All Samples(2856) | Call(2645) | Derive(0) | Import(211)
log(x[, out])
Natural logarithm, element-wise.
The natural logarithm `log` is the inverse of the exponential function,
so that `log(exp(x)) = x`. The natural logarithm is logarithm in base `e`.
Parameters
----------
x : array_like
Input value.
Returns
-------
y : ndarray
The natural logarithm of `x`, element-wise.
See Also
--------
log10, log2, log1p, emath.log
Notes
-----
Logarithm is a multivalued function: for each `x` there is an infinite
number of `z` such that `exp(z) = x`. The convention is to return the `z`
whose imaginary part lies in `[-pi, pi]`.
For real-valued input data types, `log` always returns real output. For
each value that cannot be expressed as a real number or infinity, it
yields ``nan`` and sets the `invalid` floating point error flag.
For complex-valued input, `log` is a complex analytical function that
has a branch cut `[-inf, 0]` and is continuous from above on it. `log`
handles the floating-point negative zero as an infinitesimal negative
number, conforming to the C99 standard.
References
----------
.. [1] M. Abramowitz and I.A. Stegun, "Handbook of Mathematical Functions",
10th printing, 1964, pp. 67. http://www.math.sfu.ca/~cbm/aands/
.. [2] Wikipedia, "Logarithm". http://en.wikipedia.org/wiki/Logarithm
Examples
--------
>>> np.log([1, np.e, np.e**2, 0])
array([ 0., 1., 2., -Inf])src/n/i/nipy-HEAD/nipy/neurospin/group/spatial_relaxation_onesample.py nipy(Download)
def log_gammainv_pdf(x, a, b):
"""
log density of the inverse gamma distribution with shape a and scale b,
at point x, using Stirling's approximation for a > 100
"""
return a * np.log(b) - sp.gammaln(a) - (a + 1) * np.log(x) - b / x
def log_gaussian_pdf(x, m, v):
"""
log density of the gaussian distribution with mean m and variance v at point x
"""
return -0.5 * (np.log(2 * np.pi * v) + (x - m)**2 / v)
i, b, 1.0, proposal_std,
verbose=False, reject_override=True)
mean_acceptance = np.exp(A_values).clip(0,1).mean()
L -= np.log(mean_acceptance)
for i in range(n)[::-1]:
for b in range(B)[::-1]:
n_ib = n * B - i * B - b
(np.exp(A_values).clip(0,1) * \
np.exp( -0.5 * SS_values / proposal_std**2) \
/ (np.sqrt(2 * np.pi) * proposal_std)**3).mean()
L += np.log(mean_kernel) - np.log(mean_acceptance)*(i>0 or b>0)
if not change_U:
# Restore initial displacement value
self.proposal = 'fixed'
IJ)
fc = self.log_voxel_likelihood[J]
f = - 0.5 * (\
N * np.log(2 * np.pi) + \
np.log(1 + self.m_var[self.labels[J]] * SS1) \
+ SS2 + SS3 - SS4**2 / \
(1 / self.m_var[self.labels[J]] + SS1))
Vk[xrange(nk), xrange(nk)] = v_j + m_var_j
else:
Vk[xrange(nk), xrange(nk)] = vark + m_var_j
log_region_likelihood[j] += np.log(np.linalg.det(Vk)) + datak.transpose() * np.linalg.inv(Vk) * datak
if self.std == None:
nj = n * len(L)
else:
nj = self.N[L].sum()
log_region_likelihood[j] += nj * np.log(2 * np.pi)
add_lines(np.log(tot_var[i]).reshape(p, 1), SS2.reshape(p, 1), Ii)
add_lines((Z[i]**2 / tot_var[i]).reshape(p, 1), SS3.reshape(p, 1), Ii)
