def tips(molID, isoID, temp):
"""
Evaluate the partition function for the given isotope(s) at the given
temperature(s). This is a wrapper of ctips.tips.
Parameters:
-----------
molID: Scalar or iterable
The molecular ID as given by HITRAN 2012.
isoID: Scalar or iterable
The isotope ID (AFGL) as given by HITRAN 2012.
temp: Scalar or iterable
Temperature a which to evaluate the partition function.
Notes:
------
- The molID and isoID are casted into an integer ndarray data types.
- The temp is casted into a double ndarray data type.
- If the arguments have different sizes, the code resizes them to
a same size, unless they have incompatible sizes.
"""
# Check scalar vs iterable, turn into iterable:
if isscalar(molID):
molID = [molID]
if isscalar(isoID):
isoID = [isoID]
if isscalar(temp):
temp = [temp]
# Turn them numpy arrays:
molID = np.asarray(molID, np.int)
isoID = np.asarray(isoID, np.int)
temp = np.asarray(temp, np.double)
# Set them to the same size:
if len(isoID) != len(temp):
if len(isoID) == 1:
isoID = np.repeat(isoID, len(temp))
elif len(temp) == 1:
temp = np.repeat(temp, len(isoID))
else:
sys.exit(0)
if len(molID) != len(isoID):
if len(molID) != 1:
sys.exit(0)
molID = np.repeat(molID, len(isoID))
return ct.tips(molID, isoID, temp)
def tips(molID, isoID, temp):
"""
Evaluate the partition function for the given isotope(s) at the given
temperature(s). This is a wrapper of ctips.tips.
Parameters
----------
molID: Scalar or iterable
The molecular ID as given by HITRAN 2012.
isoID: Scalar or iterable
The isotope ID (AFGL) as given by HITRAN 2012.
temp: Scalar or iterable
Temperature a which to evaluate the partition function.
Notes
-----
- The molID and isoID are casted into an integer ndarray data types.
- The temp is casted into a double ndarray data type.
- If the arguments have different sizes, the code resizes them to
a same size, unless they have incompatible sizes.
"""
# Check scalar vs iterable, turn into iterable:
if isscalar(molID):
molID = [molID]
if isscalar(isoID):
isoID = [isoID]
if isscalar(temp):
temp = [temp]
# Turn them numpy arrays:
molID = np.asarray(molID, np.int)
isoID = np.asarray(isoID, np.int)
temp = np.asarray(temp, np.double)
# Set them to the same size:
if len(isoID) != len(temp):
if len(isoID) == 1:
isoID = np.repeat(isoID, len(temp))
elif len(temp) == 1:
temp = np.repeat(temp, len(isoID))
else:
sys.exit(0)
if len(molID) != len(isoID):
if len(molID) != 1:
sys.exit(0)
molID = np.repeat(molID, len(isoID))
return ct.tips(molID, isoID, temp)
def __getitem__(self, index):
self._getitem = True
try:
out = N.ndarray.__getitem__(self, index)
finally:
self._getitem = False
if not isinstance(out, N.ndarray):
return out
if out.ndim == 0:
return out[()]
if out.ndim == 1:
sh = out.shape[0]
# Determine when we should have a column array
try:
n = len(index)
except:
n = 0
if n > 1 and isscalar(index[1]):
out.shape = (sh, 1)
else:
out.shape = (1, sh)
return out
def __getitem__(self, index):
self._getitem = True
try:
out = N.ndarray.__getitem__(self, index)
finally:
self._getitem = False
if not isinstance(out, N.ndarray):
return out
if out.ndim == 0:
return out[()]
if out.ndim == 1:
sh = out.shape[0]
# Determine when we should have a column array
try:
n = len(index)
except:
n = 0
if n > 1 and isscalar(index[1]):
out.shape = (sh, 1)
else:
out.shape = (1, sh)
return out
def __mul__(self, other):
if isinstance(other, (N.ndarray, list, tuple)):
# This promotes 1-D vectors to row vectors
return N.dot(self, asmatrix(other))
if isscalar(other) or not hasattr(other, '__rmul__'):
return N.dot(self, other)
return NotImplemented
def __init__(self, dimension=1, randomize=True, seed=None):
"""
Args:
dimension (int): dimension of samples
randomize (bool): scramble points?
seeds (list): int seed of list of seeds, one for each dimension.
"""
try:
from scipy.stats.qmc import Sobol as SobolScipyOG
except:
raise ParameterError(
"scipy.stats.qmc.Sobol not found, try updating to scipy>=1.7.0"
)
self.parameters = ['randomize', 'graycode']
if not isscalar(dimension):
raise ParameterError(
"SobolSciPy does not support vectorized dimension indexing")
self.randomize = randomize
self.graycode = True
self.mimics = 'StdUniform'
self.low_discrepancy = True
self.d_max = 21201
super(SobolSciPy, self).__init__(dimension, seed)
self.sobol = SobolScipyOG(self.d,
scramble=self.randomize,
seed=self.entropy)
self.ncurrent = 0
def apply_along_axis(func1d,axis,arr,*args):
""" Execute func1d(arr[i],*args) where func1d takes 1-D arrays
and arr is an N-d array. i varies so as to apply the function
along the given axis for each 1-d subarray in arr.
"""
arr = asarray(arr)
nd = arr.ndim
if axis < 0:
axis += nd
if (axis >= nd):
raise ValueError("axis must be less than arr.ndim; axis=%d, rank=%d."
