Implement integrate (#2653)

* added integrate.

* Docs

* Update via comment

* Update via comments

* integrate can accept multiple dimensions.

* using set instead of list

* dim -> coord

doc/api.rst

@@ -152,6 +152,7 @@ Computation
    Dataset.diff
    Dataset.quantile
    Dataset.differentiate
+   Dataset.integrate
 
 **Aggregation**:
 :py:attr:`~Dataset.all`
@@ -321,6 +322,7 @@ Computation
    DataArray.dot
    DataArray.quantile
    DataArray.differentiate
+   DataArray.integrate
 
 **Aggregation**:
 :py:attr:`~DataArray.all`

doc/computation.rst

@@ -240,6 +240,8 @@ function or method name to ``coord_func`` option,
   da.coarsen(time=7, x=2, coord_func={'time': 'min'}).mean()
 
 
+.. _compute.using_coordinates:
+
 Computation using Coordinates
 =============================
 
@@ -261,9 +263,17 @@ This method can be used also for multidimensional arrays,
                      coords={'x': [0.1, 0.11, 0.2, 0.3]})
     a.differentiate('x')
 
+:py:meth:`~xarray.DataArray.integrate` computes integration based on
+trapezoidal rule using their coordinates,
+
+.. ipython:: python
+
+    a.integrate('x')
+
 .. note::
-    This method is limited to simple cartesian geometry. Differentiation along
-    multidimensional coordinate is not supported.
+    These methods are limited to simple cartesian geometry. Differentiation
+    and integration along multidimensional coordinate are not supported.
+
 
 .. _compute.broadcasting:
 

doc/whats-new.rst

@@ -47,6 +47,13 @@ Enhancements
   ``nearest``. (:issue:`2695`)
   By `Hauke Schulz <https://github.com/observingClouds>`_.
 
