def hess_f1(self, a, z):
"Define the hessian for the convex inequalities."
## Preliminaries
z = z[1:]
_z1 = z.sum()
_zx = sp.dot(z, self.xarray)
_zxx = (z[:, None, None] *
self.xarray[:, :, None] *
self.xarray[:, None, :]).sum(0)
# Initialize the output "Hessian" array
out = sp.zeros((self.Na, self.Na))
## There are four terms to compute
_aux0 = _z1 * sp.tensordot(self.B, self.B, axes=[(-1,), (-1,)])
_Dzx = sp.dot(self.D, _zx)
_aux1 = sp.tensordot(self.B, _Dzx, axes=[(-1,), (-1,)])
_aux2 = sp.tensordot(_Dzx, self.B, axes=[(-1,), (-1,)])
_Dzxx = sp.dot(self.D, _zxx)
_aux3 = sp.tensordot(_Dzxx, self.D, axes=[(1,2), (1,2)])
## output array
out[:, :] = 2.0 * (_aux0 + _aux1 + _aux2 + _aux3)
return out
def grad_f1(self, a):
"Define the gradient for each convex inequality."
# Initialize the output vector
out = sp.zeros((self.M, self.Na))
# Preliminary calculation
_xx = sp.einsum('mi,mj->mij', self.xarray, self.xarray)
# Compute the four terms
_Da = sp.tensordot(self.D, a, axes=[(0,), (0,)])
_DDa = sp.tensordot(self.D, _Da, axes=[(1,), (0,)])
xxDDa = sp.tensordot(_xx.reshape(self.M, self.ndim**2),
_DDa.reshape(self.Na, self.ndim**2),
axes=[(-1,), (-1,)])
_BDa = sp.dot(self.B, _Da)
xBDa = sp.inner(self.xarray, _BDa)
_Ba = sp.dot(a, self.B)
_DBa = sp.dot(_Ba, self.D)
xDBa = sp.tensordot(self.xarray,
_DBa, axes=[(-1,), (-1,)])
BBa = sp.dot(self.B, _Ba)
# compute the gradient by summing the four terms
out[:, :] = 2.0 * (xxDDa + xBDa + xDBa + BBa)
return out
def subtract_frequency_modes(imap, modes, weight, freq, defer=False):
r"""Subtract frequency modes from the map.
"""
# First map.
omap = sp.empty((len(modes), ) + imap.shape[1:])
if defer:
fitted = np.zeros_like(imap1[freq, :, :])
for mode_index, mode_vector in enumerate(modes):
#mode_vector = mode_vector.reshape(self.freq.shape)
amp = sp.tensordot(mode_vector,
imap[freq, :, :] * weight[freq, :, :],
axes=(0,0))
amp /= sp.tensordot(mode_vector,
mode_vector[:, None, None] * weight[freq, :, :],
axes=(0,0))
if defer:
fitted += mode_vector[:, None, None] * amp[None, :, :]
else:
fitted = mode_vector[:, None, None] * amp[None, :, :]
imap[freq, :, :] -= fitted
omap[mode_index, :, :] = amp
if defer:
imap[freq, :, :] -= fitted
return imap, omap
def expValue( g, l, op ):
bondDim = l.shape[ 1 ]
expVals = []
for A in ( 0, 1 ):
B = ( A + 1 ) % 2
theta = l[ B ].reshape( bondDim, 1, 1 ) * g[ A ] * l[ A ]
OpTheta = sp.tensordot( theta, op, ( 1, 1 ) )
expVals.append( sp.tensordot( theta, OpTheta, ( [ 0, 1, 2 ], [ 0, 2, 1 ] ) ) )
return sum( expVals ) / 2.0
def energy( g, l, hermitonian ):
bondDim = l.shape[ 1 ]
physicalDim = g.shape[ 2 ]
energys = []
for A in ( 0, 1 ):
B = ( A + 1 ) % 2
theta = sp.tensordot( l[ B ].reshape( bondDim, 1, 1 ) * g[ A ] * l[ A ], g[ B ] * l[ B ], 1 )
Htheta = sp.tensordot( theta.reshape( bondDim, physicalDim ** 2, bondDim ), hermitonian, ( 1, 1 ) )
energys.append( sp.tensordot( theta.reshape( bondDim, physicalDim ** 2, bondDim ), Htheta, ( [ 0, 1, 2 ], [ 0, 2, 1 ] ) ) )
return sum( energys ) / 2.0
def Velocity(self):
if self._compute_velocity:
self._velocity = scipy.tensordot(self[self.attrs['Velocity']],
self._rotation,
axes=((1, ), (1, )))
self._compute_velocity = False
return self._velocity
def calc_C_mat_op_AA(op, AA):
#print "===="
#print "op:",op.shape
#print "AA:",AA.shape
res = sp.tensordot(op, AA, ((2, 3), (0, 1)))
#print "calculation successful!"
return res
def dklC2lms(dlkC_array):
""""""
diff_array = sp.tensordot(dlkC_array, DKL2LMS, axes=((-1, ), (1, )))
diff_array[..., 0] += gray_lms[0]
diff_array[..., 1] += gray_lms[1]
diff_array[..., 2] += gray_lms[2]
return diff_array
def calc_C_mat_op_AA(op, AA):
#print "===="
#print "op:",op.shape
#print "AA:",AA.shape
res = sp.tensordot(op, AA, ((2, 3), (0, 1)))
#print "calculation successful!"
return res
def classify_csp(W, V, x_train_filt, y_train, x_test_filt, y_test):
""" Classify data using CSP filter W"""
# Project data
proj_train = sp.tensordot(W.transpose(), x_train_filt, axes=[1,1])
proj_test = sp.tensordot(W.transpose(), x_test_filt, axes=[1,1])
# Calculate features
ftr = np.log( np.tensordot(proj_train**2, V, axes=[1,0]) )[:,:,0]
fte = np.log( np.tensordot(proj_test **2, V, axes=[1,0]) )[:,:,0]
# Classify
logistic = LR()
logistic.fit(ftr.transpose(), y_train[:,0])
sc = logistic.score(fte.transpose(), y_test[:,0])
return sc
def trueFeatureStats(T, R, fMap, discountFactor, stateProp=1, MAT_LIMIT=1e8):
""" Gather the statistics needed for LSTD,
assuming infinite data (true probabilities).
Option: if stateProp is < 1, then only a proportion of all
states will be seen as starting state for transitions """
dim = len(fMap)
numStates = len(T)
statMatrix = zeros((dim, dim))
statResidual = zeros(dim)
ss = range(numStates)
repVersion = False
if stateProp < 1:
ss = random.sample(ss, int(numStates * stateProp))
elif dim * numStates**2 < MAT_LIMIT:
