def reduce_vartype(self, var_type):
"""Reduce expression with given var_type. It returns a tuple
(found, remain), where 'found' is an expression that only has variables
of type == var_type. If no variables are found, found=(). The 'remain'
part contains the leftover after division by 'found' such that:
self = found*remain."""
# Sort variables according to type.
found = []
remains = []
for v in self.vrs:
if v.t == var_type:
found.append(v)
continue
remains.append(v)
# Create appropriate object for found.
if len(found) > 1:
found = create_product(found)
elif found:
found = found.pop()
# We did not find any variables.
else:
return [((), self)]
# Create appropriate object for remains.
if len(remains) > 1:
remains = create_product(remains)
elif remains:
remains = remains.pop()
# We don't have anything left.
else:
return [(self, create_float(1))]
# Return whatever we found.
return [(found, remains)]
def __sub__(self, other):
"Subtract other objects."
# Return a new sum
if other._prec == 4 and self.denom == other.denom: # frac
num = create_sum([self.num, create_product([FloatValue(-1), other.num])]).expand()
return create_fraction(num, self.denom)
return create_sum([self, create_product([FloatValue(-1), other])])
def reduce_vartype(self, var_type):
"""Reduce expression with given var_type. It returns a tuple
(found, remain), where 'found' is an expression that only has variables
of type == var_type. If no variables are found, found=(). The 'remain'
part contains the leftover after division by 'found' such that:
self = found*remain."""
# Sort variables according to type.
found = []
remains = []
for v in self.vrs:
if v.t == var_type:
found.append(v)
continue
remains.append(v)
# Create appropriate object for found.
if len(found) > 1:
found = create_product(found)
elif found:
found = found.pop()
# We did not find any variables.
else:
return [((), self)]
# Create appropriate object for remains.
if len(remains) > 1:
remains = create_product(remains)
elif remains:
remains = remains.pop()
# We don't have anything left.
else:
return [(self, create_float(1))]
# Return whatever we found.
return [(found, remains)]
def __sub__(self, other):
"Subtract other objects."
# Return a new sum
if other._prec == 4 and self.denom == other.denom: # frac
num = create_sum(
[self.num,
create_product([FloatValue(-1), other.num])]).expand()
return create_fraction(num, self.denom)
return create_sum([self, create_product([FloatValue(-1), other])])
def __sub__(self, other):
"Subtract other objects."
# NOTE: We expect expanded objects
# symbols, if other is a product, try to let product handle the addition.
if self._repr == other._repr:
return create_float(0)
elif other._prec == 2: # prod
if other.get_vrs() == (self,):
return create_product([create_float(1.0 - other.val), self]).expand()
return create_sum([self, create_product([create_float(-1), other])])
def __sub__(self, other):
"Subtract other objects."
# NOTE: We expect expanded objects here.
if other._prec == 0: # float
return create_float(self.val-other.val)
# Multiply other by -1
elif self.val == 0.0:
return create_product([create_float(-1), other])
# Return a new sum where other is multiplied by -1
return create_sum([self, create_product([create_float(-1), other])])
def __sub__(self, other):
"Subtract other objects."
# NOTE: We expect expanded objects here.
if other._prec == 0: # float
return create_float(self.val - other.val)
# Multiply other by -1
elif self.val == 0.0:
return create_product([create_float(-1), other])
# Return a new sum where other is multiplied by -1
return create_sum([self, create_product([create_float(-1), other])])
def __sub__(self, other):
"Subtract other objects."
# NOTE: We expect expanded objects
# symbols, if other is a product, try to let product handle the addition.
if self._repr == other._repr:
return create_float(0)
elif other._prec == 2: # prod
if other.get_vrs() == (self, ):
return create_product([create_float(1.0 - other.val),
self]).expand()
return create_sum([self, create_product([create_float(-1), other])])
def __sub__(self, other):
"Subtract other objects."
if other._prec == 2 and self.get_vrs() == other.get_vrs():
# Return expanded product, to get rid of 3*x + -2*x -> x, not 1*x.
return create_product([create_float(self.val - other.val)] + list(self.get_vrs())).expand()
# if self == 2*x and other == x return 3*x.
elif other._prec == 1: # sym
if self.get_vrs() == (other,):
# Return expanded product, to get rid of -x + x -> 0, not product(0).
return create_product([create_float(self.val - 1.0), other]).expand()
# Return sum
return create_sum([self, create_product([FloatValue(-1), other])])
def __mul__(self, other):
"Multiplication by other objects."
# NOTE: assuming that we get expanded variables.
# If product will be zero.
if self.val == 0.0 or other.val == 0.0:
return create_float(0)
# Create new expanded numerator and denominator and use '/' to reduce.
if other._prec != 4: # frac
return (self.num*other)/self.denom
# If we have a fraction, create new numerator and denominator and use
# '/' to reduce expression.
return create_product([self.num, other.num]).expand()/create_product([self.denom, other.denom]).expand()
def __mul__(self, other):
"Multiplication by other objects."
