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kwant
kwant
Commits
3b75da63
Commit
3b75da63
authored
Nov 28, 2018
by
Pablo Piskunow
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update tests to kpm Correlator and conductivity
parent
a99e5ae8
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142 additions
and
6 deletions
+142
-6
kwant/tests/test_kpm.py
kwant/tests/test_kpm.py
+142
-6
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kwant/tests/test_kpm.py
View file @
3b75da63
...
...
@@ -11,13 +11,15 @@ from types import SimpleNamespace
import
pytest
import
numpy
as
np
import
scipy.sparse
import
scipy.sparse.linalg
as
sla
from
scipy.integrate
import
simps
import
kwant
from
..kpm
import
_rescale
from
..kpm
import
_rescale
,
LocalVectors
,
RandomVectors
from
.._common
import
ensure_rng
SpectralDensity
=
kwant
.
kpm
.
SpectralDensity
# ### General parameters
...
...
@@ -41,6 +43,140 @@ def assert_allclose(arr1, arr2):
def
assert_allclose_sp
(
arr1
,
arr2
):
np
.
testing
.
assert_allclose
(
arr1
,
arr2
,
rtol
=
0.
,
atol
=
TOL_SP
)
def
test_mean_SD
():
kpm_params
=
dict
(
num_vectors
=
1
,
num_moments
=
10
,
rng
=
0
)
sites
=
[
np
.
random
.
randint
(
dim
),
np
.
random
.
randint
(
dim
)]
local_spectrum
=
SpectralDensity
(
ham
,
vector_factory
=
LocalVectors
(
ham
,
where
=
sites
),
mean
=
False
,
**
kpm_params
)
spectrum
=
SpectralDensity
(
ham
,
vector_factory
=
LocalVectors
(
ham
,
where
=
sites
),
mean
=
True
,
**
kpm_params
)
assert_allclose
(
local_spectrum
.
energies
,
spectrum
.
energies
)
assert_allclose
(
local_spectrum
.
densities
.
sum
(
axis
=
1
),
spectrum
.
densities
)
def
test_conductivity
():
radius
=
3
letters
=
[(
'x'
,
'x'
),
(
'x'
,
'y'
),
(
'y'
,
'x'
),
(
'y'
,
'y'
)]
syst
=
kwant
.
Builder
()
lat
=
kwant
.
lattice
.
square
(
norbs
=
1
)
syst
.
_lattice
=
lat
def
circle
(
x
):
return
np
.
linalg
.
norm
(
x
)
<
radius
syst
[
lat
.
shape
(
circle
,
(
0
,
0
))]
=
0
syst
[
lat
.
neighbors
()]
=
-
1
syst
=
syst
.
finalized
()
hamiltonian
=
syst
.
hamiltonian_submatrix
()
positions
=
np
.
array
([
s
.
pos
for
s
in
syst
.
sites
])
# results for num_moments=10, num_vectors=10
kpm_params
=
dict
(
params
=
None
,
num_vectors
=
10
,
num_moments
=
12
,
energy_resolution
=
None
,
vector_factory
=
None
,
bounds
=
None
,
eps
=
0.05
,
rng
=
0
,
accumulate_vectors
=
False
)
# test system and no positions
for
alpha
,
beta
in
letters
:
cond
=
kwant
.
kpm
.
conductivity
(
syst
,
alpha
=
alpha
,
beta
=
beta
,
positions
=
None
,
**
kpm_params
)
# test system or hamiltonian, no positions, but velocity operators
cond_xx
=
kwant
.
kpm
.
conductivity
(
syst
,
alpha
=
'x'
,
beta
=
'x'
,
positions
=
None
,
**
kpm_params
)
x_op
=
scipy
.
sparse
.
coo_matrix
(
hamiltonian
,
copy
=
True
)
displacements
=
positions
[
x_op
.
col
]
-
positions
[
x_op
.
row
]
x_op
.
data
*=
1j
*
displacements
[:,
0
]
for
ham
,
pos
in
[(
syst
,
None
),
(
hamiltonian
,
positions
)]:
# test formatting of alpha and beta
for
alpha
,
beta
in
[(
'x'
,
x_op
),
(
x_op
,
'x'
),
(
x_op
,
x_op
)]:
cond
=
kwant
.
kpm
.
conductivity
(
ham
,
alpha
=
alpha
,
beta
=
beta
,
positions
=
pos
,
**
kpm_params
)
assert_allclose
(
cond
(),
cond_xx
())
# test increase number of moments
increase_moments
=
90
kpm_params
[
'accumulate_vectors'
]
=
True
cond
=
kwant
.
kpm
.
conductivity
(
syst
,
alpha
=
'x'
,
beta
=
'x'
,
positions
=
None
,
**
kpm_params
)
cond
.
add_moments
(
num_moments
=
increase_moments
)
# assert that it's equivalent to construct the instance directly
kpm_params
[
'accumulate_vectors'
]
=
False
kpm_params
[
'num_moments'
]
=
kpm_params
[
'num_moments'
]
+
increase_moments
cond_100
=
kwant
.
kpm
.
conductivity
(
syst
,
alpha
=
'x'
,
beta
=
'x'
,
positions
=
None
,
**
kpm_params
)
assert_allclose
(
cond_100
(),
cond
())
def
test_where
():
radius
=
3
syst
=
kwant
.
Builder
()
lat
=
kwant
.
lattice
.
honeycomb
(
norbs
=
1
)
syst
.
