import functools import operator import pickle from distutils.version import LooseVersion import numpy as np import pandas as pd import pytest from numpy.testing import assert_allclose, assert_array_equal import xarray as xr from xarray.core.alignment import broadcast from xarray.core.computation import ( _UFuncSignature, apply_ufunc, broadcast_compat_data, collect_dict_values, join_dict_keys, ordered_set_intersection, ordered_set_union, result_name, unified_dim_sizes, ) from . import has_dask, raises_regex, requires_dask dask = pytest.importorskip("dask") def assert_identical(a, b): if hasattr(a, "identical"): msg = f"not identical:\n{a!r}\n{b!r}" assert a.identical(b), msg else: assert_array_equal(a, b) def test_signature_properties(): sig = _UFuncSignature([["x"], ["x", "y"]], [["z"]]) assert sig.input_core_dims == (("x",), ("x", "y")) assert sig.output_core_dims == (("z",),) assert sig.all_input_core_dims == frozenset(["x", "y"]) assert sig.all_output_core_dims == frozenset(["z"]) assert sig.num_inputs == 2 assert sig.num_outputs == 1 assert str(sig) == "(x),(x,y)->(z)" assert sig.to_gufunc_string() == "(dim0),(dim0,dim1)->(dim2)" assert ( sig.to_gufunc_string(exclude_dims=set("x")) == "(dim0_0),(dim0_1,dim1)->(dim2)" ) # dimension names matter assert _UFuncSignature([["x"]]) != _UFuncSignature([["y"]]) def test_result_name(): class Named: def __init__(self, name=None): self.name = name assert result_name([1, 2]) is None assert result_name([Named()]) is None assert result_name([Named("foo"), 2]) == "foo" assert result_name([Named("foo"), Named("bar")]) is None assert result_name([Named("foo"), Named()]) is None def test_ordered_set_union(): assert list(ordered_set_union([[1, 2]])) == [1, 2] assert list(ordered_set_union([[1, 2], [2, 1]])) == [1, 2] assert list(ordered_set_union([[0], [1, 2], [1, 3]])) == [0, 1, 2, 3] def test_ordered_set_intersection(): assert list(ordered_set_intersection([[1, 2]])) == [1, 2] assert list(ordered_set_intersection([[1, 2], [2, 1]])) == [1, 2] assert list(ordered_set_intersection([[1, 2], [1, 3]])) == [1] assert list(ordered_set_intersection([[1, 2], [2]])) == [2] def test_join_dict_keys(): dicts = [dict.fromkeys(keys) for keys in [["x", "y"], ["y", "z"]]] assert list(join_dict_keys(dicts, "left")) == ["x", "y"] assert list(join_dict_keys(dicts, "right")) == ["y", "z"] assert list(join_dict_keys(dicts, "inner")) == ["y"] assert list(join_dict_keys(dicts, "outer")) == ["x", "y", "z"] with pytest.raises(ValueError): join_dict_keys(dicts, "exact") with pytest.raises(KeyError): join_dict_keys(dicts, "foobar") def test_collect_dict_values(): dicts = [{"x": 1, "y": 2, "z": 3}, {"z": 4}, 5] expected = [[1, 0, 5], [2, 0, 5], [3, 4, 5]] collected = collect_dict_values(dicts, ["x", "y", "z"], fill_value=0) assert collected == expected def identity(x): return x def test_apply_identity(): array = np.arange(10) variable = xr.Variable("x", array) data_array = xr.DataArray(variable, [("x", -array)]) dataset = xr.Dataset({"y": variable}, {"x": -array}) apply_identity = functools.partial(apply_ufunc, identity) assert_identical(array, apply_identity(array)) assert_identical(variable, apply_identity(variable)) assert_identical(data_array, apply_identity(data_array)) assert_identical(data_array, apply_identity(data_array.groupby("x"))) assert_identical(dataset, apply_identity(dataset)) assert_identical(dataset, apply_identity(dataset.groupby("x"))) def add(a, b): return apply_ufunc(operator.add, a, b) def test_apply_two_inputs(): array = np.array([1, 2, 3]) variable = xr.Variable("x", array) data_array = xr.DataArray(variable, [("x", -array)]) dataset = xr.Dataset({"y": variable}, {"x": -array}) zero_array = np.zeros_like(array) zero_variable = xr.Variable("x", zero_array) zero_data_array = xr.DataArray(zero_variable, [("x", -array)]) zero_dataset = xr.Dataset({"y": zero_variable}, {"x": -array}) assert_identical(array, add(array, zero_array)) assert_identical(array, add(zero_array, array)) assert_identical(variable, add(variable, zero_array)) assert_identical(variable, add(variable, zero_variable)) assert_identical(variable, add(zero_array, variable)) assert_identical(variable, add(zero_variable, variable)) assert_identical(data_array, add(data_array, zero_array)) assert_identical(data_array, add(data_array, zero_variable)) assert_identical(data_array, add(data_array, zero_data_array)) assert_identical(data_array, add(zero_array, data_array)) assert_identical(data_array, add(zero_variable, data_array)) assert_identical(data_array, add(zero_data_array, data_array)) assert_identical(dataset, add(dataset, zero_array)) assert_identical(dataset, add(dataset, zero_variable)) assert_identical(dataset, add(dataset, zero_data_array)) assert_identical(dataset, add(dataset, zero_dataset)) assert_identical(dataset, add(zero_array, dataset)) assert_identical(dataset, add(zero_variable, dataset)) assert_identical(dataset, add(zero_data_array, dataset)) assert_identical(dataset, add(zero_dataset, dataset)) assert_identical(data_array, add(data_array.groupby("x"), zero_data_array)) assert_identical(data_array, add(zero_data_array, data_array.groupby("x"))) assert_identical(dataset, add(data_array.groupby("x"), zero_dataset)) assert_identical(dataset, add(zero_dataset, data_array.groupby("x"))) assert_identical(dataset, add(dataset.groupby("x"), zero_data_array)) assert_identical(dataset, add(dataset.groupby("x"), zero_dataset)) assert_identical(dataset, add(zero_data_array, dataset.groupby("x"))) assert_identical(dataset, add(zero_dataset, dataset.groupby("x"))) def