% (axis,nd))
ind = [0]*(nd-1)
i = zeros(nd,'O')
indlist = range(nd)
indlist.remove(axis)
i[axis] = slice(None,None)
outshape = asarray(arr.shape).take(indlist)
i.put(indlist, ind)
res = func1d(arr[tuple(i.tolist())],*args)
# if res is a number, then we have a smaller output array
if isscalar(res):
outarr = zeros(outshape,asarray(res).dtype)
outarr[tuple(ind)] = res
Ntot = product(outshape)
k = 1
while k < Ntot:
# increment the index
ind[-1] += 1
n = -1
while (ind[n] >= outshape[n]) and (n > (1-nd)):
ind[n-1] += 1
ind[n] = 0
n -= 1
i.put(indlist,ind)
res = func1d(arr[tuple(i.tolist())],*args)
outarr[tuple(ind)] = res
k += 1
return outarr
else:
Ntot = product(outshape)
holdshape = outshape
outshape = list(arr.shape)
outshape[axis] = len(res)
outarr = zeros(outshape,asarray(res).dtype)
outarr[tuple(i.tolist())] = res
k = 1
while k < Ntot:
# increment the index
ind[-1] += 1
n = -1
while (ind[n] >= holdshape[n]) and (n > (1-nd)):
ind[n-1] += 1
ind[n] = 0
n -= 1
i.put(indlist, ind)
res = func1d(arr[tuple(i.tolist())],*args)
outarr[tuple(i.tolist())] = res
k += 1
return outarr
def apply_along_axis(func1d, axis, arr, *args):
""" Execute func1d(arr[i],*args) where func1d takes 1-D arrays
and arr is an N-d array. i varies so as to apply the function
along the given axis for each 1-d subarray in arr.
"""
arr = asarray(arr)
nd = arr.ndim
if axis < 0:
axis += nd
if (axis >= nd):
raise ValueError("axis must be less than arr.ndim; axis=%d, rank=%d." %
(axis, nd))
ind = [0] * (nd - 1)
i = zeros(nd, 'O')
indlist = range(nd)
indlist.remove(axis)
i[axis] = slice(None, None)
outshape = asarray(arr.shape).take(indlist)
i.put(indlist, ind)
res = func1d(arr[tuple(i.tolist())], *args)
# if res is a number, then we have a smaller output array
if isscalar(res):
outarr = zeros(outshape, asarray(res).dtype)
outarr[tuple(ind)] = res
Ntot = product(outshape)
k = 1
while k < Ntot:
# increment the index
ind[-1] += 1
n = -1
while (ind[n] >= outshape[n]) and (n > (1 - nd)):
ind[n - 1] += 1
ind[n] = 0
n -= 1
i.put(indlist, ind)
res = func1d(arr[tuple(i.tolist())], *args)
outarr[tuple(ind)] = res
k += 1
return outarr
else:
Ntot = product(outshape)
holdshape = outshape
outshape = list(arr.shape)
outshape[axis] = len(res)
outarr = zeros(outshape, asarray(res).dtype)
outarr[tuple(i.tolist())] = res
k = 1
while k < Ntot:
# increment the index
ind[-1] += 1
n = -1
while (ind[n] >= holdshape[n]) and (n > (1 - nd)):
ind[n - 1] += 1
ind[n] = 0
n -= 1
i.put(indlist, ind)
res = func1d(arr[tuple(i.tolist())], *args)
outarr[tuple(i.tolist())] = res
k += 1
return outarr
def __mul__(self, other):
if isinstance(other, (N.ndarray, list, tuple)) :
# This promotes 1-D vectors to row vectors
return N.dot(self, asmatrix(other))
if isscalar(other) or not hasattr(other, '__rmul__') :
return N.dot(self, other)
return NotImplemented
def __imul__(self, other):
if not isscalar(other):
return NotImplemented
self.ent_table = self.ent_table * other
self.att_table = [t * other for t in self.att_table]
return self
def __pow__(self, other):
if not isscalar(other):
return NotImplemented
return self._copy(
(self.ent_table.power(other) if sp.issparse(self.ent_table) else
np.power(self.ent_table, other)),
[(t.power(other) if sp.issparse(t) else np.power(t, other))
for t in self.att_table])
def __ipow__(self, other):
if not isscalar(other):
return NotImplemented
self.ent_table = self.ent_table.power(2) if sp.issparse(
self.ent_table) else np.power(self.ent_table, other)
self.att_table = [
(t.power(other) if sp.issparse(t) else np.power(t, other))
for t in self.att_table
]
return self
def __rmul__(self, other):
# ! NumPy's matrix __rmul__ uses an apparently restrictive
# dot() function that cannot handle the multiplication of a
# scalar and of a matrix containing objects (when the
# arguments are given in this order). We go around this
# limitation:
if numeric.isscalar(other):
return numeric.dot(self, other)
else:
return numeric.dot(other, self) # The order is important
def __rmul__(self, other):
# ! NumPy's matrix __rmul__ uses an apparently a restrictive
# dot() function that cannot handle the multiplication of a
# scalar and of a matrix containing objects (when the
# arguments are given in this order). We go around this
# limitation:
if numeric.isscalar(other):
return numeric.dot(self, other)
else:
return numeric.dot(other, self) # The order is important
def __rmul__(self, other):
if isinstance(other, (N.ndarray, list, tuple)):
if self.trans:
return self._left_matrix_multiplication(self, asmatrix(other).T).T
else:
return self._right_matrix_multiplication(self, asmatrix(other))
if isscalar(other) or not hasattr(other, '__rmul__'):
return self._copy(self.ent_table, self.att_table, a=self.a*other)
return NotImplemented
def __pow__(self, other):
if not isscalar(other) or self.b != 0.0:
return NotImplemented
return self._copy(
(self.ent_table.power(other) if sp.issparse(self.ent_table) else np.power(self.ent_table, other)),
[(t.power(other) if sp.issparse(t) else np.power(t, other)) for t in self.att_table],
a=self.a**other, c=self.c*other,
shadow_att=([(t.power(other) if sp.issparse(t) else np.power(t, other)) for t in self.shadow_att_table]
if self.shadow_att_table is not None else None),
shadow_ent=((self.shadow_ent_table.power(other) if sp.issparse(self.shadow_ent_table)
else np.power(self.shadow_ent_table, other)) if self.shadow_ent_table is not None else None))
