TensorFlow.NET/test/TensorFlowNET.Graph.UnitTest/GradientTest/GradientTest.cs

using Microsoft.VisualStudio.TestTools.UnitTesting;
using Tensorflow.NumPy;
using System;
using System.Collections.Generic;
using System.Linq;
using Tensorflow;
using static Tensorflow.Binding;
using Tensorflow.Framework;

namespace TensorFlowNET.UnitTest.Gradient
{
    [TestClass]
    public class GradientTest : GraphModeTestBase
    {
        [TestMethod]
        public void BroadcastToGrad()
        {
            var x = tf.constant(2, dtype: dtypes.float32);
            var y = tf.broadcast_to(x, (2, 4, 3));
            var grad = tf.gradients(y, x);

            var sess = tf.Session(graph);
            float result = sess.run(grad[0]);
            Assert.AreEqual(result, 24.0f);
        }

        [TestMethod]
        public void CumsumGrad()
        {
            var x = tf.constant(2, dtype: dtypes.float32);
            var y = tf.broadcast_to(x, (2, 4, 3));
            var z = tf.cumsum(y, axis: 1);
            var grad = tf.gradients(z, x);

            var sess = tf.Session(graph);
            float result = sess.run(grad[0]);
            Assert.AreEqual(result, 60.0f);
        }

        [TestMethod, Ignore]
        public void testGradients()
        {
            var inp = tf.constant(1.0, shape: new[] { 32, 100 }, name: "in");
            var w = tf.constant(1.0, shape: new[] { 100, 10 }, name: "w");
            var b = tf.Variable(1.0, shape: new[] { 10 }, name: "b");
            var xw = math_ops.matmul(inp, w, name: "xw");
            var h = nn_ops.bias_add(xw, b, name: "h");
            var w_grad = gradients_impl.gradients(new[] { h }, new[] { w })[0];
            self.assertEquals("MatMul", w_grad.op.type);
            // TODO: Operation._original_op
            //self.assertEquals(w_grad.op._original_op, xw.op);
            self.assertTrue((bool)w_grad.op.get_attr("transpose_a"));
            self.assertFalse((bool)w_grad.op.get_attr("transpose_b"));
        }

        [TestMethod]
        public void testBatchMatMulGradient()
        {
            var a = tf.constant(np.array(Enumerable.Range(1, 18).Select(elem => (float)elem).ToArray()), shape: new[] { 2, 3, 3 });
            var b = tf.divide(a, tf.constant(2.0f));
            var c = tf.batch_matmul(a, b);
            var g = tf.gradients(c, new[] { a, b }, stop_gradients: new[] { a, b });
            var checkG = new[]
            {
                3.0f, 7.5f, 12.0f,
                3.0f, 7.5f, 12.0f,
                3.0f, 7.5f, 12.0f,
                16.5f, 21.0f, 25.5f,
                16.5f, 21.0f, 25.5f,
                16.5f, 21.0f, 25.5f,
                12.0f, 12.0f, 12.0f,
                15.0f, 15.0f, 15.0f,
                18.0f, 18.0f, 18.0f,
                39.0f, 39.0f, 39.0f,
                42.0f, 42.0f, 42.0f,
                45.0f, 45.0f, 45.0f
            };
            var sess = tf.Session();
            var result = sess.run(g);
            var resultList = result[0].ToArray<float>().ToList();
            resultList.AddRange(result[1].ToArray<float>());
            Console.WriteLine(result.ToString());
            CollectionAssert.AreEqual(resultList.ToArray(), checkG);
        }

        [TestMethod]
        public void testSimpleGradients()
        {
            (T, T) evaluateDerivatives<T>(Func<Tensor, Tensor> f, T xval) where T : unmanaged
            {
                var x = tf.constant(xval);
                var y = f(x);
                var g = tf.gradients(y, x);

                var session = tf.Session();
                var result = session.run(new[] { y, g[0] });
                return (result[0].ToArray<T>()[0], result[1].ToArray<T>()[0]);
            }

            void test(string name, Func<Tensor, Tensor> tfF, Func<double, (double, double)> targetF, double[] values)
            {
                foreach (var x in values)
                {
                    var (expectedY, expectedDY) = targetF(x);

