Source code for geometry.manifolds.todo.grassman

from contracts import contract
from geometry.manifolds.differentiable_manifold import DifferentiableManifold


class Grassman(DifferentiableManifold):
    '''
        INCOMPLETE -- The Grassman manifold Grass(n,p) is the set of rank-p
        subspaces in R^n. It is seen here as Grass(n,p) = ST(n,p)/GL_p.

        For a reference, see the paper by Absil, Mahony, and Sepulchre (2004)
        where all these operations are explained. Also their book should
        contain essentially the same info, but with more background.

    '''

    @contract(n='N,N>0', p='P,P>0,P<=N')
    def __init__(self, p, n):
        '''
            Initializes the manifold structure.

            :param n: dimension of space
            :param p: rank of subspace
        '''
        self.n = n
        self.p = p

    def belongs(self, a):
        assert False

    def distance(self, a, b):
        assert False

    def logmap(self, a, b):
        assert False

    def expmap(self, a, vel):
        assert False

    def project_ts(self, base, vx):
        assert False

    def sample_uniform(self):
        assert False

    def normalize(self, x):
        assert False