add_lines((Z[i] / tot_var[i]).reshape(p, 1), SS4.reshape(p, 1), Ii)
LL = - 0.5 * (N * np.log(2 * np.pi) + np.log(1 + m_var[self.labels] * SS1) \
+ SS2 + SS3 - SS4**2 / (1 / m_var[self.labels] + SS1))
if return_SS:
return LL, Z, tot_var, SS1, SS2, SS3, SS4
return max_log_conditional + ll_ratio.mean(axis=0)
elif not update_spatial:
return max_log_conditional \
+ np.log(np.exp(ll_ratio).sum(axis=0)) \
- np.log(nsimu)
else:
return max_log_conditional.sum() \
+ np.log(np.exp(ll_ratio.sum(axis=1)).sum()) \
- np.log(nsimu)
U = self.D.U
log_displacements_prior = \
- 0.5 * np.square(U).sum() / std**2 \
- self.D.U.size * np.log(std)
log_displacements_posterior = \
self.compute_log_conditional_displacements_posterior(\
U,
src/n/i/NiPy-OLD-HEAD/nipy/neurospin/group/spatial_relaxation_onesample.py NiPy-OLD(Download)
def log_gammainv_pdf(x, a, b):
"""
log density of the inverse gamma distribution with shape a and scale b,
at point x, using Stirling's approximation for a > 100
"""
return a * np.log(b) - sp.gammaln(a) - (a + 1) * np.log(x) - b / x
def log_gaussian_pdf(x, m, v):
"""
log density of the gaussian distribution with mean m and variance v at point x
"""
return -0.5 * (np.log(2 * np.pi * v) + (x - m)**2 / v)
i, b, 1.0, proposal_std,
verbose=False, reject_override=True)
mean_acceptance = np.exp(A_values).clip(0,1).mean()
L -= np.log(mean_acceptance)
for i in range(n)[::-1]:
for b in range(B)[::-1]:
n_ib = n * B - i * B - b
(np.exp(A_values).clip(0,1) * \
np.exp( -0.5 * SS_values / proposal_std**2) \
/ (np.sqrt(2 * np.pi) * proposal_std)**3).mean()
L += np.log(mean_kernel) - np.log(mean_acceptance)*(i>0 or b>0)
if not change_U:
# Restore initial displacement value
self.proposal = 'fixed'
IJ)
fc = self.log_voxel_likelihood[J]
f = - 0.5 * (\
N * np.log(2 * np.pi) + \
np.log(1 + self.m_var[self.labels[J]] * SS1) \
+ SS2 + SS3 - SS4**2 / \
(1 / self.m_var[self.labels[J]] + SS1))
Vk[xrange(nk), xrange(nk)] = v_j + m_var_j
else:
Vk[xrange(nk), xrange(nk)] = vark + m_var_j
log_region_likelihood[j] += np.log(np.linalg.det(Vk)) + datak.transpose() * np.linalg.inv(Vk) * datak
if self.std == None:
nj = n * len(L)
else:
nj = self.N[L].sum()
log_region_likelihood[j] += nj * np.log(2 * np.pi)
add_lines(np.log(tot_var[i]).reshape(p, 1), SS2.reshape(p, 1), Ii)
add_lines((Z[i]**2 / tot_var[i]).reshape(p, 1), SS3.reshape(p, 1), Ii)
add_lines((Z[i] / tot_var[i]).reshape(p, 1), SS4.reshape(p, 1), Ii)
LL = - 0.5 * (N * np.log(2 * np.pi) + np.log(1 + m_var[self.labels] * SS1) \
+ SS2 + SS3 - SS4**2 / (1 / m_var[self.labels] + SS1))
if return_SS:
return LL, Z, tot_var, SS1, SS2, SS3, SS4
return max_log_conditional + ll_ratio.mean(axis=0)
elif not update_spatial:
return max_log_conditional \
+ np.log(np.exp(ll_ratio).sum(axis=0)) \
- np.log(nsimu)
else:
return max_log_conditional.sum() \
+ np.log(np.exp(ll_ratio.sum(axis=1)).sum()) \
- np.log(nsimu)
U = self.D.U
log_displacements_prior = \
- 0.5 * np.square(U).sum() / std**2 \
- self.D.U.size * np.log(std)
log_displacements_posterior = \
self.compute_log_conditional_displacements_posterior(\
