r"""
Pointwise addition of dictionaries
Provides function to add dictionaries pointwise with values in a common ring and to compute linear combinations
EXAMPLES::
sage: from sage.combinat.dict_addition import dict_addition
sage: D1 = { 0:1, 1:1 }; D2 = { 0:-1, 1:1 }
sage: dict_addition( [D1,D2] )
{1: 2}
"""
from cpython cimport PyDict_Copy
cpdef dict_addition(dict_iter):
r"""
Returns the pointwise addition of dictionaries with coefficients.
:param dict_iter: iterator of dictionaries with values in a common ring.
OUTPUT:
- a dictionary containing all keys of dictionaries in ``dict_list``, with values being the sum of the values in the different dictionaries (keys with zero value are omitted)
EXAMPLES::
sage: from sage.combinat.dict_addition import dict_addition
sage: D = { 0:1, 1:1 }; D
{0: 1, 1: 1}
sage: dict_addition( D for _ in range(5) )
{0: 5, 1: 5}
sage: D1 = { 0:1, 1:1 }; D2 = { 0:-1, 1:1 }
sage: dict_addition( [D1,D2] )
{1: 2}
"""
cdef dict D, D_tmp
D = {}
for D_tmp in dict_iter:
if D == {}:
D = PyDict_Copy( D_tmp )
else:
for key in D_tmp:
value = D_tmp[key]
if key in D:
D[key] += value
else:
D[key] = value
for_removal = [key for key in D if not D[key]]
for key in for_removal:
del D[key]
return D
cpdef dict_linear_combination( dict_factor_iter, factor_on_left=True ):
r"""
Returns the pointwise addition of dictionaries with coefficients.
:param dict_factor_iter: iterator of pairs D, coeff, where
- the D's are dictionaries with values in a common ring
- the coeff's are coefficients in this ring
:param factor_on_left: if True, the coefficients are multiplied on the left, otherwise they are multiplied on the right
:type factor_on_left: boolean; optional, default ``True``
OUTPUT:
- a dictionary containing all keys of dictionaries in ``dict_list``, with values being the sum of the values in the different dictionaries, each one first multiplied by the given factor (keys with zero value are omitted)
EXAMPLES::
sage: from sage.combinat.dict_addition import dict_linear_combination
sage: D = { 0:1, 1:1 }; D
{0: 1, 1: 1}
sage: dict_linear_combination( (D,i) for i in range(5) )
{0: 10, 1: 10}
sage: dict_linear_combination( [(D,1),(D,-1)] )
{}
"""
D = {}
for D_tmp, fac_tmp in dict_factor_iter:
if D == {} and fac_tmp == 1:
D = PyDict_Copy(D_tmp)
elif fac_tmp == 1:
for key in D_tmp:
value = D_tmp[key]
if key in D:
D[ key ] += value
else:
D[ key ] = value
elif fac_tmp == -1:
for key in D_tmp:
value = D_tmp[key]
if key in D:
D[ key ] -= value
else:
D[ key ] = -value
else:
if factor_on_left:
for key in D_tmp:
value = D_tmp[key]
if key in D:
D[ key ] += fac_tmp * value
else:
D[ key ] = fac_tmp * value
else:
for key in D_tmp:
value = D_tmp[key]
if key in D:
D[ key ] += value * fac_tmp
else:
D[ key ] = value * fac_tmp
for_removal = [key for key in D if not D[key]]
for key in for_removal:
del D[key]
return D
