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simulator.py
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simulator.py
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# Scalar Field Simulator
# Yukei Murakami, [email protected]
# version 0.2.0
# last updated: 12/2/2019
import numpy as np
import matplotlib.pyplot as plt
import matplotlib as mpl
from mpl_toolkits.axes_grid1 import make_axes_locatable
from bokeh.plotting import figure, output_notebook, output_file, show
from bokeh.layouts import column, row,layout
from bokeh.models import Button,CustomJS,TextInput,RadioButtonGroup,\
ColumnDataSource,Legend,LegendItem,Toggle
from bokeh.models.widgets import Tabs, Panel
from bokeh.models.renderers import GlyphRenderer
from bokeh.palettes import viridis
from bokeh.io import curdoc
from scipy.constants import c as SOL, G, physical_constants
from astropy import units as u
############ constants #############
# TODO: check if these units are correct
G = G*u.meter**3/u.kg/u.second**2
SOL = SOL * (u.meter/u.second)
H0 = 70 *u.km/u.second/u.Mpc
rho_c = 3*(H0**2)/(8*np.pi*(G))
# set Lambda by fixing the time unit
t_unit = (1e6 * u.year).to(u.second) * SOL # sec * SOL
Lambda = 1/t_unit
# length rescaling: r_tilde = r_actual/r_unit
r_unit = (1/Lambda).to(u.kpc)
# density rescaling: rho_tilde = rho_actual/rho_unit
rho_unit = (1/(3/rho_c*((H0/SOL)/Lambda)**2))
# mass rescaling: M_tilde = M_actual/M_unit (assuming Gaussian dist.)
# R_mass = 1e-2*r_unit
# M_unit = (rho_unit * R_mass**3 * np.pi**(3/2)).to(u.solMass)
kg_per_meter = SOL**2 /G
R_s = 1 #2 * G * rho_1 / SOL**2
L_0 = 1 #SOL / np.sqrt(G*rho_0)
eps = 1 #R_s / L_0
########### parameters ##############
# plot parameters
num_plot = 10 # can be changed in GUI
num_legend = 10
def initialize():
global N,L,dt,x_axis,R_mass,M,rho_1,rho_0,rho_J,dot_0,phi_0_array,dot_0_array,y0
# Scaling params
N = 10000 # number of points
L = 1 # size of the box
dt = 1e-4#0.01*L/N
x_axis = np.linspace(0,L,N)
# Matter params
R_mass = 1e-2
M = 1
rho_1 = M/(R_mass**3 * np.pi**(3/2))
rho_0 = (0.3*rho_c/rho_unit).to(u.km/u.km).value
rho_J = rho_1 * np.exp(-(x_axis/R_mass)**2) + rho_0
# Initial Field params
phi_0 = 0
dot_0 = (H0*(1/(SOL))/Lambda).to(u.km/u.km).value #1e-5
phi_0_array = np.full(N,phi_0)
dot_0_array = np.full(N,dot_0)
y0 = [phi_0_array,dot_0_array]
return N,L,dt,x_axis,R_mass,M,rho_1,rho_0,rho_J,phi_0_array,dot_0_array,y0
############ coupling model #############
def calc_C(phi,C0,c_th,model='POWER'):
if model == 'EXPON':
C = 1+ C0*np.exp(c_th*phi)
Cp = c_th * C0*np.exp(c_th*phi)
elif model == 'POWER':
C = 1 + C0 * phi**c_th
Cp = 0 if c_th==0 else C0* c_th * phi**(c_th-1)
return C, Cp
def calc_D(phi,D0,d_th,model='POWER'):
if model == 'EXPON':
D = D0 * np.exp(d_th*phi)
Dp = d_th * D
elif model == 'POWER':
D = D0 * phi**d_th
Dp = 0 if d_th==0 else D0 * d_th * phi**(d_th-1)
return D, Dp
############ Rescaled Field Equation ############
def calc_grad(phi,x_axis):
norm = (1.-np.arange(len(phi))/float(N))**2/(x_axis[1]-x_axis[0])
grad = np.zeros(phi.shape)
grad[1:-1] = 0.5*(phi[2:]-phi[:-2])
grad[0] = 0 # boundary
grad[-1] = 0 # boundary
return grad * norm
def calc_lap(phi,x_axis):