# NOTE: assuming that we get expanded variables.
# If product will be zero.
if self.val == 0.0 or other.val == 0.0:
return create_float(0)
# Create new expanded numerator and denominator and use '/' to reduce.
if other._prec != 4: # frac
return (self.num * other) / self.denom
# If we have a fraction, create new numerator and denominator and use
# '/' to reduce expression.
return create_product([self.num, other.num]).expand() / create_product(
[self.denom, other.denom]).expand()
def __sub__(self, other):
"Subtract other objects."
if other._prec == 2 and self.get_vrs() == other.get_vrs():
# Return expanded product, to get rid of 3*x + -2*x -> x, not 1*x.
return create_product([create_float(self.val - other.val)] +
list(self.get_vrs())).expand()
# if self == 2*x and other == x return 3*x.
elif other._prec == 1: # sym
if self.get_vrs() == (other, ):
# Return expanded product, to get rid of -x + x -> 0, not product(0).
return create_product([create_float(self.val - 1.0),
other]).expand()
# Return sum
return create_sum([self, create_product([FloatValue(-1), other])])
def __add__(self, other):
"Addition by other objects."
# NOTE: Assuming expanded variables.
# If two products are equal, add their float values.
if other._prec == 2 and self.get_vrs() == other.get_vrs():
# Return expanded product, to get rid of 3*x + -2*x -> x, not 1*x.
return create_product([create_float(self.val + other.val)] + list(self.get_vrs())).expand()
# if self == 2*x and other == x return 3*x.
elif other._prec == 1: # sym
if self.get_vrs() == (other,):
# Return expanded product, to get rid of -x + x -> 0, not product(0).
return create_product([create_float(self.val + 1.0), other]).expand()
# Return sum
return create_sum([self, other])
def __add__(self, other):
"Addition by other objects."
# NOTE: Assuming expanded variables.
# If two products are equal, add their float values.
if other._prec == 2 and self.get_vrs() == other.get_vrs():
# Return expanded product, to get rid of 3*x + -2*x -> x, not 1*x.
return create_product([create_float(self.val + other.val)] +
list(self.get_vrs())).expand()
# if self == 2*x and other == x return 3*x.
elif other._prec == 1: # sym
if self.get_vrs() == (other, ):
# Return expanded product, to get rid of -x + x -> 0, not product(0).
return create_product([create_float(self.val + 1.0),
other]).expand()
# Return sum
return create_sum([self, other])
def __mul__(self, other):
"Multiplication by other objects."
# If product will be zero.
if self.val == 0.0 or other.val == 0.0:
return create_float(0)
# If other is a Sum or Fraction let them handle it.
if other._prec in (3, 4): # sum or frac
return other.__mul__(self)
# NOTE: We expect expanded sub-expressions with no nested operators.
# Create new product adding float or symbol.
if other._prec in (0, 1): # float or sym
return create_product(self.vrs + [other])
# Create new product adding all variables from other Product.
return create_product(self.vrs + other.vrs)
def __mul__(self, other):
"Multiplication by other objects."
# If product will be zero.
if self.val == 0.0 or other.val == 0.0:
return create_float(0)
# If other is a Sum or Fraction let them handle it.
if other._prec in (3, 4): # sum or frac
return other.__mul__(self)
# NOTE: We expect expanded sub-expressions with no nested operators.
# Create new product adding float or symbol.
if other._prec in (0, 1): # float or sym
return create_product(self.vrs + [other])
# Create new product adding all variables from other Product.
return create_product(self.vrs + other.vrs)
def __mul__(self, other):
"Multiplication by other objects."
# NOTE: We assume expanded objects.
# If product will be zero.
if self.val == 0.0 or other.val == 0.0:
return create_float(0)
# If other is Sum or Fraction let them handle the multiply.
if other._prec in (3, 4): # sum or frac
return other.__mul__(self)
# If other is a float or symbol, create simple product.
if other._prec in (0, 1): # float or sym
return create_product([self, other])
# Else add variables from product.
return create_product([self] + other.vrs)
def __mul__(self, other):
"Multiplication by other objects."
# NOTE: We assume expanded objects.
# If product will be zero.
if self.val == 0.0 or other.val == 0.0:
return create_float(0)
# If other is Sum or Fraction let them handle the multiply.
if other._prec in (3, 4): # sum or frac
return other.__mul__(self)
# If other is a float or symbol, create simple product.
if other._prec in (0, 1): # float or sym
return create_product([self, other])
# Else add variables from product.
return create_product([self] + other.vrs)
def __add__(self, other):
"Addition by other objects."
# NOTE: We expect expanded objects
# symbols, if other is a product, try to let product handle the addition.
# Returns x + x -> 2*x, x + 2*x -> 3*x.
if self._repr == other._repr:
return create_product([create_float(2), self])
elif other._prec == 2: # prod
return other.__add__(self)
return create_sum([self, other])
def __add__(self, other):
"Addition by other objects."
# NOTE: We expect expanded objects
# symbols, if other is a product, try to let product handle the addition.
# Returns x + x -> 2*x, x + 2*x -> 3*x.
if self._repr == other._repr:
return create_product([create_float(2), self])
elif other._prec == 2: # prod
return other.__add__(self)
return create_sum([self, other])
def __div__(self, other):
"Division by other objects."