def __add__(self, other):
if isscalar(other):
if self.isMorpheus:
raise NotImplementedError
else:
newMat = self.inner("scalarAddition", other)
return NormalizedMatrix(mat=newMat, avatar=self.avatar)
if self.isMorpheus:
return NotImplementedError
else:
newMat = self.inner("matrixAddition", other.mat)
return NormalizedMatrix(mat=newMat, avatar=self.avatar)
return self.normalizedTable.matrixAddition(other).unwrap()
def __mul__(self, other):
if self.shape == (1,1):
# extract scalars from singleton matrices (self)
return N.dot(self.flat[0], other)
if isinstance(other, N.ndarray) and other.shape == (1,1):
# extract scalars from singleton matrices (other)
return N.dot(self, other.flat[0])
if isinstance(other, (N.ndarray, list, tuple)) :
# This promotes 1-D vectors to row vectors
return N.dot(self, asmatrix(other))
if isscalar(other) or not hasattr(other, '__rmul__') :
return N.dot(self, other)
return NotImplemented
def __rpow__(self, other):
if not isscalar(other):
return NotImplemented
return self._copy(
np.power(
other,
self.ent_table.toarray()
if sp.issparse(self.ent_table) else self.ent_table), [
np.power(other,
t.toarray() if sp.issparse(t) else t)
for t in self.att_table
])
def __ipow__(self, other):
if not isscalar(other) or self.b != 0.0:
return NotImplemented
self.c = self.c * other
self.a = self.a ** other
self.ent_table = self.ent_table.power(2) if sp.issparse(self.ent_table) else np.power(self.ent_table, other)
self.att_table = [(t.power(other) if sp.issparse(t) else np.power(t, other)) for t in self.att_table]
if self.shadow_att_table is not None:
self.shadow_att_table = [(t.power(other) if sp.issparse(t) else np.power(t, other))
for t in self.shadow_att_table]
if self.shadow_ent_table is not None:
self.shadow_ent_table = (self.shadow_ent_table.power(other) if self.shadow_ent_table is not None else None)
return self
def __rdiv__(self, other):
if isscalar(other):
return self._copy(other / self.ent_table,
[other / t for t in self.att_table])
if isinstance(other, (N.ndarray, list, tuple)):
other = asmatrix(other)
if other.shape[1] == self.shape[1] and other.shape[0] == 1:
return self._copy(
other[:, :self.ent_table.shape[1]] / self.ent_table, [
other[:, self.indexes[i][0]:self.indexes[i][1]] / t
for i, t in enumerate(self.att_table)
])
return NotImplemented
def __rmul__(self, other):
if isscalar(other):
if self.isMorpheus:
raise NotImplementedError
else:
newMat = self.inner("scalarMultiplication", other)
return NormalizedMatrix(mat=newMat, avatar=self.avatar)
if isinstance(other, NormalizedMatrix):
if self.stamp == other.stamp and self.is_transposed ^ other.is_transposed:
return self.normalizedTable.crossProduct().unwrap()
else:
raise NotImplementedError
if isinstance(other, (N.ndarray, list, tuple)):
raise NotImplementedError
raise NotImplementedError
def __idiv__(self, other):
if isscalar(other):
self.ent_table = self.ent_table / other
self.att_table = [t / other for t in self.att_table]
return self
if isinstance(other, (N.ndarray, list, tuple)):
other = asmatrix(other)
if other.shape[1] == self.shape[1] and other.shape[0] == 1:
self.ent_table = self.ent_table / other[:, :self.ent_table.
shape[1]]
self.att_table = [
t / other[:, self.indexes[i][0]:self.indexes[i][1]]
for i, t in enumerate(self.att_table)
]
return self
return NotImplemented
def __mul__(self, other):
if isinstance(other, NormalizedMatrix):
if self.stamp == other.stamp and self.trans ^ other.trans:
return self._cross_prod()
else:
return NotImplemented
if isinstance(other, (N.ndarray, list, tuple)):
# This promotes 1-D vectors to row vectors
if self.trans:
return self._right_matrix_multiplication(self, asmatrix(other).T).T
else:
return self._left_matrix_multiplication(self, asmatrix(other))
if isscalar(other) or not hasattr(other, '__rmul__'):
return self._copy(self.ent_table, self.att_table, a=self.a*other)
return NotImplemented
def __mul__(self, other):
if isscalar(other):
if self.isMorpheus:
raise NotImplementedError
else:
newMat = self.inner("scalarMultiplication", other)
return NormalizedMatrix(mat=newMat, avatar=self.avatar)
return normMatrix
elif isinstance(other, NormalizedMatrix):
if self.isMorpheus:
newMat = self.inner.leftMatrixMultiplication(other.mat)
return NormalizedMatrix(mat=newMat, avatar=self.avatar)
else:
# Here the reason for the switch is that the names are backwards
newMat = self.inner("rightMatrixMultiplication", other.mat)
return NormalizedMatrix(mat=newMat, avatar=self.avatar)
return NotImplemented
def __init__(self, pressure, gravity=None):
"""
Parameters
----------
pressure: 1D float ndarray
Atmospheric pressure profile (barye).
gravity: 1D float ndarray or scalar
Atmospheric gravity profile (cm s-2).
If None, assume a constant gravity of 1 cm s-2, in which
case, one should regard the kappa parameter as
kappa' = kappa/gravity.
Note that the input gravity can be a scalar value used at all
atmospheric pressures (as it has been used so far in the
literature. However, from a parametric point of view, this is
redundant, as it only acts as a scaling factor for kappa.
Ideally, one would wish to input a pressure-dependent gravity,
but such profile would need to be derived from a hydrostatic
equilibrium calculation, for example. Unfortunately, HE cannot
be solved without knowing the temperature, thus making this a
circular problem (shrug emoji).