U,
src/c/u/CUV-HEAD/examples/rbm/datasets.py CUV(Download)
def logtransform(self):
""" adds one to (test) data and applies log """
self.ensure_float32()
self.data += 1
np.log(self.data,self.data)
if "test_data" in self.__dict__:
self.test_data += 1
np.log(self.test_data, self.test_data)
src/a/l/algopy-HEAD/documentation/sphinx/examples/first_order_forward.py algopy(Download)
import numpy; from numpy import log, exp, sin, cos, abs
import algopy; from algopy import UTPM, dot, inv, zeros
def f(x):
A = zeros((2,2),dtype=x)
A[0,0] = numpy.log(x[0]*x[1])
A[0,1] = numpy.log(x[1]) + exp(x[0])
A[1,0] = sin(x[0])**2 + abs(cos(x[0]))**3.1
A[1,1] = x[0]**cos(x[1])
return log( dot(x.T, dot( inv(A), x)))
src/a/u/aureservoir-HEAD/python/examples/filtering.py aureservoir(Download)
w0 = 2 * N.pi * f0 / Fs if( BW != None ): #print BW alpha = N.sin(w0)*N.sinh( N.log(2)/2 * BW * w0/N.sin(w0) ) #Q = ( 2*N.sinh(N.log(2)/2*BW*w0/N.sin(w0)) )**(-1) #print Q else:
# Efficient Implementation of the Patterson-Holdsworth Cochlear # Filter Bank." cf = N.arange(numChannels) + 1 cf = -(EarQ*minBW) + N.exp( cf * (-N.log(fs/2. + EarQ*minBW) + \ N.log(lowFreq + EarQ*minBW) ) / numChannels ) \ *(fs/2. + EarQ*minBW)
# Efficient Implementation of the Patterson-Holdsworth Cochlear # Filter Bank." cf = N.arange(numChannels) + 1 cf = -(EarQ*minBW) + N.exp( cf * (-N.log(fs/2. + EarQ*minBW) + \ N.log(lowFreq + EarQ*minBW) ) / numChannels ) \ *(fs/2. + EarQ*minBW)
# Efficient Implementation of the Patterson-Holdsworth Cochlear # Filter Bank." cf = N.arange(numChannels) + 1 cf = -(EarQ*minBW) + N.exp( cf * (-N.log(fs/2. + EarQ*minBW) + \ N.log(lowFreq + EarQ*minBW) ) / numChannels ) \ *(fs/2. + EarQ*minBW)
src/m/a/matplotlib-HEAD/matplotlib/examples/api/custom_scale_example.py matplotlib(Download)
if masked.mask.any():
return ma.log(np.abs(ma.tan(masked) + 1.0 / ma.cos(masked)))
else:
return np.log(np.abs(np.tan(a) + 1.0 / np.cos(a)))
def inverted(self):
"""
src/m/a/matplotlib-HEAD/matplotlib/examples/api/hinton_demo.py matplotlib(Download)
ax = fig.add_subplot(1, 1, 1)
if not maxWeight:
maxWeight = 2**np.ceil(np.log(np.abs(W).max())/np.log(2))
ax.patch.set_facecolor('gray')
ax.set_aspect('equal', 'box')
src/m/a/matplotlib-HEAD/examples/api/custom_scale_example.py matplotlib(Download)
if masked.mask.any():
return ma.log(np.abs(ma.tan(masked) + 1.0 / ma.cos(masked)))
else:
return np.log(np.abs(np.tan(a) + 1.0 / np.cos(a)))
def inverted(self):
"""
src/m/a/matplotlib-HEAD/examples/api/hinton_demo.py matplotlib(Download)
ax = fig.add_subplot(1, 1, 1)
if not maxWeight:
maxWeight = 2**np.ceil(np.log(np.abs(W).max())/np.log(2))
ax.patch.set_facecolor('gray')
ax.set_aspect('equal', 'box')
src/m/a/Matplotlib--JJ-s-dev-HEAD/examples/api/custom_scale_example.py Matplotlib--JJ-s-dev(Download)
if masked.mask.any():
return ma.log(np.abs(ma.tan(masked) + 1.0 / ma.cos(masked)))
else:
return np.log(np.abs(np.tan(a) + 1.0 / np.cos(a)))
def inverted(self):
"""
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