| Type: | Package |
| Title: | Computation of Approximate Potentials for Weakly Non-Gradient Fields |
| Version: | 1.1.0 |
| Author: | Pablo Rodríguez-Sánchez |
| Maintainer: | Pablo Rodríguez-Sánchez <pablo.rodriguez.sanchez@gmail.com> |
| Description: | Computation of approximate potentials for both gradient and non gradient fields. It is known from physics that only gradient fields, also known as conservative, have a well defined potential function. Here we present an algorithm, based on the classical Helmholtz decomposition, to obtain an approximate potential function for non gradient fields. More information in Rodríguez-Sánchez (2020) <doi:10.1371/journal.pcbi.1007788>. |
| License: | MIT + file LICENSE |
| Encoding: | UTF-8 |
| LazyData: | true |
| RoxygenNote: | 7.1.1 |
| VignetteBuilder: | knitr |
| Suggests: | testthat, knitr, rmarkdown, deSolve, dplyr, colorRamps, ggplot2, gridExtra, latticeExtra, bindrcpp |
| Imports: | numDeriv, Matrix |
| NeedsCompilation: | no |
| Packaged: | 2021-03-14 10:41:51 UTC; pablo |
| Repository: | CRAN |
| Date/Publication: | 2021-03-17 13:50:02 UTC |
Approximate potential in one dimension
Description
Approximate potential in one dimension
Usage
approxPot1D(f, xs, V0 = "auto")
Arguments
f |
One-dimensional representing the flow (right hand side of differential equation) |
xs |
Vector of positions to evaluate |
V0 |
(Optional) Value of V at first element of xs. When default, the global minimum is assigned 0 |
Value
The potential estimated at each point in xs
Author(s)
Pablo Rodríguez-Sánchez (https://pabrod.github.io)
References
https://arxiv.org/abs/1903.05615
See Also
Examples
# Flow
f = function(x) { sin(x) }
# Sampling points
xs <- seq(0, 2*pi, length.out = 1e3)
# Approximated potential
Vs <- approxPot1D(f, xs)
Approximate potential in two dimensions
Description
Approximate potential in two dimensions
Usage
approxPot2D(f, xs, ys, V0 = "auto", mode = "mixed")
Arguments
f |
Two-dimensional representing the flow (right hand side of differential equation) |
xs |
Vector xs positions to evaluate |
ys |
Vector of ys positions to evaluate |
V0 |
(Optional) Value of V at first element of (xs,ys). When default, the global minimum is assigned 0 |
mode |
(Optional) Integration mode. Options are horizontal (default), vertical and mixed |
Value
The potential estimated at each point (xs, ys)
Author(s)
Pablo Rodríguez-Sánchez (https://pabrod.github.io)
References
https://arxiv.org/abs/1903.05615
See Also
Examples
# Flow
f = function(x) {c(-x[1]*(x[1]^2 - 1.1), -x[2]*(x[2]^2 - 1))}
# Sampling points
xs <- seq(-1.5, 1.5, length.out = 10)
ys <- seq(-1.5, 1.5, length.out = 15)
# Approximated potential
Vs <- approxPot2D(f, xs, ys, mode = 'horizontal')
Approximate potential difference between two points
Description
Approximate potential difference between two points
Usage
deltaV(f, x, x0, normType = "f")
Arguments
f |
Flow equations (right hand side of differential equation) |
x |
Position where we want to know the approximate potential |
x0 |
Reference position (center of the Taylor expansion) |
normType |
(default: 'f') Matrix norm used to compute the error |
Value
A list containing the approximate potential difference between x and x0 and the estimated error
Author(s)
Pablo Rodríguez-Sánchez (https://pabrod.github.io)
References
https://arxiv.org/abs/1903.05615
See Also
approxPot1D, approxPot2D, norm
Examples
# One dimensional flow
f <- function(x) { cos(x) }
# Evaluation points
x0 <- 1
x1 <- 1.02
dV <- deltaV(f, x1, x0)
# Two dimensional flow
f <- function(x) { c(
-2*x[1]*x[2],
-x[1]^2 - 1
)}
# Evaluation points
x0 <- matrix(c(1,2), ncol = 1)
x1 <- matrix(c(0.98,2.01), ncol = 1)
dV <- deltaV(f, x1, x0)