creating a test for SGMK integration

clients/matlab/check_sgmk.m

@@ -0,0 +1,48 @@
+function check_sgmk()
+
+% An aux function to check and download the sparse grids matlab kit
+
+if exist('create_sparse_grid', 'file')==0
+    % the sgmk is not found in the current path, so either we don't have it or we are not in the right subfolder
+
+    if exist('sparse-grids-matlab-kit', 'dir')==0
+        % there is no subfolder -> we don't have sgmk. Need to download it (if we haven't yet) and unzip
+
+        if exist('sgmk.zip', 'file')==0
+            % zip not found, let's download it
+
+            try
+                disp('Sparse Grids Matlab Kit not found, downloading from github (https://github.com/lorenzo-tamellini/sparse-grids-matlab-kit/)...');
+                opts = weboptions; 
+                opts.CertificateFilename=(''); % No idea why this is needed
+                opts.Timeout = 100; % a larger timeout (in ms, default 5), just in case internet is slow today
+                websave('sgmk.zip', 'https://github.com/lorenzo-tamellini/sparse-grids-matlab-kit/archive/refs/heads/main.zip', opts);
+                disp('... done');
+            catch ME
+                fprintf('\nAutomatic download from github failed. Try manual download, from either github or project website https://sites.google.com/view/sparse-grids-kit. Download the latest version in .zip and name it sgmk.zip \n\n')                
+                error(ME.identifier,ME.message);
+            end
+        end
+
+        % now we have the zip, unzip
+        try
+            disp('unzipping ...');
+            unzip('sgmk.zip','sparse-grids-matlab-kit');
+            disp('done');
+        catch ME
+            error('%s. Automatic unzipping failed. Please extract sgmk.zip here', ME.message);
+        end
+    end
+
+    % ready to add to path. Mind the double folder
+    cd('sparse-grids-matlab-kit/sparse-grids-matlab-kit-main');
+    addpath(genpath(pwd)) 
+    disp('added Sparse Grids Matlab Kit to path')
+    cd('../..');
+
+else
+    % the sgmk is found in the current path, we're good to go
+
+    disp('Sparse Grids Matlab Kit is already in Matlab''s path')
+end
+

clients/matlab/sgmkClient.m

@@ -0,0 +1,42 @@
+clear
+
+
+% Analytic-Banana benchmark. Use the sparse grids matlab kit as a high-dimensional quadrature tool to compute the
+% integral of the posterior density defined in the benchmark. The problem is a bit challenging so even a poor result is
+% ok, this is just for testing the client. The pdfs in the benchmark are not normalized so the integral should be
+% around 3
+
+% add the Sparse Grids Matlab Kit and umbridge to your path
+check_sgmk()
+
+% uri of the service running the server
+uri = 'http://localhost:4243';
+
+% HTTPModel is an object provided by the UM-Bridge Matlab client.
+% model = HTTPModel(uri, 'posterior');
+model = HTTPModel(uri, 'posterior','webwrite');
+
+% model.evaluate(y) sends a request to the server to evaluate the model at y. Wrap it in an @-function:
+f = @(y) model.evaluate(y);
+
+% define the sparse grid. Here we create it a basic one, but it can be as sophisticated as the user wants
+N=2;
+w=7;
+% it is convenient to define the quadrature domain by a matrix D. IF the domain is [a b] x [c d], take each interval
+% as a column, so that 
+% D = [a  c ; 
+%      b  d ];
+domain = [-5 -5;  
+           5  5];
+knots={@(n) knots_CC(n,domain(1,1),domain(2,1),'nonprob'), @(n) knots_CC(n,domain(1,2),domain(2,2),'nonprob')};
+S=create_sparse_grid(N,w,knots,@lev2knots_doubling); 
+Sr=reduce_sparse_grid(S); 
+f_evals=evaluate_on_sparse_grid(f,Sr); 
+
+% from here on, do whatever UQ analysis you want with the values contained in f_evals
+figure
+plot_sparse_grids_interpolant(S,Sr,domain,exp(f_evals),'nb_plot_pts',80)
+figure
+plot_sparse_grids_interpolant(S,Sr,domain,f_evals,'with_f_values')
+
+Ev = quadrature_on_sparse_grid(exp(f_evals),Sr)