                    {
                        var (actualY, actualDY) = evaluateDerivatives(tfF, x);
                        self.assertFloat64Equal(expectedY, actualY, $"value {name}/float64 at {x}");
                        self.assertFloat64Equal(expectedDY, actualDY, $"derivative {name}/float64 at {x}");
                    }

                    {
                        var (actualY, actualDY) = evaluateDerivatives(tfF, (float)x);
                        self.assertFloat32Equal((float)expectedY, actualY, $"value {name}/float32 at {x}");
                        self.assertFloat32Equal((float)expectedDY, actualDY, $"derivative {name}/float32 at {x}");
                    }
                }
            }

            test("tf.exp",
                x => tf.exp(5 * x),
                x => (Math.Exp(5.0 * x), 5.0 * Math.Exp(5.0 * x)),
                new[] { -1.0, 0.0, 1.0, 1.5 });

            test("tf.log",
                x => tf.log(x),
                x => (Math.Log(x), 1.0 / x),
                new[] { 0.5, 1.0, 1.5, 2.0 });

            test("tf.sqrt",
                x => tf.sqrt(x),
                x => (Math.Sqrt(x), 0.5 / Math.Sqrt(x)),
                new[] { 0.5, 1.0, 1.1, 1.5, 2.0 });

            test("tf.sin",
                x => tf.sin(x),
                x => (Math.Sin(x), Math.Cos(x)),
                new[] { -1.0, 0.0, 1.0, 1.5, 2.0 });

            test("tf.sinh",
                x => tf.sinh(x),
                x => (Math.Sinh(x), Math.Cosh(x)),
                new[] { -1.0, 0.0, 1.0, 1.5, 2.0 });

            test("tf.cos",
                x => tf.cos(x),
                x => (Math.Cos(x), -Math.Sin(x)),
                new[] { -1.0, 0.0, 1.0, 1.5, 2.0 });

            test("tf.cosh",
                x => tf.cosh(x),
                x => (Math.Cosh(x), Math.Sinh(x)),
                new[] { -1.0, 0.0, 1.0, 1.5, 2.0 });

            test("tf.tanh",
                x => tf.tanh(x),
                x => (Math.Tanh(x), 1.0 - Math.Pow(Math.Tanh(x), 2.0)),
                new[] { -1.0, 0.0, 1.0, 1.5, 2.0 });

            test("tf.maximum",
                x => tf.maximum(x, tf.constant(0.0, dtype: x.dtype)),
                x => (Math.Max(x, 0.0), (x > 0.0) ? 1.0 : 0.0),
                new[] { -1.0, 1.0 });

            test("tf.minimum",
                x => tf.minimum(x, tf.constant(0.0, dtype: x.dtype)),
                x => (Math.Min(x, 0.0), (x < 0.0) ? 1.0 : 0.0),
                new[] { -1.0, 1.0 });
        }

        [TestMethod]
        public void testReduceSumGradients()
        {
            /* python code
            import tensorflow.compat.v1 as tf
            tf.disable_v2_behavior() 

            x = tf.placeholder(tf.float64, shape = (1, 1))
            m = tf.broadcast_to(x, (2, 3))
            g0 = tf.gradients(tf.reduce_sum(m), x)[0]
            g1 = tf.gradients(tf.reduce_sum(m, axis = 0)[0], x)[0]
            g2 = tf.gradients(tf.reduce_sum(m, axis = 1)[0], x)[0]
            with tf.compat.v1.Session() as sess:
                (r0, r1, r2) = sess.run((g0, g1, g2), {x: [[1.0]]})
            */

