"""
Provides function to add dictionaries pointwise with values in a common ring and to compute linear combinations
"""
def dict_addition( dict_iter ):
"""
returns the pointwise addition of dictionaries with coefficients
INPUT:
dict_iter -- iterator of dictionaries with values in a common ring R
OUTPUT:
dictionary containing all keys of dictionaries in dict_list (and non-zero values) being the the sum of the values in the different
dictionaries
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}
"""
cdef dict D, D_tmp
D = {}
for D_tmp in dict_iter:
if D == {}:
D = D_tmp.copy()
else:
for key, value in D_tmp.iteritems():
if key in D:
D[ key ] += value
else:
D[ key ] = value
for_removal = [ key for key, value in D.iteritems() if value == 0 ]
for key in for_removal:
del D[key]
return D
def dict_linear_combination( dict_factor_iter, factor_on_left=True ):
"""
returns the pointwise addition of dictionaries with coefficients
INPUT:
dict_factor_iter -- iterator of pairs D, coeff, where
the D's are dictionaries with values in a common ring R
the coeff's are coefficients in R
factor_on_left(optional) -- if True, the coefficients are multiplied on the left, otherwise they are multiplied on the right
OUTPUT:
dictionary containing all keys of dictionaries in dict_list (and non-zero values) being the the sum of the values in the different
dictionaries each one first multiplied by the given factor
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 = D_tmp.copy()
elif fac_tmp == 1:
for key, value in D_tmp.iteritems():
if key in D:
D[ key ] += value
else:
D[ key ] = value
elif fac_tmp == -1:
for key, value in D_tmp.iteritems():
if key in D:
D[ key ] -= value
else:
D[ key ] = -value
else:
if factor_on_left:
for key, value in D_tmp.iteritems():
if key in D:
D[ key ] += fac_tmp * value
else:
D[ key ] = fac_tmp * value
else:
for key, value in D_tmp.iteritems():
if key in D:
D[ key ] += value * fac_tmp
else:
D[ key ] = value * fac_tmp
for_removal = [ key for key, value in D.iteritems() if value == 0 ]
for key in for_removal:
del D[key]
return D
