117. Cheatsheet
117.1. Derivative Objects
| Gradient | Vector of first derivatives; special case of Jacobian (scalar output) | ||
| Jacobian | Matrix of first derivatives; general case for vector-valued functions | ||
| Hessian | Matrix of second derivatives; Jacobian of the gradient |
| Input/Output | Derivatives | Notation | |
| Gradient (Derivative) () |
One Input One Output Scalar Function |
First Order |
|
| Jacobian () |
One Input Multiple Output Vector Function |
First Order |
|
| Gradient () |
Multiple Input One Output Scalar Function |
First Order |
|
| Jacobian () |
Multiple Input Multiple Output Vector Function |
First Order |
|
| Hessian () |
Multiple Input One Output Scalar Function |
Second Order |
|
| Laplacian | Trace of the Hessian (sum of diagonal entries) |
|
|
| Gradient | derivative | |
| Hessian | derivative | |
| Order Tensor | derivative | |
| -th Order Tensor | derivative | |