repVersion = True
# two variants, depending on how large we can afford our matrices to become.
if repVersion:
tmp1 = tile(fMap, (numStates,1,1))
tmp2 = transpose(tmp1, (2,1,0))
tmp3 = tmp2 - discountFactor * tmp1
tmp4 = tile(T, (dim,1,1))
tmp4 *= transpose(tmp1, (1,2,0))
statMatrix = tensordot(tmp3, tmp4, axes=[[0,2], [1,2]]).T
statResidual = dot(R, dot(fMap, T).T)
else:
for sto in ss:
tmp = fMap - discountFactor * repmat(fMap[:, sto], numStates, 1).T
tmp2 = fMap * repmat(T[:, sto], dim, 1)
statMatrix += dot(tmp2, tmp.T)
statResidual += R[sto] * dot(fMap, T[:, sto])
return statMatrix, statResidual
def test_partial_dot_mat_mat_block(self):
mat1 = sp.arange(2 * 3 * 5 * 7 * 11)
mat1.shape = (2, 3, 5, 7, 11)
mat1 = algebra.make_mat(mat1,
axis_names=('time', 'x', 'y', 'ra', 'z'),
row_axes=(0, 1, 3),
col_axes=(0, 2, 3, 4))
mat2 = sp.arange(2 * 13 * 5 * 7 * 17)
mat2.shape = (2, 13, 7, 5, 17)
mat2 = algebra.make_mat(mat2,
axis_names=('time', 'w', 'ra', 'y', 'freq'),
row_axes=(0, 1, 2, 3),
col_axes=(1, 2, 4))
tmp_arr = sp.tensordot(mat1, mat2, ((2, ), (3, )))
right_ans = sp.empty((7, 13, 2, 3, 11, 17))
for ii in range(2):
for jj in range(7):
this_tmp = tmp_arr[ii, :, jj, :, ii, :, jj, :]
this_tmp = sp.rollaxis(this_tmp, 2, 0)
right_ans[jj, :, ii, ...] = this_tmp
result = algebra.partial_dot(mat1, mat2)
self.assertEqual(result.axes, ('ra', 'w', 'time', 'x', 'z', 'freq'))
self.assertEqual(result.rows, (0, 1, 2, 3))
self.assertEqual(result.cols, (0, 1, 4, 5))
self.assertTrue(sp.allclose(right_ans, result))
def decode_bayes(arr, axis=None, density=None, scale=None):
""" The density is the probabilistic equivalent of the tuning curve, with
two input arguments: the first is the value and the second the location
parameter of the density. Assumin fdomain is (0., 1.)
"""
nunits = arr.shape[axis]
values = sp.linspace(0.0, 1.0, nunits, dtype=float)
# matrix of discrete tuning curves; i: stimulus value #ID, j: preference
tuning = sp.array([[density(theta, loc=phi, scale=scale) \
for theta in values] for phi in values])
tuning /= tuning.sum(1, keepdims=True)
# normalized spike count
spksum = arr.sum(axis, keepdims=True)
spksum[spksum == 0] = 1.0
spikes = arr / spksum
# now decode
probas = sp.tensordot(spikes, tuning, ((axis, ), (0, )))
probas = sp.rollaxis(probas, axis=-1, start=axis)
mapest = values[probas.argmax(axis)]
#mapest = sp.tensordot(probas, values, ((axis,), (0,)))
spread = 1.0 / (probas.max(axis) - probas.min(axis))
return probas, mapest, spread
def test_partial_dot_mat_mat_block(self):
mat1 = sp.arange(2 * 3 * 5 * 7 * 11)
mat1.shape = (2, 3, 5, 7, 11)
mat1 = matrix.make_mat(mat1, axis_names=('time', 'x', 'y', 'ra', 'z'),
row_axes=(0, 1, 3), col_axes=(0, 2, 3, 4))
mat2 = sp.arange(2 * 13 * 5 * 7 * 17)
mat2.shape = (2, 13, 7, 5, 17)
mat2 = matrix.make_mat(mat2,
axis_names=('time', 'w', 'ra', 'y', 'freq'),
row_axes=(0, 1, 2, 3), col_axes=(1, 2, 4))
tmp_arr = sp.tensordot(mat1, mat2, ((2, ), (3, )))
right_ans = sp.empty((7, 13, 2, 3, 11, 17))
for ii in range(2):
for jj in range(7):
this_tmp = tmp_arr[ii, :, jj, :, ii, :, jj, :]
this_tmp = sp.rollaxis(this_tmp, 2, 0)
right_ans[jj, :, ii, ...] = this_tmp
result = dot_products.partial_dot(mat1, mat2)
self.assertEqual(result.axes, ('ra', 'w', 'time', 'x', 'z', 'freq'))
self.assertEqual(result.rows, (0, 1, 2, 3))
self.assertEqual(result.cols, (0, 1, 4, 5))
self.assertTrue(sp.allclose(right_ans, result))
def test_partial_dot_mat_mat(self):
mat1 = sp.asarray(self.mat)
mat1.shape = (4, 3, 2, 5)
mat1 = matrix.make_mat(mat1,
axis_names=('time', 'x', 'y', 'z'),
row_axes=(0, ),
col_axes=(1, 2, 3))
mat2 = sp.asarray(self.mat)
mat2.shape = (4, 2, 3, 5)
mat2 = matrix.make_mat(mat2,
axis_names=('w', 'y', 'x', 'freq'),
row_axes=(0, 1, 2),
col_axes=(3, ))
result = dot_products.partial_dot(mat1, mat2)
self.assertEqual(result.axes, ('time', 'w', 'z', 'freq'))
self.assertEqual(result.rows, (0, 1))
self.assertEqual(result.cols, (2, 3))
self.assertEqual(result.shape, (4, 4, 5, 5))
right_ans = sp.tensordot(mat1, mat2, ((1, 2), (2, 1)))
right_ans = sp.swapaxes(right_ans, 1, 2)
self.assertTrue(sp.allclose(right_ans, result))
def classify_csp(W, V, x_train_filt, y_train, x_test_filt, y_test):
""" Classify data using CSP filter W"""
# Project data
proj_train = sp.tensordot(W.transpose(), x_train_filt, axes=[1, 1])
proj_test = sp.tensordot(W.transpose(), x_test_filt, axes=[1, 1])
# Calculate features
ftr = np.log(np.tensordot(proj_train**2, V, axes=[1, 0]))[:, :, 0]
fte = np.log(np.tensordot(proj_test**2, V, axes=[1, 0]))[:, :, 0]
# Classify
logistic = LR()
logistic.fit(ftr.transpose(), y_train[:, 0])
sc = logistic.score(fte.transpose(), y_test[:, 0])
return sc
def test_spacing_3D_rotated_uneven(self):
net = op.network.Cubic(shape=[3, 4, 5], spacing=[1, 2, 3])
theta = 0.1
R = sp.array([[1, 0, 0], [0, sp.cos(theta), -sp.sin(theta)],
[0, sp.sin(theta), sp.cos(theta)]])
net['pore.coords'] = sp.tensordot(net['pore.coords'], R, axes=(1, 1))
assert sp.allclose(net.spacing, [1, 2, 3])
def decode(arr,
kind='vote',
axis=None,
fdomain=DEFAULT_FDOMAIN,
exclude_percent_of_max=0.,
q=4):
""""""
if axis is None:
if arr.ndim >= 3:
axis = -3
elif arr.ndim == 1:
axis = 0
else:
raise ValueError('Ambiguous axis along which to decode')
nunits = arr.shape[axis]
values = sp.linspace(fdomain[0], fdomain[1], nunits, dtype=float)
if exclude_percent_of_max > 0:
pct = arr.max(axis=axis, keepdims=True) * \
vote_exclude_percent_of_max
arr = sp.maximum(arr - pct, 0)
if kind == 'argmax':
return arr.argmax(axis=axis)/float(nunits-1) \
* (fdomain[1] - fdomain[0]) + fdomain[0]
elif kind == 'vote':
return sp.tensordot(arr, values, ((axis, ), (0, ))) / arr.sum(axis)
elif kind == 'voteExp':
return sp.tensordot(arr**q, values,
((axis, ), (0, ))) / (arr**q).sum(axis)
elif kind == 'circular_vote':
values = (values - fdomain[0]) / (fdomain[1] - fdomain[0])
sv = sp.sin(values * 2 * sp.pi - sp.pi)
cv = sp.cos(values * 2 * sp.pi - sp.pi)
sw = sp.tensordot(arr, sv, ((axis, ), (0, ))) / arr.sum(axis)
cw = sp.tensordot(arr, cv, ((axis, ), (0, ))) / arr.sum(axis)
return (sp.arctan2(sw, cw) + sp.pi)/(2*sp.pi) \
* (fdomain[1] - fdomain[0]) + fdomain[0]
else:
raise ValueError('Invalid decoder type')
def Position(self):
if self._compute_position:
self._position = scipy.tensordot(
self[self.attrs['Position']] - self._boxcenter,
self._rotation,
axes=((1, ), (1, ))) + self._translation
self._compute_position = False
return self._position
def test_spacing_3D_rotated_uneven(self):
net = op.network.Cubic(shape=[3, 4, 5], spacing=[1, 2, 3])
theta = 0.1
R = sp.array([[1, 0, 0],
[0, sp.cos(theta), -sp.sin(theta)],
[0, sp.sin(theta), sp.cos(theta)]])
net['pore.coords'] = sp.tensordot(net['pore.coords'], R, axes=(1, 1))
assert sp.allclose(net.spacing, [1, 2, 3])
def apply_MPO_local(Mn, An):
q = An.shape[0]
Dm1 = An.shape[1]
D = An.shape[2]
MAn = sp.tensordot(An, Mn, axes=[[0], [2]])
MAn = sp.transpose(MAn, axes=(4, 0, 2, 1, 3)).copy()
MAn = MAn.reshape((q, Dm1 * len(Mn), D * len(Mn[0])))
return MAn
def get_b(self, a):
"""
Compute the ellipse centroid -b.
