Dear all,
My code works fine in serial mode, and I experiment with parfor and spmd to speed it up. The code runs the same sequence of function calls 7 times (corresponding to 7 independent models), and it uses containers (vectors and arrays) of different sizes at a time. Each model utilizes fmincon with the Hessian at the minimum returned. The problem within a parallel environment appears as soon as fmincon finds a minimum for the first time and attempts to calculate the Hessian for that model.
A relevant part of the main driver looks like this
matlabpool
spmd (7)
switch labindex
case 1
lambda = 0.0604;
mu = [0.0696 -0.0249 -0.0108]';
(code omitted)
DNS1 = optimize_logL('DNS_unc',lambda,mu,state_par, ...
state_cov,meas_cov,opt_on,OPG_on);
case 2
lambda = [0.06248 0.0531];
mu = [0.0723 -0.0294 -0.012 0.063]';
(code omitted)
where optimize_logL is the constructor of a user defined class.
Through the function optimize_logL and additional function calls therein, fmincon is invoked. The relevant part is the following
options = optimset('FinDiffType','forward', 'MaxFunEvals',50000, ...
'TolX',1e-7, 'TolFun',1e-7, 'MaxIter',10000, ...
'Algorithm','interior-point', 'Hessian','bfgs', ...
'Diagnostics','on', 'UseParallel','always');
[xopt,logLmax,exitflag,output,~,grad,hessian] = ...
fmincon(@objective_fun_con,QML.param_vec,A,b,Aeq,beq,lb,ub, ...
@stability,options);
with the objective function and non-linear constraint below
objective function
[lambda mu state_par state_cov meas_cov] = extract_parameters(QML,x);
model_temp = choose_model(QML,QML.model_name,lambda,mu, ...
state_par,state_cov,meas_cov);
in_sample_yield(model_temp,false);
logL = model_temp.logL;
non-linear constraint
[~, ~, state_par] = extract_parameters(QML,x);
(comments omitted)
c = abs(eig(state_par))' - 0.9999999999999999;
ceq = [];
The containers lambda, mu, etc have different sizes per model. The temporary handle model_temp is created to initiate a series of calculations common to every model, and it should be destroyed at function exit.
The error message I get is
Error using spmd_feval (line 8)
Error detected on lab(s) 6
Caused by:
Matrix dimensions must agree.
Error stack:
parfinitedifferences>(parfor body) at 158
Sending a stop signal to all the labs ...
or if I use 'UseParallel','never'
Error using spmd_feval (line 8)
Error detected on lab(s) 6
Caused by:
CAT arguments dimensions are not consistent.
Error stack:
formJacobian.m at 26
barrier.m at 596
fmincon.m at 841
optimize_model.m at 59
optimize_logL>optimize_logL.optimize_logL at 160
Sending a stop signal to all the labs ...
I assume some of the model containers are mixed, while they are not supposed to do so. Since the evaluation of the Hessian follows the calculation of the function minimum as a part of fmincon, I cannot add a few diagnostic fprintf statements to see what is actually happening.
A few clarifications and things that I have tried:
1) I do not use global variables.
2) There is no file opening or I/O to a file involved, only some output to the screen.
3) I tried to add delete and clear statements in the objective function before it exits, without any positive result.
4) I tried a model_temp = []; before the function end but still no different result.
5) All the variables/containers that are passed in optimize_logL at the main driver are (re)defined for every case block of the switch statement.
6) There is no difference in the error messages between spmd and parfor.
7) Each of the 7 models is a user-defined class, and optimize_logL is a separate class. All 8 classes inherit a common superclass where the containers lambda, mu, etc are properties with protected access, and function in_sample_yield has public access.
Any suggestions to tackle this problem are welcome.
Georgios
