def _dstable_sym_small(alpha, x, tolr):
"""
A series expansion for small x due to Bergstrom.
Converges for x < 1.0 and in practice also for
somewhat larger x.
The function uses the Kahan summation procedure
(cf. Dahlquist, Bjorck & Anderson).
"""
summ = 0.0
c = 0.0
fact = -1.0
xx = x * x
xpart = 1.0
k = 0
zero2 = zero1 = False
while True:
k += 1
summo = summ
twokm1 = 2 * k - 1
twokm1oa = float(twokm1) / alpha
r = lngamma(twokm1oa) - lnfactorial(twokm1)
term = twokm1 * exp(r) * xpart
fact = -fact
term *= fact
y = term + c
t = summ + y
if fsign(y) == fsign(summ):
f = (0.46 * t - t) + t
c = ((summ - f) - (t - f)) + y
else:
c = (summ - t) + y
summ = t
if abs(summ - summo) < tolr * abs(summ) and abs(term) < tolr and zero2:
break
xpart *= xx
if abs(term) < tolr:
if zero1: zero2 = True
else: zero1 = True
summ += c
pdf = summ / (PI * alpha)
pdf = kept_within(0.0, pdf)
return pdf
def _dstable_sym_small(alpha, x, tolr):
"""
A series expansion for small x due to Bergstrom.
Converges for x < 1.0 and in practice also for
somewhat larger x.
The function uses the Kahan summation procedure
(cf. Dahlquist, Bjorck & Anderson).
"""
summ = 0.0
c = 0.0
fact = -1.0
xx = x*x
xpart = 1.0
k = 0
zero2 = zero1 = False
while True:
k += 1
summo = summ
twokm1 = 2*k - 1
twokm1oa = float(twokm1)/alpha
r = lngamma(twokm1oa) - lnfactorial(twokm1)
term = twokm1 * exp(r) * xpart
fact = - fact
term *= fact
y = term + c
t = summ + y
if fsign(y) == fsign(summ):
f = (0.46*t-t) + t
c = ((summ-f)-(t-f)) + y
else:
c = (summ-t) + y
summ = t
if abs(summ-summo) < tolr*abs(summ) and abs(term) < tolr and zero2:
break
xpart *= xx
if abs(term) < tolr:
if zero1: zero2 = True
else: zero1 = True
summ += c
pdf = summ / (PI*alpha)
pdf = kept_within(0.0, pdf)
return pdf
def _dstable_sym_big(alpha, x, tolr):
"""
A series expansion for large x due to Bergstrom.
Converges for x > 1.0
The function uses the Kahan summation procedure
(cf. Dahlquist, Bjorck & Anderson).
"""
summ = 0.0
c = 0.0
fact = 1.0
k = 0
zero2 = zero1 = False
while True:
k += 1
summo = summ
ak = alpha * k
akh = 0.5 * ak
r = lngamma(ak) - lnfactorial(k)
term = -ak * exp(r) * sin(PIHALF * ak) / pow(x, ak + 1)
fact = -fact
term *= fact
y = term + c
t = summ + y
if fsign(y) == fsign(summ):
f = (0.46 * t - t) + t
c = ((summ - f) - (t - f)) + y
else:
c = (summ - t) + y
summ = t
if abs(summ - summo) < tolr * abs(summ) and abs(term) < tolr and zero2:
break
if abs(term) < tolr:
if zero1: zero2 = True
else: zero1 = True
summ += c
#pdf = summ / PI
pdf = PIINV * summ
pdf = kept_within(0.0, pdf)
return pdf
def _dstable_sym_big(alpha, x, tolr):
"""
A series expansion for large x due to Bergstrom.
Converges for x > 1.0
The function uses the Kahan summation procedure
(cf. Dahlquist, Bjorck & Anderson).
"""
summ = 0.0
c = 0.0
fact = 1.0
k = 0
zero2 = zero1 = False
while True:
k += 1
summo = summ
ak = alpha * k
akh = 0.5 * ak
r = lngamma(ak) - lnfactorial(k)
term = - ak * exp(r) * sin(PIHALF*ak) / pow(x, ak+1)
fact = - fact
term *= fact
y = term + c
t = summ + y
if fsign(y) == fsign(summ):
f = (0.46*t-t) + t
c = ((summ-f)-(t-f)) + y
else:
c = (summ-t) + y
summ = t
if abs(summ-summo) < tolr*abs(summ) and abs(term) < tolr and zero2:
break
if abs(term) < tolr:
if zero1: zero2 = True
else: zero1 = True
summ += c
#pdf = summ / PI
pdf = PIINV * summ
pdf = kept_within(0.0, pdf)
return pdf