"""
self.name = 'tcea'
self.pnames = [
"log(kappa')", 'log(gamma1)', 'log(gamma2)', 'alpha', 'T_irr (K)',
'T_int (K)'
]
self.texnames = [
r"$\log_{10}(\kappa')$", r'$\log_{10}(\gamma_1)$',
r'$\log_{10}(\gamma_2)$', r'$\alpha$', r'$T_{\rm irr} (K)$',
r'$T_{\rm int} (K)$'
]
self.npars = len(self.pnames)
if gravity is None:
gravity = np.tile(1.0, len(pressure))
elif isscalar(gravity):
gravity = np.tile(gravity, len(pressure))
self.pressure = np.asarray(pressure, float)
self.gravity = np.asarray(gravity, float)
self.temp = np.zeros_like(pressure, float)
def within_tol(x, y, atol, rtol):
with errstate(invalid='ignore'):
result = less_equal(abs(x - y), atol + rtol * abs(y))
if isscalar(a) and isscalar(b):
result = bool(result)
return result
def apply_along_axis(func1d, axis, arr, *args, **kwargs):
"""
Apply a function to 1-D slices along the given axis.
Execute `func1d(a, *args)` where `func1d` operates on 1-D arrays and `a`
is a 1-D slice of `arr` along `axis`.
Parameters
----------
func1d : function
This function should accept 1-D arrays. It is applied to 1-D
slices of `arr` along the specified axis.
axis : integer
Axis along which `arr` is sliced.
arr : ndarray
Input array.
args : any
Additional arguments to `func1d`.
kwargs: any
Additional named arguments to `func1d`.
.. versionadded:: 1.9.0
Returns
-------
apply_along_axis : ndarray
The output array. The shape of `outarr` is identical to the shape of
`arr`, except along the `axis` dimension, where the length of `outarr`
is equal to the size of the return value of `func1d`. If `func1d`
returns a scalar `outarr` will have one fewer dimensions than `arr`.
See Also
--------
apply_over_axes : Apply a function repeatedly over multiple axes.
Examples
--------
>>> def my_func(a):
... \"\"\"Average first and last element of a 1-D array\"\"\"
... return (a[0] + a[-1]) * 0.5
>>> b = np.array([[1,2,3], [4,5,6], [7,8,9]])
>>> np.apply_along_axis(my_func, 0, b)
array([ 4., 5., 6.])
>>> np.apply_along_axis(my_func, 1, b)
array([ 2., 5., 8.])
For a function that doesn't return a scalar, the number of dimensions in
`outarr` is the same as `arr`.
>>> b = np.array([[8,1,7], [4,3,9], [5,2,6]])
>>> np.apply_along_axis(sorted, 1, b)
array([[1, 7, 8],
[3, 4, 9],
[2, 5, 6]])
"""
arr = asarray(arr)
nd = arr.ndim
if axis < 0:
axis += nd
if (axis >= nd):
raise ValueError("axis must be less than arr.ndim; axis=%d, rank=%d." %
(axis, nd))
ind = [0] * (nd - 1)
i = zeros(nd, 'O')
indlist = list(range(nd))
indlist.remove(axis)
i[axis] = slice(None, None)
outshape = asarray(arr.shape).take(indlist)
i.put(indlist, ind)
res = func1d(arr[tuple(i.tolist())], *args, **kwargs)
# if res is a number, then we have a smaller output array
if isscalar(res):
outarr = zeros(outshape, asarray(res).dtype)
outarr[tuple(ind)] = res
Ntot = product(outshape)
k = 1
while k < Ntot:
# increment the index
ind[-1] += 1
n = -1
while (ind[n] >= outshape[n]) and (n > (1 - nd)):
ind[n - 1] += 1
ind[n] = 0
n -= 1
i.put(indlist, ind)
res = func1d(arr[tuple(i.tolist())], *args, **kwargs)
outarr[tuple(ind)] = res
k += 1
return outarr
else:
Ntot = product(outshape)
holdshape = outshape
outshape = list(arr.shape)
outshape[axis] = len(res)
outarr = zeros(outshape, asarray(res).dtype)
outarr[tuple(i.tolist())] = res
k = 1
while k < Ntot:
# increment the index
ind[-1] += 1
n = -1
while (ind[n] >= holdshape[n]) and (n > (1 - nd)):
ind[n - 1] += 1
ind[n] = 0
n -= 1
i.put(indlist, ind)
res = func1d(arr[tuple(i.tolist())], *args, **kwargs)
outarr[tuple(i.tolist())] = res
k += 1
return outarr
def apply_along_axis(func1d,axis,arr,*args):
"""
Apply a function to 1-D slices along the given axis.
Execute `func1d(a, *args)` where `func1d` operates on 1-D arrays and `a`
is a 1-D slice of `arr` along `axis`.
Parameters
----------
func1d : function
This function should accept 1-D arrays. It is applied to 1-D
slices of `arr` along the specified axis.
axis : integer
Axis along which `arr` is sliced.
arr : ndarray
Input array.
args : any
Additional arguments to `func1d`.
Returns
-------
apply_along_axis : ndarray
The output array. The shape of `outarr` is identical to the shape of
`arr`, except along the `axis` dimension, where the length of `outarr`
is equal to the size of the return value of `func1d`. If `func1d`
returns a scalar `outarr` will have one fewer dimensions than `arr`.
See Also
--------
apply_over_axes : Apply a function repeatedly over multiple axes.
Examples
--------
>>> def my_func(a):
... \"\"\"Average first and last element of a 1-D array\"\"\"
... return (a[0] + a[-1]) * 0.5
>>> b = np.array([[1,2,3], [4,5,6], [7,8,9]])
>>> np.apply_along_axis(my_func, 0, b)
array([ 4., 5., 6.])
>>> np.apply_along_axis(my_func, 1, b)
array([ 2., 5., 8.])
For a function that doesn't return a scalar, the number of dimensions in
`outarr` is the same as `arr`.
