[MRG] Domain adaptation and unbalanced solvers with backend support (#343)

* First draft

* Add matrix inverse and square root to backend

* Eigen decomposition for older versions of pytorch (1.8.1 and older)

* Corrected eigen decomposition for pytorch 1.8.1 and older

* Spectral theorem is a thing

* Optimization

* small optimization

* More functions converted

* pep8

* remove a warning and prepare torch meshgrid for future torch release (which will change default indexing)

* dots and pep8

* Meshgrid corrected for older version and prepared for future versions changes

* New backend functions

* Base transport

* LinearTransport

* All transport classes + pep8

* PR added to release file

* Jcpot barycenter test

* unbalanced with backend

* pep8

* bug solve

* test of domain adaptation with backends

* solve bug for tic toc & macos

* solving scipy deprecation warning

* solving scipy deprecation warning attempt2

* solving scipy deprecation warning attempt3

* A warning is triggered when a float->int conversion is detected

* bug solve

* docs

* release file updated

* Better handling of float->int conversion in EMD

* Corrected test for is_floating_point

* docs

* release file updated

* cupy does not allow implicit cast

* fromnumpy

* added test

* test da tf jax

* test unbalanced with no provided histogram

* using type_as argument in unif function correctly

* pep8

* transport plan cast in emd changed behaviour, now trying to cast as histogram's dtype, defaulting to cost matrix

Co-authored-by: Rémi Flamary <remi.flamary@gmail.com>

1 files changed, 96 insertions, 61 deletions

diff --git a/test/test_unbalanced.py b/test/test_unbalanced.py
index e8349d1..db59504 100644
--- a/test/test_unbalanced.py
+++ b/test/test_unbalanced.py
@@ -9,11 +9,9 @@ import ot
 import pytest
 from ot.unbalanced import barycenter_unbalanced
 
-from scipy.special import logsumexp
-
 
 @pytest.mark.parametrize("method", ["sinkhorn", "sinkhorn_stabilized"])
-def test_unbalanced_convergence(method):
+def test_unbalanced_convergence(nx, method):
     # test generalized sinkhorn for unbalanced OT
     n = 100
     rng = np.random.RandomState(42)
@@ -28,36 +26,51 @@ def test_unbalanced_convergence(method):
     epsilon = 1.
     reg_m = 1.
 
+    a, b, M = nx.from_numpy(a, b, M)
+
     G, log = ot.unbalanced.sinkhorn_unbalanced(a, b, M, reg=epsilon,
                                                reg_m=reg_m,
                                                method=method,
                                                log=True,
                                                verbose=True)
-    loss = ot.unbalanced.sinkhorn_unbalanced2(a, b, M, epsilon, reg_m,
-                                              method=method,
-                                              verbose=True)
+    loss = nx.to_numpy(ot.unbalanced.sinkhorn_unbalanced2(
+        a, b, M, epsilon, reg_m, method=method, verbose=True
+    ))
     # check fixed point equations
     # in log-domain
     fi = reg_m / (reg_m + epsilon)
-    logb = np.log(b + 1e-16)
-    loga = np.log(a + 1e-16)
-    logKtu = logsumexp(log["logu"][None, :] - M.T / epsilon, axis=1)
-    logKv = logsumexp(log["logv"][None, :] - M / epsilon, axis=1)
+    logb = nx.log(b + 1e-16)
+    loga = nx.log(a + 1e-16)
+    logKtu = nx.logsumexp(log["logu"][None, :] - M.T / epsilon, axis=1)
+    logKv = nx.logsumexp(log["logv"][None, :] - M / epsilon, axis=1)
 
     v_final = fi * (logb - logKtu)
     u_final = fi * (loga - logKv)
 
     np.testing.assert_allclose(
-        u_final, log["logu"], atol=1e-05)
+        nx.to_numpy(u_final), nx.to_numpy(log["logu"]), atol=1e-05)
     np.testing.assert_allclose(
-        v_final, log["logv"], atol=1e-05)
+        nx.to_numpy(v_final), nx.to_numpy(log["logv"]), atol=1e-05)
 
     # check if sinkhorn_unbalanced2 returns the correct loss
-    np.testing.assert_allclose((G * M).sum(), loss, atol=1e-5)
+    np.testing.assert_allclose(nx.to_numpy(nx.sum(G * M)), loss, atol=1e-5)
+
+    # check in case no histogram is provided
+    M_np = nx.to_numpy(M)
+    a_np, b_np = np.array([]), np.array([])
+    a, b = nx.from_numpy(a_np, b_np)
+
+    G = ot.unbalanced.sinkhorn_unbalanced(
+        a, b, M, reg=epsilon, reg_m=reg_m, method=method, verbose=True
+    )
+    G_np = ot.unbalanced.sinkhorn_unbalanced(
+        a_np, b_np, M_np, reg=epsilon, reg_m=reg_m, method=method, verbose=True
+    )
+    np.testing.assert_allclose(G_np, nx.to_numpy(G))
 
 
 @pytest.mark.parametrize("method", ["sinkhorn", "sinkhorn_stabilized"])
-def test_unbalanced_multiple_inputs(method):
+def test_unbalanced_multiple_inputs(nx, method):
     # test generalized sinkhorn for unbalanced OT
     n = 100
     rng = np.random.RandomState(42)
@@ -72,6 +85,8 @@ def test_unbalanced_multiple_inputs(method):
     epsilon = 1.
     reg_m = 1.
 
