I have several sets of data that I want to fit but not all of them look the same (some look like a Gaussian with one peak, some like two Gaussians with 2 peaks or Lorentzians). I wanted to try this method
http://www.mathworks.com/matlabcentral/fileexchange/31562-data-driven-fitting-with-matlab/content/fitit.m
but the program given is not complete so I can not use it (there is no line that defines 'train' and 'test'). I am writing it so that it suits and works for my data (based on the code that it is given and the demo). I was able to find the best fit but I am also trying to use the bootstrap technique in order to find the confidence intervals. My data is xdata and ydata and they are sorted and the duplicates have been removed before I use them in my program.
cpart=cvpartition(size(xdata,1),'k',10);
tr_x=xdata(training(cpart,1));
tr_y=ydata(training(cpart,1));
tst_x=xdata(test(cpart,1));
tst_y=ydata(test(cpart,1));
all_span=linspace(0.01,0.99,99);
s=zeros(length(all_span);
for k=1:length(all_span)
f = #(tr_x,tr_y,tst_x,tst_y) norm(tst_y mylowess (tr_x, tr_y, tst_x, all_span (k)))^2
s(k) = sum(crossval(f,datax,datay,'partition',cpart));
end
[~,mj]=min(s);
n_span=all_span(mj);%n_span is the optimal span
function ys=mylowess(x1,y1,xs,span)
ys1 = smooth(x1,y1,span,'loess');
ys = interp1(x1,ys1,xs,'linear',NaN);
if any(isnan(ys))
ys(xs<x1(1)) = ys1(1);
ys(xs>x1(end)) = ys1(end);
end
So up to this point I understand the program and I have managed to find the optimal span. I want to find the confidence intervals but so far I was not able to make it work.
When I type:
NB=length(xdata);
f=#(xdata,ydata) mylowess(xdata,ydata,xdata,n_span);
yboot2 = bootstrp(NB,f,xdata,ydata)';
I get the following error
Error using griddedInterpolant
The grid vectors are not strictly monotonic increasing.
Error in interp1 (line 186)
F = griddedInterpolant(X,V,method);
Error in mylowess (line 26)
ysmooth=interp1(xdata,ysmooth1,xinput,'linear',NaN);
As I said before there are no duplicates in xdata and I have already sorted xdata before I used them in the program. Can anyone see the mistake I am making? Or is there an easier way to get the confidence intervals?
Thank you for your help.
Related
I'm trying to breakdown how bandpass function makes the filtering and stumped upon this line (after the filter is created).
y = signal.internal.filteringfcns.filterData(x,opts);
x is the data and opts has the filter structure.
I've been looking around and haven't been able to find anything about signal.internal.filteringfcns.filterData function. I compared that output with filter(opts.FilterObject,x) and they are not the same.
Next is a minimal working example (data2.txt).
load('data2.txt')
srate=64;
freqrange=[0.4 3.5];
var{1}=freqrange;
var{2}=srate;
m=numel(data2);
x=data2;
R=0.1;%10% of signal
Nr=50;
NR=min(round(m*R),Nr);%At most 50 points
x1=2*x(1)-flipud(x(2:NR+1));%maintain continuity in level and slope
x2=2*x(end)-flipud(x(end-NR:end-1));
x=[x1;x;x2];
opts=signal.internal.filteringfcns.parseAndValidateInputs(x,'bandpass',var);
opts = designFilter(opts);
xx = signal.internal.filteringfcns.filterData(x,opts);
x_fil=xx(NR+1:end-NR);
xx = filter(opts.FilterObject,x);
x_fil2=xx(NR+1:end-NR);
plot([data x_fil x_fil2])
legend('raw','filterData','filter')
Here is the plot:
And here are the psd plot of both filtered signal (filtData first).
So, any help on this ...filtData function or I doing something wrong in my analysis?
Hi again :) If you type edit signal.internal.filteringfcns.filterData, you can even look at what is inside this filterData function. You will see that this function (depending on the options opts) will either,
right zero pad the signal with N/2 zeros and call filter
call filtfilt with the signal
This is also described in the docs of bandpass. So probably this zero padding explains why your output of filter(opts.FilterObject,x) is different.
You cannot find this function described in the documentation of Matlab since it is part of the internal functions of the signal processing toolbox.
I'm using MATLAB 2013a and trying to find peak points of my data. When I tried code example given in
Find Peaks with Minimum Separation
I am getting the following error:
Error using uddpvparse (line 122)
Invalid Parameter/Value pairs.
Error in findpeaks>parse_inputs (line 84)
hopts = uddpvparse('dspopts.findpeaks',varargin{:});
Error in findpeaks (line 59)
[X,Ph,Pd,Th,Np,Str,infIdx] = parse_inputs(X,varargin{:});
I tried simple x and y vectors and got the same error. What can be the problem?
