How to plot error bars for multiple data points at a single time point

I am new on Matlab and trying to plot error bars on data points. But I have multiple data points at a single time point. Below down is my code:

EXP.t=[0 0 0 0 2.16 3.96 5.83 8.66 13.3 24];    %hours
EXP.Blood_15=[0.05 0.036 0.027 0.021 0.02 0.017 0.015 0.013 0.011 0.008]; %concentration
EXP.errhigh_B15=[0.051 0.044 0.032 0.022 0.021 0.019 0.017 0.012 NaN 0.009];  %concentration      
EXP.errlow_B15=[0.048 0.028 0.022 0.02 0.019 0.015 0.012 0.012 NaN 0.007];     %concentration

%plots

figure(1)
%Blood Pharmacokinetics of 15E-03, 183E-03, 1058E-03 mg/g dose GSH-AuNPs 
set(gcf, 'Position',[0,45,1800,900])
set(0,'defaultAxesFontName', 'Timesnewroman')
set(0,'defaultTextFontName', 'Timesnewroman')
ylabel(['%ID/g in blood(mg/g)'])%CF of (%ID/g) = mg/g
subtightplot(2,2,1, margins)
bar(EXP.t,EXP.Blood_15)
set(gca,'fontsize',12,'FontName','arial','XScale','lin','Xlim',[0,24],'XTick',[0,6,12,18,24]);
hold on
ylabel(['GSH-AuNPs conc. in blood(mg/g)'])
xlabel(['Time(h)'])
plot(t1,(m_Au_V1+m_Au_A1),'-',EXP.t,EXP.Blood_15,'o','Color', blue,'LineWidth',2)
er = errorbar(EXP.t,EXP.Blood_15,EXP.errlow_B15,EXP.errhigh_B15);    
er.Color = [0 0 0];                            
er.LineStyle = 'none';
lgd= legend('simulated data','experimental data','Location','northeast');
title(lgd,'15E-03 mg/g ID')
hold off

I tried to plot the error bar but shows the error:

Error using bar (line 182)
XData values must be unique.

Error in para_vald_GSH (line 342)
bar(EXP.t,EXP.Blood_15)

So how can I plot error bars for multiple time points at a single time point? Please help me. It will be appreciated. Thank you in advance.

[the cyclist]

The problem is not with the error bars, but with the bar chart that precedes that plotting.

Let's simplify a little, and look only at the first few points. What is your expectation about what this code's output should look like?

EXP.t=[0 0 0 0 2.16];    %hours
EXP.Blood_15=[0.05 0.036 0.027 0.021 0.02]; %concentration

%plots
bar(EXP.t,EXP.Blood_15)

Error using bar (line 182)
XData values must be unique.

Because to me, this would create (if MATLAB allowed it) several bars at X = 0, which is difficult to understand/interpret.

Answer 1

[dpb]

Plot versus ordinal value and then use xticklabels to label the times...

hB=bar(EXP.Blood_15);
hold on
hEr=errorbar(1:numel(EXP.Blood_15),EXP.Blood_15,EXP.errlow_B15,EXP.errhigh_B15,'k','LineStyle','none');
xticklabels(compose('%.2f',EXP.t))
xlabel('Time (hr)')
ylabel('GSH-AuNPs conc. in blood(mg/g)')

yields

Salt to suit; not sure about why the funky-looking y-label text...

If you try to plot() or bar() with actual t values repeated on the axis, then there's nothing to separate the four time zero cases--although I've no idea what this is/represents, those look somewhat peculiar in a decreasing pattern as is -- I presume probably the time isn't actually identically zero but something less than an hour but not recorded, maybe?

[Rajvi Amle]

Thank you for your response @the cyclist and @dpb. Although I want to plot something like I have attached an image of. As shown, there are 4 to 5 data points on 0 hour with the error bars given. I want to plot error bars for the same.

[the cyclist]

You don't need the bar command at all for that style of plot. You only need the errorbar command. It will make the line, and the errorbars.

