diff --git a/matlab/cli/dcontrib.m b/matlab/cli/dcontrib.m new file mode 100644 index 0000000000000000000000000000000000000000..ab1363392773516733fe0f96a2abfcfd52aa5bbf --- /dev/null +++ b/matlab/cli/dcontrib.m @@ -0,0 +1,347 @@ +function dcontrib(varargin) + +% Computes dynamic contributions to a subset of endogenous variables in a semi structural model. +% +% EXAMPLE +% +% >> dcontrib --model sandbox.mod --tags zpac eq:x1 --database ds --output results --range 2023Q1:2073Q1 +% +% zpac and eq:x1 are the equation tags of the equations determining the endogenous variables for which we want to compute +% the contributions of the other (exogenous) variables, sandbox.mod is the name of the file from which we exctract these +% equations, ds is a dseries object containing the data, 2023Q1:2073Q1 is the time range over which we compute the +% contributions, and results the name of the structure containing the contributions (as dseries objects) for each endogenous +% variable. +% +% INPUTS +% --model name of a mod file (with extension) +% --tags list of equations (equation tags assocated to the endogenous variables for which we want to compute the contributions) +% --database dseries object +% --baseline dseries object (path for the exogenous variables) +% --range followed by a dates range +% +% REMARKS +% [1] --baseline and --range are not compatible. +% [2] --variables is followed by a space separated list of names, it is assumed that each variable is associated with an equation tag. + +% Copyright © 2023 Dynare Team +% +% This file is part of Dynare. +% +% Dynare is free software: you can redistribute it and/or modify +% it under the terms of the GNU General Public License as published by +% the Free Software Foundation, either version 3 of the License, or +% (at your option) any later version. +% +% Dynare is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. +% +% You should have received a copy of the GNU General Public License +% along with Dynare. If not, see <https://www.gnu.org/licenses/>. + + global M_ + + if nargin==1 && strcmpi(varargin{1}, '--help') + skipline() + disp('--model followed by the name of a mod file (with extension) [mandatory]') + disp('--tags followed by a list of equation tags [mandatory]') + disp('--database followed by dseries object [mandatory]') + disp('--baseline followed by dseries object (path for the exogenous variables)') + disp('--range followed by a dates range') + disp('--output followed by a name for the structure holding the results [mandatory]') + skipline() + return + end + + model = getmodel(varargin); + + % First call to dynare to obtain the json verison of the model. + dynare(model(1:end-4), 'nopreprocessoroutput', 'notime', 'json=compute') + delete(sprintf('%s.log', model(1:end-4))) + + eqtags = geteqtags(varargin); + variables = cell(length(eqtags), 1); + for i=1:length(eqtags) + variables(i) = get_variables_and_parameters_in_expression(get_lhs_and_rhs(eqtags{i}, M_, true)); + end + + % Cherry pick equations required for the decomposition. + cherrypickdir = sprintf('cherry-pick-%s', randomstring(10)); + cherrypick(model(1:end-4), cherrypickdir, eqtags, false); + rmdir(model(1:end-4), 