function emgrtest()
%%% summary: emgrtest (run emgr tests)
%%% project: emgr - Empirical Gramian Framework ( https://gramian.de )
%%% authors: Christian Himpe ( 0000-0003-2194-6754 )
%%% license: BSD-2-Clause (2019)
rand('seed',1009); % Seed uniform random number generator
%% SYSTEM SETUP
sys.M = 4; % Number of inputs
sys.N = sys.M*sys.M*sys.M; % Number of states
sys.Q = sys.M; % Number of outputs
sys.dt = 0.01; % Time step
sys.Tf = 1.0; % Time horizon
A = -gallery('lehmer',sys.N); % System matrix
B = toeplitz(1:sys.N,1:sys.M); % Input matrix
C = B'; % Output matrix
F = diag(10.^linspace(0,-8,sys.N)); % Source matrix
sys.f = @(x,u,p,t) A*x + B*u + F*p; % Vector field
sys.g = @(x,u,p,t) C*x; % Output functional
sys.F = @(x,u,p,t) A'*x + C'*u; % Adjoint vector field
%% MODEL REDUCTION
% State-space reduction tests
sys.p = zeros(sys.N,1); % Training Parameters
sys.q = zeros(sys.N,1); % Test Parameters
curios(sys,'state-reduction','linear-balanced-truncation',{[8,6,1]});
curios(sys,'state-reduction','nonlinear-balanced-truncation',{[8,6,2]});
curios(sys,'state-reduction','linear-direct-truncation',{[8,6,3]});
curios(sys,'state-reduction','nonlinear-direct-truncation',{[8,6,4]});
curios(sys,'state-reduction','linear-dominant-subspaces',{[8,6,5]});
curios(sys,'state-reduction','nonlinear-dominant-subspaces',{[8,6,6]});
curios(sys,'state-reduction','linear-direct-truncation',{'nonsym',[8,6,9]});
curios(sys,'state-reduction','nonlinear-direct-truncation',{'nonsym',[8,6,10]});
curios(sys,'state-reduction','linear-dominant-subspaces',{'nonsym',[8,6,11]});
curios(sys,'state-reduction','nonlinear-dominant-subspaces',{'nonsym',[8,6,12]});
curios(sys,'state-reduction','linear-balanced-truncation',{'gains',[8,6,13]});
curios(sys,'state-reduction','linear-direct-truncation',{'gains',[8,6,15]});
curios(sys,'state-reduction','linear-balanced-truncation',{'jacobi',[8,6,19]});
curios(sys,'state-reduction','nonlinear-balanced-truncation',{'jacobi',[8,6,20]});
curios(sys,'state-reduction','linear-direct-truncation',{'jacobi',[8,6,21]});
curios(sys,'state-reduction','nonlinear-direct-truncation',{'jacobi',[8,6,22]});
curios(sys,'state-reduction','linear-dominant-subspaces',{'jacobi',[8,6,23]});
curios(sys,'state-reduction','nonlinear-dominant-subspaces',{'jacobi',[8,6,24]});
curios(sys,'state-reduction','linear-balanced-truncation',{'scaled',[8,6,25]});
curios(sys,'state-reduction','nonlinear-balanced-truncation',{'scaled',[8,6,26]});
curios(sys,'state-reduction','linear-direct-truncation',{'scaled',[8,6,27]});
curios(sys,'state-reduction','nonlinear-direct-truncation',{'scaled',[8,6,28]});
curios(sys,'state-reduction','linear-dominant-subspaces',{'scaled',[8,6,29]});
curios(sys,'state-reduction','nonlinear-dominant-subspaces',{'scaled',[8,6,30]});
curios(sys,'state-reduction','linear-balanced-truncation',{'active',[8,6,31]});
curios(sys,'state-reduction','nonlinear-balanced-truncation',{'active',[8,6,32]});
curios(sys,'state-reduction','linear-direct-truncation',{'active',[8,6,33]});
curios(sys,'state-reduction','nonlinear-direct-truncation',{'active',[8,6,34]});
curios(sys,'state-reduction','linear-dominant-subspaces',{'active',[8,6,35]});
curios(sys,'state-reduction','nonlinear-dominant-subspaces',{'active',[8,6,36]});
curios(sys,'state-reduction','linear-balanced-truncation',{'tweighted',[8,6,37]});
curios(sys,'state-reduction','nonlinear-balanced-truncation',{'tweighted',[8,6,38]});
curios(sys,'state-reduction','linear-direct-truncation',{'tweighted',[8,6,39]});
curios(sys,'state-reduction','nonlinear-direct-truncation',{'tweighted',[8,6,40]});
