# Author: Alexandre Gramfort # Fabian Pedregosa # Maria Telenczuk # # License: BSD 3 clause import pytest import warnings import numpy as np from scipy import sparse from scipy import linalg from sklearn.utils._testing import assert_array_almost_equal from sklearn.utils._testing import assert_array_equal from sklearn.utils._testing import assert_allclose from sklearn.linear_model import LinearRegression from sklearn.linear_model._base import _deprecate_normalize from sklearn.linear_model._base import _preprocess_data from sklearn.linear_model._base import _rescale_data from sklearn.linear_model._base import make_dataset from sklearn.datasets import make_sparse_uncorrelated from sklearn.datasets import make_regression from sklearn.datasets import load_iris from sklearn.preprocessing import StandardScaler from sklearn.preprocessing import add_dummy_feature rtol = 1e-6 def test_linear_regression(): # Test LinearRegression on a simple dataset. # a simple dataset X = [[1], [2]] Y = [1, 2] reg = LinearRegression() reg.fit(X, Y) assert_array_almost_equal(reg.coef_, [1]) assert_array_almost_equal(reg.intercept_, [0]) assert_array_almost_equal(reg.predict(X), [1, 2]) # test it also for degenerate input X = [[1]] Y = [0] reg = LinearRegression() reg.fit(X, Y) assert_array_almost_equal(reg.coef_, [0]) assert_array_almost_equal(reg.intercept_, [0]) assert_array_almost_equal(reg.predict(X), [0]) @pytest.mark.parametrize("array_constr", [np.array, sparse.csr_matrix]) @pytest.mark.parametrize("fit_intercept", [True, False]) def test_linear_regression_sample_weights( array_constr, fit_intercept, global_random_seed ): rng = np.random.RandomState(global_random_seed) # It would not work with under-determined systems n_samples, n_features = 6, 5 X = array_constr(rng.normal(size=(n_samples, n_features))) y = rng.normal(size=n_samples) sample_weight = 1.0 + rng.uniform(size=n_samples) # LinearRegression with explicit sample_weight reg = LinearRegression(fit_intercept=fit_intercept) reg.fit(X, y, sample_weight=sample_weight) coefs1 = reg.coef_ inter1 = reg.intercept_ assert reg.coef_.shape == (X.shape[1],) # sanity checks # Closed form of the weighted least square # theta = (X^T W X)^(-1) @ X^T W y W = np.diag(sample_weight) X_aug = X if not fit_intercept else add_dummy_feature(X) Xw = X_aug.T @ W @ X_aug yw = X_aug.T @ W @ y coefs2 = linalg.solve(Xw, yw) if not fit_intercept: assert_allclose(coefs1, coefs2) else: assert_allclose(coefs1, coefs2[1:]) assert_allclose(inter1, coefs2[0]) def test_raises_value_error_if_positive_and_sparse(): error_msg = "A sparse matrix was passed, but dense data is required." # X must not be sparse if positive == True X = sparse.eye(10) y = np.ones(10) reg = LinearRegression(positive=True) with pytest.raises(TypeError, match=error_msg): reg.fit(X, y) @pytest.mark.parametrize("n_samples, n_features", [(2, 3), (3, 2)]) def test_raises_value_error_if_sample_weights_greater_than_1d(n_samples, n_features): # Sample weights must be either scalar or 1D rng = np.random.RandomState(0) X = rng.randn(n_samples, n_features) y = rng.randn(n_samples) sample_weights_OK = rng.randn(n_samples) ** 2 + 1 sample_weights_OK_1 = 1.0 sample_weights_OK_2 = 2.0 reg = LinearRegression() # make sure the "OK" sample weights actually work reg.fit(X, y, sample_weights_OK) reg.fit(X, y, sample_weights_OK_1) reg.fit(X, y, sample_weights_OK_2) def test_fit_intercept(): # Test assertions on betas shape. X2 = np.array([[0.38349978, 0.61650022], [0.58853682, 0.41146318]]) X3 = np.array( [[0.27677969, 0.70693172, 0.01628859], [0.08385139, 0.20692515, 0.70922346]] ) y = np.array([1, 1]) lr2_without_intercept = LinearRegression(fit_intercept=False).fit(X2, y) lr2_with_intercept = LinearRegression().fit(X2, y) lr3_without_intercept = LinearRegression(fit_intercept=False).fit(X3, y) lr3_with_intercept = LinearRegression().fit(X3, y) assert lr2_with_intercept.coef_.shape == lr2_without_intercept.coef_.shape assert lr3_with_intercept.coef_.shape == lr3_without_intercept.coef_.shape assert lr2_without_intercept.coef_.ndim == lr3_without_intercept.coef_.ndim def test_error_on_wrong_normalize(): normalize = "wrong" error_msg = "Leave 'normalize' to its default" with pytest.raises(ValueError, match=error_msg): _deprecate_normalize(normalize, "estimator") # TODO(1.4): remove @pytest.mark.parametrize("normalize", [True, False, "deprecated"]) def test_deprecate_normalize(normalize): # test all possible case of the normalize parameter deprecation if normalize == "deprecated": # no warning output = False expected = None warning_msg = [] else: output = normalize expected = FutureWarning warning_msg = ["1.4"] if not normalize: warning_msg.append("default value") else: warning_msg.append("StandardScaler(") if expected is None: with warnings.catch_warnings(): warnings.simplefilter("error", FutureWarning) _normalize = _deprecate_normalize(normalize, "estimator") else: with pytest.warns(expected) as record: _normalize = _deprecate_normalize(normalize, "estimator") assert all([warning in str(record[0].message) for warning in warning_msg]) assert _normalize == output def test_linear_regression_sparse(global_random_seed): # Test that linear regression also works with sparse data rng = np.random.RandomState(global_random_seed) n = 100 X = sparse.eye(n, n) beta = rng.rand(n) y = X @ beta ols = LinearRegression() ols.fit(X, y.ravel()) assert_array_almost_equal(beta, ols.coef_ + ols.intercept_) assert_array_almost_equal(ols.predict(X) - y.ravel(), 0) @pytest.mark.parametrize("fit_intercept", [True, False]) def test_linear_regression_sparse_equal_dense(fit_intercept): # Test that linear regression agrees between sparse and dense rng = np.random.RandomState(0) n_samples = 200 n_features = 2 X = rng.randn(n_samples, n_features) X[X < 0.1] = 0.0 Xcsr = sparse.csr_matrix(X) y = rng.rand(n_samples) params = dict(fit_intercept=fit_intercept) clf_dense = LinearRegression(**params) clf_sparse = LinearRegression(**params) clf_dense.fit(X, y) clf_sparse.fit(Xcsr, y) assert clf_dense.intercept_ == pytest.approx(clf_sparse.intercept_) assert_allclose(clf_dense.coef_, clf_sparse.coef_) def test_linear_regression_multiple_outcome(): # Test multiple-outcome linear regressions rng = np.random.RandomState(0) X, y = make_regression(random_state=rng) Y = np.vstack((y, y)).T n_features = X.shape[1] reg = LinearRegression() reg.fit((X), Y) assert reg.coef_.shape == (2, n_features) Y_pred = reg.predict(X) reg.fit(X, y) y_pred = reg.predict(X) assert_array_almost_equal(np.vstack((y_pred, y_pred)).T, Y_pred, decimal=3) def test_linear_regression_sparse_multiple_outcome(global_random_seed): # Test multiple-outcome linear regressions with sparse data rng = np.random.RandomState(global_random_seed) X, y = make_sparse_uncorrelated(random_state=rng) X = sparse.coo_matrix(X) Y = np.vstack((y, y)).T n_features = X.shape[1] ols = LinearRegression() ols.fit(X, Y) assert ols.coef_.shape == (2, n_features) Y_pred = ols.predict(X) ols.fit(X, y.ravel()) y_pred = ols.predict(X) assert_array_almost_equal(np.vstack((y_pred, y_pred)).T, Y_pred, decimal=3) def test_linear_regression_positive(): # Test nonnegative LinearRegression on a simple dataset. X = [[1], [2]] y = [1, 2] reg = LinearRegression(positive=True) reg.fit(X, y) assert_array_almost_equal(reg.coef_, [1]) assert_array_almost_equal(reg.intercept_, [0]) assert_array_almost_equal(reg.predict(X), [1, 2]) # test it also for degenerate input X = [[1]] y = [0] reg = LinearRegression(positive=True) reg.fit(X, y) assert_allclose(reg.coef_, [0]) assert_allclose(reg.intercept_, [0]) assert_allclose(reg.predict(X), [0]) def test_linear_regression_positive_multiple_outcome(global_random_seed): # Test multiple-outcome nonnegative linear regressions rng = np.random.RandomState(global_random_seed) X, y = make_sparse_uncorrelated(random_state=rng) Y = np.vstack((y, y)).T n_features = X.shape[1] ols = LinearRegression(positive=True) ols.fit(X, Y) assert ols.coef_.shape == (2, n_features) assert np.all(ols.coef_ >= 0.0) Y_pred = ols.predict(X) ols.fit(X, y.ravel()) y_pred = ols.predict(X) assert_allclose(np.vstack((y_pred, y_pred)).T, Y_pred) def test_linear_regression_positive_vs_nonpositive(global_random_seed): # Test differences with LinearRegression when positive=False. rng = np.random.RandomState(global_random_seed) X, y = make_sparse_uncorrelated(random_state=rng) reg = LinearRegression(positive=True) reg.fit(X, y) regn = LinearRegression(positive=False) regn.fit(X, y) assert np.mean((reg.coef_ - regn.coef_) ** 2) > 1e-3 def test_linear_regression_positive_vs_nonpositive_when_positive(global_random_seed): # Test LinearRegression fitted coefficients # when the problem is positive. rng = np.random.RandomState(global_random_seed) n_samples = 200 n_features = 4 X = rng.rand(n_samples, n_features) y = X[:, 0] + 2 * X[:, 1] + 3 * X[:, 2] + 1.5 * X[:, 3] reg = LinearRegression(positive=True) reg.fit(X, y) regn = LinearRegression(positive=False) regn.fit(X, y) assert np.mean((reg.coef_ - regn.coef_) ** 2) < 1e-6 def test_linear_regression_pd_sparse_dataframe_warning(): pd = pytest.importorskip("pandas") # Warning is raised only when some of the columns is sparse df = pd.DataFrame({"0": np.random.randn(10)}) for col in range(1, 4): arr = np.random.randn(10) arr[:8] = 0 # all columns but the first column is sparse if col != 0: arr = pd.arrays.SparseArray(arr, fill_value=0) df[str(col)] = arr msg = "pandas.DataFrame with sparse columns found." reg = LinearRegression() with pytest.warns(UserWarning, match=msg): reg.fit(df.iloc[:, 0:2], df.iloc[:, 3]) # does not warn when the whole dataframe is sparse df["0"] = pd.arrays.SparseArray(df["0"], fill_value=0) assert hasattr(df, "sparse") with warnings.catch_warnings(): warnings.simplefilter("error", UserWarning) reg.fit(df.iloc[:, 0:2], df.iloc[:, 3]) def test_preprocess_data(global_random_seed): rng = np.random.RandomState(global_random_seed) n_samples = 200 n_features = 2 X = rng.rand(n_samples, n_features) y = rng.rand(n_samples) expected_X_mean = np.mean(X, axis=0) expected_X_scale = np.std(X, axis=0) * np.sqrt(X.shape[0]) expected_y_mean = np.mean(y, axis=0) Xt, yt, X_mean, y_mean, X_scale = _preprocess_data( X, y, fit_intercept=False, normalize=False ) assert_array_almost_equal(X_mean, np.zeros(n_features)) assert_array_almost_equal(y_mean, 0) assert_array_almost_equal(X_scale, np.ones(n_features)) assert_array_almost_equal(Xt, X) assert_array_almost_equal(yt, y) Xt, yt, X_mean, y_mean, X_scale = _preprocess_data( X, y, fit_intercept=True, normalize=False ) assert_array_almost_equal(X_mean, expected_X_mean) assert_array_almost_equal(y_mean, expected_y_mean) assert_array_almost_equal(X_scale, np.ones(n_features)) assert_array_almost_equal(Xt, X - expected_X_mean) assert_array_almost_equal(yt, y - expected_y_mean) Xt, yt, X_mean, y_mean, X_scale = _preprocess_data( X, y, fit_intercept=True, normalize=True ) assert_array_almost_equal(X_mean, expected_X_mean) assert_array_almost_equal(y_mean, expected_y_mean) assert_array_almost_equal(X_scale, expected_X_scale) assert_array_almost_equal(Xt, (X - expected_X_mean) / expected_X_scale) assert_array_almost_equal(yt, y - expected_y_mean) def test_preprocess_data_multioutput(global_random_seed): rng = np.random.RandomState(global_random_seed) n_samples = 200 n_features = 3 n_outputs = 2 X = rng.rand(n_samples, n_features) y = rng.rand(n_samples, n_outputs) expected_y_mean = np.mean(y, axis=0) args = [X, sparse.csc_matrix(X)] for X in args: _, yt, _, y_mean, _ = _preprocess_data( X, y, fit_intercept=False, normalize=False ) assert_array_almost_equal(y_mean, np.zeros(n_outputs)) assert_array_almost_equal(yt, y) _, yt, _, y_mean, _ = _preprocess_data( X, y, fit_intercept=True, normalize=False ) assert_array_almost_equal(y_mean, expected_y_mean) assert_array_almost_equal(yt, y - y_mean) _, yt, _, y_mean, _ = _preprocess_data(X, y, fit_intercept=True, normalize=True) assert_array_almost_equal(y_mean, expected_y_mean) assert_array_almost_equal(yt, y - y_mean) @pytest.mark.parametrize("is_sparse", [False, True]) def test_preprocess_data_weighted(is_sparse, global_random_seed): rng = np.random.RandomState(global_random_seed) n_samples = 200 n_features = 4 # Generate random data with 50% of zero values to make sure # that the sparse variant of this test is actually sparse. This also # shifts the mean value for each columns in X further away from # zero. X = rng.rand(n_samples, n_features) X[X < 0.5] = 0.0 # Scale the first feature of X to be 10 larger than the other to # better check the impact of feature scaling. X[:, 0] *= 10 # Constant non-zero feature. X[:, 2] = 1.0 # Constant zero feature (non-materialized in the sparse case) X[:, 3] = 0.0 y = rng.rand(n_samples) sample_weight = rng.rand(n_samples) expected_X_mean = np.average(X, axis=0, weights=sample_weight) expected_y_mean = np.average(y, axis=0, weights=sample_weight) X_sample_weight_avg = np.average(X, weights=sample_weight, axis=0) X_sample_weight_var = np.average( (X - X_sample_weight_avg) ** 2, weights=sample_weight, axis=0 ) constant_mask = X_sample_weight_var < 10 * np.finfo(X.dtype).eps assert_array_equal(constant_mask, [0, 0, 1, 1]) expected_X_scale = np.sqrt(X_sample_weight_var) * np.sqrt(sample_weight.sum()) # near constant features should not be scaled expected_X_scale[constant_mask] = 1 if is_sparse: X = sparse.csr_matrix(X) # normalize is False Xt, yt, X_mean, y_mean, X_scale = _preprocess_data( X, y, fit_intercept=True, normalize=False, sample_weight=sample_weight, ) assert_array_almost_equal(X_mean, expected_X_mean) assert_array_almost_equal(y_mean, expected_y_mean) assert_array_almost_equal(X_scale, np.ones(n_features)) if is_sparse: assert_array_almost_equal(Xt.toarray(), X.toarray()) else: assert_array_almost_equal(Xt, X - expected_X_mean) assert_array_almost_equal(yt, y - expected_y_mean) # normalize is True Xt, yt, X_mean, y_mean, X_scale = _preprocess_data( X, y, fit_intercept=True, normalize=True, sample_weight=sample_weight, ) assert_array_almost_equal(X_mean, expected_X_mean) assert_array_almost_equal(y_mean, expected_y_mean) assert_array_almost_equal(X_scale, expected_X_scale) if is_sparse: # X is not centered assert_array_almost_equal(Xt.toarray(), X.toarray() / expected_X_scale) else: assert_array_almost_equal(Xt, (X - expected_X_mean) / expected_X_scale) # _preprocess_data with normalize=True scales the data