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slightly wrong pv diagrams

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valentin.boettcher@mailbox.tu-dresden.de 2023-11-01 13:25:05 -04:00
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42 changed files with 11032 additions and 8617 deletions
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141
python/otto_motor/otto_utilities.py
View file

@ -1,6 +1,7 @@
import matplotlib.pyplot as plt
import plot_utils as pu
from hiro_models.otto_cycle import OttoEngine
from hiro_models.otto_cycle import OttoEngine, SmoothlyInterpolatdPeriodicMatrix
from hops.util.dynamic_matrix import *
import numpy as np
import figsaver as fs
import hiro_models.model_auxiliary as aux
@ -503,14 +504,16 @@ def plot_contour(
return cont, (x_labels, y_labels, values)
def val_relative_to_steady(model, val, steady_idx, shift=0):
def val_relative_to_steady(model, val, steady_idx, shift=0, absolute=False):
shift_idx = int(1 / model.dt * shift)
begin_idx = model.strobe[1][steady_idx] - shift_idx
end_idx = -shift_idx if shift != 0 else -2
return model.t[begin_idx : end_idx + 1], (
val.slice(slice(begin_idx - 1, end_idx, 1)) - val.slice(begin_idx - 1)
)
final_value = val.slice(slice(begin_idx - 1, end_idx, 1))
if not absolute:
final_value = final_value - val.slice(begin_idx - 1)
return (model.t[begin_idx : end_idx + 1], final_value)
def timings(τ_c, τ_i):
@ -598,121 +601,57 @@ def add_arrow(line, start_ind=None, direction="right", size=15, color=None):
)
from collections import deque
from itertools import islice
from matplotlib import collections as mc
from matplotlib.colors import colorConverter
import numpy as np
def sliding_window(iterable, n):
"""
sliding_window('ABCDEFG', 4) -> ABCD BCDE CDEF DEFG
recipe from python docs
"""
it = iter(iterable)
window = deque(islice(it, n), maxlen=n)
if len(window) == n:
yield tuple(window)
for x in it:
window.append(x)
yield tuple(window)
def color_gradient(x, y, c1, c2, **kwargs):
"""
Creates a line collection with a gradient from colors c1 to c2,
from data x and y.
"""
n = len(x)
if len(y) != n:
raise ValueError("x and y data lengths differ")
return mc.LineCollection(
sliding_window(zip(x, y), 2),
colors=np.linspace(colorConverter.to_rgb(c1), colorConverter.to_rgb(c2), n - 1),
**kwargs,
)
def plot_modulation_interaction_diagram(model, steady_idx, bath=0):
fig, ax = plt.subplots()
t, inter = val_relative_to_steady(
model,
(model.interaction_energy().for_bath(bath)),
steady_idx,
)
modulation = model.coupling_operators[bath].operator_norm(t)
@pu.wrap_plot
def plot_state_change_diagram(modulation, value, phase_indices, ax=None):
all_modulation = model.coupling_operators[bath].operator_norm(t)
phase_indices = (
np.array(model.coupling_operators[bath]._matrix._timings) * (len(t) - 1)
).astype(np.int64)
modulation_speed = modulation[1:] - modulation[:-1]
value_speed = inter.value[1:] - inter.value[:-1]
modulation_windowed = all_modulation[phase_indices[0] : phase_indices[-1]]
value_windowed = inter.value[phase_indices[0] : phase_indices[-1]]
norm = np.sqrt((modulation_speed ** 2 + value_speed ** 2))
modulation_speed = np.divide(modulation_speed, norm, where=norm > 0)
value_speed = np.divide(value_speed, norm, where=norm > 0)
ax.plot(modulation_windowed, value_windowed, linewidth=3, color="cornflowerblue")
ax.add_collection(
color_gradient(modulation, inter.value, "blue", "red", linewidth=3)
color_gradient(
modulation_windowed, value_windowed, "cornflowerblue", "red", linewidth=3
)
)
for begin, end in zip(phase_indices[:-1], phase_indices[1:]):
modulation_segment = modulation[begin:end]
value_segment = inter.value[begin:end]
interior_begin = int((end - begin) * 0.2 + begin)
interior_end = int((end - begin) * 0.9 + begin)
