def erf(x):
"""
Approximation to the erf-function with fractional error
everywhere less than 1.2e-7
@param x: value
@type x: float
@return: value
@rtype: float
"""
if x > 10.: return 1.
if x < -10.: return -1.
z = abs(x)
t = 1. / (1. + 0.5 * z)
r = t * N0.exp(-z * z - 1.26551223 + t * (1.00002368 + t * (0.37409196 + \
t * (0.09678418 + t * (-0.18628806 + t * (0.27886807 + t * \
(-1.13520398 + t * (1.48851587 + t * (-0.82215223 + t * \
0.17087277)))))))))
if x >= 0.:
return 1. - r
else:
return r - 1.
def logMean( alpha, beta ):
"""
@param alpha: mean of log-transformed distribution
@type alpha: float
@param beta: standarddev of log-transformed distribution
@type beta: float
@return: mean of the original lognormal distribution
@rtype: float
"""
return N0.exp( alpha + (beta**2)/2. )
def logMedian( alpha, beta=None ):
"""
@param alpha: mean of log-transformed distribution
@type alpha: float
@param beta: not needed
@type beta: float
@return: median of the original lognormal distribution
@rtype: float
"""
return N0.exp( alpha )
def logSigma( alpha, beta ):
"""
@param alpha: mean of log-transformed distribution
@type alpha: float
@param beta: standarddev of log-transformed distribution
@type beta: float
@return: 'standard deviation' of the original lognormal distribution
@rtype: float
"""
return logMean( alpha, beta ) * N0.sqrt( N0.exp(beta**2) - 1.)
def test_MatrixPlot(self):
"""MatrixPlot test"""
n = 30
z = N0.zeros((n, n), N0.Float)
for i in range(N0.shape(z)[0]):
for j in range(N0.shape(z)[1]):
z[i, j] = N0.exp(-0.01 * ((i - n / 2)**2 + (j - n / 2)**2))
self.p = MatrixPlot(z, palette='sausage', legend=1)
if self.local or self.VERBOSITY > 2:
self.p.show()
self.assert_(self.p is not None)
def logArea(x, alpha, beta):
"""
Area of the smallest interval of a lognormal distribution that still
includes x.
@param x: border value
@type x: float
@param alpha: mean of log-transformed distribution
@type alpha: float
@param beta: standarddev of log-transformed distribution
@type beta: float
@return: probability that x is NOT drawn from the given distribution
@rtype: float
"""
r_max = N0.exp(alpha - beta**2)
if x < r_max: x = r_max**2 / x
upper = (N0.log(x) - alpha) / beta
return 0.5 * (erf(upper / N0.sqrt(2)) - erf(-(upper + 2*beta) / N0.sqrt(2)))
def ln(r, alpha, beta):
return N0.exp(-0.5/beta**2 * (N0.log(r) - alpha)**2 \
- 0.5*N0.log(2*N0.pi)-N0.log(beta*r))
def rand_log_normal(alpha, beta, shape):
return N0.exp(R.normal(alpha, beta, shape))