def getInverse(self, s):
"""
returns the value of the inverse of the mapping for s
"""
# self.logger.info("m0:"+str(log(s[0]**2+s[1]**2)/2))
return (log(s[0]**2 + s[1]**2) / 2 -
self.Mr) * [1., 0] + (atan2(s[1], s[0]) - self.Mi) * [0, 1.]
def createAbsorptionLayerFunction(x,
absorption_zone=300 * U.m,
absorption_cut=1.e-2,
top_absorption=False):
"""
Creates a distribution which is one in the interior of the domain of `x`
and is falling down to the value 'absorption_cut' over a margin of thickness 'absorption_zone'
toward each boundary except the top of the domain.
:param x: location of points in the domain
:type x: `escript.Data`
:param absorption_zone: thickness of the absorption zone
:param absorption_cut: value of decay function on domain boundary
:return: function on 'x' which is one in the iterior and decays to almost zero over a margin
toward the boundary.
"""
if absorption_zone is None or absorption_zone == 0:
return 1
dom = x.getDomain()
bb = escript.boundingBox(dom)
DIM = dom.getDim()
decay = -escript.log(absorption_cut) / absorption_zone**2
f = 1
for i in range(DIM):
x_i = x[i]
x_l = x_i - (bb[i][0] + absorption_zone)
m_l = escript.whereNegative(x_l)
f = f * ((escript.exp(-decay * (x_l * m_l)**2) - 1) * m_l + 1)
if top_absorption or not DIM - 1 == i:
x_r = (bb[i][1] - absorption_zone) - x_i
m_r = escript.whereNegative(x_r)
f = f * ((escript.exp(-decay * (x_r * m_r)**2) - 1) * m_r + 1)
return f
def getInverse(self, s):
"""
returns the value of the inverse of the mapping for s
"""
if not (inf(s) > self.s_min and sup(s) < self.s_max):
raise ValueError("s is out of range [%f,%f]" % (inf(s), sup(s)))
return 1.0 / 2.0 * log((s - self.s_min) / (self.s_max - s))
def getInverse(self, s):
"""
returns the value of the inverse of the mapping for s
"""
ms = whereZero(s)
ms0 = whereZero(self.__sigma0)
m = 1 / self.__a * log(((1 - ms) * s + ms * 1) / ((1 - ms0) * self.__sigma0 + ms0 * 1)) * (1 - ms) * (1 - ms0)
return m
def getInverse(self, s):
"""
returns the value of the inverse of the mapping for s
"""
if not (inf(s) > self.s_min and sup(s) < self.s_max):
raise ValueError("s is out of range [%f,%f]" % (inf(s), sup(s)))
return 1. / 2. * log((s - self.s_min) / (self.s_max - s))
def getInverse(self, s):
"""
returns the value of the inverse of the mapping for s
"""
# return (s-self.__sigma0) / (self.__sigma0 * self.__k)
if inf(((self.__sigma0 * self.a) / s)) <= 1.0:
raise ValueError("sigma 0*a/s < 1 this is not valid as log cannot be 0 or negative")
m = -1.0 / self.__k * log(((self.__sigma0 * self.a) / (s - self.minVal)) - 1)
print("inv(s)=", m)
return m
def getInverse(self, s):
"""
returns the value of the inverse of the mapping for s
"""
ms = whereZero(s)
ms0 = whereZero(self.__sigma0)
m = 1 / self.__a * log(
((1 - ms) * s + ms * 1) /
((1 - ms0) * self.__sigma0 + ms0 * 1)) * (1 - ms) * (1 - ms0)
return m
def __init__(self, V_prior, Q_prior):
"""
initializes the mapping
:param V_prior: a-priori p-wave velocity
:param Q_prior: a-priori Q-index (must be positive)
"""
over2Q = 1.0 / (2 * Q_prior)
# sigma_prior=1/(V_prior*(1-I*over2Q))**2 = 1/( V_prior * (1+over2Q**2)) **2 * ( (1-over2Q**2) + I * 2* over2Q )
self.Mr = log(sqrt((1 - over2Q ** 2) ** 2 + (2 * over2Q) ** 2) / (V_prior * (1 + over2Q ** 2)) ** 2)
self.Mi = atan2(2 * over2Q, 1 - over2Q ** 2)
def getInverse(self, s):
"""
returns the value of the inverse of the mapping for s
"""
# return (s-self.__sigma0) / (self.__sigma0 * self.__k)
if inf(((self.__sigma0 * self.a) / s)) <= 1.:
raise ValueError(
"sigma 0*a/s < 1 this is not valid as log cannot be 0 or negative"
)
m = -1. / self.__k * log(((self.__sigma0 * self.a) /
(s - self.minVal)) - 1)
print("inv(s)=", m)
return m
def __init__(self, V_prior, Q_prior):
"""
initializes the mapping
:param V_prior: a-priori p-wave velocity
:param Q_prior: a-priori Q-index (must be positive)
"""
over2Q = 1. / (2 * Q_prior)
# sigma_prior=1/(V_prior*(1-I*over2Q))**2 = 1/( V_prior * (1+over2Q**2)) **2 * ( (1-over2Q**2) + I * 2* over2Q )
self.Mr = log(
sqrt((1 - over2Q**2)**2 + (2 * over2Q)**2) / (V_prior *
(1 + over2Q**2))**2)
self.Mi = atan2(2 * over2Q, 1 - over2Q**2)
def getInverse(self, s):
"""
returns the value of the inverse of the mapping for s
"""
# self.logger.info("m0:"+str(log(s[0]**2+s[1]**2)/2))
return (log(s[0] ** 2 + s[1] ** 2) / 2 - self.Mr) * [1.0, 0] + (atan2(s[1], s[0]) - self.Mi) * [0, 1.0]
