Interpolate consecutive values of a single array

Hi guys!

I have two datasets whose arrays have not the same length. The first contains Beta values and it counts 100 values; the second are temperature data and it contains 7985 values. What I would like to do is a linear interpolation between two consecutive data values from beta, in order to get the same length of temperature array.

So, if temperature values are 7985, I would require 79.85 linear interpolated beta elements from beta1 to beta2, then 79.85 linear interpolated elements from beta2 to beta3, and so on ...

In the end I would get a 7985 beta array I will be able to scatterplot Vs. 7985 temperature array data.

Is it possible to easly create such a script/function? I am trying using linspace function, but I cannot make it consecutive value after value.

Thanks in advance for your patience and help :)

[Sargondjani]

Have a look at griddedInterpolant.

x = 1:100;

intBeta = griddedInterpolant(x,Beta,'linear')

Now you can linearly interpolate between beta values: intBeta(1.5) should give you the Beta value between observation 1 and 2.

So next you would need to construct a vector where you retrieve the interpolated beta values. there's examples in the function description.

[Luca Castrogiovanni]

Thank you Sargondjani :)

Answer 1

[William Rose]

@Luca Castrogiovanni,

I assume that the values in beta are not a simple sequence such as beta=1:100. If that were tru, this would be easy.

I will illustrate a solution by example:

%You will get 100 values for beta from a file.
%Since I don't have the file, I will create 100 values.
beta=-1*(-1:.02:.98)+(-1:.02:.98).^3;         %100 beta values 
t=1:length(beta);  %values to associate with beta, to use for interpolation

%You will get 7985 temperature values from a file.
%Since I don't have the file, I will create 7985 values.
N=7985;
temp=20+10*sin(2*pi*(1:N)/2000);     %7985 temperature values

Plot the data:

subplot(311); plot(1:100,beta,'-bx'); ylabel('\beta');
subplot(312); plot(1:7985,temp,'-r'); ylabel('Temperature');

Interpolate beta:

t1=linspace(t(1),t(end),N);         %create a vector of 7985 "time" values
beta1=interp1(t,beta,t1,'linear');  %interpolate linearly between beta values

Plot temperature versus interpolated beta:

subplot(313); scatter(beta1,temp,'k');
xlabel('\beta'); ylabel('Temperature'); grid on

Try it with your data. Good luck.

[Luca Castrogiovanni]

Thank you William and thank you all for your help! It actually worked with this code. I did not think about replacing interp query with a linspace.

Why do I need to specify t = 1:length(beta)? I tried directly typing:

beta_spacing = linspace(beta(1),beta(end),7985);
beta_interp = interp1(numel(beta),beta,beta_spacing,'linear')

but of course it did not work. Just to figure out why t variable is so important. Maybe interp1 function need to knwo the number of values further than values itself in the array?

Anyway it worked. Thank you again for your help!

[William Rose]

@Luca Castrogiovanni,

beta_spacing, defined as you have defined it, draws a straight line from the first to the last point of beta. If the first and last points are zero, then beta_spacing will be a long vector of zeros, which is not useful. Even if the first and last values are not the same, beta_spacing will not track the fluctuations in beta, so it is not useful for interpolation. By creating a time vector, t=1:100, we can associate each beta with a time. Then we can use the time vector to interpolate from the known beta values at the known times, to intermediate values of beta at intermediate times.

Answer 2

[Luca Castrogiovanni]

Great! Many thanks :)