+    a, b, M = nx.from_numpy(a, b, M)
+
     loss, log = ot.unbalanced.sinkhorn_unbalanced(a, b, M, reg=epsilon,
                                                   reg_m=reg_m,
                                                   method=method,
@@ -80,23 +95,24 @@ def test_unbalanced_multiple_inputs(method):
     # check fixed point equations
     # in log-domain
     fi = reg_m / (reg_m + epsilon)
-    logb = np.log(b + 1e-16)
-    loga = np.log(a + 1e-16)[:, None]
-    logKtu = logsumexp(log["logu"][:, None, :] - M[:, :, None] / epsilon,
-                       axis=0)
-    logKv = logsumexp(log["logv"][None, :] - M[:, :, None] / epsilon, axis=1)
+    logb = nx.log(b + 1e-16)
+    loga = nx.log(a + 1e-16)[:, None]
+    logKtu = nx.logsumexp(
+        log["logu"][:, None, :] - M[:, :, None] / epsilon, axis=0
+    )
+    logKv = nx.logsumexp(log["logv"][None, :] - M[:, :, None] / epsilon, axis=1)
     v_final = fi * (logb - logKtu)
     u_final = fi * (loga - logKv)
 
     np.testing.assert_allclose(
-        u_final, log["logu"], atol=1e-05)
+        nx.to_numpy(u_final), nx.to_numpy(log["logu"]), atol=1e-05)
     np.testing.assert_allclose(
-        v_final, log["logv"], atol=1e-05)
+        nx.to_numpy(v_final), nx.to_numpy(log["logv"]), atol=1e-05)
 
     assert len(loss) == b.shape[1]
 
 
-def test_stabilized_vs_sinkhorn():
+def test_stabilized_vs_sinkhorn(nx):
     # test if stable version matches sinkhorn
     n = 100
 
@@ -112,19 +128,27 @@ def test_stabilized_vs_sinkhorn():
     M /= np.median(M)
     epsilon = 0.1
     reg_m = 1.
-    G, log = ot.unbalanced.sinkhorn_unbalanced2(a, b, M, reg=epsilon,
-                                                method="sinkhorn_stabilized",
-                                                reg_m=reg_m,
-                                                log=True,
-                                                verbose=True)
-    G2, log2 = ot.unbalanced.sinkhorn_unbalanced2(a, b, M, epsilon, reg_m,
-                                                  method="sinkhorn", log=True)
+
+    ab, bb, Mb = nx.from_numpy(a, b, M)
+
+    G, _ = ot.unbalanced.sinkhorn_unbalanced2(
+        ab, bb, Mb, epsilon, reg_m, method="sinkhorn_stabilized", log=True
+    )
+    G2, _ = ot.unbalanced.sinkhorn_unbalanced2(
+        ab, bb, Mb, epsilon, reg_m, method="sinkhorn", log=True
+    )
+    G2_np, _ = ot.unbalanced.sinkhorn_unbalanced2(
+        a, b, M, epsilon, reg_m, method="sinkhorn", log=True
+    )
+    G = nx.to_numpy(G)
+    G2 = nx.to_numpy(G2)
 
     np.testing.assert_allclose(G, G2, atol=1e-5)
+    np.testing.assert_allclose(G2, G2_np, atol=1e-5)
 
 
 @pytest.mark.parametrize("method", ["sinkhorn", "sinkhorn_stabilized"])
-def test_unbalanced_barycenter(method):
+def test_unbalanced_barycenter(nx, method):
     # test generalized sinkhorn for unbalanced OT barycenter
     n = 100
     rng = np.random.RandomState(42)
@@ -138,25 +162,29 @@ def test_unbalanced_barycenter(method):
     epsilon = 1.
     reg_m = 1.
 
