Dimensional Framework#

Overview#

Dimensional Analysis relies on Fundamental Dimensional Units (FDUs) as the building blocks for describing physical or any domain-specific (e.g.: software architecture) quantities. The Framework (or Schema) class defines which FDUs are used, their precedence in the dimensional matrix, and the validation patterns for dimensional expressions in instances of the Variable class. PyDASA implements this through two core classes: Dimension for individual FDUs and Schema for managing the domain-specific FDU set.

Fundamental Dimensional Units (FDUs)#

FDUs are the fundamental measurable quantities from which all metrics derive. Physical dimensional analysis uses seven FDUs: Length [L], Mass [M], Time [T], Electric Current [A], Temperature [K], Amount of Substance [mol], and Luminous Intensity [cd], though most applications primarily use L, M, and T. These principles can theoretically extend to other dimensional domains (e.g., computational, software).

The Dimension class in fundamental.py represents a single FDU with:

  1. Symbol (_sym): Represents LaTeX or alphanumeric notation (e.g., “M”, “L”, “T”).

  2. Index (_idx): Determines precedence in the dimensional matrix (defines row order).

  3. Unit (_unit): Specifies basic measurement unit (e.g., “m”, “s”, “kg”).

  4. Framework (_fwk): Identifies context (PHYSICAL, COMPUTATION, SOFTWARE, CUSTOM).

  5. Alias (_alias): Provides Python-compatible name for code execution.

Schema Responsibilities#

The Schema class in vaschy.py manages the dimensional framework by:

  1. Maintaining FDU Collections by storing FDUs in precedence order (_fdu_lt) and providing symbol-to-object mapping (_fdu_map).

  2. Establishing Matrix Structure by defining row order in the dimensional matrix through FDU precedence.

  3. Validating Expressions by generating regex patterns for matching and validating dimensional expressions.

  4. Enforcing Consistency by ensuring all FDUs within a framework follow Görtler’s principles of Measurability, Consistency, and Clarity.

Supported Frameworks#

PyDASA provides three predefined frameworks:

  1. PHYSICAL Framework: Provides standard physical quantities using L, M, T, A, K, mol, cd as default for engineering and scientific applications.

  2. COMPUTATION Framework: Defines computational quantities for performance analysis, including Time (T), Data (D), and Operations (O).

  3. SOFTWARE Framework: Supports software-specific dimensions for architectural analysis (experimental).

  4. CUSTOM Framework: Allows user-defined FDUs for domain-specific applications requiring explicit FDU definitions.

Creating Custom Frameworks#

To create a custom framework, define FDUs and pass them to the Schema:

from pydasa.dimensional.fundamental import Dimension
from pydasa.dimensional.vaschy import Schema

# Define custom FDUs
custom_fdus = [
    {"_idx": 0, "_sym": "T", "_unit": "s", "_name": "Time"},
    {"_idx": 1, "_sym": "D", "_unit": "bit", "_name": "Data"},
    {"_idx": 2, "_sym": "O", "_unit": "op", "_name": "Operations"}
]

# Create schema with custom FDUs
schema = Schema(_fwk="CUSTOM", _fdu_lt=custom_fdus)

# OR use Dimension class to create the FDUs
custom_fdus = [
    Dimension(_idx=0, _sym="T", _unit="s", _name="Time"),
    Dimension(_idx=1, _sym="D", _unit="bit", _name="Data"),
    Dimension(_idx=2, _sym="O", _unit="op", _name="Operations")
]

schema = Schema(_fwk="CUSTOM", _fdu_lt=custom_fdus)

The Schema automatically constructs the dimensional matrix (row order determined by FDU item index), validates expressions, and ensures consistency across all dimensional operations. Furthermore, Custom frameworks must maintain dimensional homogeneity and adhere to the defined FDU precedence.