
    -g                     *    d Z ddlZd Zd Zd Zd ZdS )z3
Created on Tue Oct 29 18:37:03 2024

@author: sam
    Nc                 p    d}t          t          |                     D ]}|| |         ||         z  z  }|S )Nr   )rangelen)v1v2dpis       N/Users/sam/Downloads/uts/35006_Numerical_Methods/Final_Project/FinalProject.pydot_productr      s?    	
B3r77^^  
beBqEkI    c                     t          j        | d         |d         z  | d         |d         z  z
  | d         |d         z  | d         |d         z  z
  | d         |d         z  | d         |d         z  z
  g          S )N      r   )nparray)r   r   s     r
   cross_productr      sw    8RU2a5[Ar!u,RU2a5[Ar!u-DRU2a5[QSTUQVWYZ[W\Q\E\]^^^r   c                     d} | ||z   |           | ||z
  |          z
  d|z  z  } | |||z              | |||z
            z
  d|z  z  }||fS )Ng&.>r    )fuvhr_ur_vs         r
   partial_derivativer      sn    A1QqS88aa!Ahh1
%C1Qqs88aa!A#hh1
%Cs7Nr   c                    d}|d         |d         z
  |z  }|d         |d         z
  |z  }d}t          |          D ]}t          |          D ]}	|d         |dz   |z  z   }
|d         |	dz   |z  z   } ||
|          }t          ||
|          \  }}||z  }t          |t          j                  r | |d         |d         |d                   }t          |t          j                  rB|t          j                            t          |t          ||                              |z  z  }||t          j                            t          ||                    z  |z  z  } | |
||          }t          |t          j                  rt          j	        | | dg          }|t          j                            |          z  }|t          j                            t          ||                    t          j                            |          z  |z  z  }||t          j
        d|dz  z   |dz  z             z  |z  z  }|S )Nd   r   r   g      ?r   )r   r   
isinstancer   ndarraylinalgnormr   r   r   sqrt)functionsurfaceu_rangev_rangenum_divisionsdudvintegralr	   jr   r   rr   r   dSFnnhats                      r
   r*   r*      so    M !*wqz
!=	0B
!*wqz
!=	0B H =!! AF AF }%% >	F >	FA 
a#g^+A
a#g^+A !A )155GC bB !BJ'' -F HQqT!A$qt,, a
++ P 	{1]3s=S=S/T/T U UXZ ZZHH BINN=S3I3I$J$J JR OOHH HQqOO a
++ F 3$tA//A RY^^A...D 	{1T/B/B C CbinnUVFWFW WZ\ \\HH BGAQJa,?$@$@ @2 EEHH}>	FB Or   )__doc__numpyr   r   r   r   r*   r   r   r
   <module>r3      sk          _ _ _  U U U U Ur   