>>> def new_func(a):
... \"\"\"Divide elements of a by 2.\"\"\"
... return a * 0.5
>>> b = np.array([[1,2,3], [4,5,6], [7,8,9]])
>>> np.apply_along_axis(new_func, 0, b)
array([[ 0.5, 1. , 1.5],
[ 2. , 2.5, 3. ],
[ 3.5, 4. , 4.5]])
"""
arr = asarray(arr)
nd = arr.ndim
if axis < 0:
axis += nd
if (axis >= nd):
raise ValueError("axis must be less than arr.ndim; axis=%d, rank=%d."
% (axis,nd))
ind = [0]*(nd-1)
i = zeros(nd,'O')
indlist = list(range(nd))
indlist.remove(axis)
i[axis] = slice(None,None)
outshape = asarray(arr.shape).take(indlist)
i.put(indlist, ind)
res = func1d(arr[tuple(i.tolist())],*args)
# if res is a number, then we have a smaller output array
if isscalar(res):
outarr = zeros(outshape,asarray(res).dtype)
outarr[tuple(ind)] = res
Ntot = product(outshape)
k = 1
while k < Ntot:
# increment the index
ind[-1] += 1
n = -1
while (ind[n] >= outshape[n]) and (n > (1-nd)):
ind[n-1] += 1
ind[n] = 0
n -= 1
i.put(indlist,ind)
res = func1d(arr[tuple(i.tolist())],*args)
outarr[tuple(ind)] = res
k += 1
return outarr
else:
Ntot = product(outshape)
holdshape = outshape
outshape = list(arr.shape)
outshape[axis] = len(res)
outarr = zeros(outshape,asarray(res).dtype)
outarr[tuple(i.tolist())] = res
k = 1
while k < Ntot:
# increment the index
ind[-1] += 1
n = -1
while (ind[n] >= holdshape[n]) and (n > (1-nd)):
ind[n-1] += 1
ind[n] = 0
n -= 1
i.put(indlist, ind)
res = func1d(arr[tuple(i.tolist())],*args)
outarr[tuple(i.tolist())] = res
k += 1
return outarr
def apply_along_axis(func1d,axis,arr,*args,**kwargs):
""" Execute func1d(arr[i],*args) where func1d takes 1-D arrays
and arr is an N-d array. i varies so as to apply the function
along the given axis for each 1-d subarray in arr.
"""
arr = core.array(arr, copy=False, subok=True)
nd = arr.ndim
if axis < 0:
axis += nd
if (axis >= nd):
raise ValueError("axis must be less than arr.ndim; axis=%d, rank=%d."
% (axis,nd))
ind = [0]*(nd-1)
i = numeric.zeros(nd,'O')
indlist = range(nd)
indlist.remove(axis)
i[axis] = slice(None,None)
outshape = numeric.asarray(arr.shape).take(indlist)
i.put(indlist, ind)
j = i.copy()
res = func1d(arr[tuple(i.tolist())],*args,**kwargs)
# if res is a number, then we have a smaller output array
asscalar = numeric.isscalar(res)
if not asscalar:
try:
len(res)
except TypeError:
asscalar = True
# Note: we shouldn't set the dtype of the output from the first result...
#...so we force the type to object, and build a list of dtypes
#...we'll just take the largest, to avoid some downcasting
dtypes = []
if asscalar:
dtypes.append(numeric.asarray(res).dtype)
outarr = zeros(outshape, object_)
outarr[tuple(ind)] = res
Ntot = numeric.product(outshape)
k = 1
while k < Ntot:
# increment the index
ind[-1] += 1
n = -1
while (ind[n] >= outshape[n]) and (n > (1-nd)):
ind[n-1] += 1
ind[n] = 0
n -= 1
i.put(indlist,ind)
res = func1d(arr[tuple(i.tolist())],*args,**kwargs)
outarr[tuple(ind)] = res
dtypes.append(asarray(res).dtype)
k += 1
else:
res = core.array(res, copy=False, subok=True)
j = i.copy()
j[axis] = ([slice(None,None)] * res.ndim)
j.put(indlist, ind)
Ntot = numeric.product(outshape)
holdshape = outshape
outshape = list(arr.shape)
outshape[axis] = res.shape
dtypes.append(asarray(res).dtype)
outshape = flatten_inplace(outshape)
outarr = zeros(outshape, object_)
outarr[tuple(flatten_inplace(j.tolist()))] = res
k = 1
while k < Ntot:
# increment the index
ind[-1] += 1
n = -1
while (ind[n] >= holdshape[n]) and (n > (1-nd)):
ind[n-1] += 1
ind[n] = 0
n -= 1
i.put(indlist, ind)
j.put(indlist, ind)
res = func1d(arr[tuple(i.tolist())],*args,**kwargs)
outarr[tuple(flatten_inplace(j.tolist()))] = res
dtypes.append(asarray(res).dtype)
k += 1
max_dtypes = numeric.dtype(numeric.asarray(dtypes).max())
if not hasattr(arr, '_mask'):
result = numeric.asarray(outarr, dtype=max_dtypes)
else:
result = core.asarray(outarr, dtype=max_dtypes)
result.fill_value = core.default_fill_value(result)
return result
def __div__(self, other):
if isscalar(other):
return self._copy(self.ent_table, self.att_table, a=self.a/other)
return NotImplemented
def __imul__(self, other):
if not isscalar(other):
return NotImplemented
self.a = self.a * other
return self
def histogramdd(sample, bins=10, range=None, normed=False, weights=None):
"""histogramdd(sample, bins=10, range=None, normed=False, weights=None)
Return the N-dimensional histogram of the sample.
Parameters:
sample : sequence or array
A sequence containing N arrays or an NxM array. Input data.
bins : sequence or scalar
A sequence of edge arrays, a sequence of bin counts, or a scalar
which is the bin count for all dimensions. Default is 10.
range : sequence
A sequence of lower and upper bin edges. Default is [min, max].
normed : boolean
If False, return the number of samples in each bin, if True,
returns the density.
weights : array
Array of weights. The weights are normed only if normed is True.