You can use code such as your own, or @dpb's example, but

• remove the call to bar
• don't use 'LineStyle','none' in the call to errorbar

[dpb]

With the data as presented, the line/errorbar plot is going to be one big blob at t=0; the error magnitudes are as large as the data and will just all mush on top of each other.

OP's data are nothing nearly so clean as the example plots show.

I still can't imagine those points are all identically t=0, though. either, the attached plots look to me like there's a very short time period there, not a perfectly vertical line. But, I could be wrong; I've no klew if there might be somesuch kind of measurement or not but it just doesn't seem likely would get such data if were.

[dpb]

Mimicking one of those with OP's data results in

which looks even more to me as though the actual plots are not all at t==0 but short initial time intervals as compared to the hourly tick marks.

Just for grins, I set

EXP.t(2:4)=[1 2 8]/60;

and it then looks more like the examples albeit still with a lot of noise comparatively.

First without the "fixup" for time was done with

hEr=errorbar(EXP.t,100*EXP.Blood_15,100*EXP.errlow_B15,100*EXP.errhigh_B15,'k-o','MarkerSize',6,'MarkerFaceColor','k');
xlim([-1 25]), ylim([-1 13])
box off
xticks([0:6:24]), yticks([0:4:12])
xlabel('Time (hr)')
ylabel('GSH-AuNPs conc. in blood(mg/g)')

I still don't understand why the 'Tex' interpreter is bolding the NP substring inside the ylabel text -- that seems bizarre behavior.

To produce the second, I just futzed with the XData property aribtrarily...

hEr.XData(2:4)=[1 2 8]/60;

[Rajvi Amle]

@dpb and @the cyclist Thank you for your response. But @dpb, is it possible that the line should not connect the data points with each other. I am already comparing simulating data with the experimental data. So the line should not be there.

[dpb]

Well, you had just posted that you wanted plots that looked like the examples which include lines. Ergo, I drew lines.

But, sure, you can do without--

hEr.LineStyle='none';

will remove it from existing plot or just leave out the "-" linestyle part of the linestyle triplet in the call in the first place.

I'm still curious about the initial data times--it just doesn't make any sense to me these really are all at identically zero times.

[Rajvi Amle]

@dpb I found the answer for the time points. The initial data points are not at all on 0 times but are calculated for 2, 5, 10 and 30 mins, 1, 3, 5, 8, 12 and 24 h.

[dpb]

SUPER!!! And thanks so much for posting back; really nice to know when we're not barking up the wrong tree... :)

Interesting, though, then that you don't actually have a "time zero" value at all.

But, it will certainly make the plots look much nicer and a smoother "decay" or dissolution with time.

Just for grins, you might try

hAx=gca; hAx.XScale='log';
xlim([0.01 25])
xticks([0.01 0.05 0.1 0.5 1 5 10 20

[Rajvi Amle]

Your welcome @dpb. But I should thank you for helping me out.

Although I have a question again. I want toplot a graph for blood concentration over time. And I have to do this for 10 virtual population (n=10). I created a loop for 10 simulations and stored result in an empty array. Next, I recorded these values for plotting as 'x' which has 146x1 dimension values. Now I want to calculate mean as rows from 'x', and based on this mean values I want to get confidence interval of 95% and plot it with simulation results for 10 simulations. Here is my code so far from loop;