modulation_directions = modulation_speed[interior_begin:interior_end]
value_directions = value_speed[interior_begin:interior_end]
# (line,) = ax.plot(modulation_segment, value_segment)
# arrow_interval = int(len(modulation_directions) / 3)
# plt.quiver(
# modulation[interior_begin:interior_end:arrow_interval],
# inter.value[interior_begin:interior_end:arrow_interval],
# modulation_directions[::arrow_interval],
# value_directions[::arrow_interval],
# angles="xy",
# headaxislength=3,
# width=0.01 / 2,
# headwidth=4,
# headlength=4,
# zorder=100,
# scale=10,
# color=line.get_color(),
# )
# add_arrow(line, start_ind=(end - begin) // 2, size=20)
ax.scatter(modulation[begin], inter.value[begin], zorder=100)
ax.scatter(modulation[begin], value[begin], zorder=100, marker=".", s=200)
for i, index in enumerate(phase_indices[:-1]):
ax.text(
modulation[index] + np.max(modulation) * 0.02,
inter.value[index] + np.max(np.abs(inter.value)) * 0.01,
value[index] + np.max(np.abs(value)) * 0.01,
str(i + 1),
)
every = 50
# ax.quiver(
# modulation[::every],
# inter.value[::every],
# 1,
# 1,
# angles="xy",
# zorder=5,
# pivot="mid",
# )
bath_names = ["c", "h"]
ax.set_xlabel(rf"$||L_{bath_names[bath]}(t)||$")
ax.set_ylabel(r"$\langle{H_\mathrm{I}}\rangle$")
return fig, ax
def get_modulation_and_value(model, operator, value, steady_idx=2):
shift = 0
timing_operator = operator
while not isinstance(timing_operator, SmoothlyInterpolatdPeriodicMatrix):
if isinstance(operator, Shift):
shift = operator._delta
timing_operator = operator._matrix
if isinstance(operator, DynamicMatrixSum):
timing_operator = operator._left
t, value = val_relative_to_steady(model, value, steady_idx, absolute=True)
all_modulation = operator.operator_norm(t)
timings = np.array(timing_operator._timings)
phase_indices = (((timings + shift / model.Θ) % 1) * (len(t) - 1)).astype(np.int64)
return value.value, all_modulation, phase_indices
def plot_modulation_system_diagram(model, steady_idx):
fig, ax = plt.subplots()

682
python/otto_motor/subprojects/cycle_shift/.ob-jupyter/189be6530967f7dd9ae5131834606f53863c1ee5.svg
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@ -69,7 +69,7 @@ We shift so that we just overlap with coupling/decoupling and one above.
#+end_src
#+RESULTS:
[[file:./.ob-jupyter/9d82da2b9de5536c2531d99dded751a02d14d12b.svg]]
[[file:./.ob-jupyter/2ec49a209af9eb6e1a91c6ba7d59e6ccffb59d86.svg]]
#+begin_src jupyter-python :tangle no
#ot.plot_cycles(models, bath=0, legend=True)
@ -93,7 +93,7 @@ We shift so that we just overlap with coupling/decoupling and one above.
#+end_src
#+RESULTS:
[[file:./.ob-jupyter/b2cc580a1f2d0e5d4ab7e54ea1a4430810c036f0.svg]]
[[file:./.ob-jupyter/296d5b609e4df5b188f4a36cdeb21217e7fffaf2.svg]]
** Integrate
Here we integrate/simulate the models. This should be run on the
@ -200,30 +200,178 @@ modulation over a cycle for the baseline model.
*** pV Diagrams
Let's attempt to draw the p_v diagrams :).
#+begin_src jupyter-python
ot.plot_modulation_interaction_diagram(baseline, 2, 0)
fs.export_fig("baseline_interaction_vs_modulation_cold", x_scaling=1, y_scaling=1)
#+begin_src jupyter-python :tangle scripts/plot_pv_diags.py
from matplotlib import collections as mc
from matplotlib.colors import colorConverter
from collections import deque
from itertools import islice
import pickle
import matplotlib.pyplot as plt
import numpy as np
def sliding_window(iterable, n):
"""
sliding_window('ABCDEFG', 4) -> ABCD BCDE CDEF DEFG
recipe from python docs
"""
it = iter(iterable)
window = deque(islice(it, n), maxlen=n)
if len(window) == n:
yield tuple(window)
for x in it:
window.append(x)
yield tuple(window)
def color_gradient(x, y, c1, c2, **kwargs):
"""
Creates a line collection with a gradient from colors c1 to c2,
from data x and y.
