Description Usage Arguments Details Value Author(s) References Examples

These are three different utility functions that create matrices containing the symbolic partial derivatives of first (`makeGrad`

) and second (`makeHess`

) order and a function for evaluating these matrices in an environment. The evaluations of the symbolic derivatives are used within the `propagate`

function to calculate the propagated uncertainty, but these functions may also be useful for other applications.

1 2 3 |

`expr` |
an expression, such as |

`order` |
order of creating partial derivatives, i.e. |

`deriv` |
a matrix returned from |

`envir` |
an environment to evaluate in. By default the workspace. |

Given a function *f(x_1, x_2, …, x_n)*, the following matrices containing symbolic derivatives of *f* are returned:

**makeGrad:**

*\nabla(f) = ≤ft[\frac{\partial f}{\partial x_1}, …, \frac{\partial f}{\partial x_n}\right]*

**makeHess:**

*H(f) = ≤ft[ \begin{array}{cccc} \frac{\partial^2 f}{\partial x_1^2} & \frac{\partial^2 f}{\partial x_1\,\partial x_2} & \cdots & \frac{\partial^2 f}{\partial x_1\,\partial x_n} \\ \frac{\partial^2 f}{\partial x_2\,\partial x_1} & \frac{\partial^2 f}{\partial x_2^2} & \cdots & \frac{\partial^2 f}{\partial x_2\,\partial x_n} \\ \vdots & \vdots & \ddots & \vdots \\ \frac{\partial^2 f}{\partial x_n\,\partial x_1} & \frac{\partial^2 f}{\partial x_n\,\partial x_2} & \cdots & \frac{\partial^2 f}{\partial x_n^2} \end{array} \right]
*

The symbolic or evaluated Gradient/Hessian matrices.

Andrej-Nikolai Spiess

The Matrix Cookbook (Version November 2012).

Petersen KB & Pedersen MS.

http://ais.informatik.uni-freiburg.de/teaching/ws12/mapping/pdf/imm3274.pdf

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | ```
EXPR <- expression(a^b + sin(c))
ENVIR <- list(a = 2, b = 3, c = 4)
## First-order partial derivatives: Gradient.
GRAD <- makeGrad(EXPR)
## This will evaluate the Gradient.
evalDerivs(GRAD, ENVIR)
## Second-order partial derivatives: Hessian.
HESS <- makeHess(EXPR)
## This will evaluate the Hessian.
evalDerivs(HESS, ENVIR)
## Change derivatives order.
GRAD <- makeGrad(EXPR, order = c(2,1,3))
evalDerivs(GRAD, ENVIR)
``` |

propagate documentation built on May 7, 2018, 1:03 a.m.

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