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August 26, 2018 08:27
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function result = LogLin( VarEndoNames, VarExoNames, Parameters, Equations, SolveMode, EvalMode, EvalString, Digits ) | |
% ------------------------------------------------------------ | |
% PURPOSE: Performs log-linearisation. | |
% ------------------------------------------------------------ | |
% SYNTAX: result = LogLin( VarEndoNames, VarExoNames, Parameters, Equations, SolveMode, EvalMode, EvalString, Digits ); | |
% ------------------------------------------------------------ | |
% EXAMPLE: result = LogLin( { 'R', 'A' }, { 'EPSILON' }, { 'beta', 'rho' }, { 'beta * R * A / A(+1) = 1', 'A = A(-1) ^ rho * exp( EPSILON )' }, 2, 2 ) | |
% ------------------------------------------------------------ | |
% OUTPUT: result: a cell array of log-linearised equations, with __d appended to variable names that are deviations from steady state. | |
% ------------------------------------------------------------ | |
% INPUT: VarEndoNames: a cell array of endogenous variable names | |
% VarExoNames: a cell array of exogenous variable names | |
% Parameters: a cell array of parameter names | |
% Equations: a cell array of equations, in Dynare notation | |
% SolveMode: specifies how the steady state is found | |
% SolveMode = 0 ---> the steady state is not found, instead __s is appended to the variable names | |
% SolveMode = 1 ---> the steady state is found analytically | |
% SolveMode = 2 ---> the steady state is found analytically, allowing all algebraic manipulations | |
% SolveMode = 3 ---> the steady state is found analytically, assuming real values | |
% SolveMode = 4 ---> the steady state is found numerically | |
% EvalMode: specifies any processing of the found equations | |
% EvalMode = 0 ---> no additional processing | |
% EvalMode = 1 ---> simplification | |
% EvalMode = 2 ---> simplification, allowing all algebraic manipulations | |
% EvalMode = 3 ---> numeric evaluation, to Digits precision | |
% EvalString: string of comma delimited equations, useful for specifying parameters or your own computed steady state values (e.g. 'beta=0.99,rho=1/2', or 'A=1') | |
% Digits: (optional) the number of digits of accuracy for numerical compuations | |
% ------------------------------------------------------------ | |
% Copyright © 2011 Tom Holden ( http://www.tholden.org/ ) | |
% All rights reserved. | |
% ------------------------------------------------------------ | |
% Redistribution and use in source and binary forms, with or without | |
% modification, are permitted provided that the following conditions are | |
% met: | |
% | |
% * Redistributions of source code must retain the above copyright | |
% notice, this list of conditions and the following disclaimer. | |
% * Redistributions in binary form must reproduce the above copyright | |
% notice, this list of conditions and the following disclaimer in | |
% the documentation and/or other materials provided with the distribution | |
% | |
% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" | |
% AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE | |
% IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE | |
% ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE | |
% LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR | |
% CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF | |
% SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS | |
% INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN | |
% CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) | |
% ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE | |
% POSSIBILITY OF SUCH DAMAGE. | |
% ------------------------------------------------------------ | |
if nargin < 6 | |
error( 'Insufficient arguments provided to LogLin.' ); | |
end | |
nl = newline; | |
ProcessedEquations = cell( size( Equations ) ); | |
SteadyEquations = cell( size( Equations ) ); | |
TempVarNames = [ VarEndoNames VarExoNames ]; | |
SteadyStateEquations = ''; | |
SteadyStateVars = ''; | |
Comma = ''; | |
for VarEndoName = VarEndoNames | |
SteadyStateVars = [ SteadyStateVars Comma VarEndoName{1} '__s' ]; | |
Comma = ', '; | |
end | |
for VarExoName = VarExoNames | |
SteadyStateEquations = [ SteadyStateEquations VarExoName{1} '__s := 0; ' ]; | |
end | |
SteadyStateEquations = [ SteadyStateEquations nl ]; | |
AllLagsAndLeads = cell( 1, 0 ); | |
SteadyStateEquationsTmp = cell( 1, 0 ); | |
for i = 1:length( Equations ) | |
SFEquation = [ ' ' Equations{i} ' ' ]; | |
for Parameter = Parameters | |
SFEquation = regexprep( SFEquation, [ '(?<=\W)' Parameter{1} '(?=\W)' ], [ '__' Parameter{1} '__' ] ); | |
end | |
SFEquation = regexprep( SFEquation, '(?<=\W)log(?=\W)', 'ln' ); | |
SFEquation = regexprep( SFEquation, '\s', '' ); | |
SFEquation = regexprep( SFEquation, '=(.*)', '-($1)' ); | |
LagsAndLeads = unique( wrap( regexp( SFEquation, '\w\(([+-]?\d+)\)', 'tokens' ) ) ); | |
AllLagsAndLeads = [ AllLagsAndLeads LagsAndLeads ]; | |
SteadyEquation = SFEquation; | |
ProcessedEquation = SFEquation; | |
for LagOrLead = LagsAndLeads | |
NLagOrLead = str2double( LagOrLead{1} ); | |
if NLagOrLead > 0 | |
ReplaceString = [ '__' repmat( 'f', 1, NLagOrLead ) ]; | |
else | |
if NLagOrLead < 0 | |
ReplaceString = [ '__' repmat( 'b', 1, -NLagOrLead ) ]; | |
else | |
ReplaceString = ''; | |
end | |
end | |
TLagOrLead = regexptranslate( 'escape', LagOrLead{1} ); | |
ProcessedEquation = regexprep( ProcessedEquation, [ '(\w+)\(' TLagOrLead '\)' ], [ '$1' ReplaceString ] ); | |
SteadyEquation = regexprep( SteadyEquation, [ '(\w+)\(' TLagOrLead '\)' ], '$1' ); | |
TempVarNames = unique( [ TempVarNames wrap( regexp( ProcessedEquation, [ '(\w+' ReplaceString ')' ], 'tokens' ) ) ] ); | |
for VarEndoName = VarEndoNames | |
SteadyStateEquationsTmp = [ SteadyStateEquationsTmp [ VarEndoName{1} ReplaceString '__s := ' VarEndoName{1} '__s;' ] ]; | |
end | |
for VarExoName = VarExoNames | |
SteadyStateEquationsTmp = [ SteadyStateEquationsTmp [ VarExoName{1} ReplaceString '__s := 0;' ] ]; | |
end | |
end | |
ProcessedEquations{i} = ProcessedEquation; | |
SteadyEquations{i} = SteadyEquation; | |
end | |
SteadyStateEquationsTmp = unique( SteadyStateEquationsTmp ); | |
for SteadyStateEquationTmp = SteadyStateEquationsTmp | |
SteadyStateEquations = [ SteadyStateEquations SteadyStateEquationTmp{1} ' ' ]; | |
end | |
SteadyStateEquations = [ SteadyStateEquations nl ]; | |
TempVarNamesList = ''; | |
SteadyTempVarNamesList = ''; | |
EvalLoc = ''; | |
Comma = ''; | |
for TempVarName = TempVarNames | |
TempVarNamesList = [ TempVarNamesList ' ' TempVarName{1} ]; | |
SteadyTempVarNamesList = [ SteadyTempVarNamesList ' ' TempVarName{1} '__s' ]; | |
EvalLoc = [ EvalLoc Comma TempVarName{1} ' = ' TempVarName{1} '__s' ]; | |
Comma = ', '; | |
end | |
if nargin >= 7 | |
NewEvalString = [ ' ' EvalString ' ' ]; | |
for Parameter = Parameters | |
NewEvalString = regexprep( NewEvalString, [ '(?<=\W)' Parameter{1} '(?=\W)' ], [ '__' Parameter{1} '__' ] ); | |