# If division is illegal (this should definitely not happen).
if other.val == 0.0:
error("Division by zero")
# TODO: Should we also support division by fraction for generality?
# It should not be needed by this module.
if other._prec == 4: # frac
error("Did not expected to divide by fraction")
# If fraction will be zero.
if self.val == 0.0:
return self
# NOTE: We expect expanded objects here i.e., Product([FloatValue])
# should not be present.
# Handle types appropriately.
if other._prec == 0: # float
return create_float(self.val / other.val)
# If other is a symbol, return a simple fraction.
elif other._prec == 1: # sym
return create_fraction(self, other)
# Don't handle division by sum.
elif other._prec == 3: # sum
# TODO: Here we could do: 4 / (2*x + 4*y) -> 2/(x + 2*y).
return create_fraction(self, other)
# If other is a product, remove any float value to avoid
# 4 / (2*x), this will return 2/x.
val = 1.0
for v in other.vrs:
if v._prec == 0: # float
val *= v.val
# If we had any floats, create new numerator and only use 'real' variables
# from the product in the denominator.
if val != 1.0:
# Check if we need to create a new denominator.
# TODO: Just use other.vrs[1:] instead.
if len(other.get_vrs()) > 1:
return create_fraction(create_float(self.val / val),
create_product(other.get_vrs()))
# TODO: Because we expect all products to be expanded we shouldn't need
# to check for this case, just use other.vrs[1].
elif len(other.get_vrs()) == 1:
return create_fraction(create_float(self.val / val),
other.vrs[1])
error("No variables left in denominator")
# Nothing left to do.
return create_fraction(self, other)
def __div__(self, other):
"Division by other objects."
# If division is illegal (this should definitely not happen).
if other.val == 0.0:
error("Division by zero")
# TODO: Should we also support division by fraction for generality?
# It should not be needed by this module.
if other._prec == 4: # frac
error("Did not expected to divide by fraction")
# If fraction will be zero.
if self.val == 0.0:
return self
# NOTE: We expect expanded objects here i.e., Product([FloatValue])
# should not be present.
# Handle types appropriately.
if other._prec == 0: # float
return create_float(self.val/other.val)
# If other is a symbol, return a simple fraction.
elif other._prec == 1: # sym
return create_fraction(self, other)
# Don't handle division by sum.
elif other._prec == 3: # sum
# TODO: Here we could do: 4 / (2*x + 4*y) -> 2/(x + 2*y).
return create_fraction(self, other)
# If other is a product, remove any float value to avoid
# 4 / (2*x), this will return 2/x.
val = 1.0
for v in other.vrs:
if v._prec == 0: # float
val *= v.val
# If we had any floats, create new numerator and only use 'real' variables
# from the product in the denominator.
if val != 1.0:
# Check if we need to create a new denominator.
# TODO: Just use other.vrs[1:] instead.
if len(other.get_vrs()) > 1:
return create_fraction(create_float(self.val/val), create_product(other.get_vrs()))
# TODO: Because we expect all products to be expanded we shouldn't need
# to check for this case, just use other.vrs[1].
elif len(other.get_vrs()) == 1:
return create_fraction(create_float(self.val/val), other.vrs[1])
error("No variables left in denominator")
# Nothing left to do.
return create_fraction(self, other)
def expand(self):
"Expand the fraction expression."
# If fraction is already expanded, simply return the expansion.
if self._expanded:
return self._expanded
# If we don't have a denominator just return expansion of numerator.
if not self.denom:
return self.num.expand()
# Expand numerator and denominator.
num = self.num.expand()
denom = self.denom.expand()
# TODO: Is it too expensive to call expand in the below?
# If both the numerator and denominator are fractions, create new
# numerator and denominator and use division to possibly reduce the
# expression.
if num._prec == 4 and denom._prec == 4: # frac
new_num = create_product([num.num, denom.denom]).expand()
new_denom = create_product([num.denom, denom.num]).expand()
self._expanded = new_num / new_denom
# If the numerator is a fraction, multiply denominators and use
# division to reduce expression.
elif num._prec == 4: # frac
new_denom = create_product([num.denom, denom]).expand()
self._expanded = num.num / new_denom
# If the denominator is a fraction multiply by the inverse and
# use division to reduce expression.
elif denom._prec == 4: # frac
new_num = create_product([num, denom.denom]).expand()
self._expanded = new_num / denom.num
# Use division to reduce the expression, no need to call expand().
else:
self._expanded = num / denom
return self._expanded
def expand(self):
"Expand the fraction expression."