EXP.t=[0 6 12 18 24];
% Enteries in a loop
n=10;
t=[];
x=[];
for i=1:n
  tspan=[0 max(EXP.t)]; 
  MAT=[SYSTEM.m_BW(i) SYSTEM.w_L(i) SYSTEM.w_K(i) SYSTEM.w_Lu(i) SYSTEM.w_BR(i) SYSTEM.w_Blood(i) SYSTEM.w_Plasma(i) SYSTEM.m_L(i) SYSTEM.m_BR(i) SYSTEM.m_K(i) SYSTEM.m_S(i) SYSTEM.m_Lu(i) SYSTEM.m_Blood(i) SYSTEM.m_Plasma(i)...
        SYSTEM.V_L(i) SYSTEM.V_BR(i) SYSTEM.V_K(i) SYSTEM.V_S(i) SYSTEM.V_Lu(i) SYSTEM.V_Blood(i) SYSTEM.V_Plasma(i) SYSTEM.F_C(i) SYSTEM.F_L(i) SYSTEM.F_BR(i) SYSTEM.F_K(i) SYSTEM.F_S(i) SYSTEM.F_Res(i) SYSTEM.F_bal(i) SYSTEM.F_Bile(i) SYSTEM.F_Urine(i)...
        SYSTEM.V_Res(i) SYSTEM.V_bal(i) SYSTEM.V_L_b(i) SYSTEM.V_L_t(i) SYSTEM.V_BR_b(i) SYSTEM.V_BR_t(i) SYSTEM.V_K_b(i)  SYSTEM.V_K_t(i) SYSTEM.V_S_b(i) SYSTEM.V_S_t(i) SYSTEM.V_Lu_b(i) SYSTEM.V_Lu_t(i) SYSTEM.V_Res_b(i) SYSTEM.V_Res_t(i)... 
        DRUG.m_Au_iv(1) DRUG.M_Au_iv(1)]';
  options=odeset('AbsTol',10e-2,'RelTol',10e-2,'Stats','on');
  col=zeros(18,1);
  [t0,x0]=ode15s(@ode_toy, tspan, col,[],ov,DRUG,MAT);    
  t=[t; t0];
  x=[x; x0];
end

for i=1:n
  m_Au_A1=x0(:,1);                             %Amount of AuNP in arterial blood
  m_Au_V1=x0(:,2);                             %Amount of AuNP in venous blood
  x=m_Au_A1+m_Au_V1;
  mean_x=mean(x);
  std_x=mean_x/size(x,1);
  ts = tinv([0.025;  0.975],length(x)-1);      % T-Score
  CI95 = mean_x + ts.*(std_x/sqrt(length(x)));

I want something like shown in the figure as attached(c1.png). Could you please have a look and help me?

[Rajvi Amle]

@dpb Looking forward to your response. Please do help me if possible.

[dpb]

Can't run your code but if you have consistent time histories as you describe, then taking mean and std over the population/2D array of those is simply calling mean() and std() with the proper direction -- either default by column if the array is each row a time history or by column (dimension 2) if the time histories are stored by column instead.

As it looks like you know, the error in the mean is std()/sqrt(N) * but you have 10 observations here, not the number in the time history.

[Rajvi Amle]

@dpb Can I send you my complete code to make you understand better? It is bit complicated but I only need to get the mean and CI values of a row vector thats it.

[dpb]

Well, taking the mean of a vector is trivial; it's not clear what that mean would be representative of in your case if it is one of the time histories.

If you mean a "vector" as the collection of time histories at a given time, then MATLAB will deal with that for you automagically as mean() is vectorized to operate by column by default over a 2D array or, with the optional DIM input argument, it will compute the means of each row (or whatever dimension is given for higher dimensionality arrays).

Example w/ dummy data array--

>> A=rand(4,3);                     % 4 rows, 3 columns
>> [mean(A); std(A)]                % by default operates by column
ans =
    0.3914    0.4985    0.3898
    0.3439    0.1605    0.4082
>>

So, the above gives the mean and std for each column of the array -- if the time histories are by row for each of the 10 histories and each column is a time step, this is what you want.

>> [mean(A,2), std(A,[],2)]         % instead go by row instead of by column
ans =
    0.5097    0.3232
    0.1475    0.1437
    0.4647    0.1904
    0.5844    0.3916
>> 

If, instead each column represents a time series and the rows are the time steps, then the above computes the statistics again over the collection of time series.

I don't know what more to tell you...

