def bessi(n, x):
"""Modified Bessel function I-sub-n(x).
@see: NRP 6.5
@param n: integer, more than 1 - modified n-th Bessel function
@param x: positive integer
@return: modified n-th Bessel function of x
"""
iacc = 40.0
bigno = 1.0e10
bigni = 1.0e-10
if n < 2:
raise FunctionParameterValueError('n must be more than 1 - use \
bessi0 or bessi1 for n = 0 or 1 respectively')
else:
if x == 0.0: ans = 0.0
else:
ans = 0.0
tox = 2.0 / float((x))
bip = 0.0
bi = 1.0
m = 2 * (n + math.floor(math.sqrt(iacc * n)))
for j in range(int(m), 1, -1):
bim = bip + j * tox * bi
bip = bi
bi = bim
if abs(bi) > bigno:
ans = ans * bigni
bi = bi * bigni
bip = bip * bigni
if j == n: ans = bip
if x < 0.0 and (n % 2) == 1: ans = -ans
return ans * bessi0(x) / (float(bi))
def changeDatum(self, name, observation, newvalue):
'''
Change the value of a datum in a data series.
@param name: Name of data series
@type name: string
@param observation: Observation number to change (starting count = 1)
@type observation: integer
@param newvalue: new value for the observation
'''
observation = int(observation)
if not self.has_series(name):
raise FunctionParameterValueError('Unknown data series: ' +
str(name))
if observation > len(self.data[name]):
raise FunctionParameterValueError('Unknown observation: ' + \
str(observation))
self.data[name][observation - 1] = newvalue
def getSeries(self, name):
'''
Get values of a data series.
@param name: Name of data series
@type name: string
@return: List of data
'''
if self.has_series(name):
return self.data[name]
else:
raise FunctionParameterValueError('Unknown data series: ' +
str(name))
def bessj(n, x):
"""Bessel function J-sub-n(x).
@see: NRP 6.5
@param x: float number
@return: float number
"""
iacc = 40.0
bigno = 1.0e10
bigni = 1.0e-10
if n < 2:
raise FunctionParameterValueError('n must be more than 1 - use \
bessj0 or bessj1 for n = 0 or 1 respectively')
if x == 0.0: ans = 0.0
else:
if abs(x) > 1.0 * n:
tox = 2.0 / abs(x)
bjm = bessj0(abs(x))
bj = bessj1(abs(x))
for j in range(1, n):
bjp = j * tox * bj - bjm
bjm = bj
bj = bjp
ans = bj
else:
tox = 2.0 / abs(x)
m = int(2 * ((n + math.floor(math.sqrt(1.0 * (iacc * n)))) % 2))
ans = 0.0
jsum = 0.0
sum = 0.0
bjp = 0.0
bj = 1.0
for j in range(m, 1, -1):
bjm = j * tox * bj - bjp
bjp = bj
bj = bjm
if abs(bj) > bigno:
bj = bj * bigni
bjp = bjp * bigni
ans = ans * bigni
sum = sum * bigni
if jsum <> 0: sum = sum + bj
jsum = 1 - jsum
if j == n: ans = bjp
sum = 2.0 * sum - bj
print sum, ans
ans = ans / sum
if x < 0.0 and (n % 2) == 1: ans = -ans
return ans
def bessk(n, x):
"""Bessel function K-sub-n(x). @see: NRP 6.5
@param n: integer, more than 1 - modified n-th Bessel function
@param x: positive integer
@return: modified n-th Bessel function of x
"""
if n < 2:
raise FunctionParameterValueError('''n must be more than 1 - \
use bessk0 or bessk1 for n = 0 or 1 respectively''')
else:
tox = 2.0 / x
bkm = bessk0(x)
bk = bessk1(x)
for j in range(1, n):
bkp = bkm * j * tox * bk
bkm = bk
bk = bkp
return bk
def changeDataType(self, name, type='float'):
'''
Change the data type for a data series
@param name: Name of data series
@type name: string
@param type: Type of data to cast data series into. Allowable = {float |
integer | string | long}. Default = float
'''
if type == 'float':
self.data[name] = [float(x) for x in self.data[name]]
elif type == 'integer':
self.data[name] = [int(x) for x in self.data[name]]
elif type == 'string':
self.data[name] = [str(x) for x in self.data[name]]
elif type == 'long':
self.data[name] = [long(x) for x in self.data[name]]
else:
raise FunctionParameterValueError('Unknown data type: ' +
str(type))
def bessy(n, x):
"""Bessel function Y-sub-n(x).
@see: NRP 6.4
@param n: integer, more than 1 - n-th Bessel function
@param x: positive integer
@return: n-th Bessel function of x
"""
if n < 2:
raise FunctionParameterValueError('n must be more than 1 - \
use bessy0 or bessy1 for n = 0 or 1 respectively')
else:
tox = 2.0 / x
by = bessy1(x)
bym = bessy0(x)
for j in range(1, n):
byp = j * tox * by - bym
bym = by
by = byp
return by
def addData(self, data, label=[]):
'''
Method to add data into the data series. If provided, the number
of elements in data and label have to be the same. However, the
labels need not be unique (duplicated labels are allowed) but this
is highly undesirable as it can cause issues which requires unique
labels.
@param data: list of data values.
@type data: list
@param label: list of labels for the data values. If not given,
a sequential number will be given as label but this does not ensure
uniqueness in label names across the entire series.
@type label: list
'''
if len(label) == 0:
label = range(len(data))
if len(data) != len(label):
raise FunctionParameterValueError()
for i in range(len(data)):
self.data.append(data[i])
self.label.append(label[i])
def chebev(a, b, c, m, x):
"""Chebyshev evaluation.
@see: NRP 5.6
@param a: float number
@param b: float number
@param c: list of Chebyshev coefficients produced by chebft with the
same 'a' and 'b'
@param m:
@param x:
@return: float number - function value
"""
if (x - a) * (x - b) > 0.0:
raise FunctionParameterValueError('x must be between a and b')
else:
d, dd = 0.0, 0.0
y = (2.0 * x - a - b) / (b - a)
y2 = 2.0 * y
for i in range(m, 0, -1):
sv = d
d = y2 * d - dd + c[i]
dd = sv
return y * d - dd + 0.5 * c[0]