_lattice
=
lat
def
circle
(
x
):
return
np
.
linalg
.
norm
(
x
)
<
radius
syst
[
lat
.
shape
(
circle
,
(
0
,
0
))]
=
0
syst
[
lat
.
neighbors
()]
=
-
1
syst
=
syst
.
finalized
()
where
=
lambda
s
:
np
.
linalg
.
norm
(
s
.
pos
)
<
2
sites
=
[
s
for
s
in
syst
.
sites
if
where
(
s
)]
kpm_params
=
dict
(
num_vectors
=
None
,
num_moments
=
10
,
rng
=
0
)
spectrum2
=
SpectralDensity
(
syst
,
vector_factory
=
LocalVectors
(
syst
,
where
=
where
),
**
kpm_params
)
spectrum1
=
SpectralDensity
(
syst
,
vector_factory
=
LocalVectors
(
syst
,
where
=
sites
),
**
kpm_params
)
assert_allclose
(
spectrum1
(),
spectrum2
())
# test local vectors
cond_xy1
=
kwant
.
kpm
.
conductivity
(
syst
,
vector_factory
=
LocalVectors
(
syst
,
where
=
sites
),
alpha
=
'x'
,
beta
=
'y'
,
**
kpm_params
)
cond_xy2
=
kwant
.
kpm
.
conductivity
(
syst
,
vector_factory
=
LocalVectors
(
syst
,
where
=
where
),
alpha
=
'x'
,
beta
=
'y'
,
**
kpm_params
)
assert_allclose
(
cond_xy1
(),
cond_xy2
())
# test random factory
kpm_params
=
dict
(
num_vectors
=
10
,
num_moments
=
10
,
rng
=
0
)
cond_xy1
=
kwant
.
kpm
.
conductivity
(
syst
,
vector_factory
=
RandomVectors
(
syst
,
sites
,
kpm_params
[
'rng'
]),
alpha
=
'x'
,
beta
=
'y'
,
**
kpm_params
)
cond_xy2
=
kwant
.
kpm
.
conductivity
(
syst
,
vector_factory
=
RandomVectors
(
syst
,
where
,
kpm_params
[
'rng'
]),
alpha
=
'x'
,
beta
=
'y'
,
**
kpm_params
)
assert_allclose
(
cond_xy1
(),
cond_xy2
())
def
test_vector_factory
():
vectors
=
np
.
identity
(
dim
)
def
vectors2
():
count
=
0
while
count
<
6
:
yield
'string'
[
count
]
count
+=
1
vf
=
lambda
n
,
v
:
kwant
.
kpm
.
_VectorFactory
(
num_vectors
=
n
,
vectors
=
v
)
this_vf
=
vf
(
None
,
vectors
)
assert
this_vf
.
num_vectors
==
dim
this_vf
=
vf
(
3
,
vectors
)
assert
this_vf
.
num_vectors
==
3
this_vf
.
add_vectors
(
num_vectors
=
2
)
assert
this_vf
.
num_vectors
==
5
spectrum
=
lambda
n
,
v
:
SpectralDensity
(
ham
,
vector_factory
=
v
,
num_vectors
=
n
)
corr
=
lambda
n
,
v
:
kwant
.
kpm
.
Correlator
(
ham
,
vector_factory
=
v
,
num_vectors
=
n
)
for
instance
in
[
spectrum
,
corr
]:
this_instance
=
instance
(
None
,
vectors
)
assert
this_instance
.
num_vectors
==
dim
this_instance
=
instance
(
3
,
vectors
)
assert
this_instance
.
num_vectors
==
3
this_instance
.
add_vectors
(
num_vectors
=
2
)
assert
this_instance
.
num_vectors
==
5
def
make_spectrum
(
ham
,
p
,
operator
=
None
,
vector_factory
=
None
,
rng
=
None
,
params
=
None
):
"""Create an instance of SpectralDensity class."""
...
...
@@ -99,8 +235,7 @@ def kpm_derivative(spectrum, e, order=1):
i
+=
1
coef_cheb
=
np
.
polynomial
.
chebyshev
.
chebder
(
coef_cheb
)
return
np
.
real
(
np
.
polynomial
.
chebyshev
.
chebval
(
rescaled_energy
,
coef_cheb
)
/
g_e
)
return
np
.
polynomial
.
chebyshev
.
chebval
(
rescaled_energy
,
coef_cheb
)
/
g_e
def
make_spectrum_and_peaks
(
ham
,
precise
,
threshold
=
0.005
):
...
...
@@ -449,8 +584,9 @@ def test_check_convergence_decreasing_values():
def
test_convergence_custom_vector_factory
():
rng
=
ensure_rng
(
1
)
def
random_binary_vectors
(
dim
):
return
np
.
rint
(
rng
.
random_sample
(
dim
))
*
2
-
1
def
random_binary_vectors
():
while
True
:
yield
np
.
rint
(
rng
.
random_sample
(
dim
))
*
2
-
1
# extracted from `deviation_from_eigenvalues
def
deviation
(
ham
,
spectrum
):
...
...
@@ -482,7 +618,7 @@ def test_convergence_custom_vector_factory():
for
ii
in
range
(
iterations
):
ham
=
kwant
.
rmt
.
gaussian
(
dim
)
spectrum
=
make_spectrum
(
ham
,
precise
,
vector_factory
=
random_binary_vectors
)
vector_factory
=
random_binary_vectors
()
)
results
.
append
(
deviation
(
ham
,
spectrum
))
difference_list
.
append
(
results
)
...
...
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