I have the same problem as you (R2013a on OSX) with the example by the Mathworks. For some reason it seems we can't use findpeaks with the x-and y-data as input arguments, We need to call the function with the y data and use the [peaks,locations] output to get the peaks/plot them.
It looks like in R2014b they changed some stuff about findpeaks that does not work with older versions...like calling the function with not output argument in R2014b plots the data/peaks without any additional step...but it does not for earlier versions.
Anyhow here is a way to workaround the problem. Call findpeaks with a single input argument (y data that is, you can use property/value pairs as well) and use the indices (locations) to show the peaks:
clc
clear
load sunspot.dat
year = sunspot(:,1);
avSpots = sunspot(:,2);
[peaks, locations] = findpeaks(avSpots)
plot(year,avSpots)
hold on
scatter(year(locations),avSpots(locations),40,'filled')
hold off
Output:
It might be worthwhile to contact The Mathworks about this. Hope that helps!
I have a Matlab project in which I need to make a GUI that receives two mathematical functions from the user. I then need to find their intersection point, and then plot the two functions.
So, I have several questions:
Do you know of any algorithm I can use to find the intersection point? Of course I prefer one to which I can already find a Matlab code for in the internet. Also, I prefer it wouldn't be the Newton-Raphson method.
I should point out I'm not allowed to use built in Matlab functions.
I'm having trouble plotting the functions. What I basically did is this:
fun_f = get(handles.Function_f,'string');
fun_g = get(handles.Function_g,'string');
cla % To clear axes when plotting new functions
ezplot(fun_f);
hold on
ezplot(fun_g);
axis ([-20 20 -10 10]);
The problem is that sometimes, the axes limits do not allow me to see the other function. This will happen, if, for example, I will have one function as log10(x) and the other as y=1, the y=1 will not be shown.
I have already tried using all the axis commands but to no avail. If I set the limits myself, the functions only exist in certain limits. I have no idea why.
3 . How do I display numbers in a static text? Or better yet, string with numbers?
I want to display something like x0 = [root1]; x1 = [root2]. The only solution I found was turning the roots I found into strings but I prefer not to.
As for the equation solver, this is the code I have so far. I know it is very amateurish but it seemed like the most "intuitive" way. Also keep in mind it is very very not finished (for example, it will show me only two solutions, I'm not so sure how to display multiple roots in one static text as they are strings, hence question #3).
function [Sol] = SolveEquation(handles)
fun_f = get(handles.Function_f,'string');
fun_g = get(handles.Function_g,'string');
f = inline(fun_f);
g = inline(fun_g);
i = 1;
Sol = 0;
for x = -10:0.1:10;
if (g(x) - f(x)) >= 0 && (g(x) - f(x)) < 0.01
Sol(i) = x;
i = i + 1;
end
end
solution1 = num2str(Sol(1));
solution2 = num2str(Sol(2));
set(handles.roots1,'string',solution1);
set(handles.roots2,'string',solution2);
The if condition is because the subtraction will never give me an absolute zero, and this seems to somewhat solve it, though it's really not perfect, sometimes it will give me more than two very similar solutions (e.g 1.9 and 2).
The range of x is arbitrary, chosen by me.
I know this is a long question, so I really appreciate your patience.
Thank you very much in advance!
Question 1
I think this is a more robust method for finding the roots given data at discrete points. Looking for when the difference between the functions changes sign, which corresponds to them crossing over.
S=sign(g(x)-f(x));
h=find(diff(S)~=0)
Sol=x(h);
If you can evaluate the function wherever you want there are more methods you can use, but it depends on the size of the domain and the accuracy you want as to what is best. For example, if you don't need a great deal of accurac, your f and g functions are simple to calculate, and you can't or don't want to use derivatives, you can get a more accurate root using the same idea as the first code snippet, but do it iteratively:
G=inline('sin(x)');
F=inline('1');
g=vectorize(G);
f=vectorize(F);
tol=1e-9;
tic()
x = -2*pi:.001:pi;
S=sign(g(x)-f(x));
h=find(diff(S)~=0); % Find where two lines cross over
Sol=zeros(size(h));
Err=zeros(size(h));
if ~isempty(h) % There are some cross-over points
for i=1:length(h) % For each point, improve the approximation
xN=x(h(i):h(i)+1);
err=1;
while(abs(err)>tol) % Iteratively improve aproximation
S=sign(g(xN)-f(xN));
hF=find(diff(S)~=0);
xN=xN(hF:hF+1);
[~,I]=min(abs(f(xN)-g(xN)));
xG=xN(I);
err=f(xG)-g(xG);
xN=linspace(xN(1),xN(2),15);
end
Sol(i)=xG;
Err(i)=f(xG)-g(xG);
end
else % No crossover points - lines could meet at tangents
[h,I]=findpeaks(-abs(g(x)-f(x)));
Sol=x(I(abs(f(x(I))-g(x(I)))<1e-5));
Err=f(Sol)-g(Sol)
end
% We also have to check each endpoint
if abs(f(x(end))-g(x(end)))<tol && abs(Sol(end)-x(end))>1e-12
Sol=[Sol x(end)];
Err=[Err g(x(end))-f(x(end))];
end
if abs(f(x(1))-g(x(1)))<tol && abs(Sol(1)-x(1))>1e-12
Sol=[x(1) Sol];
Err=[g(x(1))-f(x(1)) Err];
end
toc()
Sol
Err
This will "zoom" in to the region around each suspected root, and iteratively improve the accuracy. You can tweak the parameters to see whether they give better behaviour (the tolerance tol, the 15, number of new points to generate, could be higher probably).