The ellipse is,
||dot(A, x) + b||^{2} <= 1.
for array A and centroid vector -b.
"""
return sp.tensordot(self.B, a, axes=[(0,), (0,)])
def Areml_K_grad_i(self,i):
dLWt = self.dLW().reshape((self.mean._N, self.mean._P, self.mean.n_covs), order = 'F')
if i < self.covar.Cg.getNumberParams():
SrdLWt = self.covar.Sr()[:, sp.newaxis, sp.newaxis] * dLWt
else:
SrdLWt = dLWt
SrdLWtC = sp.tensordot(SrdLWt, self.covar.Ctilde(i), axes=(1, 1))
SroCdLW = SrdLWtC.swapaxes(1,2).reshape((self.mean._N * self.mean._P, self.mean.n_covs), order = 'F')
return -sp.dot(self.dLW().T, SroCdLW)
def apply_MPO_local(Mn, An):
q = An.shape[0]
Dm1 = An.shape[1]
D = An.shape[2]
MAn = sp.tensordot(An, Mn, axes=[[0], [2]])
MAn = sp.transpose(MAn, axes=(4, 0, 2, 1, 3)).copy()
MAn = MAn.reshape((q, Dm1 * len(Mn), D * len(Mn[0])))
return MAn
def lms2dklC(lms_array):
""" DKL := (L-M [red-green], S-(L+M) [blue-yellow], L+M [luminance])
"""
# get cone differences w.r.t. the background
diff_array = lms_array.copy()
diff_array[..., 0] -= gray_lms[0]
diff_array[..., 1] -= gray_lms[1]
diff_array[..., 2] -= gray_lms[2]
dkl_array = sp.tensordot(diff_array, LMS2DKL, axes=((-1, ), (1, )))
return dkl_array
def calc_C(self, n_low=-1, n_high=-1):
"""Generates the C matrices used to calculate the K's and ultimately the B's
These are to be used on one side of the super-operator when applying the
nearest-neighbour Hamiltonian, similarly to C in eqn. (44) of
arXiv:1103.0936v2 [cond-mat.str-el], except being for the non-norm-preserving case.
Makes use only of the nearest-neighbour hamiltonian, and of the A's.
C[n] depends on A[n] and A[n + 1].
This calculation can be significantly faster if a matrix form for h_nn
is available. See gen_h_matrix().
"""
if self.h_nn is None:
return 0
if n_low < 1:
n_low = 0
if n_high < 1:
n_high = self.N + 1
if self.h_nn_mat is None:
for n in xrange(n_low, n_high):
self.C[n].fill(0)
for u in xrange(self.q[n]):
for v in xrange(self.q[n + 1]):
AA = mm.mmul(self.A[n][u], self.A[n + 1][v]) #only do this once for each
for s in xrange(self.q[n]):
for t in xrange(self.q[n + 1]):
h_nn_stuv = self.h_nn(n, s, t, u, v)
if h_nn_stuv != 0:
self.C[n][s, t] += h_nn_stuv * AA
else:
dot = sp.dot
for n in xrange(n_low, n_high):
An = self.A[n]
Anp1 = self.A[n + 1]
AA = sp.empty_like(self.C[n])
for u in xrange(self.q[n]):
for v in xrange(self.q[n + 1]):
AA[u, v] = dot(An[u], Anp1[v])
if n == 0: #FIXME: Temp. hack
self.AA0 = AA
elif n == 1:
self.AA1 = AA
res = sp.tensordot(AA, self.h_nn_mat[n], ((0, 1), (2, 3)))
res = sp.rollaxis(res, 3)
res = sp.rollaxis(res, 3)
self.C[n][:] = res
def tensordot2(A, B, sum=None, multiply=None):
""" Tensordot that supports elementwise multiplication of axes
without a subsequent sum-contraction.
A sum contraction "can be prevented" if the corresponding axis is
diagonalized. This principle can be seen in the most simple case by
comparing
..code::
a = np.arange(5)
b = np.arange(5)
a @ b # sum-contracted to scalar
np.diag(a) @ b # vector with elementwise products
Diagonalizing axes on a dense array would of course be prohibitevly
costly but it is really cheap for sparse matrices.
Parameters
----------
A, B : COO
The input arrays.
sum : list[list[int]]
The axes to multiply and sum-contract over.
multiply : list[list[int]]
The axes to multiply over.
Returns
-------
COO
The output of the computation.
See Also
--------
einsum : Einstein summation function using this
COO.diag_axis : Diagonalize axes of sparse array
"""
if sum is None:
sum = [[], []]
else:
sum = list(sum)
if multiply is None:
multiply = [[], []]
else:
multiply = list(multiply)
# For each multiply[0] we are adding one axis, thus we need to increment
# all following items by one: (0, 1, 2) -> (0, 2, 4)
# We need to account that the array may be unsorted
idx = np.argsort(multiply[0])
post_multiply = multiply[0]
for i, v in enumerate(idx):
post_multiply[v] += i
for i in post_multiply:
A = A.diag_axis(i)
sum[0] += post_multiply
sum[1] += multiply[1]
return tensordot(A, B, axes=sum)
def Areml_K_grad_i(self, i):
dLWt = self.dLW().reshape(
(self.mean._N, self.mean._P, self.mean.n_covs), order='F')
if i < self.covar.Cg.getNumberParams():
SrdLWt = self.covar.Sr()[:, sp.newaxis, sp.newaxis] * dLWt
else:
SrdLWt = dLWt
SrdLWtC = sp.tensordot(SrdLWt, self.covar.Ctilde(i), axes=(1, 1))
SroCdLW = SrdLWtC.swapaxes(1, 2).reshape(
(self.mean._N * self.mean._P, self.mean.n_covs), order='F')
return -sp.dot(self.dLW().T, SroCdLW)
def groundState( hermitonian, bondDim, timeIssue = None, wavefunc = None, out = None ):
physicalDim = 5
if not timeIssue:
timeIssue = ( 0.05, 5.0 )
if wavefunc:
gamma, l = wavefunc
else:
gamma, l = sp.randn( 2, bondDim, 5, bondDim ), sp.randn( 2, bondDim )
U = slg.expm( -timeIssue[ 0 ] * hermitonian )
t = 0
while t <= timeIssue[ 1 ]:
if out:
S_a, S_b = -sum( l[ 0 ] ** 2 * sp.log( l[ 0 ] ** 2 ) ), -sum( l[ 1 ] ** 2 * sp.log( l[ 1 ] ** 2 ) )
expSz, expE = expValue( gamma, l, sz ), energy( gamma, l, hermitonian )
print( " {0:^+10.6f}{1:^+25.16f}{2:^+25.16f}{3:^+25.16f}{4:^+25.16f}".format( t, expE, expSz, S_a, S_b ), file = out )
try:
for A in range( 2 ):
B = ( A + 1 ) % 2
theta = sp.tensordot( l[ B ].reshape( bondDim, 1, 1 ) * gamma[ A ] * l[ A ], gamma[ B ] * l[ B ], 1 )
theta = sp.tensordot( theta.reshape( bondDim, physicalDim ** 2, bondDim ), U, ( 1, 1 ) ).swapaxes( 1, 2 )
X, Y, Z = slg.svd( theta.reshape( physicalDim * bondDim, physicalDim * bondDim ) )
l[ A ] = Y[ 0:bondDim ] / slg.norm( Y[ 0:bondDim ] )
gamma[ A ] = X[ :, 0:bondDim ].reshape( bondDim, 5, bondDim ) / l[ B ].reshape( bondDim, 1, 1 )
gamma[ B ] = Z[ 0:bondDim, : ].reshape( bondDim, 5, bondDim ) / l[ B ]
t += timeIssue[ 0 ]
except slg.LinAlgError:
print( "raise an exception", file = stderr )
gamma += sp.random.normal( size = ( 2, bondDim, 5, bondDim ) )
t = 0.0
return gamma, l
def project_tensor(tensor, axes, projection_components, projected_axes):
"""
Project a tensor array of rank > 2 to lower dimensions
along given axes.