's') + rmdir(sprintf('+%s', model(1:end-4)), 's') + modfilename = sprintf('dcontrib_%s.mod', randomstring(10)); + aggregate(modfilename, {}, '', cherrypickdir); + rmdir(cherrypickdir, 's') + + % Second call to dynare (on the exctracted equations) + dynare(modfilename(1:end-4), 'nopreprocessoroutput', 'notime', 'json=compute') + + % Get dataset + dname = getdatasetname(varargin); + ds = evalin('caller', dname); + if ~isdseries(ds) + error('dcontrib:getdataset: --dataset must be followed by a dseries object.') + end + + % Create a dseries object for the paths of the exogenous variables + xvariables = ds{M_.exo_names{:}}; + + % Get initial and terminal periods (if defined) + [firstperiod, lastperiod] = getperiods(varargin); + if firstperiod<=ds.dates(1)+M_.orig_maximum_lag + error('dcontrib:: Try increase firstperiod (>%s).', char(ds.dates(1)+M_.orig_maximum_lag)) + end + if lastperiod>ds.dates(end) + error('dcontrib:: Try reduce lastperiod (<=%s).', char(ds.dates(end))) + end + + % Load baseline (if it makes sense) + if isempty(firstperiod) + baselinename = getbaselinename(varargin); + baseline = evalin('caller', baselinename); + if ~isdseries(baseline) + error('dcontrib:getdataset: --baseline must be followed by a dseries object.') + end + firstperiod = baseline.dates(1); + lastperiod = baseline.dates(end); + baseline = baseline{M_.exo_names{:}}; + else + % Set default baseline (exogenous variable levels in firstperiod-1) + baseline = xvariables(firstperiod-1); + baseline = repmat(baseline.data, lastperiod-firstperiod+1, 1); + baseline = dseries(baseline, firstperiod, M_.exo_names); + end + + % Restrict the observations for the exogenous variables to the pertinent tim range + xvariables = xvariables(firstperiod:lastperiod); + + % Set initial conditions for the simulation. + initialconditions = ds(ds.dates(1):firstperiod-1); + + % Simulation on the baseline (track the effects of the initial state if the model is autoregressive) + S.baseline = simul_backward_model(initialconditions, lastperiod-firstperiod+1, baseline); + + % contributions is a dseries object holding the marginal contribution of the baseline and + % each exogenous variable to endogenous variable z + % contributions.baseline = S.baseline(firstperiod:lastperiod); + + % Add exogenous variables one by one and simulate the model (-> cumulated contributions) + for i=1:xvariables.vobs + name = xvariables.name{i}; + baseline{name} = xvariables{name}; + S.(name) = simul_backward_model(initialconditions, lastperiod-firstperiod+1, baseline); + end + + % Compute marginal contributions + for j=1:length(variables) + cumulatedcontribs = S.baseline{variables{j}}(firstperiod:lastperiod).data; + contributions.(variables{j}) = dseries(cumulatedcontribs, firstperiod, 'baseline'); + for i=1:xvariables.vobs + name = xvariables.name{i}; + ts = S.(name); + data = ts{variables{j}}(firstperiod:lastperiod).data; + contributions.(variables{j}) = [contributions.(variables{j}), dseries(data-cumulatedcontribs, firstperiod, name)]; + cumulatedcontribs = data; + end + contributions.