README.md

In wrathematics/lptools: Linear Programming Tools

lptools

• Version: 0.1
• Status:
• License:
• Author: Drew Schmidt

Linear programming tools to make doing my homework easier.

Example

Say we have the system inspired from a linear program:

library(lptools)

A <- matrix(c(1, 1, 1, 1, 0, -1, 1, 2, 0 , 1), byrow=TRUE, nrow=2)
b <- c(5, 6)

TODO

latex(A)

## \begin{align*}
## A &= \left[
## \begin{array}{rrrrr}
## 1 &1 &1 &1 &0 \\
## -1 &1 &2 &0 &1 \\
## \end{array}\right]
## \end{align*}

TODO

bfs <- find.bfs(A, b)
latex(bfs)

## \begin{align*}
## B^{-1}b = [a_1, a_2]^{-1}b &=   \left[
## \begin{array}{rr}
## -0.5 &5.5 \\
## \end{array}\right]^T
## \\
## B^{-1}b = [a_1, a_3]^{-1}b &=   \left[
## \begin{array}{rr}
## 1.333 &3.667 \\
## \end{array}\right]^T
## \\
## B^{-1}b = [a_1, a_4]^{-1}b &=   \left[
## \begin{array}{rr}
## -6 &11 \\
## \end{array}\right]^T
## \\
## B^{-1}b = [a_1, a_5]^{-1}b &=   \left[
## \begin{array}{rr}
## 5 &11 \\
## \end{array}\right]^T
## \\
## B^{-1}b = [a_2, a_3]^{-1}b &=   \left[
## \begin{array}{rr}
## 4 &1 \\
## \end{array}\right]^T
## \\
## B^{-1}b = [a_2, a_4]^{-1}b &=   \left[
## \begin{array}{rr}
## 6 &-1 \\
## \end{array}\right]^T
## \\
## B^{-1}b = [a_2, a_5]^{-1}b &=   \left[
## \begin{array}{rr}
## 5 &1 \\
## \end{array}\right]^T
## \\
## B^{-1}b = [a_3, a_4]^{-1}b &=   \left[
## \begin{array}{rr}
## 3 &2 \\
## \end{array}\right]^T
## \\
## B^{-1}b = [a_3, a_5]^{-1}b &=   \left[
## \begin{array}{rr}
## 5 &-4 \\
## \end{array}\right]^T
## \\
## B^{-1}b = [a_4, a_5]^{-1}b &=   \left[
## \begin{array}{rr}
## 5 &6 \\
## \end{array}\right]^T
## \\
## \end{align*}

TODO

ep <- find.ep(bfs)
latex(ep)

## \begin{align*}
## \bf{x}_1  = \left[\begin{array}{rrrrr}x_1 &x_2 &x_3 &x_4 &x_5 \end{array}\right]^T
##  &=   \left[
## \begin{array}{rrrrr}
## 1.333 &0 &3.667 &0 &0 \\
## \end{array}\right]^T
## \\
## \bf{x}_2  = \left[\begin{array}{rrrrr}x_1 &x_2 &x_3 &x_4 &x_5 \end{array}\right]^T
##  &=   \left[
## \begin{array}{rrrrr}
## 5 &0 &0 &0 &11 \\
## \end{array}\right]^T
## \\
## \bf{x}_3  = \left[\begin{array}{rrrrr}x_1 &x_2 &x_3 &x_4 &x_5 \end{array}\right]^T
##  &=   \left[
## \begin{array}{rrrrr}
## 0 &4 &1 &0 &0 \\
## \end{array}\right]^T
## \\
## \bf{x}_4  = \left[\begin{array}{rrrrr}x_1 &x_2 &x_3 &x_4 &x_5 \end{array}\right]^T
##  &=   \left[
## \begin{array}{rrrrr}
## 0 &5 &0 &0 &1 \\
## \end{array}\right]^T
## \\
## \bf{x}_5  = \left[\begin{array}{rrrrr}x_1 &x_2 &x_3 &x_4 &x_5 \end{array}\right]^T
##  &=   \left[
## \begin{array}{rrrrr}
## 0 &0 &3 &2 &0 \\
## \end{array}\right]^T
## \\
## \bf{x}_6  = \left[\begin{array}{rrrrr}x_1 &x_2 &x_3 &x_4 &x_5 \end{array}\right]^T
##  &=   \left[
## \begin{array}{rrrrr}
## 0 &0 &0 &5 &6 \\
## \end{array}\right]^T
## \\
## \end{align*}

Matrix Printing

There are numerous options for displaying matrices in LaTeX. By default, the matrix will print inside of an align* environment and have its R name preceeding it. However, we can print "inline" (without the automatic math mode), without showing the object name, or even print the transpose instead:

x <- matrix(1:30, nrow=10)
latex(x, inline=TRUE, asTranspose=TRUE, showName=FALSE)

##   \left[
## \begin{array}{rrrrrrrrrr}
## 1 &2 &3 &4 &5 &6 &7 &8 &9 &10 \\
## 11 &12 &13 &14 &15 &16 &17 &18 &19 &20 \\
## 21 &22 &23 &24 &25 &26 &27 &28 &29 &30 \\
## \end{array}\right]^T

wrathematics/lptools documentation built on May 4, 2019, 10:52 a.m.