ENH Add lapack driver argument to randomized svd function (scikit-learn#20617)

skailasa · glemaitre · lesteve · commit 16adc8f79f06 · 2022-05-19T18:16:48.000+02:00
Co-authored-by: Guillaume Lemaitre &lt;g.lemaitre58@gmail.com&gt;
diff --git a/doc/whats_new/v1.2.rst b/doc/whats_new/v1.2.rst
@@ -94,11 +94,11 @@ Changelog
   :pr:`23139` by `Tom Dupre la Tour`_.
 
 :mod:`sklearn.preprocessing`
-.............................
+............................
 
 - |Fix| :class:`preprocessing.PolynomialFeatures` with ``degree`` equal to 0 will raise
   error when ``include_bias`` is set to False, and outputs a single constant array when
-  ``include_bias`` is set to True. :pr:`23370` by :user:`Zhehao Liu <MaxwellLZH>`. 
+  ``include_bias`` is set to True. :pr:`23370` by :user:`Zhehao Liu <MaxwellLZH>`.
 
 :mod:`sklearn.tree`
 ...................
@@ -107,6 +107,14 @@ Changelog
   :class:`tree.DecisionTreeRegressor` and :class:`tree.DecisionTreeClassifier`.
   :pr:`23273` by `Thomas Fan`_.
 
+:mod:`sklearn.utils`
+....................
+
+- |Enhancement| :func:`utils.extmath.randomized_svd` now accepts an argument,
+  `lapack_svd_driver`, to specify the lapack driver used in the internal
+  deterministic SVD used by the randomized SVD algorithm.
+  :pr:`20617` by :user:`Srinath Kailasa <skailasa>`
+
 Code and Documentation Contributors
 -----------------------------------
 
diff --git a/sklearn/utils/extmath.py b/sklearn/utils/extmath.py
@@ -256,11 +256,12 @@ def randomized_svd(
     transpose="auto",
     flip_sign=True,
     random_state="warn",
+    svd_lapack_driver="gesdd",
 ):
     """Computes a truncated randomized SVD.
 
-    This method solves the fixed-rank approximation problem described in the
-    Halko et al paper (problem (1.5), p5).
+    This method solves the fixed-rank approximation problem described in [1]_
+    (problem (1.5), p5).
 
     Parameters
     ----------
@@ -278,8 +279,8 @@ def randomized_svd(
         approximation of singular vectors and singular values. Users might wish
         to increase this parameter up to `2*k - n_components` where k is the
         effective rank, for large matrices, noisy problems, matrices with
-        slowly decaying spectrums, or to increase precision accuracy. See Halko
-        et al (pages 5, 23 and 26).
+        slowly decaying spectrums, or to increase precision accuracy. See [1]_
+        (pages 5, 23 and 26).
 
     n_iter : int or 'auto', default='auto'
         Number of power iterations. It can be used to deal with very noisy
@@ -291,7 +292,7 @@ def randomized_svd(
         more costly power iterations steps. When `n_components` is equal
         or greater to the effective matrix rank and the spectrum does not
         present a slow decay, `n_iter=0` or `1` should even work fine in theory
-        (see Halko et al paper, page 9).
+        (see [1]_ page 9).
 
         .. versionchanged:: 0.18
 
@@ -332,6 +333,14 @@ def randomized_svd(
             the value of `random_state` explicitly to suppress the deprecation
             warning.
 
+    svd_lapack_driver : {"gesdd", "gesvd"}, default="gesdd"
+        Whether to use the more efficient divide-and-conquer approach
+        (`"gesdd"`) or more general rectangular approach (`"gesvd"`) to compute
+        the SVD of the matrix B, which is the projection of M into a low
+        dimensional subspace, as described in [1]_.
+
+        .. versionadded:: 1.2
+
     Notes
     -----
     This algorithm finds a (usually very good) approximate truncated
@@ -346,17 +355,16 @@ def randomized_svd(
 
     References
     ----------
-    * :arxiv:`"Finding structure with randomness:
+    .. [1] :arxiv:`"Finding structure with randomness:
       Stochastic algorithms for constructing approximate matrix decompositions"
       <0909.4061>`
       Halko, et al. (2009)
 
-    * A randomized algorithm for the decomposition of matrices
+    .. [2] A randomized algorithm for the decomposition of matrices
       Per-Gunnar Martinsson, Vladimir Rokhlin and Mark Tygert
 
-    * An implementation of a randomized algorithm for principal component
-      analysis
-      A. Szlam et al. 2014
+    .. [3] An implementation of a randomized algorithm for principal component
+      analysis A. Szlam et al. 2014
     """
     if isinstance(M, (sparse.lil_matrix, sparse.dok_matrix)):
         warnings.warn(
@@ -405,7 +413,7 @@ def randomized_svd(
     B = safe_sparse_dot(Q.T, M)
 
     # compute the SVD on the thin matrix: (k + p) wide
-    Uhat, s, Vt = linalg.svd(B, full_matrices=False)
+    Uhat, s, Vt = linalg.svd(B, full_matrices=False, lapack_driver=svd_lapack_driver)
 
     del B
     U = np.dot(Q, Uhat)
diff --git a/sklearn/utils/tests/test_extmath.py b/sklearn/utils/tests/test_extmath.py
@@ -3,7 +3,6 @@
 #          Denis Engemann <denis-alexander.engemann@inria.fr>
 #
 # License: BSD 3 clause
-
 import numpy as np
 from scipy import sparse
 from scipy import linalg
@@ -568,6 +567,32 @@ def max_loading_is_positive(u, v):
     assert not v_based
 
 
+@pytest.mark.parametrize("n", [50, 100, 300])
+@pytest.mark.parametrize("m", [50, 100, 300])
+@pytest.mark.parametrize("k", [10, 20, 50])
+@pytest.mark.parametrize("seed", range(5))
+def test_randomized_svd_lapack_driver(n, m, k, seed):
+    # Check that different SVD drivers provide consistent results
+
+    # Matrix being compressed
+    rng = np.random.RandomState(seed)
+    X = rng.rand(n, m)
+
+    # Number of components
+    u1, s1, vt1 = randomized_svd(X, k, svd_lapack_driver="gesdd", random_state=0)
+    u2, s2, vt2 = randomized_svd(X, k, svd_lapack_driver="gesvd", random_state=0)
+
+    # Check shape and contents
+    assert u1.shape == u2.shape
+    assert_allclose(u1, u2, atol=0, rtol=1e-3)
+
+    assert s1.shape == s2.shape
+    assert_allclose(s1, s2, atol=0, rtol=1e-3)
+
+    assert vt1.shape == vt2.shape
+    assert_allclose(vt1, vt2, atol=0, rtol=1e-3)
+
+
 def test_cartesian():
     # Check if cartesian product delivers the right results
 