# If fraction is already expanded, simply return the expansion.
if self._expanded:
return self._expanded
# If we don't have a denominator just return expansion of numerator.
if not self.denom:
return self.num.expand()
# Expand numerator and denominator.
num = self.num.expand()
denom = self.denom.expand()
# TODO: Is it too expensive to call expand in the below?
# If both the numerator and denominator are fractions, create new
# numerator and denominator and use division to possibly reduce the
# expression.
if num._prec == 4 and denom._prec == 4: # frac
new_num = create_product([num.num, denom.denom]).expand()
new_denom = create_product([num.denom, denom.num]).expand()
self._expanded = new_num/new_denom
# If the numerator is a fraction, multiply denominators and use
# division to reduce expression.
elif num._prec == 4: # frac
new_denom = create_product([num.denom, denom]).expand()
self._expanded = num.num/new_denom
# If the denominator is a fraction multiply by the inverse and
# use division to reduce expression.
elif denom._prec == 4: # frac
new_num = create_product([num, denom.denom]).expand()
self._expanded = new_num/denom.num
# Use division to reduce the expression, no need to call expand().
else:
self._expanded = num/denom
return self._expanded
def expand(self):
"Expand all members of the product."
# If we just have one variable, compute the expansion of it
# (it is not a Product, so it should be safe). We need this to get
# rid of Product([Symbol]) type expressions.
if len(self.vrs) == 1:
self._expanded = self.vrs[0].expand()
return self._expanded
# If product is already expanded, simply return the expansion.
if self._expanded:
return self._expanded
# Sort variables such that we don't call the '*' operator more than we have to.
float_syms = []
sum_fracs = []
for v in self.vrs:
if v._prec in (0, 1): # float or sym
float_syms.append(v)
continue
exp = v.expand()
# If the expanded expression is a float, sym or product,
# we can add the variables.
if exp._prec in (0, 1): # float or sym
float_syms.append(exp)
elif exp._prec == 2: # prod
float_syms += exp.vrs
else:
sum_fracs.append(exp)
# If we have floats or symbols add the symbols to the rest as a single
# product (for speed).
if len(float_syms) > 1:
sum_fracs.append(create_product(float_syms))
elif float_syms:
sum_fracs.append(float_syms[0])
# Use __mult__ to reduce list to one single variable.
# TODO: Can this be done more efficiently without creating all the
# intermediate variables?
self._expanded = reduce(lambda x, y: x * y, sum_fracs)
return self._expanded
def expand(self):
"Expand all members of the product."
# If we just have one variable, compute the expansion of it
# (it is not a Product, so it should be safe). We need this to get
# rid of Product([Symbol]) type expressions.
if len(self.vrs) == 1:
self._expanded = self.vrs[0].expand()
return self._expanded
# If product is already expanded, simply return the expansion.
if self._expanded:
return self._expanded
# Sort variables such that we don't call the '*' operator more than we have to.
float_syms = []
sum_fracs = []
for v in self.vrs:
if v._prec in (0, 1): # float or sym
float_syms.append(v)
continue
exp = v.expand()
# If the expanded expression is a float, sym or product,
# we can add the variables.
if exp._prec in (0, 1): # float or sym
float_syms.append(exp)
elif exp._prec == 2: # prod
float_syms += exp.vrs
else:
sum_fracs.append(exp)
# If we have floats or symbols add the symbols to the rest as a single
# product (for speed).
if len(float_syms) > 1:
sum_fracs.append( create_product(float_syms) )
elif float_syms:
sum_fracs.append(float_syms[0])
# Use __mult__ to reduce list to one single variable.
# TODO: Can this be done more efficiently without creating all the
# intermediate variables?
self._expanded = reduce(lambda x,y: x*y, sum_fracs)
return self._expanded
def reduce_vartype(self, var_type):
"""Reduce expression with given var_type. It returns a tuple
(found, remain), where 'found' is an expression that only has variables
of type == var_type. If no variables are found, found=(). The 'remain'
part contains the leftover after division by 'found' such that:
self = found*remain."""
# Reduce the numerator by the var type.
# print "self.num._prec: ", self.num._prec
# print "self.num: ", self.num
if self.num._prec == 3:
foo = self.num.reduce_vartype(var_type)
if len(foo) == 1:
num_found, num_remain = foo[0]
# num_found, num_remain = self.num.reduce_vartype(var_type)[0]
else:
# meg: I have only a marginal idea of what I'm doing here!
# print "here: "
new_sum = []
for num_found, num_remain in foo:
if num_found == ():
new_sum.append(create_fraction(num_remain, self.denom))
else:
new_sum.append(create_fraction(create_product([num_found, num_remain]), self.denom))
return create_sum(new_sum).expand().reduce_vartype(var_type)
else:
# num_found, num_remain = self.num.reduce_vartype(var_type)
foo = self.num.reduce_vartype(var_type)
if len(foo) != 1:
raise RuntimeError("This case is not handled")
num_found, num_remain = foo[0]
# # TODO: Remove this test later, expansion should have taken care of
# # no denominator.
# if not self.denom:
# error("This fraction should have been expanded.")
# If the denominator is not a Sum things are straightforward.
denom_found = None
denom_remain = None
# print "self.denom: ", self.denom
# print "self.denom._prec: ", self.denom._prec
if self.denom._prec != 3: # sum
# denom_found, denom_remain = self.denom.reduce_vartype(var_type)
foo = self.denom.reduce_vartype(var_type)
if len(foo) != 1:
raise RuntimeError("This case is not handled")
denom_found, denom_remain = foo[0]
# If we have a Sum in the denominator, all terms must be reduced by
# the same terms to make sense
else:
remain = []
for m in self.denom.vrs:
# d_found, d_remain = m.reduce_vartype(var_type)
foo = m.reduce_vartype(var_type)
d_found, d_remain = foo[0]