norm = (1.-np.arange(len(phi))/float(N))**2/(x_axis[1]-x_axis[0])
lap = np.zeros(phi.shape)
lap[1:-1] = (phi[2:] + phi[:-2] - 2.*phi[1:-1]) + (phi[2:]-phi[:-2])/(np.arange(len(phi)-2)+1)
lap[0] = (phi[1] - 1.*phi[0]) # boundary
lap[-1] = (phi[-2] - 1.*phi[-1]) # boundary
return lap*(norm**2)
def calc_deriv(y,eqn_params):
# unpacking
phi,dot = y
if len(eqn_params)==4:
eqn_params.append('POWER')
C0,c_th,D0,d_th,model = eqn_params
# quantities
C,Cp = calc_C(phi,C0,c_th,model)
D,Dp = calc_D(phi,D0,d_th,model)
grad = calc_grad(phi,x_axis)
lap = calc_lap(phi,x_axis)
X = 0.5*(dot**2 - grad**2)
rho_E = np.zeros(rho_J.shape)
rho_E[(1.-2.*D*X/C)>=0] = (rho_J * C**3)[(1-2*D*X/C)>=0] * np.sqrt((1.-2.*D*X/C)[(1.-2.*D*X/C)>=0])
# equation terms
mathcalD = (C - D*(dot**2 - grad**2))
Q1 = lap * mathcalD
Q2 = rho_E * (Cp/2. + ((Cp/C)*D - Dp/2.)*(dot**2))
Q3 = mathcalD + D*rho_E
# check conditions
## TODO: avoid using global variable
if np.any(C<0) or np.any(Q3<0):
cauthy_sanity = False
return 1;
else:
cauthy_sanity = True
dot = dot
dot2 = (Q1 + Q2) / Q3
derivs = [dot,dot2]
return np.array(derivs)
############ Evolution methods ################
def get_next_Euler(val_old,dt,eqn_params):
val_old = np.array(val_old)
return val_old + dt * calc_deriv(val_old,eqn_params)
def get_next_RK4(val_old,dt,eqn_params,return_D=False):
val_old = np.array(val_old)
k1 = val_old + 0.5*dt*calc_deriv(val_old,eqn_params)
k2 = val_old + 0.5*dt*calc_deriv(k1,eqn_params)
k3 = val_old + dt*calc_deriv(k2,eqn_params)
k4 = dt*calc_deriv(k3,eqn_params)
return (k1 + 2*k2 + k3)/3 + k4/6 - val_old/3
############# simulator (no gui) #############
def simulate(C0,c_th,D0,d_th,ti,tf,dt,save_interval=0.5,
method='RK4',model='POWER'):
# initialize
N,L,dt,x_axis,R_mass,M,rho_1,rho_0,rho_J,phi_0_array,dot_0_array,y0 = initialize()
eqn_params = [C0,c_th,D0,d_th,model]
val = y0
# initial values
t = 0
cauthy_sanity = True
phi_list = [phi_0_array]
dot_list = [dot_0_array]
t_list = [t]
## main loop
t_precision = int(abs(np.log10(dt))+1)
save_counter = 0
while (t<=tf and cauthy_sanity):
if (t%save_interval <= 10**(-t_precision)) or \
(abs(t%save_interval-save_interval) <= 10**(-t_precision)) : #save_interval:
print(f'\rSimulating... t = {t:.1f}/{tf}',end='')
if t==0 or t==dt/2:
sim_dt = dt/2
else:
sim_dt = dt
t = np.around(t+sim_dt,t_precision)
if method=='Euler':
phi_new, dot_new = get_next_Euler(val,sim_dt,eqn_params)
if method=='RK4':
phi_new, dot_new = get_next_RK4(val,sim_dt,eqn_params)
if (t%save_interval <= 10**(-t_precision)) or \
(abs(t%save_interval-save_interval) <= 10**(-t_precision)) : #save_interval:
t_list.append(t)
phi_list.append(phi_new)
dot_list.append(dot_new)
val = [phi_new,dot_new]
t_list = np.array(t_list)
phi_list = np.array(phi_list)
dot_list = np.array(dot_list)
return phi_list,dot_list,t_list
def plot(x_axis,phi,t,N_plots=10,fig=None,ax=None,cmap='winter_r',figsize=(8,6),
xlim=(1e-4,1),xlabel=r'$\tilde{r}$',ylabel=r'$\tilde\phi$',yscale='linear',return_axes=False,
return_norm=False,add_colorbar=True):
if ax == None and fig==None:
fig,ax = plt.subplots(1,1,figsize=figsize,dpi=100)
elif ax==None or fig==None:
raise ValueError('When axis is specified, both fig and ax need to be provided.')
