def calc_diff_trends(sthext_cube, notsthext_cube, window=109):
"""Calculate trends in difference between southern extratropics and rest of globe.
A window of 109 matches the length of the Argo record
(i.e. 10 years of annually smoothed monthly data)
"""
diff = sthext_cube - notsthext_cube
diff_windows = rolling_window(diff.data, window=window, axis=0)
x_axis_windows = rolling_window(diff.coord('time').points,
window=window,
axis=0)
ntimes = diff_windows.shape[0]
trends = numpy.zeros(ntimes)
for i in range(0, ntimes):
x = x_axis_windows[i, :]
y = diff_windows[i, :]
slope, intercept, r_value, p_value, std_err = stats.linregress(x, y)
trends[i] = slope
# convert units from J/month to J/s so can be expressed as Watts (1 J = W.s)
assert 'days' in str(diff.coord('time').units)
hours_in_day = 24
minutes_in_hour = 60
seconds_in_minute = 60
trends = trends / (hours_in_day * minutes_in_hour * seconds_in_minute)
return trends
def test_1d(self):
# 1-d array input
a = np.array([0, 1, 2, 3, 4], dtype=np.int32)
expected_result = np.array([[0, 1], [1, 2], [2, 3], [3, 4]],
dtype=np.int32)
result = rolling_window(a, window=2)
self.assertArrayEqual(result, expected_result)
def test_step(self):
# step should control how far apart consecutive windows are
a = np.array([[0, 1, 2, 3, 4], [5, 6, 7, 8, 9]], dtype=np.int32)
expected_result = np.array(
[[[0, 1, 2], [2, 3, 4]], [[5, 6, 7], [7, 8, 9]]], dtype=np.int32)
result = rolling_window(a, window=3, step=2, axis=1)
self.assertArrayEqual(result, expected_result)
def test_1d(self):
# 1-d array input
a = np.array([0, 1, 2, 3, 4], dtype=np.int32)
expected_result = np.array([[0, 1], [1, 2], [2, 3], [3, 4]],
dtype=np.int32)
result = rolling_window(a, window=2)
self.assertArrayEqual(result, expected_result)
def test_2d(self):
# 2-d array input
a = np.array([[0, 1, 2, 3, 4], [5, 6, 7, 8, 9]], dtype=np.int32)
expected_result = np.array([[[0, 1, 2], [1, 2, 3], [2, 3, 4]],
[[5, 6, 7], [6, 7, 8], [7, 8, 9]]],
dtype=np.int32)
result = rolling_window(a, window=3, axis=1)
self.assertArrayEqual(result, expected_result)
def test_1d_masked(self):
# 1-d masked array input
a = ma.array([0, 1, 2, 3, 4], mask=[0, 0, 1, 0, 0], dtype=np.int32)
expected_result = ma.array([[0, 1], [1, 2], [2, 3], [3, 4]],
mask=[[0, 0], [0, 1], [1, 0], [0, 0]],
dtype=np.int32)
result = rolling_window(a, window=2)
self.assertMaskedArrayEqual(result, expected_result)
def test_step(self):
# step should control how far apart consecutive windows are
a = np.array([[0, 1, 2, 3, 4], [5, 6, 7, 8, 9]], dtype=np.int32)
expected_result = np.array([[[0, 1, 2], [2, 3, 4]],
[[5, 6, 7], [7, 8, 9]]],
dtype=np.int32)
result = rolling_window(a, window=3, step=2, axis=1)
self.assertArrayEqual(result, expected_result)
def test_2d(self):
# 2-d array input
a = np.array([[0, 1, 2, 3, 4], [5, 6, 7, 8, 9]], dtype=np.int32)
expected_result = np.array([[[0, 1, 2], [1, 2, 3], [2, 3, 4]],
[[5, 6, 7], [6, 7, 8], [7, 8, 9]]],
dtype=np.int32)
result = rolling_window(a, window=3, axis=1)
self.assertArrayEqual(result, expected_result)
def count_spells(data, threshold, axis, spell_length):
"""
Count data occurrences.
Define a function to perform the custom statistical operation.
Note: in order to meet the requirements of iris.analysis.Aggregator,
it must do the calculation over an arbitrary (given) data axis.
