1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
|
// RUN: %target-run-simple-swift(-Xfrontend -enable-experimental-forward-mode-differentiation)
// REQUIRES: executable_test
import StdlibUnittest
import DifferentiationUnittest
var ForwardModeTests = TestSuite("ForwardModeDifferentiation")
//===----------------------------------------------------------------------===//
// Array methods from ArrayDifferentiation.swift
//===----------------------------------------------------------------------===//
typealias FloatArrayTan = Array<Float>.TangentVector
ForwardModeTests.test("Array.+") {
func sumFirstThreeConcatenating(_ a: [Float], _ b: [Float]) -> Float {
let c = a + b
return c[0] + c[1] + c[2]
}
expectEqual(3, differential(at: [0, 0], [0, 0], of: sumFirstThreeConcatenating)(.init([1, 1]), .init([1, 1])))
expectEqual(0, differential(at: [0, 0], [0, 0], of: sumFirstThreeConcatenating)(.init([0, 0]), .init([0, 1])))
expectEqual(1, differential(at: [0, 0], [0, 0], of: sumFirstThreeConcatenating)(.init([0, 1]), .init([0, 1])))
expectEqual(1, differential(at: [0, 0], [0, 0], of: sumFirstThreeConcatenating)(.init([1, 0]), .init([0, 1])))
expectEqual(1, differential(at: [0, 0], [0, 0], of: sumFirstThreeConcatenating)(.init([0, 0]), .init([1, 1])))
expectEqual(2, differential(at: [0, 0], [0, 0], of: sumFirstThreeConcatenating)(.init([1, 1]), .init([0, 1])))
expectEqual(
3,
differential(at: [0, 0, 0, 0], [0, 0], of: sumFirstThreeConcatenating)(.init([1, 1, 1, 1]), .init([1, 1])))
expectEqual(
3,
differential(at: [0, 0, 0, 0], [0, 0], of: sumFirstThreeConcatenating)(.init([1, 1, 1, 0]), .init([0, 0])))
expectEqual(
3,
differential(at: [], [0, 0, 0, 0], of: sumFirstThreeConcatenating)(.init([]), .init([1, 1, 1, 1])))
expectEqual(
0,
differential(at: [], [0, 0, 0, 0], of: sumFirstThreeConcatenating)(.init([]), .init([0, 0, 0, 1])))
}
ForwardModeTests.test("Array.init(repeating:count:)") {
@differentiable(reverse)
func repeating(_ x: Float) -> [Float] {
Array(repeating: x, count: 10)
}
expectEqual(Float(10), derivative(at: .zero) { x in
repeating(x).differentiableReduce(0, {$0 + $1})
})
expectEqual(Float(20), differential(at: .zero, of: { x in
repeating(x).differentiableReduce(0, {$0 + $1})
})(2))
}
ForwardModeTests.test("Array.DifferentiableView.init") {
@differentiable(reverse)
func constructView(_ x: [Float]) -> Array<Float>.DifferentiableView {
return Array<Float>.DifferentiableView(x)
}
let forward = differential(at: [5, 6, 7, 8], of: constructView)
expectEqual(
FloatArrayTan([1, 2, 3, 4]),
forward(FloatArrayTan([1, 2, 3, 4])))
}
ForwardModeTests.test("Array.DifferentiableView.base") {
@differentiable(reverse)
func accessBase(_ x: Array<Float>.DifferentiableView) -> [Float] {
return x.base
}
let forward = differential(
at: Array<Float>.DifferentiableView([5, 6, 7, 8]),
of: accessBase)
expectEqual(
FloatArrayTan([1, 2, 3, 4]),
forward(FloatArrayTan([1, 2, 3, 4])))
}
ForwardModeTests.test("Array.differentiableMap") {
let x: [Float] = [1, 2, 3]
let tan = Array<Float>.TangentVector([1, 1, 1])
func multiplyMap(_ a: [Float]) -> [Float] {
return a.differentiableMap({ x in 3 * x })
}
expectEqual([3, 3, 3], differential(at: x, of: multiplyMap)(tan))
func squareMap(_ a: [Float]) -> [Float] {
return a.differentiableMap({ x in x * x })
}
expectEqual([2, 4, 6], differential(at: x, of: squareMap)(tan))
}
ForwardModeTests.test("Array.differentiableReduce") {
let x: [Float] = [1, 2, 3]
let tan = Array<Float>.TangentVector([1, 1, 1])
func sumReduce(_ a: [Float]) -> Float {
return a.differentiableReduce(0, { $0 + $1 })
}
expectEqual(1 + 1 + 1, differential(at: x, of: sumReduce)(tan))
func productReduce(_ a: [Float]) -> Float {
return a.differentiableReduce(1, { $0 * $1 })
}
expectEqual(x[1] * x[2] + x[0] * x[2] + x[0] * x[1], differential(at: x, of: productReduce)(tan))
func sumOfSquaresReduce(_ a: [Float]) -> Float {
return a.differentiableReduce(0, { $0 + $1 * $1 })
}
expectEqual(2 * x[0] + 2 * x[1] + 2 * x[2], differential(at: x, of: sumOfSquaresReduce)(tan))
}
runAllTests()
|