cm = plt.get_cmap(cmap)
for j,i in enumerate(range(0,len(t),int((len(t)-1)/N_plots))):
ax.plot(x_axis,phi[i],c=cm(j/N_plots))
ax.set_xlim(xlim)
ax.set_xscale('log')
ax.set_xlabel(xlabel)
ax.set_ylabel(ylabel)
ax.set_yscale(yscale)
# colorbar
norm = mpl.colors.Normalize(vmin=t[0], vmax=np.round(t[-1]))
if add_colorbar:
divider = make_axes_locatable(ax)
ax_cb = divider.new_horizontal(size="5%", pad=0.05)
cb1 = mpl.colorbar.ColorbarBase(ax_cb, cmap=cm, norm=norm,orientation='vertical')
cb1.ax.set_title(r'$\tilde{t}$')
fig.add_axes(ax_cb)
if return_norm:
return norm
if return_axes:
return ax,ax_cb
def calc_Drho(phi,dot,eqn_params):
C0,c_th,D0,d_th,model = eqn_params
# quantities
C,Cp = calc_C(phi,C0,c_th,model)
D,Dp = calc_D(phi,D0,d_th,model)
grad = calc_grad(phi,x_axis)
X = 0.5*(dot**2 - grad**2)
rho_E = np.zeros(rho_J.shape)
rho_E[(1.-2.*D*X/C)>=0] = (rho_J * C**3)[(1-2*D*X/C)>=0] * np.sqrt((1.-2.*D*X/C)[(1.-2.*D*X/C)>=0])
return D*rho_E
def calc_mathcalD(phi,dot,eqn_params):
C0,c_th,D0,d_th,model = eqn_params
# quantities
C,Cp = calc_C(phi,C0,c_th,model)
D,Dp = calc_D(phi,D0,d_th,model)
grad = calc_grad(phi,x_axis)
X = 0.5*(dot**2 - grad**2)
rho_E = np.zeros(rho_J.shape)
rho_E[(1.-2.*D*X/C)>=0] = (rho_J * C**3)[(1-2*D*X/C)>=0] * np.sqrt((1.-2.*D*X/C)[(1.-2.*D*X/C)>=0])
# equation terms
mathcalD = (C - D*(dot**2 - grad**2))
return mathcalD
############ plotter ###############
def simulate_fancy(source_phi,source_dot,C0,c_th,D0,d_th,ti,tf,dt,\
fig_list,num_plot=10,title="No Title",method='RK4'):
# initialize
N,L,dt,x_axis,R_mass,M,rho_1,rho_0,rho_J,phi_0_array,dot_0_array,y0 = initialize()
p1,p2,p3,p4 = fig_list
eqn_params = [C0,c_th,D0,d_th,'POWER']
plot_interval = (tf-ti) /num_plot
val = y0
print('Eqn_params:',eqn_params)
# prepare color map
cm = []
cm_LG = []
plt_cm = plt.get_cmap('winter')
for i in range(num_plot+1):
r,g,b,_ = 255*np.array(plt_cm(i/(num_plot)))
cm.append("#%02x%02x%02x" % (int(r), int(g), int(b)))
# initial values
cauthy_sanity = True
t = 0
source_phi.stream({'x':[list(x_axis)],
'y':[list(phi_0_array)],
'labels':['t = 0'],
'color':[cm[int(0/tf*num_plot)]]})
source_dot.stream({'x':[list(x_axis)],
'y':[list(dot_0_array)],
'labels':['t = 0'],
'color':[cm[int(0/tf*num_plot)]]})
## plot initial values
t_precision = 10**(-1*int(abs(np.log10(dt))+1))
phi_LG = []
dot_LG = []
t_list = []
print(f'\rSimulating... t = {t:.1f}/{tf}',end='')
while (t<=tf and cauthy_sanity):
if t==0 or t==dt/2:
sim_dt = dt/2
else:
sim_dt = dt
t = np.around(t+sim_dt,int(abs(np.log10(dt))+1))
if method=='Euler':
phi_new, dot_new = get_next_Euler(val,sim_dt,eqn_params)
if method=='RK4':
phi_new, dot_new = get_next_RK4(val,sim_dt,eqn_params)
# save occasionally
shouldSave = (t%plot_interval <= t_precision) or \
(abs(t%plot_interval-plot_interval) <= t_precision)
if shouldSave:
print(f'\rSimulating... t = {t:.1f}/{tf}',end='')
label = 't = {:.2f}'.format(t)
