copul.wrapper package

Submodules

copul.wrapper.cd1_wrapper module

class copul.wrapper.cd1_wrapper.CD1Wrapper(sympy_func: SymPyFuncWrapper | Expr | float | int)[source]

Bases: SymPyFuncWrapper

Wrapper for ∂C/∂u (first coordinate). Bivariate boundaries:

  • CD1(u, 0) = 0

  • CD1(u, 1) = 1

These boundary rules must hold even after partial substitution of u, i.e., when only v (or u2) remains free.

copul.wrapper.cd2_wrapper module

class copul.wrapper.cd2_wrapper.CD2Wrapper(sympy_func: SymPyFuncWrapper | Expr | float | int)[source]

Bases: SymPyFuncWrapper

Wrapper for ∂C/∂v (second coordinate). Bivariate boundaries:

  • CD2(0, v) = 0

  • CD2(1, v) = 1

These boundary rules must hold even after partial substitution of v (i.e., when only u / u1 remains free).

copul.wrapper.cdf_wrapper module

class copul.wrapper.cdf_wrapper.CDFWrapper(sympy_func: SymPyFuncWrapper | Expr | float | int)[source]

Bases: SymPyFuncWrapper

Wrapper for copula cumulative distribution functions.

Boundary handling (dimension-agnostic):

  • C(…, 0, …) = 0 if any coordinate is 0

  • C(1, …, 1) = 1 if all coordinates are 1 (for those present)

Bivariate margins (u,v) or (u1,u2):

  • C(1, v) = v

  • C(u, 1) = u

copul.wrapper.cdi_wrapper module

class copul.wrapper.cdi_wrapper.CDiWrapper(func, i)[source]

Bases: ConditionalWrapper

General wrapper for the conditional distribution when conditioning on the i-th variable. Handles multivariate case (u1, u2, …, un).

Boundary conditions: - If ui = 0, returns 0 - If ui = 1, returns 1 (representing the unconditional distribution of the remaining variables) - If any other variable is 0 or 1, handles according to conditional distribution rules

copul.wrapper.conditional_wrapper module

class copul.wrapper.conditional_wrapper.ConditionalWrapper(func, condition_index=None)[source]

Bases: SymPyFuncWrapper

Base class for conditional distribution wrappers. Handles multivariate cases with symbols u1, u2, …, un.

copul.wrapper.inv_gen_wrapper module

class copul.wrapper.inv_gen_wrapper.InvGenWrapper(expr, y_symbol, copula_instance)[source]

Bases: SymPyFuncWrapper

numpy_func()[source]

Create a vectorized numpy function that can be called with array inputs.

When called without arguments, returns a callable function that can evaluate the expression with numpy arrays. When called with arguments, evaluates the expression directly with those arguments.

Parameters:

*args (array_like, optional) – If provided, input arrays corresponding to the symbols in the expression.

Returns:

If args are provided, returns the result of evaluating the expression. If no args are provided, returns a function that can be called later.

Return type:

callable or numpy.ndarray

Examples

>>> import sympy
>>> from copul.wrapper.sympy_wrapper import SymPyFuncWrapper
>>> x, y = sympy.symbols('x y')
>>> expr = SymPyFuncWrapper(x**2 + y)
>>> import numpy as np
>>>
>>> # Get a function and call it later
>>> f = expr.numpy_func()
>>> f(np.array([1, 2]), np.array([3, 4]))
array([4, 8])
>>>
>>> # Or evaluate directly
>>> expr.numpy_func(np.array([1, 2]), np.array([3, 4]))
array([4, 8])
subs(*args, **kwargs)[source]

Substitute values in the expression.

This method directly uses SymPy’s subs method.

