Merge pull request #1052 from JohannesPfeifer/lin_solve_robust

Integrate robust linear solver for stack_solve_algo=0

doc/dynare.texi

@@ -2879,6 +2879,9 @@ add new variables one by one.
 Determines the maximum number of iterations used in the non-linear solver. The
 default value of @code{maxit} is 50. 
 
+@item robust_lin_solve
+Triggers the use of a robust linear solver for the default @code{solve_algo=4}. 
+
 @item solve_algo = @var{INTEGER}
 @anchor{solve_algo}
 Determines the non-linear solver to use. Possible values for the option are:

matlab/global_initialization.m

@@ -63,6 +63,7 @@ options_.minimal_workspace = 0;
 options_.dp.maxit = 3000;
 options_.steady.maxit = 50;
 options_.simul.maxit = 50;
+options_.simul.robust_lin_solve = 0;
 
 options_.mode_check.status = 0;
 options_.mode_check.neighbourhood_size = .5;

matlab/perfect-foresight-models/perfect_foresight_solver.m

@@ -176,7 +176,7 @@ end
 if oo_.deterministic_simulation.status == 1
     disp('Perfect foresight solution found.')
 else
-    warning('Failed to solve perfect foresight model')
+    disp('Failed to solve perfect foresight model')
 end
 
 skipline()

matlab/perfect-foresight-models/sim1.m

@@ -162,9 +162,17 @@ for iter = 1:options.simul.maxit
 
     if endogenous_terminal_period && iter>1
         dy = ZERO;
-        dy(1:i_rows(end)) = -A(1:i_rows(end),1:i_rows(end))\res(1:i_rows(end));
+        if options.simul.robust_lin_solve
+            dy(1:i_rows(end)) = -lin_solve_robust( A(1:i_rows(end),1:i_rows(end)), res(1:i_rows(end)),verbose );            
+        else
+            dy(1:i_rows(end)) = -lin_solve( A(1:i_rows(end),1:i_rows(end)), res(1:i_rows(end)), verbose );
+        end
     else
-        dy = -A\res;
+        if options.simul.robust_lin_solve
+            dy = -lin_solve_robust( A, res, verbose );            
+        else
+            dy = -lin_solve( A, res, verbose );
+        end
     end
 
     Y(i_upd) =   Y(i_upd) + dy;
@@ -223,3 +231,84 @@ end
 if verbose
     skipline();
 end
+
+function x = lin_solve( A, b,verbose)
+    if norm( b ) < sqrt( eps ) % then x = 0 is a solution
+        x = 0;
+        return
+    end
+    
+    x = A\b;
+    x( ~isfinite( x ) ) = 0;
+    relres = norm( b - A * x ) / norm( b );
+    if relres > 1e-6 && verbose
+        fprintf( 'WARNING : Failed to find a solution to the linear system.\n' );
+    end
+    
+function [ x, flag, relres ] = lin_solve_robust( A, b , verbose)
+    if norm( b ) < sqrt( eps ) % then x = 0 is a solution
+        x = 0;
+        flag = 0;
+        relres = 0;
+        return
+    end
+    
+    x = A\b;
+    x( ~isfinite( x ) ) = 0;
+    [ x, flag, relres ] = bicgstab( A, b, [], [], [], [], x ); % returns immediately if x is a solution
+    if flag == 0
+        return
+    end
+
+    disp( relres );
+
+    if verbose
+        fprintf( 'Initial bicgstab failed, trying alternative start point.\n' );
+    end
+    old_x = x;
+    old_relres = relres;
+    [ x, flag, relres ] = bicgstab( A, b );
+    if flag == 0
+        return
+    end
+
+    if verbose
+        fprintf( 'Alternative start point also failed with bicgstab, trying gmres.\n' );
+    end
+    if old_relres < relres
+        x = old_x;
+    end
+    [ x, flag, relres ] = gmres( A, b, [], [], [], [], [], x );
+    if flag == 0
+        return
+    end
+
+    if verbose
+        fprintf( 'Initial gmres failed, trying alternative start point.\n' );
+    end
+    old_x = x;
+    old_relres = relres;
+    [ x, flag, relres ] = gmres( A, b );
+    if flag == 0
+        return
+    end
+
+    if verbose
+        fprintf( 'Alternative start point also failed with gmres, using the (SLOW) Moore-Penrose Pseudo-Inverse.\n' );
+    end
+    if old_relres < relres
+        x = old_x;
+        relres = old_relres;
+    end
+    old_x = x;
+    old_relres = relres;
+    x = pinv( full( A ) ) * b;
+    relres = norm( b - A * x ) / norm( b );
+    if old_relres < relres
+        x = old_x;
+        relres = old_relres;
+    end
+    flag = relres > 1e-6;
+    if flag ~= 0 && verbose
+        fprintf( 'WARNING : Failed to find a solution to the linear system\n' );
+    end