"""
n = len(x)
if len(y) != n:
raise ValueError("x and y data lengths differ")
return mc.LineCollection(
sliding_window(zip(x, y), 2),
colors=np.linspace(colorConverter.to_rgb(c1), colorConverter.to_rgb(c2), n - 1),
,**kwargs,
)
def assemble_segments(data, segments):
final = []
for begin, end in zip(segments, segments[1:]):
if begin > end:
final.append(np.concatenate([data[begin:-1], data[:end]]))
else:
final.append(data[begin:end])
return np.concatenate(final)
def plot_modulation_interaction_diagram(all_value, all_modulation, phase_indices):
fig, ax = plt.subplots()
closed = abs(all_value[phase_indices[0]]- all_value[phase_indices[-1]])< 1e-3
if not closed:
phase_indices = np.concatenate([phase_indices, [phase_indices[0]]])
ax.plot(all_modulation, all_value, linewidth=3, color="cornflowerblue")
modulation = assemble_segments(all_modulation, phase_indices)
value = assemble_segments(all_value, phase_indices)
ax.add_collection(
color_gradient(modulation, value, "cornflowerblue", "red", linewidth=3)
)
phase_indices = phase_indices[:-1]
last = np.array([np.nan, np.nan])
for i, index in enumerate(phase_indices):
ax.scatter(
all_modulation[index], all_value[index], zorder=100, marker=".", s=200, color="black"
)
next = np.array((all_modulation[index], all_value[index]))
ax.annotate(
str(i + 1),
xy=next,
xytext=(5, 5) if (np.linalg.norm(next- last)) > 1e-2 else (5, -10),
xycoords="data",
textcoords="offset points",
)
last = next
x0,x1 = ax.get_xlim()
y0,y1 = ax.get_ylim()
ax.set_aspect(abs(x1-x0)/abs(y1-y0))
return fig, ax
def plot_diagrams(name):
with open(f"data/pv_{name}.pickle", "rb") as file:
diagram_data = pickle.load(file)
for data in diagram_data:
fig, ax = plot_modulation_interaction_diagram(*data["args"])
ax.set_xlabel(data["xlabel"])
ax.set_ylabel(data["ylabel"])
plt.savefig(f"figures/{name}_{data['name']}")
#+end_src
#+RESULTS:
[[file:./.ob-jupyter/a85fb92dfb3cde613c524e8d3e97f7325a87275c.svg]]
#+begin_src jupyter-python
ot.plot_modulation_interaction_diagram(baseline, 2, 1)
fs.export_fig("baseline_interaction_vs_modulation_hot", x_scaling=1, y_scaling=1)
import pickle
def save_data(model, name):
data = [
{
"name": f"bath_modulation_interaction_{bath_name}",
"xlabel": rf"$||L_{bath_name}(t)||$",
"ylabel": r"$\langle{H_\mathrm{I}}\rangle$",
"args": ot.get_modulation_and_value(
model,
model.coupling_operators[bath],
model.interaction_energy().for_bath(bath),
),
}
for bath, bath_name in zip([0, 1], ["c", "h"])
] + [
{
"name": f"system_modulation_system_energy",
"xlabel": r"$||H_\mathrm{S}||$",
"ylabel": r"$\langle{H_\mathrm{S}}\rangle$",
"args": ot.get_modulation_and_value(
model,
model.H,
model.system_energy(),
steady_idx=2
),
}
]
with open(f"data/pv_{name}.pickle", "wb") as file:
pickle.dump(data, file)
# vals = ot.get_modulation_and_value(model, model.coupling_operators[0], model.interaction_energy().for_bath(0))
# plot_modulation_interaction_diagram(*vals)
#+end_src
#+RESULTS:
[[file:./.ob-jupyter/7ced09d05012d2f5f96fd1c5633577d232d0336b.svg]]
#+begin_src jupyter-python
ot.plot_modulation_system_diagram(baseline, 2)
fs.export_fig("baseline_system_vs_modulation", x_scaling=1, y_scaling=1)
save_data(baseline, "baseline")
#+end_src
#+begin_src jupyter-python :tangle scripts/plot_pv_diags.py
plot_diagrams("baseline")
#+end_src
#+RESULTS:
[[file:./.ob-jupyter/189be6530967f7dd9ae5131834606f53863c1ee5.svg]]
:RESULTS:
[[file:./.ob-jupyter/e20cfdce26aee3e6cc09aa2c71aab1d9c8fa0e6d.svg]]
[[file:./.ob-jupyter/f32476d9a3f65abb9e89a849288cca3d8dd4b8ab.svg]]
[[file:./.ob-jupyter/4dfab3022746c37d5d757f95907cda1233b06505.svg]]
:END:
*** Shifted Models
Let us print the power output (relative to the baseline = unshifted model) and efficiency.
