oberbichler / HyperJet-Net

Algorithmic differentiation with multivariate hyper-dual numbers in C#

HyperJet.NET — Algorithmic differentiation with multivariate hyper-dual numbers in C#

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Examples

HyperJet contains data types for multivariate hyper-dual numbers with fixed dimension. D2Scalar e.g., can be used to compute gradients of functions with two parameters.

using static System.Console;

using HyperJet;

// Import standard math (Pow, Sqrt, ...)
using static HyperJet.MathD;

// Initialize variables
var (a, b) = D2Scalar.Variables(3, 4);

// Compute value
var c = Sqrt(Pow(a, 2) + Pow(b, 2));

// Get derivatives
WriteLine($"dc/da = {c.D0}");
WriteLine($"dc/db = {c.D1}");

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Using DD5Scalar, gradients and hessians of functions with 5 parameters can be computed. DD6Vector3 enables vector operations.

using static System.Console;

using HyperJet;

// Import standard math (Pow, Sqrt, ...)
using static HyperJet.MathD;

// Import linear algebra (Norm, Dot, ...)
using static HyperJet.LinearAlgebraD;

// Initialize variables
var (x1, y1, z1, x2, y2, z2) = DD6Scalar.Variables(0, 0, 2, 3, 4, 2);

var p1 = new DD6Vector3(x1, y1, z1);
var p2 = new DD6Vector3(x2, y2, z2);

// Compute value
var l = Norm(p2 - p1);

// Get derivatives
WriteLine($"dl/dx1 = {l.D0}");
WriteLine($"dl/dy1 = {l.D1}");
WriteLine($"dl/dz1 = {l.D2}");
WriteLine($"dl/dx2 = {l.D3}");
WriteLine($"dl/dy2 = {l.D4}");
WriteLine($"dl/dz2 = {l.D5}");

// Get hessian
WriteLine($"d2l/dx1dx1 = {l.D0D0}");
WriteLine($"d2l/dx1dy1 = {l.D0D1}");
WriteLine($"d2l/dx1dz1 = {l.D0D2}");
//...

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