replaced CubatureSmoothing option with new CubatureAcceleration optio…

…n, based on iterating Aitken's delta squared transformation

Core/OBCSimulation/PerformCubature.m

@@ -35,6 +35,7 @@
         end
     end
 
+    CubatureWeights = [ [ 1; zeros( NumPoints( end ) - 1, 1 ) ], CubatureWeights ];
     NumPoints = [ 1 NumPoints ];
 
     if nargin > 6
@@ -44,13 +45,12 @@
     end
 
     yMatrix = y * CubatureWeights( 1, : );
-    yPure = y;
 
     if ~isempty( p )
         p.progress;
     end
 
-    CubatureSmoothing = dynareOBC.CubatureSmoothing;
+    CubatureAcceleration = dynareOBC.CubatureAcceleration;
 
     WarningGenerated = false;
     for i = 1 : CubatureOrder
@@ -91,14 +91,13 @@
                 end
             end
         end
-
-        yPureNew = yMatrix( :, i );
-        if dynareOBC.FastCubature || ( CubatureSmoothing <= 0 ) || ( CubatureSmoothing >= 1 ) || ( dynareOBC.QuasiMonteCarloLevel > 0 )
-            yNew = yPureNew;
+
+        if CubatureAcceleration
+            yNew = IteratedAitkensDeltaSquaredTransformation( yMatrix( :, 1 : ( i + 1 ) ) );
         else
-            yNew = ( 1 - CubatureSmoothing ) * yPureNew + CubatureSmoothing * yPure;
+            yNew = yMatrix( :, i + 1 );
         end
-        yPure = yPureNew;
+
         yError = max( abs( y - yNew ) );
         y = yNew;
 

Core/SetDefaultOptions.m

@@ -3,8 +3,8 @@
     dynareOBC = SetDefaultOption( dynareOBC, 'Bypass', false );    
     dynareOBC = SetDefaultOption( dynareOBC, 'CalculateTheoreticalVariance', false );
     dynareOBC = SetDefaultOption( dynareOBC, 'CompileSimulationCode', false );
+    dynareOBC = SetDefaultOption( dynareOBC, 'CubatureAcceleration', false );
     dynareOBC = SetDefaultOption( dynareOBC, 'CubaturePruningCutOff', 0.01 );
-    dynareOBC = SetDefaultOption( dynareOBC, 'CubatureSmoothing', -eps );
     dynareOBC = SetDefaultOption( dynareOBC, 'CubatureTolerance', eps ^ 0.375 );
     dynareOBC = SetDefaultOption( dynareOBC, 'DataFile', [ dynareOBC.BaseFileName '.xlsx' ] );
     dynareOBC = SetDefaultOption( dynareOBC, 'Debug', false );

Core/Utils/IteratedAitkensDeltaSquaredTransformation.m

@@ -0,0 +1,33 @@
+function Seq = IteratedAitkensDeltaSquaredTransformation( Seq )
+
+    N = size( Seq, 2 );
+
+    if N >= 3
+
+        if mod( N, 2 ) == 0
+            Seq = Seq( :, 2:end );
+            N = N - 1;
+        end
+
+        for Idx = 1 : ( 0.5 * ( N - 1 ) )
+
+            DSeq = diff( Seq, 1, 2 );
+
+            Seq = Seq( :, 3:end );
+            LDSeq = DSeq( :, 1:(end-1) );
+            DSeq = DSeq( :, 2:end );
+
+            Adj = DSeq .* DSeq ./ ( DSeq - LDSeq );
+            FiniteAdj = isfinite( Adj );
+
+            Seq( FiniteAdj ) = Seq( FiniteAdj ) - Adj( FiniteAdj );
+
+        end
+
+    else
+
+        Seq = Seq( :, N );
+
+    end
+
+end

README.md

@@ -121,11 +121,11 @@ Note:
     * `FastCubature`
       Causes DynareOBC to ignore the value specified in `MaxCubatureDegree` and `QuasiMonteCarlo`, and to instead use a degree 3 monomial cubature rule without negative weights, but involving evaluations further from the origin.
     * `QuasiMonteCarloLevel=INTEGER` (default: `0`)
-      If this is non-zero, then Gaussian cubature is not used (so the MaxCubatureDegree option is ignored). Instead, quasi- Monte Carlo integration with at most `2^(1+INTEGER) - 1` samples is used.
+      If this is non-zero, then Gaussian cubature is not used (so the `MaxCubatureDegree` option is ignored). Instead, quasi-Monte Carlo integration with at most `2^(1+INTEGER) - 1` samples is used.
     * `MaxCubatureDegree=INTEGER` (default: `5`)
-      Specifies the degree of polynomial which will be integrated exactly in the highest degree cubature performed. Values above `51` are treated as equal to `51`. Note that setting `CubatureSmoothing>0` will reduce the effective maximum accuracy by 2 degrees. Setting `CubatureTolerance>0` may also mean that the result does not integrate the stated degree polynomials exactly as well.
-        * `CubatureSmoothing=FLOAT_IN_UNIT_INTERVAL` (default: `0`)
-          When this is larger than 0, and less than 1, DynareOBC takes a weighted combination of the results of cubature rules of adjacent degrees. Large numbers imply larger weights on lower degree rules. A good setting is often 0.01 - 0.3.
+      Specifies the degree of polynomial which will be integrated exactly in the highest degree cubature performed. Values above `51` are treated as equal to `51`. Note that enabling the option `CubatureSmoothing` or setting `CubatureTolerance>0` may mean that the result does not integrate the stated degree polynomials exactly.
+    * `CubatureAcceleration`
+      When DynareOBC is invoked with this option, DynareOBC accelerates convergence of the cubature rules towards their limit using an iterated version of Aitken's delta-squared transformation.
     * `CubaturePruningCutOff=FLOAT` (default: `0.01`)
       Eigenvalues of the covariance matrix of the distribution from which we integrate that are below `FLOAT` times the maximum eigenvalue are "pruned" to zero, in order to increase integration speed.
     * `MaxCubatureDimension=INTEGER` (default: `128`)

