Base

base

Abstract Base Class for classical Design of Experiments (DoE) matrices.

This module defines DesignMatrix, the abstract foundation for all classical DoE modeling schemes. It enforces standard construction patterns for factors, levels, and generation, supporting both screen designs (fractional, screening, Plackett-Burman) and response surface methods.

CLASS	DESCRIPTION
DesignMatrix	Abstract base class representing a Design Matrix in Classical Design of Experiments (DoE).

DesignMatrix

DesignMatrix(factors: Dict[str, List[float]])

Bases: ABC

Abstract base class representing a Design Matrix in Classical Design of Experiments (DoE).

A Design Matrix is a structured layout of factor combinations designed to evaluate treatment effects, screening active factors, or modeling multi-factor non-linear responses with the minimal possible experiment run footprint.

Mathematical Context

Let \(k\) be the number of independent factors (variables). A design matrix \(X\) is an \(N \times k\) matrix where each row represents a specific experiment run (a combination of factor levels) and each column represents a factor. In standardized designs, factor levels are typically mapped to coded values: - Continuous factors: mapped to \([-1, 0, +1]\) representing low, medium, and high levels. - Categorical factors: mapped to discrete integer indices.

The primary goal of classical DoE is to construct \(X\) such that the parameter estimation variance of the linear model: $$ Y = X\beta + \varepsilon $$ is minimized, which is equivalent to maximizing the information matrix \(X^T X\).

ATTRIBUTE	DESCRIPTION
factors	A dictionary mapping factor names (str) to their list of possible levels (floats/integers). For example: {"temperature": [100.0, 150.0], "pressure": [1.0, 2.0]}. TYPE: Dict[str, List[float]]

PARAMETER	DESCRIPTION
factors	Mapping of factor labels to their designated levels. TYPE: Dict[str, List[float]]

METHOD	DESCRIPTION
generate	Generates and returns the specific classical DoE design matrix.

Source code in src\xpyrment\design\doe\base.py

def __init__(self, factors: Dict[str, List[float]]):
    """Initializes a new DesignMatrix.

    Args:
        factors (Dict[str, List[float]]): Mapping of factor labels to their designated levels.
    """
    self.factors = factors

generate abstractmethod

generate() -> DataFrame

Generates and returns the specific classical DoE design matrix.

RETURNS	DESCRIPTION
DataFrame	pd.DataFrame: A pandas DataFrame containing the design matrix, where columns represent factors and rows represent specific experimental runs.

Source code in src\xpyrment\design\doe\base.py

@abstractmethod
def generate(self) -> pd.DataFrame:
    """Generates and returns the specific classical DoE design matrix.

    Returns:
        pd.DataFrame: A pandas DataFrame containing the design matrix, where columns represent
            factors and rows represent specific experimental runs.
    """
    pass