def _hist_bin_fd(x):
"""
The Freedman-Diaconis histogram bin estimator.
The Freedman-Diaconis rule uses interquartile range (IQR) to
estimate binwidth. It is considered a variation of the Scott rule
with more robustness as the IQR is less affected by outliers than
the standard deviation. However, the IQR depends on fewer points
than the standard deviation, so it is less accurate, especially for
long tailed distributions.
If the IQR is 0, this function returns 1 for the number of bins.
Binwidth is inversely proportional to the cube root of data size
(asymptotically optimal).
Parameters
----------
x : array_like
Input data that is to be histogrammed, trimmed to range. May not
be empty.
Returns
-------
h : An estimate of the optimal bin width for the given data.
"""
iqr = np.subtract(*np.percentile(x, [75, 25]))
return 2.0 * iqr * x.size**(-1.0 / 3.0)
def test_pure_subclass_info_preservation(self):
# Test that ufuncs and methods conserve extra information consistently;
# see gh-7122.
arr1 = SubMaskedArray('test', data=[1, 2, 3, 4, 5, 6])
arr2 = SubMaskedArray(data=[0, 1, 2, 3, 4, 5])
diff1 = np.subtract(arr1, arr2)
assert_('info' in diff1._optinfo)
assert_(diff1._optinfo['info'] == 'test')
diff2 = arr1 - arr2
assert_('info' in diff2._optinfo)
assert_(diff2._optinfo['info'] == 'test')
def _unsigned_subtract(a, b):
"""
Subtract two values where a >= b, and produce an unsigned result
This is needed when finding the difference between the upper and lower
bound of an int16 histogram
"""
# coerce to a single type
signed_to_unsigned = {
np.byte: np.ubyte,
np.short: np.ushort,
np.intc: np.uintc,
np.int_: np.uint,
np.longlong: np.ulonglong
}
dt = np.result_type(a, b)
try:
dt = signed_to_unsigned[dt.type]
except KeyError:
return np.subtract(a, b, dtype=dt)
else:
# we know the inputs are integers, and we are deliberately casting
# signed to unsigned
return np.subtract(a, b, casting='unsafe', dtype=dt)
def test_testArithmetic(self):
# Test of basic arithmetic.
(x, y, a10, m1, m2, xm, ym, z, zm, xf, s) = self.d
a2d = array([[1, 2], [0, 4]])
a2dm = masked_array(a2d, [[0, 0], [1, 0]])
assert_(eq(a2d * a2d, a2d * a2dm))
assert_(eq(a2d + a2d, a2d + a2dm))
assert_(eq(a2d - a2d, a2d - a2dm))
for s in [(12,), (4, 3), (2, 6)]:
x = x.reshape(s)
y = y.reshape(s)
xm = xm.reshape(s)
ym = ym.reshape(s)
xf = xf.reshape(s)
assert_(eq(-x, -xm))
assert_(eq(x + y, xm + ym))
assert_(eq(x - y, xm - ym))
assert_(eq(x * y, xm * ym))
with np.errstate(divide='ignore', invalid='ignore'):
assert_(eq(x / y, xm / ym))
assert_(eq(a10 + y, a10 + ym))
assert_(eq(a10 - y, a10 - ym))
assert_(eq(a10 * y, a10 * ym))
with np.errstate(divide='ignore', invalid='ignore'):
assert_(eq(a10 / y, a10 / ym))
assert_(eq(x + a10, xm + a10))
assert_(eq(x - a10, xm - a10))
assert_(eq(x * a10, xm * a10))
assert_(eq(x / a10, xm / a10))
assert_(eq(x ** 2, xm ** 2))
assert_(eq(abs(x) ** 2.5, abs(xm) ** 2.5))
assert_(eq(x ** y, xm ** ym))
assert_(eq(np.add(x, y), add(xm, ym)))
assert_(eq(np.subtract(x, y), subtract(xm, ym)))
assert_(eq(np.multiply(x, y), multiply(xm, ym)))
with np.errstate(divide='ignore', invalid='ignore'):
assert_(eq(np.divide(x, y), divide(xm, ym)))
def test_half_ufuncs(self):
"""Test the various ufuncs"""
a = np.array([0, 1, 2, 4, 2], dtype=float16)
b = np.array([-2, 5, 1, 4, 3], dtype=float16)
c = np.array([0, -1, -np.inf, np.nan, 6], dtype=float16)
assert_equal(np.add(a, b), [-2, 6, 3, 8, 5])
assert_equal(np.subtract(a, b), [2, -4, 1, 0, -1])
assert_equal(np.multiply(a, b), [0, 5, 2, 16, 6])
assert_equal(np.divide(a, b), [0, 0.199951171875, 2, 1, 0.66650390625])
assert_equal(np.equal(a, b), [False, False, False, True, False])
assert_equal(np.not_equal(a, b), [True, True, True, False, True])
