How can I use ss2tf for big matrices A,B,C,D?

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adn Bouli
adn Bouli 2021-3-18
回答： AR 2025-2-7
Hello everyone,
I am trying to creat a tf from huge matrices A B C and D, the A matrice is a 250000x250000, to compute it i had to use sparse(A), the probleme is ss2tf dosnt accept sparse matrices, it gives the following error:
[nom1, denom1] = ss2tf(A,B,C,D);
Error using ss2tf (line 26)
Input matrix must be real and symmetric when matrix is sparse. Use eigs to compute a subset of
eigenvectors and eigenvalues of a sparse matrix.
full(A) couldnt work because of the size of A.
Ill be thankfull if somone shares a solution or an alternative to go throught this probleme.

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回答（1 个）

AR
AR 2025-2-7
Ran in:
Hi! I encountered the same issue where “ss2tf” expected a dense matrix but got a sparse one instead. It can be addressed by reducing the dimensionality of the system using "eigs" and constructing a reduced state-space model.
The “eigs” function extracts a subset of important eigenvalues and eigenvectors, allowing a reduced representation of the state-space model. Here's an example code to use "eigs" function:
load variable_used.mat %Load example variables used
numModes = 100; % Adjust based on your system's dynamics
% Extract a reduced model using eigs
[V, D_eigs] = eigs(A, numModes); % V: eigenvectors, D_eigs: eigenvalues (diagonal matrix)
% Reduce the state-space matrices
A_red = V' * A * V; % Project A onto the reduced subspace
B_red = V' * B; % Transform B to the reduced subspace
C_red = C * V; % Transform C to the reduced subspace
% Adjust D to match C_red's rows and B_red's columns
if size(C_red, 1) > size(D, 1)
D_red = repmat(D, size(C_red, 1), 1);
else
D_red = D(1:size(C_red, 1), :);
end
if size(B_red, 2) > size(D_red, 2)
D_red = [D_red, zeros(size(C_red, 1), size(B_red, 2) - size(D_red, 2))];
else
D_red = D_red(:, 1:size(B_red, 2));
end
% Use the reduced state-space model with ss2tf
input_index = 1; % Choose the desired input index (1 ≤ input_index ≤ number of inputs in B_red)
[nom, denom] = ss2tf(A_red, B_red, C_red, D_red, input_index);
% Display the result
disp('Numerator coefficients:');
Numerator coefficients:
disp(nom);
1.0e+41 * Columns 1 through 9 0.0000 + 0.0000i 0.0000 - 0.0000i 0.0000 - 0.0000i 0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 + 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i 0.0000 - 0.0000i 0.0000 - 0.0000i 0.0000 - 0.0000i 0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 - 0.0000i 0.0000 + 0.0000i 0.0000 - 0.0000i 0.0000 - 0.0000i 0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i Columns 10 through 18 -0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 + 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i Columns 19 through 27 0.0000 + 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i 0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i 0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i 0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i Columns 28 through 36 -0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 + 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i 