            var x = tf.placeholder(tf.float64, shape: new Shape(1, 1));
            var m = tf.broadcast_to(x, new Shape(2, 3));
            var g0 = tf.gradients(tf.reduce_sum(m), x)[0];
            var g1 = tf.gradients(tf.reduce_sum(m, axis: 0)[0], x)[0];
            var g2 = tf.gradients(tf.reduce_sum(m, axis: 1)[0], x)[0];

            var session = tf.Session();
            var (r0, r1, r2) = session.run((g0, g1, g2), new FeedItem(x, new[,] { { 1.0 } }));
            self.assertFloat64Equal(6.0, r0[0], $"tf.reduce_sum(...)");
            self.assertFloat64Equal(2.0, r1[0], $"tf.reduce_sum(..., axis = 0)");
            self.assertFloat64Equal(3.0, r2[0], $"tf.reduce_sum(..., axis = 1)");
        }

        [TestMethod]
        public void testTanhGradient()
        {
            var a = tf.constant(1f);
            var b = tf.tanh(a);
            var g = tf.gradients(b, a);
            var sess = tf.Session();
            var result = sess.run(g);
            var actual = result[0];
            Assert.AreEqual(actual, 0.41997434127f);
        }


        [TestMethod]
        public void testLgammaGrad()
        {
            var a = tf.constant(5f);
            var b = tf.lgamma(a);
            var g = tf.gradients(b, a);
            var sess = tf.Session();
            var result = sess.run(new object[] { g, b });
            var actualDeriv = result[0];
            var actual = result[1];
            Assert.AreEqual(actualDeriv, 1.5061177f);
            Assert.AreEqual(actual, 3.17805386f);
        }

        [TestMethod]
        public void testSliceGrad()
        {
            var a = tf.tanh(tf.constant(new[] { 2f, 3f }, shape: new[] { 2, 1 }));
            var b = tf.strided_slice(a,
                tf.constant(new[] { 0 }, tf.int32, new[] { 1 }),
                tf.constant(new[] { 1 }, tf.int32, new[] { 1 }),
                tf.constant(new[] { 1 }, tf.int32, new[] { 1 })
            );
            var g = tf.gradients(b, a);
            var sess = tf.Session();
            var result = sess.run(new object[] { g, b });
            var actualDeriv = np.squeeze(result[0]);
            var actual = np.squeeze(result[1]);
            Assert.AreEqual(actualDeriv, new float[] { 1, 0 });
            Assert.AreEqual(actual, 0.9640276f);
        }

        [TestMethod]
        public void testConcatGrad()
        {
            var a1 = tf.constant(new[] { 2f }, shape: new[] { 1 });
            var a2 = tf.constant(new[] { 3f }, shape: new[] { 1 });
            var a = tf.concat(new List<Tensor>(new[] { a1, a2 }), 0);
            var g = tf.gradients(a, a1);
            var sess = tf.Session();
            var result = sess.run(new object[] { g, a });
            var actualDeriv = result[0][0];
            var actual = result[1][0];
            Assert.AreEqual(actualDeriv, 1f);
            Assert.AreEqual(actual, 2f);
        }

        [TestMethod]
        public void testStopGradientFunction()
        {
            var ap = tf.constant(1f);
            var b = tf.tanh(ap) + array_ops.stop_gradient(ap);
            var g = tf.gradients(b, ap);
            var sess = tf.Session();
            var result = sess.run(g);
            var actual = result[0];
            Assert.AreEqual(actual, 0.41997434127f);
        }

        [Ignore("TODO")]
        [TestMethod]
        public void testUnusedOutput()
        {
            //def testUnusedOutput(self):
            //  with ops.Graph().as_default():
            //    w = constant(1.0, shape=[2, 2])
            //    x = constant(1.0, shape=[2, 2])
            //    wx = math_ops.matmul(w, x)
            //    split_wx = array_ops.split(value=wx, num_or_size_splits=2, axis=0)
            //    c = math_ops.reduce_sum(split_wx[1])
            //    gw = gradients.gradients(c, [w])[0]
            //  self.assertEquals("MatMul", gw.op.type)
        }

