.301     -34.93    -34.572     -34.23    -33.902    -33.588    -33.291    -33.008    -32.738    -32.485    -32.251    -32.033    -31.829    -33.453    -31.449    -31.275     -31.119      -30.98     -30.864     -30.758     -30.672     -30.619      -30.584       -30.556      -30.558      -30.591      -30.581      -32.419      -32.463      -30.689     -30.74     -30.806     -30.896     -31.001     -31.128     -31.277     -31.432     -31.615     -31.822    -32.043     -32.259     -32.491     -32.743    -33.021     -33.319     -33.636     -33.977     -34.336     -32.889     -33.265     -33.653     -34.051     -36.264     -36.672      -37.08     -37.504     -36.132     -36.545     -36.969     -37.399     -37.832     -38.274     -38.719     -37.356     -39.559     -39.976     -40.396     -40.815     -41.232     -39.887     -40.285     -40.682     -41.074     -41.463     -43.574     -43.932    -42.537     -42.854     -43.159    -43.451     -43.727     -43.991     -44.239     -42.712     -44.651     -44.812     -44.954    -45.076     -45.178     -45.262     -45.321     -45.358     -43.627    -43.608    -45.314    -45.238    -45.141    -45.025    -44.874    -44.699      -44.5    -44.289     -44.06    -43.811    -43.533    -43.239    -42.931    -42.613     -42.28    -43.676    -43.306     -42.93    -42.548    -42.156    -41.751     -41.34    -40.929    -40.517    -40.098     -39.68    -39.261    -38.849    -38.435    -38.025    -37.617    -37.209
    RMS      72.094     71.749     71.411     71.083      70.77     70.469       72.8     72.506     72.222     71.948     71.688     71.442     71.207     70.986     70.778      70.58     70.395      70.22     70.055     69.902     72.379     69.594      69.42     69.252     69.096     68.951      68.82     68.704     68.614     68.537     68.485     68.452     68.443     68.454     71.129     71.143     68.508     68.519     68.555     68.615     68.694     68.793     68.912     69.045     69.192     69.357     69.538       69.7     69.828     69.973     70.135     70.308     70.493     70.695      70.91     71.141    68.666       68.89     69.143     69.412     72.284     72.534     72.801     70.48      70.727     70.995     71.284     71.587       71.9     72.226     69.904     72.807     73.075     73.356     73.638     73.924     74.219     71.932     72.188      72.46     72.737     75.491     75.718     73.473     73.654     73.835     74.019     74.207     74.394     74.578     74.761     74.885     74.973      75.06     75.141     75.217     75.284     75.344     75.399     75.447     72.928      72.92     75.401      75.34     75.277      75.19     75.091     74.975     74.846     74.707     74.555     74.393     74.219     74.035     73.842     73.633      73.41     75.666     75.422     75.173     74.919      74.66     74.396     74.125     73.855     73.584     73.313     73.043     72.774     72.506     72.237     71.968     71.701     71.441     71.188     70.939     70.698     73.071     72.823     72.578     72.337     72.102     71.876     71.655     71.439     71.233     71.033     70.843     70.664     70.496     70.338     70.194     72.669     69.908     69.767     69.635     69.517     69.417     69.333     69.265      69.21     69.173     69.151     69.142     69.152     69.186     69.235     71.918     71.966     72.027     69.435     69.497     69.577     69.671     69.784     69.914     70.064     70.228     70.407     70.608     70.821     70.985     71.161      71.35     71.558     71.784     72.021     72.274     72.547     70.192     70.461      70.75     71.059     71.384     74.257     74.571     74.898      72.67    72.965      73.278     73.603     73.936     74.259     74.586      72.33     75.178      75.46      75.75     76.046     76.354     74.177     74.452     74.733     75.017     75.306     77.996     78.238     76.048     76.249     76.445     76.636     76.823     76.998     77.169     74.834     77.392     77.458     77.514     77.566     77.608     77.639     77.657     77.665      75.17     77.586     77.493     77.386     77.273     77.138     76.989     76.825      76.65     76.465     76.266     76.054     75.831     75.599     75.349     77.509     77.221     76.929     76.629     76.321     75.997     75.664     75.327     74.987     74.642     74.296     73.942     73.584     73.225     72.869     72.515     72.161      71.81     71.463     71.125     70.794     70.466     70.143     69.831     72.159     71.841      71.53     71.228     70.937     70.658      70.39     70.138     69.894     69.661     69.443     69.241     69.051     68.876     71.344     68.496     68.297      68.115       67.95      67.801      67.674      67.568      67.499        67.45        67.426       67.423       67.442       67.445       70.136        70.16       67.507     67.536      67.588      67.662      67.772      67.904      68.057      68.229      68.421      68.631     68.861      69.027      69.188      69.366     69.567      69.781       70.01      70.263      70.533      68.123      68.382      68.656      68.951      71.899      72.184      72.482      72.803      70.513       70.81      71.133      71.475      71.833      72.213      72.603      70.332      73.265      73.587      73.922      74.265      74.614      72.437      72.754      73.079      73.408      73.737      76.499      76.781     74.605      74.838      75.068     75.297      75.518      75.739      75.953      73.646       76.29      76.403      76.509     76.608      76.695      76.778      76.847      76.907       74.47     74.471     76.946     76.895     76.832     76.755     76.657     76.541     76.407     76.266      76.11     75.938     75.743      75.54     75.323     75.094     74.851     77.054     76.786      76.51     76.224     75.931     75.637     75.339     75.034     74.725     74.417     74.107     73.798     73.492     73.187     72.868      72.54     72.216
