class Basis:
"""
Represents the basis of a vector-space or lattice.
"""
def __init__(self, arg, *, row_vectors=False):
try:
if isinstance(arg, Basis):
self.matrix = arg.matrix.copy()
elif isinstance(arg, list) and isinstance(arg[0], Matrix):
self.matrix = Matrix.hstack(*arg)
elif isinstance(arg, tuple) and isinstance(arg[0], Matrix):
self.matrix = Matrix.hstack(*arg)
else:
self.matrix = Matrix(arg)
if row_vectors:
self.matrix = self.matrix.T
except TypeError:
raise TypeError('Cannot construct a Basis from an object of type {}'.format(type(arg)))
def __str__(self):
return self.matrix.__str__()
def __repr__(self):
return 'Basis({})'.format(self.matrix.__str__())
def __len__(self):
return self.matrix.cols
def __getitem__(self, i):
return self.matrix.__getitem__((slice(None), i))
def __setitem__(self, i, val):
return self.matrix.__setitem__((slice(None), i), val)
def __iter__(self):
for i in range(self.__len__()):
yield self.__getitem__(i)
def copy(self):
return Basis(self.matrix.copy())
def vol(self):
return abs(self.matrix.det())
def mat(self):
return self.matrix
def inv(self):
return self.matrix.inv()
def map(self, f):
return Basis(self.matrix.applyfunc(f))