        [Ignore("TODO")]
        [TestMethod]
        public void testColocateGradients()
        {

            //def testColocateGradients(self):
            //  with ops.Graph().as_default() as g:
            //    w = constant(1.0, shape=[1, 1])
            //    x = constant(1.0, shape=[1, 2])
            //    with g.device("/device:GPU:0"):
            //      wx = math_ops.matmul(w, x)
            //    gw = gradients.gradients(wx, [w], colocate_gradients_with_ops=True)[0]
            //  self.assertEqual(gw.op.colocation_groups(), wx.op.colocation_groups())
        }

        [Ignore("TODO")]
        [TestMethod]
        public void testColocateGradientsWithAggregation()
        {
            //def testColocateGradientsWithAggregation(self):
            //  with ops.Graph().as_default() as g:
            //    with g.device("/device:GPU:1"):
            //      w = constant(1.0, shape=[1, 1])
            //    x = constant(1.0, shape=[1, 2])
            //    y = constant(1.0, shape=[1, 2])
            //    wx = math_ops.matmul(w, x)
            //    wy = math_ops.matmul(w, y)
            //    with g.device("/device:GPU:0"):
            //      z = wx + wy

            //    gw1 = gradients.gradients(z, [w], colocate_gradients_with_ops=True)[0]
            //    self.assertEqual(gw1.op.colocation_groups(), wx.op.colocation_groups())

            //    gw2 = gradients.gradients(z, [w], colocate_gradients_with_ops=False)[0]
            //    self.assertTrue(wx.op.colocation_groups() != gw2.op.colocation_groups())

        }

        [Ignore("TODO")]
        [TestMethod]
        public void testColocateGradientsWithAggregationInMultipleDevices()
        {
            //def testColocateGradientsWithAggregationInMultipleDevices(self):
            //  with ops.Graph().as_default() as g:
            //    with g.device("/device:GPU:1"):
            //      w = constant(1.0, shape=[1, 1])
            //    x = constant(1.0, shape=[1, 2])
            //    y = constant(1.0, shape=[1, 2])
            //    with g.device("/task:1"):
            //      wx = math_ops.matmul(w, x)
            //    with g.device("/task:2"):
            //      wy = math_ops.matmul(w, y)
            //    with g.device("/device:GPU:0"):
            //      z = wx + wy

            //    gw1 = gradients.gradients(z, [w], colocate_gradients_with_ops=True)[0]
            //    self.assertEqual(gw1.op.colocation_groups(), w.op.colocation_groups())

            //    gw2 = gradients.gradients(z, [w], colocate_gradients_with_ops=False)[0]
            //    self.assertTrue(w.op.colocation_groups() != gw2.op.colocation_groups())
        }


        [Ignore("TODO")]
        [TestMethod]
        public void testColocateGradientsWithGateGradients()
        {

            //def testColocateGradientsWithGateGradients(self):
            //  if not test_util.is_gpu_available():
            //    self.skipTest("No GPU available")
            //  with ops.Graph().as_default() as g:
            //    with g.device("/device:CPU:0"):
            //      x = constant(1.0, shape=[1, 1])
            //      y = constant(1.0, shape=[1, 1])
            //      s = x + y
            //    with g.device("/device:GPU:0"):
            //      z = math_ops.reduce_sum(s)

            //    gz_x = gradients.gradients(z, [x], colocate_gradients_with_ops=True,
            //                               gate_gradients=True)[0]
            //    with session.Session():
            //      # Make sure the placer doesn't complain.
            //      self.evaluate(gz_x)

        }

        [Ignore("TODO")]
        [TestMethod]
        public void testBoundaryStop()
        {
            //def testBoundaryStop(self):
            //  # Test that we don't differentiate 'x'. The gradient function for 'x' is
            //  # set explicitly to None so we will get an exception if the gradient code
            //  # tries to differentiate 'x'.
            //  with ops.Graph().as_default():
            //    c = constant(1.0)
            //    x = array_ops.identity(c)
            //    y = x + 1.0
            //    z = y + 1
            //    grads = gradients.gradients(z, [x])
            //    self.assertTrue(all(x is not None for x in grads))

        }

        [TestMethod]
        public void testBoundaryContinue()
        {
            // Test that we differentiate both 'x' and 'y' correctly when x is a
            // predecessor of y.