curios(sys,'state-reduction','linear-dominant-subspaces',{'tweighted',[8,6,41]});
curios(sys,'state-reduction','nonlinear-dominant-subspaces',{'tweighted',[8,6,42]});
curios(sys,'state-reduction','linear-balanced-truncation',{'polynomial',[8,6,43]});
curios(sys,'state-reduction','nonlinear-balanced-truncation',{'polynomial',[8,6,44]});
curios(sys,'state-reduction','linear-direct-truncation',{'polynomial',[8,6,45]});
curios(sys,'state-reduction','nonlinear-direct-truncation',{'polynomial',[8,6,46]});
curios(sys,'state-reduction','linear-dominant-subspaces',{'polynomial',[8,6,47]});
curios(sys,'state-reduction','nonlinear-dominant-subspaces',{'polynomial',[8,6,48]});
% Parametric state-space reduction
sys.p = ones(sys.N,1)*[0.01,0.5,1.0]; % Training parameter
sys.q = rand(sys.N,5); % Test parameter
curios(sys,'state-reduction','linear-balanced-truncation',{[3,6,1]});
curios(sys,'state-reduction','nonlinear-balanced-truncation',{[3,6,2]});
curios(sys,'state-reduction','linear-direct-truncation',{[3,6,3]});
curios(sys,'state-reduction','nonlinear-direct-truncation',{[3,6,4]});
curios(sys,'state-reduction','linear-dominant-subspaces',{[3,6,5]});
curios(sys,'state-reduction','nonlinear-dominant-subspaces',{[3,6,6]});
curios(sys,'state-reduction','linear-direct-truncation',{'nonsym',[3,6,9]});
curios(sys,'state-reduction','nonlinear-direct-truncation',{'nonsym',[3,6,10]});
curios(sys,'state-reduction','linear-dominant-subspaces',{'nonsym',[3,6,11]});
curios(sys,'state-reduction','nonlinear-dominant-subspaces',{'nonsym',[3,6,12]});
curios(sys,'state-reduction','linear-direct-truncation',{'nonsym','polynomial',[3,6,15]});
curios(sys,'state-reduction','nonlinear-direct-truncation',{'nonsym','polynomial',[3,6,16]});
curios(sys,'state-reduction','linear-dominant-subspaces',{'nonsym','polynomial',[3,6,17]});
curios(sys,'state-reduction','nonlinear-dominant-subspaces',{'nonsym','polynomial',[3,6,18]});
% Parameter-space reduction tests
sys.p = ones(sys.N,1)*[0.01,1.0]; % Training parameter range
sys.q = rand(sys.N,5); % Test parameter
curios(sys,'parameter-reduction','controllability-based',{[4,4,1]});
curios(sys,'parameter-reduction','observability-based',{[4,4,2]});
curios(sys,'parameter-reduction','minimality-based',{[4,4,3]});
curios(sys,'parameter-reduction','minimality-based',{'nonsym',[4,4,4]});
curios(sys,'parameter-reduction','controllability-based',{'coarse',[4,4,5]});
curios(sys,'parameter-reduction','observability-based',{'coarse',[4,4,6]});
curios(sys,'parameter-reduction','minimality-based',{'coarse',[4,4,7]});
curios(sys,'parameter-reduction','minimality-based',{'nonsym','coarse',[4,4,8]});
curios(sys,'parameter-reduction','controllability-based',{'linpar',[4,4,9]});
curios(sys,'parameter-reduction','observability-based',{'linpar',[4,4,10]});
curios(sys,'parameter-reduction','minimality-based',{'linpar',[4,4,11]});
curios(sys,'parameter-reduction','minimality-based',{'nonsym','linpar',[4,4,12]});
curios(sys,'parameter-reduction','controllability-based',{'logpar',[4,4,13]});
curios(sys,'parameter-reduction','observability-based',{'logpar',[4,4,14]});
curios(sys,'parameter-reduction','minimality-based',{'logpar',[4,4,15]});
curios(sys,'parameter-reduction','minimality-based',{'nonsym','logpar',[4,4,16]});
% Combined state and parameter reduction
curios(sys,'combined-reduction','controllability-based',{[1,6,1]});
curios(sys,'combined-reduction','observability-based',{'linpar',[1,6,2]});
curios(sys,'combined-reduction','minimality-based',{'linpar',[1,6,3]});
curios(sys,'combined-reduction','minimality-based',{'linpar','dominant',[1,6,4]});
