---
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---
```{code-cell} ipython3
%pylab inline --no-import-all
import mmf_setup;mmf_setup.nbinit()
```
For an analytic example, consider the SEQ for an HO in a rotating frame with angular velocity $\Omega = \omega$ equal to the trapping frequency:
$$
\I\hbar \dot{\psi} = \left\{
\frac{-\hbar^2\nabla^2}{2m} + \frac{m\omega^2r^2}{2} - \overbrace{\hbar\omega \left(x\pdiff{}{y} - y\pdiff{}{x}\right)}^{\Omega \op{L}_{z}}\right\}\psi.
$$
This should have as a family of solutions:
$$
\psi(x, y, t) = e^{\I\mu t}\sqrt{\frac{m\omega}{\pi \hbar}}
\exp\left\{
-m\omega\frac{(x-R)^2+y^2}{2\hbar}
\right\}.
$$
```{code-cell} ipython3
from multiprocessing import Process
from mmfutils.contexts import NoInterrupt
from mmfutils.plot import imcontourf
from IPython.display import clear_output
import time
class HOServer(Process):
"""Simple computation with superfluid rotating in an HO trap.
This is an exact solution to test performance etc.
"""
def __init__(self, Nxy=(256,)*2, Lxy=(10., 10.)):
self.Nxy = Nxy
self.Lxy = Lxy
self.xy = x, y = np.meshgrid(
*[np.arange(_N) * (_L/_N) - _L/2
for (_N, _L) in zip(Nxy, Lxy)],
sparse=True, indexing='ij')
self._z = x + 1j*y
self.w = 1.0
self.r0 = 2.5
def get_density(self, t):
"""Return the exact solution at time `t`."""
r = abs((np.exp(-1j*self.w*t) * self._z - self.r0))
return np.exp(-r**2)
```
```{code-cell} ipython3
# Check the maximum possible frame-rate
s = HOServer()
ts = np.linspace(0, 10, 100)
tic = time.time()
for t in ts:
n = s.get_density(t)
toc = time.time()
print(f"maximum {len(ts)/(toc-tic):.2f}fps")
```
```{code-cell} ipython3
# See what we get with mpl
ts = np.linspace(0, 10, 100)
fig = plt.figure(figsize=(5,5))
NoInterrupt.unregister()
with NoInterrupt() as interrupted:
x, y = s.xy
tic = time.time()
frame = 0
ax = plt.gca()
for t in ts:
if interrupted:
break
n = s.get_density(t)
ax.cla()
imcontourf(x, y, n)
ax.set_aspect(1)
toc = time.time()
frame += 1
plt.title(f"t={t:.2f}, {frame/(toc-tic):.2}fps")
display(fig)
clear_output(wait=True)
```
```{code-cell} ipython3
from matplotlib import cm
from super_hydro.widgets import Canvas, Label, VBox
def get_rgba(density):
density = density
array = cm.viridis(density/density.max())
array *= int(255/array.max()) # normalize values
rgba = array.astype(dtype='uint8')
return rgba
```
```{code-cell} ipython3
# See what we get with Canvas
ts = np.linspace(0, 10, 100)
canvas = Canvas(name='density', width=300, height=300)
msg = Label(name='messages')
NoInterrupt.unregister()
display(VBox([msg, canvas]))
```
```{code-cell} ipython3
with NoInterrupt() as interrupted:
x, y = s.xy
tic = time.time()
frame = 0
for t in ts:
if interrupted:
break
n = s.get_density(t)
canvas.rgba = get_rgba(n)
toc = time.time()
frame += 1
msg.value = f"t={t:.2f}, {frame/(toc-tic):.2f}fps"
```
# WebSockets
```{code-cell} ipython3
%%HTML
WebSocket Test
WebSocket Test
```
```{code-cell} ipython3
%%javascript
var wsUri = "wss://echo.websocket.org/";
var output;
var websocket;
function init(){
output = document.getElementById("my_output");
testWebSocket();
}
function testWebSocket(){
debugger;
websocket = new WebSocket(wsUri);
websocket.onopen = function(evt) { onOpen(evt) };
websocket.onclose = function(evt) { onClose(evt) };
websocket.onmessage = function(evt) { onMessage(evt) };
websocket.onerror = function(evt) { onError(evt) };
}
function onOpen(evt){
writeToScreen("CONNECTED");
doSend("WebSocket rocks");
}
function onClose(evt){
writeToScreen("DISCONNECTED");
}
function onMessage(evt){
writeToScreen('RESPONSE: ' + evt.data+'');
websocket.close();
}
function onError(evt){
writeToScreen('ERROR: ' + evt.data);
}
function doSend(message){
writeToScreen("SENT: " + message);
websocket.send(message);
}
function writeToScreen(message){
var pre = document.createElement("p");
pre.style.wordWrap = "break-word";
pre.innerHTML = message;
output.appendChild(pre);
}
//window.addEventListener("load", init, false);
init();
```
```{code-cell} ipython3
%%javascript
var wsUri = "wss://echo.websocket.org/";
new WebSocket(wsUri);
```
```{code-cell} ipython3
%%javascript
function writeToScreen(message){
var pre = document.createElement("p");
pre.style.wordWrap = "break-word";
pre.innerHTML = message;
output.appendChild(pre);
}
//init();
element.text("helo");
element.text("hell");
//pre.innerHTML = "Hello";
var pre = document.createElement("p");
pre.style.wordWrap = "break-word";
pre.innerHTML = "Hi";
element.appendChild(pre);
```
```{code-cell} ipython3
from IPython.display import HTML
s = HTML(r"""
WebSocket Test
WebSocket Test
""")
display(s)
```
```{code-cell} ipython3
```