(variables{j}) = contributions.(variables{j})(firstperiod:lastperiod); + end + + % Save output in caller workspace + oname = getoutputname(varargin); + assignin('caller', oname, contributions) + + % Cleanup + rmdir(modfilename(1:end-4), 's') + rmdir(sprintf('+%s', modfilename(1:end-4)), 's') + delete(sprintf('%s.mod', modfilename(1:end-4))) + delete(sprintf('%s.log', modfilename(1:end-4))) +end + + +function model = getmodel(cellarray) + + % Return variables for which we want to compute the contributions. + % + % INPUTS + % - cellarray [char] 1×n cell array of row char arrays. + % + % OUTPUTS + % - var [char] name of the model (with extension) + + mpos = positions(cellarray); + + model = cellarray{mpos+1}; + +end + + +function eqtags = geteqtags(cellarray) + +% Return equation tags for the equations we want to compute the contributions. +% +% INPUTS +% - cellarray [char] 1×n cell array of row char arrays. +% +% OUTPUTS +% - eqtags [char] 1×p cell array of row char arrays. + + [~, vpos, ~, ~, ~, ~, indices] = positions(cellarray); + + lastvalue = indices(find(indices==vpos)+1)-1; + + eqtags = cellarray(vpos+1:lastvalue); + +end + + +function dname = getdatasetname(cellarray) + +% Return the name of the dataset. +% +% INPUTS +% - cellarray [char] 1×n cell array of row char arrays. +% +% OUTPUTS +% - dname [char] dataset name for endogenous and exogenous variables + + [~, ~, dpos] = positions(cellarray); + + dname = cellarray{dpos+1}; + +end + + +function [firstperiod, lastperiod] = getperiods(cellarray) + +% Return variables for which we want to compute the contributions. +% +% INPUTS +% - cellarray [char] 1×n cell array of row char arrays. +% +% OUTPUTS +% - ds [dseries] dataset for endogenous and exogenous variables + + [~, ~, ~, rpos] = positions(cellarray); + + firstperiod = dates(); + lastperiod = dates(); + + if ~isempty(rpos) + try + tmp = strsplit(cellarray{rpos+1},':'); + firstperiod = dates(tmp{1}); + lastperiod = dates(tmp{2}); + catch + error('dcontrib:getperiods: Cannot convert the --range argument to dates objects.') + end + if lastperiod<=firstperiod + error('dcontrib:getperiods: In --range A:B we must have B>A.') + end + end + +end + + +function dname = getbaselinename(cellarray) + +% Return the name of the dataset. +% +% INPUTS +% - cellarray [char] 1×n cell array of row char arrays. +% +% OUTPUTS +% - dname [char] baseline name for endogenous and exogenous variables + + [~, ~, ~, ~, bpos] = positions(cellarray); + + dname = cellarray{bpos+1}; + +end + + +function oname = getoutputname(cellarray) + +% Return the name of the output. +% +% INPUTS +% - cellarray [char] 1×n cell array of row char arrays. +% +% OUTPUTS +% - dname [char] baseline name for endogenous and exogenous variables + + [~, ~, ~, ~, ~, opos] = positions(cellarray); + + oname = cellarray{opos+1}; + +end + + +function [mpos, vpos, dpos, rpos, bpos, opos, indices] = positions(cellarray) + + % Return positions of the arguments. + % + % INPUTS + % - cellarray [char] 1×n cell array of row char arrays. + % + % OUTPUTS + % - mpos [integer] scalar, index for the --model argument. + % - vpos [integer] scalar, index for the --tags arguments. + % - dpos [integer] scalar, index for the --database argument. + % - rpos [integer] scalar, index for the --range argument. + % - bpos [integer] scalar. index for the --baseline argument. + % - opos [integer] scalar, index for the --output argument. + + % Index for --model argument + mpos = find(strcmp('--model', cellarray)); + if isempty(mpos) + error('dcontrib::positions: --model argument is mandatory.') + elseif length(mpos)>1 + error('dplot::positions: Only one --model argument is allowed.') + end + + % Index for --tags argument + vpos = find(strcmp('--tags', cellarray)); + if isempty(vpos) + error('dplot::positions: --tags argument is mandatory.') + elseif length(vpos)>1 + error('dplot::positions: Only one --tags argument is allowed.') + end + + % Index for the --initialconditions argument + dpos = find(strcmp('--database', cellarray)); + if isempty(dpos) + error('dplot::positions: --database argument is mandatory.') + elseif length(dpos)>1 + error('dplot::positions: Only one --database argument is allowed.') + end + + % Index for the --range argument + rpos = find(strcmp('--range', cellarray)); + if length(rpos)>1 + error('dplot::positions: Only one --range argument is allowed.') + end + + % Index for the --baseline argument + bpos = find(strcmp('--baseline', cellarray)); + if length(bpos)>1 + error('dplot::positions: Only one --baseline argument is allowed.') + end + + if ~isempty(rpos) && ~isempty(bpos) + error('dplot::positions: --baseline and --range arguments are not allowed simultaneously.') + end + + % Index for the --output argument. + opos = find(strcmp('--output', cellarray)); + if isempty(opos) + error('dplot::positions: --output argument is mandatory.') + elseif length(opos)>1 + error('dplot::positions: Only one --periods argument is allowed.') + end + + % Sorted vector of indices + indices = sort([mpos; vpos; dpos; rpos; bpos; opos]); + +end diff --git a/tests/Makefile.am b/tests/Makefile.am index 2d974779e82130a906b3c0880a8d579924afe02e..2817e9886270087226921d9cf4fc9f379bcfdd83 100644 --- a/tests/Makefile.am +++ b/tests/Makefile.am @@ -1269,7 +1269,8 @@ M_TRS_FILES += run_block_byte_tests_matlab.m.trs \ nonlinearsolvers.m.trs \ cyclereduction.m.trs \ logarithmicreduction.m.trs \ - riccatiupdate.m.trs + riccatiupdate.m.trs \ + contribs.m.trs M_XFAIL_TRS_FILES = $(patsubst %.mod, %.m.trs, $(XFAIL_MODFILES)) @@ -1284,7 +1285,8 @@ O_TRS_FILES += run_block_byte_tests_octave.o.trs \ nonlinearsolvers.o.trs \ cyclereduction.o.trs \ logarithmicreduction.o.trs \ - riccatiupdate.o.trs + riccatiupdate.o.trs \ + contribs.o.trs O_XFAIL_TRS_FILES = $(patsubst %.mod, %.o.trs, $(XFAIL_MODFILES)) @@ -1491,7 +1493,10 @@ EXTRA_DIST = \ solve_algo_12_14/simul_backward_common.inc \ solve_algo_12_14/purely_backward_common.inc \ solve_algo_12_14/purely_static_common.inc \ - solve_algo_12_14/purely_forward_common.inc + solve_algo_12_14/purely_forward_common.inc \ + sandbox.mod \ + simulateddata.m + if ENABLE_MATLAB check-local: check-matlab diff --git a/tests/contribs.m b/tests/contribs.m new file mode 100644 index 