by the feature-wise # euclidean norms while StandardScaler scales the data by the feature-wise # standard deviations. # The two are equivalent up to a ratio of np.sqrt(n_samples) if unweighted # or np.sqrt(sample_weight.sum()) if weighted. if is_sparse: scaler = StandardScaler(with_mean=False).fit(X, sample_weight=sample_weight) # Non-constant features are scaled similarly with np.sqrt(n_samples) assert_array_almost_equal( scaler.transform(X).toarray()[:, :2] / np.sqrt(sample_weight.sum()), Xt.toarray()[:, :2], ) # Constant features go through un-scaled. assert_array_almost_equal( scaler.transform(X).toarray()[:, 2:], Xt.toarray()[:, 2:] ) else: scaler = StandardScaler(with_mean=True).fit(X, sample_weight=sample_weight) assert_array_almost_equal(scaler.mean_, X_mean) assert_array_almost_equal( scaler.transform(X) / np.sqrt(sample_weight.sum()), Xt, ) assert_array_almost_equal(yt, y - expected_y_mean) def test_sparse_preprocess_data_offsets(global_random_seed): rng = np.random.RandomState(global_random_seed) n_samples = 200 n_features = 2 X = sparse.rand(n_samples, n_features, density=0.5, random_state=rng) X = X.tolil() y = rng.rand(n_samples) XA = X.toarray() expected_X_scale = np.std(XA, axis=0) * np.sqrt(X.shape[0]) Xt, yt, X_mean, y_mean, X_scale = _preprocess_data( X, y, fit_intercept=False, normalize=False ) assert_array_almost_equal(X_mean, np.zeros(n_features)) assert_array_almost_equal(y_mean, 0) assert_array_almost_equal(X_scale, np.ones(n_features)) assert_array_almost_equal(Xt.A, XA) assert_array_almost_equal(yt, y) Xt, yt, X_mean, y_mean, X_scale = _preprocess_data( X, y, fit_intercept=True, normalize=False ) assert_array_almost_equal(X_mean, np.mean(XA, axis=0)) assert_array_almost_equal(y_mean, np.mean(y, axis=0)) assert_array_almost_equal(X_scale, np.ones(n_features)) assert_array_almost_equal(Xt.A, XA) assert_array_almost_equal(yt, y - np.mean(y, axis=0)) Xt, yt, X_mean, y_mean, X_scale = _preprocess_data( X, y, fit_intercept=True, normalize=True ) assert_array_almost_equal(X_mean, np.mean(XA, axis=0)) assert_array_almost_equal(y_mean, np.mean(y, axis=0)) assert_array_almost_equal(X_scale, expected_X_scale) assert_array_almost_equal(Xt.A, XA / expected_X_scale) assert_array_almost_equal(yt, y - np.mean(y, axis=0)) def test_csr_preprocess_data(): # Test output format of _preprocess_data, when input is csr X, y = make_regression() X[X < 2.5] = 0.0 csr = sparse.csr_matrix(X) csr_, y, _, _, _ = _preprocess_data(csr, y, True) assert csr_.getformat() == "csr" @pytest.mark.parametrize("is_sparse", (True, False)) @pytest.mark.parametrize("to_copy", (True, False)) def test_preprocess_copy_data_no_checks(is_sparse, to_copy): X, y = make_regression() X[X < 2.5] = 0.0 if is_sparse: X = sparse.csr_matrix(X) X_, y_, _, _, _ = _preprocess_data(X, y, True, copy=to_copy, check_input=False) if to_copy and is_sparse: assert not np.may_share_memory(X_.data, X.data) elif to_copy: assert not np.may_share_memory(X_, X) elif is_sparse: assert np.may_share_memory(X_.data, X.data) else: assert np.may_share_memory(X_, X) def test_dtype_preprocess_data(global_random_seed): rng = np.random.RandomState(global_random_seed) n_samples = 200 n_features = 2 X = rng.rand(n_samples, n_features) y = rng.rand(n_samples) X_32 = np.asarray(X, dtype=np.float32) y_32 = np.asarray(y, dtype=np.float32) X_64 = np.asarray(X, dtype=np.float64) y_64 = np.asarray(y, dtype=np.float64) for fit_intercept in [True, False]: for normalize in [True, False]: Xt_32, yt_32, X_mean_32, y_mean_32, X_scale_32 = _preprocess_data( X_32, y_32, fit_intercept=fit_intercept, normalize=normalize, ) Xt_64, yt_64, X_mean_64, y_mean_64, X_scale_64 = _preprocess_data( X_64, y_64, fit_intercept=fit_intercept, normalize=normalize, ) Xt_3264, yt_3264, X_mean_3264, y_mean_3264, X_scale_3264 = _preprocess_data( X_32, y_64, fit_intercept=fit_intercept, normalize=normalize, ) Xt_6432, yt_6432, X_mean_6432, y_mean_6432, X_scale_6432 = _preprocess_data( X_64, y_32, fit_intercept=fit_intercept, normalize=normalize, ) assert Xt_32.dtype == np.float32 assert yt_32.dtype == np.float32 assert X_mean_32.dtype == np.float32 assert y_mean_32.dtype == np.float32 assert X_scale_32.dtype == np.float32 assert Xt_64.dtype == np.float64 assert yt_64.dtype == np.float64 assert X_mean_64.dtype == np.float64 assert y_mean_64.dtype == np.float64 assert X_scale_64.dtype == np.float64 assert Xt_3264.dtype == np.float32 assert yt_3264.dtype == np.float32 assert X_mean_3264.dtype == np.float32 assert y_mean_3264.dtype == np.float32 assert X_scale_3264.dtype == np.float32 assert Xt_6432.dtype == np.float64 assert yt_6432.dtype == np.float64 assert X_mean_6432.dtype == np.float64 assert y_mean_6432.dtype == np.float64 assert X_scale_6432.dtype == np.float64 assert X_32.dtype == np.float32 assert y_32.dtype == np.float32 assert X_64.dtype == np.float64 assert y_64.dtype == np.float64 assert_array_almost_equal(Xt_32, Xt_64) assert_array_almost_equal(yt_32, yt_64) assert_array_almost_equal(X_mean_32, X_mean_64) assert_array_almost_equal(y_mean_32, y_mean_64) assert_array_almost_equal(X_scale_32, X_scale_64) @pytest.mark.parametrize("n_targets", [None, 2]) def test_rescale_data_dense(n_targets, global_random_seed): rng = np.random.RandomState(global_random_seed) n_samples = 200 n_features = 2 sample_weight = 1.0 + rng.rand(n_samples) X = rng.rand(n_samples, n_features) if n_targets is None: y = rng.rand(n_samples) else: y = rng.rand(n_samples, n_targets) rescaled_X, rescaled_y, sqrt_sw = _rescale_data(X, y, sample_weight) rescaled_X2 = X * sqrt_sw[:, np.newaxis] if n_targets is None: rescaled_y2 = y * sqrt_sw else: rescaled_y2 = y * sqrt_sw[:, np.newaxis] assert_array_almost_equal(rescaled_X, rescaled_X2) assert_array_almost_equal(rescaled_y, rescaled_y2) def test_fused_types_make_dataset(): iris = load_iris() X_32 = iris.data.astype(np.float32) y_32 = iris.target.astype(np.float32) X_csr_32 = sparse.csr_matrix(X_32) sample_weight_32 = np.arange(y_32.size, dtype=np.float32) X_64 = iris.data.astype(np.float64) y_64 = iris.target.astype(np.float64) X_csr_64 = sparse.csr_matrix(X_64) sample_weight_64 = np.arange(y_64.size, dtype=np.float64) # array dataset_32, _ = make_dataset(X_32, y_32, sample_weight_32) dataset_64, _ = make_dataset(X_64, y_64, sample_weight_64) xi_32, yi_32, _, _ = dataset_32._next_py() xi_64, yi_64, _, _ = dataset_64._next_py() xi_data_32, _, _ = xi_32 xi_data_64, _, _ = xi_64 assert xi_data_32.dtype == np.float32 assert xi_data_64.dtype == np.float64 assert_allclose(yi_64, yi_32, rtol=rtol) # csr datasetcsr_32, _ = make_dataset(X_csr_32, y_32, sample_weight_32) datasetcsr_64, _ = make_dataset(X_csr_64, y_64, sample_weight_64) xicsr_32, yicsr_32, _, _ = datasetcsr_32._next_py() xicsr_64, yicsr_64, _, _ = datasetcsr_64._next_py() xicsr_data_32, _, _ = xicsr_32 xicsr_data_64, _, _ = xicsr_64 assert xicsr_data_32.dtype == np.float32 assert xicsr_data_64.dtype == np.float64 assert_allclose(xicsr_data_64, xicsr_data_32, rtol=rtol) assert_allclose(yicsr_64, yicsr_32, rtol=rtol) assert_array_equal(xi_data_32, xicsr_data_32) assert_array_equal(xi_data_64, xicsr_data_64) assert_array_equal(yi_32, yicsr_32) assert_array_equal(yi_64, yicsr_64)