def quicksum(args, start=0, linear=None):
"""
A utility function to compute a sum of Pyomo expressions.
The behavior of :func:`quicksum` is similar to the builtin :func:`sum`
function, but this function generates a more compact Pyomo
expression.
Args:
args: A generator for terms in the sum.
start: A value that is initializes the sum. If
this value is not a numeric constant, then the +=
operator is used to add terms to this object.
Defaults to zero.
linear: If :attr:`start` is not a numeric constant, then this
option is ignored. Otherwise, this value indicates
whether the terms in the sum are linear. If the value
is :const:`False`, then the terms are
treated as nonlinear, and if :const:`True`, then
the terms are treated as linear. Default is
:const:`None`, which indicates that the first term
in the :attr:`args` is used to determine this value.
Returns:
The value of the sum, which may be a Pyomo expression object.
"""
#
# If we're starting with a numeric value, then
# create a new nonlinear sum expression but
# return a static version to the user.
#
if start.__class__ in native_numeric_types:
if linear is None:
#
# Get the first term, which we will test for linearity
#
try:
first = next(args, None)
except:
try:
args = args.__iter__()
first = next(args, None)
except:
raise RuntimeError("The argument to quicksum() is not iterable!")
if first is None:
return start
#
# Check if the first term is linear, and if so return the terms
#
linear, terms = decompose_term(first)
#
# Right now Pyomo5 expressions can only handle single linear
# terms.
#
# Also, we treat linear expressions as nonlinear if the constant
# term is not a native numeric type. Otherwise, large summation
# objects are created for the constant term.
#
if linear:
nvar=0
for term in terms:
c,v = term
if not v is None:
nvar += 1
elif not c.__class__ in native_numeric_types:
linear = False
if nvar > 1:
linear = False
start = start+first
if linear:
with EXPR.linear_expression() as e:
e += start
for arg in args:
e += arg
# Return the constant term if the linear expression does not contains variables
if e.is_constant():
return e.constant
return e
else:
with EXPR.nonlinear_expression() as e:
e += start
for arg in args:
e += arg
if e.nargs() == 0:
return 0
elif e.nargs() == 1:
return e.arg(0)
return e
#
# Otherwise, use the context that is provided and return it.
#
e = start
for arg in args:
e += arg
return e
def quicksum(args, start=0, linear=None):
"""
A utility function to compute a sum of Pyomo expressions.
The behavior of :func:`quicksum` is similar to the builtin :func:`sum`
function, but this function generates a more compact Pyomo
expression.
Args:
args: A generator for terms in the sum.
start: A value that is initializes the sum. If
this value is not a numeric constant, then the +=
operator is used to add terms to this object.
Defaults to zero.
linear: If :attr:`start` is not a numeric constant, then this
option is ignored. Otherwise, this value indicates
whether the terms in the sum are linear. If the value
is :const:`False`, then the terms are
treated as nonlinear, and if :const:`True`, then
the terms are treated as linear. Default is
:const:`None`, which indicates that the first term
in the :attr:`args` is used to determine this value.
Returns:
The value of the sum, which may be a Pyomo expression object.
"""
#
# If we're starting with a numeric value, then
# create a new nonlinear sum expression but
# return a static version to the user.
#
if start.__class__ in native_numeric_types:
if linear is None:
#
# Get the first term, which we will test for linearity
#
try:
first = next(args, None)
except:
try:
args = args.__iter__()
first = next(args, None)
except:
raise RuntimeError(
"The argument to quicksum() is not iterable!")
if first is None:
return start
#
# Check if the first term is linear, and if so return the terms
#
linear, terms = decompose_term(first)
#
# Right now Pyomo5 expressions can only handle single linear
# terms.
#
# Also, we treat linear expressions as nonlinear if the constant
# term is not a native numeric type. Otherwise, large summation
# objects are created for the constant term.
#
if linear:
nvar = 0
for term in terms:
c, v = term
if not v is None:
nvar += 1
elif not c.__class__ in native_numeric_types:
linear = False
if nvar > 1:
linear = False
start = start + first
if linear:
with EXPR.linear_expression() as e:
e += start
for arg in args:
e += arg
# Return the constant term if the linear expression does not contains variables
if e.is_constant():
return e.constant
return e
else:
with EXPR.nonlinear_expression() as e:
e += start
for arg in args:
e += arg
if e.nargs() == 0:
return 0
elif e.nargs() == 1:
return e.arg(0)
return e
#
# Otherwise, use the context that is provided and return it.
#
e = start
for arg in args:
e += arg
return e
def sum_product(*args, **kwds):
"""
A utility function to compute a generalized dot product.
This function accepts one or more components that provide terms
that are multiplied together. These products are added together
to form a sum.
Args:
*args: Variable length argument list of generators that
create terms in the summation.
**kwds: Arbitrary keyword arguments.
Keyword Args:
index: A set that is used to index the components used to
create the terms
denom: A component or tuple of components that are used to
create the denominator of the terms
start: The initial value used in the sum
Returns:
The value of the sum.