0000000000000000000000000000000000000000..94efddf9605a9390e71e395b1e1dc90ae730b755 --- /dev/null +++ b/tests/contribs.m @@ -0,0 +1,82 @@ +debug = false; + +if debug + [top_test_dir, ~, ~] = fileparts(mfilename('fullpath')); +else + top_test_dir = getenv('TOP_TEST_DIR'); +end + +addpath(sprintf('%s/matlab', top_test_dir(1:end-6))) + +if ~debug + % Test Dynare Version + if ~strcmp(dynare_version(), getenv('DYNARE_VERSION')) + error('Incorrect version of Dynare is being tested') + end +end + +dynare_config; + +NumberOfTests = 0; +testFailed = 0; + +if ~debug + skipline() + disp('*** TESTING: nonlinearsolvers.m ***'); +end + +% +% TEST +% + +t0 = clock; + +NumberOfTests = NumberOfTests+1; + +try + dataset = dseries('simulateddata.m'); + + dcontrib --model sandbox.mod --tags zpac eq:x1 --database dataset --output results --range 2023Q1:2073Q1 + + if max(abs(sum(results.z.data, 2)-dataset.z(dates('2023Q1'):dates('2073Q1')).data))>1e-5 + + error('Computation of dynamic contributions failed.') + end + +catch + + testFailed = testFailed+1; + +end + +t1 = clock; + + +if ~debug + cd(getenv('TOP_TEST_DIR')); +else + dprintf('FAILED tests: %i', testFailed) +end + +if isoctave + fid = fopen('contribs.o.trs', 'w+'); +else + fid = fopen('contribs.m.trs', 'w+'); +end +if testFailed + fprintf(fid,':test-result: FAIL\n'); + fprintf(fid,':list-of-failed-tests: nonlinearsolvers.m\n'); +else + fprintf(fid,':test-result: PASS\n'); +end +fprintf(fid,':number-tests: %i\n', NumberOfTests); +fprintf(fid,':number-failed-tests: %i\n', testFailed); +fprintf(fid,':elapsed-time: %f\n', etime(t1, t0)); +fclose(fid); + +if ~debug + exit; +end +% +% END OF TEST +% diff --git a/tests/sandbox.mod b/tests/sandbox.mod new file mode 100644 index 0000000000000000000000000000000000000000..6b4a3556a9963628371ff9552a70d8f47e875b0a --- /dev/null +++ b/tests/sandbox.mod @@ -0,0 +1,134 @@ +// --+ options: json=compute, stochastic +-- + +@#define simulate = false + +var x1 x2 x1bar x2bar z y x u v s azertyuiopiop z1 z2 z3; + +varexo ex1 + ex2 + ex1bar + ex2bar + ez + ey + ex + eu + ev + es; + +parameters + rho_1 rho_2 rho_3 rho_4 + a_x1_0 a_x1_1 a_x1_2 a_x1_x2_1 a_x1_x2_2 + a_x2_0 a_x2_1 a_x2_2 a_x2_x1_1 a_x2_x1_2 + e_c_m c_z_1 c_z_2 c_z_dx2 c_z_u c_z_dv c_z_s cx cy beta + lambda; + +rho_1 = .9; +rho_2 = -.2; +rho_3 = .4; +rho_4 = -.3; + + +a_x1_0 = -.9; +a_x1_1 = .4; +a_x1_2 = .3; +a_x1_x2_1 = .1; +a_x1_x2_2 = .2; + +a_x2_0 = -.9; +a_x2_1 = .2; +a_x2_2 = -.1; +a_x2_x1_1 = -.1; +a_x2_x1_2 = .2; + +beta = .2; +e_c_m = .5; +c_z_1 = .2; +c_z_2 = -.1; +c_z_dx2 = .3; +c_z_u = .3; +c_z_dv = .4; +c_z_s = -.2; +cx = 1.0; +cy = 1.0; + + +lambda = 0.5; // Share of optimizing agents. + +trend_component_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar'], targets=['eq:x1bar', 'eq:x2bar']); + +pac_model(auxiliary_model_name=toto, discount=beta, model_name=pacman, auxname=rototo); + +model; + +[name='eq:u'] +s = .3*s(-1) - .1*s(-2) + es; + +[name='eq:diff(v)'] +diff(v) = .5*diff(v(-1)) + ev; + +[name='eq:u'] +u = .5*u(-1) - .2*u(-2) + eu; + +[name='eq:y'] +y = rho_1*y(-1) + rho_2*y(-2) + ey; + +[name='eq:x'] +x = rho_3*x(-1) + rho_4*x(-2) + ex; + +[name='eq:azertyuiopiop', rename='azertyuiopiop->qsdfghjklm'] +azertyuiopiop = x + y; + +[name='eq:x1'] +diff(x1) = a_x1_0*(x1(-1)-x1bar(-1)) + a_x1_1*diff(x1(-1)) + a_x1_2*diff(x1(-2)) + a_x1_x2_1*diff(x2(-1)) + a_x1_x2_2*diff(x2(-2)) + ex1; + +[name='eq:x2'] +diff(x2) = a_x2_0*(x2(-1)-x2bar(-1)) + a_x2_1*diff(x1(-1)) + a_x2_2*diff(x1(-2)) + a_x2_x1_1*diff(x2(-1)) + a_x2_x1_2*diff(x2(-2)) + ex2; + +[name='eq:x1bar'] +x1bar = x1bar(-1) + ex1bar; + +[name='eq:x2bar'] +x2bar = x2bar(-1) + ex2bar; + +[name='zpac'] +diff(z) = lambda*(e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1)) + c_z_2*diff(z(-2)) + pac_expectation(pacman) + c_z_s*s + c_z_dv*diff(v) ) + (1-lambda)*( cy*y + cx*x) + c_z_u*u + c_z_dx2*diff(x2) + ez; + +[name='z1'] +z1 = z+y-x+u; + +[name='z2'] +z2 = z-y+x-u; + +[name='z3'] +z3 = u-diff(v); + +end; + +shocks; + var ex1 = 1.0; + var ex2 = 1.0; + var ex1bar = 1.0; + var ex2bar = 1.0; + var ez = 1.0; + var ey = 0.1; + var ex = 0.1; + var eu = 0.05; + var ev = 0.05; + var es = 0.07; +end; + +// Initialize the PAC model (build the Companion VAR representation for the auxiliary model). +pac.initialize('pacman'); + +// Update the parameters of the PAC expectation model (h0 and h1 vectors). +pac.update.expectation('pacman'); + +@#if simulate +verbatim; +// Simulate the model to create an artificial sample. +initialconditions = dseries(zeros(10, M_.endo_nbr+M_.exo_nbr), 2000Q1, vertcat(M_.endo_names,M_.exo_names)); +TrueData = simul_backward_model(initialconditions, 300); +TrueData.save('simulateddata', 'm') +end; + +@#endif diff --git a/tests/simulateddata.m b/tests/simulateddata.m new file mode 100644 index 0000000000000000000000000000000000000000..5f3456fe26b47c97bfe208aec2157f96d95a849f --- /dev/null +++ b/tests/simulateddata.m @@ -0,0 +1,7497 @@ +% File created on 05-Jul-2023 14:55:50. + +FREQ__ = 4; +INIT__ = '2000Q1'; + +NAMES__ = {'x1'; 'x2'; 'x1bar'; 'x2bar'; 'z'; 'y'; 'x'; 'u'; 'v'; 's'; 'azertyuiopiop'; 'z1'; 'z2'; 'z3'; 'ex1'; 'ex2'; 'ex1bar'; 'ex2bar'; 'ez'; 'ey'; 'ex'; 'eu'; 'ev'; 'es'}; +TEX__ = {'x1'; 'x2'; 'x1bar'; 'x2bar'; 'z'; 'y'; 'x'; 'u'; 'v'; 's'; 'azertyuiopiop'; 'z1'; 'z2'; 'z3'; 'ex1'; 'ex2'; 'ex1bar'; 'ex2bar'; 'ez'; 'ey'; 'ex'; 'eu'; 'ev'; 'es'}; +OPS__ = {[];[];[];[];[];[];[];[];[];[];[];[];[];[];[];[];[];[];[];[];[];[];[];[]}; + +x1 = [ + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0.53766714 + 2.5389865 + 0.61933601 + 2.4875444 + 2.5744943 + 2.8895704 + 3.0657897 + 3.1778697 + 7.6027825 + 8.6889742 + 6.4968587 + 8.8546193 + 7.7842277 + 6.3563086 + 6.8392259 + 4.6536952 + 4.103382 + 6.3190467 + 8.1453529 + 10.420006 + 11.844469 + 10.720772 + 11.490495 + 13.308723 + 13.329577 + 12.47984 + 10.815459 + 9.9428638 + 10.504423 + 10.719483 + 11.66302 + 10.734868 + 9.5985063 + 8.4261078 + 6.132975 + 10.161524 + 10.461626 + 10.092594 + 9.6322906 + 3.2525286 + 0.98135013 + -0.23231286 + 0.45792094 + 1.2684469 + 0.26456826 + -0.82644379 + -2.2776798 + -0.36641077 + 0.61476643 + 2.1997944 + -0.39425191 + -2.3865738 + -4.9560541 + -4.635863 + -0.9388924 + 3.040834 + 1.5564486 + -0.072965461 + -1.7054894 + -1.4769812 + -3.072308 + -1.0758726 + -1.2118069 + -1.3249373 + -2.4300817 + -5.649957 + -7.7497077 + -7.8995914 + -7.2107996 + -2.2292524 + -1.6315767 + -0.64229867 + -3.0730861 + -2.6096611 + -3.4111837 + -1.3811425 + 0.80394117 + 4.4738981 + 5.3356127 + 2.951523 + 2.3758115 + 0.9199683 + -0.5502125 + 0.62400965 + -0.92191491 + -0.61477588 + -0.75749807 + -0.86668152 + -1.0326082 + -3.3889793 + -4.7993783 + -3.5559812 + -0.74217759 + 3.384809 + 1.0985908 + -1.0180361 + -4.8027612 + -7.0043564 + -5.8894208 + -4.6778056 + -2.0188431 + -0.9242161 + -0.58465221 + -0.72726254 + -1.2814241 + -1.8587837 + -0.54939872 + 1.6330022 + 2.1276215 + -1.3801944 + -6.6188175 + -9.3751146 + -6.6853221 + -6.6262503 + -4.1452993 + -6.0853695 + -4.3175157 + -7.135522 + -6.6691581 + -6.7095589 + -3.0647154 + -2.6827042 + -2.0688667 + -4.9165634 + -7.0887498 + -7.2523135 + -5.5810188 + -5.7864548 + -5.7801328 + -8.3790271 + -9.1101423 + -10.225563 + -11.360857 + -9.4022425 + -11.073981 + -13.521666 + -17.744385 + -17.730843 + -16.893256 + -15.798019 + -13.32666 + -13.359582 + -15.38649 + -18.207904 + -20.595597 + -21.943149 + -21.728567 + -18.935191 + -18.731031 + -15.799653 + -17.74453 + -18.041875 + -17.549327 + -17.040852 + -15.094286 + -14.570703 + -16.000036 + -15.969809 + -16.708353 + -18.240686 + -20.563166 + -21.348191 + -21.052445 + -16.112064 + -14.515455 + -13.876292 + -16.463711 + -18.001201 + -17.505794 + -14.871731 + -16.002582 + -19.209687 + -19.795898 + -17.912228 + -15.921755 + -15.284445 + -18.104918 + -20.015004 + -21.856287 + -18.96434 + -18.520962 + -14.417111 + -15.244119 + -16.758823 + -18.64182 + -18.790356 + -18.140316 + -14.149054 + -13.034088 + -13.22604 + -15.839002 + -19.075183 + -19.465441 + -18.805695 + -17.053375 + -14.372046 + -12.333252 + -12.507297 + -15.230697 + -15.901724 + -14.356753 + -14.063411 + -12.96257 + -13.670377 + -14.874399 + -14.743454 + -14.87345 + -15.05562 + -14.362763 + -14.382686 + -16.636319 + -14.226102 + -17.244708 + -17.689709 + -18.050048 + -18.45686 + -16.974814 + -16.748661 + -15.423603 + -16.638585 + -18.127149 + -17.537325 + -18.077065 + -18.708432 + -22.190629 + -23.306229 + -22.590766 + -21.75213 + -20.641867 + -21.62112 + -21.489537 + -22.630293 + -22.669867 + -22.095786 + -20.743351 + -19.64649 + -18.759249 + -23.128905 + -21.840484 + -20.507146 + -22.728046 + -20.339156 + -20.77427 + -20.319445 + -20.803131 + -24.04415 + -26.385589 + -25.629136 + -25.482327 + -24.942546 + -24.879117 + -25.657734 + -26.686959 + -26.444067 + -25.873711 + -26.643562 + -26.648198 + -32.018826 + -28.970572 + -28.57816 + -25.537359 + -28.976267 + -30.401039 + -31.86352 + -31.756587 + -33.864031 + -33.270631 + -34.298135 + -34.372859 + -33.49747 + -34.461301 + -34.100857 + -34.547714 + -35.221298 + -34.243868 + -34.426924 + -36.739995 + -36.958432 + -39.273746 + -37.169543 + -33.898876 + -32.000445 + -33.490276 + -35.760323 + -37.287275 + -36.529241 + -37.279102 + -37.618659 + -36.139682 + -40.167397 + -39.724087 + -42.461009 + -37.885059 + -35.328021 + -34.333485 + -36.506329 + -42.027785 + -42.564315 + -44.367937 + -41.996027]; 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