add tests from swift-numerics implementation

Author: JaapWijnen

Tests/ComplexModuleDifferentiableTests/Complex+DifferentiableTests.swift

@@ -0,0 +1,63 @@
+import ComplexModuleDifferentiable
+import Testing
+
+#if canImport(_Differentiation)
+@Suite
+struct ComplexDifferentiableTests {
+    @Test
+    func componentGetter() {
+        #expect(gradient(at: Complex<Float>(5, 5)) { $0.real * 2 } == Complex(2, 0))
+        #expect(gradient(at: Complex<Float>(5, 5)) { $0.imaginary * 2 } == Complex(0, 2))
+        #expect(gradient(at: Complex<Float>(5, 5)) {
+            $0.real * 5 + $0.imaginary * 2
+        } == Complex(5, 2))
+    }
+
+    @Test
+    func initializer() {
+        let pb1 = pullback(at: 4, -3) { r, i in Complex<Float>(r, i) }
+        let tan1 = pb1(Complex(-1, 2))
+        #expect(tan1.0 == -1)
+        #expect(tan1.1 == 2)
+
+        let pb2 = pullback(at: 4, -3) { r, i in Complex<Float>(r * r, i + i)
+        }
+        let tan2 = pb2(Complex(-1, 1))
+        #expect(tan2.0 == -8)
+        #expect(tan2.1 == 2)
+    }
+
+    @Test
+    func conjugate() {
+        let pullback = pullback(at: Complex<Float>(20, -4)) { x in x.conjugate }
+        #expect(pullback(Complex(1, 0)) == Complex(1, 0))
+        #expect(pullback(Complex(0, 1)) == Complex(0, -1))
+        #expect(pullback(Complex(-1, 1)) == Complex(-1, -1))
+    }
+
+    @Test
+    func arithmetics() {
+        let additionPullback = pullback(at: Complex<Float>(2, 3)) { x in
+            x + Complex(5, 6)
+        }
+        #expect(additionPullback(Complex(1, 1)) == Complex(1, 1))
+
+        let subtractPullback = pullback(at: Complex<Float>(2, 3)) { x in
+            Complex(5, 6) - x
+        }
+        #expect(subtractPullback(Complex(1, 1)) == Complex(-1, -1))
+
+        let multiplyPullback = pullback(at: Complex<Float>(2, 3)) { x in x * x }
+        #expect(multiplyPullback(Complex(1, 0)) == Complex(4, 6))
+        #expect(multiplyPullback(Complex(0, 1)) == Complex(-6, 4))
+        #expect(multiplyPullback(Complex(1, 1)) == Complex(-2, 10))
+
+        let dividePullback = pullback(at: Complex<Float>(20, -4)) { x in
+            x / Complex(2, 2)
+        }
+        #expect(dividePullback(Complex(1, 0)) == Complex(0.25, -0.25))
+        #expect(dividePullback(Complex(0, 1)) == Complex(0.25, 0.25))
+    }
+}
+
+#endif