curios(sys,'combined-reduction','minimality-based',{'nonsym','linpar',[1,6,5]});
curios(sys,'combined-reduction','minimality-based',{'nonsym','linpar','dominant',[1,6,6]});
% Distributed cross operator
curios(sys,'state-reduction','nonlinear-direct-truncation',{[2,3,1]});
curios(sys,'state-reduction','nonlinear-direct-truncation',{'partitioned',[2,3,4]});
curios(sys,'parameter-reduction','minimality-based',{[2,3,2]});
curios(sys,'parameter-reduction','minimality-based',{'partitioned',[2,3,5]});
curios(sys,'combined-reduction','minimality-based',{[2,3,3]});
curios(sys,'combined-reduction','minimality-based',{'partitioned',[2,3,6]});
%% SENSITIVITY ANALYSIS
curios(sys,'sensitivity-analysis','input-state-based');
curios(sys,'sensitivity-analysis','input-output-based',{'hold'});
%% PARAMETER IDENTIFICATION
curios(sys,'parameter-identification','state-output-based');
curios(sys,'parameter-identification','input-output-based',{'hold'});
curios(sys,'parameter-identification','state-output-based',{'coarse','hold'});
curios(sys,'parameter-identification','input-output-based',{'coarse','hold'});
%% DECENTRALIZED CONTROL
sys.p = zeros(sys.N,1); % Training Parameters
sys.q = zeros(sys.N,1); % Test Parameters
curios(sys,'decentralized-control','linear',{[1,4,1]});
curios(sys,'decentralized-control','nonlinear',{[1,4,2]});
curios(sys,'decentralized-control','linear',{'coherence',[1,4,3]});
curios(sys,'decentralized-control','nonlinear',{'coherence',[1,4,4]});
% NONLINEARITY QUANTIFICATION
% Input Nonlinearity
sys.f = @(x,u,p,t) A*x + B*atan(u) + F*p; % Vector field
sys.g = @(x,u,p,t) C*x; % Output functional
curios(sys,'nonlinearity-quantification','input-based',{[1,4,1]});
curios(sys,'nonlinearity-quantification','state-based',{'hold',[1,4,1]});
curios(sys,'nonlinearity-quantification','output-based',{'hold',[1,4,1]});
% State Nonlinearity
sys.f = @(x,u,p,t) A*atan(x) + B*u + F*p; % Vector field
sys.g = @(x,u,p,t) C*x; % Output functional
curios(sys,'nonlinearity-quantification','input-based',{[1,4,2]});
curios(sys,'nonlinearity-quantification','state-based',{'hold',[1,4,2]});
curios(sys,'nonlinearity-quantification','output-based',{'hold',[1,4,2]});
% Output Nonlinearity
sys.f = @(x,u,p,t) A*x + B*u + F*p; % Vector field
sys.g = @(x,u,p,t) C*atan(x); % Output functional
curios(sys,'nonlinearity-quantification','input-based',{[1,4,3]});
curios(sys,'nonlinearity-quantification','state-based',{'hold',[1,4,3]});
curios(sys,'nonlinearity-quantification','output-based',{'hold',[1,4,3]});
% Linear System
sys.f = @(x,u,p,t) A*x + B*u + F*p; % Vector field
sys.g = @(x,u,p,t) C*x; % Output functional
curios(sys,'nonlinearity-quantification','input-based',{[1,4,4]});
curios(sys,'nonlinearity-quantification','state-based',{'hold',[1,4,4]});
curios(sys,'nonlinearity-quantification','output-based',{'hold',[1,4,4]});
%% STATE INDEX
curios(sys,'state-index','controllability');
curios(sys,'state-index','observability',{'hold'});
curios(sys,'state-index','minimality',{'hold'});
%% SYSTEM INDEX
curios(sys,'system-index','cauchy-index');
curios(sys,'system-index','system-entropy',{'cached'});
curios(sys,'system-index','system-gain',{'cached'});
curios(sys,'system-index','hinf-bound',{'cached','hold'})
curios(sys,'system-index','hankel-bound',{'cached','hold'})
curios(sys,'system-index','nyquist-area',{'cached','hold'});
curios(sys,'system-index','energy-fraction',{'cached','hold'});
curios(sys,'system-index','storage-efficiency',{'cached','hold'});
curios(sys,'system-index','ellipsoid-volume',{'cached','hold'});
curios(sys,'system-index','io-coherence',{'cached','hold'});
end
