The least square with changing number of lines of matrix

Hello. I do some research. I have some measured data - vector, And I have my own linear equations ( - each line of this matrix equation belongs to specific measurement and the point is that sometimes some measurement can not ve taken account) And I have the result- probable vector solved by the least square method. Probable vector is matrix 1x6. Linear equation is 6xn and measured data is 1xn. Minimum of n is 6 and maximum of n is 24. Because I dont know mathlab, I use excel...but some program in mathlab would help me with time. Each time I have to change size of matrixes in excel. And this is pissing me of :-) can you tell me how to do it in mathlab? Actually the first question would be: how many of measurements do you have? Or what is size of vector of measurement data? This changes the size of my linear equation. Maybe I found something like erase the line of matrix. But maybe you found the better way. Thank you for any opinion. Girl from Czechia saying hi😁

Answer 1

[Star Strider]

I am not certain what you want.

This calculates regressions on each column of ‘y’ and then plots it in the same colours as the original data —

x = (1:6).';
y = randn(6,8);

B = [x, ones(size(x))] \ y

B = 2×8

-0.2606 -0.4523 0.1271 0.0608 0.1484 0.0588 0.3563 0.2241 1.0738 0.4900 -0.9696 -0.3685 -0.4606 0.0353 -0.9595 0.0233

figure
hold on
for k = 1:size(y,2)
    hp = plot(x, y(:,k), 'o:');
    hp.MarkerFaceColor = hp.Color;
    rl = [x, ones(size(x))] * B(:,k);
    plot(x, rl, '-', 'Color',hp.Color, 'LineWidth',1)
end
hold off
grid
xlabel('X')
ylabel('Y')
title('Linear Regressions')

B = [x.^2, x, ones(size(x))] \ y

B = 3×8

0.0486 0.3034 0.1011 0.0333 0.0173 0.1494 0.1843 0.1570 -0.6006 -2.5761 -0.5806 -0.1724 0.0271 -0.9871 -0.9338 -0.8746 1.5271 3.3217 -0.0260 -0.0577 -0.2988 1.4299 0.7607 1.4882

figure
hold on
for k = 1:size(y,2)
    hp = plot(x, y(:,k), 'o:');
    hp.MarkerFaceColor = hp.Color;
    rl = [x.^2, x, ones(size(x))] * B(:,k);
    plot(x, rl, '-', 'Color',hp.Color, 'LineWidth',1)
end
hold off
grid
xlabel('X')
ylabel('Y')
title('Quadratic Regressions')

B = [x.^3,  x.^2, x, ones(size(x))] \ y

B = 4×8

-0.0095 -0.1095 0.0626 0.1919 0.1352 0.0674 -0.0872 0.0085 0.1479 1.4536 -0.5560 -1.9816 -1.4023 -0.5585 1.0998 0.0680 -0.9005 -6.0487 1.4034 5.9108 4.3131 1.1502 -3.6976 -0.6060 1.7655 6.0822 -1.6032 -4.8935 -3.7060 -0.2691 2.9578 1.2746

figure
hold on
for k = 1:size(y,2)
    hp = plot(x, y(:,k), 'o:');
    hp.MarkerFaceColor = hp.Color;
    rl = [x.^3, x.^2, x, ones(size(x))] * B(:,k);
    plot(x, rl, '-', 'Color',hp.Color, 'LineWidth',1)
end
hold off
grid
xlabel('X')
ylabel('Y')
title('Third-Order Regressions')

.

[Petlice]

Hello Star Thank you very much for your answer, but the regression of each column is not interesting for me. Your answer showed me I have to explain more in detail. I measure deformation of the body. I search probable vector of stress until body was loaded and finally between these two there is matrix that gives a relationship of linear elasticity and transformation. The probable vector of stress vector- always of 6 values is determinated by the least square method. If the vector of measurement vector is called "b" and vector of searched stress vector is named "x". Between them stays relationship matrix A. Then the probable stress vector is found by the least square as following: x=(A^T x A)^-1 x A^T x b The least square in matrix form is very easy. I would like to do it in Mathlab, because I already using some function in Mathlab. But only problem I have with Mathlab, is that each turn is of different amount of lines. So how to say to Mathlab: I have measurement - vector b: 3,5,8,11,15,17,21,24...(please understand, that all 24 measurements can be used) Command: Please Mathlab calculate stress 😁 (that means that matrix A will use only lines that belongs to these measurements - the other lines will not be used - if all 24 measurements will be used, than full size of matrix A is used that means 6x24)...another turn: I have measurement 1,2,4,9,12,15,18,19,21,22,22. Please calculate stress for me. (Each turn matrixes will be different size) And so on...many variations. Thank you very much for another opinion.

[Star Strider]

It would be necessary to have your data and a description of what you want to do with it to provide an appropriate response.

To find change points in data, there are a few options, one if which is the ischange function. That can possibly determine where your data changes fron linear to something else, so that you can do a linear regression on the linear part.

[Petlice]

Thank you again, Star. No, what I want is really very basic. I have more equations than 6 unknown. And very basically I want only do basic matrix operations (least square) with same linear equations but each time - each turn - each measurement set - has different amount of rows. (completely I have 24 measurements and to this vector 24*1, matrix of 24*6 belongs, so the result is always vector 6*1) and I always have some errors in measurements, so I want to erase some rows from the system. For example, I have wrong, the first, the forth, and the last one measurement, so I want to do for example transponse matrix of A, but the A is of smaller size now. And I dont know how to program the smaller size of matrix....basically, now I am doing this manually. Each time I am choosing which rows will be used and I put them manually to make new matrix of A. Maybe my problem is very stupid. 😁

[Star Strider]

Not stupid at all.

I just fail to understand what you want to do from the description.

Answer 2

[Bruno Luong]

A = rand(24,6); % your full matrix
b = rand(24,1); % your measurements

% which data you want to remove?
removeidx = [1 4 24]; % removeidx = []; % to remove nothing

keep = setdiff(1:size(b,1), removeidx);
x = A(keep,:) \ b(keep,:)

x = 6×1

0.0582 -0.1722 0.5744 -0.0733 0.2111 0.1379

That's all