def zeta(s):
"""
zeta(s) -- calculate the Riemann zeta function of a real or complex
argument s.
"""
Float.store()
Float._prec += 8
si = s
s = ComplexFloat(s)
if s.real < 0:
# Reflection formula (XXX: gets bad around the zeros)
pi = pi_float()
y = power(2, s) * power(pi, s-1) * sin(pi*s/2) * gamma(1-s) * zeta(1-s)
else:
p = Float._prec
n = int((p + 2.28*abs(float(s.imag)))/2.54) + 3
d = _zeta_coefs(n)
if isinstance(si, (int, long)):
t = 0
for k in range(n):
t += (((-1)**k * (d[k] - d[n])) << p) // (k+1)**si
y = (Float((t, -p)) / -d[n]) / (Float(1) - Float(2)**(1-si))
else:
t = Float(0)
for k in range(n):
t += (-1)**k * Float(d[k]-d[n]) * exp(-_logk(k+1)*s)
y = (t / -d[n]) / (Float(1) - exp(log(2)*(1-s)))
Float.revert()
if isinstance(y, ComplexFloat) and s.imag == 0:
return +y.real
else:
return +y
def getSlope(times,
valueList,
maxCoverage,
sqrt=False,
verbose=False,
tmpFileName="tmpFig.png"):
x = np.array(times)
x = np.array(times).astype(float)[0:maxCoverage]
averageValues = np.array(valueList).astype(float)[0:maxCoverage]
try:
a, b = np.polyfit(x, averageValues, 1)
popt = curve_fit(f.power, x, averageValues)
aPower = popt[0][0]
bPower = popt[0][1]
if verbose:
plt.figure(num=None,
figsize=(3, 3),
dpi=80,
facecolor='w',
edgecolor='k')
label = "{}x+{}".format(a, b)
print(label)
plt.plot(x, averageValues)
y = a * np.array(x) + b
plt.plot(x, y, label=label)
y = f.power(x, aPower, bPower)
label = "{}x^{}".format(aPower, bPower)
plt.plot(x, y, label=label)
plt.legend(loc='upper left', prop={'size': 6})
plt.savefig(tmpFileName)
plt.close()
if sqrt:
valueSlope = aPower
else:
valueSlope = a
except (TypeError, RuntimeError, ValueError):
if (verbose):
print("Error fitting...")
print(x)
print(averageValues)
traceback.print_exc(file=sys.stdout)
valueSlope = 0
return valueSlope
def plot(x, y):
maxCoverage = 31
#gyradiusList vs averageSizes
indexes = range(1, maxCoverage)
xPlot = np.array(x)[indexes]
xPlot = [np.mean(i) for i in xPlot]
yPlot = np.array(y)
plt.xlabel("Gyradius")
plt.ylabel("Island size")
plt.grid(True)
plt.loglog(xPlot, yPlot, ".")
# fit
popt = curve_fit(f.power, xPlot, yPlot)
aPower = popt[0][0]
bPower = popt[0][1]
label = "{}x^{}".format(aPower, bPower)
yPlot = f.power(xPlot, aPower, bPower)
plt.loglog(xPlot, yPlot, label=label)
plt.legend(loc='upper left', prop={'size': 12})
plt.savefig("gyradiusVsSize.png")
plt.close()
folder = "flux3.5e" + str(i)
flux = float("3.5e" + str(i))
print(folder)
try:
os.chdir(folder)
meanValues = mk.getIslandDistribution(temperatures, False, False)
except OSError:
print("error changing to {}".format(folder))
a = 0 #do nothing
os.chdir(workingPath)
mtt = meanValues.getAeRatioTimesPossible() #/flux**.063
r = np.array(mk.getRtt(temperatures)) #/flux**0.5
plt.loglog(mtt, r, "-", label="N " + folder)
if (i < -7):
popt = curve_fit(f.power, r, mtt)
a = popt[0][0]
b = popt[0][1]
x = r
a = 2e2
b = 2 / 3
label = "{}x^{}".format(a, b)
y = f.power(x, a, b)
plt.loglog(x, y, label=label)
plt.legend(loc='lower right', prop={'size': 6})
plt.savefig("aeRatioVsRate.png")
plt.close()
print("Good bye!")
