Difference of two Losses
Contents
Loss functions 
and 
are defined on the Matrices of Scenarios with 
and 
scenarios. Suppose that we need to calculate Loss function 
that is defined on Matrix of Scenarios:
,
where 
, 
,
,
,
, 
, 
.
Loss function 
equals to the difference of two Loss functions: 
.
Similarly, is defined the sum of two Loss functions: 
.
Difference (sum) of two Loss functions is used to avoid generating one large matrix of scenarios (containing all possible differences (sums) of scenarios).
Example
Syntax
calculate
point: point_1
value:
avg(L(matrix_I)-L(matrix_II))
avg(L(matrix_III))
Description
avg is Average Loss function,
matrix_I:
x1 |
x2 |
x3 |
x4 |
scenario_benchmark |
scenario_probability |
1 7 |
4 -5 |
8 4 |
3 -6 |
-2 11 |
0.4 0.6 |
The matrix_I is in file matrix_I.txt in Matrix of Scenarios format (see, PSG Matrix in General (Text) Format).
matrix_II:
x1 |
x2 |
3 -2 |
2 -6 |
The matrix_II is in file matrix_II.txt in Matrix of Scenarios format (see, PSG Matrix in General (Text) Format).
matrix_III:
x1 |
x2 |
-2 4 3 9 |
2 -7 10 1 |
The matrix_III is in file matrix_III.txt in Matrix of Scenarios format (see, PSG Matrix in General (Text) Format).
avg function is calculated at point_1:
component_name |
value |
x1 x2 |
1 1 |
Value of avg(L(matrix_I)-L(matrix_II)) at point_1 equals -5.
Value of avg(L(matrix_III)) at point_1 equals -5.
Files problem_diff_of_two_Losses.txt, matrix_I.txt, matrix_II.txt, matrix_III.txt, and point_1.txt are in folder .\Aorda\PSG\Examples\Functions\diff_of_two_losses_test.