
    sg                     T    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y)	    )Function)symbols)exp)variance_prop)RandomSymbolVariance
Covariancec                     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}|j                         D ]  \  }}t        ||      }||k(  rJ  y )	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                  T/var/www/html/venv/lib/python3.12/site-packages/sympy/stats/tests/test_error_prop.pytest_variance_propr"   	   s   gGAq!g&&FCVQAQKE\!_%E\!_%EaA	Auu}	Auu}	A	55=5(	!QuW	!U1a4Z%1*$	!U1a4Z	!eAqDj5A:%q!t+Ac!A#hAaC!E'#ac("QBqD	1a4:c"Q$q&k)	8A;
E KKM SC/czz    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	}|j                         D ]  \  }}t        ||d      }||k(  rJ  y )	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QKEQAQKEQAQKE1a I1a I1a I	Auu}q{*	Auu}q{*	A	55=5(Y;!"9-/0{;	!QuW	!U1a4Z%1*$q{AaC'88	!U1a4ZAc!A#hAaC!E'#ac("QBqD	1a4:c"Q$q&k)
E KKM SCdCczz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 0 2r#   