# If we've found a denom, but the new found is different from
# the one already found, terminate loop since it wouldn't make
# sense to reduce the fraction.
# TODO: handle I0/((I0 + I1)/(G0 + G1) + (I1 + I2)/(G1 + G2))
# better than just skipping.
# if len(foo) != 1:
# raise RuntimeError("This case is not handled")
if len(foo) != 1 or (denom_found is not None and repr(d_found) != repr(denom_found)):
# If the denominator of the entire sum has a type which is
# lower than or equal to the vartype that we are currently
# reducing for, we have to move it outside the expression
# as well.
# TODO: This is quite application specific, but I don't see
# how we can do it differently at the moment.
if self.denom.t <= var_type:
if not num_found:
num_found = create_float(1)
return [(create_fraction(num_found, self.denom), num_remain)]
else:
# The remainder is always a fraction
return [(num_found, create_fraction(num_remain, self.denom))]
# Update denom found and add remainder.
denom_found = d_found
remain.append(d_remain)
# There is always a non-const remainder if denominator was a sum.
denom_remain = create_sum(remain)
# print "den f: ", denom_found
# print "den r: ", denom_remain
# If we have found a common denominator, but no found numerator,
# create a constant.
# TODO: Add more checks to avoid expansion.
found = None
# There is always a remainder.
remain = create_fraction(num_remain, denom_remain).expand()
# print "remain: ", repr(remain)
if num_found:
if denom_found:
found = create_fraction(num_found, denom_found)
else:
found = num_found
else:
if denom_found:
found = create_fraction(create_float(1), denom_found)
else:
found = ()
# print "found: ", found
# print len((found, remain))
return [(found, remain)]
def __div__(self, other):
"Division by other objects."
# If division is illegal (this should definitely not happen).
if other.val == 0.0:
error("Division by zero.")
# If fraction will be zero.
if self.val == 0.0:
return self.vrs[0]
# If other is a Sum we can only return a fraction.
# NOTE: Expect that other is expanded i.e., x + x -> 2*x which can be handled
# TODO: Fix x / (x + x*y) -> 1 / (1 + y).
# Or should this be handled when reducing a fraction?
if other._prec == 3: # sum
return create_fraction(self, other)
# Handle division by FloatValue, Symbol, Product and Fraction.
# NOTE: assuming that we get expanded variables.
# Copy numerator, and create list for denominator.
num = self.vrs[:]
denom = []
# Add floatvalue, symbol and products to the list of denominators.
if other._prec in (0, 1): # float or sym
denom = [other]
elif other._prec == 2: # prod
# Get copy.
denom = other.vrs[:]
# fraction.
else:
error("Did not expected to divide by fraction.")
# Loop entries in denominator and remove from numerator (and denominator).
for d in denom[:]:
# Add the inverse of a float to the numerator and continue.
if d._prec == 0: # float
num.append(create_float(1.0 / d.val))
denom.remove(d)
continue
if d in num:
num.remove(d)
denom.remove(d)
# Create appropriate return value depending on remaining data.
if len(num) > 1:
# TODO: Make this more efficient?
# Create product and expand to reduce
# Product([5, 0.2]) == Product([1]) -> Float(1).
num = create_product(num).expand()
elif num:
num = num[0]
# If all variables in the numerator has been eliminated we need to add '1'.
else:
num = create_float(1)
if len(denom) > 1:
return create_fraction(num, create_product(denom))
elif denom:
return create_fraction(num, denom[0])
# If we no longer have a denominater, just return the numerator.
return num
def reduce_ops(self):
"Reduce the number of operations needed to evaluate the sum."
# global ind
# ind += " "
# print "\n%sreduce_ops, start" % ind
if self._reduced:
return self._reduced
# NOTE: Assuming that sum has already been expanded.
# TODO: Add test for this and handle case if it is not.
# TODO: The entire function looks expensive, can it be optimised?
# TODO: It is not necessary to create a new Sum if we do not have more
# than one Fraction.
# First group all fractions in the sum.
new_sum = _group_fractions(self)
if new_sum._prec != 3: # sum
self._reduced = new_sum.reduce_ops()
return self._reduced
# Loop all variables of the sum and collect the number of common
# variables that can be factored out.
common_vars = {}
for var in new_sum.vrs:
# Get dictonary of occurrences and add the variable and the number
# of occurrences to common dictionary.
for k, v in var.get_var_occurrences().iteritems():
# print
# print ind + "var: ", var
# print ind + "k: ", k
# print ind + "v: ", v
if k in common_vars:
common_vars[k].append((v, var))
else:
common_vars[k] = [(v, var)]
# print
# print "common vars: "
# for k,v in common_vars.items():
# print "k: ", k
# print "v: ", v
# print
# Determine the maximum reduction for each variable
# sorted as: {(x*x*y, x*y*z, 2*y):[2, [y]]}.
terms_reductions = {}
for k, v in sorted(common_vars.iteritems()):
# print
# print ind + "k: ", k
# print ind + "v: ", v
# If the number of expressions that can be reduced is only one
# there is nothing to be done.
if len(v) > 1:
# TODO: Is there a better way to compute the reduction gain
# and the number of occurrences we should remove?
# Get the list of number of occurences of 'k' in expressions
# in 'v'.
occurrences = [t[0] for t in v]
# Determine the favorable number of occurences and an estimate
# of the maximum reduction for current variable.
fav_occur = 0
reduc = 0
for i in set(occurrences):
# Get number of terms that has a number of occcurences equal
# to or higher than the current number.
num_terms = len([o for o in occurrences if o >= i])
# An estimate of the reduction in operations is:
# (number_of_terms - 1) * number_occurrences.
new_reduc = (num_terms - 1) * i
if new_reduc > reduc:
reduc = new_reduc
fav_occur = i
# Extract the terms of v where the number of occurrences is
# equal to or higher than the most favorable number of occurrences.
terms = sorted([t[1] for t in v if t[0] >= fav_occur])
# We need to reduce the expression with the favorable number of
# occurrences of the current variable.
red_vars = [k] * fav_occur
# If the list of terms is already present in the dictionary,
# add the reduction count and the variables.
if tuple(terms) in terms_reductions:
terms_reductions[tuple(terms)][0] += reduc
terms_reductions[tuple(terms)][1] += red_vars
else:
terms_reductions[tuple(terms)] = [reduc, red_vars]
# print "\nterms_reductions: "
# for k,v in terms_reductions.items():
# print "k: ", create_sum(k)
# print "v: ", v
# print "red: self: ", self
if terms_reductions:
# Invert dictionary of terms.
reductions_terms = dict([((v[0], tuple(v[1])), k)
for k, v in terms_reductions.iteritems()])
# Create a sorted list of those variables that give the highest
# reduction.
sorted_reduc_var = [k for k, v in reductions_terms.iteritems()]
# print
# print ind + "raw"
# for k in sorted_reduc_var:
# print ind, k[0], k[1]
sorted_reduc_var.sort()
# sorted_reduc_var.sort(lambda x, y: cmp(x[0], y[0]))
sorted_reduc_var.reverse()
# print ind + "sorted"
# for k in sorted_reduc_var:
# print ind, k[0], k[1]
# Create a new dictionary of terms that should be reduced, if some
# terms overlap, only pick the one which give the highest reduction to
# ensure that a*x*x + b*x*x + x*x*y + 2*y -> x*x*(a + b + y) + 2*y NOT
# x*x*(a + b) + y*(2 + x*x).
reduction_vars = {}
rejections = {}
for var in sorted_reduc_var:
terms = reductions_terms[var]
if _overlap(terms, reduction_vars) or _overlap(
terms, rejections):
rejections[var[1]] = terms
else:
reduction_vars[var[1]] = terms
# print "\nreduction_vars: "
# for k,v in reduction_vars.items():
# print "k: ", k
# print "v: ", v
# Reduce each set of terms with appropriate variables.
all_reduced_terms = []
reduced_expressions = []
for reduc_var, terms in sorted(reduction_vars.iteritems()):
# Add current terms to list of all variables that have been reduced.
all_reduced_terms += list(terms)
# Create variable that we will use to reduce the terms.
reduction_var = None
if len(reduc_var) > 1:
reduction_var = create_product(list(reduc_var))
else:
reduction_var = reduc_var[0]
# Reduce all terms that need to be reduced.
reduced_terms = [t.reduce_var(reduction_var) for t in terms]
# Create reduced expression.
reduced_expr = None
if len(reduced_terms) > 1:
# Try to reduce the reduced terms further.
reduced_expr = create_product([
reduction_var,
create_sum(reduced_terms).reduce_ops()
])
else:
reduced_expr = create_product(reduction_var,
reduced_terms[0])
# Add reduced expression to list of reduced expressions.
reduced_expressions.append(reduced_expr)
# Create list of terms that should not be reduced.
dont_reduce_terms = []
for v in new_sum.vrs:
if not v in all_reduced_terms:
dont_reduce_terms.append(v)
# Create expression from terms that was not reduced.
not_reduced_expr = None
if dont_reduce_terms and len(dont_reduce_terms) > 1:
# Try to reduce the remaining terms that were not reduced at first.
not_reduced_expr = create_sum(dont_reduce_terms).reduce_ops()
elif dont_reduce_terms:
not_reduced_expr = dont_reduce_terms[0]
# Create return expression.
if not_reduced_expr:
self._reduced = create_sum(reduced_expressions +
[not_reduced_expr])
elif len(reduced_expressions) > 1:
self._reduced = create_sum(reduced_expressions)
else:
self._reduced = reduced_expressions[0]
# # NOTE: Only switch on for debugging.
# if not self._reduced.expand() == self.expand():
# print reduced_expressions[0]
# print reduced_expressions[0].expand()
# print "self: ", self
# print "red: ", repr(self._reduced)
# print "self.exp: ", self.expand()
# print "red.exp: ", self._reduced.expand()
# error("Reduced expression is not equal to original expression.")
return self._reduced
# Return self if we don't have any variables for which we can reduce
# the sum.
self._reduced = self
return self._reduced
def __sub__(self, other):
"Subtract other objects."