end | |
for VarEndoName = VarEndoNames | |
NewEvalString = regexprep( NewEvalString, [ '(?<=\W)' VarEndoName{1} '(?=\W)' ], [ VarEndoName{1} '__s' ] ); | |
end | |
NewEvalString = regexprep( NewEvalString, '(?<=\W)log(?=\W)', 'ln' ); | |
NewEvalString = regexprep( NewEvalString, '\s', '' ); | |
MuPADString = ''; | |
MuPADStringPrefix = [ SteadyStateEquations 'EvalLoc := { ' EvalLoc Comma NewEvalString ' };' nl ]; | |
else | |
MuPADString = ''; | |
MuPADStringPrefix = [ SteadyStateEquations 'EvalLoc := { ' EvalLoc ' };' nl ]; | |
end | |
switch EvalMode | |
case 1 | |
Prefix = 'simplify( '; | |
Suffix = ' )'; | |
case 2 | |
Prefix = 'simplify( '; | |
Suffix = ', IgnoreAnalyticConstraints )'; | |
case 3 | |
Prefix = 'float( '; | |
Suffix = ' )'; | |
otherwise | |
Prefix = ''; | |
Suffix = ''; | |
end | |
if nargin >= 8 | |
MuPADStringPrefix = [ MuPADStringPrefix 'DIGITS := ' int2str( Digits ) ';' nl ]; | |
end | |
MuPADStringSuffix = ''; | |
Comma = ''; | |
for i = 1:length( Equations ) | |
MuPADString = [ MuPADString 'eq__' int2str( i ) ' := ' Prefix 'evalAt( evalAt( ' ProcessedEquations{i} ' , EvalLoc ), EvalLocSteadyState )' Suffix ]; %#ok<*AGROW> | |
for TempVarName = TempVarNames | |
MuPADString = [ MuPADString ' + ' Prefix 'evalAt( evalAt( ' TempVarName{1} ' * diff( ' ProcessedEquations{i} ' , ' TempVarName{1} ' ), EvalLoc ), EvalLocSteadyState ) * ' lower( TempVarName{1} ) '__d' Suffix ]; | |
end | |
MuPADString = [ MuPADString ';' nl ]; | |
MuPADStringSuffix = [ MuPADStringSuffix Comma 'eq__' int2str( i ) ]; | |
Comma = ', '; | |
end | |
if SolveMode > 0 | |
MuPADStringPrefix = [ MuPADStringPrefix 'EvalLocSteadyState := ' ]; | |
if SolveMode == 4 | |
MuPADStringPrefix = [ MuPADStringPrefix 'numeric::f' ]; | |
end | |
MuPADStringPrefix = [ MuPADStringPrefix 'solve( evalAt( { ' ]; | |
Comma = ''; | |
for i = 1:length( Equations ) | |
MuPADStringPrefix = [ MuPADStringPrefix Comma SteadyEquations{i} ]; | |
Comma = ', '; | |
end | |
switch SolveMode | |
case 2 | |
SolveOption = ', IgnoreAnalyticConstraints'; | |
case 3 | |
SolveOption = ', Real'; | |
otherwise | |
SolveOption = ''; | |
end | |
MuPADStringPrefix = [ MuPADStringPrefix ' }, EvalLoc ), { ' SteadyStateVars ' } ' SolveOption ' );' nl ]; | |
else | |
MuPADStringPrefix = [ MuPADStringPrefix 'EvalLocSteadyState := { };' nl ]; | |
end | |
disp( 'MUPAD CODE USED:' ); | |
MuPADString = regexprep( [ MuPADStringPrefix MuPADString '{ ' MuPADStringSuffix ' }' ], '\n+', '\n' ); | |
disp( MuPADString ); | |
eqs = evalin( symengine, MuPADString ); | |
result = cell( size( eqs ) ); | |
for i = 1:length( eqs ) | |
ResEq = char( eqs( i ) ); | |
for LagOrLead = AllLagsAndLeads | |
NLagOrLead = str2double( LagOrLead{1} ); | |
if NLagOrLead > 0 | |
ReplaceString = [ '__' repmat( 'f', 1, NLagOrLead ) ]; | |
else | |
if NLagOrLead < 0 | |
ReplaceString = [ '__' repmat( 'b', 1, -NLagOrLead ) ]; | |
else | |
ReplaceString = ''; | |
end | |
end | |
ResEq = regexprep( ResEq, [ '(\w+)' ReplaceString '__d' ], [ '$1__d(' LagOrLead{1} ')' ] ); | |
end | |
for Parameter = Parameters | |
ResEq = regexprep( ResEq, [ '__' Parameter{1} '__' ], Parameter{1} ); | |
end | |
ResEq = regexprep( ResEq, '(?<=\W)ln(?=\W)', 'log' ); | |
result{i} = ResEq; | |
end | |
end | |
function out = wrap( in ) | |
if isempty( in ) | |
out = cell( 1, 0 ); | |
elseif ischar( in ) | |
out = { in }; | |
elseif iscell( in ) | |
out = cellfun( @cellstr, in ); | |
else | |
out = cellstr( in ); | |
end | |
end |
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