Why are my line plots are coming out improperly?

The plot lines generated from the code below are coming out in improper way. I have attached an image file of the plot as well. The line generated from h4 and h8 are coming in an odd manner. Can I know why is it coming out in such a way?

clc;clear;close all;
%for head on collision
L= 4;
D= 3.860;
lam= 0.397;
% lamda will go from 0.4 m/sec (water, 0.25, 0.5, 0.75, 1) then 1m/sec
% (same thing) and finally 1.65 m/sec (same thing)
lam_org= [0.394 0.2091 0.284 0.404 0.374 0.423 0.358 0.523 0.493 0.567 0.359 0.424 0.296 0.445 0.447];
%lam_15_times = [0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397];
lam_l = log(lam_org);
psi_e= (2^0.33)/(2-lam);
Oh= 10^(-3)*[1.679 2.457 2.679 2.922 3.398 1.597 2.1782 2.505 2.958 1.487 3.129 1.934 2.478 2.728 2.893];

md_ho = [1.0690 2.02 1.3474 1.3580 1.3966 1.6701 1.4901 1.669 1.476 2.848 1.3871 2.8008 3.0724 2.3614 2.7726];
L_o = log(md_ho);
We = [8.518 9.903 16.473 22.68 26.214 58.84 78.77 117.76 138.37 184.842 193.155 272.054 327.49 443.05 615.34];
We_log = log(We);

%for 2mm offset
md_2= [1.0431 1.1251 0.9519 0.9691 0.9380 1.5003 1.2390 1.3260 1.2584 2.2003 1.2260 1.9754 2.125 1.6842 2.098];
L_2 = log(md_2);
We= [8.518 9.903 16.473 22.68 26.214 58.84 78.77 117.76 138.37 184.842 193.155 272.054 327.49 443.05 615.34];

%for 3mm offset
md_3= [0.9819 0.9916 1.0444 0.9938 0.9807 1.3555 1.2052 1.227 1.1849 1.747 1.2106 1.5462 1.6876 1.5860 1.726];
L_3 = log(md_3);
We= [8.518 9.903 16.473 22.68 26.214 58.84 78.77 117.76 138.37 184.842 193.155 272.054 327.49 443.05 615.34];


%for 4mm offset
md_4= [1.015 0.9875 1.0682 1.0763 1.0021 1.295 1.119 1.1112 1.125 1.681 1.1667 1.6932 1.862 1.677 1.6443 ];
L_4 = log(md_4);
We= [8.518 9.903 16.473 22.68 26.214 58.84 78.77 117.76 138.37 184.842 193.155 272.054 327.49 443.05 615.34];

for i= 1:length(We)
   psi_m(i)= 0.9759*((1+L/D)^(-0.7594))*We(i).^0.2283; % Graham et al.
end

for j=1:length(We)
    psi2_m(j)= (D+L)*We(j).^0.25; % Clanet et al.
end

for k= 1:length(We)
   for l= 1:length(Oh)
    psi_m3(k,l)= 0.8353*(psi_e^0.3774)*(We(k)^0.0571)*(Oh(l)^(-0.0430)); % Li et al.
   end
end

for m= 1: length(We)
    for n= 1: length(lam_org)
        psi_m_4(m,n)= 0.6046*(We(m)^0.1453)*(lam_org(n)^(-0.1062)); % my correlation
    end
end

%h1= plot(We,md_ho,'s','MarkerFaceColor','red','MarkerEdgeColor','black','MarkerSize',9); hold on
%h5= plot(We,md_2,'o','MarkerFaceColor','red','MarkerEdgeColor','black','MarkerSize',9); hold on
%h6= plot(We,md_3,'<','MarkerFaceColor','green','MarkerEdgeColor','black','MarkerSize',9); hold on
h7= plot(We,md_4,'d','MarkerFaceColor','red','MarkerEdgeColor','black','MarkerSize',9); hold on