# Return a new sum
return create_sum([self, create_product([FloatValue(-1), other])])
def reduce_vartype(self, var_type):
"""Reduce expression with given var_type. It returns a tuple
(found, remain), where 'found' is an expression that only has variables
of type == var_type. If no variables are found, found=(). The 'remain'
part contains the leftover after division by 'found' such that:
self = found*remain."""
# Reduce the numerator by the var type.
# print "self.num._prec: ", self.num._prec
# print "self.num: ", self.num
if self.num._prec == 3:
foo = self.num.reduce_vartype(var_type)
if len(foo) == 1:
num_found, num_remain = foo[0]
# num_found, num_remain = self.num.reduce_vartype(var_type)[0]
else:
# meg: I have only a marginal idea of what I'm doing here!
# print "here: "
new_sum = []
for num_found, num_remain in foo:
if num_found == ():
new_sum.append(create_fraction(num_remain, self.denom))
else:
new_sum.append(
create_fraction(
create_product([num_found, num_remain]),
self.denom))
return create_sum(new_sum).expand().reduce_vartype(var_type)
else:
# num_found, num_remain = self.num.reduce_vartype(var_type)
foo = self.num.reduce_vartype(var_type)
if len(foo) != 1:
raise RuntimeError("This case is not handled")
num_found, num_remain = foo[0]
# # TODO: Remove this test later, expansion should have taken care of
# # no denominator.
# if not self.denom:
# error("This fraction should have been expanded.")
# If the denominator is not a Sum things are straightforward.
denom_found = None
denom_remain = None
# print "self.denom: ", self.denom
# print "self.denom._prec: ", self.denom._prec
if self.denom._prec != 3: # sum
# denom_found, denom_remain = self.denom.reduce_vartype(var_type)
foo = self.denom.reduce_vartype(var_type)
if len(foo) != 1:
raise RuntimeError("This case is not handled")
denom_found, denom_remain = foo[0]
# If we have a Sum in the denominator, all terms must be reduced by
# the same terms to make sense
else:
remain = []
for m in self.denom.vrs:
# d_found, d_remain = m.reduce_vartype(var_type)
foo = m.reduce_vartype(var_type)
d_found, d_remain = foo[0]
# If we've found a denom, but the new found is different from
# the one already found, terminate loop since it wouldn't make
# sense to reduce the fraction.
# TODO: handle I0/((I0 + I1)/(G0 + G1) + (I1 + I2)/(G1 + G2))
# better than just skipping.
# if len(foo) != 1:
# raise RuntimeError("This case is not handled")
if len(foo) != 1 or (denom_found is not None
and repr(d_found) != repr(denom_found)):
# If the denominator of the entire sum has a type which is
# lower than or equal to the vartype that we are currently
# reducing for, we have to move it outside the expression
# as well.
# TODO: This is quite application specific, but I don't see
# how we can do it differently at the moment.
if self.denom.t <= var_type:
if not num_found:
num_found = create_float(1)
return [(create_fraction(num_found,
self.denom), num_remain)]
else:
# The remainder is always a fraction
return [(num_found,
create_fraction(num_remain, self.denom))]
# Update denom found and add remainder.
denom_found = d_found
remain.append(d_remain)
# There is always a non-const remainder if denominator was a sum.
denom_remain = create_sum(remain)
# print "den f: ", denom_found
# print "den r: ", denom_remain
# If we have found a common denominator, but no found numerator,
# create a constant.
# TODO: Add more checks to avoid expansion.
found = None
# There is always a remainder.
remain = create_fraction(num_remain, denom_remain).expand()
# print "remain: ", repr(remain)
if num_found:
if denom_found:
found = create_fraction(num_found, denom_found)
else:
found = num_found
else:
if denom_found:
found = create_fraction(create_float(1), denom_found)
else:
found = ()
# print "found: ", found
# print len((found, remain))
return [(found, remain)]
def __div__(self, other):
"Division by other objects."
# NOTE: We assume expanded objects.
# If division is illegal (this should definitely not happen).
if other.val == 0.0:
error("Division by zero.")
# Return 1 if the two symbols are equal.
if self._repr == other._repr:
return create_float(1)
# If other is a Sum we can only return a fraction.
# TODO: Refine this later such that x / (x + x*y) -> 1 / (1 + y)?
if other._prec == 3: # sum
return create_fraction(self, other)
# Handle division by FloatValue, Symbol, Product and Fraction.
# Create numerator and list for denominator.
num = [self]
denom = []
# Add floatvalue, symbol and products to the list of denominators.
if other._prec in (0, 1): # float or sym
denom = [other]
elif other._prec == 2: # prod
# Need copies, so can't just do denom = other.vrs.
denom += other.vrs
# fraction.
else:
# TODO: Should we also support division by fraction for generality?
# It should not be needed by this module.
error("Did not expected to divide by fraction.")
