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Inconsistency in ODE solution using solve_ivp when adding events

I am using scipy.solve_ivp to solve an ODE in a loop, such that in every iteration I change some term in the ODE (which is like the force applied).
In terms of my problem - I just cant seem to understand why when I track events of zero crossing the solution sometimes stalls and essentially zeros out (as the figure below shows).
The code is a bit long, but only a small portion of it is actually relevant to my problem
(1) initialize some constants
MASS = 2.6e-4
WING_LENGTH = 0.07 # meters
GYRATION_RADIUS = 0.6 * WING_LENGTH
MoI = MASS * GYRATION_RADIUS ** 2 # Moment of Inertia
AIR_DENSITY = 1.2
WING_AREA = 0.5 * WING_LENGTH * (0.5 * WING_LENGTH) * np.pi # 1/2 ellipse with minor radios ~ 1/2 major = length/2
# drag coefficients from whitney & wood (JFM 2010):
C_D_MAX = 3.4
C_D_0 = 0.4
C_L_MAX = 1.8
ZERO_CROSSING = 1
RADIAN45 = np.pi / 4
RADIAN135 = 3 * RADIAN45
(2) Define a wrapper which is a RobotSimulation class - it's an easy interface that allows to easily change the values of the ODE. The important function is solve_dynamics (the others are not part of the problem I believe)
def phi_dot_zero_crossing_event(t, y):
"""
this event is given to solve_ivp to track if phi_dot == 0
:param t: unused time variable
:param y: a vector of [phi,phi_dot]
:return:
"""
return y[1]
class RobotSimulation:
def __init__(self, motor_torque=lambda x: 0, alpha=RADIAN45, phi0=0.0, phi_dot0=0.01, start_t=0, end_t=0.05, delta_t=0.001):
self.solution = 0
self.motor_torque = motor_torque
self.alpha = alpha # angle of attack
self.phi0 = phi0
self.phi_dot0 = phi_dot0
self.start_t = start_t
self.end_t = end_t
self.delta_t = delta_t
def set_time(self, new_start, new_end) -> None:
"""
we update the start time to be the end of the prev time and the end time
as the last end time + the window size we wish
"""
self.start_t = new_start
self.end_t = new_end
def set_init_cond(self, new_phi0, new_phi_dot0) -> None:
"""
we update the initial conditions to be the last value of previous iterations
"""
self.phi0 = new_phi0
self.phi_dot0 = new_phi_dot0
def set_motor_torque(self, new_motor_torque) -> None:
"""
sets the moment to the new value
"""
self.motor_torque = new_motor_torque
def flip_alpha(self) -> None:
"""
(Irrelevant for my question) changes the angle of attack's sign
:return:
"""
self.alpha = RADIAN135 if self.alpha == RADIAN45 else RADIAN45
def c_drag(self) -> float:
"""
calculates the drag coefficient based on the angle of attack
"""
return (C_D_MAX + C_D_0) / 2 - (C_D_MAX - C_D_0) / 2 * np.cos(2 * self.alpha)
def drag_torque(self, phi_dot):
"""
the drag moment
"""
return 0.5 * AIR_DENSITY * WING_AREA * self.c_drag() * GYRATION_RADIUS * phi_dot * np.abs(phi_dot)
def phi_derivatives(self, t, y):
"""
A function that defines the ODE that is to be solved: I * phi_ddot = tau_z - tau_drag.
We think of y as a vector y = [phi,phi_dot]. the ode solves dy/dt = f(y,t)
:return:
"""
phi, phi_dot = y[0], y[1]
dy_dt = [phi_dot, (self.motor_torque(t) - self.drag_torque(phi_dot)) / MoI]
return dy_dt
def solve_dynamics(self, phiarr, phidotarr, phiddotarr, angarr, torquearr):
"""
solves the ODE
:return:
"""
phi_0, phi_dot_0 = self.phi0, self.phi_dot0
start_t, end_t, delta_t = self.start_t, self.end_t, self.delta_t
phi_dot_zero_crossing_event.terminal = True
ang = []
times_between_zero_cross = []
sol_between_zero_cross = []
while start_t < end_t:
torquearr.append(self.motor_torque(start_t))
sol = solve_ivp(self.phi_derivatives, t_span=(start_t, end_t), y0=[phi_0,phi_dot_0],events=phi_dot_zero_crossing_event)
self.solution = sol.y
ang.append(self.alpha * np.ones(len(sol.t))) # set alpha for every t based on solution's size
times_between_zero_cross.append(sol.t)
sol_between_zero_cross.append(sol.y)
if sol.status == ZERO_CROSSING:
start_t = sol.t[-1] + delta_t
phi_0, phi_dot_0 = sol.y[0][-1], sol.y[1][-1] # last step is now initial value
self.flip_alpha()
else: # no zero crossing
break
time = np.concatenate(times_between_zero_cross)
phi, phi_dot = np.concatenate(sol_between_zero_cross, axis=1)
ang = np.concatenate(ang)
_, phi_ddot = self.phi_derivatives(time, [phi, phi_dot])
phiarr.append(phi)
phidotarr.append(phi_dot)
phiddotarr.append(phi_ddot)
angarr.append(ang)
(3) Finally the main function calls solve_dynamics sequentially for different values of actions and updates the time window and initial conditions:
phi_arr, phi_dot_arr, phi_ddot_arr, angarr, torquearr = [], [], [], [], []
phi0, phidot0 = 0, 0.01
start_t, end_t, delta_t = 0, 0.05, 0.001
sim = RobotSimulation()
for action in [1, -1, 1, -1, 1, -1]:
sim.set_motor_torque(lambda x: action)
sim.solve_dynamics(phi_arr, phi_dot_arr, phi_ddot_arr, angarr, torquearr)
phi0, phidot0 = sim.solution[0][-1], sim.solution[1][-1]
start_t = end_t
end_t += 0.05
sim.set_init_cond(phi0, phidot0)
sim.set_time(start_t, end_t)
phi_arr = np.concatenate(phi_arr)
phi_dot_arr = np.concatenate(phi_dot_arr)
phi_ddot_arr = np.concatenate(phi_ddot_arr)
angle_arr = np.concatenate(angarr)
Intuitively, as the actions I apply are just repeating +1 and -1, I cannot understand why the blue points in the figure (see below) act so different