[Rajvi Amle]

Thank you for your efforts and time @dpb. Further, in my code, when I tried to plot the simulated and experimental data together, they were not much closer to each other so I tried to optimize the parameter values and used 'fmincon' function. However I am getting the error when the code is run. I tried to solve it but wasn't able to overcome it. Could you please have a look and help me with this? Following is the part of my code where fmincon function was used:

%Initial and boundary conditions for optimization
% Optimization variables - Initial conditions, lower and upper bounds
ov_ini(1) = 4.338;         lb_1=0;  ub_1=ov_ini(1)*2;       % 1.85 K_max_L    [h-1]
ov_ini(2) = 233.06;         lb_2=0;  ub_2=ov_ini(2)*2;       % 4.06 K_max_S    [h-1]
ov_ini(3) = 0.804;      lb_3=0;  ub_3=ov_ini(3)*2;       % 0.0192 K_max_K  [h-1]
ov_ini(4) = 0.173;      lb_4=0;  ub_4=ov_ini(4)*2;       % 0.0643 K_max_Lu [h-1]
ov_ini(5) = 5.4E-05;       lb_5=0;  ub_5=1;                  % 0.08 PL [-]
ov_ini(6) = 0.0447;       lb_6=0;  ub_6=1;                  % 0.15 PBR [-]
ov_ini(7) = 0.3435;       lb_7=0;  ub_7=1;                  % 0.15 PK [-]
ov_ini(8) = 0.6327;       lb_8=0;  ub_8=1;                  % 0.15 PS [-]
ov_ini(9) = 0.0095;       lb_9=0;  ub_9=1;                  % 0.15 PLu [-]
ov_ini(10) = 4.9E-06;      lb_10=0; ub_10=1;                 % 0.15 PRes [-]
ov_ini(11) = 0.00099304;     lb_11=0; ub_11=1;                 % 0.001 PALC [-]
ov_ini(12) = 7.04E-06;     lb_12=0; ub_12=ov_ini(12)*2;     % 0.001 PASC [-]
ov_ini(13) = 2.6E-04;   lb_13=0; ub_13=ov_ini(13)*2;     % 0.00034 PAKC [-]
ov_ini(14) = 8.13E-06;     lb_14=0; ub_14=ov_ini(14)*2;     % 0.001 PALuC [-]
ov_ini(15) = 0.01;  lb_15=0; ub_15=ov_ini(15)*2;      % 0.000001 PABRC [-]
ov_ini(16) = 0.01;  lb_16=0; ub_16=ov_ini(16)*2;      % 0.000001 PAResC [-]
ov_ini(17) = 3.3E-04;    lb_17=0; ub_17=ov_ini(17)*2;     % 0.0075/3 K_rel_L [h-1]
ov_ini(18) = 0.0022;    lb_18=0; ub_18=ov_ini(18)*2;     % 0.003/3 K_rel_S [h-1]
ov_ini(19) = 2.03E-05;   lb_19=0; ub_19=ov_ini(19)*2;     % 0.000385 K_rel_K [h-1]
ov_ini(20) = 0.0043;    lb_20=0; ub_20=ov_ini(20)*2;     % 0.005/10 K_rel_Lu [h-1]

lb = [lb_1 lb_2 lb_3 lb_4 lb_5 lb_6 lb_7 lb_8 lb_9 lb_10 lb_11 lb_12 lb_13 lb_14 lb_15 lb_16 lb_17 lb_18 lb_19 lb_20];% lower boundary
ub = [ub_1 ub_2 ub_3 ub_4 ub_5 ub_6 ub_7 ub_8 ub_9 ub_10 ub_11 ub_12 ub_13 ub_14 ub_15 ub_16 ub_17 ub_18 ub_19 ub_20];% upper boundary

ov0 = [ov_ini];