Returns:

A new SymPyFuncWrapper with the substitutions applied.

copul.wrapper.pickands_wrapper module

class copul.wrapper.pickands_wrapper.PickandsWrapper(expr, t_symbol, delta_val=None)[source]

Bases: object

evalf()[source]
subs(*args, **kwargs)[source]

copul.wrapper.sympy_wrapper module

class copul.wrapper.sympy_wrapper.SymPyFuncWrapper(sympy_func: SymPyFuncWrapper | Expr | float | int)[source]

Bases: object

A wrapper class for SymPy expressions that provides additional functionality and a more intuitive interface for working with symbolic mathematics.

This class allows for easier function substitution, differentiation, and arithmetic operations with proper type handling.

diff(*args, **kwargs) → SymPyFuncWrapper[source]

Differentiate the expression.

This method directly uses SymPy’s diff method.

Returns:

A new SymPyFuncWrapper with the differentiated expression.

evalf(n: int | None = None) → float | Expr | SymPyFuncWrapper[source]

Evaluate the expression numerically.

Parameters:

n – Optional number of significant digits.

Returns:

  • For numeric expressions, returns a float

  • For expressions with symbols, returns the evalf’d SymPy expression

Return type:

For backward compatibility

expand() → SymPyFuncWrapper[source]

Expand the expression.

Returns:

A new SymPyFuncWrapper with the expanded expression.

factor() → SymPyFuncWrapper[source]

Factor the expression.

Returns:

A new SymPyFuncWrapper with the factored expression.

property free_symbols: Set[Symbol]

Return the set of free symbols in the expression.

property func: Expr

Return the underlying SymPy expression.

has(*args, **kwargs) → bool[source]

Check if the expression has a certain property.

This method directly uses SymPy’s has method.

Returns:

True if the expression has the specified property, False otherwise.

integrate(*args, **kwargs) → SymPyFuncWrapper[source]

Integrate the expression.

This method directly uses SymPy’s integrate method.

Returns:

A new SymPyFuncWrapper with the integrated expression.

isclose(other, tolerance: float = 1e-10) → bool[source]

Check if this expression is numerically close to another expression or value.

Parameters:

  • other – Another SymPyFuncWrapper, SymPy expression, or numeric value.

  • tolerance – Maximum absolute difference allowed for equality (default: 1e-10).

Returns:

True if expressions are numerically close, False otherwise.

numpy() → ndarray[source]

Convert the expression to a numpy function.

Returns:

A numpy function that evaluates the expression with numpy inputs.

Raises:

ValueError – If the expression cannot be converted to a numpy function.

numpy_func(*args)[source]

Create a vectorized numpy function that can be called with array inputs.

When called without arguments, returns a callable function that can evaluate the expression with numpy arrays. When called with arguments, evaluates the expression directly with those arguments.

Parameters:

*args (array_like, optional) – If provided, input arrays corresponding to the symbols in the expression.

Returns:

If args are provided, returns the result of evaluating the expression. If no args are provided, returns a function that can be called later.

Return type:

callable or numpy.ndarray

Examples

>>> import sympy
>>> from copul.wrapper.sympy_wrapper import SymPyFuncWrapper
>>> x, y = sympy.symbols('x y')
>>> expr = SymPyFuncWrapper(x**2 + y)
>>> import numpy as np
>>>
>>> # Get a function and call it later
>>> f = expr.numpy_func()
>>> f(np.array([1, 2]), np.array([3, 4]))
array([4, 8])
>>>
>>> # Or evaluate directly
>>> expr.numpy_func(np.array([1, 2]), np.array([3, 4]))
array([4, 8])
simplify() → SymPyFuncWrapper[source]

Simplify the expression.

Returns:

A new SymPyFuncWrapper with the simplified expression.

subs(*args, **kwargs) → SymPyFuncWrapper[source]

Substitute values in the expression.

This method directly uses SymPy’s subs method.

Returns:

A new SymPyFuncWrapper with the substitutions applied.

to_latex() → str[source]

Convert the expression to LaTeX.

Returns:

A LaTeX string representation of the expression.

Module contents