Args:
tensor: numpy array whose shape has length > 2
axes: dictionary whose keys are the names of the variables
to be projected to and whose values are their
respective ranges as rank-1 numpy arrays.
projection_components: dictionary of axes to project along, whose
keys are the names of the projected axis variablse and
whose values indicate the component along which to
take the projection. Index must be less than or equal
to the length of this axis.
projected_axes: 2-element list indicated which indices of axes
are to be projected to.
Returns:
tensor: the projected tensor of shape 1 less than the input tensor.
"""
assert len(tensor.shape) > 2, \
'Cannot project a rank 1 or 2 tensor to two dimensions'
assert len(projected_axes) == 2, 'Can only project to two dimensions'
for idx, name in enumerate(axes.keys()):
if idx == projected_axes[0]:
pass
elif idx == projected_axes[1]:
pass
else:
proj_axis = list(axes.keys()).index(name)
try:
print(('Setting %s fixed..' % name))
proj_element = projection_components[name]
except:
print ('Need to specify iterated variable values that ' \
'are not being plotted in projection_components ' \
'dictionary')
quit()
assert (proj_element < len(axes[name])), \
'Fixed index out of range, %s >= %s'\
% (proj_element, len(axes[name]))
proj_vec = sp.zeros(len(axes[name]))
proj_vec[proj_element] = 1.0
tensor = sp.tensordot(tensor, proj_vec, [proj_axis, 0])
return tensor
def sub_modes(map, modes):
outmap = np.empty((len(modes), ) + map.shape[1:])
for mode_index, mode_vector in enumerate(modes):
mode_vector = mode_vector.reshape([map.shape[0],])
amp = sp.tensordot(mode_vector, map, axes=(0,0))
fitted = mode_vector[:, None, None] * amp[None, :, :]
map -= fitted
outmap[mode_index, :, :] = amp
def vei_CoR_veX(X, C=None, R=None):
"""
Args:
X: NxPxS tensor
C: CxC row covariance (if None: C set to I_PP)
R: NxN row covariance (if None: R set to I_NN)
Returns:
NxPxS tensor obtained as ve^{-1}((C \kron R) ve(X))
where ve(X) reshapes X as a NPxS matrix.
"""
_X = X.transpose((0,2,1))
if R is not None: RV = sp.tensordot(R, _X, (1,0))
else: RV = _X
if C is not None: RV = sp.dot(RV, C.T)
return RV.transpose((0,2,1))
def expect_string_1s(self, op, n, d):
"""Calculates the expectation values of finite strings
with lengths 1 to d, starting at position n.
"""
if callable(op):
op = sp.vectorize(op, otypes=[sp.complex128])
op = sp.fromfunction(op, (self.q, self.q))
res = sp.zeros((d), dtype=self.A[1].dtype)
x = self.l[n - 1]
for j in range(n, n + d + 1):
Aop = sp.tensordot(op, self.A[j], axes=([1],[0]))
x = tm.eps_l_noop(x, self.A[j], Aop)
res[j - n - 1] = m.adot(x, self.r[j])
return res
def expect_string_1s(self, op, n, d):
"""Calculates the expectation values of finite strings
with lengths 1 to d, starting at position n.
"""
if callable(op):
op = sp.vectorize(op, otypes=[sp.complex128])
op = sp.fromfunction(op, (self.q, self.q))
res = sp.zeros((d), dtype=self.A[1].dtype)
x = self.l[n - 1]
for j in xrange(n, n + d + 1):
Aop = sp.tensordot(op, self.A[j], axes=([1],[0]))
x = tm.eps_l_noop(x, self.A[j], Aop)
res[j - n - 1] = m.adot(x, self.r[j])
return res
def test_partial_dot_mat_mat(self):
mat1 = sp.asarray(self.mat)
mat1.shape = (4, 3, 2, 5)
mat1 = algebra.make_mat(mat1, axis_names=('time', 'x', 'y', 'z'),
row_axes=(0,), col_axes=(1, 2, 3))
mat2 = sp.asarray(self.mat)
mat2.shape = (4, 2, 3, 5)
mat2 = algebra.make_mat(mat2, axis_names=('w', 'y', 'x', 'freq'),
row_axes=(0, 1, 2), col_axes=(3,))
result = algebra.partial_dot(mat1, mat2)
self.assertEqual(result.axes, ('time', 'w', 'z', 'freq'))
self.assertEqual(result.rows, (0, 1))
self.assertEqual(result.cols, (2, 3))
self.assertEqual(result.shape, (4, 4, 5, 5))
right_ans = sp.tensordot(mat1, mat2, ((1, 2), (2, 1)))
right_ans = sp.swapaxes(right_ans, 1, 2)
self.assertTrue(sp.allclose(right_ans, result))
def sdss_to_usno(sdss_ugriz):
"""
Return the estimated USNO 1m estimated magnitudes from SDSS 2.5m ones.
Args:
sdss_ugriz(5xN scipy.array): The values of the u, g, r, and z
magnitudes in the SDSS 2.5m system. Each magnitude is a column.
Returns:
5 x N scipy array:
The values of the u', g', r', i', and z' magnitudes in the USNO 1m
system in the same format as the input.
"""
assert sdss_ugriz.shape[0] == 5
return scipy.tensordot(_sdss_to_usno_matrix,
(sdss_ugriz.T + _sdss_to_usno_offset.T).T, 1)
def apply_rsd(self, velocity_offset, los='local'):
if not scipy.isscalar(los):
unit_vector = scipy.array(los, dtype='f8')
unit_vector /= distance(unit_vector)
elif los == 'local':
unit_vector = self.Position / distance(self.Position)[:, None]
elif los == 'global':
unit_vector = self.glos
else:
axis = los
if isinstance(los, str): axis = 'xyz'.index(axis)
unit_vector = scipy.zeros((3), dtype=scipy.float64)
unit_vector[axis] = 1.
unit_vector = scipy.tensordot(unit_vector,
self._rotation,
axes=((0, ), (1, )))
return self.Position + (unit_vector * velocity_offset).sum(
axis=-1)[:, None] * unit_vector
def solve_t(self, Mt):
"""
Mt is dim_r x dim_c x d tensor
"""
if len(Mt.shape) == 2: _Mt = Mt[:, :, sp.newaxis]
else: _Mt = Mt
M = _Mt.transpose([0, 2, 1])
MLc = sp.tensordot(M, self.Lc().T, (2, 0))
MLcLc = sp.tensordot(MLc, self.Lc(), (2, 0))
WrMLcWc = sp.tensordot(sp.tensordot(self.Wr(), MLc, (1, 0)),
self.Wc().T, (2, 0))
DWrMLcWc = sp.tensordot(self.D()[:, sp.newaxis, :] * WrMLcWc,
self.Wc(), (2, 0))
WrDWrMLcWcLc = sp.tensordot(self.Wr().T,
sp.tensordot(DWrMLcWc, self.Lc(), (2, 0)),
(1, 0))
RV = (MLcLc - WrDWrMLcWcLc).transpose([0, 2, 1])
if len(Mt.shape) == 2: RV = RV[:, :, 0]
return RV
def atensor(theta, lmax=500):
"""
Compute the tensor for given angles and lmax.
