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BUG: Fixes #5184 gradient calculation behavior at boundaries #5186

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Merged
merged 1 commit into from
Oct 16, 2014
Merged

BUG: Fixes #5184 gradient calculation behavior at boundaries #5186

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49 changes: 30 additions & 19 deletions numpy/lib/function_base.py
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Original file line number Diff line number Diff line change
Expand Up @@ -883,28 +883,33 @@ def copy(a, order='K'):
# Basic operations


def gradient(f, *varargs):
def gradient(f, *varargs, **kwargs):
"""
Return the gradient of an N-dimensional array.

The gradient is computed using second order accurate central differences
in the interior and second order accurate one-sides (forward or backwards)
differences at the boundaries. The returned gradient hence has the same
shape as the input array.
in the interior and either first differences or second order accurate
one-sides (forward or backwards) differences at the boundaries. The
returned gradient hence has the same shape as the input array.

Parameters
----------
f : array_like
An N-dimensional array containing samples of a scalar function.
`*varargs` : scalars
0, 1, or N scalars specifying the sample distances in each direction,
that is: `dx`, `dy`, `dz`, ... The default distance is 1.
An N-dimensional array containing samples of a scalar function.
varargs : list of scalar, optional
N scalars specifying the sample distances for each dimension,
i.e. `dx`, `dy`, `dz`, ... Default distance: 1.
edge_order : {1, 2}, optional
Gradient is calculated using N\ :sup:`th` order accurate differences
at the boundaries. Default: 1.

.. versionadded:: 1.9.1

Returns
-------
gradient : ndarray
N arrays of the same shape as `f` giving the derivative of `f` with
respect to each dimension.
N arrays of the same shape as `f` giving the derivative of `f` with
respect to each dimension.

Examples
--------
Expand All @@ -916,15 +921,14 @@ def gradient(f, *varargs):

>>> np.gradient(np.array([[1, 2, 6], [3, 4, 5]], dtype=np.float))
[array([[ 2., 2., -1.],
[ 2., 2., -1.]]),
array([[ 1. , 2.5, 4. ],
[ 1. , 1. , 1. ]])]
[ 2., 2., -1.]]), array([[ 1. , 2.5, 4. ],
[ 1. , 1. , 1. ]])]

>>> x = np.array([0,1,2,3,4])
>>> dx = gradient(x)
>>> x = np.array([0, 1, 2, 3, 4])
>>> dx = np.gradient(x)
>>> y = x**2
>>> gradient(y,dx)
array([0., 2., 4., 6., 8.])
>>> np.gradient(y, dx, edge_order=2)
array([-0., 2., 4., 6., 8.])
"""
f = np.asanyarray(f)
N = len(f.shape) # number of dimensions
Expand All @@ -939,6 +943,13 @@ def gradient(f, *varargs):
raise SyntaxError(
"invalid number of arguments")

edge_order = kwargs.pop('edge_order', 1)
if kwargs:
raise TypeError('"{}" are not valid keyword arguments.'.format(
'", "'.join(kwargs.keys())))
if edge_order > 2:
raise ValueError("'edge_order' greater than 2 not supported")

# use central differences on interior and one-sided differences on the
# endpoints. This preserves second order-accuracy over the full domain.

Expand Down Expand Up @@ -978,7 +989,7 @@ def gradient(f, *varargs):
"at least two elements are required.")

# Numerical differentiation: 1st order edges, 2nd order interior
if y.shape[axis] == 2:
if y.shape[axis] == 2 or edge_order == 1:
# Use first order differences for time data
out = np.empty_like(y, dtype=otype)

Expand Down
6 changes: 3 additions & 3 deletions numpy/lib/tests/test_function_base.py
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Original file line number Diff line number Diff line change
Expand Up @@ -536,7 +536,7 @@ def test_datetime64(self):
'1910-10-12', '1910-12-12', '1912-12-12'],
dtype='datetime64[D]')
dx = np.array(
[-7, -3, 0, 31, 61, 396, 1066],
[-5, -3, 0, 31, 61, 396, 731],
dtype='timedelta64[D]')
assert_array_equal(gradient(x), dx)
assert_(dx.dtype == np.dtype('timedelta64[D]'))
Expand All @@ -547,7 +547,7 @@ def test_timedelta64(self):
[-5, -3, 10, 12, 61, 321, 300],
dtype='timedelta64[D]')
dx = np.array(
[-3, 7, 7, 25, 154, 119, -161],
[2, 7, 7, 25, 154, 119, -21],
dtype='timedelta64[D]')
assert_array_equal(gradient(x), dx)
assert_(dx.dtype == np.dtype('timedelta64[D]'))
Expand All @@ -561,7 +561,7 @@ def test_second_order_accurate(self):
dx = x[1] - x[0]
y = 2 * x ** 3 + 4 * x ** 2 + 2 * x
analytical = 6 * x ** 2 + 8 * x + 2
num_error = np.abs((np.gradient(y, dx) / analytical) - 1)
num_error = np.abs((np.gradient(y, dx, edge_order=2) / analytical) - 1)
assert_(np.all(num_error < 0.03) == True)


Expand Down