0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i 0.0000 - 0.0000i 0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i Columns 37 through 45 -0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i 0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 + 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i 0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i Columns 46 through 54 0.0000 - 0.0000i -0.0003 - 0.0000i 0.0010 + 0.0004i -0.0020 - 0.0009i 0.0014 + 0.0012i 0.0019 + 0.0002i -0.0066 - 0.0033i 0.0150 + 0.0050i -0.0151 - 0.0113i 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0001 + 0.0000i 0.0005 + 0.0001i -0.0011 - 0.0004i 0.0014 + 0.0006i -0.0038 - 0.0013i 0.0071 + 0.0035i -0.0020 - 0.0054i -0.0000 + 0.0000i 0.0003 + 0.0001i -0.0010 - 0.0004i 0.0019 + 0.0009i -0.0013 - 0.0013i -0.0030 - 0.0002i 0.0157 + 0.0054i -0.0375 - 0.0153i 0.0236 + 0.0265i 0.0000 + 0.0000i -0.0003 - 0.0001i 0.0011 + 0.0004i -0.0028 - 0.0011i 0.0038 + 0.0022i -0.0015 - 0.0020i -0.0099 - 0.0021i 0.0293 + 0.0114i -0.0229 - 0.0216i -0.0000 - 0.0000i -0.0002 - 0.0000i 0.0006 + 0.0003i -0.0008 - 0.0003i -0.0009 - 0.0000i 0.0061 + 0.0016i -0.0147 - 0.0069i 0.0308 + 0.0109i -0.0162 - 0.0197i Columns 55 through 63 -0.0008 + 0.0046i 0.0067 + 0.0029i -0.0224 + 0.0006i 0.1182 + 0.0336i -0.1062 - 0.0644i -0.0323 - 0.0002i -0.0565 + 0.0041i 0.1953 + 0.0846i -0.1126 - 0.0892i 0.0125 - 0.0022i -0.0271 - 0.0092i 0.0643 + 0.0210i -0.1383 - 0.0396i 0.1258 + 0.0937i -0.0502 - 0.0212i -0.0394 + 0.0168i -0.2951 - 0.0064i 0.3391 + 0.2131i 0.0482 + 0.0077i -0.1187 - 0.0589i 0.1865 + 0.0875i -0.2631 - 0.1498i 0.2799 + 0.1562i -0.2732 - 0.1642i 0.4976 + 0.1821i -0.5523 - 0.3620i 0.1267 + 0.2767i 0.0037 + 0.0041i 0.0179 + 0.0048i -0.0657 - 0.0223i 0.1022 + 0.0640i -0.1043 - 0.0490i 0.1332 + 0.0740i -0.3454 - 0.0927i 0.3656 + 0.2375i -0.1618 - 0.2051i -0.0074 + 0.0010i 0.0409 + 0.0105i -0.1255 - 0.0337i 0.0944 + 0.0862i -0.0470 + 0.0270i 0.0880 + 0.0654i -0.4120 - 0.1125i 0.2201 + 0.2145i 0.2103 - 0.0084i Columns 64 through 72 -0.0405 + 0.0231i 0.3476 + 0.0401i -0.3349 - 0.2459i -0.3398 + 0.1558i 0.6601 + 0.3561i -0.0726 - 0.3629i -0.3595 - 0.1502i 0.0657 + 0.2280i 0.0284 + 0.0957i 0.1252 - 0.1166i -0.2236 - 0.1675i 0.4673 + 0.0699i 0.4532 - 0.2724i -1.0651 - 0.5531i -0.1029 + 0.4122i 0.4644 + 0.3706i 0.0299 - 0.0097i -0.1805 - 0.0205i 0.4915 + 0.1927i -0.6645 - 0.4438i -0.3580 + 0.1766i 1.2267 + 0.6193i -0.6793 - 0.7074i -0.6112 + 0.0108i 0.7655 + 0.6298i 0.1169 - 0.2872i -0.1642 - 0.3419i -0.1874 - 0.0720i 0.4464 + 0.2328i 0.5017 - 0.1025i -0.7936 - 0.6243i -0.0408 + 0.2053i 0.3195 + 0.2593i -0.2727 - 0.0585i -0.1171 + 0.2229i 0.0926 + 0.2409i -0.2283 - 0.1976i 0.5995 + 0.0956i 0.5059 - 0.3290i -0.7641 - 0.6904i -0.4843 + 0.0398i 0.2976 + 0.5236i -0.0612 + 0.2954i -0.0585 + 0.2944i -0.0636 + 0.1589i Columns 73 through 81 -0.0440 + 0.0297i 0.0527 + 0.0367i 0.0031 - 0.0289i -0.0079 - 0.0151i 0.0030 + 0.0001i -0.0070 - 0.0008i -0.0034 + 0.0053i 0.0010 + 0.0052i 0.0004 + 0.0020i 0.0190 + 0.0733i -0.0439 - 0.0007i -0.0058 + 0.0304i 0.0012 + 0.0281i 0.0044 + 0.0195i 0.0042 + 0.0037i 0.0037 - 0.0036i 0.0004 - 0.0052i -0.0001 - 0.0031i 0.1138 - 0.0330i -0.0261 - 0.0725i -0.0611 - 0.0218i 0.0354 + 0.0415i -0.0162 - 0.0113i 0.0098 + 0.0054i 0.0077 - 0.0033i -0.0029 - 0.0081i -0.0000 - 0.0022i -0.0439 + 0.0143i 0.0221 - 0.0111i 0.0412 - 0.0309i -0.0131 - 0.0403i 0.0103 + 0.0001i -0.0047 - 0.0044i -0.0064 + 0.0004i 0.0018 + 0.0039i -0.0001 + 0.0003i -0.0075 + 0.0588i -0.0148 - 0.0074i 0.0188 + 0.0079i -0.0155 + 0.0047i 0.0094 + 0.0191i -0.0040 + 0.0034i 0.0008 + 0.0031i 0.0007 - 0.0000i 0.0002 - 0.0007i Columns 82 through 90 0.0003 + 0.0006i 0.0001 - 0.0000i -0.0000 - 0.0001i 0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i -0.0001 - 0.0012i -0.0001 - 0.0003i -0.0000 - 0.0000i -0.0000 + 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0007 - 0.0011i -0.0002 + 0.0000i 0.0000 + 0.0002i -0.0000 + 0.0001i 0.0000 + 0.0001i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 - 0.0000i 0.0004 + 0.0003i 0.0001 - 0.0001i -0.0000 - 0.0002i 0.0000 - 0.0000i 0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 + 0.0000i 0.0001 - 0.0005i 0.0000 - 0.0003i -0.0000 - 0.0002i 0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i Columns 91 through 99 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i Columns 100 through 101 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
disp('Denominator coefficients:');
Denominator coefficients:
disp(denom);
1.0e+41 * Columns 1 through 9 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 + 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 + 0.0000i Columns 10 through 18 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i 0.0000 - 0.0000i -0.0000 - 0.0000i Columns 19 through 27 -0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i 0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i Columns 28 through 36 0.0000 + 0.0000i -0.0000 - 0.0000i 0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i 0.0000 - 0.0000i -0.0000 - 0.0000i Columns 37 through 45 0.0000 + 0.0000i 0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 + 0.0000i Columns 46 through 54 -0.0001 + 0.0000i 0.0008 + 0.0002i -0.0030 - 0.0010i 0.0063 + 0.0027i -0.0060 - 0.0042i -0.0013 + 0.0016i 0.0212 + 0.0067i -0.0470 - 0.0203i 0.0048 + 0.0256i Columns 55 through 63 0.0640 + 0.0258i -0.1151 - 0.0483i 0.3069 + 0.1080i -0.4397 - 0.2582i 0.2524 + 0.1529i -0.2361 - 0.1209i 0.8526 + 0.2673i -0.7918 - 0.5489i 0.1405 + 0.2889i Columns 64 through 72 0.7023 + 0.2472i -1.4789 - 0.6347i -1.0668 + 0.5173i 2.4499 + 1.6315i -0.1430 - 0.8019i -1.1907 - 0.7962i 0.9387 + 0.3210i 0.2583 - 0.5671i -0.2094 - 0.5684i Columns 73 through 81 0.1264 - 0.0422i -0.0276 + 0.0025i -0.1141 + 0.0197i 0.0472 + 0.0732i -0.0264 - 0.0153i 0.0129 + 0.0031i 0.0142 - 0.0041i -0.0040 - 0.0103i 0.0001 - 0.0021i Columns 82 through 90 -0.0010 - 0.0010i -0.0003 + 0.0002i 0.0001 + 0.0004i -0.0001 + 0.0001i 0.0000 + 0.0001i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 - 0.0000i Columns 91 through 99 -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i Columns 100 through 101 -0.0000 - 0.0000i -0.0000 - 0.0000i
This approach avoids memory issues while ensuring the system dynamics are preserved.
Some helpful reference links for the same:
https://www.mathworks.com/help/matlab/ref/eigs.html
https://www.mathworks.com/help/matlab/math/sparse-matrix-operations.html

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