Should the sum of the weights not equal N, the total bin count will
not be equal to the number of samples.
Returns:
hist : array
Histogram array.
edges : list
List of arrays defining the lower bin edges.
SeeAlso:
histogram
Example
>>> x = random.randn(100,3)
>>> hist3d, edges = histogramdd(x, bins = (5, 6, 7))
"""
try:
# Sample is an ND-array.
N, D = sample.shape
except (AttributeError, ValueError):
# Sample is a sequence of 1D arrays.
sample = atleast_2d(sample).T
N, D = sample.shape
nbin = empty(D, int)
edges = D*[None]
dedges = D*[None]
if weights is not None:
weights = asarray(weights)
try:
M = len(bins)
if M != D:
raise AttributeError, 'The dimension of bins must be a equal to the dimension of the sample x.'
except TypeError:
bins = D*[bins]
# Select range for each dimension
# Used only if number of bins is given.
if range is None:
smin = atleast_1d(array(sample.min(0), float))
smax = atleast_1d(array(sample.max(0), float))
else:
smin = zeros(D)
smax = zeros(D)
for i in arange(D):
smin[i], smax[i] = range[i]
# Make sure the bins have a finite width.
for i in arange(len(smin)):
if smin[i] == smax[i]:
smin[i] = smin[i] - .5
smax[i] = smax[i] + .5
# Create edge arrays
for i in arange(D):
if isscalar(bins[i]):
nbin[i] = bins[i] + 2 # +2 for outlier bins
edges[i] = linspace(smin[i], smax[i], nbin[i]-1)
else:
edges[i] = asarray(bins[i], float)
nbin[i] = len(edges[i])+1 # +1 for outlier bins
dedges[i] = diff(edges[i])
nbin = asarray(nbin)
# Compute the bin number each sample falls into.
Ncount = {}
for i in arange(D):
Ncount[i] = digitize(sample[:,i], edges[i])
# Using digitize, values that fall on an edge are put in the right bin.
# For the rightmost bin, we want values equal to the right
# edge to be counted in the last bin, and not as an outlier.
outliers = zeros(N, int)
for i in arange(D):
# Rounding precision
decimal = int(-log10(dedges[i].min())) +6
# Find which points are on the rightmost edge.
on_edge = where(around(sample[:,i], decimal) == around(edges[i][-1], decimal))[0]
# Shift these points one bin to the left.
Ncount[i][on_edge] -= 1
# Flattened histogram matrix (1D)
hist = zeros(nbin.prod(), float)
# Compute the sample indices in the flattened histogram matrix.
ni = nbin.argsort()
shape = []
xy = zeros(N, int)
for i in arange(0, D-1):
xy += Ncount[ni[i]] * nbin[ni[i+1:]].prod()
xy += Ncount[ni[-1]]
# Compute the number of repetitions in xy and assign it to the flattened histmat.
if len(xy) == 0:
return zeros(nbin-2, int), edges
flatcount = bincount(xy, weights)
a = arange(len(flatcount))
hist[a] = flatcount
# Shape into a proper matrix
hist = hist.reshape(sort(nbin))
for i in arange(nbin.size):
j = ni[i]
hist = hist.swapaxes(i,j)
ni[i],ni[j] = ni[j],ni[i]
# Remove outliers (indices 0 and -1 for each dimension).
core = D*[slice(1,-1)]
hist = hist[core]
# Normalize if normed is True
if normed:
s = hist.sum()
for i in arange(D):
shape = ones(D, int)
shape[i] = nbin[i]-2
hist = hist / dedges[i].reshape(shape)
hist /= s
return hist, edges
def apply_along_axes(func1d, axis, arrs, *args):
"""
Apply a function to 1-D slices along the given axis.
Execute `func1d(a, *args)` where `func1d` operates on a set of 1-D arrays and `a`
is a 1-D slice of `arr` along `axis`.
Parameters
----------
func1d : function
This function should accept 1-D arrays. It is applied to 1-D
slices of `arr` along the specified axis.
axis : integer
Axis along which `arr` is sliced.
arrs : tuple
tuple of input arrays. All arrays must have the same shape
args : any
Additional arguments to `func1d`.
Returns
-------
outarr : ndarray
The output array. The shape of `outarr` is identical to the shape of
`arr`, except along the `axis` dimension, where the length of `outarr`
is equal to the size of the return value of `func1d`. If `func1d`
returns a scalar `outarr` will have one fewer dimensions than `arr`.
See Also
--------
apply_over_axis : Apply a function over 1-D slices of a single array.
apply_over_axes : Apply a function repeatedly over multiple axes.
"""
arrs = list(map(asarray, arrs))
arr = arrs[0]
nd = arr.ndim
if axis < 0:
axis += nd
if (axis >= nd):
raise ValueError("axis must be less than arr.ndim; axis=%d, rank=%d." %
(axis, nd))
ind = [0] * (nd - 1)
i = zeros(nd, 'O')
indlist = list(range(nd))
indlist.remove(axis)
i[axis] = slice(None, None)
outshape = asarray(arr.shape).take(indlist)
for arr in arrs[1:]:
if tuple(asarray(arr.shape).take(indlist)) != tuple(outshape):
raise ValueError(
"Shape of all input arrays must match in all but the selected dimension."