pcoeff= polyfit(We,md_4,2)
%pcoeff2= polyfit(We,md_ho,2)
%axis([0 625 0 0.5]);
yp= polyval(pcoeff,We);
%yp2= polyval(pcoeff2,We);
h2= plot(We,yp,'k','LineWidth',1.2); hold on
h3= plot(We,psi_m, 'b','LineWidth', 1.5); hold on  % (psi_m is the Graham-Farhangi's correlated maximum deformation)
%plot(We,psi2_m,'LineStyle','--','Color','g','LineWidth',1.5); %(Clanet et al's correlation)
h4= plot(We,psi_m3,'LineStyle','-.','Color','#0B0'); hold on %(Li et al's correlation)
h8= plot(We,psi_m_4,'LineStyle','-','LineWidth',1.2,'Color','magenta');
%p = polyfit(We,md_ho, 1);
%px = [min(We) max(We)];
%py = polyval(p, px);
%hold on
%plot(px, py, 'LineWidth', 2);
legend([h7(1), h2(1), h3(1),h4(1), h8(1)], 'Experimental data for \lambda = 0.397 (4mm offset)','Fitted curve', 'Graham et al.','Li et al.', 'my correlation');
xlabel('We','FontSize',14,'FontWeight','normal');ylabel('\psi_{max}','FontSize',16,'FontWeight','bold');

[VBBV]

h4 and h8 line plots contain 2D matrices

clc;clear;close all;
%for head on collision
L= 4;
D= 3.860;
lam= 0.397;
% lamda will go from 0.4 m/sec (water, 0.25, 0.5, 0.75, 1) then 1m/sec
% (same thing) and finally 1.65 m/sec (same thing)
lam_org= [0.394 0.2091 0.284 0.404 0.374 0.423 0.358 0.523 0.493 0.567 0.359 0.424 0.296 0.445 0.447];
%lam_15_times = [0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397];
lam_l = log(lam_org);
psi_e= (2^0.33)/(2-lam);
Oh= 10^(-3)*[1.679 2.457 2.679 2.922 3.398 1.597 2.1782 2.505 2.958 1.487 3.129 1.934 2.478 2.728 2.893];

md_ho = [1.0690 2.02 1.3474 1.3580 1.3966 1.6701 1.4901 1.669 1.476 2.848 1.3871 2.8008 3.0724 2.3614 2.7726];
L_o = log(md_ho);
We = [8.518 9.903 16.473 22.68 26.214 58.84 78.77 117.76 138.37 184.842 193.155 272.054 327.49 443.05 615.34];
We_log = log(We);

%for 2mm offset
md_2= [1.0431 1.1251 0.9519 0.9691 0.9380 1.5003 1.2390 1.3260 1.2584 2.2003 1.2260 1.9754 2.125 1.6842 2.098];
L_2 = log(md_2);
We= [8.518 9.903 16.473 22.68 26.214 58.84 78.77 117.76 138.37 184.842 193.155 272.054 327.49 443.05 615.34];

%for 3mm offset
md_3= [0.9819 0.9916 1.0444 0.9938 0.9807 1.3555 1.2052 1.227 1.1849 1.747 1.2106 1.5462 1.6876 1.5860 1.726];
L_3 = log(md_3);
We= [8.518 9.903 16.473 22.68 26.214 58.84 78.77 117.76 138.37 184.842 193.155 272.054 327.49 443.05 615.34];


%for 4mm offset
md_4= [1.015 0.9875 1.0682 1.0763 1.0021 1.295 1.119 1.1112 1.125 1.681 1.1667 1.6932 1.862 1.677 1.6443 ];
L_4 = log(md_4);
We= [8.518 9.903 16.473 22.68 26.214 58.84 78.77 117.76 138.37 184.842 193.155 272.054 327.49 443.05 615.34];

for i= 1:length(We)
   psi_m(i)= 0.9759*((1+L/D)^(-0.7594))*We(i).^0.2283; % Graham et al.
end

for j=1:length(We)
    psi2_m(j)= (D+L)*We(j).^0.25; % Clanet et al.
end

for k= 1:length(We)
   for l= 1:length(Oh)
    psi_m3(k,l)= 0.8353*(psi_e^0.3774)*(We(k)^0.0571)*(Oh(l)^(-0.0430)); % Li et al.
   end
end

for m= 1: length(We)
    for n= 1: length(lam_org)
        psi_m_4(m,n)= 0.6046*(We(m)^0.1453)*(lam_org(n)^(-0.1062)); % my correlation
    end
end
psi_m_4

