src.pydasa.dimensional.buckingham#

Module for representing Dimensionless Coefficients in Dimensional Analysis for PyDASA.

This module provides the Coefficient class which models dimensionless numbers used in Vaschy-Buckingham’s Pi-theorem for dimensional analysis.

Classes:

Coefficient: Represents a dimensionless coefficient with properties, validation, and symbolic expression.

IMPORTANT: Based on the theory from:

# H.Gorter, Dimensionalanalyse: Eine Theoririe der physikalischen Dimensionen mit Anwendungen

Classes#

Coefficient

Coefficient class for Dimensional Analysis in PyDASA.

Module Contents#

class src.pydasa.dimensional.buckingham.Coefficient#

Bases: pydasa.core.basic.Foundation, pydasa.elements.specs.numerical.BoundsSpecs

Coefficient class for Dimensional Analysis in PyDASA.

A comprehensive implementation that represents dimensionless coefficients (Pi numbers) used in the Vaschy-Buckingham Pi-theorem method.

Inherits From:

Foundation: Base class providing symbol validation and framework context. BoundsSpecs: Provides numerical bounds and ranges (setpoint, min, max, mean, dev).

# From Foundation

name (str): User-friendly name of the dimensionless coefficient. description (str): Brief summary of the dimensionless coefficient. _idx (int): Index/precedence in the dimensional matrix. _sym (str): Symbol representation (LaTeX or alphanumeric). _alias (str): Python-compatible alias for use in code. _fwk (str): Frameworks context (PHYSICAL, COMPUTATION, SOFTWARE, CUSTOM).

Type:

inherited

# From BoundsSpecs

_setpoint (Optional[float]): Specific value/point of interest (always in standardized units). _min (Optional[float]): Minimum value (always in standardized units). _max (Optional[float]): Maximum value (always in standardized units). _mean (Optional[float]): Average value (always in standardized units). _dev (Optional[float]): Standard deviation (always in standardized units).

Type:

inherited

# Coefficient-Specific Attributes

_cat (str): Category (COMPUTED, DERIVED). relevance (bool): Flag indicating if coefficient is relevant for analysis. _variables (Dict[str, Variable]): Variable symbols used in coefficient construction. _dim_col (List[int]): Dimensional column for matrix operations. _pivot_lt (List[int]): Pivot indices in dimensional matrix. _pi_expr (str): Symbolic expression of the coefficient. var_dims (Dict[str, int]): Dimensional variable exponents. _step (Optional[float]): Step size for simulations (always in standardized units). _data (np.ndarray): Array of coefficient values for analysis.

_cat: str = 'COMPUTED'#

Category of the coefficient (COMPUTED, DERIVED).

_variables: Dict[str, pydasa.elements.parameter.Variable]#

Variables symbols used in the coefficient.

_dim_col: List[int] = []#

Dimensional column for matrix operations.

var_dims: Dict[str, int]#

Dimensional variable exponents in coefficient.

_pivot_lt: List[int] | None = []#

Pivot indices in dimensional matrix.

_pi_expr: str | None = None#

Symbolic expression of coefficient.

_min: float | None = None#

Standardized minimum value of the dimensionless coefficient.

_max: float | None = None#

Standardized maximum value of the dimensionless coefficient.

_mean: float | None = None#

Standardized average value of the dimensionless coefficient.

_dev: float | None = None#

Standardized standard deviation of the dimensionless coefficient.

_step: float | None = 0.001#

Step size for simulations, always in standardized units.

_data: numpy.typing.NDArray[numpy.float64]#

Data array for the dimensionless coefficient for analysis.

relevance: bool = True#

Flag indicating if coefficient is relevant for analysis.

_build_expression(var_lt, dim_col)#

_build_expression() Builds LaTeX expression for coefficient.

Parameters:

  • var_lt (List[str]) – List of variable symbols.

  • dim_col (List[int]) – List of dimensional exponents.

Raises:

ValueError – If variable list and dimensional column have different lengths.

Returns:

LaTeX expression and variable exponents.

Return type:

tuple[str, Dict[str, int]]

property cat: str#

cat Get the coefficient category.

Returns:

Category (COMPUTED, DERIVED).

Return type:

str

property variables: Dict[str, pydasa.elements.parameter.Variable]#

variables Get the variable symbols dictionary.

Returns:

Variables symbols dictionary.

Return type:

Dict[str, Variable]

property dim_col: List[int]#

dim_col Get the dimensional column.

Returns:

Dimensional column.

Return type:

List[int]

property pivot_lt: List[int] | None#

pivot_lt Get the pivot indices list.

Returns:

Pivot indices list.

Return type:

Optional[List[int]]

property pi_expr: str | None#

pi_expr Get the coefficient expression.

Returns:

Coefficient expression.

Return type:

Optional[str]

property step: float | None#

step Get standardized step size.

Returns:

Step size (always standardized).

Return type:

Optional[float]

property data: numpy.typing.NDArray[numpy.float64]#

data Get standardized data array.

Returns:

Data array for range (always standardized).

Return type:

NDArray[np.float64]

calculate_setpoint(vars=None)#

calculate_setpoint() Calculate coefficient setpoint value based on provided variable setpoints. If no variables are provided uses the ones stored in the variables standardized attribute.

Parameters:

vars (Optional[Dict[str, float]]) – Variable setpoints dictionary.

Raises:

  • ValueError – If variable setpoints are missing or invalid.

  • ValueError – If number of variable setpoints does not match coefficient variables.

Return type:

float

generate_data()#

generate_data() Generate a linear standardized data array from min, max, using step value.

Raises:

ValueError – If needed values are missing.

Return type:

None

get_data()#

get_data() Get data array from the dimensionless coefficient and its variables.

Returns:

Data dictionary with ‘symbol’: data_list entries.

Return type:

Dict[str, List]

clear()#

clear() Reset all attributes to default values.

Resets all coefficient properties to their initial state.

Return type:

None

to_dict()#

to_dict() Convert variable to dictionary representation.

Returns:

Dictionary representation of variable.

Return type:

Dict[str, Any]

classmethod from_dict(data)#

from_dict() Create variable from dictionary representation.

Parameters:

data (Dict[str, Any]) – Dictionary representation of variable.

Returns:

New variable instance.

Return type:

Variable