Description Usage Arguments Details Value Note Author(s) Examples

These two functions create Gradient and Hessian matrices by Richardson's central finite difference method of the partial derivatives for any expression.

1 2 |

`expr` |
an expression, such as |

`envir` |
the |

Calculates first- and second-order numerical approximation using Richardson's **central difference formula**:

*f'_i(x) \approx \frac{f(x_1, …, x_i + d, …, x_n) - f(x_1, …, x_i - d, …, x_n)}{2d}*

*f''_i(x) \approx \frac{f(x_1, …, x_i + d, …, x_n) - 2f(x_1, …, x_n) + f(x_1, …, x_i - d, …, x_n)}{d^2}*

The numeric Gradient/Hessian matrices.

The two functions are modified versions of the `genD`

function in the 'numDeriv' package, but a bit more easy to handle because they use expressions and the function's `x`

value must not be defined as splitted scalar values `x[1], x[2], ... x[n]`

in the body of the function.

Andrej-Nikolai Spiess

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
## Check for equality of symbolic
## and numerical derivatives.
EXPR <- expression(2^x + sin(2 * y) - cos(z))
x <- 5
y <- 10
z <- 20
symGRAD <- evalDerivs(makeGrad(EXPR))
numGRAD <- numGrad(EXPR)
all.equal(symGRAD, numGRAD)
symHESS <- evalDerivs(makeHess(EXPR))
numHESS <- numHess(EXPR)
all.equal(symHESS, numHESS)
``` |

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

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