test_apply_1d_and_0d(): array = np.array([1, 2, 3]) variable = xr.Variable("x", array) data_array = xr.DataArray(variable, [("x", -array)]) dataset = xr.Dataset({"y": variable}, {"x": -array}) zero_array = 0 zero_variable = xr.Variable((), zero_array) zero_data_array = xr.DataArray(zero_variable) zero_dataset = xr.Dataset({"y": zero_variable}) assert_identical(array, add(array, zero_array)) assert_identical(array, add(zero_array, array)) assert_identical(variable, add(variable, zero_array)) assert_identical(variable, add(variable, zero_variable)) assert_identical(variable, add(zero_array, variable)) assert_identical(variable, add(zero_variable, variable)) assert_identical(data_array, add(data_array, zero_array)) assert_identical(data_array, add(data_array, zero_variable)) assert_identical(data_array, add(data_array, zero_data_array)) assert_identical(data_array, add(zero_array, data_array)) assert_identical(data_array, add(zero_variable, data_array)) assert_identical(data_array, add(zero_data_array, data_array)) assert_identical(dataset, add(dataset, zero_array)) assert_identical(dataset, add(dataset, zero_variable)) assert_identical(dataset, add(dataset, zero_data_array)) assert_identical(dataset, add(dataset, zero_dataset)) assert_identical(dataset, add(zero_array, dataset)) assert_identical(dataset, add(zero_variable, dataset)) assert_identical(dataset, add(zero_data_array, dataset)) assert_identical(dataset, add(zero_dataset, dataset)) assert_identical(data_array, add(data_array.groupby("x"), zero_data_array)) assert_identical(data_array, add(zero_data_array, data_array.groupby("x"))) assert_identical(dataset, add(data_array.groupby("x"), zero_dataset)) assert_identical(dataset, add(zero_dataset, data_array.groupby("x"))) assert_identical(dataset, add(dataset.groupby("x"), zero_data_array)) assert_identical(dataset, add(dataset.groupby("x"), zero_dataset)) assert_identical(dataset, add(zero_data_array, dataset.groupby("x"))) assert_identical(dataset, add(zero_dataset, dataset.groupby("x"))) def test_apply_two_outputs(): array = np.arange(5) variable = xr.Variable("x", array) data_array = xr.DataArray(variable, [("x", -array)]) dataset = xr.Dataset({"y": variable}, {"x": -array}) def twice(obj): def func(x): return (x, x) return apply_ufunc(func, obj, output_core_dims=[[], []]) out0, out1 = twice(array) assert_identical(out0, array) assert_identical(out1, array) out0, out1 = twice(variable) assert_identical(out0, variable) assert_identical(out1, variable) out0, out1 = twice(data_array) assert_identical(out0, data_array) assert_identical(out1, data_array) out0, out1 = twice(dataset) assert_identical(out0, dataset) assert_identical(out1, dataset) out0, out1 = twice(data_array.groupby("x")) assert_identical(out0, data_array) assert_identical(out1, data_array) out0, out1 = twice(dataset.groupby("x")) assert_identical(out0, dataset) assert_identical(out1, dataset) @requires_dask def test_apply_dask_parallelized_two_outputs(): data_array = xr.DataArray([[0, 1, 2], [1, 2, 3]], dims=("x", "y")) def twice(obj): def func(x): return (x, x) return apply_ufunc(func, obj, output_core_dims=[[], []], dask="parallelized") out0, out1 = twice(data_array.chunk({"x": 1})) assert_identical(data_array, out0) assert_identical(data_array, out1) def test_apply_input_core_dimension(): def first_element(obj, dim): def func(x): return x[..., 0] return apply_ufunc(func, obj, input_core_dims=[[dim]]) array = np.array([[1, 2], [3, 4]]) variable = xr.Variable(["x", "y"], array) data_array = xr.DataArray(variable, {"x": ["a", "b"], "y": [-1, -2]}) dataset = xr.Dataset({"data": data_array}) expected_variable_x = xr.Variable(["y"], [1, 2]) expected_data_array_x = xr.DataArray(expected_variable_x, {"y": [-1, -2]}) expected_dataset_x = xr.Dataset({"data": expected_data_array_x}) expected_variable_y = xr.Variable(["x"], [1, 3]) expected_data_array_y = xr.DataArray(expected_variable_y, {"x": ["a", "b"]}) expected_dataset_y = xr.Dataset({"data": expected_data_array_y}) assert_identical(expected_variable_x, first_element(variable, "x")) assert_identical(expected_variable_y, first_element(variable, "y")) assert_identical(expected_data_array_x, first_element(data_array, "x")) assert_identical(expected_data_array_y, first_element(data_array, "y")) assert_identical(expected_dataset_x, first_element(dataset, "x")) assert_identical(expected_dataset_y, first_element(dataset, "y")) assert_identical(expected_data_array_x, first_element(data_array.groupby("y"), "x")) assert_identical(expected_dataset_x, first_element(dataset.groupby("y"), "x")) def multiply(*args): val = args[0] for arg in args[1:]: val = val * arg return val # regression test for GH:2341 with pytest.raises(ValueError): apply_ufunc( multiply, data_array, data_array["y"].values, input_core_dims=[["y"]], output_core_dims=[["y"]], ) expected = xr.DataArray( multiply(data_array, data_array["y"]), dims=["x", "y"], coords=data_array.coords ) actual = apply_ufunc( multiply, data_array, data_array["y"].values, input_core_dims=[["y"], []], output_core_dims=[["y"]], ) assert_identical(expected, actual) def test_apply_output_core_dimension(): def stack_negative(obj): def func(x): return np.stack([x, -x], axis=-1) result = apply_ufunc(func, obj, output_core_dims=[["sign"]]) if isinstance(result, (xr.Dataset, xr.DataArray)): result.coords["sign"] = [1, -1] return result array = np.array([[1, 2], [3, 4]]) variable = xr.Variable(["x", "y"], array) data_array = xr.DataArray(variable, {"x": ["a", "b"], "y": [-1, -2]}) dataset = xr.Dataset({"data": data_array}) stacked_array = np.array([[[1, -1], [2, -2]], [[3, -3], [4, -4]]]) stacked_variable = xr.Variable(["x", "y", "sign"], stacked_array) stacked_coords = {"x": ["a", "b"], "y": [-1, -2], "sign": [1, -1]} stacked_data_array = xr.DataArray(stacked_variable, stacked_coords) stacked_dataset = xr.Dataset({"data": stacked_data_array}) assert_identical(stacked_array, stack_negative(array)) assert_identical(stacked_variable, stack_negative(variable)) assert_identical(stacked_data_array, stack_negative(data_array)) assert_identical(stacked_dataset, stack_negative(dataset)) assert_identical(stacked_data_array, stack_negative(data_array.groupby("x"))) assert_identical(stacked_dataset, stack_negative(dataset.groupby("x"))) def original_and_stack_negative(obj): def func(x): return (x, np.stack([x, -x], axis=-1)) result = apply_ufunc(func, obj, output_core_dims=[[], ["sign"]]) if isinstance(result[1], (xr.Dataset, xr.DataArray)): result[1].coords["sign"] = [1, -1] return result out0, out1 = original_and_stack_negative(array) assert_identical(array, out0) assert_identical(stacked_array, out1) out0, out1 = original_and_stack_negative(variable) assert_identical(variable, out0) assert_identical(stacked_variable, out1) out0, out1 = original_and_stack_negative(data_array) assert_identical(data_array, out0) assert_identical(stacked_data_array, out1) out0, out1 = original_and_stack_negative(dataset) assert_identical(dataset, out0) assert_identical(stacked_dataset, out1) out0, out1 = original_and_stack_negative(data_array.groupby("x")) assert_identical(data_array, out0) assert_identical(stacked_data_array, out1) out0, out1 = original_and_stack_negative(dataset.groupby("x")) assert_identical(dataset, out0) assert_identical(stacked_dataset, out1) def test_apply_exclude(): def concatenate(objects, dim="x"): def func(*x): return np.concatenate(x, axis=-1) result = apply_ufunc( func, *objects, input_core_dims=[[dim]] * len(objects), output_core_dims=[[dim]], exclude_dims={dim}, ) if isinstance(result, (xr.Dataset, xr.DataArray)): # note: this will fail if dim is not a coordinate on any input new_coord = np.concatenate([obj.coords[dim] for obj in objects]) result.coords[dim] = new_coord return result arrays = [np.array([1]), np.array([2, 3])] variables = [xr.Variable("x", a) for a in arrays] data_arrays = [ xr.DataArray(v, {"x": c, "y": ("x", range(len(c)))}) for v, c in zip(variables, [["a"], ["b", "c"]]) ] datasets = [xr.Dataset({"data": data_array}) for data_array in data_arrays] expected_array = np.array([1, 2, 3]) expected_variable = xr.Variable("x", expected_array) expected_data_array = xr.DataArray(expected_variable, [("x", list("abc"))]) expected_dataset = xr.Dataset({"data": expected_data_array}) assert_identical(expected_array, concatenate(arrays)) assert_identical(expected_variable, concatenate(variables)) assert_identical(expected_data_array, concatenate(data_arrays)) assert_identical(expected_dataset, concatenate(datasets)) # must also be a core dimension with pytest.raises(ValueError): apply_ufunc(identity, variables[0], exclude_dims={"x"}) def test_apply_groupby_add(): array = np.arange(5) variable = xr.Variable("x", array) coords = {"x": -array, "y": ("x", [0, 0, 1, 1, 2])} data_array = xr.DataArray(variable, coords, dims="x") dataset = xr.Dataset({"z": variable}, coords) other_variable = xr.Variable("y", [0, 10]) other_data_array = xr.DataArray(other_variable, dims="y") other_dataset = xr.Dataset({"z": other_variable}) expected_variable = xr.Variable("x", [0, 1, 12, 13, np.nan]) expected_data_array = xr.DataArray(expected_variable, coords, dims="x") expected_dataset = xr.Dataset({"z": expected_variable}, coords) assert_identical( expected_data_array, add(data_array.groupby("y"), other_data_array) ) assert_identical(expected_dataset, add(data_array.groupby("y"), other_dataset)) assert_identical(expected_dataset, add(dataset.groupby("y"), other_data_array)) assert_identical(expected_dataset, add(dataset.groupby("y"), other_dataset)) # cannot be performed with xarray.Variable objects that share a dimension with pytest.raises(ValueError): add(data_array.groupby("y"), other_variable) # if they are all grouped the same way with pytest.raises(ValueError): add(data_array.groupby("y"), data_array[:4].groupby("y")) with pytest.raises(ValueError): add(data_array.groupby("y"), data_array[1:].groupby("y")) with pytest.raises(ValueError): add(data_array.groupby("y"), other_data_array.groupby("y")) with pytest.raises(ValueError): add(data_array.groupby("y"), data_array.groupby("x")) def test_unified_dim_sizes(): assert unified_dim_sizes([xr.Variable((), 0)]) == {} assert unified_dim_sizes([xr.Variable("x", [1]), xr.Variable("x", [1])]) == {"x": 1} assert unified_dim_sizes([xr.Variable("x", [1]), xr.Variable("y", [1, 2])]) == { "x": 1, "y": 2, } assert ( unified_dim_sizes( [xr.Variable(("x", "z"), [[1]]), xr.Variable(("y", "z"), [[1, 2], [3, 4]])], exclude_dims={"z"}, ) == {"x": 1, "y": 2} ) # duplicate dimensions with pytest.raises(ValueError): unified_dim_sizes([xr.Variable(("x", "x"), [[1]])]) # mismatched lengths with pytest.raises(ValueError): unified_dim_sizes([xr.Variable("x", [1]), xr.Variable("x", [1, 2])]) def test_broadcast_compat_data_1d(): data = np.arange(5) var = xr.Variable("x", data) assert_identical(data, broadcast_compat_data(var, ("x",), ())) assert_identical(data, broadcast_compat_data(var, (), ("x",))) assert_identical(data[:], broadcast_compat_data(var, ("w",), ("x",))) assert_identical(data[:, None], broadcast_compat_data(var, ("w", "x", "y"), ())) with pytest.raises(ValueError): broadcast_compat_data(var, ("x",), ("w",)) with pytest.raises(ValueError): broadcast_compat_data(var, (), ()) def test_broadcast_compat_data_2d(): data = np.arange(12).reshape(3, 4) var = xr.Variable(["x", "y"], data) assert_identical(data, broadcast_compat_data(var, ("x", "y"), ())) assert_identical(data, broadcast_compat_data(var, ("x",), ("y",))) assert_identical(data, broadcast_compat_data(var, (), ("x", "y"))) assert_identical(data.T, broadcast_compat_data(var, ("y", "x"), ())) assert_identical(data.T, broadcast_compat_data(var, ("y",), ("x",))) assert_identical(data, broadcast_compat_data(var, ("w", "x"), ("y",))) assert_identical(data, broadcast_compat_data(var, ("w",), ("x", "y"))) assert_identical(data.T, broadcast_compat_data(var, ("w",), ("y", "x"))) assert_identical( data[:, :, None], broadcast_compat_data(var, ("w", "x", "y", "z"), ()) ) assert_identical( data[None, :, :].T, broadcast_compat_data(var, ("w", "y", "x", "z"), ()) ) def test_keep_attrs(): def add(a, b, keep_attrs): if keep_attrs: return apply_ufunc(operator.add, a, b, keep_attrs=keep_attrs) else: return apply_ufunc(operator.add, a, b) a = xr.DataArray([0, 1], [("x", [0, 1])]) a.attrs["attr"] = "da" a["x"].attrs["attr"] = "da_coord" b = xr.DataArray([1, 2], [("x", [0, 1])]) actual = add(a, b, keep_attrs=False) assert not actual.attrs actual = add(a, b, keep_attrs=True) assert_identical(actual.attrs, a.attrs) assert_identical(actual["x"].attrs, a["x"].attrs) actual = add(a.variable, b.variable, keep_attrs=False) assert not actual.attrs actual = add(a.variable, b.variable, keep_attrs=True) assert_identical(actual.attrs, a.attrs) a = xr.Dataset({"x": [0, 1]}) a.attrs["attr"] = "ds" a.x.attrs["attr"] = "da" b = xr.Dataset({"x": [0, 1]}) actual = add(a, b, keep_attrs=False) assert not actual.attrs actual = add(a, b, keep_attrs=True) assert_identical(actual.attrs, a.attrs) assert_identical(actual.x.attrs, a.x.attrs) def test_dataset_join(): ds0 = xr.Dataset({"a": ("x", [1, 2]), "x": [0, 1]}) ds1 = xr.Dataset({"a": ("x", [99, 3]), "x": [1, 2]}) # by default, cannot have different labels with raises_regex(ValueError, "indexes .* are not equal"): apply_ufunc(operator.add, ds0, ds1) with raises_regex(TypeError, "must supply"): apply_ufunc(operator.add, ds0, ds1, dataset_join="outer") def add(a, b, join, dataset_join): return apply_ufunc( operator.add, a, b, join=join, dataset_join=dataset_join, dataset_fill_value=np.nan, ) actual = add(ds0, ds1, "outer", "inner") expected = xr.Dataset({"a": ("x", [np.nan, 101, np.nan]), "x": [0, 1, 2]}) assert_identical(actual, expected) actual = add(ds0, ds1, "outer", "outer") assert_identical(actual, expected) with raises_regex(ValueError, "data variable names"): apply_ufunc(operator.add, ds0, xr.Dataset({"b": 1})) ds2 = xr.Dataset({"b": ("x", [99, 3]), "x": [1, 2]}) actual = add(ds0, ds2, "outer", "inner") expected = xr.Dataset({"x": [0, 1, 2]}) assert_identical(actual, expected) # we used np.nan as the fill_value in add() above actual = add(ds0, ds2, "outer", "outer") expected = xr.Dataset( { "a": ("x", [np.nan, np.nan, np.nan]), "b": ("x", [np.nan, np.nan, np.nan]), "x": [0, 1, 2], } ) assert_identical(actual, expected) @requires_dask def test_apply_dask(): import dask.array as da array = da.ones((2,), chunks=2) variable = xr.Variable("x", array) coords = xr.DataArray(variable).coords.variables data_array = xr.DataArray(variable, dims=["x"], coords=coords) dataset = xr.Dataset({"y": variable}) # encountered dask array, but did not set dask='allowed' with pytest.raises(ValueError): apply_ufunc(identity, array) with pytest.raises(ValueError): apply_ufunc(identity, variable) with pytest.raises(ValueError): apply_ufunc(identity, data_array) with pytest.raises(ValueError): apply_ufunc(identity, dataset) # unknown setting for dask array handling with pytest.raises(ValueError): apply_ufunc(identity, array, dask="unknown") def dask_safe_identity(x): return apply_ufunc(identity, x, dask="allowed") assert array is dask_safe_identity(array) actual = dask_safe_identity(variable) assert isinstance(actual.data, da.Array) assert_identical(variable, actual) actual = dask_safe_identity(data_array) assert isinstance(actual.data, da.Array) assert_identical(data_array, actual) actual = dask_safe_identity(dataset) assert isinstance(actual["y"].data, da.Array) assert_identical(dataset, actual) @requires_dask def test_apply_dask_parallelized_one_arg(): import dask.array as da array = da.ones((2, 2), chunks=(1, 1)) data_array = xr.DataArray(array, dims=("x", "y")) def parallel_identity(x): return apply_ufunc(identity, x, dask="parallelized", output_dtypes=[x.dtype]) actual = parallel_identity(data_array) assert isinstance(actual.data, da.Array) assert actual.data.chunks == array.chunks assert_identical(data_array, actual) computed = data_array.compute() actual = parallel_identity(computed) assert_identical(computed, actual) @requires_dask def test_apply_dask_parallelized_two_args(): import dask.array as da array = da.ones((2, 2), chunks=(1, 1), dtype=np.int64) data_array = xr.DataArray(array, dims=("x", "y")) data_array.name = None def parallel_add(x, y): return apply_ufunc( operator.add, x, y, dask="parallelized", output_dtypes=[np.int64] ) def check(x, y): actual = parallel_add(x, y) assert