def _subSquare(vectors, var, full=False):
"""
given a series of vectors, this function calculates:
(variances,vectors)=numpy.linalg.eigh(vectors.H*vectors)
it's a seperate function because if there are less vectors
than dimensions the process can be accelerated, it just takes some dancing
it is based on this:
>>> vectors=Matrix(helpers.ascomplex(numpy.random.randn(
... numpy.random.randint(1,10),numpy.random.randint(1,10),2
... )))
>>> cov = vectors.H*vectors
>>> Xcov = vectors*vectors.H
>>> (Xval,Xvec) = numpy.linalg.eigh(Xcov)
>>> vec = Xvec.H*vectors
>>> assert vec.H*vec == cov
"""
vectors = Matrix(vectors)
shape = vectors.shape
if not all(shape):
val = numpy.zeros([0])
vec = numpy.zeros([0, shape[1]])
return (val, vec)
eig = numpy.linalg.eigh
if shape[0] >= shape[1] or full or not vectors.any() or (var < 0).any():
scaled = Matrix(var[:, None]*numpy.array(vectors))
cov = vectors.H*scaled
(val, vec) = eig(cov)
vec = vec.H
elif not var.any():
cov = vectors.H*vectors
(_,vec) = eig(cov)
vec = vec.H
val = numpy.zeros(vec.shape[0])
else:
scaled = Matrix(scipy.sqrt(var)[:, None]*numpy.array(vectors))
Xcov = scaled*scaled.H
#Xcov = var[:,None]*numpy.array(vectors)*vectors.H
(_, Xvec) = eig(Xcov)
Xscaled = (Xvec.H*scaled)
val = helpers.mag2(Xscaled)
vec = numpy.array(Xscaled)/scipy.sqrt(val[:, numpy.newaxis])
return (val, vec)
def _subSquare(vectors, var, full=False):
"""
given a series of vectors, this function calculates:
(variances,vectors)=numpy.linalg.eigh(vectors.H*vectors)
it's a seperate function because if there are less vectors
than dimensions the process can be accelerated, it just takes some dancing
it is based on this:
>>> vectors=Matrix(helpers.ascomplex(numpy.random.randn(
... numpy.random.randint(1,10),numpy.random.randint(1,10),2
... )))
>>> cov = vectors.H*vectors
>>> Xcov = vectors*vectors.H
>>> (Xval,Xvec) = numpy.linalg.eigh(Xcov)
>>> vec = Xvec.H*vectors
>>> assert vec.H*vec == cov
"""
vectors = Matrix(vectors)
shape = vectors.shape
if not all(shape):
val = numpy.zeros([0])
vec = numpy.zeros([0, shape[1]])
return (val, vec)
eig = numpy.linalg.eigh
if shape[0] >= shape[1] or full or not vectors.any() or (var < 0).any():
scaled = Matrix(var[:, None] * numpy.array(vectors))
cov = vectors.H * scaled
(val, vec) = eig(cov)
vec = vec.H
elif not var.any():
cov = vectors.H * vectors
(_, vec) = eig(cov)
vec = vec.H
val = numpy.zeros(vec.shape[0])
else:
scaled = Matrix(scipy.sqrt(var)[:, None] * numpy.array(vectors))
Xcov = scaled * scaled.H
#Xcov = var[:,None]*numpy.array(vectors)*vectors.H
(_, Xvec) = eig(Xcov)
Xscaled = (Xvec.H * scaled)
val = helpers.mag2(Xscaled)
vec = numpy.array(Xscaled) / scipy.sqrt(val[:, numpy.newaxis])
return (val, vec)
def testDist2(self):
if not fix.A.flat:
self.assertTrue(
Matrix((fix.A**0).dist2(numpy.zeros((1,fix.ndim)))) ==
helpers.mag2((fix.A**0).mean)
)
def testScaled(self):
self.assertTrue( fix.A.scaled.H*fix.A.scaled == abs(fix.A).cov )
self.assertTrue( Matrix(helpers.mag2(fix.A.scaled)) == fix.A.var )
self.assertTrue( fix.A.vectors.H*fix.A.scaled == fix.A.transform() )
