1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
|
function [SAmeas, OutMatrix] = Morris_Measure_Groups(NumFact, Sample, Output, p, Group)
% [SAmeas, OutMatrix] = Morris_Measure_Groups(NumFact, Sample, Output, p, Group)
%
% Given the Morris sample matrix, the output values and the group matrix compute the Morris measures
% -------------------------------------------------------------------------
% INPUTS
% -------------------------------------------------------------------------
% Group [NumFactor, NumGroups] := Matrix describing the groups.
% Each column represents one group.
% The element of each column are zero if the factor is not in the
% group. Otherwise it is 1.
%
% Sample := Matrix of the Morris sampled trajectories
%
% Output := Matrix of the output(s) values in correspondence of each point
% of each trajectory
%
% k = Number of factors
% -------------------------------------------------------------------------
% OUTPUTS
% OutMatrix (NumFactor*NumOutputs, 3)= [Mu*, Mu, StDev]
% for each output it gives the three measures of each factor
% -------------------------------------------------------------------------
% Copyright (C) 2012 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 <http://www.gnu.org/licenses/>.
if nargin==0,
disp(' ')
disp('[SAmeas, OutMatrix] = Morris_Measure_Groups(NumFact, Sample, Output, p, Group);')
return
end
OutMatrix=[];
if nargin < 5, Group=[]; end
NumGroups = size(Group,2);
if nargin < 4 | isempty(p),
p = 4;
end
Delt = p/(2*p-2);
if NumGroups ~ 0
sizea = NumGroups; % Number of groups
GroupMat=Group;
GroupMat = GroupMat';
else
sizea = NumFact;
end
r=size(Sample,1)/(sizea+1); % Number of trajectories
% For Each Output
for k=1:size(Output,2)
OutValues=Output(:,k);
% For each r trajectory
for i=1:r
% For each step j in the trajectory
% Read the orientation matrix fact for the r-th sampling
% Read the corresponding output values
Single_Sample = Sample(i+(i-1)*sizea:i+(i-1)*sizea+sizea,:);
Single_OutValues = OutValues(i+(i-1)*sizea:i+(i-1)*sizea+sizea,:);
A = (Single_Sample(2:sizea+1,:)-Single_Sample(1:sizea,:))';
Delta = A(find(A));
% For each point of the fixed trajectory compute the values of the Morris function. The function
% is partitioned in four parts, from order zero to order 4th.
for j=1:sizea % For each point in the trajectory i.e for each factor
% matrix of factor which changes
if NumGroups ~ 0;
AuxFind (:,1) = A(:,j);
% AuxFind(find(A(:,j)),1)=1;
% Pippo = sum((Group - repmat(AuxFind,1,NumGroups)),1);
% Change_factor(j,i) = find(Pippo==0);
Change_factor = find(abs(AuxFind)>1e-010);
% If we deal with groups we can only estimate the new mu*
% measure since factors in the same groups can move in
% opposite direction and the definition of the standard
% Morris mu cannopt be applied.
% In the new version the elementary effect is defined with
% the absolute value.
%SAmeas(find(GroupMat(Change_factor(j,i),:)),i) = abs((Single_OutValues(j) - Single_OutValues(j+1) )/Delt); %(2/3));
SAmeas(i,Change_factor') = abs((Single_OutValues(j) - Single_OutValues(j+1) )/Delt);
else
Change_factor(j,i) = find(Single_Sample(j+1,:)-Single_Sample(j,:));
% If no groups --> we compute both the original and
% modified measure
if Delta(j) > 0 %=> +Delta
SAmeas(Change_factor(j,i),i) = (Single_OutValues(j+1) - Single_OutValues(j) )/Delt; %(2/3);
else %=> -Delta
SAmeas(Change_factor(j,i),i) = (Single_OutValues(j) - Single_OutValues(j+1) )/Delt; %(2/3);
end
end
end %for j=1:sizea
end %for i=1:r
if NumGroups ~ 0
SAmeas = SAmeas';
end
% Compute Mu AbsMu and StDev
if any(any(isnan(SAmeas)))
for j=1:NumFact,
SAm = SAmeas(j,:);
SAm = SAm(find(~isnan(SAm)));
rr=length(SAm);
AbsMu(j,1) = sum(abs(SAm),2)/rr;
if NumGroups == 0
Mu(j,1) = sum(SAm,2)/rr;
StDev(j,1) = sum((SAm - repmat(Mu(j),1,rr)).^2/(rr*(rr-1)),2).^0.5;
end
end
else
AbsMu = sum(abs(SAmeas),2)/r;
if NumGroups == 0
Mu = sum(SAmeas,2)/r;
StDev = sum((SAmeas - repmat(Mu,1,r)).^2/(r*(r-1)),2).^0.5;
end
end
% Define the output Matrix - if we have groups we cannot define the old
% measure mu, only mu* makes sense
if NumGroups > 0
OutMatrix = [OutMatrix; AbsMu];
else
OutMatrix = [OutMatrix; AbsMu, Mu, StDev];
end
end % For Each Output
|