isinstance(actual.data, da.Array) assert actual.data.chunks == array.chunks assert_identical(data_array, actual) check(data_array, 0), check(0, data_array) check(data_array, xr.DataArray(0)) check(data_array, 0 * data_array) check(data_array, 0 * data_array[0]) check(data_array[:, 0], 0 * data_array[0]) check(data_array, 0 * data_array.compute()) @requires_dask def test_apply_dask_parallelized_errors(): import dask.array as da array = da.ones((2, 2), chunks=(1, 1)) data_array = xr.DataArray(array, dims=("x", "y")) # from apply_array_ufunc with raises_regex(ValueError, "at least one input is an xarray object"): apply_ufunc(identity, array, dask="parallelized") # formerly from _apply_blockwise, now from apply_variable_ufunc with raises_regex(ValueError, "consists of multiple chunks"): apply_ufunc( identity, data_array, dask="parallelized", output_dtypes=[float], input_core_dims=[("y",)], output_core_dims=[("y",)], ) # it's currently impossible to silence these warnings from inside dask.array: # https://github.com/dask/dask/issues/3245 @requires_dask @pytest.mark.filterwarnings("ignore:Mean of empty slice") def test_apply_dask_multiple_inputs(): import dask.array as da def covariance(x, y): return ( (x - x.mean(axis=-1, keepdims=True)) * (y - y.mean(axis=-1, keepdims=True)) ).mean(axis=-1) rs = np.random.RandomState(42) array1 = da.from_array(rs.randn(4, 4), chunks=(2, 4)) array2 = da.from_array(rs.randn(4, 4), chunks=(2, 4)) data_array_1 = xr.DataArray(array1, dims=("x", "z")) data_array_2 = xr.DataArray(array2, dims=("y", "z")) expected = apply_ufunc( covariance, data_array_1.compute(), data_array_2.compute(), input_core_dims=[["z"], ["z"]], ) allowed = apply_ufunc( covariance, data_array_1, data_array_2, input_core_dims=[["z"], ["z"]], dask="allowed", ) assert isinstance(allowed.data, da.Array) xr.testing.assert_allclose(expected, allowed.compute()) parallelized = apply_ufunc( covariance, data_array_1, data_array_2, input_core_dims=[["z"], ["z"]], dask="parallelized", output_dtypes=[float], ) assert isinstance(parallelized.data, da.Array) xr.testing.assert_allclose(expected, parallelized.compute()) @requires_dask def test_apply_dask_new_output_dimension(): import dask.array as da array = da.ones((2, 2), chunks=(1, 1)) data_array = xr.DataArray(array, dims=("x", "y")) def stack_negative(obj): def func(x): return np.stack([x, -x], axis=-1) return apply_ufunc( func, obj, output_core_dims=[["sign"]], dask="parallelized", output_dtypes=[obj.dtype], dask_gufunc_kwargs=dict(output_sizes={"sign": 2}), ) expected = stack_negative(data_array.compute()) actual = stack_negative(data_array) assert actual.dims == ("x", "y", "sign") assert actual.shape == (2, 2, 2) assert isinstance(actual.data, da.Array) assert_identical(expected, actual) @requires_dask def test_apply_dask_new_output_sizes(): ds = xr.Dataset({"foo": (["lon", "lat"], np.arange(10 * 10).reshape((10, 10)))}) ds["bar"] = ds["foo"] newdims = {"lon_new": 3, "lat_new": 6} def extract(obj): def func(da): return da[1:4, 1:7] return apply_ufunc( func, obj, dask="parallelized", input_core_dims=[["lon", "lat"]], output_core_dims=[["lon_new", "lat_new"]], dask_gufunc_kwargs=dict(output_sizes=newdims), ) expected = extract(ds) actual = extract(ds.chunk()) assert actual.dims == {"lon_new": 3, "lat_new": 6} assert_identical(expected.chunk(), actual) def pandas_median(x): return pd.Series(x).median() def test_vectorize(): data_array = xr.DataArray([[0, 1, 2], [1, 2, 3]], dims=("x", "y")) expected = xr.DataArray([1, 2], dims=["x"]) actual = apply_ufunc( pandas_median, data_array, input_core_dims=[["y"]], vectorize=True ) assert_identical(expected, actual) @requires_dask def test_vectorize_dask(): # run vectorization in dask.array.gufunc by using `dask='parallelized'` data_array = xr.DataArray([[0, 1, 2], [1, 2, 3]], dims=("x", "y")) expected = xr.DataArray([1, 2], dims=["x"]) actual = apply_ufunc( pandas_median, data_array.chunk({"x": 1}), input_core_dims=[["y"]], vectorize=True, dask="parallelized", output_dtypes=[float], ) assert_identical(expected, actual) @requires_dask def test_vectorize_dask_dtype(): # ensure output_dtypes is preserved with vectorize=True # GH4015 # integer data_array = xr.DataArray([[0, 1, 2], [1, 2, 3]], dims=("x", "y")) expected = xr.DataArray([1, 2], dims=["x"]) actual = apply_ufunc( pandas_median, data_array.chunk({"x": 1}), input_core_dims=[["y"]], vectorize=True, dask="parallelized", output_dtypes=[int], ) assert_identical(expected, actual) assert expected.dtype == actual.dtype # complex data_array = xr.DataArray([[0 + 0j, 1 + 2j, 2 + 1j]], dims=("x", "y")) expected = data_array.copy() actual = apply_ufunc( identity, data_array.chunk({"x": 1}), vectorize=True, dask="parallelized", output_dtypes=[complex], ) assert_identical(expected, actual) assert expected.dtype == actual.dtype @requires_dask @pytest.mark.parametrize( "data_array", [ xr.DataArray([[0, 1, 2], [1, 2, 3]], dims=("x", "y")), xr.DataArray([[0 + 0j, 1 + 2j, 2 + 1j]], dims=("x", "y")), ], ) def test_vectorize_dask_dtype_without_output_dtypes(data_array): # ensure output_dtypes is preserved with vectorize=True # GH4015 expected = data_array.copy() actual = apply_ufunc( identity, data_array.chunk({"x": 1}), vectorize=True, dask="parallelized", ) assert_identical(expected, actual) assert expected.dtype == actual.dtype @pytest.mark.xfail(LooseVersion(dask.