Eventually, the problem was with how solve_ivp finds zero crossing points. It seems that the solution kept on finding the same crossings from + to - crossing every time (Thanks Lutz), so I've added a restriction using the .direction variable:
before entering the while loop: phi_dot_zero_crossing_event.direction = -np.sign(phi_dot_0). This makes sure we start by finding a crossing in the direction of the initial velocity.
when identifying an event in if sol.status == 1: I changed the sign of the direction with phi_dot_zero_crossing_event.direction *= -1

Need help understanding what this data analysis code (for optics lab) is doing

I am working in an undergraduate optics lab and we were given a few codes for data analysis. I need help understanding what two of them are doing exactly. To give some background on the experiment: light from a pulsed laser is injected into the back of a PTFE diffuser. Across from the diffuser is a photomultiplier tube that detects the optical signal. During the experiment, the diffuser is rotated and data is collected about the pulse waveform for every three degrees. I am just not sure what the code does to interpret this data, I hope that makes sense. Thank you in advance.
Here is the first code:
import numpy as np
DEFAULT_FMAX = 0.2
class Waveform(object):
def __init__(self, X, Y, fmax=None, peaknorm=False, areanorm=False):
self.X = np.copy(X)
self.Y = np.copy(Y)
if fmax is not None:
self.lowpass_filter(fmax)
if peaknorm:
self.normalise_peak()
if areanorm:
self.normalise_area()
def lowpass_filter(self, fmax):
# Fourier transform
freq_Y = np.fft.rfft(self.Y)
freq_X = np.fft.rfftfreq(self.Y.size, d=((max(self.X)-min(self.X))/self.Y.size))
# Apply max frequency cut
freq_Y[freq_X>fmax] = 0.0
# Inverse fourier transform
self.Y = np.fft.irfft(freq_Y)
def normalise_peak(self):
self.Y /= abs(np.min(self.Y))
def normalise_area(self):
self.Y /= np.sum(self.Y)
#property
def fft(self):
freq_Y = np.fft.rfft(self.Y)
freq_X = np.fft.rfftfreq(self.Y.size, d=((max(self.X)-min(self.X))/self.Y.size))
return freq_X, freq_Y
#property
def pedestal(self):
return np.mean(self.Y[0:100])
#property
def amplitude(self):
return abs(min(self.Y) - self.pedestal)
#property
def peak_index(self):
return np.argmin(self.Y)
#property
def peak_time(self):
return self.X[self.peak_index]
def _find_half_maxima_indices(self):
peak = self.peak_index
Y = np.copy(self.Y - self.pedestal)
Y += (self.amplitude / 2.0)
# find first half maximum
try:
first = np.argmax(Y[:peak] < 0)
except ValueError:
# can fail eg if peak == 0
first = peak
try:
second = peak + np.argmax(Y[peak:] > 0)
except ValueError:
# can fail eg if peak == last bin
second = peak
return first, second
#property
def fwhm(self):
return self.rise + self.fall
#property
def fall(self):
_, second = self._find_half_maxima_indices()
fall = self.X[second] - self.peak_time
return fall
#property
def rise(self):
first, _ = self._find_half_maxima_indices()
rise = self.peak_time - self.X[first]
return rise
#property
def integralindex_high(self):
pedestal = self.pedestal
#integrate falling edge
for ii in range(self.peak_index, self.Y.shape[0] - 1):
if (self.Y[ii] - pedestal) > 0.0:
break
return ii
#property
def integralindex_low(self):
pedestal = self.pedestal
#integrate falling edge
ii = 0
for ii in reversed(range(0, self.peak_index)):
if (self.Y[ii] - pedestal) > 0.0:
break
return ii
#property
def area(self):
area = 0.0
pedestal = self.pedestal
#integrate falling edge
for ii in range(self.peak_index, self.integralindex_high):
area += (self.Y[ii] - pedestal) * (self.X[ii + 1] - self.X[ii])
#integrate rising edge
for ii in reversed(range(self.integralindex_low, self.peak_index)):
area += (self.Y[ii] - pedestal) * (self.X[ii + 1] - self.X[ii])
return abs(area)
And the second:
import ROOT
import numpy as np
import datetime
from collections import namedtuple
from collections import defaultdict
from .waveform import Waveform
class ScanPoint:
def __init__(self, time_epoch, coord_angle, coord_y, lab_temp, lab_humid, dt, samples_PMT,
samples_PD, num_entry):
self.time_epoch = time_epoch
self.coord_angle = coord_angle
self.coord_y = coord_y
self.lab_temp = lab_temp
self.lab_humid = lab_humid
self.samples_PMT = np.array(list(samples_PMT), dtype=float)
self.samples_PD = np.array(list(samples_PD), dtype=float)
self.axis_time = np.arange(len(samples_PMT), dtype=float) * dt * 1.e9
self.num_entry = num_entry
def getWaveformPMT(self, fmax=None, peaknorm=False, areanorm=False):
return Waveform(self.axis_time, self.samples_PMT, fmax, peaknorm, areanorm)
def getWaveformPD(self, fmax=None, peaknorm=False, areanorm=False):
return Waveform(self.axis_time, self.samples_PD, fmax, peaknorm, areanorm)
def getDatetime(self):
return datetime.datetime.fromtimestamp(self.time_epoch)
# Tuple containing metadata and scanpoints for a full scan
DiffuserScan = namedtuple("DiffuserScan", ["ID_diffuser",
"ID_PMT",
"ID_PD",
"ID_lightsource",
"ID_experimentalist",
"notes",
"pulse_rate",
"pulse_N",
"scanpoints"])
def readscan(filename, treename):
file = ROOT.TFile.Open(filename, "READ")
tree = getattr(file, treename)
tree.GetEntry(0)
formatversion = (
int(tree.version_major),
int(tree.version_minor),
int(tree.version_patch),
)
# Check that input file format is implemented
if formatversion[:2] == (1, 0):
diffuserscan = DiffuserScan(
str(tree.ID_diffuser),
str(tree.ID_PMT),
str(tree.ID_PD),
str(tree.ID_lightsource),
str(tree.ID_experimentalist),
str(tree.notes),
float(tree.pulse_rate),
int(tree.pulse_N),
[],
)
for i, entry in enumerate(tree):
scanpoint = ScanPoint(entry.time_epoch,
entry.coord_angle,
entry.coord_y,
entry.lab_temp,
entry.lab_humid,
entry.dt,
entry.waveform_PMT,
entry.waveform_PD,
i)
diffuserscan.scanpoints.append(scanpoint)
else:
raise NotImplementedError("Input format version not implemented")
return diffuserscan
def combinefiles(scans):
combined_scan = scans[0]
compare_vars = ["ID_PMT", "ID_PD", "ID_lightsource", "pulse_rate", "pulse_N"]
for scan in scans[1:]:
combined_scan.scanpoints.extend(scan.scanpoints)
if scan.ID_diffuser != combined_scan.ID_diffuser:
combined_scan.ID_diffuser = "multi"
for var in compare_vars:
if getattr(scan, var) != getattr(combined_scan, var):
print('WARNING: Variable "{}" does not match between files! Should we be comparing
them?'.format(var))
return combined_scan