psi_m_4 = 15×15

0.9112 0.9746 0.9434 0.9088 0.9162 0.9043 0.9205 0.8842 0.8897 0.8766 0.9202 0.9041 0.9393 0.8995 0.8990 0.9313 0.9962 0.9643 0.9289 0.9365 0.9243 0.9409 0.9037 0.9094 0.8960 0.9406 0.9241 0.9601 0.9194 0.9189 1.0028 1.0726 1.0383 1.0002 1.0084 0.9953 1.0131 0.9731 0.9792 0.9648 1.0128 0.9950 1.0337 0.9899 0.9895 1.0505 1.1236 1.0877 1.0477 1.0563 1.0426 1.0613 1.0194 1.0258 1.0107 1.0609 1.0424 1.0829 1.0370 1.0365 1.0729 1.1475 1.1108 1.0700 1.0788 1.0648 1.0838 1.0411 1.0476 1.0322 1.0835 1.0645 1.1059 1.0591 1.0586 1.2066 1.2906 1.2493 1.2034 1.2133 1.1975 1.2189 1.1708 1.1782 1.1608 1.2186 1.1972 1.2438 1.1911 1.1905 1.2588 1.3464 1.3034 1.2555 1.2658 1.2494 1.2717 1.2215 1.2292 1.2111 1.2713 1.2491 1.2977 1.2427 1.2421 1.3346 1.4275 1.3818 1.3310 1.3420 1.3245 1.3482 1.2950 1.3032 1.2840 1.3478 1.3242 1.3757 1.3174 1.3168 1.3662 1.4613 1.4146 1.3626 1.3738 1.3560 1.3802 1.3257 1.3341 1.3144 1.3798 1.3556 1.4083 1.3487 1.3480 1.4249 1.5241 1.4753 1.4211 1.4328 1.4142 1.4395 1.3827 1.3914 1.3709 1.4391 1.4139 1.4689 1.4066 1.4060

%h1= plot(We,md_ho,'s','MarkerFaceColor','red','MarkerEdgeColor','black','MarkerSize',9); hold on
%h5= plot(We,md_2,'o','MarkerFaceColor','red','MarkerEdgeColor','black','MarkerSize',9); hold on
%h6= plot(We,md_3,'<','MarkerFaceColor','green','MarkerEdgeColor','black','MarkerSize',9); hold on
h7= plot(We,md_4,'d','MarkerFaceColor','red','MarkerEdgeColor','black','MarkerSize',9); hold on

pcoeff= polyfit(We,md_4,2)

pcoeff = 1×3

-0.0000 0.0032 0.9539

%pcoeff2= polyfit(We,md_ho,2)
%axis([0 625 0 0.5]);
yp= polyval(pcoeff,We);
%yp2= polyval(pcoeff2,We);

h2= plot(We,yp,'k','LineWidth',1.2); hold on
h3= plot(We,psi_m, 'b','LineWidth', 1.5); hold on  % (psi_m is the Graham-Farhangi's correlated maximum deformation)
%plot(We,psi2_m,'LineStyle','--','Color','g','LineWidth',1.5); %(Clanet et al's correlation)
h4= plot(We,psi_m3(:,1),'LineStyle','-.','Color','#0B0','linewidth',2); hold on %(Li et al's correlation)
h8= plot(We,psi_m_4(:,1),'LineStyle','-','LineWidth',1.2,'Color','magenta','linewidth',2);
%p = polyfit(We,md_ho, 1);
%px = [min(We) max(We)];
%py = polyval(p, px);
%hold on
%plot(px, py, 'LineWidth', 2);
legend([h7(1), h2(1), h3(1),h4(1), h8(1)], 'Experimental data for \lambda = 0.397 (4mm offset)','Fitted curve', 'Graham et al.','Li et al.', 'my correlation','location','best');
xlabel('We','FontSize',14,'FontWeight','normal');ylabel('\psi_{max}','FontSize',16,'FontWeight','bold');

[dpb]

Unlike the others, those two are 2D arrays instead of vectors; MATLAB plot() treats columns as independent variables plotted against the x variable. It is doing exactly what you told it to do...

We don't know what you were expecting; you didn't tell us what you were expecting instead.

The Q? is why are those 2D arrays when being calculated and what were you expecting them to be: you've parameterized the two against variables (Oh) and (lam_org), respectively.

[Pragyan Kumar Sarma]

Ok, that seems to be the problem then. I wanted psi_m3 and psi_m_4 to be a vector only. Is there a problem with the nested 'for' loop? I wanted

psi_m3(k,l)= 0.8353*(psi_e^0.3774)*(We(k)^0.0571)*(Oh(l)^(-0.0430))

to simulatneously take the respective values and return a single product value for one set of datas from each vectors We and Oh.

