def test_quadratic1():
'''
Check if area under quadratic function for Trap
Is approx equal to analytical solution
(A/3)(b^3 - a^3) + (B/2)(b^2-a^2) + C(b-a)
'''
A, B, C, a, b = 2, 4, 5, 0, 100
area1 = (A/3)*(b**3 + a**3) + (B/2)*(b**2 + a**2) + C*(b-a)
area2 = trap(quadraticfunc, 0, 100, 1000)
assert isclose(area1, area2) is True
def test_gensin1():
'''
Check if area under sin function for Trap
Is approx equal to analytical solution
sin(x) = cos(a) - cos(b)
'''
A, w, a, b = 2, 4, 0, 100
area1 = (A/w)*(cos(w*a) - cos(w*b))
area2 = trap(gensinfunc, 0, 100, 1000, A=A, w=w)
assert isclose(area1, area2, atol=0.05) is True
def test_genlinear1():
'''
Check if area under linear function for Trap
Is approx equal to analytical solution
(1/2)A(b^2 - a^2)+B(b-a)
'''
A, B, a, b = 3, 4, 0, 100
area1 = .5*A*(b**2 - a**2) + B*(b-a)
area2 = trap(genlinearfunc, 0, 100, 1000, A=A, B=B)
assert isclose(area1, area2) is True
def test_sin1():
'''
Check if area under sin function for Trap
Is approx equal to analytical solution
sin(x) = cos(a) - cos(b)
'''
a, b = 0, 100
area1 = cos(a) - cos(b)
area2 = trap(sinfunc, 0, 100, 1000)
assert isclose(area1, area2, atol=0.05) is True
def test_gensin2():
'''
Checks if area under curve computed for Trap func
Is approximately equal to Trapz function from Numpy
For f(x) = Asin(wx) - generalized
'''
xvector = range(100)
yvector = []
for i in xvector:
yvector.append(gensinfunc(i, A=2, w=3))
area1 = trapz(yvector, x=xvector)
x1, x2 = xvector[0], xvector[-1]
step = len(xvector)
area2 = trap(gensinfunc, x1, x2, step, A=2, w=3)
assert isclose(area1, area2, atol=0.05) is True
def test_genquadratic2():
'''
Checks if area under curve computed for Trap func
Is approximately equal to Trapz function from Numpy
For f(x) = ax + b - generalized
'''
xvector = range(100)
yvector = []
for i in xvector:
yvector.append(genquadraticfunc(i, A=2, B=2, C=2))
area1 = trapz(yvector, x=xvector)
x1, x2 = xvector[0], xvector[-1]
step = len(xvector)
area2 = trap(genquadraticfunc, x1, x2, step, A=2, B=2, C=2)
assert isclose(area1, area2) is True
def test_linear2():
'''
Checks if area under curve computed for Trap func
Is approximately equal to Trapz function from Numpy
For f(x) = ax + b
'''
xvector = range(100)
yvector = []
for i in xvector:
yvector.append(linearfunc(i))
area1 = trapz(yvector, x=xvector)
x1, x2 = xvector[0], xvector[-1]
step = len(xvector)
area2 = trap(linearfunc, x1, x2, step)
assert isclose(area1, area2) is True
Np, A, B, vs = 2, 4, 1, 1
theta1, theta2 = 90, 300
print 'No input given. Taking the default values!'
#theta1, theta2 = 90, 300
dim = 3 # dimensionality of the problem
eta = 1.0/6 # viscosity of the fluid simulated
a = 1 # radius of the particle
k = vs/A # stiffness of the trap
S0, D0 = 0.01, 0.01 # strength of the stresslet and potDipole
ljrmin, ljeps = 3, .01 # lennard-jones parameters
Tf, Npts = 400000, 5000 # final time and number of points
# instantiate the class trap for simulating active particles in a harmonic potential
rm = trap.trap(a, Np, vs, eta, dim, S0, D0, k, ljeps, ljrmin)
# module to initialise the system.
def initialConfig(rp0, trapCentre, theta, a, a0, vs, k, Np):
'''initialise the system'''
rr = np.pi*vs*a/k; #confinement radius
t1 = np.pi/180
if Np==1:
rp0[0], rp0[1], rp0[2] = 0, 0, 8 # particle 1 Position
rp0[3], rp0[4], rp0[5] = 0, 0, -1 # Orientation
elif Np==3:
t1 = np.pi/180
trapCentre[0] = 0
trapCentre[1] = a0
"""
Integral of (4 - x**2)**(1/2) from a = 0 and b = 2 computed by trapezoidal
rule
"""
import math as mt
from trap import trap
def f(x):
return (4 - x**2)**(1/2)
a = 0
b = 2
for n in range(0, 2):
er = 10. **(-n)
Inew = trap(f, a, b, tol = er)
print('tol=', er, 'Integral=', Inew)
tol= 1.0 Integral= (2.9957090681024408+0.75j)
tol= 0.1 Integral= (0.13601901796103003+0.001235730667189656j)
''' Parameters:
Np= number of particles, vs=active velocity,
k = spring constant of the trap, S0 = stresslet strength
A = vs/k; B = S0/k'''
try:
Np, A, B, vs = int(sys.argv[1]), float(sys.argv[2]), float(
sys.argv[3]), float(sys.argv[4])
except:
Np, A, B, vs = 100, 4, 1, 1
print 'No input given. Taking the default values!'
dim = 3 # dimensionality of the problem
eta = 1.0 / 6 # viscosity of the fluid simulated
a = 1 # radius of the particle
mu = 1 / (6 * np.pi * eta * a) # particle mobility
k = vs / A # stiffness of the trap
S0 = B * k # strength of the stresslet
D0 = 0.01
ljrmin, ljeps = 4.0, .01 # Lennard Jones Parameters
Tf, Npts = 8000, 2000 # Final time and number of points on which integrator returns the data
# instantiate the class trap for simulating active particles in a harmonic potential
rm = trap.trap(a, Np, vs, eta, dim, S0, D0, k, ljeps, ljrmin)
# initialise the system. Current version supports either Np=2 or initialization on a sphere or on a cube
rm.initialise('sphere')
# simulate the resulting system
rm.simulate(Tf, Npts)
import trap
a = -1
b = 1
h1 = 0.5
h2 = 0.25
qqq = trap.trap(a, b, h2)
print("F =")
print(qqq)
