def demean(arr, axis=None):
"""
Subtract the mean along the specified axis.
Parameters
----------
arr : ndarray
Input array.
axis : {int, None}, optional
The axis along which to remove the mean. The default (None) is
to subtract the mean of the flattened array.
Returns
-------
y : ndarray
A copy with the mean along the specified axis removed.
Examples
--------
>>> arr = np.array([1, np.nan, 2, 3])
>>> demean(arr)
array([ -1., NaN, 0., 1.])
"""
# Adapted from pylab.demean
if axis != 0 and not axis is None:
ind = [slice(None)] * arr.ndim
ind[axis] = np.newaxis
arr = arr - nanmean(arr, axis)[ind]
else:
arr = arr - nanmean(arr, axis)
return arr
def demean(arr, axis=None):
"""
Subtract the mean along the specified axis.
Parameters
----------
arr : ndarray
Input array.
axis : {int, None}, optional
The axis along which to remove the mean. The default (None) is
to subtract the mean of the flattened array.
Returns
-------
y : ndarray
A copy with the mean along the specified axis removed.
Examples
--------
>>> arr = np.array([1, np.nan, 2, 3])
>>> demean(arr)
array([ -1., NaN, 0., 1.])
"""
# Adapted from pylab.demean
if axis != 0 and not axis is None:
ind = [slice(None)] * arr.ndim
ind[axis] = np.newaxis
arr = arr - nanmean(arr, axis)[ind]
else:
arr = arr - nanmean(arr, axis)
return arr
def test_nanmean_all(self):
"""Check nanmean when all values are nan."""
m = nanmean(self.Xall)
assert np.isnan(m)
def test_nanmean_some(self):
"""Check nanmean when some values only are nan."""
m = nanmean(self.Xsome)
assert_approx_equal(m, 5.5)
def test_nanmean_none(self):
"""Check nanmean when no values are nan."""
m = nanmean(X)
assert_approx_equal(m, X[4])
def test_nanmean_all(self):
"""Check nanmean when all values are nan."""
m = nanmean(self.Xall)
assert np.isnan(m)
def test_nanmean_some(self):
"""Check nanmean when some values only are nan."""
m = nanmean(self.Xsome)
assert_approx_equal(m, 5.5)
def test_nanmean_none(self):
"""Check nanmean when no values are nan."""
m = nanmean(X)
assert_approx_equal(m, X[4])
def correlation(arr1, arr2, axis=None):
"""
Correlation between two Numpy arrays along the specified axis.
This is not a cross correlation function. If the two input arrays have
shape (n, m), for example, then the output will have shape (m,) if axis
is 0 and shape (n,) if axis is 1.
Parameters
----------
arr1 : Numpy ndarray
Input array.
arr2 : Numpy ndarray
Input array.
axis : {int, None}, optional
The axis along which to measure the correlation. The default, axis
None, flattens the input arrays before finding the correlation and
returning it as a scalar.
Returns
-------
corr : Numpy ndarray, scalar
The correlation between `arr1` and `arr2` along the specified axis.
Examples
--------
Make two Numpy arrays:
>>> a1 = np.array([[1, 2], [3, 4]])
>>> a2 = np.array([[2, 1], [4, 3]])
>>> a1
array([[1, 2],
[3, 4]])
>>> a2
array([[2, 1],
[4, 3]])
Find the correlation between the two arrays along various axes:
>>> correlation(a1, a2)
0.59999999999999998
>>> correlation(a1, a2, axis=0)
array([ 1., 1.])
>>> correlation(a1, a2, axis=1)
array([-1., -1.])