Propagated Solution of Lambert Solver Leads to Wrong Orbit

Excuse me for the length of the title please but this is a pretty specific question. I'm currently simulating a launch of a rocket to mars in the 2022 launch window and I noticed that my rocket is a far distance away from Mars, even though it's traveling in the right direction. After simplifying my code to narrow down the problem, I simply plotted the orbits of the Earth and Mars (Using data from NASA's SPICE library) and propagated the position and velocity given to me by the lambert solver I implemented (Universal variables) to plot the final orbit of the rocket.
I'm only letting the Sun's gravity effect the rocket, not the Earth or Mars, to minimize my problem space. Yet even though I've simplified my problem so far, the intersection between Mars' and my rocket's orbits happens well before the time of flight has been simulated all the way, and the minimum distance between the two bodies is more than a million kilometers at all times.
That being said, something must be wrong but I cannot find the problem. I've made sure the lambert solver code I copied is correct by comparing it to Dario Izzo's method and both gave the same results. Furthermore, I've also checked that my orbit propagator works by propagating Mars' and the Earth's orbits and comparing those ellipses to the data from SPICE.
In conclusion, I assume this must be a stupid little mistake I made somewhere, but cannot find because I lack experience in this field. Thank you for any help! :)
This is the JupyterLab notebook I used:
import numpy as np
import matplotlib.pyplot as plt
import json
import math
import spiceypy as spice
# Physics
G = 6.6741e-11
class Entity:
def __init__(self, x, v, m, do_gravity):
self.x = x
self.v = v
self.a = np.array([0,0,0])
self.m = m
self.do_gravity = do_gravity
def apply_force(self, f):
self.a = np.add(self.a, f / self.m);
def step(self, dt):
self.v = np.add(self.v, self.a * dt)
self.x = np.add(self.x, self.v * dt)
self.a = np.array([0,0,0])
class StaticEntity(Entity):
def __init__(self, body, t, do_gravity):
super().__init__(self.get_state(body, t)[:3], self.get_state(body, t)[3:], self.get_mass(body), do_gravity)
self.body = body
self.t = t
def step(self, dt):
self.t += dt
state = self.get_state(self.body, self.t)
self.x = state[:3]
self.v = state[3:]
#classmethod
def get_state(self, body, t):
[state, lt] = spice.spkezr(body, t, "J2000", "NONE", "SSB")
return state * 1000
#classmethod
def get_mass(self, body):
[dim, gm] = spice.bodvrd(body, "GM", 1)
return gm * 1e9 / G
def get_position(self, t):
return self.get_state(self.body, t)[:3]
def get_velocity(self, t):
return self.get_state(self.body, t)[3:]
class Propagator:
def __init__(self, entities):
self.entities = entities
def step(self, dt):
for e1 in self.entities:
for e2 in self.entities:
if (e1 is e2) or (not e1.do_gravity) or isinstance(e2, StaticEntity):
continue
diff = np.subtract(e1.x, e2.x)
fg = G * e1.m * e2.m / np.dot(diff, diff)
force = fg * diff / np.linalg.norm(diff)
e2.apply_force(force)
for entity in self.entities:
entity.step(dt)
# Lambert solver
def C2(psi):
if psi >= 0.0:
sp = math.sqrt(psi)
return (1 - math.cos(sp)) / psi
else:
sp = math.sqrt(-psi)
return (1 - math.cosh(sp)) / psi
def C3(psi):
if psi >= 0.0:
sp = math.sqrt(psi)
return (sp - math.sin(sp)) / (psi * sp)
else:
sp = math.sqrt(-psi)
return (sp - math.sinh(sp)) / (psi * sp)
def lambert_solve(r1, r2, tof, mu, iterations, tolerance):
R1 = np.linalg.norm(r1)
R2 = np.linalg.norm(r2)
cos_a = np.dot(r1, r2) / (R1 * R2)
A = math.sqrt(R1 * R2 * (1.0 + cos_a))
sqrt_mu = math.sqrt(mu)
if A == 0.0:
return None
psi = 0.0
psi_lower = -4.0 * math.pi * math.pi
psi_upper = 4.0 * math.pi * math.pi
c2 = 1.0 / 2.0
c3 = 1.0 / 6.0
for i in range(iterations):
B = R1 + R2 + A * (psi * c3 - 1.0) / math.sqrt(c2)
if A > 0.0 and B < 0.0:
psi_lower += math.pi
B = -B
chi = math.sqrt(B / c2)
chi3 = chi * chi * chi
tof_new = (chi3 * c3 + A * math.sqrt(B)) / sqrt_mu
if math.fabs(tof_new - tof) < tolerance:
f = 1.0 - B / R1
g = A * math.sqrt(B / mu)
g_dot = 1.0 - B / R2
v1 = (r2 - f * r1) / g
v2 = (g_dot * r2 - r1) / g
return (v1, v2)
if tof_new <= tof:
psi_lower = psi
else:
psi_upper = psi
psi = (psi_lower + psi_upper) * 0.5
c2 = C2(psi)
c3 = C3(psi)
return None