Same is the case with

 psi_m_4(m,n)= 0.6046*(We(m)^0.1453)*(lam_org(n)^(-0.1062))

psi_m_4 should return a vector by taking each data value from the respective We and lam_org vector and getting a product.

[Pragyan Kumar Sarma]

I wanted psi_m3 and psi_m_4 to return only one vector.

Maybe the nested for loop is causing it.

For this line

psi_m3(k,l)= 0.8353*(psi_e^0.3774)*(We(k)^0.0571)*(Oh(l)^(-0.0430))

I wanted the corresponding data value from the vector We and Oh to appear simultaneously and return only one value of psi_m3 for a given value of We and Oh. I guess this is not happening in here.

Same thing should happen on this line

psi_m_4(m,n)= 0.6046*(We(m)^0.1453)*(lam_org(n)^(-0.1062))

It should return only one value of psi_m_4 as a product valuer for a particular value of We and lam_org. So in total psi_m_4 should return a total of 15 values as a vector.

[Torsten]

So you want

psi_m3 = 0.8353*(psi_e.^0.3774).*(We.^0.0571).*(Oh.^(-0.0430))
psi_m_4 = 0.6046*(We.^0.1453).*(lam_org.^(-0.1062))

?

[VBBV]

Ok, For each case of We you can obtain different values for psi parameter and compare your correlation with that of others. To do this you can use only one for loop instead of multiple loops.

clc;clear;close all;
%for head on collision
L= 4;
D= 3.860;
lam= 0.397;
% lamda will go from 0.4 m/sec (water, 0.25, 0.5, 0.75, 1) then 1m/sec
% (same thing) and finally 1.65 m/sec (same thing)
lam_org= [0.394 0.2091 0.284 0.404 0.374 0.423 0.358 0.523 0.493 0.567 0.359 0.424 0.296 0.445 0.447];
%lam_15_times = [0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397];
lam_l = log(lam_org);
length(lam_org)

ans = 15

psi_e= (2^0.33)/(2-lam);
Oh= 10^(-3)*[1.679 2.457 2.679 2.922 3.398 1.597 2.1782 2.505 2.958 1.487 3.129 1.934 2.478 2.728 2.893];

md_ho = [1.0690 2.02 1.3474 1.3580 1.3966 1.6701 1.4901 1.669 1.476 2.848 1.3871 2.8008 3.0724 2.3614 2.7726];
L_o = log(md_ho);
We = [8.518 9.903 16.473 22.68 26.214 58.84 78.77 117.76 138.37 184.842 193.155 272.054 327.49 443.05 615.34];
We_log = log(We);

length(We)

ans = 15

%for 2mm offset
md_2= [1.0431 1.1251 0.9519 0.9691 0.9380 1.5003 1.2390 1.3260 1.2584 2.2003 1.2260 1.9754 2.125 1.6842 2.098];
L_2 = log(md_2);
We= [8.518 9.903 16.473 22.68 26.214 58.84 78.77 117.76 138.37 184.842 193.155 272.054 327.49 443.05 615.34];

%for 3mm offset
md_3= [0.9819 0.9916 1.0444 0.9938 0.9807 1.3555 1.2052 1.227 1.1849 1.747 1.2106 1.5462 1.6876 1.5860 1.726];
L_3 = log(md_3);
We= [8.518 9.903 16.473 22.68 26.214 58.84 78.77 117.76 138.37 184.842 193.155 272.054 327.49 443.05 615.34];


%for 4mm offset
md_4= [1.015 0.9875 1.0682 1.0763 1.0021 1.295 1.119 1.1112 1.125 1.681 1.1667 1.6932 1.862 1.677 1.6443 ];
L_4 = log(md_4);
We= [8.518 9.903 16.473 22.68 26.214 58.84 78.77 117.76 138.37 184.842 193.155 272.054 327.49 443.05 615.34];


for m= 1: length(We)
    psi_m(m)= 0.9759*((1+L/D)^(-0.7594))*We(m).^0.2283; % Graham et al.
    psi2_m(m)= (D+L)*We(m).^0.25; % Clanet et al.
    psi_m3(m)= 0.8353*(psi_e^0.3774)*(We(m)^0.0571)*(Oh(m)^(-0.0430)); % Li et al.
    psi_m_4(m)= 0.6046*(We(m)^0.1453)*(lam_org(m)^(-0.1062)); % my correlation    
end