+- :py:meth:`~xarray.DataArray.integrate` and
+  :py:meth:`~xarray.Dataset.integrate` are newly added.
+  See :ref:`_compute.using_coordinates` for the detail.
+  (:issue:`1332`)
+  By `Keisuke Fujii <https://github.com/fujiisoup>`_.
+
+
 Bug fixes
 ~~~~~~~~~
 
@@ -115,6 +122,7 @@ Breaking changes
   (:issue:`2565`). The previous behavior was to decode them only if they
   had specific time attributes, now these attributes are copied
   automatically from the corresponding time coordinate. This might
+  break downstream code that was relying on these variables to be
   brake downstream code that was relying on these variables to be
   not decoded.
   By `Fabien Maussion <https://github.com/fmaussion>`_.

xarray/core/dataarray.py

@@ -2425,6 +2425,53 @@ def differentiate(self, coord, edge_order=1, datetime_unit=None):
             coord, edge_order, datetime_unit)
         return self._from_temp_dataset(ds)
 
+    def integrate(self, dim, datetime_unit=None):
+        """ integrate the array with the trapezoidal rule.
+
+        .. note::
+            This feature is limited to simple cartesian geometry, i.e. coord
+            must be one dimensional.
+
+        Parameters
+        ----------
+        dim: str, or a sequence of str
+            Coordinate(s) used for the integration.
+        datetime_unit
+            Can be specify the unit if datetime coordinate is used. One of
+            {'Y', 'M', 'W', 'D', 'h', 'm', 's', 'ms', 'us', 'ns', 'ps', 'fs',
+             'as'}
+
+        Returns
+        -------
+        integrated: DataArray
+
+        See also
+        --------
+        numpy.trapz: corresponding numpy function
+
+        Examples
+        --------
+
+        >>> da = xr.DataArray(np.arange(12).reshape(4, 3), dims=['x', 'y'],
+        ...                   coords={'x': [0, 0.1, 1.1, 1.2]})
+        >>> da
+        <xarray.DataArray (x: 4, y: 3)>
+        array([[ 0,  1,  2],
+               [ 3,  4,  5],
+               [ 6,  7,  8],
+               [ 9, 10, 11]])
+        Coordinates:
+          * x        (x) float64 0.0 0.1 1.1 1.2
+        Dimensions without coordinates: y
+        >>>
+        >>> da.integrate('x')
+        <xarray.DataArray (y: 3)>
+        array([5.4, 6.6, 7.8])
+        Dimensions without coordinates: y
+        """
+        ds = self._to_temp_dataset().integrate(dim, datetime_unit)
+        return self._from_temp_dataset(ds)
+
 
 # priority most be higher than Variable to properly work with binary ufuncs
 ops.inject_all_ops_and_reduce_methods(DataArray, priority=60)

xarray/core/dataset.py

@@ -3869,6 +3869,78 @@ def differentiate(self, coord, edge_order=1, datetime_unit=None):
                 variables[k] = v
         return self._replace_vars_and_dims(variables)
 
+    def integrate(self, coord, datetime_unit=None):
+        """ integrate the array with the trapezoidal rule.
+
+        .. note::
+            This feature is limited to simple cartesian geometry, i.e. coord
+            must be one dimensional.
+
+        Parameters
+        ----------
+        dim: str, or a sequence of str
+            Coordinate(s) used for the integration.
+        datetime_unit
+            Can be specify the unit if datetime coordinate is used. One of
+            {'Y', 'M', 'W', 'D', 'h', 'm', 's', 'ms', 'us', 'ns', 'ps', 'fs',
+             'as'}
+
+        Returns
+        -------
+        integrated: Dataset
+
+        See also
+        --------
+        DataArray.integrate
+        numpy.trapz: corresponding numpy function
+        """
+        if not isinstance(coord, (list, tuple)):
+            coord = (coord, )
+        result = self
+        for c in coord:
+            result = result._integrate_one(c, datetime_unit=datetime_unit)
+        return result
+
+    def _integrate_one(self, coord, datetime_unit=None):
+        from .variable import Variable
+
+        if coord not in self.variables and coord not in self.dims:
+            raise ValueError('Coordinate {} does not exist.'.format(dim))
+
+        coord_var = self[coord].variable
+        if coord_var.ndim != 1:
+            raise ValueError('Coordinate {} must be 1 dimensional but is {}'
+                             ' dimensional'.format(coord, coord_var.ndim))
+
+        dim = coord_var.dims[0]
+        if _contains_datetime_like_objects(coord_var):
+            if coord_var.dtype.kind in 'mM' and datetime_unit is None:
+                datetime_unit, _ = np.datetime_data(coord_var.dtype)
+            elif datetime_unit is None:
+                datetime_unit = 's'  # Default to seconds for cftime objects
+            coord_var = datetime_to_numeric(
+                coord_var, datetime_unit=datetime_unit)
+
+        variables = OrderedDict()
+        coord_names = set()
+        for k, v in self.variables.items():
+            if k in self.coords:
+                if dim not in v.dims:
+                    variables[k] = v
+                    coord_names.add(k)
+            else:
+                if k in self.data_vars and dim in v.dims:
+                    if _contains_datetime_like_objects(v):
+                        v = datetime_to_numeric(v, datetime_unit=datetime_unit)
+                    integ = duck_array_ops.trapz(
+                        v.data, coord_var.data, axis=v.get_axis_num(dim))
+                    v_dims = list(v.dims)
+                    v_dims.remove(dim)
+                    variables[k] = Variable(v_dims, integ)
+                else:
+                    variables[k] = v
+        return self._replace_vars_and_dims(variables, coord_names=coord_names)
+
     @property
     def real(self):
         return self._unary_op(lambda x: x.real,

xarray/core/duck_array_ops.py

@@ -99,6 +99,18 @@ def gradient(x, coord, axis, edge_order):
     return npcompat.gradient(x, coord, axis=axis, edge_order=edge_order)
 
 
+def trapz(y, x, axis):
+    if axis < 0:
+        axis = y.ndim + axis
+    x_sl1 = (slice(1, None), ) + (None, ) * (y.ndim - axis - 1)
+    x_sl2 = (slice(None, -1), ) + (None, ) * (y.ndim - axis - 1)
+    slice1 = (slice(None),) * axis + (slice(1, None), )
+    slice2 = (slice(None),) * axis + (slice(None, -1), )
+    dx = (x[x_sl1] - x[x_sl2])
+    integrand = dx * 0.5 * (y[tuple(slice1)] + y[tuple(slice2)])
+    return sum(integrand, axis=axis, skipna=False)
+
+
 masked_invalid = _dask_or_eager_func(
     'masked_invalid', eager_module=np.ma,
     dask_module=getattr(dask_array, 'ma', None))

xarray/tests/test_dataset.py

@@ -4716,3 +4716,82 @@ def test_differentiate_cftime(dask):
     # Test the differentiation of datetimes themselves
     actual = da['time'].differentiate('time', edge_order=1, datetime_unit='D')
     assert_allclose(actual, xr.ones_like(da['time']).astype(float))
+
+
+@pytest.mark.parametrize('dask', [True, False])
+def test_integrate(dask):
+    rs = np.random.RandomState(42)
+    coord = [0.2, 0.35, 0.4, 0.6, 0.7, 0.75, 0.76, 0.8]
+
+    da = xr.DataArray(rs.randn(8, 6), dims=['x', 'y'],
+                      coords={'x': coord, 'x2': (('x', ), rs.randn(8)),
+                              'z': 3, 'x2d': (('x', 'y'), rs.randn(8, 6))})
+    if dask and has_dask:
+        da = da.chunk({'x': 4})
+
+    ds = xr.Dataset({'var': da})
+
+    # along x
+    actual = da.integrate('x')
+    # coordinate that contains x should be dropped.
+    expected_x = xr.DataArray(
+        np.trapz(da, da['x'], axis=0), dims=['y'],
+        coords={k: v for k, v in da.coords.items() if 'x' not in v.dims})
+    assert_allclose(expected_x, actual.compute())
+    assert_equal(ds['var'].integrate('x'), ds.integrate('x')['var'])
+
+    # make sure result is also a dask array (if the source is dask array)
+    assert isinstance(actual.data, type(da.data))
+
+    # along y
+    actual = da.integrate('y')
+    expected_y = xr.DataArray(
+        np.trapz(da, da['y'], axis=1), dims=['x'],
+        coords={k: v for k, v in da.coords.items() if 'y' not in v.dims})
+    assert_allclose(expected_y, actual.compute())
+    assert_equal(actual, ds.integrate('y')['var'])
+    assert_equal(ds['var'].integrate('y'), ds.integrate('y')['var'])
+
+    # along x and y
+    actual = da.integrate(('y', 'x'))
+    assert actual.ndim == 0
+
+    with pytest.raises(ValueError):
+        da.integrate('x2d')
+
+
+@pytest.mark.parametrize('dask', [True, False])
+@pytest.mark.parametrize('which_datetime', ['np', 'cftime'])
+def test_trapz_datetime(dask, which_datetime):
+    rs = np.random.RandomState(42)
+    if which_datetime == 'np':
+        coord = np.array(
+            ['2004-07-13', '2006-01-13', '2010-08-13', '2010-09-13',
+             '2010-10-11', '2010-12-13', '2011-02-13', '2012-08-13'],
+            dtype='datetime64')
+    else:
+        if not has_cftime:
+            pytest.skip('Test requires cftime.')
+        coord = xr.cftime_range('2000', periods=8, freq='2D')
+
+    da = xr.DataArray(
+        rs.randn(8, 6),
+        coords={'time': coord, 'z': 3, 't2d': (('time', 'y'), rs.randn(8, 6))},
+        dims=['time', 'y'])
+
+    if dask and has_dask:
+        da = da.chunk({'time': 4})
+
+    actual = da.integrate('time', datetime_unit='D')
+    expected_data = np.trapz(
+        da, utils.datetime_to_numeric(da['time'], datetime_unit='D'), axis=0)
+    expected = xr.DataArray(
+        expected_data, dims=['y'],
+        coords={k: v for k, v in da.coords.items() if 'time' not in v.dims})
+    assert_allclose(expected, actual.compute())
+
+    # make sure result is also a dask array (if the source is dask array)
+    assert isinstance(actual.data, type(da.data))
+
+    actual2 = da.integrate('time', datetime_unit='h')
+    assert_allclose(actual, actual2 / 24.0)