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docs: update R tutorial to modern Rvolesti syntax #343 #410

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78 changes: 55 additions & 23 deletions docs/tutorials/general.md
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Expand Up @@ -4,7 +4,11 @@

`volesti` is a `C++` package (with an `R` interface) for computing estimations of volume of polytopes given by a set of points or linear inequalities or Minkowski sum of segments (zonotopes). There are two algorithms for volume estimation and algorithms for sampling, rounding and rotating polytopes.

We can download the `R` package from the [CRAN webpage](https://CRAN.R-project.org/package=volesti).
# How you can download volesti

Install the latest version from GitHub
install.packages("devtools")
devtools::install_github("GeomScale/Rvolesti")

```r
# first load the volesti library
Expand All @@ -22,7 +26,7 @@ help("sample_points")
Let’s try our first volesti command to estimate the volume of a 3-dimensional cube $\{-1\leq x_i \leq 1,x_i \in \mathbb R\ |\ i=1,2,3\}$

```r
P <- GenCube(3,'H')
P <- gen_cube(3,'H')
print(volume(P))
```

Expand Down Expand Up @@ -123,13 +127,32 @@ There are two important parameters `cost per step` and `mixing time` that affect
#run in few secs
library(ggplot2)
library(volesti)
for (step in c(1,20,100,150)){
for (walk in c("CDHR", "RDHR", "BW")){
P <- GenCube(100, 'H')
points1 <- sample_points(P, WalkType = walk, walk_step = step, N=1000)
g<-plot(ggplot(data.frame( x=points1[1,], y=points1[2,] )) +
geom_point( aes(x=x, y=y, color=walk)) + coord_fixed(xlim = c(-1,1),
ylim = c(-1,1)) + ggtitle(sprintf("walk length=%s", step, walk)))

# Parameters to iterate through
walk_steps <- c(1, 20, 100, 150)
walk_types <- c("CDHR", "RDHR", "BW")

for (step in walk_steps) {
for (walk in walk_types) {
# Updated: gen_cube instead of GenCube
P <- gen_cube(100, 'H')

# Updated: sample_points function call
# Note: ensure WalkType and walk_step are lowercase as per latest API
points1 <- sample_points(P, WalkType = walk, walk_step = step, n = 1000)

# ggplot2 visualization
# Converting matrix to data frame: points1 is usually d x n
df <- data.frame(x = points1[1, ], y = points1[2, ])

g <- ggplot(df, aes(x = x, y = y)) +
geom_point(color = "steelblue", alpha = 0.6) +
coord_fixed(xlim = c(-1, 1), ylim = c(-1, 1)) +
labs(title = paste("Walk:", walk, "| Length:", step),
subtitle = "Projection of 100D Cube to 2D") +
theme_minimal()

print(g)
}
}
```
Expand All @@ -151,10 +174,10 @@ Now let's compute our first example. The volume of the 3-dimensional cube.
```r
library(geometry)

PV <- GenCube(3,'V')
PV <- gen_cube(3,'V')
str(PV)

#P = GenRandVpoly(3, 6, body = 'cube')
#P = gen_rand_vpoly(3, 6, body = 'cube')
tim1 <- system.time({ geom_values = convhulln(PV$V, options = 'FA') })
tim2 <- system.time({ vol2 = volume(PV) })

Expand All @@ -165,7 +188,7 @@ cat(sprintf("exact vol = %f\napprx vol = %f\nrelative error = %f\n",
Now try a higher dimensional example. By setting the `error` parameter we can control the apporximation of the algorithm.

```r
PH = GenCube(10,'H')
PH = gen_cube(10,'H')
volumes <- list()
for (i in 1:10) {
# default parameters
Expand All @@ -188,7 +211,7 @@ Deterministic algorithms for volume are limited to low dimensions (e.g. less tha
```r
library(geometry)

P = GenRandVpoly(15, 30)
P = gen_rand_vpoly(15, 30)
# this will return an error about memory allocation, i.e. the dimension is too high for qhull
tim1 <- system.time({ geom_values = convhulln(P$V, options = 'FA') })

Expand All @@ -207,8 +230,17 @@ obtained via massive parallel computation.

