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implementation: started writing impl; finished technology section
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2025-04-20 12:18:40 +02:00
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thesis/chapters/conceptdesign.tex
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@ -1,5 +1,3 @@
RE-READ to ensure that concepts why this is done to improve performance and why this should be the "locally best" implementation (most should be in implementation though)
\chapter{Concept and Design}
\label{cha:conceptdesign}
% introduction to what needs to be done. also clarify terms "Host" and "Device" here
@ -29,7 +27,9 @@ The main goal of both prototypes or evaluators is to provide a speed-up compared
With this, the required capabilities are outlined. However, for a better understanding, the input and output data need to be explained further. The first input contains the expressions that need to be evaluated. These can be of any length and can contain constant values, variables and parameters, all of which are linked together with the supported operations. In the simplified example shown in Figure \ref{fig:input_output_explanation}, there are six expressions $e_1$ to $e_6$.
Next is the variable matrix. An entry in this matrix corresponds to one variable in every expression. The row indicates which variable it holds the value for. For example the values in row three, are used to parameterise the variable $x_3$. Each column holds a different set of variables. Each expression must be evaluated using each set of variable. In the provided example, there are three variable sets, each containing the values for four variables $x_1$ to $x_4$. After all expressions have been evaluated using all variable sets, the results of these evaluations must be stored in the result matrix. Each entry in this matrix holds the result of the evaluation of one expression parameterised with one variable set. The row indicates the variable set and the column indicates the expression.
Next is the variable matrix. An entry in this matrix corresponds to one variable in every expression. The row indicates which variable it holds the value for. For example the values in row three, are used to parameterise the variable $x_3$. Each column holds a different set of variables. Each expression must be evaluated using each set of variables. In the provided example, there are three variable sets, each containing the values for four variables $x_1$ to $x_4$.
After all expressions have been evaluated using all variable sets, the results of these evaluations must be stored in the result matrix. Each entry in this matrix holds the result of the evaluation of one expression parameterised with one variable set. The row indicates the variable set and the column indicates the expression.
The prototypes developed in this thesis, are part of a GP algorithm for symbolic regression. This means that the expressions that are evaluated, represent parts of the search space of all expressions being made up of any combination of allowed operators, the set of input variables, a set of parameters and constants. This means that the size of the search space grows exponentially. Exploring this search space by simply generating expressions, evaluating them once and then generating the next set of expressions leaves much of the search space unexplored. To combat this, parameters are introduced. These allow the algorithm to perform some kind of local search. To enable this, the prototypes must support not only variables, but also parameters.