assert_equal(np.less(a, b), [False, True, False, False, True])
assert_equal(np.less_equal(a, b), [False, True, False, True, True])
assert_equal(np.greater(a, b), [True, False, True, False, False])
assert_equal(np.greater_equal(a, b), [True, False, True, True, False])
assert_equal(np.logical_and(a, b), [False, True, True, True, True])
assert_equal(np.logical_or(a, b), [True, True, True, True, True])
assert_equal(np.logical_xor(a, b), [True, False, False, False, False])
assert_equal(np.logical_not(a), [True, False, False, False, False])
assert_equal(np.isnan(c), [False, False, False, True, False])
assert_equal(np.isinf(c), [False, False, True, False, False])
assert_equal(np.isfinite(c), [True, True, False, False, True])
assert_equal(np.signbit(b), [True, False, False, False, False])
assert_equal(np.copysign(b, a), [2, 5, 1, 4, 3])
assert_equal(np.maximum(a, b), [0, 5, 2, 4, 3])
x = np.maximum(b, c)
assert_(np.isnan(x[3]))
x[3] = 0
assert_equal(x, [0, 5, 1, 0, 6])
assert_equal(np.minimum(a, b), [-2, 1, 1, 4, 2])
x = np.minimum(b, c)
assert_(np.isnan(x[3]))
x[3] = 0
assert_equal(x, [-2, -1, -np.inf, 0, 3])
assert_equal(np.fmax(a, b), [0, 5, 2, 4, 3])
assert_equal(np.fmax(b, c), [0, 5, 1, 4, 6])
assert_equal(np.fmin(a, b), [-2, 1, 1, 4, 2])
assert_equal(np.fmin(b, c), [-2, -1, -np.inf, 4, 3])
assert_equal(np.floor_divide(a, b), [0, 0, 2, 1, 0])
assert_equal(np.remainder(a, b), [0, 1, 0, 0, 2])
assert_equal(np.divmod(a, b), ([0, 0, 2, 1, 0], [0, 1, 0, 0, 2]))
assert_equal(np.square(b), [4, 25, 1, 16, 9])
assert_equal(np.reciprocal(b),
[-0.5, 0.199951171875, 1, 0.25, 0.333251953125])
assert_equal(np.ones_like(b), [1, 1, 1, 1, 1])
assert_equal(np.conjugate(b), b)
assert_equal(np.absolute(b), [2, 5, 1, 4, 3])
assert_equal(np.negative(b), [2, -5, -1, -4, -3])
assert_equal(np.positive(b), b)
assert_equal(np.sign(b), [-1, 1, 1, 1, 1])
assert_equal(np.modf(b), ([0, 0, 0, 0, 0], b))
assert_equal(np.frexp(b),
([-0.5, 0.625, 0.5, 0.5, 0.75], [2, 3, 1, 3, 2]))
assert_equal(np.ldexp(b, [0, 1, 2, 4, 2]), [-2, 10, 4, 64, 12])
def ediff1d(ary, to_end=None, to_begin=None):
"""
The differences between consecutive elements of an array.
Parameters
----------
ary : array_like
If necessary, will be flattened before the differences are taken.
to_end : array_like, optional
Number(s) to append at the end of the returned differences.
to_begin : array_like, optional
Number(s) to prepend at the beginning of the returned differences.
Returns
-------
ediff1d : ndarray
The differences. Loosely, this is ``ary.flat[1:] - ary.flat[:-1]``.
See Also
--------
diff, gradient
Notes
-----
When applied to masked arrays, this function drops the mask information
if the `to_begin` and/or `to_end` parameters are used.
Examples
--------
>>> x = np.array([1, 2, 4, 7, 0])
>>> np.ediff1d(x)
array([ 1, 2, 3, -7])
>>> np.ediff1d(x, to_begin=-99, to_end=np.array([88, 99]))
array([-99, 1, 2, 3, -7, 88, 99])
The returned array is always 1D.
>>> y = [[1, 2, 4], [1, 6, 24]]
>>> np.ediff1d(y)
array([ 1, 2, -3, 5, 18])
"""
# force a 1d array
ary = np.asanyarray(ary).ravel()
# fast track default case
if to_begin is None and to_end is None:
return ary[1:] - ary[:-1]
if to_begin is None:
l_begin = 0
else:
to_begin = np.asanyarray(to_begin).ravel()
l_begin = len(to_begin)
if to_end is None:
l_end = 0
else:
to_end = np.asanyarray(to_end).ravel()
l_end = len(to_end)
# do the calculation in place and copy to_begin and to_end
l_diff = max(len(ary) - 1, 0)
result = np.empty(l_diff + l_begin + l_end, dtype=ary.dtype)
result = ary.__array_wrap__(result)
if l_begin > 0:
result[:l_begin] = to_begin
if l_end > 0:
result[l_begin + l_diff:] = to_end
np.subtract(ary[1:], ary[:-1], result[l_begin:l_begin + l_diff])
return result