            //TODO: @test_util.run_v1_only("b/120545219")

            using (self.cached_session())
            {
                var x = tf.constant(1.0);
                var y = x * 2.0;
                var z = y * 3.0;
                var grads = tf.gradients(z, new[] { x, y });
                self.assertTrue(all(grads.Select(x => x != null)));
                self.assertEqual(6.0, grads[0].eval());
            }
        }

        [TestMethod]
        public void testAggregationMethodAccumulateN()
        {
            //TODO: @test_util.run_v1_only("b/120545219")

            using (self.cached_session())
            {
                var x = tf.constant(1.0);
                var y = x * 2.0;
                var z = y + y + y + y + y + y + y + y + y + y;
                var grads = tf.gradients(z, new[] { x, y },
                        aggregation_method: AggregationMethod.EXPERIMENTAL_ACCUMULATE_N);
                self.assertTrue(all(grads.Select(x => x != null)));
                self.assertEqual(20.0, grads[0].eval());
                self.assertEqual(10.0, grads[1].eval());
            }
        }

        [TestMethod]
        public void testAggregationMethodAddN()
        {
            //TODO: @test_util.run_v1_only("b/120545219")

            using (self.cached_session())
            {
                var x = tf.constant(1.0);
                var y = x * 2.0;
                var z = y + y + y + y + y + y + y + y + y + y;
                var grads = tf.gradients(z, new[] { x, y },
                        aggregation_method: AggregationMethod.ADD_N);
                self.assertTrue(grads.All(x => x != null));
                self.assertEqual(20.0, grads[0].eval());
                self.assertEqual(10.0, grads[1].eval());
            }
        }

        [TestMethod]
        public void testAggregationMethodTree()
        {
            //TODO: @test_util.run_v1_only("b/120545219")

            using (self.cached_session())
            {
                var x = tf.constant(1.0);
                var y = x * 2.0;
                var z = y + y + y + y + y + y + y + y + y + y;
                var grads = tf.gradients(z, new[] { x, y },
                        aggregation_method: AggregationMethod.EXPERIMENTAL_TREE);
                self.assertTrue(grads.All(x => x != null));
                self.assertEqual(20.0, grads[0].eval());
                self.assertEqual(10.0, grads[1].eval());
            }
        }

        [Ignore("TODO")]
        [TestMethod]
        public void testNoGradientForStringOutputs()
        {

            //def testNoGradientForStringOutputs(self):
            //  with ops.Graph().as_default():

            //    def _TestOpGrad(_, float_grad, string_grad):
            //      """Gradient function for TestStringOutput."""
            //      self.assertEquals(float_grad.dtype, dtypes.float32)
            //      self.assertFalse(string_grad)
            //      return float_grad

            //    ops.RegisterGradient("TestStringOutput")(_TestOpGrad)

            //    c = constant(1.0)
            //    x, _ = test_ops.test_string_output(c)
            //    z = x * 2.0
            //    w = z * 3.0
            //    grads = gradients.gradients(z, [c])
            //    self.assertTrue(isinstance(grads[0], ops.Tensor))
            //    grads = gradients.gradients(w, [c])
            //    self.assertTrue(isinstance(grads[0], ops.Tensor))
        }

        [Ignore("TODO: CompositeTensors are not supported yet.")]
        [TestMethod]
        public void testSingletonIndexedSlices()
        {
            tf.Graph().as_default();