Question 2
You would probably be best off avoiding ezplot, and using plot, which gives you greater control. You can vectorise inline functions so that you can evaluate them like anonymous functions, as I did in the previous code snippet, using
f=inline('x^2')
F=vectorize(f)
F(1:5)
and this should make plotting much easier:
plot(x,f(x),'b',Sol,f(Sol),'ro',x,g(x),'k',Sol,G(Sol),'ro')
Question 3
I'm not sure why you don't want to display your roots as strings, what's wrong with this:
text(xPos,yPos,['x0=' num2str(Sol(1))]);
I'm interested in understanding the variety of zeroes that a given function produces with the ultimate goal of identifying the what frequencies are passed in high/low pass filters. My idea is that finding the lowest value zero of a filter will identify the passband for a LPF specifically. I'm attempting to use the [hz,hp,ht] = zplane(z,p) function to do so.
The description for that function reads "returns vectors of handles to the zero lines, hz". Could someone help me with what a vector of a handle is and what I do with one to be able to find the various zeros?
For example, a simple 5-point running average filter:
runavh = (1/5) * ones(1,5);
using zplane(runavh) gives an acceptable pole/zero plot, but running the [hz,hp,ht] = zplane(z,p) function results in hz=175.1075. I don't know what this number represents and how to use it.
Many thanks.
Using the get command, you can find out things about the data.
For example, type G=get(hz) to get a list of properties of the zero lines. Then the XData is given by G.XData, i.e. X=G.XData.
Alternatively, you can only pull out the data you want
X=get(hz,'XData')
Hope that helps.
I am a complete novice at using matlab and am trying to work out if there is a way of optimising my code. Essentially I have data from model outputs and I need to plot them using matlab. In addition I have reference data (with 95% confidence intervals) which I plot on the same graph to get a visual idea on how close the model outputs and reference data is.
In terms of the model outputs I have several thousand files (number sequentially) which I open in a loop and plot. The problem/question I have is whether I can preprocess the data and then plot later - to save time. The issue I seem to be having when I try this is that I have a legend which either does not appear or is inaccurate.
My code (apolgies if it not elegant):
fn= xlsread(['tbobserved' '.xls']);
time= fn(:,1);
totalreference=fn(:,4);
totalreferencelowerci=fn(:,6);
totalreferenceupperci=fn(:,7);
figure
plot(time,totalrefrence,'-', time, totalreferencelowerci,'--', time, totalreferenceupperci,'--');
xlabel('Year');
ylabel('Reference incidence per 100,000 population');
title ('Total');
clickableLegend('Observed reference data', 'Totalreferencelowerci', 'Totalreferenceupperci','Location','BestOutside');
xlim([1910 1970]);
hold on
start_sim=10000;
end_sim=10005;
h = zeros (1,1000);
for i=start_sim:end_sim %is there any way of doing this earlier to save time?
a=int2str(i);
incidenceFile =strcat('result_', 'Sim', '_', a, 'I_byCal_total.xls');
est_tot=importdata(incidenceFile, '\t', 1);
cal_tot=est_tot.data;
magnitude=1;
t1=cal_tot(:,1)+1750;
totalmodel=cal_tot(:,3)+cal_tot(:,5);
h(a)=plot(t1,totalmodel);
xlim([1910 1970]);
ylim([0 500]);
hold all
clickableLegend(h(a),a,'Location','BestOutside')
end
Essentially I was hoping to have a way of reading in the data and then plot later - ie. optimise the code.
I hope you might be able to help.
Thanks.
mp
Regarding your issue concerning
I have a legend which either does not
appear or is inaccurate.
have a look at the following extracts from your code.
...
h = zeros (1,1000);
...
a=int2str(i);
...
h(a)=plot(t1,totalmodel);
...
You are using a character array as index. Instead of h(a) you should use h(i). MATLAB seems to cast the character array a to double as shown in the following example with a = 10;.
>> double(int2str(10))
ans = 49 48
Instead of h(10) the plot handle will be assigned to h([49 48]) which is not your intention.