Adding Matrices into main diagonal of Matrix

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Thomas Rodriguez
Thomas Rodriguez on 21 Mar 2023
Commented: Stephen23 on 28 Mar 2023
Ran in:
I'm trying to add main diagonal matrices into a defined matrix such as:
clc; clear; close all;
n = 10;
x = linspace(0,1,n);
F = @(x) [x.^2, sin(x), cos(x);
1, 0, 1;
x, cos(x), sin(x)];
A_mat = zeros(n,n);
for i = 1:n
tmp = F(x(i));
A = blkdiag(tmp);
end
A
A = 3×3
1.0000 0.8415 0.5403 1.0000 0 1.0000 1.0000 0.5403 0.8415
As we can see, matrix is not a 10x10 matrix with the main diagonal filled with the intended values above. How can I adjust this code to do such?

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Accepted Answer

Stephen23
Stephen23 on 21 Mar 2023
Edited: Stephen23 on 21 Mar 2023
Ran in:
"As we can see, matrix is not a 10x10 matrix with the main diagonal filled with the intended values above."
After calling BLKDIAG with 10 3x3 matrices I would expect a 30x30 matrix as the output.
"How can I adjust this code to do such?"
A simpler, much more robust alternative (which also works for any sized input matrices):
N = 10;
F = @(x) [x.^2,sin(x),cos(x);1,0,1;x,cos(x),sin(x)];
C = arrayfun(F,linspace(0,1,N),'uni',0);
M = blkdiag(C{:})
M = 30×30
0 0 1.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.0000 0 1.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0123 0.1109 0.9938 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.0000 0 1.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.1111 0.9938 0.1109 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0494 0.2204 0.9754 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.0000 0 1.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.2222 0.9754 0.2204 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.1111 0.3272 0.9450 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
https://www.mathworks.com/help/matlab/matlab_prog/comma-separated-lists.html
https://www.mathworks.com/matlabcentral/answers/1656435-tutorial-comma-separated-lists-and-how-to-use-them
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Thomas Rodriguez
Thomas Rodriguez on 27 Mar 2023
Ran in:
@Stephen23 From your defined "container array", I tried to conduct "numerical manipulation"
N = 10;
F = @(x) [x.^2,sin(x),cos(x);1,0,1;x,cos(x),sin(x)];
C = cell(10,10);
C(diag(true(1,10))) = arrayfun(F,linspace(0,1,N),'uni',0)
C = 10×10 cell array
{3×3 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {3×3 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {3×3 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {3×3 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {3×3 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {3×3 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {3×3 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {3×3 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {3×3 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {0×0 double} {3×3 double}
pi.*C + C
Operator '.*' is not supported for operands of type 'cell'.
With this array, I plan to use some matrix manipulations like above. So, is their a particular way of doing manipulation with this array type? Or is it not possible to do so?
Stephen23
Stephen23 on 28 Mar 2023
"So, is their a particular way of doing manipulation with this array type?"
You can loop over the elements (cells) of a cell array, or you can apply any function that is defined to operate on cell arrays. Perhaps CELLFUN helps you:
C = cellfun(@(m) pi.*m+m, C, 'uni',0)
"Or is it not possible to do so?"
Numeric operations (e.g. arithmetic) are defined for numeric arrays, not for container classes.

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More Answers (1)

Cameron
Cameron on 21 Mar 2023
Ran in:
Why would your matrix be 10x10 instead of 30x30? This is how I would do it if you haven't already calculated your tmp values ahead of time. I also made the code a bit more robust so you can add different size matrices instead of just 3x3 or any other square matrix.
clc; clear; close all;
n = 10;
x = linspace(0,1,n);
F = @(x) [x.^2, sin(x), cos(x);
1, 0, 1;
x, cos(x), sin(x)];
A_mat = zeros(n*size(F(x(1)),1),n*size(F(x(1)),2));
for i = 1:n
tmp = F(x(i));
rowindx = size(tmp,1)*i-(size(tmp,1)-1):size(tmp,1)*i;
colindx = size(tmp,2)*i-(size(tmp,2)-1):size(tmp,2)*i;
A(rowindx,colindx) = tmp;
end
disp(A)
Columns 1 through 19 0 0 1.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.0000 0 1.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0123 0.1109 0.9938 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.0000 0 1.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.1111 0.9938 0.1109 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0494 0.2204 0.9754 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.0000 0 1.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.2222 0.9754 0.2204 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.1111 0.3272 0.9450 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.0000 0 1.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.3333 0.9450 0.3272 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.1975 0.4300 0.9028 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.0000 0 1.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.4444 0.9028 0.4300 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.3086 0.5274 0.8496 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.0000 0 1.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.5556 0.8496 0.5274 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.4444 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.6667 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 20 through 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.6184 0.7859 0 0 0 0 0 0 0 0 0 0 1.0000 0 0 0 0 0 0 0 0 0 0.7859 0.6184 0 0 0 0 0 0 0 0 0 0 0 0.6049 0.7017 0.7125 0 0 0 0 0 0 0 0 1.0000 0 1.0000 0 0 0 0 0 0 0 0 0.7778 0.7125 0.7017 0 0 0 0 0 0 0 0 0 0 0 0.7901 0.7764 0.6303 0 0 0 0 0 0 0 0 1.0000 0 1.0000 0 0 0 0 0 0 0 0 0.8889 0.6303 0.7764 0 0 0 0 0 0 0 0 0 0 0 1.0000 0.8415 0.5403 0 0 0 0 0 0 0 0 1.0000 0 1.0000 0 0 0 0 0 0 0 0 1.0000 0.5403 0.8415

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