%h1= plot(We,md_ho,'s','MarkerFaceColor','red','MarkerEdgeColor','black','MarkerSize',9); hold on
%h5= plot(We,md_2,'o','MarkerFaceColor','red','MarkerEdgeColor','black','MarkerSize',9); hold on
%h6= plot(We,md_3,'<','MarkerFaceColor','green','MarkerEdgeColor','black','MarkerSize',9); hold on
h7= plot(We,md_4,'d','MarkerFaceColor','red','MarkerEdgeColor','black','MarkerSize',9); hold on

pcoeff= polyfit(We,md_4,2)

pcoeff = 1×3

-0.0000 0.0032 0.9539

%pcoeff2= polyfit(We,md_ho,2)
%axis([0 625 0 0.5]);
yp= polyval(pcoeff,We);
%yp2= polyval(pcoeff2,We);

h2= plot(We,yp,'k','LineWidth',1.2); hold on
h3= plot(We,psi_m, 'b','LineWidth', 1.5); hold on  % (psi_m is the Graham-Farhangi's correlated maximum deformation)
%plot(We,psi2_m,'LineStyle','--','Color','g','LineWidth',1.5); %(Clanet et al's correlation)
h4= plot(We,psi_m3,'LineStyle','-.','Color','#0B0','linewidth',2); hold on %(Li et al's correlation)
h8= plot(We,psi_m_4,'LineStyle','-','LineWidth',1.2,'Color','magenta','linewidth',2);

grid 
legend([h7(1), h2(1), h3(1),h4(1), h8(1)], 'Experimental data for \lambda = 0.397 (4mm offset)','Fitted curve', 'Graham et al.','Li et al.', 'my correlation','location','best');
xlabel('We','FontSize',14,'FontWeight','normal');ylabel('\psi_{max}','FontSize',16,'FontWeight','bold');

[Pragyan Kumar Sarma]

I wanted to get vector multiplication.

[dpb]

Vector multiplication of what??? An Nx1 by 1xN results in an NxN while a [1xN] by [Nx1] yields a single value. Neither of those two possibilities will result in a 1xN vector that you say you want/were expecting.

It certainly is not at all clear just what any of this means or how to try to interpret the two variables in each of the "correlations". You've got 15 values of two variables each, but what either of those represents and how they were determined is completely a black box to us.

It certainly isn't at all clear where the formulations you're using come from or what they are trying to correlate; it certainly is especially unclear in your correlation where there are the two variables(?) as to what it means that both are changing and how that relates to anything else...but the only way to get the 1x15 vector is as we've shown, use the two pairwise for each element in the two vectors. Now, whether that makes any sense or not to have done so is another question entirely. We have absolutely no way to know about that from what information has been shared here.

[Torsten]

If you want

a = [1 2 3];
b = [4 25 36];
c = a.^2.*b.^0.5

c = 1×3

2 20 54

then you found what you are looking for.

Answer 1

[dpb]

Well, there's no "problem" with the nested loop other than apparently it isn't what you intended... :) It iterates through each value of the Oh or lam_org for each We in turn.

If the intent is instead to use the i_th value of each We and Oh at the same time such that both are changing simultaneously but the combinations of I,J for I~=J aren't computed, then you don't need (or want) the nested loop but just a single loop -- or, in MATLAB don't need the loop at all;, just write the vectorized expressions.

...
for k= 1:length(We)
  psi_m3(k)= 0.8353*(psi_e^0.3774)*(We(k)^0.0571)*(Oh(k)^(-0.0430));   % Li et al.
  psi_m_4(k)= 0.6046*(We(k)^0.1453)*(lam_org(k)^(-0.1062));           % my correlation
end

where I've moved them both into a single loop since iterating over same thing for both.

"The MATLAB way" to do the above is to use the "dot" operators and vectorize the expressions...

psi_m3 = 0.8353*(psi_e^0.3774).*(We.^0.0571).*(Oh.^(-0.0430));   % Li et al.
psi_m_4= 0.6046*(We.^0.1453).*lam_org.^(-0.1062);                % my correlation

See the doc for times, .* to learn about element-wise operators.