I have some travel time data stored as column vectors. I want to write a script that will allow me run a linear interpolation from specified initial and final values, to make a column of distances, so I can calculate velocity.
example: Column 1: t1,t2,t3......tn; Column 2: (using the linear interpolation we create) d1, d2, d3....dn
So here we have generated a distance for each travel time based on an initial distance and a final distance.
then it should be simple to generate a new column that is simply the interpolated distances / travel times. Thanks for your help. Cheers
interp1 is your friend here:
% from zero to one hour
measuredTime = [0 1];
% from 0 to 100 km
measuredDistance = [0 100];
% 10 minute intervals
intermediateTimes = measuredTime(1):10/60:measuredTime(end);
% interpolated distances
intermediateDistances = interp1(measuredTime,measuredDistance,intermediateTimes);
Related
In Matlab, given a vector A (please, find it here: https://www.dropbox.com/s/otropedwxj0lki7/A.mat?dl=0 ), how could I find the n-samples vector subset with the smallest range (or standard deviation)?
I am trying a potential solution: reshaping the vector in columns, performing range of each column and selecting the smallest. However, reshape does not always works well when applied to other examples with different lengths. How could this be worked around in an easier and more efficient way?
Fs = 1000; % sampling frequency
time = round(length(A)/Fs)-1; % calculate approximated rounded total length in time
A_reshaped = reshape(A(1:time*Fs), [], time/2); % reshape A (deleting some samples at the end) in time/2 columns
D(1,:) = mean(A_reshaped);
D(2,:) = range(A_reshaped);
[~,idx] = min(D(2,:));
Value = D(1,idx);
Any help is much appreciated.
To find the n-sample with minimum range you can sort the vector and subtract the first section of the sorted vector from the last section. Then use index of the minimum to find the n-sample:
n=4
a= rand(1,10);
s= sort(a);
[~,I]=min(s(n:end)-s(1:end-n+1))
result = s(I:I+n-1)
I have 2 FFT spectrums on a plot. I want to get the top 5 maximum points of the overall plot. I get the maximum points separately for each spectrum. How can i combine these spectrums into one and get the overall maximum 5 points?
You have two separate maximum matrix: lets Max1 and Max2
Now combine both of them to form third matrix
Max3 = [Matx1 Max2]
Sort the Max3 in descending order
Max3 = sort(Max3,'descend');
Extract the first 5 element
peaks = Max3(1:5)
Put the spectra in one vector and sort them in descending order.
spec1 = fft(x1); % a spectrum (column vector)
spec2 = fft(x2); % another spectrum (column vector)
dummy = abs([spec1; spec2]); % concatenate absolute values
sorted = sort(dummy, 'descending');
five_greatest = sorted(1:5);
I have a vector of 3D points lets say A as shown below,
A=[
-0.240265581092000 0.0500598627544876 1.20715641293013
-0.344503191645519 0.390376667574812 1.15887540716612
-0.0931248606994074 0.267137193112796 1.24244644549763
-0.183530493218807 0.384249186312578 1.14512014134276
-0.0201358671977785 0.404732019283683 1.21816745283019
-0.242108038906952 0.229873488902244 1.24229940627651
-0.391349107031230 0.262170158259873 1.23856838565023
]
what I want to do is to connect 3D points with lines which only have distance less than a specific threshold T. I want to get a list of pairs of points needed to be connected. Such as,
[
( -0.240265581092000 0.0500598627544876 1.20715641293013), (-0.344503191645519 0.390376667574812 1.15887540716612);
(-0.0931248606994074 0.267137193112796 1.24244644549763),(-0.183530493218807 0.384249186312578 1.14512014134276),.....
]
So as shown, I'll have a vector of pairs of points needed to be connected. So if anyone could please advise how this can be done in Matlab.
The following example demonstrates how to accomplish this.
%# Build an example matrix
A = [1 2 3; 0 0 0; 3 1 3; 2 0 2; 0 1 0];
Threshold = 3;
%# Calculate distance between all points
D = pdist2(A, A);
%# Discard any points with distance greater than threshold
D(D > Threshold) = nan;
If you wish to extract an index of all observation pairs that are linked by a distance less than (or equal to) Threshold, as well as the corresponding distance (your question didn't specify what form you wanted the output to take, so I am essentially guessing here), then instead use the following:
%# Obtain a list of linear indices of observations less than or equal to TH
I1 = find(D <= Threshold);
%#Extract the actual distances, as well as the corresponding observation indices from A
[Obs1Index, Obs2Index] = ind2sub(size(D), I1);
DList = [Obs1Index, Obs2Index, D(I1)];
Note, pdist2 uses Euclidean distance by default, but there are other options - see the documentation here.
UPDATE: Based on the OP's comments, the following code will express the output as a K*6 matrix, where K is the number of distance measures less than the threshold value, and the first three columns of each row is the first data point (3 dimensions) and the second three columns of each row is the connected data point.
