source: branches/2994-AutoDiffForIntervals/HeuristicLab.Problems.DataAnalysis.Symbolic/3.4/Interpreter/MultivariateDual.cs @ 17295

Last change on this file since 17295 was 17295, checked in by gkronber, 12 months ago

#2994: refactoring: moved types into separate files

File size: 5.1 KB
Line 
1using System.Diagnostics;
2
3namespace HeuristicLab.Problems.DataAnalysis.Symbolic {
4  /// <summary>
5  /// An algebraic type which has a value as well as the partial derivatives of the value over multiple variables.
6  /// </summary>
7  /// <typeparam name="V"></typeparam>
8  [DebuggerDisplay("v={Value}; dv={dv}")]
9  public class MultivariateDual<V> : IAlgebraicType<MultivariateDual<V>> where V : IAlgebraicType<V>, new() {
10    [DebuggerBrowsable(DebuggerBrowsableState.Never)]
11    private V v;
12    public V Value => v;
13
14    [DebuggerBrowsable(DebuggerBrowsableState.Never)]
15    private AlgebraicSparseVector<object, V> dv;
16    public AlgebraicSparseVector<object, V> Gradient => dv; // <key,value> partial derivative identified via the key
17
18    private MultivariateDual(MultivariateDual<V> orig) { this.v = orig.v.Clone(); this.dv = orig.dv.Clone(); }
19
20    /// <summary>
21    /// Constructor without partial derivative
22    /// </summary>
23    /// <param name="v"></param>
24    public MultivariateDual(V v) { this.v = v.Clone(); this.dv = new AlgebraicSparseVector<object, V>(); }
25
26    /// <summary>
27    /// Constructor for multiple partial derivatives
28    /// </summary>
29    /// <param name="v"></param>
30    /// <param name="keys"></param>
31    /// <param name="dv"></param>
32    public MultivariateDual(V v, object[] keys, V[] dv) { this.v = v.Clone(); this.dv = new AlgebraicSparseVector<object, V>(keys, dv); }
33
34    /// <summary>
35    /// Constructor for a single partial derivative
36    /// </summary>
37    /// <param name="v"></param>
38    /// <param name="key"></param>
39    /// <param name="dv"></param>
40    public MultivariateDual(V v, object key, V dv) { this.v = v.Clone(); this.dv = new AlgebraicSparseVector<object, V>(new[] { key }, new[] { dv }); }
41
42    /// <summary>
43    /// Constructor with a given value and gradient. For internal use.
44    /// </summary>
45    /// <param name="v">The value (not cloned).</param>
46    /// <param name="gradient">The gradient (not cloned).</param>
47    internal MultivariateDual(V v, AlgebraicSparseVector<object, V> gradient) { this.v = v; this.dv = gradient; }
48
49    public MultivariateDual<V> Clone() { return new MultivariateDual<V>(this); }
50
51    public MultivariateDual<V> Zero => new MultivariateDual<V>(Value.Zero, Gradient.Zero);
52    public MultivariateDual<V> One => new MultivariateDual<V>(Value.One, Gradient.Zero);
53
54    public MultivariateDual<V> Scale(double s) { v.Scale(s); dv.Scale(s); return this; }
55
56    public MultivariateDual<V> Add(MultivariateDual<V> a) { v.Add(a.v); dv.Add(a.dv); return this; }
57    public MultivariateDual<V> Sub(MultivariateDual<V> a) { v.Sub(a.v); dv.Sub(a.dv); return this; }
58    public MultivariateDual<V> Assign(MultivariateDual<V> a) { v.Assign(a.v); dv.Assign(a.dv); return this; }
59    public MultivariateDual<V> Mul(MultivariateDual<V> a) {
60      // (a(x) * b(x))' = b(x)*a(x)' + b(x)'*a(x);
61      var t1 = a.dv.Clone().Scale(v);
62      var t2 = dv.Clone().Scale(a.v);
63      dv.Assign(t1).Add(t2);
64
65      v.Mul(a.v);
66      return this;
67    }
68    public MultivariateDual<V> Div(MultivariateDual<V> a) { v.Div(a.v); dv.Mul(a.dv.Inv()); return this; }
69    public MultivariateDual<V> AssignNeg(MultivariateDual<V> a) { v.AssignNeg(a.v); dv.AssignNeg(a.dv); return this; }
70    public MultivariateDual<V> AssignInv(MultivariateDual<V> a) { v.AssignInv(a.v); dv.AssignNeg(a.dv).Scale(v).Scale(v); return this; }   // (1/f(x))' = - f(x)' / f(x)^2
71
72    public MultivariateDual<V> AssignSin(MultivariateDual<V> a) { v.AssignSin(a.v); dv.Assign(a.dv).Scale(a.v.Clone().Cos()); return this; }
73    public MultivariateDual<V> AssignCos(MultivariateDual<V> a) { v.AssignCos(a.v); dv.AssignNeg(a.dv).Scale(a.v.Clone().Sin()); return this; }
74    public MultivariateDual<V> AssignTanh(MultivariateDual<V> a) { v.AssignTanh(a.v); dv.Assign(a.dv.Scale(v.Clone().IntPower(2).Neg().Add(Value.One))); return this; }     // tanh(f(x))' = f(x)'sech²(f(x)) = f(x)'(1 - tanh²(f(x)))
75
76    public MultivariateDual<V> AssignIntPower(MultivariateDual<V> a, int p) { v.AssignIntPower(a.v, p); dv.Assign(a.dv).Scale(p).Scale(a.v.Clone().IntPower(p - 1)); return this; }
77    public MultivariateDual<V> AssignIntRoot(MultivariateDual<V> a, int r) { v.AssignIntRoot(a.v, r); dv.Assign(a.dv).Scale(1.0 / r).Scale(a.v.IntRoot(r - 1)); return this; }
78
79    public MultivariateDual<V> AssignExp(MultivariateDual<V> a) { v.AssignExp(a.v); dv.Assign(a.dv).Scale(v); return this; } // exp(f(x)) = exp(f(x))*f(x)'     
80    public MultivariateDual<V> AssignLog(MultivariateDual<V> a) { v.AssignLog(a.v); dv.Assign(a.dv).Scale(a.v.Clone().Inv()); return this; }     // log(x)' = 1/f(x) * f(x)'
81
82    public MultivariateDual<V> AssignAbs(MultivariateDual<V> a) { v.AssignAbs(a.v); dv.Assign(a.dv).Scale(a.v.Clone().Sgn()); return this; }      // abs(f(x))' = f(x)*f'(x) / |f(x)|  doesn't work for intervals     
83    public MultivariateDual<V> AssignSgn(MultivariateDual<V> a) { v.AssignSgn(a.v); dv = a.dv.Zero; return this; } // sign(f(x))' = 0;     
84
85    public MultivariateDual<V> AssignMin(MultivariateDual<V> other) {
86      XXX
87    }
88
89    public MultivariateDual<V> AssignMax(MultivariateDual<V> other) {
90      XXX
91    }
92  }
93}
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