-    q, log = barycenter_unbalanced(A, M, reg=epsilon, reg_m=reg_m,
-                                   method=method, log=True, verbose=True)
+    A, M = nx.from_numpy(A, M)
+
+    q, log = barycenter_unbalanced(
+        A, M, reg=epsilon, reg_m=reg_m, method=method, log=True, verbose=True
+    )
     # check fixed point equations
     fi = reg_m / (reg_m + epsilon)
-    logA = np.log(A + 1e-16)
-    logq = np.log(q + 1e-16)[:, None]
-    logKtu = logsumexp(log["logu"][:, None, :] - M[:, :, None] / epsilon,
-                       axis=0)
-    logKv = logsumexp(log["logv"][None, :] - M[:, :, None] / epsilon, axis=1)
+    logA = nx.log(A + 1e-16)
+    logq = nx.log(q + 1e-16)[:, None]
+    logKtu = nx.logsumexp(
+        log["logu"][:, None, :] - M[:, :, None] / epsilon, axis=0
+    )
+    logKv = nx.logsumexp(log["logv"][None, :] - M[:, :, None] / epsilon, axis=1)
     v_final = fi * (logq - logKtu)
     u_final = fi * (logA - logKv)
 
     np.testing.assert_allclose(
-        u_final, log["logu"], atol=1e-05)
+        nx.to_numpy(u_final), nx.to_numpy(log["logu"]), atol=1e-05)
     np.testing.assert_allclose(
-        v_final, log["logv"], atol=1e-05)
+        nx.to_numpy(v_final), nx.to_numpy(log["logv"]), atol=1e-05)
 
 
-def test_barycenter_stabilized_vs_sinkhorn():
+def test_barycenter_stabilized_vs_sinkhorn(nx):
     # test generalized sinkhorn for unbalanced OT barycenter
     n = 100
     rng = np.random.RandomState(42)
@@ -170,21 +198,24 @@ def test_barycenter_stabilized_vs_sinkhorn():
     epsilon = 0.5
     reg_m = 10
 
-    qstable, log = barycenter_unbalanced(A, M, reg=epsilon,
-                                         reg_m=reg_m, log=True,
-                                         tau=100,
-                                         method="sinkhorn_stabilized",
-                                         verbose=True
-                                         )
-    q, log = barycenter_unbalanced(A, M, reg=epsilon, reg_m=reg_m,
-                                   method="sinkhorn",
-                                   log=True)
+    Ab, Mb = nx.from_numpy(A, M)
 
-    np.testing.assert_allclose(
-        q, qstable, atol=1e-05)
+    qstable, _ = barycenter_unbalanced(
+        Ab, Mb, reg=epsilon, reg_m=reg_m, log=True, tau=100,
+        method="sinkhorn_stabilized", verbose=True
+    )
+    q, _ = barycenter_unbalanced(
+        Ab, Mb, reg=epsilon, reg_m=reg_m, method="sinkhorn", log=True
+    )
+    q_np, _ = barycenter_unbalanced(
+        A, M, reg=epsilon, reg_m=reg_m, method="sinkhorn", log=True
+    )
+    q, qstable = nx.to_numpy(q, qstable)
+    np.testing.assert_allclose(q, qstable, atol=1e-05)
+    np.testing.assert_allclose(q, q_np, atol=1e-05)
 
 
-def test_wrong_method():
+def test_wrong_method(nx):
 
     n = 10
     rng = np.random.RandomState(42)
@@ -199,19 +230,20 @@ def test_wrong_method():
     epsilon = 1.
     reg_m = 1.
 
+    a, b, M = nx.from_numpy(a, b, M)
+
     with pytest.raises(ValueError):
-        ot.unbalanced.sinkhorn_unbalanced(a, b, M, reg=epsilon,
-                                          reg_m=reg_m,
-                                          method='badmethod',
-                                          log=True,
-                                          verbose=True)
+        ot.unbalanced.sinkhorn_unbalanced(
+            a, b, M, reg=epsilon, reg_m=reg_m, method='badmethod',
+            log=True, verbose=True
+        )
     with pytest.raises(ValueError):
-        ot.unbalanced.sinkhorn_unbalanced2(a, b, M, epsilon, reg_m,
-                                           method='badmethod',
-                                           verbose=True)
+        ot.unbalanced.sinkhorn_unbalanced2(
+            a, b, M, epsilon, reg_m, method='badmethod', verbose=True
+        )
 
 
-def test_implemented_methods():
+def test_implemented_methods(nx):
     IMPLEMENTED_METHODS = ['sinkhorn', 'sinkhorn_stabilized']
     TO_BE_IMPLEMENTED_METHODS = ['sinkhorn_reg_scaling']
     NOT_VALID_TOKENS = ['foo']
@@ -228,6 +260,9 @@ def test_implemented_methods():
     M = ot.dist(x, x)
     epsilon = 1.
     reg_m = 1.
+
+    a, b, M, A = nx.from_numpy(a, b, M, A)
+
     for method in IMPLEMENTED_METHODS:
         ot.unbalanced.sinkhorn_unbalanced(a, b, M, epsilon, reg_m,
                                           method=method)