** usage **
To construct an array for sampling angles to the following.
A = atensor(theta, lmax)
ssa = SingleScatteringArray(defining_scattering_data)
[f_i(theta_j)]_ij... = sp.einsum('ijkl, kl...->ij...', A, ssa)
"""
x = sp.cos(theta)
out = sp.zeros((6, theta.size, 6, lmax))
out[(0,3),:,(0,3),:] = gensph(x, 0, 0, lmax)
out[(4,5),:,(4,5),:] = gensph(x, 0, 2, lmax)
out[1,:,1,:] = gensph(x,2,2,lmax)
out[2,:,2,:] = gensph(x,2,-2,lmax)
# pre and post arrays
a = sp.eye(6)
a[1:3, 1:3] = .5 * sp.array([[1,1],[1,-1]])
b = sp.eye(6)
b[1:3, 1:3] = sp.array([[1,1],[1,-1]])
# make the final array
# out = sp.einsum('ij,jklm->iklm', a, out)
# print(dict(a=a.shape,b=b.shape,out=out.shape))
out[:] = sp.tensordot(a,out,axes=[1,0])
# next step
# out = sp.einsum('iklm,lo->ikom', out, b)
I = sp.arange(out.ndim)
out[...] = sp.dot(
out.transpose((I-1)%I.size), b).transpose((I+1)%I.size)
return out
def angle_eval(self, theta):
"""
Use atensor to evaluate the scattering matrix elements at vector
of angles.
* in *
theta - angles to sample scattering matrix elements [radians]
"""
# OLD WAYS to compute this
#
# # this is a big temporary array
# big = self.atensor(theta) * self
# return big.sum(3).sum(2)
# return sp.einsum("ijkl...,kl...->ij...", self.atensor(theta), self)
#
# These were raising SEG FAULTS!!! WHY???
#
# Scattering matrix
aten = self.atensor(theta)
P = sp.tensordot(aten, self, axes=[(-2, -1), (0, 1)])
return P
def WGradient(W,sampleX,sampleY,alpha,C,stepSize,iteratorMu,sigma):
## Calculate dGammadW
derivGammadW=dGammadW(sampleY,alpha,W,stepSize,iteratorMu,sigma)
derivGammadW=-np.dot(C,derivGammadW)
## Calculate dFdW (dFdW= dFdG*dGammadW)
dFdG=dFdGamma(sampleX,sampleY,alpha,W,C,stepSize,iteratorMu,sigma)
dFdW=scipy.tensordot(dFdG,derivGammadW, axes=[0,0])
return dFdW
def svd_spec_time(data, params, file_ind, freq=None, time=None):
# data[...,:100] = np.inf
# data[...,-100:] = np.inf
# data[...,1640:1740] = np.inf
# data[...,2066:2166] = np.inf
time_mask = np.logical_not(np.all(np.logical_not(np.isfinite(data)), axis=(2, 3)))
freq_mask = np.all(np.isfinite(data[time_mask[..., None, None]]), axis=(0, 2))
data[freq_mask[None, :, None, :]] = np.ma.masked
# freq_mask = np.any(np.isfinite(data), axis=(0, 2))
weights = np.ones(data.shape)
data_mask = np.logical_not(np.isfinite(data))
weights[data_mask] = 0.0
data[data_mask] = 0.0
# if np.sum(weights) < np.prod(weights.shape) * 0.1:
# #print "Warning: too much data masked, no svd performed"
# msg = ("WARNING: too much data masked, no svd performed")
# warnings.warn(msg)
# data[data_mask] = np.inf
# return data
sh = data.shape
# for XX
data_svd = data[:, 0, :, :].reshape([-1, sh[-1]])[:, freq_mask[0, :]]
weight_svd = weights[:, 0, :, :].reshape([-1, sh[-1]])[:, freq_mask[0, :]]
# check flag percent
weight_svd = np.ma.array(weight_svd)
weight_svd[weight_svd == 0] = np.ma.masked
percent = float(np.ma.count_masked(weight_svd)) / weight_svd.size * 100
print "Flag percent XX: %f%%" % percent
if np.sum(weight_svd) < np.prod(weight_svd.shape) * 0.1 or data_svd.shape[-1] < 10:
# print "Warning: too much data masked, no svd performed"
msg = "WARNING: too much data masked for XX, no svd performed"
warnings.warn(msg)
data[data_mask] = np.inf
return data
vec_t, val, vec_f = linalg.svd(data_svd)
vec_f = vec_f.T
sorted_index = np.argsort(val)[::-1]
vec_t = vec_t[:, sorted_index]
vec_f = vec_f[:, sorted_index]
val = val[sorted_index]
modes = params["modes"]
amps = sp.empty((modes, data_svd.shape[0]))
for i in np.arange(modes):
amp = sp.tensordot(vec_f[:, i], data_svd * weight_svd, axes=(0, 1))
amp /= sp.tensordot(vec_f[:, i], vec_f[:, i][None, :] * weight_svd, axes=(0, 1))
data_svd -= vec_f[:, i][None, :] * amp[:, None]
amps[i, :] = amp
del amp
data[:, 0, :, :][..., freq_mask[0, :]] = data_svd.reshape([sh[0], 2, -1])
if params["save_svd"]:
f_name = params["output_root"] + params["file_middles"][file_ind] + "_svd_XX.hdf5"
utils.mkparents(f_name)
f = h5py.File(f_name, "w")
f["singular_values"] = val
f["left_vectors"] = vec_t.T
f["right_vectors"] = vec_f.T
# f['outmap_left'] = outmap_left
f["outmap_right"] = amps
# f['map_left'] = map1
f["map_right"] = data[:, 0, :, :]
f["freq_mask"] = freq_mask[0, :]
f["freq"] = freq
f["time"] = time
f.close()
if params["save_plot"]:
f_name = params["output_root"] + params["file_middles"][file_ind] + "_svd_XX.hdf5"
utils.mkparents(f_name)
check_svd(f_name, [val, vec_t.T, vec_f.T], freq_mask[0, :], freq)
check_map(f_name, np.ma.array(data[:, 0, :, :]), time, freq)
del data_svd, weight_svd, val, vec_t, vec_f, amps
gc.collect()
# for YY
data_svd = data[:, 3, :, :].reshape([-1, sh[-1]])[:, freq_mask[3, :]]
weight_svd = weights[:, 3, :, :].reshape([-1, sh[-1]])[:, freq_mask[3, :]]
# check flag percent
weight_svd = np.ma.array(weight_svd)
weight_svd[weight_svd == 0] = np.ma.masked
percent = float(np.ma.count_masked(weight_svd)) / weight_svd.size * 100
print "Flag percent XX: %f%%" % percent
if np.sum(weight_svd) < np.prod(weight_svd.shape) * 0.1 or data_svd.shape[-1] < 10:
# print "Warning: too much data masked, no svd performed"
msg = "WARNING: too much data masked for YY, no svd performed"
warnings.warn(msg)
data[data_mask] = np.inf
return data
vec_t, val, vec_f = linalg.svd(data_svd)
vec_f = vec_f.T
sorted_index = np.argsort(val)[::-1]
vec_t = vec_t[:, sorted_index]
vec_f = vec_f[:, sorted_index]
val = val[sorted_index]
modes = params["modes"]
amps = sp.empty((modes, data_svd.shape[0]))
for i in np.arange(modes):
amp = sp.tensordot(vec_f[:, i], data_svd * weight_svd, axes=(0, 1))
amp /= sp.tensordot(vec_f[:, i], vec_f[:, i][None, :] * weight_svd, axes=(0, 1))
data_svd -= vec_f[:, i][None, :] * amp[:, None]
amps[i, :] = amp
del amp
data[:, 3, :, :][..., freq_mask[3, :]] = data_svd.reshape([sh[0], 2, -1])
if params["save_svd"]:
f_name = params["output_root"] + params["file_middles"][file_ind] + "_svd_YY.hdf5"
utils.mkparents(f_name)
f = h5py.File(f_name, "w")
f["singular_values"] = val
f["left_vectors"] = vec_t.T
f["right_vectors"] = vec_f.T
# f['outmap_left'] = outmap_left
f["outmap_right"] = amps
# f['map_left'] = map1
f["map_right"] = data[:, 3, :, :]
f["freq_mask"] = freq_mask[3, :]
f["freq"] = freq
f["time"] = time
f.close()
if params["save_plot"]:
f_name = params["output_root"] + params["file_middles"][file_ind] + "_svd_YY.hdf5"
utils.mkparents(f_name)
check_svd(f_name, [val, vec_t.T, vec_f.T], freq_mask[0, :], freq)
check_map(f_name, np.ma.array(data[:, 0, :, :]), time, freq)
del data_svd, weight_svd, val, vec_t, vec_f, amps
gc.collect()
data[data_mask] = np.inf
return data
def calc_BHB_prereq(self, tdvp, tdvp2):
"""Calculates prerequisites for the application of the effective Hamiltonian in terms of tangent vectors.
