ENH: re-implement DataFrame.lookup.

DataFrame.lookup was deprecated in #35224 in 1.2. After some feedback (#39171 ) I opened this ticket to discuss re-implentation of lookup in a performant way. As mentioned in the discussion on 35244: "but it would have to be performant and not be yet another indexing api".

This ticket can be a starting point for proposed methods, although the old implementation was actually quite performant look at given tests in the discussion of 35244:

pandas/pandas/core/frame.py

Lines 3848 to 3861 in b5958ee

    
           if not self._is_mixed_type or n > thresh: 
        
               values = self.values 
        
               ridx = self.index.get_indexer(row_labels) 
        
               cidx = self.columns.get_indexer(col_labels) 
        
               if (ridx == -1).any(): 
        
                   raise KeyError("One or more row labels was not found") 
        
               if (cidx == -1).any(): 
        
                   raise KeyError("One or more column labels was not found") 
        
               flat_index = ridx * len(self.columns) + cidx 
        
               result = values.flat[flat_index] 
        
           else: 
        
               result = np.empty(n, dtype="O") 
        
               for i, (r, c) in enumerate(zip(row_labels, col_labels)): 
        
                   result[i] = self._get_value(r, c)

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ENH: re-implement DataFrame.lookup. #40140

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	if not self._is_mixed_type or n > thresh:
	values = self.values
	ridx = self.index.get_indexer(row_labels)
	cidx = self.columns.get_indexer(col_labels)
	if (ridx == -1).any():
	raise KeyError("One or more row labels was not found")
	if (cidx == -1).any():
	raise KeyError("One or more column labels was not found")
	flat_index = ridx * len(self.columns) + cidx
	result = values.flat[flat_index]
	else:
	result = np.empty(n, dtype="O")
	for i, (r, c) in enumerate(zip(row_labels, col_labels)):
	result[i] = self._get_value(r, c)

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ENH: re-implement DataFrame.lookup. #40140

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