%% Parameter Optimization

   MAT=[SYSTEM.m_BW(1) SYSTEM.w_L(1) SYSTEM.w_K(1) SYSTEM.w_Lu(1) SYSTEM.w_BR(1) SYSTEM.w_Blood(1) SYSTEM.w_Plasma(1) SYSTEM.m_L(1) SYSTEM.m_BR(1) SYSTEM.m_K(1) SYSTEM.m_S(1) SYSTEM.m_Lu(1) SYSTEM.m_Blood(1) SYSTEM.m_Plasma(1)...
        SYSTEM.V_L(1) SYSTEM.V_BR(1) SYSTEM.V_K(1) SYSTEM.V_S(1) SYSTEM.V_Lu(1) SYSTEM.V_Blood(1) SYSTEM.V_Plasma(1) SYSTEM.F_C(1) SYSTEM.F_L(1) SYSTEM.F_BR(1) SYSTEM.F_K(1) SYSTEM.F_S(1) SYSTEM.F_Res(1) SYSTEM.F_bal(1) SYSTEM.F_Bile(1) SYSTEM.F_Urine(1)... 
        SYSTEM.V_Res(1) SYSTEM.V_bal(1) SYSTEM.V_L_b(1) SYSTEM.V_L_t(1) SYSTEM.V_BR_b(1) SYSTEM.V_BR_t(1) SYSTEM.V_K_b(1)  SYSTEM.V_K_t(1) SYSTEM.V_S_b(1) SYSTEM.V_S_t(1) SYSTEM.V_Lu_b(1) SYSTEM.V_Lu_t(1) SYSTEM.V_Res_b(1) SYSTEM.V_Res_t(1)... 
        DRUG.m_Au_iv(1) DRUG.M_Au_iv(1)]';
              
opt = optimset('MaxFunEval',1E5,'Maxiter',1E3,'Algorithm','interior-point',...
     'TolX',1E-5,'TolFun',1E-6,'Display','iter');
[val_par, fval, v3, v4, v5, v6, H] = ...
    fmincon(@obfun_chitosan,ov0,[],[],[],[],lb,ub,[],opt,SYSTEM,DRUG,CF,EXP,MAT);

%% Solver
%   ov = val_par(1:20);
%     ov = ov0;
    ov_val = ov';
    save('val_para','ov_val')  

for i=1
    if i == 1
        %Dosing
        MAT=[SYSTEM.m_BW(1) SYSTEM.w_L(1) SYSTEM.w_K(1) SYSTEM.w_Lu(1) SYSTEM.w_BR(1) SYSTEM.w_Blood(1) SYSTEM.w_Plasma(1) SYSTEM.m_L(1) SYSTEM.m_BR(1) SYSTEM.m_K(1) SYSTEM.m_S(1) SYSTEM.m_Lu(1) SYSTEM.m_Blood(1) SYSTEM.m_Plasma(1)...
        SYSTEM.V_L(1) SYSTEM.V_BR(1) SYSTEM.V_K(1) SYSTEM.V_S(1) SYSTEM.V_Lu(1) SYSTEM.V_Blood(1) SYSTEM.V_Plasma(1) SYSTEM.F_C(1) SYSTEM.F_L(1) SYSTEM.F_BR(1) SYSTEM.F_K(1) SYSTEM.F_S(1) SYSTEM.F_Res(1) SYSTEM.F_bal(1) SYSTEM.F_Bile(1) SYSTEM.F_Urine(1)... 
        SYSTEM.V_Res(1) SYSTEM.V_bal(1) SYSTEM.V_L_b(1) SYSTEM.V_L_t(1) SYSTEM.V_BR_b(1) SYSTEM.V_BR_t(1) SYSTEM.V_K_b(1)  SYSTEM.V_K_t(1) SYSTEM.V_S_b(1) SYSTEM.V_S_t(1) SYSTEM.V_Lu_b(1) SYSTEM.V_Lu_t(1) SYSTEM.V_Res_b(1) SYSTEM.V_Res_t(1)... 
        DRUG.m_Au_iv(1) DRUG.M_Au_iv(1)]';
        tspan = [0 max(EXP.t)];
        options=odeset('AbsTol',10e-2,'RelTol',10e-2,'Stats','on');
        x0=zeros(19,1);
        tic;
        [t1,X1] = ode15s(@ode_chitosan, tspan,x0, [], SYSTEM,DRUG, CF, ov, MAT);
        toc;    
    end
    
function out = obfun_chitosan(ov,SYSTEM,DRUG,CF,EXP,MAT)

for i=1
%% Initial conditions and Input variables

     
        if i == 1                                                                     
        % Initial conditions for ODEs
        x0=zeros(19,1);
        end