# Set up solar system
spice.furnsh('solar_system.tm')
inject_time = spice.str2et('2022 Sep 28 00:00:00')
exit_time = spice.str2et('2023 Jun 1 00:00:00')
sun = StaticEntity("Sun", inject_time, True)
earth = StaticEntity("Earth", inject_time, False)
mars = StaticEntity("Mars Barycenter", inject_time, False)
(v1, v2) = lambert_solve(earth.get_position(inject_time), mars.get_position(exit_time), exit_time - inject_time, G * sun.m, 1000, 1e-4)
rocket = Entity(earth.x, v1, 100000, False)
propagator = Propagator([sun, earth, mars, rocket])
# Generate data
earth_pos = [[], [], []]
mars_pos = [[], [], []]
rocket_pos = [[], [], []]
t = inject_time
dt = 3600 # seconds
while t < exit_time:
propagator.step(dt)
earth_pos[0].append(earth.x[0])
earth_pos[1].append(earth.x[1])
earth_pos[2].append(earth.x[2])
mars_pos[0].append(mars.x[0])
mars_pos[1].append(mars.x[1])
mars_pos[2].append(mars.x[2])
rocket_pos[0].append(rocket.x[0])
rocket_pos[1].append(rocket.x[1])
rocket_pos[2].append(rocket.x[2])
t += dt
# Plot data
plt.figure()
plt.title('Transfer orbit')
plt.xlabel('x-axis')
plt.ylabel('y-axis')
plt.plot(earth_pos[0], earth_pos[1], color='blue')
plt.plot(mars_pos[0], mars_pos[1], color='orange')
plt.plot(rocket_pos[0], rocket_pos[1], color='green')
EDIT:
I recently remodeled my code so that it uses orbit class to represent the entities. This actually gave me acceptable results, even though the code is, in theory, not doing anything differently (as far as I can tell; obviously something must be different)
def norm(a):
return np.dot(a, a)**0.5
def fabs(a):
return -a if a < 0 else a
def newton_raphson(f, f_dot, x0, n):
res = x0
for i in range(n):
res = res - f(res) / f_dot(res)
return res
def get_ephemeris(body, time):
state, _ = sp.spkezr(body, time, "J2000", "NONE", "SSB")
return np.array(state[:3]) * ap.units.km, np.array(state[3:]) * ap.units.km / ap.units.s
def get_mu(body):
_, mu = sp.bodvrd(body, "GM", 1)
return mu * ap.units.km**3 / ap.units.s**2
class orbit:
def __init__(self, position, velocity, mu):
self.position = position
self.velocity = velocity
self.mu = mu
#staticmethod
def from_body(name, center, time):
return static_orbit(name, center, time)
def get_ephemerides(self, t, dt):
time = 0
positions = []
velocities = []
#M = self.M
position = self.position
velocity = self.velocity
delta_t = dt * ap.units.s
t1 = t * ap.units.s
while time < t1:
g = self.mu / np.dot(position, position)
g_vec = g * -position / norm(position)
velocity = np.add(velocity, g_vec * delta_t)
position = np.add(position, velocity * delta_t)
positions.append(position)
velocities.append(velocity)
time = time + delta_t
return positions, velocities
class static_orbit(orbit):
def __init__(self, name, center, time):
p, v = get_ephemeris(name, time)
pc, vc = get_ephemeris(center, time)
super().__init__(p - pc, v - vc, get_mu(center))
self.name = name
self.center = center
self.time = time
def get_ephemerides(self, t, dt):
time = 0
positions = []
velocities = []
while time < t:
p, v = get_ephemeris(self.name, time + self.time)
pc, vc = get_ephemeris(self.center, time + self.time)
positions.append(p - pc)
velocities.append(v - vc)
time += dt
return positions, velocities
sp.furnsh('solar_system.tm')
t1 = sp.str2et('2022 Sep 28 00:00:00')
t2 = sp.str2et('2023 Jun 10 00:00:00')
eo = orbit.from_body("Earth", "Sun", t1)
mo = orbit.from_body("Mars Barycenter", "Sun", t1)
earth_x, earth_v = eo.get_ephemerides(t2 - t1, 3600)
mars_x, mars_v = mo.get_ephemerides(t2 - t1, 3600)
l = lambert(earth_x[0], mars_x[-1], t2 - t1, get_mu("Sun"), 1000, 1e-6)
ro = orbit(earth_x[0], l.v1, get_mu("Sun"))
rocket_x, rocket_v = ro.get_ephemerides(t2 - t1, 60)
earth_x = np.array(earth_x)
mars_x = np.array(mars_x)
rocket_x = np.array(rocket_x)
fig = go.Figure()
fig.add_trace(go.Scatter3d(x=earth_x[:,0], y=earth_x[:,1], z=earth_x[:,2], marker_size=1, marker_color='blue'))
fig.add_trace(go.Scatter3d(x=mars_x[:,0], y=mars_x[:,1], z=mars_x[:,2], marker_size=1, marker_color='orange'))
fig.add_trace(go.Scatter3d(x=rocket_x[:,0], y=rocket_x[:,1], z=rocket_x[:,2], marker_size=1, marker_color='green'))
fig.show()
This method generated following plot:
Also, before this is mentioned again, I have varied my integration step size and lambert solver tolerance to no avail, the result was qualitatively different.