"""
mask = np.logical_or(np.isnan(arr1), np.isnan(arr2))
if mask.any():
# arr1 and/or arr2 contain NaNs, so use slower NaN functions if needed
if axis == None:
x1 = arr1.flatten()
x2 = arr2.flatten()
idx = ~mask.flatten()
x1 = x1[idx]
x2 = x2[idx]
x1 = x1 - x1.mean()
x2 = x2 - x2.mean()
num = (x1 * x2).sum()
den = np.sqrt((x1 * x1).sum() * (x2 * x2).sum())
else:
x1 = arr1.copy()
x2 = arr2.copy()
x1[mask] = np.nan
x2[mask] = np.nan
if axis == 0:
x1 = x1 - nanmean(x1, axis)
x2 = x2 - nanmean(x2, axis)
else:
idx = [slice(None)] * x1.ndim
idx[axis] = None
x1 = x1 - nanmean(x1, axis)[idx]
x2 = x2 - nanmean(x2, axis)[idx]
num = np.nansum(x1 * x2, axis)
den = np.sqrt(np.nansum(x1 * x1, axis) * np.nansum(x2 * x2, axis))
else:
# Neither arr1 or arr2 contains nans, so use faster non-nan functions
if axis == None:
x1 = arr1.flatten()
x2 = arr2.flatten()
x1 = x1 - x1.mean()
x2 = x2 - x2.mean()
num = (x1 * x2).sum()
den = np.sqrt((x1 * x1).sum() * (x2 * x2).sum())
else:
x1 = arr1
x2 = arr2
if axis == 0:
x1 = x1 - x1.mean(axis)
x2 = x2 - x2.mean(axis)
else:
idx = [slice(None)] * x1.ndim
idx[axis] = None
x1 = x1 - x1.mean(axis)[idx]
x2 = x2 - x2.mean(axis)[idx]
num = np.sum(x1 * x2, axis)
den = np.sqrt(np.sum(x1 * x1, axis) * np.sum(x2 * x2, axis))
return num / den
def correlation(arr1, arr2, axis=None):
"""
Correlation between two Numpy arrays along the specified axis.
This is not a cross correlation function. If the two input arrays have
shape (n, m), for example, then the output will have shape (m,) if axis
is 0 and shape (n,) if axis is 1.
Parameters
----------
arr1 : Numpy ndarray
Input array.
arr2 : Numpy ndarray
Input array.
axis : {int, None}, optional
The axis along which to measure the correlation. The default, axis
None, flattens the input arrays before finding the correlation and
returning it as a scalar.
Returns
-------
corr : Numpy ndarray, scalar
The correlation between `arr1` and `arr2` along the specified axis.
Examples
--------
Make two Numpy arrays:
>>> a1 = np.array([[1, 2], [3, 4]])
>>> a2 = np.array([[2, 1], [4, 3]])
>>> a1
array([[1, 2],
[3, 4]])
>>> a2
array([[2, 1],
[4, 3]])
Find the correlation between the two arrays along various axes:
>>> correlation(a1, a2)
0.59999999999999998
>>> correlation(a1, a2, axis=0)
array([ 1., 1.])
>>> correlation(a1, a2, axis=1)
array([-1., -1.])
"""
mask = np.logical_or(np.isnan(arr1), np.isnan(arr2))
if mask.any():
# arr1 and/or arr2 contain NaNs, so use slower NaN functions if needed
if axis == None:
x1 = arr1.flatten()
x2 = arr2.flatten()
idx = ~mask.flatten()
x1 = x1[idx]
x2 = x2[idx]
x1 = x1 - x1.mean()
x2 = x2 - x2.mean()
num = (x1 * x2).sum()
den = np.sqrt((x1 * x1).sum() * (x2 * x2).sum())
else:
x1 = arr1.copy()
x2 = arr2.copy()
x1[mask] = np.nan
x2[mask] = np.nan
if axis == 0:
x1 = x1 - nanmean(x1, axis)
x2 = x2 - nanmean(x2, axis)
else:
idx = [slice(None)] * x1.ndim
idx[axis] = None
x1 = x1 - nanmean(x1, axis)[idx]
x2 = x2 - nanmean(x2, axis)[idx]
num = np.nansum(x1 * x2, axis)
den = np.sqrt(np.nansum(x1 * x1, axis) * np.nansum(x2 * x2, axis))
else:
# Neither arr1 or arr2 contains nans, so use faster non-nan functions
if axis == None:
x1 = arr1.flatten()
x2 = arr2.flatten()
x1 = x1 - x1.mean()
x2 = x2 - x2.mean()
num = (x1 * x2).sum()
den = np.sqrt((x1 * x1).sum() * (x2 * x2).sum())
else:
x1 = arr1
x2 = arr2
if axis == 0:
x1 = x1 - x1.mean(axis)
x2 = x2 - x2.mean(axis)
else:
idx = [slice(None)] * x1.ndim
idx[axis] = None
x1 = x1 - x1.mean(axis)[idx]
x2 = x2 - x2.mean(axis)[idx]
num = np.sum(x1 * x2, axis)
den = np.sqrt(np.sum(x1 * x1, axis) * np.sum(x2 * x2, axis))
return num / den