    AUC      1.3271     1.3339     1.3409     1.3478     1.3544     1.3609     1.3918     1.3985      1.405     1.4115     1.4179     1.4241     1.4304     1.4367     1.4429     1.4492     1.4557     1.4622     1.4687     1.4755     1.5081     1.4891     1.4959     1.5027     1.5096     1.5165     1.5237     1.5309     1.5382     1.5454     1.5527       1.56     1.5673     1.5746     1.6109     1.6178     1.5949     1.6012     1.6074     1.6137     1.6202     1.6268     1.6336     1.6406     1.6477     1.6552     1.6631      1.671     1.6786     1.6866     1.6949     1.7037     1.7126     1.7219     1.7311     1.7405    1.7166      1.7257      1.735     1.7443     1.7854      1.794     1.8024    1.7788      1.7866     1.7946     1.8027     1.8105     1.8183     1.8262     1.7997     1.8409      1.848     1.8551     1.8622     1.8691     1.8762     1.8515     1.8582     1.8649     1.8717     1.9075      1.913     1.8893     1.8942     1.8988     1.9032     1.9074     1.9114      1.915     1.9183     1.9208     1.9229     1.9247     1.9261     1.9273     1.9281     1.9288     1.9292     1.9295     1.8969     1.8963     1.9276     1.9263     1.9251     1.9234     1.9215     1.9194      1.917     1.9145     1.9117     1.9088     1.9057     1.9024     1.8989      1.895     1.8907     1.9156     1.9108     1.9056     1.9001     1.8942     1.8879     1.8813     1.8741     1.8667      1.859     1.8511      1.843     1.8345      1.826     1.8174     1.8088     1.8002     1.7918     1.7836     1.7757     1.7986      1.791     1.7837     1.7766     1.7696     1.7629     1.7562     1.7497     1.7434     1.7371     1.7309     1.7247     1.7185     1.7124     1.7063     1.7282     1.6937     1.6872     1.6804     1.6738     1.6672     1.6605     1.6538     1.6471     1.6405     1.6341     1.6276     1.6212      1.615     1.6088     1.6277     1.6211     1.6144     1.5819     1.5755     1.5691     1.5626     1.5562     1.5498     1.5434      1.537     1.5307     1.5244     1.5181     1.5111     1.5041     1.4971     1.4902     1.4832     1.4761     1.4691      1.462     1.4321     1.4249     1.4178     1.4106     1.4034     1.4154     1.4072      1.399     1.3717    1.3632      1.3545     1.3455     1.3364     1.3272     1.3178     1.2895     1.2985     1.2884     1.2784     1.2682     1.2579     1.2308     1.2204       1.21     1.1994     1.1887     1.1931     1.1817     1.1554     1.1438      1.132     1.1202     1.1081     1.0959     1.0836     1.0562      1.058     1.0448     1.0313     1.0179     1.0042    0.99038    0.97631    0.96215    0.93468    0.93382    0.91898    0.90401    0.88896    0.86585    0.85058    0.83522    0.81981    0.80433    0.78878    0.77315    0.75745    0.74168    0.72579    0.72008    0.70384    0.68761    0.67135    0.65504    0.63869    0.62227    0.60584    0.58943    0.57303    0.55666    0.54019    0.52371     0.5073    0.49094    0.47466    0.45849    0.44243    0.42647    0.41063    0.39492    0.37932    0.36382    0.34847    0.34028    0.32489    0.30961    0.29445    0.27939    0.26444     0.2496    0.23484    0.22013    0.20548    0.19086    0.17632    0.16181    0.14724    0.13593    0.11823    0.10375    0.089302    0.074967    0.060681    0.046414    0.032391    0.018353    0.0044501    -0.0092272    -0.022865    -0.036396    -0.049784    -0.063592    -0.077045    -0.089225    -0.1022    -0.11521    -0.12812    -0.14097    -0.15392    -0.16696    -0.17999    -0.19316    -0.20648    -0.2199    -0.23337    -0.24702    -0.26076    -0.2747    -0.28882    -0.30311    -0.31757    -0.33223    -0.34048    -0.35508    -0.36982    -0.38465    -0.40688    -0.42205    -0.43719    -0.45243    -0.45964    -0.47462    -0.48964    -0.50469    -0.51971    -0.53479    -0.54987    -0.55463    -0.57948    -0.59426    -0.60904    -0.62379    -0.63857    -0.64288    -0.65743    -0.67201    -0.68663    -0.70127    -0.72653    -0.74117    -0.7448    -0.75913    -0.77342    -0.7877    -0.80196    -0.81625    -0.83048    -0.83114    -0.85848    -0.87222    -0.88589    -0.8995    -0.91302    -0.92651    -0.93986    -0.95309    -0.95128     -0.964    -0.9918    -1.0042    -1.0166    -1.0363    -1.0483      -1.06    -1.0715     -1.083    -1.0944    -1.1056    -1.1164    -1.1269    -1.1374    -1.1477    -1.1578     -1.185    -1.1949    -1.2047    -1.2143    -1.2237    -1.2329     -1.242    -1.2509    -1.2597    -1.2682    -1.2767    -1.2851    -1.2936    -1.3016    -1.3096    -1.3174    -1.3252