source_phi.stream({'x':[list(x_axis)],
'y':[list(phi_new)],
'labels':[label],
'color':[cm[int(t/tf*num_plot)]]})
source_dot.stream({'x':[list(x_axis)],
'y':[list(dot_new)],
'labels':[label],
'color':[cm[int(t/tf*num_plot)]]})
phi_LG.append('' if np.isnan(phi_new[0]/phi_new[-1]) else phi_new[0]/phi_new[-1])
dot_LG.append('' if np.isnan(dot_new[0]/dot_new[-1]) else dot_new[0]/dot_new[-1])
t_list.append(t)
val = [phi_new,dot_new]
# LG plot
# TODO: change this to the ColumnDataSource so that all-reset function can be added
for j in range(len(phi_LG)):
r,g,b,_ = 255*np.array(plt_cm(j/len(phi_LG)))
cm_LG.append("#%02x%02x%02x" % (int(r), int(g), int(b)))
p3.line(t_list,phi_LG)
p3.circle(t_list,phi_LG,size=1,color=cm_LG,legend_label=title)
p4.line(t_list,dot_LG)
p4.circle(t_list,dot_LG,size=1,color=cm_LG,legend_label=title)
# phi & dot plot
r1 = p1.multi_line('x','y',legend_field='labels',line_color='color',\
line_width=1.5,source=source_phi)
r2 = p2.multi_line('x','y',legend_field='labels',line_color='color',\
line_width=1.5,source=source_dot)
# formatting
#####################################
## TODO: make legends individual
##legend_list_1 = []
##legend_list_2 = []
##for i in range(num_plot):
## legend_list_1.append(LegendItem(label=source_phi.data['labels'][i],\
## renderers=[r1],index=i))
## legend_list_2.append(LegendItem(label=source_dot.data['labels'][i],\
## renderers=[r2],index=i))
##p1.add_layout(Legend(items=legend_list_1),'right')
##p2.add_layout(Legend(items=legend_list_2))
#####################################
p1.legend.click_policy="hide"
p2.legend.click_policy="hide"
p3.legend.click_policy="hide"
p4.legend.click_policy="hide"
for p in [p1,p2]:
p.x_range.start = x_axis[1]
p.x_range.end = x_axis[-1]
# for p in [p1,p2,p3,p4]:
# p.x_range.start = None
# p.x_range.end = None
# p.y_range.start = None
# p.y_range.end = None
print('\nSimulation Completed')
########### wrapping GUI ###########
def start_gui():
#### internally called functions ####
def generate_figs():
p1 = figure(plot_width=1200,plot_height=900, title="phi", x_axis_label='r',x_axis_type='log')
p2 = figure(plot_width=1200,plot_height=900, title="dot", x_axis_label='r',x_axis_type='log')
p3 = figure(plot_width=1200,plot_height=900, title="phi Local / Global", x_axis_label='t')
p4 = figure(plot_width=1200,plot_height=900, title="dot Local / Global", x_axis_label='t')
p1.sizing_mode = 'stretch_both'
p2.sizing_mode = 'stretch_both'
p3.sizing_mode = 'stretch_both'
p4.sizing_mode = 'stretch_both'
# TODO: make plot width responsive
return p1,p2,p3,p4
def switch_plot():
plot_shown.children[0] = fig_list[plot_selector.active]
def refresh_plot():
# temporary bug fix: newly generated plot is broken without this
plot_shown.children[0] = dummy_fig
plot_shown.children[0] = fig_list[plot_selector.active]
def start_click():
print('Run clicked, simulating...')