This is called (indirectly) by the self.excite.. functions.
Parameters
----------
tdvp2: EvoMPS_TDVP_Uniform
Second state (may be the same, or another ground state).
Returns
-------
A lot of stuff.
"""
l = tdvp.l[0]
r_ = tdvp2.r[0]
r__sqrt = tdvp2.r_sqrt[0]
r__sqrt_i = tdvp2.r_sqrt_i[0]
A = tdvp.A[0]
A_ = tdvp2.A[0]
AA = tdvp.AA[0]
AA_ = tdvp2.AA[0]
AAA_ = tdvp2.AAA[0]
eyed = np.eye(self.q**self.ham_sites)
eyed = eyed.reshape(tuple([self.q] * self.ham_sites * 2))
ham_ = self.ham - tdvp.h_expect.real * eyed
V_ = sp.transpose(tdvp2.Vsh[0], axes=(0, 2, 1)).conj().copy(order='C')
Vri_ = sp.zeros_like(V_)
try:
for s in range(self.q):
Vri_[s] = r__sqrt_i.dot_left(V_[s])
except AttributeError:
for s in range(self.q):
Vri_[s] = V_[s].dot(r__sqrt_i)
Vr_ = sp.zeros_like(V_)
try:
for s in range(self.q):
Vr_[s] = r__sqrt.dot_left(V_[s])
except AttributeError:
for s in range(self.q):
Vr_[s] = V_[s].dot(r__sqrt)
Vri_A_ = tm.calc_AA(Vri_, A_)
if self.ham_sites == 2:
_C_AhlA = np.empty((self.q, self.q, A.shape[2], A.shape[2]), dtype=tdvp.typ)
for u in range(self.q):
for s in range(self.q):
_C_AhlA[u, s] = A[u].conj().T.dot(l.dot(A[s]))
C_AhlA = sp.tensordot(ham_, _C_AhlA, ((0, 2), (0, 1)))
C_AhlA = sp.transpose(C_AhlA, axes=(1, 0, 2, 3)).copy(order='C')
_C_A_Vrh_ = tm.calc_AA(A_, sp.transpose(Vr_, axes=(0, 2, 1)).conj())
C_A_Vrh_ = sp.tensordot(ham_, _C_A_Vrh_, ((3, 1), (0, 1)))
C_A_Vrh_ = sp.transpose(C_A_Vrh_, axes=(1, 0, 2, 3)).copy(order='C')
C_Vri_A_conj = tm.calc_C_conj_mat_op_AA(ham_, Vri_A_).copy(order='C')
C_ = tm.calc_C_mat_op_AA(ham_, AA_).copy(order='C')
C_conj = tm.calc_C_conj_mat_op_AA(ham_, AA_).copy(order='C')
rhs10 = tm.eps_r_op_2s_AA12_C34(r_, AA_, C_Vri_A_conj)
return C_, C_conj, V_, Vr_, Vri_, C_Vri_A_conj, C_AhlA, C_A_Vrh_, rhs10
elif self.ham_sites == 3:
C_Vri_AA_ = np.empty((self.q, self.q, self.q, Vri_.shape[1], A_.shape[2]), dtype=tdvp.typ)
for s in range(self.q):
for t in range(self.q):
for u in range(self.q):
C_Vri_AA_[s, t, u] = Vri_[s].dot(AA_[t, u])
C_Vri_AA_ = sp.tensordot(ham_, C_Vri_AA_, ((3, 4, 5), (0, 1, 2))).copy(order='C')
C_AAA_r_Ah_Vrih = np.empty((self.q, self.q, self.q, self.q, self.q, #FIXME: could be too memory-intensive
A_.shape[1], Vri_.shape[1]),
dtype=tdvp.typ)
for s in range(self.q):
for t in range(self.q):
for u in range(self.q):
for k in range(self.q):
for j in range(self.q):
C_AAA_r_Ah_Vrih[s, t, u, k, j] = AAA_[s, t, u].dot(r_.dot(A_[k].conj().T)).dot(Vri_[j].conj().T)
C_AAA_r_Ah_Vrih = sp.tensordot(ham_, C_AAA_r_Ah_Vrih, ((3, 4, 5, 2, 1), (0, 1, 2, 3, 4))).copy(order='C')
C_AhAhlAA = np.empty((self.q, self.q, self.q, self.q,
A_.shape[2], A.shape[2]), dtype=tdvp.typ)
for t in range(self.q):
for j in range(self.q):
for i in range(self.q):
for s in range(self.q):
C_AhAhlAA[j, t, i, s] = AA[i, j].conj().T.dot(l.dot(AA[s, t]))
C_AhAhlAA = sp.tensordot(ham_, C_AhAhlAA, ((4, 1, 0, 3), (1, 0, 2, 3))).copy(order='C')
C_AA_r_Ah_Vrih_ = np.empty((self.q, self.q, self.q, self.q,
A_.shape[1], Vri_.shape[1]), dtype=tdvp.typ)
for t in range(self.q):
for u in range(self.q):
for k in range(self.q):
for j in range(self.q):
C_AA_r_Ah_Vrih_[u, t, k, j] = AA_[t, u].dot(r_.dot(A_[k].conj().T)).dot(Vri_[j].conj().T)
C_AA_r_Ah_Vrih_ = sp.tensordot(ham_, C_AA_r_Ah_Vrih_, ((4, 5, 2, 1), (1, 0, 2, 3))).copy(order='C')
C_AAA_Vrh_ = np.empty((self.q, self.q, self.q, self.q,
A_.shape[1], Vri_.shape[1]), dtype=tdvp.typ)
for s in range(self.q):
for t in range(self.q):
for u in range(self.q):
for k in range(self.q):
C_AAA_Vrh_[s, t, u, k] = AAA_[s, t, u].dot(Vr_[k].conj().T)
C_AAA_Vrh_ = sp.tensordot(ham_, C_AAA_Vrh_, ((3, 4, 5, 2), (0, 1, 2, 3))).copy(order='C')
C_Vri_A_r_Ah_ = np.empty((self.q, self.q, self.q,
A_.shape[2], Vri_.shape[1]), dtype=tdvp.typ)
for u in range(self.q):
for k in range(self.q):
for j in range(self.q):
C_Vri_A_r_Ah_[u, k, j] = Vri_[j].dot(A_[k]).dot(r_.dot(A_[u].conj().T))
C_Vri_A_r_Ah_ = sp.tensordot(ham_.conj(), C_Vri_A_r_Ah_, ((5, 2, 1), (0, 1, 2))).copy(order='C')
C_AhlAA = np.empty((self.q, self.q, self.q,
A_.shape[2], A.shape[2]), dtype=tdvp.typ)
for j in range(self.q):
for i in range(self.q):
for s in range(self.q):
C_AhlAA[j, i, s] = A[s].conj().T.dot(l.dot(AA[i, j]))
C_AhlAA_conj = sp.tensordot(ham_.conj(), C_AhlAA, ((1, 0, 3), (0, 1, 2))).copy(order='C')
C_AhlAA = sp.tensordot(ham_, C_AhlAA, ((4, 3, 0), (0, 1, 2)))
C_AhlAA = sp.transpose(C_AhlAA, axes=(2, 0, 1, 3, 4)).copy(order='C')
C_AA_Vrh = np.empty((self.q, self.q, self.q,
A_.shape[2], Vr_.shape[1]), dtype=tdvp.typ)
for t in range(self.q):
for u in range(self.q):
for k in range(self.q):
C_AA_Vrh[k, u, t] = AA_[t, u].dot(Vr_[k].conj().T)
C_AA_Vrh = sp.tensordot(ham_, C_AA_Vrh, ((4, 5, 2), (2, 1, 0))).copy(order='C')
C_ = sp.tensordot(ham_, AAA_, ((3, 4, 5), (0, 1, 2))).copy(order='C')
rhs10 = tm.eps_r_op_3s_C123_AAA456(r_, AAA_, C_Vri_AA_)
#NOTE: These C's are good as C12 or C34, but only because h is Hermitian!