            // TODO: uncomment when CompositeTensors are supported.
            /*
            var x = tf.placeholder(TF_DataType.TF_FLOAT);
            var y = tf.identity(x);
            var dy_indices = tf.placeholder(TF_DataType.TF_INT32);
            var dy_values = tf.placeholder(TF_DataType.TF_FLOAT);
            var dy = new IndexedSlices(dy_values, dy_indices);
           
            var dx = tf.gradients(new[] { y }, new[] { x }, grad_ys: new[] { dy })[0];
            // The IndexedSlices gradient of tf.identity is the identity map.
            using (var sess = self.cached_session())
            {
                var feed_dict = new FeedItem[]
                {
                    ( x, new Tensor(new float[] { 1.0f }) ),
                    (dy_indices, new Tensor(new int[] { 0 })),
                    (dy_values, new Tensor(new float[] { 2.0f }))
                };
                var result = sess.run(new[] { dx, dy }, feed_dict);
                var vdx = result[0];
                var vdy = result[1];
                self.assertEqual(vdx, vdy);
            }
            */

        }

        [Ignore("TODO")]
        [TestMethod]
        public void testNonDifferentiableSwitchInWhileLoop()
        {


            //@test_util.run_v1_only("b/120545219")
            //def testNonDifferentiableSwitchInWhileLoop(self):
            //  with ops.Graph().as_default():
            //    v = array_ops.placeholder(dtypes.float32, [])

            //    def _Step(i, a, ta):
            //      a += math_ops.cast(v, dtypes.int32)
            //      return (i + 1, a, ta.write(i, a))

            //    n = 4
            //    i, _, ta = control_flow_ops.while_loop(
            //        lambda i, *_: i < n,
            //        _Step, [0, 0, tensor_array_ops.TensorArray(
            //            dtypes.int32, size=n)])
            //    target = ta.read(i - 1)
            //    grad, = gradients.gradients(target, v)
            //    self.assertIsNone(grad)

        }

        [Ignore("TODO")]
        [TestMethod]
        public void testVariableReadValueGradient()
        {

            //def testVariableReadValueGradient(self):
            //  with ops.Graph().as_default():
            //    init = constant_op.constant(100.0)
            //    var = variables.Variable(init)
            //    gradient = gradients.gradients(var.read_value(), var)
            //    self.assertIsNotNone(gradient)
        }

        [Ignore("TODO")]
        [TestMethod]
        public void testVariableAsGraphElementGradient()
        {
            //def testVariableAsGraphElementGradient(self):
            //  with ops.Graph().as_default() as graph:
            //    init = constant_op.constant(100.0)
            //    var = variables.Variable(init)
            //    gradient = gradients.gradients(graph.as_graph_element(var), var)
            //    self.assertIsNotNone(gradient)
        }

        [Ignore("TODO")]
        [TestMethod]
        public void testVariableRefGradient()
        {

            //@test_util.run_v1_only("b/120545219")
            //def testVariableRefGradient(self):
            //  with ops.Graph().as_default():
            //    init = constant_op.constant(100.0)
            //    var = variables.VariableV1(init)
            //    gradient = gradients.gradients(var._ref(), var)
            //    self.assertIsNotNone(gradient)
        }

        [TestMethod]
        public void testDependentYs()
        {
            //TODO: @test_util.run_v1_only("b/120545219")
            using (self.cached_session())
            {
                var x = constant_op.constant(3.0);
                var y = math_ops.square(x);
                var y1 = math_ops.square(y);
                var y2 = math_ops.square(y1);
                var g = tf.gradients(new[] { y, y2 }, new[] { x });
                self.assertAllClose(17502.0, g[0].eval());
                g = tf.gradients(y + y2, x);
                self.assertAllClose(17502.0, g[0].eval());
                var z = array_ops.identity(y);
                var z2 = array_ops.identity(y2);
                g = tf.gradients(new[] { z, z2 }, new[] { x });
                self.assertAllClose(17502.0, g[0].eval());
            }
        }

