Module Utils

**Arguments**:

  - the code to be considered

  - branchSubtract: (optional) the constant that was subtracted off
    the number of neighbors before integrating it into the code.  
    This is used by the topological torsions code.
    

>>> m = Chem.MolFromSmiles('C=CC(=O)O')
>>> code = GetAtomCode(m.GetAtomWithIdx(0))
>>> ExplainAtomCode(code)
('C', 1, 1)
>>> code = GetAtomCode(m.GetAtomWithIdx(1))
>>> ExplainAtomCode(code)
('C', 2, 1)
>>> code = GetAtomCode(m.GetAtomWithIdx(2))
>>> ExplainAtomCode(code)
('C', 3, 1)
>>> code = GetAtomCode(m.GetAtomWithIdx(3))
>>> ExplainAtomCode(code)
('O', 1, 1)
>>> code = GetAtomCode(m.GetAtomWithIdx(4))
>>> ExplainAtomCode(code)
('O', 1, 0)

GetAtomPairAtomCode( (Atom)atom [, (int)branchSubtract=0]) -> int :
    Returns the atom code (hash) for an atom

    C++ signature :
        unsigned int GetAtomPairAtomCode(RDKit::Atom const* [,unsigned int=0])

Returns the number of bits in common between two vectors

**Arguments**:

  - two vectors (sequences of bit ids)

**Returns**: an integer

**Notes**

  - the vectors must be sorted

  - duplicate bit IDs are counted more than once

>>> BitsInCommon( (1,2,3,4,10), (2,4,6) )
2

Here's how duplicates are handled:
>>> BitsInCommon( (1,2,2,3,4), (2,2,4,5,6) )
3
 

Implements the DICE similarity metric.
 This is the recommended metric in both the Topological torsions
 and Atom pairs papers.

**Arguments**:

  - two vectors (sequences of bit ids)

**Returns**: a float.

**Notes**

  - the vectors must be sorted

  
>>> DiceSimilarity( (1,2,3), (1,2,3) )
1.0
>>> DiceSimilarity( (1,2,3), (5,6) )
0.0
>>> DiceSimilarity( (1,2,3,4), (1,3,5,7) )
0.5
>>> DiceSimilarity( (1,2,3,4,5,6), (1,3) )
0.5

Note that duplicate bit IDs count multiple times:
>>> DiceSimilarity( (1,1,3,4,5,6), (1,1) )
0.5

but only if they are duplicated in both vectors:
>>> DiceSimilarity( (1,1,3,4,5,6), (1,) )==2./7
True

Returns the Dot product between two vectors:

**Arguments**:

  - two vectors (sequences of bit ids)

**Returns**: an integer

**Notes**

  - the vectors must be sorted

  - duplicate bit IDs are counted more than once

>>> Dot( (1,2,3,4,10), (2,4,6) )
2

Here's how duplicates are handled:
>>> Dot( (1,2,2,3,4), (2,2,4,5,6) )
5
>>> Dot( (1,2,2,3,4), (2,4,5,6) )
2
>>> Dot( (1,2,2,3,4), (5,6) )
0
>>> Dot( (), (5,6) )
0

Implements the Cosine similarity metric.
 This is the recommended metric in the LaSSI paper

**Arguments**:

  - two vectors (sequences of bit ids)

**Returns**: a float.

**Notes**

  - the vectors must be sorted

>>> print '%.3f'%CosineSimilarity( (1,2,3,4,10), (2,4,6) )
0.516
>>> print '%.3f'%CosineSimilarity( (1,2,2,3,4), (2,2,4,5,6) )
0.714
>>> print '%.3f'%CosineSimilarity( (1,2,2,3,4), (1,2,2,3,4) )
1.000
>>> print '%.3f'%CosineSimilarity( (1,2,2,3,4), (5,6,7) )
0.000
>>> print '%.3f'%CosineSimilarity( (1,2,2,3,4), () )
0.000