Reference.Variables.reduce

Variable "reduce" in MATLAB/Octave version of WavePacket

This structure contains all parameters that are necessary for dimension reduction techniques either by balanced truncation with qm_balance and qm_truncate or by ℋ2 optimal model reduction with qm_H2model. Note that often it is advisable to set the variables A_shift, A_split, and BN_scale to different values for the two approaches which is the reason why they exist twice (and yet once more for qm_H2error).

reduce.balance	Balancing transformation (using qm_balance)	default
A_stable	choice of method for stabilizing A matrix 'ssu'= Separating Stable from Unstable 'evs'= EigenValue Shift	'ssu'
A_split	for method 'ssu' only: dimension of instable part of A to be split off	1
A_shift	for method 'evs' only: magnitude of eigenvalue shift	1e-6
BN_scale	Scaling factor (normally >1) for control/input: During dimension reduction, divide vectors B, matrices N by this number to ensure solvability of (generalized) Lyapunov equations	1 (i.e. no scaling)
acf_couple	Additional Control Field: coupling terms between A and state vector	false
method	Method for solving the generalized Lyapunov equation 'iter' = Iterative solver 'bicg' = Bi-conjugate gradients	'iter'
transform	Method of the balancing transform 'srbt' : Square Root Balanced Truncation 'mrmr' : Minima Realization and Model Reduction	'srbt'

reduce.glyap	Parameters for solving the generalized Lyapunov equation (in qm_balance)	default
conv_tol	Convergence threshold	1e-10
max_iter	Maximal number of iterations	10
dev_max	Initial maximal deviation ('iter' only; not available for 'bicg')	1e10

reduce.H2model	H2 optimal model reduction (using qm_H2model)	default
A_stable	choice of method for stabilizing A matrix 'ssu'= Separating Stable from Unstable 'evs'= EigenValue Shift	'ssu'
A_split	for method 'ssu' only: dimension of instable part of A to be split off	1
A_shift	for method 'evs' only: magnitude of eigenvalue shift	1e-6
BN_scale	Scaling factor (normally >1) for control/input: During dimension reduction, divide vectors B, matrices N by this number to ensure solvability of (generalized) Lyapunov equations	1 (i.e. no scaling)
acf_couple	Additional Control Field: coupling terms between A and state vector	false
conv_tol	Convergence threshold for BIRKA iteration	1e-6
max_iter	Maximal number of BIRKA iterations	100
method	Method for solving the generalized Sylvester equation 'iter' : Iterative solver 'bicg' : Bi-conjugate gradients	'iter'

reduce.gsylv	Parameters for solving the generalized Sylvester equation (in qm_H2model)	default
conv_tol	Convergence threshold	1e-10
max_iter	Maximal number of iterations	10

reduce.H2error	H2 error from BT and/or H2 model reduction (using qm_H2error)	default
A_shift	magnitude of eigenvalue shift to stabilize A matrix of the error system	1e-6
BN_scale	Scaling factor (normally >1) for B and N matrices of the error system to ensure solvability of (generalized) Lyapunov equations	1 (i.e. no scaling).
method	Method for solving the generalized Lyapunov equation for the error system 'iter' : Iterative solver 'bicg' : Bi-conjugate gradients	'iter'