Biorthogonal decomposition: Difference between revisions
No edit summary |
|||
| Line 21: | Line 21: | ||
:<math>Y = U S V^T.\,</math> | :<math>Y = U S V^T.\,</math> | ||
where ''S'' is a diagonal ''N×M'' matrix and ''S<sub>kk</sub>'' = λ<sub>k</sub>, the first min(''N,M'') columns of ''U'' (''N×N'') are the chronos and the first min(''N,M'') columns of ''V'' (''M×M'') are the topos. | where ''S'' is a diagonal ''N×M'' matrix and ''S<sub>kk</sub>'' = λ<sub>k</sub>, the first min(''N,M'') columns of ''U'' (''N×N'') are the chronos and the first min(''N,M'') columns of ''V'' (''M×M'') are the topos. <ref>[[:Wikipedia:MATLAB|MATLAB]] code: <code>[U,S,V] = svd(Y,'econ');</code></ref> | ||
Thus, the oscillations of the spatiotemporal fluctuating field are represented by means of a very small number of spatio-temporal modes that are constructed from the data themselves, without prejudice regarding the mode shape. | Thus, the oscillations of the spatiotemporal fluctuating field are represented by means of a very small number of spatio-temporal modes that are constructed from the data themselves, without prejudice regarding the mode shape. | ||