DList2 = [A(Obs1Index, :), A(Obs2Index, :)];
SECOND UPDATE: I have not made any assumptions on the distance measure in this answer. That is, I'm deliberately using pdist2 in case your distance measure is not symmetric. However, if you are using a symmetric distance measure, then you could probably speed up the run-time by using pdist instead, although my indexing code would need to be adjusted accordingly.
Plot3 and pdist2 can be used to achieve what you want.
D=pdist2(A,A);
T=0.2;
for i=1:7
for j=i+1:7
if D(i,j)<T & D(i,j)~=0
i
j
plot3(A([i j],1),A([i j],2),A([i j],3));
hold on;
fprintf('line is plotted\n');
pause;
end
end
end
I have a matrix of multiple particle trajectories that I would like to analyze separately The trajectory number is one of the columns of the matrix, so I am trying to sort based on that number. I am using some of the code from this answer: MSD with matlab (which was very helpful, thank you!) to calculate MSD, but I am having difficulty parsing out the individual trajectories. To explain in more detail what I am trying to do: I have trajectory outputs that are in matrix format, with one column for trajectory number, one column for x-position, one column for y-position, etc. I want to be able to take this information and calculate the mean-squared displacement for each trajectory. In order to do this, I have to create a way to distinguish data points based on trajectory number (which is listed in row 7 of mymatrix). This seems to be where I am having trouble. The important columns in this matrix are 1: x-position, 2: y-position and 7: trajectory number. So far I have
total_rows=size(mymatrix,1);
max_trajectory_number=mymatrix(total_rows,7);
nData=0;
msd=zeros(total_rows, 4)
for i=0:max_trajectory_number
trajectornumber= mymatrix(i,7);
if trajectorynumber.equals(i)
nData=nData+1; %counts the number of instances of this trajectory number, which is the number of data points in the trajectory
for dt = 1:nData
deltaCoords = mymatrix(1+dt:end,1:2) - traj0mat(1:end-dt,1:2); %calculates time-averaged MSD based on y and y positions in colums 1 and 2 respectively
squaredDisplacement = sum(deltaCoords.^2,2); %# dx^2+dy^2+dz^2
msd(dt,1) = trajectorynumber; %trajectory number
msd(dt,2) = mean(squaredDisplacement); %# average
msd(dt,3) = std(squaredDisplacement); %# std
msd(dt,4) = length(squaredDisplacement); %# n
end
end
Unfortunately when I run this on mymatrix, the resulting msd matrix remains all zeros. I think this is likely due to an error in sorting based on the trajectory number. I do not get an error just not the results I was looking for
If anyone has any suggestions on how to fix this, it would be greatly appreciated.
It looks like you want to bundle all rows identified by the same trajectory number. I assume that they show up in chronological order as you continue down a column. Then try something like
tnumbs = unique(mymatrix(:,7)); % identify unique trajectory numbers
for i=1:length(tnumbs) % loop through trajectories
icurr = find(mymatrix(:,7)==tnumbs(i)); % find indices to entries for current trajectory
% perform your averaging
deltaCoords = mymatrix(icurr(1+dt:end),1:2) - traj0mat(icurr(1:end-dt),1:2); %calculates time-averaged MSD based on y and y positions in colums 1 and 2 respectively
squaredDisplacement = sum(deltaCoords.^2,2); %# dx^2+dy^2+dz^2
msd(i,1) = tnumbs(i); %trajectory number
msd(i,2) = mean(squaredDisplacement); %# average
msd(i,3) = std(squaredDisplacement); %# std
msd(i,4) = length(squaredDisplacement); %# n
end
Imagine a set of data with given x-values (as a column vector) and several y-values combined in a matrix (row vector of column vectors). Some of the values in the matrix are not available:
%% Create the test data
N = 1e2; % Number of x-values
x = 2*sort(rand(N, 1))-1;
Y = [x.^2, x.^3, x.^4, x.^5, x.^6]; % Example values
Y(50:80, 4) = NaN(31, 1); % Some values are not avaiable
Now i have a column vector of new x-values for interpolation.
K = 1e2; % Number of interplolation values
x_i = rand(K, 1);
My goal is to find a fast way to interpolate all y-values for the given x_i values. If there are NaN values in the y-values, I want to use the y-value which is before the missing data. In the example case this would be the data in Y(49, :).
If I use interp1, I get NaN-values and the execution is slow for large x and x_i:
starttime = cputime;
Y_i1 = interp1(x, Y, x_i);
executiontime1 = cputime - starttime
An alternative is interp1q, which is about two times faster.
What is a very fast way which allows my modifications?
Possible ideas:
Do postprocessing of Y_i1 to eliminate NaN-values.
Use a combination of a loop and the find-command to always use the neighbour without interpolation.
Using interp1 with spline interpolation (spline) ignores NaN's.