@ -466,8 +614,8 @@ switch slower.
#+RESULTS:
:RESULTS:
: <matplotlib.legend.Legend at 0x7f2401d01d30>
[[file:./.ob-jupyter/ab754a91833374afaab5ef6e50c895e6d05f9f58.svg]]
: <matplotlib.legend.Legend at 0x7f24dc503550>
[[file:./.ob-jupyter/33dae463427019962039419fbf34de0e92f69a32.svg]]
:END:
@ -748,6 +896,33 @@ And do it again, but in a more convenient format.
**** pV Diagrams
Let's attempt to draw the p_v diagrams :).
#+begin_src jupyter-python
plt.plot(best_cold_model.t, best_cold_model.coupling_operators[0].operator_norm(best_cold_model.t))
plt.plot(best_cold_model.t, best_cold_model.H.operator_norm(best_cold_model.t))
#+end_src
#+RESULTS:
:RESULTS:
| <matplotlib.lines.Line2D | at | 0x7f24d9cb6370> |
[[file:./.ob-jupyter/85b4e10a2cbe7c5dd912e90d64e1fba3df180eb7.svg]]
:END:
#+begin_src jupyter-python
save_data(best_cold_model, "slow_shifted")
#+end_src
#+begin_src jupyter-python :tangle scripts/plot_pv_diags.py
plot_diagrams("slow_shifted")
#+end_src
#+RESULTS:
:RESULTS:
[[file:./.ob-jupyter/105a183ce89c8401f7e7d8f3066ef0f3ba6bcc8b.svg]]
[[file:./.ob-jupyter/7935e5fd5e40c078825f4fd488cb28c4f9a0564c.svg]]
[[file:./.ob-jupyter/87c5e40252e68db07bbebce0f5f30434f3646feb.svg]]
:END:
#+begin_src jupyter-python
ot.plot_modulation_interaction_diagram(best_cold_model, 2, 0)
fs.export_fig("best_model_interaction_vs_modulation_cold", x_scaling=1, y_scaling=1)

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@ -0,0 +1,108 @@
from matplotlib import collections as mc
from matplotlib.colors import colorConverter
from collections import deque
from itertools import islice
import pickle
import matplotlib.pyplot as plt
import numpy as np
def sliding_window(iterable, n):
"""
sliding_window('ABCDEFG', 4) -> ABCD BCDE CDEF DEFG
recipe from python docs
"""
it = iter(iterable)
window = deque(islice(it, n), maxlen=n)
if len(window) == n:
yield tuple(window)
for x in it:
window.append(x)
yield tuple(window)
def color_gradient(x, y, c1, c2, **kwargs):
"""
Creates a line collection with a gradient from colors c1 to c2,
from data x and y.