#TODO: Make this consistent with the updated 2-site case above.
return V_, Vr_, Vri_, Vri_A_, C_, C_Vri_AA_, C_AAA_r_Ah_Vrih, C_AhAhlAA, C_AA_r_Ah_Vrih_, C_AAA_Vrh_, C_Vri_A_r_Ah_, C_AhlAA, C_AhlAA_conj, C_AA_Vrh, rhs10,
def calc_C_conj_mat_op_AA(op, AA):
return sp.tensordot(op.conj(), AA, ((0, 1), (0, 1)))
def calc_C_3s_mat_op_AAA(op, AAA):
return sp.tensordot(op, AAA, ((3, 4, 5), (0, 1, 2)))
def XYZ2lms(XYZimage):
""""""
return sp.tensordot(XYZimage, CIECAM02_CAT, axes=(-1, 1))
def calc_C_mat_op_AA(op, AA):
return sp.tensordot(op, AA, ((2, 3), (0, 1)))
def lms2rgb(lmsimage):
""""""
return xyz2rgb(
sp.tensordot(lmsimage, sp.linalg.inv(CIECAM02_CAT), axes=(-1, 1)))
def _LMLgrad_covar(self,covar,**kw_args):
"""
calculates LMLgrad for covariance parameters
"""
# precompute some stuff
if covar=='Cr':
trR = self.cache['trXrXr']
RLZ = self.cache['XrXrLZ']
SrDWLZ = self.cache['SgDWLZ']
WrRLZ = self.cache['WrXrXrLZ']
diagSr = self.cache['Sg']
n_params = self.Cr.getNumberParams()
if self.F is not None:
SrDWLY = self.cache['SgDWLY']
WrRLY = self.cache['WrXrXrLY']
SrDWLV_t = self.cache['SgDWLV_t']
WrRLF = self.cache['WrXrXrLrF']
FRF = self.cache['FLrXrXrLrF']
FRLrY = self.cache['FXrXrLrY']
elif covar=='Cn':
trR = self.N
RLZ = self.cache['LZ']
SrDWLZ = self.cache['DWLZ']
WrRLZ = self.cache['WrLZ']
diagSr = SP.ones(self.S)
n_params = self.Cn.getNumberParams()
if self.F is not None:
SrDWLY = self.cache['DWLY']
WrRLY = self.cache['WrLY']
SrDWLV = self.cache['DWLV']
WrRLF = self.cache['WrLrF']
SrDWLV_t = self.cache['DWLV_t']
FRF = self.cache['FF']
FRLrY = self.cache['FY']
# fill gradient vector
RV = SP.zeros(n_params)
for i in range(n_params):
#0. calc LCL
start = TIME.time()
if covar=='Cr': C = self.Cr.Kgrad_param(i)
elif covar=='Cn': C = self.Cn.Kgrad_param(i)
LCL = SP.dot(self.cache['Lc'],SP.dot(C,self.cache['Lc'].T))
LLCLL = SP.dot(self.cache['Lc'].T,SP.dot(LCL,self.cache['Lc']))
LCLW = SP.dot(LCL,self.cache['Wc'].T)
WLCLW = SP.dot(self.cache['Wc'],LCLW)
CoRLZ = SP.dot(RLZ,LCL.T)
CoSrDWLZ = SP.dot(SrDWLZ,WLCLW.T)
WCoRLZ = SP.dot(WrRLZ,LCLW)
if self.F is not None:
WcCLcA = SP.dot(SP.dot(self.cache['Wc'],LCL),self.cache['LcA'])
CoSrDWLY = SP.dot(SrDWLY,WLCLW.T)
DCoSrDWLY = self.cache['D']*CoSrDWLY
WCoRLY = SP.dot(WrRLY,LCLW)
DWCoRLY = self.cache['D']*WCoRLY
#0a. grad of Areml
if 1:
Areml_grad = SP.dot(SP.kron(WcCLcA,WrRLF).T,self.cache['DWLV'])
else:
Areml_grad = SP.tensordot(SP.tensordot(WrRLF,self.cache['DWLV_t'],axes=(0,0)),WcCLcA,axes=(1,0))
