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array.py
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array.py
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"""Module for creating NomialArray instances.
Example
-------
>>> x = gpkit.Monomial('x')
>>> px = gpkit.NomialArray([1, x, x**2])
"""
from operator import eq, le, ge, xor
from functools import reduce # pylint: disable=redefined-builtin
import numpy as np
from .map import NomialMap
from ..small_classes import Numbers, HashVector, EMPTY_HV
from ..small_scripts import try_str_without, mag
from ..constraints import ArrayConstraint
from ..repr_conventions import ReprMixin
from ..exceptions import DimensionalityError
@np.vectorize
def vec_recurse(element, function, *args, **kwargs):
"Vectorizes function with particular args and kwargs"
return function(element, *args, **kwargs)
def array_constraint(symbol, func):
"Return function which creates constraints of the given operator."
vecfunc = np.vectorize(func)
def wrapped_func(self, other):
"Creates array constraint from vectorized operator."
if not isinstance(other, NomialArray):
other = NomialArray(other)
result = vecfunc(self, other)
return ArrayConstraint(result, getattr(self, "key", self),
symbol, getattr(other, "key", other))
return wrapped_func
class NomialArray(ReprMixin, np.ndarray):
"""A Numpy array with elementwise inequalities and substitutions.
Arguments
---------
input_array : array-like
Example
-------
>>> px = gpkit.NomialArray([1, x, x**2])
"""
def __mul__(self, other, *, reverse_order=False):
astorder = (self, other) if not reverse_order else (other, self)
out = NomialArray(np.ndarray.__mul__(self, other))
out.ast = ("mul", astorder)
return out
def __truediv__(self, other):
out = NomialArray(np.ndarray.__truediv__(self, other))
out.ast = ("div", (self, other))
return out
def __rtruediv__(self, other):
out = (np.ndarray.__mul__(self**-1, other))
out.ast = ("div", (other, self))
return out
def __add__(self, other, *, reverse_order=False):
astorder = (self, other) if not reverse_order else (other, self)
out = (np.ndarray.__add__(self, other))
out.ast = ("add", astorder)
return out
# pylint: disable=multiple-statements
def __rmul__(self, other): return self.__mul__(other, reverse_order=True)
def __radd__(self, other): return self.__add__(other, reverse_order=True)
def __pow__(self, expo): # pylint: disable=arguments-differ
out = (np.ndarray.__pow__(self, expo)) # pylint: disable=too-many-function-args
out.ast = ("pow", (self, expo))
return out
def __neg__(self):
out = (np.ndarray.__neg__(self))
out.ast = ("neg", self)
return out
def __getitem__(self, idxs):
out = np.ndarray.__getitem__(self, idxs)
if not getattr(out, "shape", None):
return out
out.ast = ("index", (self, idxs))
return out
def str_without(self, excluded=()):
"Returns string without certain fields (such as 'lineage')."
if self.ast:
return self.parse_ast(excluded)
if hasattr(self, "key"):
return self.key.str_without(excluded)
if not self.shape:
return try_str_without(self.flatten()[0], excluded)
return "[%s]" % ", ".join(
[try_str_without(np.ndarray.__getitem__(self, i), excluded)
for i in range(self.shape[0])]) # pylint: disable=unsubscriptable-object
def latex(self, excluded=()):
"Returns latex representation without certain fields."
units = self.latex_unitstr() if "units" not in excluded else ""
if hasattr(self, "key"):
return self.key.latex(excluded) + units
return np.ndarray.__str__(self)
def __hash__(self):
return reduce(xor, map(hash, self.flat), 0)
def __new__(cls, input_array):
"Constructor. Required for objects inheriting from np.ndarray."
# Input is an already formed ndarray instance cast to our class type
return np.asarray(input_array).view(cls)
def __array_finalize__(self, obj):
"Finalizer. Required for objects inheriting from np.ndarray."
def __array_wrap__(self, out_arr, context=None): # pylint: disable=arguments-differ
"""Called by numpy ufuncs.
Special case to avoid creation of 0-dimensional arrays
See http://docs.scipy.org/doc/numpy/user/basics.subclassing.html"""
if out_arr.ndim:
return np.ndarray.__array_wrap__(self, out_arr, context) # pylint: disable=too-many-function-args
val = out_arr.item()
return np.float(val) if isinstance(val, np.generic) else val
__eq__ = array_constraint("=", eq)
__le__ = array_constraint("<=", le)
__ge__ = array_constraint(">=", ge)
def outer(self, other):
"Returns the array and argument's outer product."
return NomialArray(np.outer(self, other))
def vectorize(self, function, *args, **kwargs):
"Apply a function to each terminal constraint, returning the array"
return vec_recurse(self, function, *args, **kwargs)
def sub(self, subs, require_positive=True):
"Substitutes into the array"
return self.vectorize(lambda nom: nom.sub(subs, require_positive))
@property
def units(self):
"""units must have same dimensions across the entire nomial array"""
units = None
for el in self.flat: # pylint: disable=not-an-iterable
el_units = getattr(el, "units", None)
if units is None:
units = el_units
elif ((el_units and units != el_units) or
(isinstance(el, Numbers) and not (el == 0 or np.isnan(el)))):
raise DimensionalityError(el_units, units)
return units
def sum(self, *args, **kwargs): # pylint: disable=arguments-differ
"Returns a sum. O(N) if no arguments are given."
if args or kwargs or not self.shape:
return np.ndarray.sum(self, *args, **kwargs)
hmap = NomialMap()
hmap.units = self.units
it = np.nditer(self, flags=["multi_index", "refs_ok"])
while not it.finished:
m = self[it.multi_index]
it.iternext()
if isinstance(mag(m), Numbers):
if mag(m):
hmap[EMPTY_HV] = mag(m) + hmap.get(EMPTY_HV, 0)
else:
hmap += m.hmap
out = Signomial(hmap)
out.ast = ("sum", (self, None))
return out
def prod(self, *args, **kwargs): # pylint: disable=arguments-differ
"Returns a product. O(N) if no arguments and only contains monomials."
if args or kwargs:
return np.ndarray.prod(self, *args, **kwargs)
c, unitpower = 1.0, 0
exp = HashVector()
it = np.nditer(self, flags=["multi_index", "refs_ok"])
while not it.finished:
m = self[it.multi_index]
it.iternext()
if not hasattr(m, "hmap") and len(m.hmap) == 1:
return np.ndarray.prod(self, *args, **kwargs)
c *= mag(m.c)
unitpower += 1
exp += m.exp
hmap = NomialMap({exp: c})
units = self.units
hmap.units = units**unitpower if units else None
out = Signomial(hmap)
out.ast = ("prod", (self, None))
return out
from .math import Signomial # pylint: disable=wrong-import-position