title = title_input.value
C0 = float(C0_input.value)
D0 = float(D0_input.value)
c_th = float(c_th_input.value)
d_th = float(d_th_input.value)
ti = float(ti_input.value)
tf = float(tf_input.value)
dt = float(dt_input.value)
N_plot = int(N_plot_input.value)
simulate_fancy(source_phi,source_dot,\
C0=C0,c_th=c_th,D0=D0,d_th=d_th,ti=ti,tf=tf,fig_list=fig_list,\
dt=dt,num_plot=N_plot,title=title,method='RK4')
refresh_plot()
def clear_plot():
source_phi.data = {k: [] for k in source_phi.data}
source_dot.data = {k: [] for k in source_dot.data}
refresh_plot()
def reset_fig():
return 0
# TODO: add a function to reset without restarting the window
#fig_list = generate_figs()
#p1,p2,p3,p4 = fig_list
def legend_showhide():
Labels = ['Hide Legend','Show Legend']
status = legend_switch.active
print(status)
legend_switch.label=Labels[status]
for p in fig_list:
p.legend.visible=False if status else True
#### generate gui ####
# figures (tabs)
dummy_fig = figure(plot_width=1200,plot_height=900,sizing_mode='stretch_both')
fig_list = generate_figs()
p1,p2,p3,p4 = fig_list
plot_shown = row(children=[p1],sizing_mode='stretch_both')
# data for phi & dot
source_phi = ColumnDataSource(data=dict(x=[], y=[], labels=[], color=[]))
source_dot = ColumnDataSource(data=dict(x=[], y=[], labels=[], color=[]))
# User inputs
title_input = TextInput(value="Title",title="Title",sizing_mode='stretch_both')
C0_input = TextInput(value="1e-2",title="C0",sizing_mode='stretch_both')
D0_input = TextInput(value="0",title="D0",sizing_mode='stretch_both')
c_th_input = TextInput(value="1",title="c_th",sizing_mode='stretch_both')
d_th_input = TextInput(value="0",title="d_th",sizing_mode='stretch_both')
ti_input = TextInput(value="0",title="ti",sizing_mode='stretch_both')
tf_input = TextInput(value="1",title="tf",sizing_mode='stretch_both')
dt_input = TextInput(value="0.0001",title="dt",sizing_mode='stretch_both')
N_plot_input = TextInput(value='10',title='Number of Plotted Lines',sizing_mode='stretch_both')
# button, selector
start_button = Button(label='Run',button_type="success",sizing_mode='scale_both')
clear_button = Button(label='Clear',button_type='warning',sizing_mode='scale_both')
legend_switch = Toggle(label='Hide Legend',button_type='primary',sizing_mode='scale_both')
#reset_button = Button(label='Reset All',button_type='warning',sizing_mode='scale_both')
method_switch = RadioButtonGroup(labels=["RK4","Euler"],active=0,sizing_mode='scale_both')
plot_selector = RadioButtonGroup(\
labels=["Field (phi)","Velocity (dot)","Field Local/Global","Velocity Local/Global"],\
active=0,sizing_mode='scale_both')
# button behavior
start_button.on_click(start_click)
clear_button.on_click(clear_plot)
legend_switch.on_click(lambda new: legend_showhide())
#reset_button.on_click(reset_fig)
plot_selector.on_change('active',lambda attr,old,new: switch_plot())
# layout
cols = column([
row(title_input,sizing_mode='scale_width'),
row([C0_input,c_th_input],sizing_mode='scale_width'),
row([D0_input,d_th_input],sizing_mode='scale_width'),
row([ti_input,tf_input],sizing_mode='scale_width'),
row([dt_input,N_plot_input],sizing_mode='scale_width'),
row([method_switch,clear_button,legend_switch,start_button],sizing_mode='scale_width'),
row([plot_selector],sizing_mode='scale_width'),
plot_shown],
sizing_mode='stretch_both')
curdoc().add_root(cols)
def start_jupyter(doc):
#### internally called functions ####
def generate_figs():
p1 = figure(plot_width=1200,plot_height=600, title="phi", x_axis_label='r',x_axis_type='log')
p2 = figure(plot_width=1200,plot_height=600, title="dot", x_axis_label='r',x_axis_type='log')
p3 = figure(plot_width=1200,plot_height=600, title="phi Local / Global", x_axis_label='t')
p4 = figure(plot_width=1200,plot_height=600, title="dot Local / Global", x_axis_label='t')
p1.sizing_mode = "scale_width"
p2.sizing_mode = "scale_width"
p3.sizing_mode = "scale_width"
p4.sizing_mode = "scale_width"
# TODO: make plot width responsive
return p1,p2,p3,p4
def switch_plot():
plot_shown.children[0] = fig_list[plot_selector.active]
def refresh_plot():
# temporary bug fix: newly generated plot is broken without this
plot_shown.children[0] = dummy_fig
plot_shown.children[0] = fig_list[plot_selector.active]
def start_click():
print('Run clicked, simulating...')