__version__) < "2.3", reason="dask GH5274") @requires_dask def test_vectorize_dask_dtype_meta(): # meta dtype takes precedence data_array = xr.DataArray([[0, 1, 2], [1, 2, 3]], dims=("x", "y")) expected = xr.DataArray([1, 2], dims=["x"]) actual = apply_ufunc( pandas_median, data_array.chunk({"x": 1}), input_core_dims=[["y"]], vectorize=True, dask="parallelized", output_dtypes=[int], dask_gufunc_kwargs=dict(meta=np.ndarray((0, 0), dtype=np.float)), ) assert_identical(expected, actual) assert np.float == actual.dtype def pandas_median_add(x, y): # function which can consume input of unequal length return pd.Series(x).median() + pd.Series(y).median() def test_vectorize_exclude_dims(): # GH 3890 data_array_a = xr.DataArray([[0, 1, 2], [1, 2, 3]], dims=("x", "y")) data_array_b = xr.DataArray([[0, 1, 2, 3, 4], [1, 2, 3, 4, 5]], dims=("x", "y")) expected = xr.DataArray([3, 5], dims=["x"]) actual = apply_ufunc( pandas_median_add, data_array_a, data_array_b, input_core_dims=[["y"], ["y"]], vectorize=True, exclude_dims=set("y"), ) assert_identical(expected, actual) @requires_dask def test_vectorize_exclude_dims_dask(): # GH 3890 data_array_a = xr.DataArray([[0, 1, 2], [1, 2, 3]], dims=("x", "y")) data_array_b = xr.DataArray([[0, 1, 2, 3, 4], [1, 2, 3, 4, 5]], dims=("x", "y")) expected = xr.DataArray([3, 5], dims=["x"]) actual = apply_ufunc( pandas_median_add, data_array_a.chunk({"x": 1}), data_array_b.chunk({"x": 1}), input_core_dims=[["y"], ["y"]], exclude_dims=set("y"), vectorize=True, dask="parallelized", output_dtypes=[float], ) assert_identical(expected, actual) def test_corr_only_dataarray(): with pytest.raises(TypeError, match="Only xr.DataArray is supported"): xr.corr(xr.Dataset(), xr.Dataset()) def arrays_w_tuples(): da = xr.DataArray( np.random.random((3, 21, 4)), coords={"time": pd.date_range("2000-01-01", freq="1D", periods=21)}, dims=("a", "time", "x"), ) arrays = [ da.isel(time=range(0, 18)), da.isel(time=range(2, 20)).rolling(time=3, center=True).mean(), xr.DataArray([[1, 2], [1, np.nan]], dims=["x", "time"]), xr.DataArray([[1, 2], [np.nan, np.nan]], dims=["x", "time"]), ] array_tuples = [ (arrays[0], arrays[0]), (arrays[0], arrays[1]), (arrays[1], arrays[1]), (arrays[2], arrays[2]), (arrays[2], arrays[3]), (arrays[3], arrays[3]), ] return arrays, array_tuples @pytest.mark.parametrize("ddof", [0, 1]) @pytest.mark.parametrize( "da_a, da_b", [arrays_w_tuples()[1][0], arrays_w_tuples()[1][1], arrays_w_tuples()[1][2]], ) @pytest.mark.parametrize("dim", [None, "time"]) def test_cov(da_a, da_b, dim, ddof): if dim is not None: def np_cov_ind(ts1, ts2, a, x): # Ensure the ts are aligned and missing values ignored ts1, ts2 = broadcast(ts1, ts2) valid_values = ts1.notnull() & ts2.notnull() # While dropping isn't ideal here, numpy will return nan # if any segment contains a NaN. ts1 = ts1.where(valid_values) ts2 = ts2.where(valid_values) return np.ma.cov( np.ma.masked_invalid(ts1.sel(a=a, x=x).data.flatten()), np.ma.masked_invalid(ts2.sel(a=a, x=x).data.flatten()), ddof=ddof, )[0, 1] expected = np.zeros((3, 4)) for a in [0, 1, 2]: for x in [0, 1, 2, 3]: expected[a, x] = np_cov_ind(da_a, da_b, a=a, x=x) actual = xr.cov(da_a, da_b, dim=dim, ddof=ddof) assert_allclose(actual, expected) else: def np_cov(ts1, ts2): # Ensure the ts are aligned and missing values ignored ts1, ts2 = broadcast(ts1, ts2) valid_values = ts1.notnull() & ts2.notnull() ts1 = ts1.where(valid_values) ts2 = ts2.where(valid_values) return np.ma.cov( np.ma.masked_invalid(ts1.data.flatten()), np.ma.masked_invalid(ts2.data.flatten()), ddof=ddof, )[0, 1] expected = np_cov(da_a, da_b) actual = xr.cov(da_a, da_b, dim=dim, ddof=ddof) assert_allclose(actual, expected) @pytest.mark.parametrize( "da_a, da_b", [arrays_w_tuples()[1][0], arrays_w_tuples()[1][1], arrays_w_tuples()[1][2]], ) @pytest.mark.parametrize("dim", [None, "time"]) def test_corr(da_a, da_b, dim): if dim is not None: def np_corr_ind(ts1, ts2, a, x): # Ensure the ts are aligned and missing values ignored ts1, ts2 = broadcast(ts1, ts2) valid_values = ts1.notnull() & ts2.notnull() ts1 = ts1.where(valid_values) ts2 = ts2.where(valid_values) return np.ma.corrcoef( np.ma.masked_invalid(ts1.sel(a=a, x=x).data.flatten()), np.ma.masked_invalid(ts2.sel(a=a, x=x).data.flatten()), )[0, 1] expected = np.zeros((3, 4)) for a in [0, 1, 2]: for x in [0, 1, 2, 3]: expected[a, x] = np_corr_ind(da_a, da_b, a=a, x=x) actual = xr.corr(da_a, da_b, dim) assert_allclose(actual, expected) else: def np_corr(ts1, ts2): # Ensure the ts are aligned and missing values ignored ts1, ts2 = broadcast(ts1, ts2) valid_values = ts1.notnull() & ts2.notnull() ts1 = ts1.where(valid_values) ts2 = ts2.where(valid_values) return np.ma.corrcoef( np.ma.masked_invalid(ts1.data.flatten()), np.ma.masked_invalid(ts2.data.flatten()), )[0, 1] expected = np_corr(da_a, da_b) actual = xr.corr(da_a, da_b, dim) assert_allclose(actual, expected) @pytest.mark.parametrize( "da_a, da_b", arrays_w_tuples()[1], ) @pytest.mark.parametrize("dim", [None, "time", "x"]) def test_covcorr_consistency(da_a, da_b, dim): # Testing that xr.corr and xr.cov are consistent with each other # 1. Broadcast the two arrays da_a, da_b = broadcast(da_a, da_b) # 2. Ignore the nans valid_values = da_a.notnull() & da_b.notnull() da_a = da_a.where(valid_values) da_b = da_b.where(valid_values) expected = xr.cov(da_a, da_b, dim=dim, ddof=0) / ( da_a.std(dim=dim) * da_b.std(dim=dim) ) actual = xr.corr(da_a, da_b, dim=dim) assert_allclose(actual, expected) @pytest.mark.parametrize( "da_a", arrays_w_tuples()[0], ) @pytest.mark.parametrize("dim", [None, "time", "x", ["time", "x"]]) def