        [Ignore("TODO")]
        [TestMethod]
        public void testPartialDerivatives()
        {

            //TODO: @test_util.run_v1_only("b/120545219")
            using (self.cached_session())
            {
                var x = tf.constant(1.0);
                var y = 2 * x;
                var z = x + y;
                var totalg = tf.gradients(z, new[] { x, y });
                self.assertEqual(new[] { 3.0, 1.0 }, totalg.Select(g => g.eval()));
                var partialg = tf.gradients(z, new[] { x, y }, stop_gradients: new[] { x, y });
                self.assertEqual(new[] { 1.0, 1.0 }, partialg.Select(g => g.eval()));
            }
        }

        private struct Case
        {
            public Tensor[] grad1;
            public Tensor[] grad2;
            public string constants;
            public string variables;
        }

        [Ignore("FIXME")]
        [TestMethod]
        public void testStopGradients()
        {
            
            //TODO: @test_util.run_v1_only("b/120545219")
            Dictionary<char, Tensor> makeGraph(RandomizedImpl rng, string stop_gradients)
            {
                Tensor functionOf(Tensor[] xs, int k)
                {
                    var shape = new Shape(k, k);
                    // TODO: replace by DefaultIfEmpty() before Aggregate().
                    if (!xs.Any())
                    {
                        return rng.random(shape).astype(np.float32);
                    }
                    return xs.Select(x => gen_math_ops.mat_mul(rng.random(shape).astype(np.float32), x))
                        .Aggregate((t1, t2) => t1 + t2)
                    + rng.random(shape).astype(np.float32);
                }

                var a = functionOf(Array.Empty<Tensor>(), 3);
                if (stop_gradients.Contains('a')) a = array_ops.stop_gradient(a);
                var b = functionOf(new Tensor[] { a }, 3);
                if (stop_gradients.Contains('b')) b = array_ops.stop_gradient(b);
                var c = functionOf(new Tensor[] { a, b }, 3);
                if (stop_gradients.Contains('c')) c = array_ops.stop_gradient(c);
                var d = functionOf(new Tensor[] { b, c }, 3);
                if (stop_gradients.Contains('d')) d = array_ops.stop_gradient(d);

                return new Dictionary<char, Tensor>
                    {
                        { 'a', a },
                        { 'b', b },
                        { 'c', c },
                        { 'd', d }
                    };
            }

            Tensor[] gradients(Tensor[] ys, Tensor[] xs, Tensor[] stop_gradients = null)
            {
                var dydxs = tf.gradients(ys, xs, stop_gradients);
                dydxs = dydxs.Select((dydx, i) => dydx == null ? xs[i] * 0 : dydx).ToArray();
                return dydxs;
            }

            var seed = np.random.randint(1000);
            // TODO: remove next line when np.random.RandomState implemented.
            tf.set_random_seed(seed);
            var cases = new List<Case>();
            // TODO: add "" case.
            var subsets = new List<string> { "" }.Concat("a b c d ab ac ad bc bd cd abc abd acd bcd abcd".Split());
            // TODO: pass np.random.RandomState(seed) instead of np.random
            var graph = makeGraph(np.random, string.Empty);
            foreach (var constants in subsets)
            {
                var graphWithStops = makeGraph(np.random, constants);
                foreach (var variables_ in subsets)
                {
                    // compute the gradient when stopped using tf.stop_gradients
                    var grad1 = gradients(
                        new[] { graphWithStops['d'] },
                        variables_.ToCharArray().Select(v => graphWithStops[v]).ToArray()
                    );
                    // compute the gradient when stopped using the stop_gradients from args
                    var grad2 = gradients(
                        new[] { graph['d'] },
                        variables_.ToCharArray().Select(v => graph[v]).ToArray(),
                        constants.ToCharArray().Select(c => graph[c]).DefaultIfEmpty(null)?.ToArray()
                    );
                    cases.Add(new Case
                    {
                        grad1 = grad1,
                        grad2 = grad2,
                        variables = variables_,
                        constants = constants,
                    }) ;
                }
            }