        
        %% Solver
   
    ov = ov(1:20);

    if i == 1
        [t1,X1] = ode15s(@ode_chitosan, EXP.t, x0,[], SYSTEM,DRUG, CF, ov,MAT);
        m_Au_A1=X1(:,1);                             % Amount of AuNP in arterial blood
        m_Au_V1=X1(:,2);                             % Amount of AuNP in venous blood
        m_Au_Lu_b1=X1(:,3);                          % Amount of AuNP in lung capillary blood
        m_Au_Lu_t1=X1(:,4);                          % Amount of AuNP in lung tissue
        m_Au_Lu_PC1=X1(:,5);                         % Amount of AuNP in lung PC
        m_Au_BR_b1=X1(:,6);                          % Amount of AuNP in brain capillary blood
        m_Au_BR_t1=X1(:,7);                          % Amount of AuNP in brain tissue
        m_Au_Res_b1=X1(:,8);                         % Amount of AuNP in rest of body capillary blood
        m_Au_Res_t1=X1(:,9);                         % Amount of AuNP in rest of body tissue
        m_Au_K_b1=X1(:,10);                          % Amount of AuNP in kidney capillary blood
        m_Au_K_t1=X1(:,11);                          % Amount of AuNP in kidney tissue
        m_Au_K_PC1=X1(:,12);                         % Amount of AuNP in kidney PC
        m_Au_S_b1=X1(:,13);                          % Amount of AuNP in spleen capillary blood
        m_Au_S_t1=X1(:,14);                          % Amount of AuNP in spleen tissue
        m_Au_S_PC1=X1(:,15);                         % Amount of AuNP in spleen PC
        m_Au_L_b1=X1(:,16);                          % Amount of AuNP in liver capillary blood
        m_Au_L_t1=X1(:,17);                          % Amount of AuNP in liver tissue
        m_Au_L_PC1=X1(:,18);                         % Amount of AuNP in liver PC
        AUC1=X1(:,19);
        for k = 1:length(m_Au_A1)
        h = ae_chitosan(X1(k,:),SYSTEM,DRUG,CF,ov,t1(k),MAT);
        M_Au_iv1(k)=h.M_Au_iv;
        rho_Au_A1(k)=h.rho_Au_A;
        rho_Au_V1(k)=h.rho_Au_V;
        rho_Au_Lu1(k)=h.rho_Au_Lu;
        rho_Au_L1(k)=h.rho_Au_L;
        rho_Au_K1(k)=h.rho_Au_K;
        rho_Au_S1(k)=h.rho_Au_S;
        m_Au_Lu_total1(k)=h.m_Au_Lu_total;
        m_Au_L_total1(k)=h.m_Au_L_total;
        m_Au_K_total1(k)=h.m_Au_K_total;
        m_Au_S_total1(k)=h.m_Au_S_total;
        w_Au_Kidney_Tissue1(k)=h.w_Au_Kidney_Tissue;
        w_Au_Spleen_Tissue1(k)=h.w_Au_Spleen_Tissue;
        w_Au_Liver_Tissue1(k)=h.w_Au_Liver_Tissue;
        w_Au_Lung_Tissue1(k)=h.w_Au_Lung_Tissue;
        w_Au_Brain_Tissue1(k)=h.w_Au_Brain_Tissue;
        w_Au_Plasma1(k)=h.w_Au_Plasma;
       end
    end
end

%% Objective Function - Minimizing sum of squared residuals
% 
out = (sum((abs(EXP.Blood_C' - (rho_Au_A1+rho_Au_V1))/max(EXP.Blood_C)).^2));  

The error shown is:

Error using fmincon (line 639)
Supplied objective function must return a scalar value.

Error in para_vald_chitosan (line 119)
    fmincon(@obfun_chitosan,ov0,[],[],[],[],lb,ub,[],opt,SYSTEM,DRUG,CF,EXP,MAT);
    
    

the size of each input is:

ov0= 20x1

lb=1x20

ub=1x20

SYSTEM=1x1 struct

DRUG=1x1 struct

CF=1x1 struct

EXP=1x1 struct

MAT=46x1