def test_power():
assert f.power(1, 1) == 1
assert f.power(5, 2) == 25
assert f.power(2, -2) == 0.25
assert f.power(-2, 2) == 4
- To quit, press X
""")
op = input("> Enter operator key: ").lower()
if op == 'x':
break
elif op == 'a':
print("> The answer is: ", f.add(num1, num2))
elif op == 's':
in_order = bool(
int(input(
">> Enter 1 -> num1 - num2 OR Enter 0 -> num2 - num1: ")))
print("> The answer is: ", f.subtract(num1, num2, in_order=in_order))
elif op == 'm':
print("> The answer is: ", f.multiply(num1, num2))
elif op == 'd':
in_order = bool(
int(input(">> Enter 1 -> num1 / num2 OR Enter 0 -> num2 / num1")))
print("> The answer is: ", f.divide(num1, num2, in_order=in_order))
elif op == 'p':
print("> The answer is: ", f.power(num1, num2))
else:
print("> Invalid entry, try again...")
def plot(ax, ax2, data, i):
marker = ["o", "s", "H", "D", "^", "d", "h", "p", "o"]
cm = plt.get_cmap("Accent")
alpha = 0.5
mew = 0
lw = 3
data = np.array(data)
flux = data[0, 0]
x = data[:, 6] / flux**0.17
if ax2 != None:
ax2.plot(x, data[:, 5], label="isld", lw=lw, ls="--", color=cm(i / 8))
ax2.text(x[0] / 8,
data[:, 5][0],
fun.base10(flux),
color=cm(i / 8),
size=10)
lg1, = ax.plot(x,
data[:, 3],
label=r"$F=$" + fun.base10(flux),
lw=lw,
marker="",
ls="-",
mew=mew,
ms=8,
alpha=alpha,
color=cm(i / 8))
ax.plot(x,
data[:, 4],
label=r"$N_h$" + fun.base10(flux),
lw=lw + 1,
marker="",
ls="-.",
mew=1,
color=cm(i / 8),
markeredgecolor=cm(i / 8),
ms=7,
alpha=1)
ax.text(x[0] / 8,
data[:, 4][0],
fun.base10(flux),
color=cm(i / 8),
size=10)
if i == 0:
ax.annotate("",
xytext=(x[1], data[:, 4][1] * 1.5),
xy=(x[1] / 80, data[:, 4][1] * 3),
arrowprops=dict(arrowstyle="->",
connectionstyle="angle3",
ls="-",
color="gray"),
ha="center",
va="center")
if i == 4:
xFit = np.array([1e2, 1e12])
ax2.plot(xFit, fun.power(xFit, 4e4, -0.3333), ls=":", color="black")
bbox_props = dict(boxstyle="round", fc="w", ec="0.5", alpha=0.3)
label = r"$\theta=0.30$"
ax.annotate(r"$1/3$", xy=(1e5, 3e2), bbox=bbox_props)
ax.annotate(label,
xy=(0.5, 0.93),
xycoords="axes fraction",
bbox=bbox_props)
ax.annotate("",
xy=(1e9, 1e-5),
xycoords='data',
xytext=(1e9, 1e4),
arrowprops=dict(arrowstyle="-",
connectionstyle="arc3",
ls="--",
color="gray"))
ax.annotate("",
xy=(8e10, 1e-5),
xycoords='data',
xytext=(8e10, 1e4),
arrowprops=dict(arrowstyle="-",
connectionstyle="arc3",
ls="--",
color="gray"))
addEllipses()
alpha = 0.2
arrow = dict(arrowstyle="-[", ls="-", color="gray", alpha=0)
ax.annotate("A",
xy=(7e2, 3),
xytext=(7e2, 1),
ha="center",
va="center",
arrowprops=arrow,
color="green",
alpha=alpha)
ax.annotate("B",
xy=(7e2, 1e-4),
xytext=(7e2, 1e-4),
ha="center",
va="center",
arrowprops=arrow,
color="blue",
alpha=alpha)
ax.annotate("C",
xy=(8e9, 1),
xytext=(8e9, 5e-1),
ha="center",
va="center",
arrowprops=arrow,
color="red",
alpha=alpha)
ax.annotate("D",
xy=(8e11, 2e2),
xytext=(8e11, 7e2),
ha="center",
va="center",
arrowprops=arrow,
color="brown",
alpha=alpha)
y = 3e-5
ax.text(2e7, y, "$I$", color="gray")
ax.text(5e9, y, "$II$", color="gray")
ax.text(2e11, y, "$III$", color="gray")
ax2.annotate("",
xy=(x[-1] * 18, data[:, 5][-1]),
xytext=(x[-1] * 2, data[:, 5][-1] / 1.5),
arrowprops=dict(arrowstyle="->",
connectionstyle="angle3",
ls="-",
color="gray"),
ha="center",
va="center")
