How do I perform state linear interpolation?

Hi everyone. I would like to perform state linear interpolation. In other words, I have a gigantic table that has 14 columns (and a great amount of rows). The first 6 columns represents the input state and the remaining 8 columns represent the corresponding output state. What I want to do is essentially write a piece of MATLAB code that I give it the desired input state X = [a, b, c, d, e, f], and it will output for me the best estimate of the output state based on interpolating the table, Y = [g, h, i, j, k, l, m, n]. This is really diffcuilt because X and Y are not a single variable, but actual states that are greatly interconnected. I really have no idea where to start and I hope someone can guide or help me here. Or maybe there is an existing MATLAB function?! That would be heaven to me. Thank you in advance.

Answer 1

[Vidhi Agarwal]

To perform state linear interpolation in MATLAB, you can use the interp1 function. This function performs linear interpolation between points in a table based on the input data.

We first define the input state X as a 6-element vector. We then load the data table from a file or generate it in MATLAB as a variable dataTable. The input and output states are extracted from the table and stored in variables inputStates and outputStates, respectively.

Finally, the interp1 function is called to compute the best estimate of the output state Y based on linear interpolation between the points in the table. The function takes the input states, output states, and the desired input state X as arguments, along with the interpolation method (in this case, 'linear'). The resulting output state Y is a vector with 8 elements corresponding to the corresponding output state for the given input state.

% Define input state
X = [a, b, c, d, e, f];

Unrecognized function or variable 'a'.

% Load data table
dataTable = load('data.mat'); % Load data from file or generate the table

% Extract input and output states from the table
inputStates = dataTable(:, 1:6);
outputStates = dataTable(:, 7:14);

% Compute best estimate of output state using linear interpolation
Y = interp1(inputStates, outputStates, X, 'linear');

[Ali Almakhmari]

are you sure this works, cause I get the following error with the aero.mat having 7 input columns and 8 output columns:

Error using interp1>reshapeAndSortXandV

X must be a vector.

Error in interp1 (line 128)

[X,V,orig_size_v] = reshapeAndSortXandV(X,V);

Error in ANNCODE (line 171)

Y = interp1(inputStates', outputStates', Desired, 'linear');

From this code:

%% Linear Interpolation
Desired = [0.7,2.3,-4.1,2.3,-2.1,18.9865,0.5];
dataTable = load('C:\Users\Ali\Desktop\aero_corrected\aero.mat'); % Load data from file or generate the table
Tables = dataTable.AM03_a02b;
Tables = Tables{:,:};
% Extract input and output states from the table
inputStates = Tables(:, 1:7);
outputStates = Tables(:, 8:15);
% Compute best estimate of output state using linear interpolation
Y = interp1(inputStates, outputStates, Desired, 'linear');

[Vidhi Agarwal]

The error you're encountering occurs when the input vector X in the interp1 function is not a vector, but instead is an invalid input. The X vector argument in the interp1 function must be a one-dimensional vector.

Looking at the example code you provided, it seems that the input vector inputStates is a 2D matrix. To use interp1 with a 2D matrix inputStates as input, you need to transpose the matrix to ensure that the interpolation is performed along the correct dimension.

inputStates = [1 2 3; 4 5 6; 7 8 10]; % Must be transposed
outputStates = [10 20 30 40 50 60 70 80; 20 30 40 50 60 70 80 90; 30 40 50 60 70 80 90 100];

% Define Desired State
Desired = [2.5 6.5 9];

% Perform Linear interpolation
Y = interp1(inputStates', outputStates', Desired, 'linear');
disp(Y);

In this example, before calling the interp1 function, we have transposed the input matrix inputStates using the apostrophe (') to ensure that inputStates is a mxn matrix, where m is the number of points on the x-axis and n is the length of X. This ensures that the interp1 interpolation is performed along the correct dimension.

Transposing the input matrix does not change the values' order within the input matrix; rather, it swaps the rows and columns' positions.

Hence, by transposing the input matrix inputStates to inputStates', the values of the input matrix remain consistent with the original input matrix for handling the input values of the examples.

[Ali Almakhmari]

I am starting to think that your answers are generated by ChatGPT because your answers are super close (if not exactly the same) to ChatGPT's responses (which I tried using before coming here). And just so you know the snippt of code you posted still gives me the same error, its of no help.