)
i.put(indlist, ind)
arglist = tuple([arr[tuple(i.tolist())] for arr in arrs]) + args
res = func1d(*arglist)
# if res is a number, then we have a smaller output array
if isscalar(res):
outarr = zeros(outshape, asarray(res).dtype)
outarr[tuple(ind)] = res
Ntot = product(outshape)
k = 1
while k < Ntot:
# increment the index
ind[-1] += 1
n = -1
while (ind[n] >= outshape[n]) and (n > (1 - nd)):
ind[n - 1] += 1
ind[n] = 0
n -= 1
i.put(indlist, ind)
arglist = tuple([arr[tuple(i.tolist())] for arr in arrs]) + args
res = func1d(*arglist)
outarr[tuple(ind)] = res
k += 1
return outarr
else:
Ntot = product(outshape)
holdshape = outshape
outshape = list(arr.shape)
outshape[axis] = len(res)
outarr = zeros(outshape, asarray(res).dtype)
outarr[tuple(i.tolist())] = res
k = 1
while k < Ntot:
# increment the index
ind[-1] += 1
n = -1
while (ind[n] >= holdshape[n]) and (n > (1 - nd)):
ind[n - 1] += 1
ind[n] = 0
n -= 1
i.put(indlist, ind)
arglist = tuple([arr[tuple(i.tolist())] for arr in arrs]) + args
res = func1d(*arglist)
#res = func1d(arr[tuple(i.tolist())],*args)
outarr[tuple(i.tolist())] = res
k += 1
return outarr
def isclose(a, b, rtol=1.e-5, atol=1.e-8, equal_nan=False):
"""
Returns a boolean array where two arrays are element-wise equal within a
tolerance.
The tolerance values are positive, typically very small numbers. The
relative difference (`rtol` * abs(`b`)) and the absolute difference
`atol` are added together to compare against the absolute difference
between `a` and `b`.
Parameters
----------
a, b : array_like
Input arrays to compare.
rtol : float
The relative tolerance parameter (see Notes).
atol : float
The absolute tolerance parameter (see Notes).
equal_nan : bool
Whether to compare NaN's as equal. If True, NaN's in `a` will be
considered equal to NaN's in `b` in the output array.
Returns
-------
y : array_like
Returns a boolean array of where `a` and `b` are equal within the
given tolerance. If both `a` and `b` are scalars, returns a single
boolean value.
See Also
--------
allclose
Notes
-----
.. versionadded:: 1.7.0
For finite values, isclose uses the following equation to test whether
two floating point values are equivalent.
absolute(`a` - `b`) <= (`atol` + `rtol` * absolute(`b`))
The above equation is not symmetric in `a` and `b`, so that
`isclose(a, b)` might be different from `isclose(b, a)` in
some rare cases.
Examples
--------
>>> np.isclose([1e10,1e-7], [1.00001e10,1e-8])
array([True, False])
>>> np.isclose([1e10,1e-8], [1.00001e10,1e-9])
array([True, True])
>>> np.isclose([1e10,1e-8], [1.0001e10,1e-9])
array([False, True])
>>> np.isclose([1.0, np.nan], [1.0, np.nan])
array([True, False])
>>> np.isclose([1.0, np.nan], [1.0, np.nan], equal_nan=True)
array([True, True])
"""
def within_tol(x, y, atol, rtol):
with errstate(invalid='ignore'):
result = less_equal(abs(x - y), atol + rtol * abs(y))
if isscalar(a) and isscalar(b):
result = bool(result)
return result
x = array(a, copy=False, subok=True, ndmin=1)
y = array(b, copy=False, subok=True, ndmin=1)
# Make sure y is an inexact type to avoid bad behavior on abs(MIN_INT).
# This will cause casting of x later. Also, make sure to allow subclasses
# (e.g., for numpy.ma).
dt = multiarray.result_type(y, 1.)
y = array(y, dtype=dt, copy=False, subok=True)
xfin = isfinite(x)
yfin = isfinite(y)
if all(xfin) and all(yfin):
return within_tol(x, y, atol, rtol)
else:
finite = xfin & yfin
cond = zeros_like(finite, subok=True)
# Because we're using boolean indexing, x & y must be the same shape.
# Ideally, we'd just do x, y = broadcast_arrays(x, y). It's in
# lib.stride_tricks, though, so we can't import it here.
x = x * ones_like(cond)
y = y * ones_like(cond)
# Avoid subtraction with infinite/nan values...
cond[finite] = within_tol(x[finite], y[finite], atol, rtol)
# Check for equality of infinite values...
cond[~finite] = (x[~finite] == y[~finite])
if equal_nan:
# Make NaN == NaN
both_nan = isnan(x) & isnan(y)
cond[both_nan] = both_nan[both_nan]
if isscalar(a) and isscalar(b):
return bool(cond)
else:
return cond
def __rdiv__(self, other):
if isscalar(other):
return self._copy(self.ent_table, self.att_table, a=other/self.a, c=-self.c)
return NotImplemented
def histogramdd(sample, bins=10, range=None, normed=False, weights=None):
"""histogramdd(sample, bins=10, range=None, normed=False, weights=None)
Return the N-dimensional histogram of the sample.
Parameters:
sample : sequence or array
A sequence containing N arrays or an NxM array. Input data.
bins : sequence or scalar
A sequence of edge arrays, a sequence of bin counts, or a scalar
which is the bin count for all dimensions. Default is 10.
range : sequence
A sequence of lower and upper bin edges. Default is [min, max].
normed : boolean
If False, return the number of samples in each bin, if True,
returns the density.
weights : array
Array of weights. The weights are normed only if normed is True.
Should the sum of the weights not equal N, the total bin count will
not be equal to the number of samples.
Returns:
hist : array
Histogram array.
edges : list
List of arrays defining the lower bin edges.
