def EMA(x, a, c, xa, xc, xsca, xscc, sigmaa, sigmac, b):
#c=f*c
#assume that xsca=xscc and sigmaa=sigmac
sqrt2 = np.sqrt(2.)
#print xa,xc,a,c,scdtm,fc
#print (xsc - x[0]) / xa, (sigmaa ** 2) / 2. / (xa ** 2), (xsc - x[0]) / xc, (sigmac ** 2) / 2. / (xc ** 2)
aexpterm = np.exp((xsca - x) / xa + (sigmaa**2) / 2. / (xa**2))
aexpterm[np.isinf(aexpterm) == True] = 0.
EMA1=0.5 * a * aexpterm \
* serfc((xsca - x) / sqrt2 / sigmaa + sigmaa / sqrt2 / xa)
if (np.absolute(a) < 1.e-20) | (np.absolute(sigmaa) < 1.e-20):
EMA1[:] = 0.
# in the case of gamma distribution
if np.absolute(xa - xc) / xa < 1.e-10:
tsterm = (x - xscc) / (sigmac**2) - 1. / xc
erfterm = serf((sigmac**2 - xc * (x - xscc)) / sqrt2 / sigmac / xc)
gausterm = np.exp(-1 * ((x - xscc)**2) / 2. / (sigmac**2))
convterm = sigmac**2 / 2. * tsterm * np.exp(
((sigmac * tsterm)**2) /
2.) * (1. - erfterm) + sigmac / sqrt2 / np.sqrt(np.pi)
outEMA = EMA1 + convterm * gausterm * c / xc + b
outEMA[np.isnan(outEMA)
| np.isinf(outEMA)] = EMA1[np.isnan(outEMA)
| np.isinf(outEMA)] + b
return outEMA
scdtm = c * xa / (xa - xc)
bexpterm = np.exp((xscc - x) / xa + (sigmac**2) / 2. / (xa**2))
bexpterm[np.isinf(bexpterm) == True] = 0.
EMA2 = 0.5 * scdtm *bexpterm \
* serfc((xscc - x) / sqrt2 / sigmac + sigmac / sqrt2 / xa)
cexpterm = np.exp((xscc - x) / xc + (sigmac**2) / 2. / (xc**2))
cexpterm[np.isinf(cexpterm) == True] = 0.
EMA3 = -0.5 * scdtm *cexpterm \
* serfc((xscc - x) / sqrt2 / sigmac + sigmac / sqrt2 / xc)
if (np.absolute(scdtm) < 1.e-20) | (np.absolute(sigmac) < 1.e-20):
EMA2[:] = 0.
EMA3[:] = 0.
return EMA1 + EMA2 + EMA3 + b
def EMALeft(x, a, xa, xsc, sigmaa):
sqrt2 = np.sqrt(2.)
#print xa,xc,a,c,scdtm,fc
#print (xsc - x[0]) / xa, (sigmaa ** 2) / 2. / (xa ** 2), (xsc - x[0]) / xc, (sigmac ** 2) / 2. / (xc ** 2)
return 0.5 * a* np.exp((xsc - x) / xa + (sigmaa ** 2) / 2. / (xa ** 2)) \
* serfc((xsc - x) /sqrt2 / sigmaa + sigmaa /sqrt2 / xa)
def EMG2D(x, y, a, x0, ux, uy, sigma, b, eta):
xp = x - ux
yp = y - uy
sqrt2 = np.sqrt(2.)
sigmay = np.zeros(x.shape) + sigma
sigmay = np.sqrt(sigma**2 + np.absolute(xp) * eta)
yfactor = np.exp(-0.5 * (yp**2) / (sigmay**2)) / sigmay
return a / 2 / np.sqrt(np.pi) / sqrt2 / x0 * np.exp(
sigma**2 / 2. / (x0**2) - xp / x0) * serfc(
(sigma / x0 - xp / sigma) / sqrt2) * yfactor + b
def EMARight(x, c, xa, xc, xsc, sigmac):
sqrt2 = np.sqrt(2.)
if (np.absolute(xc - xa) / xa < 0.0001):
xt = 0.
else:
xt = 1. / (1. / xc - 1. / xa)
scdtm = c * xt / xc
#return \
#0.5*scdtm* np.exp((xsc - x) / xa + (sigmaa ** 2) / 2. / (xa ** 2)) \
#* erfc((xsc - x) /sqrt2 / sigmaa + sigmaa /sqrt2 / xa) \
return -0.5 * scdtm * np.exp((xsc - x) / xc + (sigmac ** 2) / 2. / (xc ** 2))\
* serfc((xsc - x) /sqrt2 / sigmac + sigmac /sqrt2 / xc)
def EMAMiddle(x, c, xa, xc, xsc, sigmac):
sqrt2 = np.sqrt(2.)
if (np.absolute(xc - xa) / xa < 0.0001):
xt = 0.
else:
xt = 1. / (1. / xc - 1. / xa)
scdtm = c * xt / xc
# print xa,xc,a,c,scdtm,fc
# print (xsc - x[0]) / xa, (sigmaa ** 2) / 2. / (xa ** 2), (xsc - x[0]) / xc, (sigmac ** 2) / 2. / (xc ** 2)
return 0.5 * scdtm * np.exp((xsc - x) / xa + (sigmac ** 2) / 2. / (xa ** 2)) \
* serfc((xsc - x) /sqrt2 / sigmac + sigmac /sqrt2 / xa)
def EMG(x, a, x0, xsc, sigma, b, **kwargs):
sqrt2 = np.sqrt(2.)
if 'Gaussian' in kwargs:
return a / np.sqrt(2 * np.pi) / sigma * np.exp(-1 * (x**2) / 2 /
(sigma**2)) + b
# else:
# efct=sigma**2/(x-xsc)/x0
# ld=a / (1 + efct) * np.exp(-1 * (x - xsc) / x0 * (1 - 0.5 * efct)) + b
# ld[x<=xsc]=b
#
# return ld
else:
expterm = np.exp((xsc - x) / x0 + (sigma**2) / 2. / (x0**2))
expterm[
np.isinf(expterm) ==
True] = 0. #since erfc function in large exp term is very small
return 0.5 * a / x0 * expterm * serfc(
(xsc - x) / sqrt2 / sigma + sigma / sqrt2 / x0) + b