ReadMe.txt

@@ -180,18 +180,16 @@ OPTIONS (NOT CASE SENSITIVE!) include:
       evaluations further from the origin. 
     * QuasiMonteCarloLevel=INTEGER (default: 0) 
       If this is non-zero, then Gaussian cubature is not used (so the MaxCubatureDegree option is 
-      ignored). Instead, quasi- Monte Carlo integration with at most 2^(1+INTEGER) - 1 samples is 
+      ignored). Instead, quasi-Monte Carlo integration with at most 2^(1+INTEGER) - 1 samples is 
       used. 
     * MaxCubatureDegree=INTEGER (default: 5) 
       Specifies the degree of polynomial which will be integrated exactly in the highest degree 
-      cubature performed. Values above 51 are treated as equal to 51. Note that setting 
-      CubatureSmoothing>0 will reduce the effective maximum accuracy by 2 degrees. Setting 
-      CubatureTolerance>0 may also mean that the result does not integrate the stated degree 
-      polynomials exactly as well. 
-        * CubatureSmoothing=FLOAT_IN_UNIT_INTERVAL (default: 0) 
-          When this is larger than 0, and less than 1, DynareOBC takes a weighted combination of 
-          the results of cubature rules of adjacent degrees. Large numbers imply larger weights on 
-          lower degree rules. A good setting is often 0.01 - 0.3. 
+      cubature performed. Values above 51 are treated as equal to 51. Note that enabling the option 
+      CubatureSmoothing or setting CubatureTolerance>0 may mean that the result does not integrate 
+      the stated degree polynomials exactly. 
+    * CubatureAcceleration 
+      When DynareOBC is invoked with this option, DynareOBC accelerates convergence of the cubature 
+      rules towards their limit using an iterated version of Aitken's delta-squared transformation. 
     * CubaturePruningCutOff=FLOAT (default: 0.01) 
       Eigenvalues of the covariance matrix of the distribution from which we integrate that are 
       below FLOAT times the maximum eigenvalue are "pruned" to zero, in order to increase 

dynareOBC.m

@@ -181,18 +181,16 @@ function dynareOBC( InputFileName, varargin )
 %       evaluations further from the origin. 
 %     * QuasiMonteCarloLevel=INTEGER (default: 0) 
 %       If this is non-zero, then Gaussian cubature is not used (so the MaxCubatureDegree option is 
-%       ignored). Instead, quasi- Monte Carlo integration with at most 2^(1+INTEGER) - 1 samples is 
+%       ignored). Instead, quasi-Monte Carlo integration with at most 2^(1+INTEGER) - 1 samples is 
 %       used. 
 %     * MaxCubatureDegree=INTEGER (default: 5) 
 %       Specifies the degree of polynomial which will be integrated exactly in the highest degree 
-%       cubature performed. Values above 51 are treated as equal to 51. Note that setting 
-%       CubatureSmoothing>0 will reduce the effective maximum accuracy by 2 degrees. Setting 
-%       CubatureTolerance>0 may also mean that the result does not integrate the stated degree 
-%       polynomials exactly as well. 
-%         * CubatureSmoothing=FLOAT_IN_UNIT_INTERVAL (default: 0) 
-%           When this is larger than 0, and less than 1, DynareOBC takes a weighted combination of 
-%           the results of cubature rules of adjacent degrees. Large numbers imply larger weights on 
-%           lower degree rules. A good setting is often 0.01 - 0.3. 
+%       cubature performed. Values above 51 are treated as equal to 51. Note that enabling the option 
+%       CubatureSmoothing or setting CubatureTolerance>0 may mean that the result does not integrate 
+%       the stated degree polynomials exactly. 
+%     * CubatureAcceleration 
+%       When DynareOBC is invoked with this option, DynareOBC accelerates convergence of the cubature 
+%       rules towards their limit using an iterated version of Aitken's delta-squared transformation. 
 %     * CubaturePruningCutOff=FLOAT (default: 0.01) 
 %       Eigenvalues of the covariance matrix of the distribution from which we integrate that are 
 %       below FLOAT times the maximum eigenvalue are "pruned" to zero, in order to increase