title = title_input.value
C0 = float(C0_input.value)
D0 = float(D0_input.value)
c_th = float(c_th_input.value)
d_th = float(d_th_input.value)
ti = float(ti_input.value)
tf = float(tf_input.value)
dt = float(dt_input.value)
N_plot = int(N_plot_input.value)
simulate_fancy(source_phi,source_dot,\
C0=C0,c_th=c_th,D0=D0,d_th=d_th,ti=ti,tf=tf,fig_list=fig_list,\
dt=dt,num_plot=N_plot,title=title,method='RK4')
# refresh_plot()
def clear_plot():
source_phi.data = {k: [] for k in source_phi.data}
source_dot.data = {k: [] for k in source_dot.data}
refresh_plot()
def reset_fig():
return 0
# TODO: add a function to reset without restarting the window
#fig_list = generate_figs()
#p1,p2,p3,p4 = fig_list
def legend_showhide():
Labels = ['Hide Legend','Show Legend']
status = legend_switch.active
legend_switch.label=Labels[status]
for p in fig_list:
p.legend.visible=False if status else True
#### generate gui ####
# figures (tabs)
dummy_fig = figure(plot_width=1200,plot_height=900,sizing_mode='stretch_both')
fig_list = generate_figs()
p1,p2,p3,p4 = fig_list
plot_shown = row(children=[p1],sizing_mode='scale_width')
# data for phi & dot
source_phi = ColumnDataSource(data=dict(x=[], y=[], labels=[], color=[]))
source_dot = ColumnDataSource(data=dict(x=[], y=[], labels=[], color=[]))
# User inputs
title_input = TextInput(value="Title",title="Title",sizing_mode='stretch_both')
C0_input = TextInput(value="1e-2",title="C0",sizing_mode='stretch_both')
D0_input = TextInput(value="0",title="D0",sizing_mode='stretch_both')
c_th_input = TextInput(value="1",title="c_th",sizing_mode='stretch_both')
d_th_input = TextInput(value="0",title="d_th",sizing_mode='stretch_both')
ti_input = TextInput(value="0",title="ti",sizing_mode='stretch_both')
tf_input = TextInput(value="1",title="tf",sizing_mode='stretch_both')
dt_input = TextInput(value="0.0001",title="dt",sizing_mode='stretch_both')
N_plot_input = TextInput(value='10',title='Number of Plotted Lines',sizing_mode='stretch_both')
# button, selector
start_button = Button(label='Run',button_type="success",sizing_mode='scale_both')
clear_button = Button(label='Clear',button_type='warning',sizing_mode='scale_both')
legend_switch = Toggle(label='Hide Legend',button_type='primary',sizing_mode='scale_both')
#reset_button = Button(label='Reset All',button_type='warning',sizing_mode='scale_both')
method_switch = RadioButtonGroup(labels=["RK4","Euler"],active=0,sizing_mode='scale_both')
plot_selector = RadioButtonGroup(\
labels=["Field (phi)","Velocity (dot)","Field Local/Global","Velocity Local/Global"],\
active=0,sizing_mode='scale_both')
# button behavior
start_button.on_click(start_click)
clear_button.on_click(clear_plot)
legend_switch.on_click(lambda new: legend_showhide())
#reset_button.on_click(reset_fig)
plot_selector.on_change('active',lambda attr,old,new: switch_plot())
# layout
cols = column([
row(title_input,sizing_mode='scale_width'),
row([C0_input,c_th_input],sizing_mode='scale_width'),
row([D0_input,d_th_input],sizing_mode='scale_width'),
row([ti_input,tf_input],sizing_mode='scale_width'),
row([dt_input,N_plot_input],sizing_mode='scale_width'),
row([method_switch,clear_button,legend_switch,start_button],sizing_mode='scale_width'),
row([plot_selector],sizing_mode='scale_width'),
plot_shown],
sizing_mode='stretch_both')
doc.add_root(cols)
# if __name__=="__main__":
start_gui()