Function to calculate the number of points in a sequence where the value
has exceeded a threshold value for at least a certain number of timepoints.
Generalised to operate on multiple time sequences arranged on a specific
axis of a multidimensional array.
Parameters
----------
data: ndarray
raw data to be compared with value threshold.
threshold: float
threshold point for 'significant' datapoints.
axis: int
number of the array dimension mapping the time sequences.
(Can also be negative, e.g. '-1' means last dimension)
spell_length: int
number of consecutive times at which value > threshold to "count".
Returns
-------
int
Number of counts.
"""
if axis < 0:
# just cope with negative axis numbers
axis += data.ndim
# Threshold the data to find the 'significant' points.
if not threshold:
data_hits = data
else:
data_hits = data > float(threshold)
# Make an array with data values "windowed" along the time axis.
###############################################################
# WARNING: default step is = window size i.e. no overlapping
# if you want overlapping windows set the step to be m*spell_length
# where m is a float
###############################################################
hit_windows = rolling_window(data_hits,
window=spell_length,
step=spell_length,
axis=axis)
# Find the windows "full of True-s" (along the added 'window axis').
full_windows = np.all(hit_windows, axis=axis + 1)
# Count points fulfilling the condition (along the time axis).
spell_point_counts = np.sum(full_windows, axis=axis, dtype=int)
return spell_point_counts
def test_degenerate_mask(self):
a = ma.array([[0, 1, 2, 3, 4], [5, 6, 7, 8, 9]], dtype=np.int32)
expected_result = ma.array([[[0, 1, 2], [1, 2, 3], [2, 3, 4]],
[[5, 6, 7], [6, 7, 8], [7, 8, 9]]],
mask=[[[0, 0, 0], [0, 0, 0], [0, 0, 0]],
[[0, 0, 0], [0, 0, 0], [0, 0, 0]]],
dtype=np.int32)
result = rolling_window(a, window=3, axis=1)
self.assertMaskedArrayEqual(result, expected_result)
def test_degenerate_mask(self):
a = ma.array([[0, 1, 2, 3, 4], [5, 6, 7, 8, 9]], dtype=np.int32)
expected_result = ma.array([[[0, 1, 2], [1, 2, 3], [2, 3, 4]],
[[5, 6, 7], [6, 7, 8], [7, 8, 9]]],
mask=[[[0, 0, 0], [0, 0, 0], [0, 0, 0]],
[[0, 0, 0], [0, 0, 0], [0, 0, 0]]],
dtype=np.int32)
result = rolling_window(a, window=3, axis=1)
self.assertMaskedArrayEqual(result, expected_result)
def test_1d_masked(self):
# 1-d masked array input
a = ma.array([0, 1, 2, 3, 4], mask=[0, 0, 1, 0, 0],
dtype=np.int32)
expected_result = ma.array([[0, 1], [1, 2], [2, 3], [3, 4]],
mask=[[0, 0], [0, 1], [1, 0], [0, 0]],
dtype=np.int32)
result = rolling_window(a, window=2)
self.assertMaskedArrayEqual(result, expected_result)
def count_spells(data, threshold, axis, spell_length):
if axis < 0:
axis += data.ndim
data_hits = data > threshold
hit_windows = rolling_window(data_hits, window=spell_length, axis=axis)
full_windows = np.all(hit_windows, axis=axis + 1)
spell_point_counts = np.sum(full_windows, axis=axis, dtype=int)
return spell_point_counts
def count_spells(data, threshold, axis, spell_length):
"""
Function to calculate the number of points in a sequence where the value
has exceeded a threshold value for at least a certain number of timepoints.
Generalised to operate on multiple time sequences arranged on a specific
axis of a multidimensional array.
Args:
* data (array):
raw data to be compared with value threshold.
* threshold (float):
threshold point for 'significant' datapoints.
* axis (int):
number of the array dimension mapping the time sequences.
(Can also be negative, e.g. '-1' means last dimension)
* spell_length (int):
number of consecutive times at which value > threshold to "count".
