README.Rmd

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always_allow_html: yes
output:
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    keep_md: yes
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  md_document:
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<!-- README.md is generated from README.Rmd. Please edit that file -->

```{r, echo = FALSE}
library(knitr)
opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.path = "man/figures/README-",
  fig.align = "center",
  fig.retina = 2,
  out.width = "75%",
  dpi = 96
)
knit_hooks$set(pngquant = hook_pngquant)
```


# IsotoneOptimization

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The goal of IsotoneOptimization is to implement the Sequential Block Merging algorithm for solving isotonic regression with constraints represented by arbitrary directed acyclic graph.

## Installation

You can install the development version of IsotoneOptimization from [GitHub](https://github.com/) with:

``` r
# install.packages("devtools")
devtools::install_github("Xiwen1997/IsotoneRpkg")
```

## Example

This is a basic example which shows you how to solve a general isotonic regression problem:

```{r}
library(IsotoneOptimization)
## basic example code

Emat <- t(matrix( c(1,2,  1,3,  1,4,  2,5,  2,6,  3,7,  4,8,  5,8,  6,9,  6,10),2,10))
x_ordered <- solve_isotone_DAG(rnorm(10), rep(1,10), Emat)
```

Using package __igraph__, we can better view the ordered vector by regarding isotonic constraints as the edges of a graph. Namely, $x_i\leq x_j$ if there exists an arrow from node $i$ to node $j$

```{r}
library(igraph)
grid_graph <- graph_from_edgelist(Emat)
V(grid_graph)$name <- as.character(round(x_ordered,2))
plot(grid_graph,  vertex.size = 4,          # Smaller nodes
    vertex.label = V(grid_graph)$name, # Set the labels
    vertex.label.cex = 1,   # Slightly smaller font
    vertex.label.dist = 1.4,  # Offset the labels
    vertex.label.color = "black")
```

Some typical isotonic constraints, including chain, binary tree, 2d-grid isotonic constraints, can be defined directed. Simply using __solve_isotone_chain__, __solve_isotone_binary_tree__, and __solve_isotone_2d_grid__, you can solve the corresponding isotone optimization problem!