def trRV(X=None, V=None):
"""
If V is None it defaults to identity.
If X is None, it defaults to the 0-dimensional subspace,
i.e. R is the identity.
>>> import numpy as np
>>> from numpy.random import standard_normal
>>>
>>> X = standard_normal((100, 4))
>>> np.allclose(trRV(X), (96.0, 96.0))
True
>>> V = np.identity(100)
>>> np.allclose(trRV(X), (96.0, 96.0))
True
>>>
>>> X[:,3] = X[:,1] + X[:,2]
>>> np.allclose(trRV(X), (97.0, 97.0))
True
>>>
>>> u = orth(X)
>>> V = np.dot(u, u.T)
>>> print np.allclose(trRV(X, V), 0)
True
"""
n, p = X.shape
if V is None:
V = np.identity(n)
if X is None:
if V is None:
trRV = trRVRV = n
else:
trRV = _trace(V)
trRVRV = _frobenius(V, V)
else:
u = orth(X)
if V is None:
trRV = trRVRV = n - u.shape[1]
else:
Vu = np.dot(V, u)
utVu = np.dot(u.T, Vu)
trRV = _trace(V) - _frobenius(u, Vu)
trRVRV = _frobenius(V, V) - 2 * _frobenius(Vu, Vu) + _frobenius(
utVu, utVu)
return trRV, trRVRV
def trRV(X=None, V=None):
"""
If V is None it defaults to identity.
If X is None, it defaults to the 0-dimensional subspace,
i.e. R is the identity.
>>> import numpy as np
>>> from numpy.random import standard_normal
>>>
>>> X = standard_normal((100, 4))
>>> np.allclose(trRV(X), (96.0, 96.0))
True
>>> V = np.identity(100)
>>> np.allclose(trRV(X), (96.0, 96.0))
True
>>>
>>> X[:,3] = X[:,1] + X[:,2]
>>> np.allclose(trRV(X), (97.0, 97.0))
True
>>>
>>> u = orth(X)
>>> V = np.dot(u, u.T)
>>> print np.allclose(trRV(X, V), 0)
True
"""
n, p = X.shape
if V is None:
V = np.identity(n)
if X is None:
if V is None:
trRV = trRVRV = n
else:
trRV = _trace(V)
trRVRV = _frobenius(V, V)
else:
u = orth(X)
if V is None:
trRV = trRVRV = n - u.shape[1]
else:
Vu = np.dot(V, u)
utVu = np.dot(u.T, Vu)
trRV = _trace(V) - _frobenius(u, Vu)
trRVRV = _frobenius(V, V) - 2 * _frobenius(Vu, Vu) + _frobenius(utVu, utVu)
return trRV, trRVRV
trRVRV = _frobenius(V, V)
else:
u = orth(X)
if V is None:
trRV = trRVRV = n - u.shape[1]
else:
Vu = np.dot(V, u)
utVu = np.dot(u.T, Vu)
trRV = _trace(V) - _frobenius(u, Vu)
trRVRV = _frobenius(V, V) - 2 * _frobenius(Vu, Vu) + _frobenius(utVu, utVu)
return trRV, trRVRV
if __name__ == "__main__":
from numpy.random import standard_normal
X = standard_normal((100, 4))
print trRV(X) # should be (96,96)
V = np.identity(100)
print trRV(X, V) # should be (96,96)
X[:,3] = X[:,1] + X[:,2]
print trRV(X, V) # should be (97,97)
u = orth(X)
V = np.dot(u, u.T)
print trRV(X, V) # should be (0,0)
else:
u = orth(X)
if V is None:
trRV = trRVRV = n - u.shape[1]
else:
Vu = np.dot(V, u)
utVu = np.dot(u.T, Vu)
trRV = _trace(V) - _frobenius(u, Vu)
trRVRV = _frobenius(V, V) - 2 * _frobenius(Vu, Vu) + _frobenius(
utVu, utVu)
return trRV, trRVRV
if __name__ == "__main__":
from numpy.random import standard_normal
X = standard_normal((100, 4))
print trRV(X) # should be (96,96)
V = np.identity(100)
print trRV(X, V) # should be (96,96)
X[:, 3] = X[:, 1] + X[:, 2]
print trRV(X, V) # should be (97,97)
u = orth(X)
V = np.dot(u, u.T)
print trRV(X, V) # should be (0,0)