"""
denom = kwds.pop('denom', tuple() )
if type(denom) not in (list, tuple):
denom = [denom]
nargs = len(args)
ndenom = len(denom)
if nargs == 0 and ndenom == 0:
raise ValueError("The sum_product() command requires at least an " + \
"argument or a denominator term")
if 'index' in kwds:
index=kwds['index']
else:
if nargs > 0:
iarg=args[-1]
if not isinstance(iarg,pyomo.core.base.var.Var) and not isinstance(iarg, pyomo.core.base.expression.Expression):
raise ValueError("Error executing sum_product(): The last argument value must be a variable or expression object if no 'index' option is specified")
else:
iarg=denom[-1]
if not isinstance(iarg,pyomo.core.base.var.Var) and not isinstance(iarg, pyomo.core.base.expression.Expression):
raise ValueError("Error executing sum_product(): The last denom argument value must be a variable or expression object if no 'index' option is specified")
index = iarg.index_set()
start = kwds.get("start", 0)
vars_ = []
params_ = []
for arg in args:
if isinstance(arg, pyomo.core.base.var.Var):
vars_.append(arg)
else:
params_.append(arg)
nvars = len(vars_)
num_index = range(0,nargs)
if ndenom == 0:
#
# Sum of polynomial terms
#
if start.__class__ in native_numeric_types:
if nvars == 1:
v = vars_[0]
if len(params_) == 0:
with EXPR.linear_expression() as expr:
expr += start
for i in index:
expr += v[i]
elif len(params_) == 1:
p = params_[0]
with EXPR.linear_expression() as expr:
expr += start
for i in index:
expr += p[i]*v[i]
else:
with EXPR.linear_expression() as expr:
expr += start
for i in index:
term = 1
for j in params_:
term *= params_[j][i]
expr += term * v[i]
return expr
#
with EXPR.nonlinear_expression() as expr:
expr += start
for i in index:
term = 1
for j in num_index:
term *= args[j][i]
expr += term
return expr
#
return quicksum((prod(args[j][i] for j in num_index) for i in index), start)
elif nargs == 0:
#
# Sum of reciprocals
#
denom_index = range(0,ndenom)
return quicksum((1/prod(denom[j][i] for j in denom_index) for i in index), start)
else:
#
# Sum of fractions
#
denom_index = range(0,ndenom)
return quicksum((prod(args[j][i] for j in num_index)/prod(denom[j][i] for j in denom_index) for i in index), start)
def sum_product(*args, **kwds):
"""
A utility function to compute a generalized dot product.
This function accepts one or more components that provide terms
that are multiplied together. These products are added together
to form a sum.
Args:
*args: Variable length argument list of generators that
create terms in the summation.
**kwds: Arbitrary keyword arguments.
Keyword Args:
index: A set that is used to index the components used to
create the terms
denom: A component or tuple of components that are used to
create the denominator of the terms
start: The initial value used in the sum
Returns:
The value of the sum.
"""
denom = kwds.pop('denom', tuple())
if type(denom) not in (list, tuple):
denom = [denom]
nargs = len(args)
ndenom = len(denom)
if nargs == 0 and ndenom == 0:
raise ValueError("The sum_product() command requires at least an " + \
"argument or a denominator term")
if 'index' in kwds:
index = kwds['index']
else:
if nargs > 0:
iarg = args[-1]
if not isinstance(iarg, Var) and not isinstance(iarg, Expression):
raise ValueError(
"Error executing sum_product(): The last argument value must be a variable or expression object if no 'index' option is specified"
)
else:
iarg = denom[-1]
if not isinstance(iarg, Var) and not isinstance(iarg, Expression):
raise ValueError(
"Error executing sum_product(): The last denom argument value must be a variable or expression object if no 'index' option is specified"
)
index = iarg.index_set()
start = kwds.get("start", 0)
vars_ = []
params_ = []
for arg in args:
if isinstance(arg, Var):
vars_.append(arg)
else:
params_.append(arg)
nvars = len(vars_)
num_index = range(0, nargs)
if ndenom == 0:
#
# Sum of polynomial terms
#
if start.__class__ in native_numeric_types:
if nvars == 1:
v = vars_[0]
if len(params_) == 0:
with EXPR.linear_expression() as expr:
expr += start
for i in index:
expr += v[i]
elif len(params_) == 1:
p = params_[0]
with EXPR.linear_expression() as expr:
expr += start
for i in index:
expr += p[i] * v[i]
else:
with EXPR.linear_expression() as expr:
expr += start
for i in index:
term = 1
for j in params_:
term *= params_[j][i]
expr += term * v[i]
return expr
#
with EXPR.nonlinear_expression() as expr:
expr += start
for i in index:
term = 1
for j in num_index:
term *= args[j][i]
expr += term
return expr
#
return quicksum((prod(args[j][i] for j in num_index) for i in index),
start)
elif nargs == 0:
#
# Sum of reciprocals
#
denom_index = range(0, ndenom)
return quicksum(
(1 / prod(denom[j][i] for j in denom_index) for i in index), start)
else:
#
# Sum of fractions
#
denom_index = range(0, ndenom)
return quicksum((prod(args[j][i]
for j in num_index) / prod(denom[j][i]
for j in denom_index)
for i in index), start)