figure
hs1 = scatter(x, y, '.', 'DisplayName','Data');
hold on
hp1 = plot(x(kb), y(kb), '-r', 'LineWidth',3, 'DisplayName','Boundary');
for k1 = 1:size(xr,2)
    hp2 = plot(xr(:,k1), yr(:,k1), '-c', 'LineWidth',0.5, 'DisplayName','Regression Lines');
end

for k1 = 1:10:numel(xp)
    if (min(yp{k1} >= yl(1)) & (max(yp{k1} <= yl(2))))
        hp3 = plot(xp{k1}, yp{k1}, '-r', 'DisplayName','Selected Linear Regression Lines Used To Compute ‘Reesult’');
    end
end
hp4 = plot(cx, cy, 'pg', 'MarkerSize',15, 'MarkerFaceColor','g', 'DisplayName','Centroid');
hold off
grid
axis('equal')
xlabel('X')
ylabel('Y')
title('Top Surface At 50s Showing Regression Lines')
legend([hs1(1) hp1 hp2(1) hp3(1) hp4], 'Location','northoutside')

EDIT — (9 Sep 2024 at 13:07)

Added .‘Bref’

.

[Rohit]

@Sam Chak y=0.2x+0.0160, point A(0.005,0.017), B(0.0375,0.0235)

[Sam Chak]

@Rohit, So, it has to be one of the lines plotted by @Star Strider in this region.

[Star Strider]

@Rohit — Thank you for finally defining the regression line you want, after two days (and hours of work on my part). I would have much preferred knowing that two days ago!

Column 26 of my results (y = 0.2071*x + 0.159) match the data you want. You can check that with the ‘Bref’ matrix I just added. (Nothing new in my code other than that addition.)

@Sam Chak — Thank you for gettiing that information! I asked several times for clarification and received only ambiguous responses.

(This could be cited as tthe perfect example of how not to ask a question on MATLAB Answers!)

.

[Rohit]

@Star Strider thank you for your efforts.

[Star Strider]

As always, my pleasure!

This is an interesting problem!

Answer 2

[Walter Roberson]

m = (y2 - y1) ./ (x2 - x1);
b = y1 - x1 .* m;

LD1= load('uu.mat');
uu = LD1.uu;

LD2 = load('PntP.mat');
x = LD2.PntP(:,1);
y = LD2.PntP(:,2);

F = scatteredInterpolant(x, y, uu, 'linear', 'none');

xq = linspace(min(x), max(x));
yq = m * xq + b;

interpolated_data = F(xq, yq);

plot3(xq, yq, interpolated_data)

[Rohit]

If we replace F = scatteredInterpolant(x, y, uu, 'linear', 'none'); by

F = scatteredInterpolant(x, y, uu(:,50), 'linear', 'none'); Than it will give the temperature on line at time 50 sec. it will work but my concern is that line should paas through the center (0.02,0.02) and both point (x1,y1) and (x2,y2) should satisfy the line. suppose I choose first cordinate like (0.03,0.022). How i will choose the second coordinate so that it satisfy the equation of line. After getting the line it may be possible some coordinates of the given PntP not lies in line so we will use interpolation. Now on this equation of line each coordinate i have to find the temperature also.