
    Qi                     V    d dl mZ d dlmZ d dlmZ d dlmZ d dlm	Z	m
Z
mZ d Zd ZdS )	    )Function)symbols)exp)variance_prop)RandomSymbolVariance
Covariancec                  h   t          d          \  } }}t          d          x\  }}}t          |           }t          |          }t          t          |                    }t          t          |                    }	 t          d          |           }
| |z   ||z   ||z   ||z   | |z   |z   ||z   |	z   d| z  d|z  | |z  ||dz  z  || dz  z  z   d| z  || dz  z  | |z  ||dz  z  || dz  z  z   |dz  z  t	          |           |t	          d| z            z  t	          d| z            d|z  t	          d| z            z  t	          |  |z            |dz  |z  t	          d|z  | z            z  |
t          |
          i}|                                D ]\  }}t          ||          }||k    sJ d S )	Nx y zphi tf         )consts)r   r   r   r   r   itemsr   )xyzphitr   avar_xvar_yvar_zr   casesinpoutobss                  y/var/www/development/aibuddy-work/election-extract/venv/lib/python3.11/site-packages/sympy/stats/tests/test_error_prop.pytest_variance_propr"   	   s   gGAq!g&&&FCVQAQKKE\!__%%E\!__%%EaA	Auu}	Auu}	A	55=5(	!QuW	!U1a4Z%1*$	!U1a4Z	!eAqDj5A:%q!t+Ac!A#hhAaC!E'#ac(("QBqD		1a4:c"Q$q&kk)	8A;;
E KKMM  SC///czzzzz     c                     t          d          \  } }}t          d          x\  }}}t          |           }t          |          }t          |          }t          |          }	t          |          }
t          |
          }t          ||          }t          ||
          }t          ||
          }| |z   ||	z   d|z  z   ||z   ||	z   d|z  z   | |z   |z   ||	z   |z   d|z  z   d|z  z   d|z  z   d| z  d|z  | |z  ||dz  z  |	| dz  z  z   d|z  | |z  z  z   d| z  || dz  z  t	          |           |t	          d| z            z  t	          d| z            d|z  t	          d| z            z  t	          |  |z            |dz  |z  t	          d|z  | z            z  i	}|                                D ]\  }}t          ||d          }||k    sJ  d S )	Nr   r   r   r   r   r   T)r   include_covar)r   r   r   r	   r   r   r   )r   r   r   r   r   r   r   r   br   cr   	covar_x_y	covar_x_z	covar_y_zr   r   r   r    s                      r!   test_variance_prop_with_covarr+   "   s   gGAq!g&&&FCVQAQKKEQAQKKEQAQKKE1a  I1a  I1a  I	Auu}q{*	Auu}q{*	A	55=5(Y;!"9-/0{;	!QuW	!U1a4Z%1*$q{AaC'88	!U1a4ZAc!A#hhAaC!E'#ac(("QBqD		1a4:c"Q$q&kk)
E KKMM  SCdCCCczzzzz r#   N)sympy.core.functionr   sympy.core.symbolr   &sympy.functions.elementary.exponentialr   sympy.stats.error_propr    sympy.stats.symbolic_probabilityr   r   r	   r"   r+    r#   r!   <module>r2      s    ( ( ( ( ( ( % % % % % % 6 6 6 6 6 6 0 0 0 0 0 0           2    r#   