So, I managed to figure out what the problem was after much head-scratching. I was simply not taking into account that the Sun is not located at (0,0,0) in my coordinate system. I thought this was negligible, but that is what made the difference. In the end, I simply passed the difference between the Earth and Mars's and the Sun's position vectors and passed those into the Lambert solver. This finally gave me the desired results.
The reason that the error ended up being so "small" (It didn't seem like an obvious bug at first) was because my coordinates are centered at the solar system barycenter which is a few million kilometers away from the Sun, as one would expect.
Thanks for the comments!

Scipy minimize constraint in pandas df

I am trying to run the minimization process found in this publication. The equation is seen on page 6 of the document 16 of the pdf.
I have a dataframe that looks like the below
df = pd.DataFrame({'h_t':[7.06398,6.29948,5.04570,6.20774,4.80106],
'p_atm':[101057.772801,101324.416001,101857.702401,101724.380801,101991.024001],
'q_p':[5.768132,3.825600,2.772215,5.830429,2.619304],
'q_s':[2.684433,3.403679,2.384275,1.008078,2.387106],
'tdg_f':[117.678100,110.131579,108.376963,103.669725,113.594771],
'tdg_tw':[121.052635,119.710907,114.921463,112.156868,115.444900],
'temp_water':[11.92,19.43,16.87,7.45,11.83]})
I have a constraint that says the below function must be positive where b1 and b3 are the coefficients I am optimizing.
def q_ge(q_p,q_s,b1,b3):
return min(q_p,(b1*q_s+b3))
I wrote my constraint below, but I am not sure if it is right.
def constraint_q_ge(x):
b1,b2,b3=x
power_flow = df.apply(lambda x:q_ge(x['q_p'],x['q_s'],b1,b3), axis = 1)
const = power_flow<0
return -const.sum()
Is this correct? I run the function on all rows and check if any are less than 0 and sum this. The negative of that sum should be greater than or equal to 0. If there is even a single value less than 0 this constraint is not met.
EDIT:
Below is the full problem.
from scipy.constants import g as gravity
from sklearn.metrics import mean_squared_error
from math import sqrt
from scipy.optimize import minimize
import warnings
try:
from numpy import any as _any
except ImportError:
def _any(arg):
if arg is True:
return True
if arg is False:
return False
return any(arg)
def water_density(T=None, T0=None, units=None, a=None,
just_return_a=False, warn=True):
if units is None:
K = 1
m = 1
kg = 1
else:
K = units.Kelvin
m = units.meter
kg = units.kilogram
if T is None:
T = 298.15*K
m3 = m**3
if a is None:
a = (-3.983035*K, # C
301.797*K, # C
522528.9*K*K, # C**2
69.34881*K, # C
999.974950*kg/m3)
if just_return_a:
return a
if T0 is None:
T0 = 273.15*K
t = T - T0
if warn and (_any(t < 0*K) or _any(t > 40*K)):
warnings.warn("Temperature is outside range (0-40 degC)")
return a[4]*(1-((t + a[0])**2*(t + a[1]))/(a[2]*(t + a[3])))
def celsius_to_kelvin(t_celsius):
return t_celsius+273.15
def tailwater(h_t, temp_water, p_atm):
t_water_kelvin = celsius_to_kelvin(temp_water)
rho = water_density(t_water_kelvin)
g = gravity
return (1+(rho*g*h_t)/(2*p_atm))
def tailwater_tdg(q_s,q_p,x, h_t,temp_water,p_atm,tdg_f):
b1,b2,b3=x
A = ((q_s+b1*q_s+b3)/(q_s+q_p))
B = tailwater(h_t, temp_water, p_atm)
C = ((q_p-b1*q_s-b3)/(q_s+q_p))
return 100*A*B*b2+tdg_f*C
def q_ge(q_p,q_s,b1,b3):
return min(q_p,(b1*q_s+b3))
def rmse(y, y_hat):
return sqrt(mean_squared_error(y,y_hat))
def objective(x):
y_hat = df.apply(lambda r:tailwater_tdg(q_s=r['q_s'],q_p=r['q_p'],x=x, h_t=r['h_t'],temp_water=r['temp_water'],p_atm=r['p_atm'],tdg_f=r['tdg_f']), axis = 1)
y = df['tdg_tw']
return rmse(y, y_hat)
#constraints and bounds for optimization model. See reference for more information
def constraint_q_ge(x):
b1,b2,b3=x
power_flow = df.apply(lambda x:q_ge(x['q_p'],x['q_s'],b1,b3), axis = 1)
const = power_flow<0
return -const.sum()
constraints = [{'type':'ineq', 'fun':constraint_q_ge}]
bounds = [(-500,10000),(.00001,10000),(-500,10000)]
x0=[1,1,1]
sol = minimize(objective, x0, method = 'SLSQP',constraints = constraints, bounds = bounds,options={'disp':True, 'maxiter':100})

