def testSquare(self):
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
self.assertTrue( vec.H*vec == cov )
def patch(self, nstd=2, alpha='auto', slope=0.5, minalpha=0.3, **kwargs):
"""
:param nstd:
:param alpha:
:param slope:
:param minalpha:
:param ** kwargs:
get a matplotlib Ellipse patch representing the Mvn, all **kwargs are
passed on to the call to matplotlib.patches.Ellipse
not surprisingly Ellipse only works for 2d data.
the number of standard deviations, 'nstd', is just a multiplier for
the eigen values. So the standard deviations are projected, if you
want volumetric standard deviations I think you need to multiply by
sqrt(ndim)
if you don't specify a value for alpha it is set to the exponential of
the area, as if it has a fixed amount if ink that is spread over it's area.
the 'slope' and 'minalpha' parameters control this auto-alpha:
'slope' controls how quickly the the alpha drops to zero
'minalpha' is used to make sure that very large elipses are not invisible.
"""
shape = self.dist.shape
assert shape[
1] == 2, 'this method can only produce patches for 2d data'
if shape[0] < 2:
kwargs = self._kwargs2Marker(**kwargs)
coords = self.dist.getX(nstd=nstd)
return matplotlib.lines.Line2D(coords[:, 0], coords[:, 1],
**kwargs)
if alpha == 'auto':
alpha = numpy.max(
[minalpha,
numpy.exp(-slope * mvn.sqrt(self.dist.det()))])
facecolor = kwargs.get('facecolor', None)
if facecolor is None:
kwargs['alpha'] = alpha
else:
kwargs['facecolor'] = self._convertAlpha(facecolor, alpha)
edgecolor = kwargs.get('edgecolor', None)
if edgecolor is not None:
kwargs['edgecolor'] = self._convertAlpha(edgecolor, alpha)
else:
kwargs['alpha'] = alpha
#unpack the width and height from the scale matrix
wh = nstd * mvn.sqrt(self.dist.var)
wh[wh > 1e5] = 1e5
#convert from radius to diameters
width, height = 2 * wh
#calculate angle
angle = 180 / numpy.pi * (numpy.angle(
helpers.ascomplex(self.dist.vectors)[0]))
#return an Ellipse patch
return matplotlib.patches.Ellipse(
#with the Mvn's mean at the centre
xy=tuple(self.dist.mean.flatten()),
#matching width and height
width=width,
height=height,
#and rotation angle pulled from the vectors matrix
angle=angle,
#while transmitting any kwargs.
**kwargs)
def patch(self, nstd=2, alpha='auto', slope=0.5, minalpha=0.3, **kwargs):
"""
:param nstd:
:param alpha:
:param slope:
:param minalpha:
:param ** kwargs:
get a matplotlib Ellipse patch representing the Mvn, all **kwargs are
passed on to the call to matplotlib.patches.Ellipse
not surprisingly Ellipse only works for 2d data.
the number of standard deviations, 'nstd', is just a multiplier for
the eigen values. So the standard deviations are projected, if you
want volumetric standard deviations I think you need to multiply by
sqrt(ndim)
if you don't specify a value for alpha it is set to the exponential of
the area, as if it has a fixed amount if ink that is spread over it's area.
the 'slope' and 'minalpha' parameters control this auto-alpha:
'slope' controls how quickly the the alpha drops to zero
'minalpha' is used to make sure that very large elipses are not invisible.
"""
shape = self.dist.shape
assert shape[1] == 2,'this method can only produce patches for 2d data'
if shape[0] < 2:
kwargs = self._kwargs2Marker(**kwargs)
coords = self.dist.getX(nstd = nstd)
return matplotlib.lines.Line2D(
coords[:, 0],
coords[:, 1],
**kwargs
)
if alpha == 'auto':
alpha = numpy.max([
minalpha,
numpy.exp(-slope*mvn.sqrt(self.dist.det()))
])
facecolor = kwargs.get('facecolor', None)
if facecolor is None:
kwargs['alpha'] = alpha
else:
kwargs['facecolor'] = self._convertAlpha(facecolor,alpha)
edgecolor = kwargs.get('edgecolor', None)
if edgecolor is not None:
kwargs['edgecolor'] = self._convertAlpha(edgecolor,alpha)
else:
kwargs['alpha'] = alpha
#unpack the width and height from the scale matrix
wh = nstd*mvn.sqrt(self.dist.var)
wh[wh>1e5] = 1e5
#convert from radius to diameters
width,height = 2*wh
#calculate angle
angle = 180/numpy.pi*(
numpy.angle(helpers.ascomplex(self.dist.vectors)[0])
)
#return an Ellipse patch
return matplotlib.patches.Ellipse(
#with the Mvn's mean at the centre
xy=tuple(self.dist.mean.flatten()),
#matching width and height
width=width, height=height,
#and rotation angle pulled from the vectors matrix
angle=angle,
#while transmitting any kwargs.
**kwargs
)
