Here is the project page of , the #opensource empirical gramian framework for #octave and #matlab . #emgr focusses on model order reduction of nonlinear systems by utilizing empirical gramians. The six #gramian types provided are:

Empirical Controllability Gramian (WC)
Empirical Observability Gramian (WO)
Empirical Cross Gramian (WX)
Empirical Sensitivity Gramian (WS)
Empirical Identifiability Gramian (WI)
Empirical Joint Gramian (WJ)

These allow state reduction by balanced truncation of WC+WO or direct truncation of WX, parameter reduction through WS or WI and combined reduction – concurrent reduction of state and parameter spaces – using WJ.

Visit http://gramian.de for examples on gramian based model reduction, including large-scale systems or pre-estimation combined state and parameter reduction of bayesian inverse problems.

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