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optimization_loop.m
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optimization_loop.m
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function [ Pc, A_cell, chi, val_vec, opt_vec ] = optimization_loop( P, ...
sd, EVS, A_cell, kmin, kmax, parameters, fileid )
% This file is part of GPCCA.
%
% Copyright (c) 2018, 2017 Bernhard Reuter
%
% If you use this code or parts of it, cite the following reference:
%
% Reuter, B., Weber, M., Fackeldey, K., Röblitz, S., & Garcia, M. E. (2018). Generalized
% Markov State Modeling Method for Nonequilibrium Biomolecular Dynamics: Exemplified on
% Amyloid β Conformational Dynamics Driven by an Oscillating Electric Field. Journal of
% Chemical Theory and Computation, 14(7), 3579–3594. https://doi.org/10.1021/acs.jctc.8b00079
%
% GPCCA is free software: you can redistribute it and/or modify
% it under the terms of the GNU Lesser General Public License as published
% by the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU Lesser General Public License
% along with this program. If not, see <http://www.gnu.org/licenses/>.
% -------------------------------------------------------------------------
%loop over opt_soft() for cluster numbers kt in [kmin,kmax].
% [ Pc, A_cell, chi, val_vec, opt_vec ] = optimization_loop( P, sd, ...
% EVS, A_cell, kmin, kmax, parameters, fileid )
%
% Input:
% P (N,N)-matrix to be clustered (row-stochastic)
% sd "initial distribution".
% EVS (N,k)-matrix with eigen- or Schur-vectors (column
% by column).
% A_cell cell vector of initial (k,k)-tranformation
% matrices A.
% kmin minimum number of clusters.
% kmax maximum number of clusters.
% parameters structure with parameters (see gpcca()).
% fileid Identification string for naming of the output
% files.
%
% Output:
% Pc Coarse grained stochastic transition matrix as
% returned from the last optimization.
% A_cell cell vector of (k,k)-tranformation matrices A.
% chi (N,k)-matrix with membership values.
% val_vec vector of optimality values.
% opt_vec vector of crispnesses.
% Written by Bernhard Reuter, Theoretical Physics II,
% University of Kassel, 2017
% -----------------------------------------------------------------------
assert(isa(A_cell,'cell'),'optimization_loop:DataTypeError1', ...
'Variable is type %s not %s', class(A_cell),'cell')
assert(isa(EVS,'double'),'optimization_loop:DataTypeError2', ...
'Variable is type %s not %s', class(EVS),'double')
assert(ischar(fileid),'optimization_loop:DataTypeError3', ...
'Variable is type %s not %s', class(fileid),'char')
assert(isstruct(parameters),'optimization_loop:DataTypeError4', ...
'Variable is type %s not %s', class(parameters),'struct')
dummy = ( abs(EVS(:,1) - 1) < ( 100 * eps ) ) ;
assert(all(dummy(:)), 'optimization_loop:FirstColumnError', ...
'EVS(:,1) isnt equal 1!')
clearvars dummy
opt_vec = NaN(kmax-kmin+1,2) ;
opt_vec(:,1) = kmin:kmax ;
val_vec = NaN(kmax-kmin+1,2) ;
val_vec(:,1) = kmin:kmax ;
% compute optimal solution for every desired number of clusters
if parameters.parallel == 0 %l2
for kt = kmin:kmax %l4
if isempty(A_cell{kt}) == false
evs = EVS(:,1:kt) ;
% pass cluster number to opt_soft for naming the optimization
% output plots
counter = kt ;
% call to optimization routine
[chi, A_cell{kt}, val] = opt_soft(A_cell{kt}, evs, counter, ...
fileid, parameters) ;
% -----------------------------------------------------------
% put the actual optimality value 'val' and crispness in two
% vectors
opt_vec(kt-kmin+1,2) = (kt-val)/kt ;
val_vec(kt-kmin+1,2) = val ;
% postprocess (display, pot, save, calculate) the relevant
% output quantities
Pc = postprocess( kt, val, chi, sd, A_cell{kt}, P, fileid ) ;
else
dummy = ['No optimization will be performed for ', ...
num2str(kt),' clusters, '] ;
disp(' ')
disp(dummy)
clearvars dummy
disp('since this would split a 2x2-block of eigenvalues!')
disp(' ')
end
end
elseif parameters.parallel == 1 %l3
disp(' ')
disp('You are performing the first optimization loop in')
disp('parallel. Hence the iterations are executed in non-')
disp('deterministic order. Therefore the output will also')
disp('occur in non-deterministic order. This is no error')
disp('and no reason to worry.')
disp(' ')
% delete active parallel pool, if there is one
delete(gcp('nocreate')) ;
% get the number of physical cores of the machine
numCores = feature('numcores') ;
% create a new pool with #workers=#cores
parpool(numCores) ;
% create extra variables needed for parfor loop
shift_pf = kmin-1 ;
Pc_cell = cell([1,kmax]) ;
chi_cell = cell([1,kmax]) ;
evs_cell = cell([1,kmax]) ;
for kt = kmin:kmax %l5
evs_cell{kt} = EVS(:,1:kt) ;
end
% perform parallel loop iteration
parfor kt = kmin:kmax %l6
% little hack to ensure that, if kmin is an invalid cluster
% number (leading to splitting of a 2x2-block), the
% associated opt and val values are NaN. If the following two
% lines are removed, the opt and val values will be 0 in such
% a case, which is not intended. This seems to be a MATLAB
% bug only appearing in parallel by unknown reasons...
opt_vec(kt-shift_pf,2) ;
val_vec(kt-shift_pf,2) ;
if isempty(A_cell{kt}) == false
try %l7
evs = evs_cell{kt} ;
% pass cluster number to opt_soft for naming the
% optimization output plots
counter = kt ;
% call to optimization routine
[chi_cell{kt},A_cell{kt},val]=opt_soft(A_cell{kt}, ...
evs, counter, fileid, parameters) ;
% -----------------------------------------------------------
% put the actual optimality value 'val' and crispness in
% two vectors
opt_vec(kt-shift_pf,2) = (kt-val)/kt ;
val_vec(kt-shift_pf,2) = val ;
% postprocess (display, pot, save, calculate) the
% relevant output quantities
Pc_cell{kt} = postprocess( kt, val, chi_cell{kt}, ...
sd, A_cell{kt}, P, fileid ) ;
catch ME %l8
disp(' ')
disp(['Error in iteration ' num2str(kt) ...
' of the parfors loop in gpcca.m!'])
disp('ME.identifier:')
disp(ME.identifier)
disp('ME.message:')
disp(ME.message)
rethrow(ME)
end
else
dummy = ['No optimization will be performed for ', ...
num2str(kt),' clusters, '] ;
disp(' ')
disp(dummy)
disp('since this would split a 2x2-block of eigenvalues!')
disp(' ')
end
end
Pc = Pc_cell{kmax} ;
clearvars Pc_cell
chi = chi_cell{kmax} ;
clearvars chi_cell
else %l1
error('optimization_loop:PoolInitializationError',['Couldnt ' ...
'initialize parallel pool since parameters.parallel was ' ...
'neither =0 nor =1!'])
end
end