tests/Makefile.am

@@ -149,7 +149,8 @@ MODFILES = \
 	simul/Solow_no_varexo.mod \
 	simul/simul_ZLB_purely_forward.mod \
 	simul/simul_ZLB_purely_forward_no_solution.mod \
-	conditional_forecasts/1/fs2000_cal.mod \
+
+	simul/Irreversible_investment.mod \
 	conditional_forecasts/2/fs2000_est.mod \
 	conditional_forecasts/3/fs2000_conditional_forecast_initval.mod \
 	conditional_forecasts/4/fs2000_conditional_forecast_histval.mod \

tests/simul/Irreversible_investment.mod

@@ -0,0 +1,112 @@
+@#define NumberOfCountries = 2
+
+var log_kappa;
+@#for Country in 1:NumberOfCountries
+    var mu@{Country}, logit_l@{Country}, k@{Country}, a@{Country};
+@#endfor
+
+parameters alpha beta varrho delta theta rhoA sigmaA;
+
+alpha = 0.3;
+beta = 0.99;
+varrho = 1.5;
+delta = 0.025;
+theta = 0.9;
+rhoA = 0.95;
+sigmaA = 0.05;
+
+@#for Country in 1:NumberOfCountries
+    varexo epsilonA@{Country};
+@#endfor
+
+model;
+
+    #kappa = exp( log_kappa );
+    #LEAD_kappa = exp( log_kappa(+1) );
+
+    #min_A = theta ^ ( 1/alpha );
+    #mean_a = log( 1 - min_A );
+
+    @#for Country in 1:NumberOfCountries
+
+        #K@{Country}        = exp( k@{Country} );
+        #LAG_K@{Country}    = exp( k@{Country}(-1) );
+        #LEAD_A@{Country}   = min_A + exp( a@{Country}(+1) );
+        #A@{Country}        = min_A + exp( a@{Country} );
+        #LAG_A@{Country}    = min_A + exp( a@{Country}(-1) );
+        #L@{Country}        = 1 / ( 1 + exp( -logit_l@{Country} ) );
+        #LEAD_L@{Country}   = 1 / ( 1 + exp( -logit_l@{Country}(+1) ) );
+
+        #C@{Country} = kappa ^ ( -1/varrho ) - theta / ( 1-alpha ) * ( A@{Country}*(1-L@{Country}) ) ^ ( 1-alpha );
+        #LEAD_phi@{Country} = ( 1 - theta * ( LEAD_A@{Country}*(1-LEAD_L@{Country}) ) ^ ( -alpha ) ) * LEAD_kappa;
+        #I@{Country} = K@{Country} - ( 1-delta ) * LAG_K@{Country};
+
+    @#endfor
+
+    @#for Country in 1:NumberOfCountries
+
+        ( a@{Country} - mean_a ) = rhoA * ( a@{Country}(-1) - mean_a ) - sigmaA * epsilonA@{Country};
+        L@{Country} = min( LAG_K@{Country} / A@{Country}, 1 - theta ^ ( 1/alpha ) / A@{Country} );
+        kappa - mu@{Country} = beta * ( ( 1-delta ) * ( LEAD_kappa - mu@{Country}(+1) ) + LEAD_phi@{Country} );
+        kappa = max( beta * ( ( 1-delta ) * ( LEAD_kappa - mu@{Country}(+1) ) + LEAD_phi@{Country} ), ( theta / ( 1-alpha ) * ( A@{Country}*(1-L@{Country}) ) ^ ( 1-alpha )
+        @#for OtherCountry in 1:NumberOfCountries
+            + A@{OtherCountry} * L@{OtherCountry}
+            @#if OtherCountry != Country
+                - C@{OtherCountry} - I@{OtherCountry}
+            @#endif
+        @#endfor
+        ) ^ ( -varrho ) );
+
+    @#endfor
+
+    0 = 0
+    @#for OtherCountry in 1:NumberOfCountries
+        + A@{OtherCountry} * L@{OtherCountry}
+        - C@{OtherCountry} - I@{OtherCountry}
+    @#endfor
+    ;
+
+end;
+
+steady_state_model;
+
+    a = log( 1 - theta ^ ( 1/alpha ) );
+    mu = 0;
+    L = 1 - ( 1/theta * ( 2 - 1/beta - delta ) ) ^ ( -1/alpha );
+    K = L;
+    I = delta * K;
+    C = ( 1 - delta ) * L;
+
+    kappa_ = ( C + theta / ( 1-alpha ) * ( 1-L ) ^ ( 1-alpha ) ) ^ ( -varrho );
+
+    log_kappa = log( kappa_ );
+
+    @#for Country in 1:NumberOfCountries
+
+        mu@{Country} = mu;
+        logit_l@{Country} = log( L / ( 1 - L ) );
+        k@{Country} = log( K );
+        a@{Country} = a;
+
+    @#endfor
+
+end;
+
+steady;
+check;
+
+shocks;
+
+var epsilonA1; periods 1; values 2;
+@#for Country in 2:NumberOfCountries
+    var epsilonA@{Country}; periods 1; values 0;    
+@#endfor
+
+end;
+
+options_.simul.robust_lin_solve=1;
+simul( periods = 400 );
+
+if ~oo_.deterministic_simulation.status
+    error('Model did not solve')
+end