            // evaluate all tensors in one call to session.run for speed
            using (var sess = self.cached_session())
            {
                var results = sess.run(
                    cases.Select(case_ => (
                        case_.grad1,
                        case_.grad2
                    )).ToArray()
                );

                foreach (var (result, case_) in results.Zip(cases))
                {
                    var npgrad1 = result[0];
                    var npgrad2 = result[1];
                    foreach (var (a, b) in npgrad1.Zip(npgrad2))
                    {
                        self.assertAllClose(a, b);
                    }
                }
            }
        }



        [Ignore("TODO: Unconnected gradients are not implemented")]
        [TestMethod]
        public void testUnconnectedGradientsNoneUnconnectedGradients()
        {


            //def testUnconnectedGradientsNoneUnconnectedGradients(self):
            //  with ops.Graph().as_default():
            //    x = constant(1.0, shape=[2, 2])
            //    y = constant(3.0, shape=[3, 1])
            //    grad = gradients.gradients(
            //        [y], [x], unconnected_gradients="none")
            //  self.assertIsNone(grad[0])
        }

        [Ignore("TODO: Unconnected gradients are not implemented")]
        [TestMethod]
        public void testUnconnectedGradientsZerosUnconnectedGradients()
        {
            //def testUnconnectedGradientsZerosUnconnectedGradients(self):
            //  with ops.Graph().as_default():
            //    x = constant(1.0, shape=[2, 2])
            //    y = constant(3.0, shape=[3, 1])
            //    grads = gradients.gradients(
            //        [y], [x], unconnected_gradients="zero")
            //    with self.cached_session() as sess:
            //      self.assertAllEqual([[0.0, 0.0], [0.0, 0.0]], self.evaluate(grads)[0])

            // tf.Graph().as_default();
            // var x = tf.constant(1.0, shape: new long[] { 2, 2 });
            // var y = tf.constant(3.0, shape: new long[] { 3, 1 });
            // var grads = tf.gradients(new[] { y }, new[] { x }, unconnected_gradients: "zero");
            // using (self.cached_session())
            // {
            //     self.assertAllEqual(new[,] { { 0.0, 0.0 }, { 0.0, 0.0 } }, self.evaluate(grads)[0]);
            // }
        }

        [Ignore("TODO: Unconnected gradients are not implemented")]
        [TestMethod]
        public void testUnconnectedGradientsZeroConnectedGradients()
        {
            //def testUnconnectedGradientsZeroConnectedGradients(self):
            //  with ops.Graph().as_default():
            //    x = constant(1.0)
            //    y = x * 3.0
            //    grad = gradients.gradients(
            //        [y], [x], unconnected_gradients="zero")
            //    with self.cached_session() as sess:
            //      self.assertEquals(3.0, self.evaluate(grad)[0])

            // tf.Graph().as_default();

            // var x = tf.constant(1.0f);
            // var y = x * 3.0f;
            // var grad = tf.gradients(new [] { y }, new [] { x }, unconnected_gradients: "zero");
            // using (var sess = tf.Session())
            // {
            //     self.assertEquals(3.0, self.evaluate(grad)[0]);
            // }
        }

        [Ignore("TODO: Unconnected gradients are not implemented")]
        [TestMethod]
        public void testUnknownUnconnectedGradientsValueGiven()
        {
            //def testUnknownUnconnectedGradientsValueGiven(self):
            //  with ops.Graph().as_default():
            //    x = constant(1.0)
            //    y = constant(1.0)
            //    with self.assertRaisesRegexp(
            //        ValueError, "Unknown value for unconnected_gradients: 'nonsense'"):
            //      gradients.gradients([y], [x], unconnected_gradients="nonsense")
        }
    }
}