python random mouse movements

I would like to make random mouse movements in specified rectangle area (limited with coordinates x1, y1, x2, y2, x3, y3, x4, y4).
Movements should be smooth, random, not just straight lines, go randomly up/down/left/right/etc for specified time duration.
Could you give me a hand or working example I can learn from?
many thanks

This code works on Windows only. You can experiment with the parameters inside the random_movement function to get better results. Good luck!
import ctypes
import random
import time
import math
def move_mouse(pos):
x_pos, y_pos = pos
screen_size = ctypes.windll.user32.GetSystemMetrics(0), ctypes.windll.user32.GetSystemMetrics(1)
x = 65536L * x_pos / screen_size[0] + 1
y = 65536L * y_pos / screen_size[1] + 1
return ctypes.windll.user32.mouse_event(32769, x, y, 0, 0)
def random_movement(top_left_corner, bottom_right_corner, min_speed=100, max_speed=200):
'''speed is in pixels per second'''
x_bound = top_left_corner[0], bottom_right_corner[0]
y_bound = top_left_corner[1], bottom_right_corner[1]
pos = (random.randrange(*x_bound),
random.randrange(*y_bound))
speed = min_speed + random.random()*(max_speed-min_speed)
direction = 2*math.pi*random.random()
def get_new_val(min_val, max_val, val, delta=0.01):
new_val = val + random.randrange(-1,2)*(max_val-min_val)*delta
if new_val<min_val or new_val>max_val:
return get_new_val(min_val, max_val, val, delta)
return new_val
steps_per_second = 35.0
while True:
move_mouse(pos)
time.sleep(1.0/steps_per_second)
speed = get_new_val(min_speed, max_speed, speed)
direction+=random.randrange(-1,2)*math.pi/5.0*random.random()
new_pos = (int(round(pos[0]+speed*math.cos(direction)/steps_per_second)),
int(round(pos[1]+speed*math.sin(direction)/steps_per_second)))
while new_pos[0] not in xrange(*x_bound) or new_pos[1] not in xrange(*y_bound):
direction = 2*math.pi*random.random()
new_pos = (int(round(pos[0]+speed*math.cos(direction)/steps_per_second)),
int(round(pos[1]+speed*math.sin(direction)/steps_per_second)))
pos=new_pos
Example:
random_movement((300,300),(600,600))

For random smooth movements constrained to a rectangle I'd try to use Lissajous curves with randomly changing coefficients.