test_autocov(da_a, dim): # Testing that the autocovariance*(N-1) is ~=~ to the variance matrix # 1. Ignore the nans valid_values = da_a.notnull() # Because we're using ddof=1, this requires > 1 value in each sample da_a = da_a.where(valid_values.sum(dim=dim) > 1) expected = ((da_a - da_a.mean(dim=dim)) ** 2).sum(dim=dim, skipna=True, min_count=1) actual = xr.cov(da_a, da_a, dim=dim) * (valid_values.sum(dim) - 1) assert_allclose(actual, expected) @requires_dask def test_vectorize_dask_new_output_dims(): # regression test for GH3574 # run vectorization in dask.array.gufunc by using `dask='parallelized'` data_array = xr.DataArray([[0, 1, 2], [1, 2, 3]], dims=("x", "y")) func = lambda x: x[np.newaxis, ...] expected = data_array.expand_dims("z") actual = apply_ufunc( func, data_array.chunk({"x": 1}), output_core_dims=[["z"]], vectorize=True, dask="parallelized", output_dtypes=[float], dask_gufunc_kwargs=dict(output_sizes={"z": 1}), ).transpose(*expected.dims) assert_identical(expected, actual) with raises_regex(ValueError, "dimension 'z1' in 'output_sizes' must correspond"): apply_ufunc( func, data_array.chunk({"x": 1}), output_core_dims=[["z"]], vectorize=True, dask="parallelized", output_dtypes=[float], dask_gufunc_kwargs=dict(output_sizes={"z1": 1}), ) with raises_regex( ValueError, "dimension 'z' in 'output_core_dims' needs corresponding" ): apply_ufunc( func, data_array.chunk({"x": 1}), output_core_dims=[["z"]], vectorize=True, dask="parallelized", output_dtypes=[float], ) def test_output_wrong_number(): variable = xr.Variable("x", np.arange(10)) def identity(x): return x def tuple3x(x): return (x, x, x) with raises_regex(ValueError, "number of outputs"): apply_ufunc(identity, variable, output_core_dims=[(), ()]) with raises_regex(ValueError, "number of outputs"): apply_ufunc(tuple3x, variable, output_core_dims=[(), ()]) def test_output_wrong_dims(): variable = xr.Variable("x", np.arange(10)) def add_dim(x): return x[..., np.newaxis] def remove_dim(x): return x[..., 0] with raises_regex(ValueError, "unexpected number of dimensions"): apply_ufunc(add_dim, variable, output_core_dims=[("y", "z")]) with raises_regex(ValueError, "unexpected number of dimensions"): apply_ufunc(add_dim, variable) with raises_regex(ValueError, "unexpected number of dimensions"): apply_ufunc(remove_dim, variable) def test_output_wrong_dim_size(): array = np.arange(10) variable = xr.Variable("x", array) data_array = xr.DataArray(variable, [("x", -array)]) dataset = xr.Dataset({"y": variable}, {"x": -array}) def truncate(array): return array[:5] def apply_truncate_broadcast_invalid(obj): return apply_ufunc(truncate, obj) with raises_regex(ValueError, "size of dimension"): apply_truncate_broadcast_invalid(variable) with raises_regex(ValueError, "size of dimension"): apply_truncate_broadcast_invalid(data_array) with raises_regex(ValueError, "size of dimension"): apply_truncate_broadcast_invalid(dataset) def apply_truncate_x_x_invalid(obj): return apply_ufunc( truncate, obj, input_core_dims=[["x"]], output_core_dims=[["x"]] ) with raises_regex(ValueError, "size of dimension"): apply_truncate_x_x_invalid(variable) with raises_regex(ValueError, "size of dimension"): apply_truncate_x_x_invalid(data_array) with raises_regex(ValueError, "size of dimension"): apply_truncate_x_x_invalid(dataset) def apply_truncate_x_z(obj): return apply_ufunc( truncate, obj, input_core_dims=[["x"]], output_core_dims=[["z"]] ) assert_identical(xr.Variable("z", array[:5]), apply_truncate_x_z(variable)) assert_identical( xr.DataArray(array[:5], dims=["z"]), apply_truncate_x_z(data_array) ) assert_identical(xr.Dataset({"y": ("z", array[:5])}), apply_truncate_x_z(dataset)) def apply_truncate_x_x_valid(obj): return apply_ufunc( truncate, obj, input_core_dims=[["x"]], output_core_dims=[["x"]], exclude_dims={"x"}, ) assert_identical(xr.Variable("x", array[:5]), apply_truncate_x_x_valid(variable)) assert_identical( xr.DataArray(array[:5], dims=["x"]), apply_truncate_x_x_valid(data_array) ) assert_identical( xr.Dataset({"y": ("x", array[:5])}), apply_truncate_x_x_valid(dataset) ) @pytest.mark.parametrize("use_dask", [True, False]) def test_dot(use_dask): if use_dask: if not has_dask: pytest.skip("test for dask.") a = np.arange(30 * 4).reshape(30, 4) b = np.arange(30 * 4 * 5).reshape(30, 4, 5) c = np.arange(5 * 60).reshape(5, 60) da_a = xr.DataArray(a, dims=["a", "b"], coords={"a": np.linspace(0, 1, 30)}) da_b = xr.DataArray(b, dims=["a", "b", "c"], coords={"a": np.linspace(0, 1, 30)}) da_c = xr.DataArray(c, dims=["c", "e"]) if use_dask: da_a = da_a.chunk({"a": 3}) da_b = da_b.chunk({"a": 3}) da_c = da_c.chunk({"c": 3}) actual = xr.dot(da_a, da_b, dims=["a", "b"]) assert actual.dims == ("c",) assert (actual.data == np.einsum("ij,ijk->k", a, b)).all() assert isinstance(actual.variable.data, type(da_a.variable.data)) actual = xr.dot(da_a, da_b) assert actual.dims == ("c",) assert (actual.data == np.einsum("ij,ijk->k", a, b)).all() assert isinstance(actual.variable.data, type(da_a.variable.data)) # for only a single array is passed without dims argument, just return # as is actual = xr.dot(da_a) assert da_a.identical(actual) # test for variable actual = xr.dot(da_a.variable, da_b.variable) assert actual.dims == ("c",) assert (actual.data == np.einsum("ij,ijk->k", a, b)).all() assert isinstance(actual.data, type(da_a.variable.data)) if use_dask: da_a = da_a.chunk({"a": 3}) da_b = da_b.chunk({"a": 3}) actual = xr.dot(da_a, da_b, dims=["b"]) assert actual.dims == ("a", "c") assert (actual.data == np.einsum("ij,ijk->ik", a, b)).all() assert isinstance(actual.variable.data, type(da_a.variable.data)) actual = xr.dot(da_a, da_b, dims=["b"]) assert actual.dims == ("a", "c") assert (actual.data == np.einsum("ij,ijk->ik", a, b)).all() actual = xr.dot(da_a, da_b, dims="b") assert actual.dims == ("a", "c") assert (actual.data == np.einsum("ij,ijk->ik", a, b)).all() actual = xr.dot(da_a, da_b, dims="a") assert actual.dims == ("b", "c") assert (actual.data == np.einsum("ij,ijk->jk", a, b)).all() actual = xr.dot(da_a, da_b, dims="c") assert actual.dims == ("a", "b") assert (actual.data == np.einsum("ij,ijk->ij", a, b)).all() actual = xr.dot(da_a, da_b, da_c, dims=["a", "b"]) assert actual.dims == ("c", "e") assert (actual.data == np.einsum("ij,ijk,kl->kl ", a, b, c)).all() # should work with tuple actual = xr.dot(da_a, da_b, dims=("c",)) assert actual.dims == ("a", "b") assert (actual.data == np.einsum("ij,ijk->ij", a, b)).all() # default dims actual = xr.dot(da_a, da_b, da_c) assert actual.dims == ("e",) assert (actual.data == np.einsum("ij,ijk,kl->l ", a, b, c)).all() # 1 array summation actual = xr.dot(da_a, dims="a") assert actual.dims == ("b",) assert (actual.data == np.einsum("ij->j ", a)).all() # empty dim actual = xr.dot(da_a.sel(a=[]), da_a.sel(a=[]), dims="a") assert actual.dims == ("b",) assert (actual.data == np.zeros(actual.shape)).all() # Ellipsis (...) sums over all dimensions actual = xr.dot(da_a, da_b, dims=...) assert actual.dims == () assert (actual.data == np.einsum("ij,ijk->", a, b)).all() actual = xr.dot(da_a, da_b, da_c, dims=...) assert actual.dims == () assert (actual.data == np.einsum("ij,ijk,kl-> ", a, b, c)).all() actual = xr.dot(da_a, dims=...) assert actual.dims == () assert (actual.data == np.einsum("ij-> ", a)).all() actual = xr.dot(da_a.sel(a=[]), da_a.sel(a=[]), dims=...) assert actual.dims == () assert (actual.data == np.zeros(actual.shape)).all() # Invalid cases if not use_dask: with pytest.raises(TypeError): xr.dot(da_a, dims="a", invalid=None) with pytest.raises(TypeError): xr.dot(da_a.to_dataset(name="da"), dims="a") with pytest.raises(TypeError): xr.dot(dims="a") # einsum parameters actual = xr.dot(da_a, da_b, dims=["b"], order="C") assert (actual.data == np.einsum("ij,ijk->ik", a, b)).all() assert actual.values.flags["C_CONTIGUOUS"] assert not actual.values.flags["F_CONTIGUOUS"] actual = xr.dot(da_a, da_b, dims=["b"], order="F") assert (actual.data == np.einsum("ij,ijk->ik", a, b)).all() # dask converts Fortran arrays to C order when merging the final array if not use_dask: assert not actual.values.flags["C_CONTIGUOUS"] assert actual.values.flags["F_CONTIGUOUS"] # einsum has a constant string as of the first parameter, which makes # it hard to pass to xarray.apply_ufunc. # make sure dot() uses functools.partial(einsum, subscripts), which # can be pickled, and not a lambda, which can't. pickle.loads(pickle.dumps(xr.dot(da_a))) @pytest.mark.parametrize("use_dask", [True, False]) def test_dot_align_coords(use_dask): # GH 3694 if use_dask: if not has_dask: pytest.skip("test for dask.") a = np.arange(30 * 4).reshape(30, 4) b = np.arange(30 * 4 * 5).reshape(30, 4, 5) # use partially overlapping coords coords_a = {"a": np.arange(30), "b": np.arange(4)} coords_b = {"a": np.arange(5, 35), "b": np.arange(1, 5)} da_a = xr.DataArray(a, dims=["a", "b"], coords=coords_a) da_b = xr.DataArray(b, dims=["a", "b", "c"], coords=coords_b) if use_dask: da_a = da_a.chunk({"a": 3}) da_b = da_b.chunk({"a": 3}) # join="inner" is the default actual = xr.dot(da_a, da_b) # `dot` sums over the common dimensions of the arguments expected = (da_a * da_b).sum(["a", "b"]) xr.testing.assert_allclose(expected, actual) actual = xr.dot(da_a, da_b, dims=...) expected = (da_a * da_b).sum() xr.testing.assert_allclose(expected, actual) with xr.set_options(arithmetic_join="exact"): with raises_regex(ValueError, "indexes along dimension"): xr.dot(da_a, da_b) # NOTE: dot always uses `join="inner"` because `(a * b).sum()` yields the same for all # join method (except "exact") with xr.set_options(arithmetic_join="left"): actual = xr.dot(da_a, da_b) expected = (da_a * da_b).sum(["a", "b"]) xr.testing.assert_allclose(expected, actual) with xr.set_options(arithmetic_join="right"): actual = xr.dot(da_a, da_b) expected = (da_a * da_b).sum(["a", "b"]) xr.testing.assert_allclose(expected, actual) with xr.set_options(arithmetic_join="outer"): actual = xr.dot(da_a, da_b) expected = (da_a * da_b).sum(["a", "b"]) xr.testing.assert_allclose(expected, actual) def test_where(): cond = xr.DataArray([True, False], dims="x") actual = xr.where(cond, 1, 0) expected = xr.DataArray([1, 0], dims="x") assert_identical(expected, actual) @pytest.mark.parametrize("use_dask", [True, False]) @pytest.mark.parametrize("use_datetime", [True, False]) def test_polyval(use_dask, use_datetime): if use_dask and not has_dask: pytest.skip("requires dask") if use_datetime: xcoord = xr.DataArray( pd.date_range("2000-01-01", freq="D", periods=10), dims=("x",), name="x" ) x = xr.core.missing.get_clean_interp_index(xcoord, "x") else: xcoord = x = np.arange(10) da = xr.DataArray( np.stack((1.0 + x + 2.0 * x ** 2, 1.0 + 2.0 * x + 3.0 * x ** 2)), dims=("d", "x"), coords={"x": xcoord, "d": [0, 1]}, ) coeffs = xr.DataArray( [[2, 1, 1], [3, 2, 1]], dims=("d", "degree"), coords={"d": [0, 1], "degree": [2, 1, 0]}, ) if use_dask: coeffs = coeffs.chunk({"d": 2}) da_pv = xr.polyval(da.x, coeffs) xr.testing.assert_allclose(da, da_pv.T)