Ramnath Vaidyanathan
Assistant Professor, McGill
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\[
\begin{aligned}
\nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\
\nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\
\nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned}
\]
\[
\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix}
\mathbf{i} & \mathbf{j} & \mathbf{k} \\
\frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\
\frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0
\end{vmatrix}
\]
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We can make this function more robust by adding a simple error checking statement to prevent illegal parameters from generating invalid results.
qpareto <- function(p, scale, loc) {
if ((scale <= 0) | (loc <= 0)) {
stop("'qpareto' parameters must be greater than zero.")
}
q <- loc * (1 - p)^(-1/scale)
return(q)
}
Entering a negative parameter now raises an exception, instead of an invalid result that could silently corrupt subsequent results.
qpareto(0.4, 5, -1)
## Error: 'qpareto' parameters must be greater than zero.
We could improve this further by checking to ensure that p
is a valid probability.
library(ggplot2)
library(ggthemes)
## Warning: package 'ggthemes' was built under R version 2.15.3
qplot(wt, mpg, data = mtcars) + theme_solarized()
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