"""
if axis < 0:
# just cope with negative axis numbers
axis += data.ndim
# Threshold the data to find the 'significant' points.
data_hits = data > threshold
# Make an array with data values "windowed" along the time axis.
###############################################################
# WARNING: default step is = window size i.e. no overlapping
# if you want overlapping windows set the step to be m*spell_length
# where m is a float
###############################################################
hit_windows = rolling_window(data_hits,
window=spell_length,
step=spell_length,
axis=axis)
# Find the windows "full of True-s" (along the added 'window axis').
full_windows = np.all(hit_windows, axis=axis + 1)
# Count points fulfilling the condition (along the time axis).
spell_point_counts = np.sum(full_windows, axis=axis, dtype=int)
return spell_point_counts
def test_2d_masked(self):
# 2-d masked array input
a = ma.array(
[[0, 1, 2, 3, 4], [5, 6, 7, 8, 9]],
mask=[[0, 0, 1, 0, 0], [1, 0, 1, 0, 0]],
dtype=np.int32,
)
expected_result = ma.array(
[
[[0, 1, 2], [1, 2, 3], [2, 3, 4]],
[[5, 6, 7], [6, 7, 8], [7, 8, 9]],
],
mask=[
[[0, 0, 1], [0, 1, 0], [1, 0, 0]],
[[1, 0, 1], [0, 1, 0], [1, 0, 0]],
],
dtype=np.int32,
)
result = rolling_window(a, window=3, axis=1)
self.assertMaskedArrayEqual(result, expected_result)
def count_spells(data, threshold, axis, spell_length):
"""
Function to calculate the number of points in a sequence where the value
has exceeded a threshold value for at least a certain number of timepoints.
Generalised to operate on multiple time sequences arranged on a specific
axis of a multidimensional array.
Args:
* data (array):
raw data to be compared with value threshold.
* threshold (float):
threshold point for 'significant' datapoints.
* axis (int):
number of the array dimension mapping the time sequences.
(Can also be negative, e.g. '-1' means last dimension)
* spell_length (int):
number of consecutive times at which value > threshold to "count".
"""
if axis < 0:
# just cope with negative axis numbers
axis += data.ndim
# Threshold the data to find the 'significant' points.
data_hits = data > threshold
# Make an array with data values "windowed" along the time axis.
hit_windows = rolling_window(data_hits, window=spell_length, axis=axis)
# Find the windows "full of True-s" (along the added 'window axis').
full_windows = np.all(hit_windows, axis=axis+1)
# Count points fulfilling the condition (along the time axis).
spell_point_counts = np.sum(full_windows, axis=axis, dtype=int)
return spell_point_counts
def num_frozen(data, threshold, axis, frozen_length):
"""
Count valid frozen points.
Function to calculate the number of points in a sequence where the value
is less than freezing for at least a certain number of timepoints.
Generalised to operate on multiple time sequences arranged on a specific
axis of a multidimensional array.
"""
if axis < 0:
# just cope with negative axis numbers
axis += data.ndim
# Threshold the data to find the 'significant' points.
data_hits = data < threshold
# Make an array with data values "windowed" along the time axis.
hit_windows = ut.rolling_window(data_hits, window=frozen_length, axis=axis)
# Find the windows "full of True-s" (along the added 'window axis').
full_windows = np.all(hit_windows, axis=axis + 1)
# Count points fulfilling the condition (along the time axis).
frozen_point_counts = np.sum(full_windows, axis=axis, dtype=int)
return frozen_point_counts
def test_invalid_step(self):
# raise an error if the step between windows is less than 1
a = np.empty([5])
with self.assertRaises(ValueError):
rolling_window(a, step=0)
def test_window_too_long(self):
# raise an error if the window length is longer than the
# corresponding array dimension
a = np.empty([7, 5])
with self.assertRaises(ValueError):
rolling_window(a, window=6, axis=1)
def test_window_too_short(self):
# raise an error if the window length is less than 1
a = np.empty([5])
with self.assertRaises(ValueError):
rolling_window(a, window=0)
def test_invalid_step(self):
# raise an error if the step between windows is less than 1
a = np.empty([5])
with self.assertRaises(ValueError):
rolling_window(a, step=0)
def test_window_too_short(self):
# raise an error if the window length is less than 1
a = np.empty([5])
with self.assertRaises(ValueError):
rolling_window(a, window=0)
def test_window_too_long(self):
# raise an error if the window length is longer than the
# corresponding array dimension
a = np.empty([7, 5])
with self.assertRaises(ValueError):
rolling_window(a, window=6, axis=1)