# Remove one instance of self in numerator and denominator if
# present in denominator i.e., x/(x*y) --> 1/y.
if self in denom:
denom.remove(self)
num.remove(self)
# Loop entries in denominator and move float value to numerator.
for d in denom:
# Add the inverse of a float to the numerator, remove it from
# the denominator and continue.
if d._prec == 0: # float
num.append(create_float(1.0 / other.val))
denom.remove(d)
continue
# Create appropriate return value depending on remaining data.
# Can only be for x / (2*y*z) -> 0.5*x / (y*z).
if len(num) > 1:
num = create_product(num)
# x / (y*z) -> x/(y*z),
elif num:
num = num[0]
# else x / (x*y) -> 1/y.
else:
num = create_float(1)
# If we have a long denominator, create product and fraction.
if len(denom) > 1:
return create_fraction(num, create_product(denom))
# If we do have a denominator, but only one variable don't create a
# product, just return a fraction using the variable as denominator.
elif denom:
return create_fraction(num, denom[0])
# If we don't have any donominator left, return the numerator.
# x / 2.0 -> 0.5*x.
return num.expand()
def __div__(self, other):
"Division by other objects."
# If division is illegal (this should definitely not happen).
if other.val == 0.0:
error("Division by zero.")
# If fraction will be zero.
if self.val == 0.0:
return self.vrs[0]
# If other is a Sum we can only return a fraction.
# NOTE: Expect that other is expanded i.e., x + x -> 2*x which can be handled
# TODO: Fix x / (x + x*y) -> 1 / (1 + y).
# Or should this be handled when reducing a fraction?
if other._prec == 3: # sum
return create_fraction(self, other)
# Handle division by FloatValue, Symbol, Product and Fraction.
# NOTE: assuming that we get expanded variables.
# Copy numerator, and create list for denominator.
num = self.vrs[:]
denom = []
# Add floatvalue, symbol and products to the list of denominators.
if other._prec in (0, 1): # float or sym
denom = [other]
elif other._prec == 2: # prod
# Get copy.
denom = other.vrs[:]
# fraction.
else:
error("Did not expected to divide by fraction.")
# Loop entries in denominator and remove from numerator (and denominator).
for d in denom[:]:
# Add the inverse of a float to the numerator and continue.
if d._prec == 0: # float
num.append(create_float(1.0/d.val))
denom.remove(d)
continue
if d in num:
num.remove(d)
denom.remove(d)
# Create appropriate return value depending on remaining data.
if len(num) > 1:
# TODO: Make this more efficient?
# Create product and expand to reduce
# Product([5, 0.2]) == Product([1]) -> Float(1).
num = create_product(num).expand()
elif num:
num = num[0]
# If all variables in the numerator has been eliminated we need to add '1'.
else:
num = create_float(1)
if len(denom) > 1:
return create_fraction(num, create_product(denom))
elif denom:
return create_fraction(num, denom[0])
# If we no longer have a denominater, just return the numerator.
return num
def __div__(self, other):
"Division by other objects."
# NOTE: We assume expanded objects.
# If division is illegal (this should definitely not happen).
if other.val == 0.0:
error("Division by zero.")
# Return 1 if the two symbols are equal.
if self._repr == other._repr:
return create_float(1)
# If other is a Sum we can only return a fraction.
# TODO: Refine this later such that x / (x + x*y) -> 1 / (1 + y)?
if other._prec == 3: # sum
return create_fraction(self, other)
# Handle division by FloatValue, Symbol, Product and Fraction.
# Create numerator and list for denominator.
num = [self]
denom = []
# Add floatvalue, symbol and products to the list of denominators.
if other._prec in (0, 1): # float or sym
denom = [other]
elif other._prec == 2: # prod
# Need copies, so can't just do denom = other.vrs.
denom += other.vrs
# fraction.
else:
# TODO: Should we also support division by fraction for generality?
# It should not be needed by this module.
error("Did not expected to divide by fraction.")
# Remove one instance of self in numerator and denominator if
# present in denominator i.e., x/(x*y) --> 1/y.
if self in denom:
denom.remove(self)
num.remove(self)
# Loop entries in denominator and move float value to numerator.
for d in denom:
# Add the inverse of a float to the numerator, remove it from
# the denominator and continue.
if d._prec == 0: # float
num.append(create_float(1.0/other.val))
denom.remove(d)
continue
# Create appropriate return value depending on remaining data.
# Can only be for x / (2*y*z) -> 0.5*x / (y*z).
if len(num) > 1:
num = create_product(num)
# x / (y*z) -> x/(y*z),
elif num:
num = num[0]
# else x / (x*y) -> 1/y.
else:
num = create_float(1)
# If we have a long denominator, create product and fraction.
if len(denom) > 1:
return create_fraction(num, create_product(denom))
# If we do have a denominator, but only one variable don't create a
# product, just return a fraction using the variable as denominator.
elif denom:
return create_fraction(num, denom[0])
# If we don't have any donominator left, return the numerator.
# x / 2.0 -> 0.5*x.
return num.expand()