Here is a demo of random X,Y positions you can play as your requirements:
from time import sleep
import pyautogui
import numpy as np
# Check your screen size
print(pyautogui.size())
count=0
while count<1000:
x=np.random.randint(1,1792)
y=np.random.randint(1,1120)
pyautogui.moveTo(x, y)
print(x)
print(y)
sleep(20)
count+=1
Note: install first
pip3 install pyautogui

I made this based on Piotr Dabkowski's code, with some extra features (taking random breaks, random scrolls, and users can end early by right clicking). This works for Python 3, and again, for Windows only.
import ctypes
import random
import time
import math
import win32gui
xmax = ctypes.windll.user32.GetSystemMetrics(0)
ymax = ctypes.windll.user32.GetSystemMetrics(1)
def get_position():
_, _, (x,y) = win32gui.GetCursorInfo()
return (x,y)
def move_mouse(pos):
x_pos, y_pos = pos
x = int(65536 * x_pos / xmax + 1)
y = int(65536 * y_pos / ymax + 1)
return ctypes.windll.user32.mouse_event(32769, x, y, 0, 0)
def start(t=30, min_speed=10, max_speed=500, x_bound=[0,xmax], y_bound=[0,ymax],
p_break = 0.005, break_range = (10, 60), p_scroll = 0.01, scroll_range = (100, 1000)):
def get_new_speed(min_val, max_val, val, delta=0.01):
new_val = val + random.randrange(-1,2)*(max_val-min_val)*delta
if new_val<min_val or new_val>max_val:
return get_new_speed(min_val, max_val, val, delta)
return new_val
steps_per_second = 35.0
print('Started.')
endtime = time.time() + int(t*60)
# Initialize position, speed and direction
pos = get_position()
speed = min_speed + random.random()*(max_speed-min_speed)
direction = 2*math.pi*random.random()
inside_boundary = False
right_clicked = False
# Keep moving mouse until end time, or until right click
while (not right_clicked) and (time.time() < endtime):
if ctypes.windll.user32.GetKeyState(0x02) not in [0,1]:
right_clicked = True
time.sleep(1.0/steps_per_second)
# Taking a break of random duration
duration = random.randint(*break_range) # in unit of seconds
break_endtime = time.time() + duration
r = random.random()
if (1-p_break) <= r < 1:
# Keep checking for right click to exit loop
while (not right_clicked) and (time.time() < break_endtime):
if ctypes.windll.user32.GetKeyState(0x02) not in [0,1]:
right_clicked = True
time.sleep(1.0/steps_per_second)
time_left = break_endtime - time.time()
print('Paused %d / %ds' % (time_left,duration) + ' '*50, end='\r')
pos = get_position()
print(' '*50, end='\r')
# Random scroll
r = random.random()
lines = random.randint(*scroll_range)
sign = random.random()
sign = -1 if sign < 0.5 else 1
if (1-p_scroll) <= r < 1:
time.sleep(random.random())
ctypes.windll.user32.mouse_event(2048, 0, 0, sign*lines, 0)
time.sleep(random.random())
pos = get_position()
# Random move
move_mouse(pos)
time_left = endtime - time.time()
print('Running (time left: %ds)' % time_left + ' '*50, end='\r')
if (pos[0] in range(*x_bound)) and (pos[1] in range(*y_bound)):
inside_boundary = True
# Update position, speed and direction
speed = get_new_speed(min_speed, max_speed, speed)
direction+=random.randrange(-1,2)*math.pi/5.0*random.random()
new_pos = (int(round(pos[0]+speed*math.cos(direction)/steps_per_second)),
int(round(pos[1]+speed*math.sin(direction)/steps_per_second)))
# Once mouse position is inside boundary, new position must also be inside
if inside_boundary:
while new_pos[0] not in range(*x_bound) or new_pos[1] not in range(*y_bound):
direction = 2*math.pi*random.random()
new_pos = (int(round(pos[0]+speed*math.cos(direction)/steps_per_second)),
int(round(pos[1]+speed*math.sin(direction)/steps_per_second)))
pos=new_pos
print('Stopped.' + ' ' * 50)

For performing the movements there is a third-party package call PyUserInput that will allow you to control mouse or keyboard, and it is cross-platform. Install it using pip:
$ pip install PyUserInput
For doing smooth movements you can try what 9000 proposes in his answer.