# and then resize...
Areml_grad+= Areml_grad.T
Areml_grad-= SP.kron(LLCLL,FRF) #TODO: think about LLCLL
CoSrDWLV_t = SP.tensordot(SrDWLV_t,WLCLW,axes=(1,1))
Areml_grad-= SP.tensordot(self.cache['DWLV_t'],CoSrDWLV_t,axes=([0,1],[0,2]))
#0b. grad of beta
B_grad1 = -SP.dot(FRLrY,LLCLL)
B_grad1-= SP.dot(SP.dot(self.cache['WrLrF'].T,DCoSrDWLY),self.cache['WcLcA'])
B_grad1+= SP.dot(SP.dot(WrRLF.T,self.cache['DWLY']),WcCLcA)
B_grad1+= SP.dot(SP.dot(self.cache['WrLrF'].T,DWCoRLY),self.cache['WcLcA'])
b_grad = SP.reshape(B_grad1,(self.K*self.P,1),order='F')
b_grad-= SP.dot(Areml_grad,self.cache['b'])
b_grad = SP.dot(self.cache['Areml_inv'],b_grad)
#1. der of log det
start = TIME.time()
trC = LCL.diagonal().sum()
RV[i] = trC*trR
RV[i]-= SP.dot(self.cache['d'],SP.kron(WLCLW.diagonal(),diagSr))
smartSum(self.time,'lmlgrad_trace',TIME.time()-start)
smartSum(self.count,'lmlgrad_trace',1)
#2. der of quad form
start = TIME.time()
RV[i]-= SP.sum(self.cache['LZ']*CoRLZ)
RV[i]-= SP.sum(self.cache['DWLZ']*CoSrDWLZ)
RV[i]+= 2*SP.sum(self.cache['DWLZ']*WCoRLZ)
if self.F is not None:
RV[i]-= 2*SP.dot(self.cache['vecVKiZ'].T,b_grad)
smartSum(self.time,'lmlgrad_quadform',TIME.time()-start)
smartSum(self.count,'lmlgrad_quadform',1)
if self.F is not None:
#3. reml term
RV[i] += (self.cache['Areml_inv']*Areml_grad).sum()
RV[i] *= 0.5
return RV
def _update_cache(self):
"""
Update cache
"""
cov_params_have_changed = self.Cr.params_have_changed or self.Cg.params_have_changed or self.Cn.params_have_changed
if self.XX_has_changed:
start = TIME.time()
""" Row SVD Bg + Noise """
self.cache['Srstar'],Urstar = LA.eigh(self.XX)
self.cache['Lr'] = Urstar.T
self.mean.setRowRotation(Lr=self.cache['Lr'])
smartSum(self.time,'cache_XXchanged',TIME.time()-start)
smartSum(self.count,'cache_XXchanged',1)
if self.Xr_has_changed or self.XX_has_changed:
start = TIME.time()
""" rotate Xr and XrXr """
self.cache['LXr'] = SP.dot(self.cache['Lr'],self.Xr)
smartSum(self.time,'cache_Xrchanged',TIME.time()-start)
smartSum(self.count,'cache_Xrchanged',1)
if cov_params_have_changed:
start = TIME.time()
""" Col SVD Bg + Noise """
S2,U2 = LA.eigh(self.Cn.K()+self.offset*SP.eye(self.P))
self.cache['Sc2'] = S2
US2 = SP.dot(U2,SP.diag(SP.sqrt(S2)))
USi2 = SP.dot(U2,SP.diag(SP.sqrt(1./S2)))
Cstar = SP.dot(USi2.T,SP.dot(self.Cg.K(),USi2))
self.cache['Scstar'],Ucstar = LA.eigh(Cstar)
self.cache['Lc'] = SP.dot(Ucstar.T,USi2.T)
""" pheno """
self.mean.setColRotation(self.cache['Lc'])
""" region part """
self.cache['A'] = SP.reshape(self.Cr.getParams(),(self.P,self.rank),order='F')
self.cache['LAc'] = SP.dot(self.cache['Lc'],self.cache['A'])
if cov_params_have_changed or self.XX_has_changed:
""" S """
self.cache['s'] = SP.kron(self.cache['Scstar'],self.cache['Srstar'])+1
self.cache['d'] = 1./self.cache['s']
self.cache['D'] = SP.reshape(self.cache['d'],(self.N,self.P), order='F')
""" pheno """
self.cache['LY'] = self.mean.evaluate()
self.cache['DLY'] = self.cache['D']*self.cache['LY']
smartSum(self.time,'cache_colSVDpRot',TIME.time()-start)
smartSum(self.count,'cache_colSVDpRot',1)
if cov_params_have_changed or self.XX_has_changed or self.Xr_has_changed:
""" calculate B = I + kron(LcA,LrXr).T*D*kron(kron(LcA,LrXr)) """
start = TIME.time()
W = SP.kron(self.cache['LAc'],self.cache['LXr'])
self.cache['DW'] = W*self.cache['d'][:,SP.newaxis]
self.cache['DWt'] = self.cache['DW'].reshape((self.N,self.P,self.rank*self.S),order='F')
#B = NP.einsum('ijk,jl->ilk',self.cache['DWt'],self.cache['LAc'])
#B = NP.einsum('ji,jlk->ilk',self.cache['LXr'],B)
B = SP.tensordot(self.cache['DWt'],self.cache['LAc'],axes=(1,0))
B = NP.transpose(B, (0, 2, 1))
B = SP.tensordot(self.cache['LXr'],B,axes=(0,0))
B = B.reshape((self.rank*self.S,self.rank*self.S),order='F')
B+= SP.eye(self.rank*self.S)
smartSum(self.time,'cache_calcB',TIME.time()-start)
smartSum(self.count,'cache_calcB',1)
""" invert B """
start = TIME.time()
self.cache['cholB'] = LA.cholesky(B).T
self.cache['Bi'] = LA.cho_solve((self.cache['cholB'],True),SP.eye(self.S*self.rank))
smartSum(self.time,'cache_invB',TIME.time()-start)
smartSum(self.count,'cache_invB',1)
""" pheno """
start = TIME.time()
Z = SP.dot(self.cache['LXr'].T,SP.dot(self.cache['DLY'],self.cache['LAc']))
self.cache['z'] = SP.reshape(Z,(self.S*self.rank), order='F')
self.cache['Biz'] = LA.cho_solve((self.cache['cholB'],True),self.cache['z'])
BiZ = SP.reshape(self.cache['Biz'],(self.S,self.rank), order='F')
self.cache['DLYpDLXBiz'] = SP.dot(self.cache['LXr'],SP.dot(BiZ,self.cache['LAc'].T))
self.cache['DLYpDLXBiz'] *= -self.cache['D']
self.cache['DLYpDLXBiz'] += self.cache['DLY']
smartSum(self.time,'cache_phenoCalc',TIME.time()-start)
smartSum(self.count,'cache_phenoCalc',1)
self.XX_has_changed = False
self.Xr_has_changed = False
self.Y_has_changed = False
self.Cr.params_have_changed = False
self.Cg.params_have_changed = False
self.Cn.params_have_changed = False
def subtract_frequency_modes(self, modes1, modes2=None,
weighted=False, defer=False):
r"""Subtract frequency modes from the map.
"""
if modes2 == None:
modes2 = modes1
# First map.
outmap_left = sp.empty((len(modes1), ) + self.map1.shape[1:])
outmap_left = algebra.make_vect(outmap_left,
axis_names=('freq', 'ra', 'dec'))
outmap_left.copy_axis_info(self.map1)
if defer:
fitted = np.zeros_like(self.map1[self.freq, :, :])
for mode_index, mode_vector in enumerate(modes1):
mode_vector = mode_vector.reshape(self.freq.shape)
if weighted:
amp = sp.tensordot(mode_vector, self.map1[self.freq, :, :] *
self.noise_inv1[self.freq, :, :], axes=(0,0))
amp /= sp.tensordot(mode_vector, mode_vector[:, None, None] *
self.noise_inv1[self.freq, :, :], axes=(0,0))
else:
amp = sp.tensordot(mode_vector,
self.map1[self.freq, :, :], axes=(0,0))
#amp /= sp.dot(mode_vector, mode_vector)
if defer:
fitted += mode_vector[:, None, None] * amp[None, :, :]
else:
fitted = mode_vector[:, None, None] * amp[None, :, :]
self.map1[self.freq, :, :] -= fitted
outmap_left[mode_index, :, :] = amp
if defer:
self.map1 -= fitted
self.left_modes = outmap_left
# Second map.
outmap_right = sp.empty((len(modes2), ) + self.map2.shape[1:])
outmap_right = algebra.make_vect(outmap_right,
axis_names=('freq', 'ra', 'dec'))
outmap_right.copy_axis_info(self.map2)
if defer:
fitted = np.zeros_like(self.map2[self.freq, :, :])
for mode_index, mode_vector in enumerate(modes2):
mode_vector = mode_vector.reshape(self.freq.shape)
if weighted:
amp = sp.tensordot(mode_vector, self.map2[self.freq, :, :] *
self.noise_inv2[self.freq, :, :], axes=(0,0))
amp /= sp.tensordot(mode_vector, mode_vector[:, None, None] *
self.noise_inv2[self.freq, :, :], axes=(0,0))
else:
amp = sp.tensordot(mode_vector,
self.map2[self.freq, :, :], axes=(0,0))
#amp /= sp.dot(mode_vector, mode_vector)
if defer:
fitted += mode_vector[:, None, None] * amp[None, :, :]
else:
fitted = mode_vector[:, None, None] * amp[None, :, :]
self.map2[self.freq, :, :] -= fitted
outmap_right[mode_index, :, :] = amp
if defer:
self.map2 -= fitted
self.right_modes = outmap_right