"""
n = len(x)
if len(y) != n:
raise ValueError("x and y data lengths differ")
return mc.LineCollection(
sliding_window(zip(x, y), 2),
colors=np.linspace(colorConverter.to_rgb(c1), colorConverter.to_rgb(c2), n - 1),
**kwargs,
)
def assemble_segments(data, segments):
final = []
for begin, end in zip(segments, segments[1:]):
if begin > end:
final.append(np.concatenate([data[begin:-1], data[:end]]))
else:
final.append(data[begin:end])
return np.concatenate(final)
def plot_modulation_interaction_diagram(all_value, all_modulation, phase_indices):
fig, ax = plt.subplots()
closed = abs(all_value[phase_indices[0]]- all_value[phase_indices[-1]])< 1e-3
if not closed:
phase_indices = np.concatenate([phase_indices, [phase_indices[0]]])
ax.plot(all_modulation, all_value, linewidth=3, color="cornflowerblue")
modulation = assemble_segments(all_modulation, phase_indices)
value = assemble_segments(all_value, phase_indices)
ax.add_collection(
color_gradient(modulation, value, "cornflowerblue", "red", linewidth=3)
)
phase_indices = phase_indices[:-1]
last = np.array([np.nan, np.nan])
for i, index in enumerate(phase_indices):
ax.scatter(
all_modulation[index], all_value[index], zorder=100, marker=".", s=200, color="black"
)
next = np.array((all_modulation[index], all_value[index]))
ax.annotate(
str(i + 1),
xy=next,
xytext=(5, 5) if (np.linalg.norm(next- last)) > 1e-2 else (5, -10),
xycoords="data",
textcoords="offset points",
)
last = next
x0,x1 = ax.get_xlim()
y0,y1 = ax.get_ylim()
ax.set_aspect(abs(x1-x0)/abs(y1-y0))
return fig, ax
def plot_diagrams(name):
with open(f"data/pv_{name}.pickle", "rb") as file:
diagram_data = pickle.load(file)
for data in diagram_data:
fig, ax = plot_modulation_interaction_diagram(*data["args"])
ax.set_xlabel(data["xlabel"])
ax.set_ylabel(data["ylabel"])
plt.savefig(f"figures/{name}_{data['name']}")
plot_diagrams("baseline")
plot_diagrams("slow_shifted")

49
python/otto_motor/subprojects/cycle_shift/tangle/cycle_shift.py
View file

@ -67,14 +67,46 @@ fs.export_fig("state_evolution", y_scaling=.7)
ot.plot_steady_energy_changes([baseline], 2, label_fn=lambda _: "")
fs.export_fig("prototype_energy_change", y_scaling=.7)
ot.plot_modulation_interaction_diagram(baseline, 2, 0)
fs.export_fig("baseline_interaction_vs_modulation_cold", x_scaling=1, y_scaling=1)
import pickle
ot.plot_modulation_interaction_diagram(baseline, 2, 1)
fs.export_fig("baseline_interaction_vs_modulation_hot", x_scaling=1, y_scaling=1)
def save_data(model, name):
data = [
{
"name": f"bath_modulation_interaction_{bath_name}",
"xlabel": rf"$||L_{bath_name}(t)||$",
"ylabel": r"$\langle{H_\mathrm{I}}\rangle$",
"args": ot.get_modulation_and_value(
model,
model.coupling_operators[bath],
model.interaction_energy().for_bath(bath),
),
}
for bath, bath_name in zip([0, 1], ["c", "h"])
] + [
{
"name": f"system_modulation_system_energy",
"xlabel": r"$||H_\mathrm{S}||$",
"ylabel": r"$\langle{H_\mathrm{S}}\rangle$",
"args": ot.get_modulation_and_value(
model,
model.H,
model.system_energy(),
steady_idx=2
),
}
]
ot.plot_modulation_system_diagram(baseline, 2)
fs.export_fig("baseline_system_vs_modulation", x_scaling=1, y_scaling=1)
with open(f"data/pv_{name}.pickle", "wb") as file:
pickle.dump(data, file)
# vals = ot.get_modulation_and_value(model, model.coupling_operators[0], model.interaction_energy().for_bath(0))
# plot_modulation_interaction_diagram(*vals)
save_data(baseline, "baseline")
for model in models:
print(model.power(steady_idx=2).value / baseline.power(steady_idx=2).value, model.efficiency(steady_idx=2).value)
@ -341,6 +373,11 @@ best_cold_shift = shifts[np.argmax([-model.power(steady_idx=2).value for model i
best_cold_model = sc.make_model(best_cold_shift, best_cold_shift, switch_t=6., only_cold=True)
best_cold_shift
plt.plot(best_cold_model.t, best_cold_model.coupling_operators[0].operator_norm(best_cold_model.t))
plt.plot(best_cold_model.t, best_cold_model.H.operator_norm(best_cold_model.t))
save_data(best_cold_model, "slow_shifted")
ot.plot_modulation_interaction_diagram(best_cold_model, 2, 0)
fs.export_fig("best_model_interaction_vs_modulation_cold", x_scaling=1, y_scaling=1)