SeeAlso:
histogram
Example
>>> x = random.randn(100,3)
>>> hist3d, edges = histogramdd(x, bins = (5, 6, 7))
"""
try:
# Sample is an ND-array.
N, D = sample.shape
except (AttributeError, ValueError):
# Sample is a sequence of 1D arrays.
sample = atleast_2d(sample).T
N, D = sample.shape
nbin = empty(D, int)
edges = D * [None]
dedges = D * [None]
if weights is not None:
weights = asarray(weights)
try:
M = len(bins)
if M != D:
raise AttributeError, 'The dimension of bins must be a equal to the dimension of the sample x.'
except TypeError:
bins = D * [bins]
# Select range for each dimension
# Used only if number of bins is given.
if range is None:
smin = atleast_1d(array(sample.min(0), float))
smax = atleast_1d(array(sample.max(0), float))
else:
smin = zeros(D)
smax = zeros(D)
for i in arange(D):
smin[i], smax[i] = range[i]
# Make sure the bins have a finite width.
for i in arange(len(smin)):
if smin[i] == smax[i]:
smin[i] = smin[i] - .5
smax[i] = smax[i] + .5
# Create edge arrays
for i in arange(D):
if isscalar(bins[i]):
nbin[i] = bins[i] + 2 # +2 for outlier bins
edges[i] = linspace(smin[i], smax[i], nbin[i] - 1)
else:
edges[i] = asarray(bins[i], float)
nbin[i] = len(edges[i]) + 1 # +1 for outlier bins
dedges[i] = diff(edges[i])
nbin = asarray(nbin)
# Compute the bin number each sample falls into.
Ncount = {}
for i in arange(D):
Ncount[i] = digitize(sample[:, i], edges[i])
# Using digitize, values that fall on an edge are put in the right bin.
# For the rightmost bin, we want values equal to the right
# edge to be counted in the last bin, and not as an outlier.
outliers = zeros(N, int)
for i in arange(D):
# Rounding precision
decimal = int(-log10(dedges[i].min())) + 6
# Find which points are on the rightmost edge.
on_edge = where(
around(sample[:, i], decimal) == around(edges[i][-1], decimal))[0]
# Shift these points one bin to the left.
Ncount[i][on_edge] -= 1
# Flattened histogram matrix (1D)
hist = zeros(nbin.prod(), float)
# Compute the sample indices in the flattened histogram matrix.
ni = nbin.argsort()
shape = []
xy = zeros(N, int)
for i in arange(0, D - 1):
xy += Ncount[ni[i]] * nbin[ni[i + 1:]].prod()
xy += Ncount[ni[-1]]
# Compute the number of repetitions in xy and assign it to the flattened histmat.
if len(xy) == 0:
return zeros(nbin - 2, int), edges
flatcount = bincount(xy, weights)
a = arange(len(flatcount))
hist[a] = flatcount
# Shape into a proper matrix
hist = hist.reshape(sort(nbin))
for i in arange(nbin.size):
j = ni[i]
hist = hist.swapaxes(i, j)
ni[i], ni[j] = ni[j], ni[i]
# Remove outliers (indices 0 and -1 for each dimension).
core = D * [slice(1, -1)]
hist = hist[core]
# Normalize if normed is True
if normed:
s = hist.sum()
for i in arange(D):
shape = ones(D, int)
shape[i] = nbin[i] - 2
hist = hist / dedges[i].reshape(shape)
hist /= s
return hist, edges
def __idiv__(self, other):
if isscalar(other):
self.a = self.a / other
return self
return NotImplemented
def apply_along_axis(func1d, axis, arr, *args):
"""
Apply function to 1-D slices along the given axis.
Execute `func1d(a[i],*args)` where `func1d` takes 1-D arrays, `a` is
the input array, and `i` is an integer that varies in order to apply the
function along the given axis for each 1-D subarray in `a`.
Parameters
----------
func1d : function
This function should be able to take 1-D arrays. It is applied to 1-D
slices of `a` along the specified axis.
axis : integer
Axis along which `func1d` is applied.
a : ndarray
Input array.
args : any
Additional arguments to `func1d`.
Returns
-------
out : ndarray
The output array. The shape of `out` is identical to the shape of `a`,
except along the `axis` dimension, whose length is equal to the size
of the return value of `func1d`.
See Also
--------
apply_over_axes : Apply a function repeatedly over multiple axes.
Examples
--------
>>> def my_func(a):
... \"\"\"Average first and last element of a 1-D array\"\"\"
... return (a[0] + a[-1]) * 0.5
>>> b = np.array([[1,2,3], [4,5,6], [7,8,9]])
>>> np.apply_along_axis(my_func, 0, b)
array([4., 5., 6.])
>>> np.apply_along_axis(my_func, 1, b)
array([2., 5., 8.])
"""
arr = asarray(arr)
nd = arr.ndim
if axis < 0:
axis += nd
if (axis >= nd):
raise ValueError("axis must be less than arr.ndim; axis=%d, rank=%d." %
(axis, nd))
ind = [0] * (nd - 1)
i = zeros(nd, 'O')
indlist = range(nd)
indlist.remove(axis)
i[axis] = slice(None, None)
outshape = asarray(arr.shape).take(indlist)
i.put(indlist, ind)
res = func1d(arr[tuple(i.tolist())], *args)
# if res is a number, then we have a smaller output array
if isscalar(res):
outarr = zeros(outshape, asarray(res).dtype)
outarr[tuple(ind)] = res
Ntot = product(outshape)
k = 1
while k < Ntot:
# increment the index
ind[-1] += 1
n = -1
while (ind[n] >= outshape[n]) and (n > (1 - nd)):
ind[n - 1] += 1
ind[n] = 0
n -= 1
i.put(indlist, ind)
res = func1d(arr[tuple(i.tolist())], *args)
outarr[tuple(ind)] = res
k += 1
return outarr
else:
Ntot = product(outshape)
holdshape = outshape
outshape = list(arr.shape)
outshape[axis] = len(res)
outarr = zeros(outshape, asarray(res).dtype)
outarr[tuple(i.tolist())] = res
k = 1
while k < Ntot:
# increment the index
ind[-1] += 1
n = -1
while (ind[n] >= holdshape[n]) and (n > (1 - nd)):
ind[n - 1] += 1
ind[n] = 0
n -= 1
i.put(indlist, ind)
res = func1d(arr[tuple(i.tolist())], *args)
outarr[tuple(i.tolist())] = res
k += 1
return outarr