def test_shifted_exp_cos_inv_laplace_euler():
TOL = 1e-6
N = 1001
N = 101
omega = 4.0
a = 0.8
tshft = 1.5
delt = np.linspace(0.01,6,N)
t = delt+ tshft
yexact = np.exp(-a*(t-tshft))*np.cos(omega*(t-tshft))+1.0
yexact = np.exp(-a*(t-tshft))*np.cos(omega*(t-tshft))+1.0
yexact[t<tshft] = 0.0
lapfun0 = lambda s, a=a, omega=omega: \
np.exp(-s*tshft)*( (s+a)/((s+a)**2+omega**2) + 1.0/s )
# ynuminv = hsmix.inv_laplace_euler( lapfun0, t, tshft=0.0 )
ynuminv = hsmix.inv_laplace_euler( lapfun0, delt, tshft=tshft )
# NOTE nan value at first value
dely = ynuminv-yexact
dely = dely[~np.isnan(dely)]
#plt.clf()
#plt.plot(t,yexact,'r-',t,ynuminv,'k-')
assert np.all( np.abs(dely) < TOL ), \
'numerical inverse not within tolerance'
def test_invsqrt_cos_inv_laplace_euler():
TOL = 1e-6
t=np.linspace(0.1,20,100)
# Bessel function test (ringing oscillation)
lapfun0 = lambda s: 1.0/np.sqrt(s)*np.exp(-1.0/s)
ynuminv = hsmix.inv_laplace_euler( lapfun0, t, tshft=0.0 )
yexact = 1.0/np.sqrt(np.pi*t)*np.cos(np.sqrt(4*t))
assert np.all( np.abs(ynuminv-yexact) < TOL ), \
'numerical inverse not within tolerance'
def test_bessel_inv_laplace_euler():
TOL = 1e-6
t=np.linspace(1e-3,15,100)
# Bessel function test (ringing oscillation)
lapfun0 = lambda s: 1.0/np.sqrt(s**2+1)
ynuminv = hsmix.inv_laplace_euler( lapfun0, t, tshft=0.0 )
yexact = sp.special.jv(0,t)
assert np.all( np.abs(ynuminv-yexact) < TOL ), \
'numerical inverse not within tolerance'
def test_exp_cos_inv_laplace_euler():
TOL = 1e-6
t=np.linspace(0.1,20,100)
omega = 2.0
a = 1.0
# Bessel function test (ringing oscillation)
lapfun0 = lambda s, a=a, omega=omega: (s+a)/((s+a)**2+omega**2)
ynuminv = hsmix.inv_laplace_euler( lapfun0, t, tshft=0.0 )
yexact = np.exp(-a*t)*np.cos(omega*t)
assert np.all( np.abs(ynuminv-yexact) < TOL ), \
'numerical inverse not within tolerance'
def test_hard_sphere_PDF():
dHS = 1.0
test_hard_sphere_PDF( V, xHS, dHS, rmax=5.0, N=101 ):
N = 301
dHS = 1.0
V = 1.3
V = 3.
lapfun0 = lambda s, V=V, xHS=1.0, dHS=dHS:\
np.squeeze( hsmix.hard_sphere_LT_PDF( s, V, np.array([xHS]),
np.array([dHS]) ) )
delt = np.linspace(0.01,6,N)
ynuminv = hsmix.inv_laplace_euler( lapfun0, delt, tshft=dHS )
fpack = np.pi/6*dHS**3/V
lam0 = 2*np.pi/(1-fpack)
lam1 = np.pi**2*(dHS**2/V)/(1-fpack)**2
fpack = np.pi/6*dHS**3/V
zeta = fpack*dHS**3
((1-zeta) + 1.5*fpack*dHS**3)/(1.0-zeta)**2
gij_contact = hsmix.hard_sphere_contact_PDF( V, np.array([xHS]),
np.array([dHS]) )
hsmix.hard_sphere_PDF( V, xHS, dHS, rmax=5.0, N=101 ):
r = np.linspace(dHS, 6*dHS,100)
gij = hsmix.hard_sphere_PDF( r, V, np.array([xHS]), np.array([dHS]) )
gii =
gij = 1.0/(2*np.pi)*(lam0 + 0.5*lam1*dHS + 1.0/18*lam1**2/lam0*dHS**2)
# lapfun = lambda s: np.exp(s*tshft)*lapfun0(s)
# ynuminv = hsmix.nlinvsteh( lapfun, delt, n=10 )
plt.plot( delt+dHS, ynuminv/(delt+dHS), 'k-')