```r
library(volesti)
P <- fileToMatrix('data/birk10.ine')
exact <- 727291284016786420977508457990121862548823260052557333386607889/828160860106766855125676318796872729344622463533089422677980721388055739956270293750883504892820848640000000
library(volesti)

# This finds the internal path to the example file provided by the package
path <- system.file("extdata", "birk10.ine", package = "volesti")

# Check if the file exists before trying to read it
if (path == "") {
stop("Example file not found. Please ensure volesti is installed correctly.")
}

P <- fileToMatrix(path)

# warning the following will take around half an hour
#print(volume(P, Algo = 'CG'))
Expand All @@ -233,20 +265,20 @@ Our random walks perform poorly on those polytopes espacially as the dimension i
```r
library(ggplot2)

P = GenSkinnyCube(2)
P = gen_skinny_cube(2)
points1 = sample_points(P, WalkType = "CDHR", N=1000)
ggplot(data.frame(x = c(points1[1,]), y = c(points1[2,])), aes(x=x, y=y)) + geom_point() +labs(x =" ", y = " ")+coord_fixed(ylim = c(-10,10))
points1 = sample_points(P, WalkType = "RDHR", N=1000)
ggplot(data.frame(x = c(points1[1,]), y = c(points1[2,])), aes(x=x, y=y)) + geom_point() +labs(x =" ", y = " ")+coord_fixed(ylim = c(-10,10))
```

```r
P = GenSkinnyCube(10)
P = gen_skinny_cube(10)
points1 = sample_points(P, WalkType = "CDHR", N=1000)
ggplot(data.frame(x = c(points1[1,]), y = c(points1[2,])), aes(x=x, y=y)) + geom_point() +labs(x =" ", y = " ")+coord_fixed(xlim = c(-100,100), ylim = c(-10,10))
points1 = sample_points(P, WalkType = "RDHR", N=1000)
ggplot(data.frame(x = c(points1[1,]), y = c(points1[2,])), aes(x=x, y=y)) + geom_point() +labs(x =" ", y = " ")+coord_fixed(xlim = c(-100,100), ylim = c(-10,10))
P = GenSkinnyCube(100)
P = gen_skinny_cube(100)
points1 = sample_points(P, WalkType = "RDHR", N=1000)
ggplot(data.frame(x = c(points1[1,]), y = c(points1[2,])), aes(x=x, y=y)) + geom_point() +labs(x =" ", y = " ")+coord_fixed(xlim = c(-100,100), ylim = c(-10,10))
```
Expand All @@ -259,11 +291,11 @@ library(ggplot2)

d <- 10

P = GenSkinnyCube(d)
P = gen_skinny_cube(d)
points1 = sample_points(P, WalkType = "CDHR", N=1000)
ggplot(data.frame(x = c(points1[1,]), y = c(points1[2,])), aes(x=x, y=y)) + geom_point() +labs(x =" ", y = " ")+coord_fixed(ylim = c(-10,10))

P <- rand_rotate(P)$P
P <- rotate_polytope(P)

points1 = sample_points(P, WalkType = "RDHR", N=1000)
ggplot(data.frame(x = c(points1[1,]), y = c(points1[2,])), aes(x=x, y=y)) + geom_point() +labs(x =" ", y = " ")+coord_fixed()
Expand Down Expand Up @@ -308,7 +340,7 @@ adaptIntegrate(f, lowerLimit = c(-1, -1, -1), upperLimit = c(1, 1, 1))$integral

# Simple Monte Carlo integration
# https://en.wikipedia.org/wiki/Monte_Carlo_integration
P = GenCube(3, 'H')
P = gen_cube(3, 'H')
num_of_points <- 10000
points1 <- sample_points(P, WalkType = "RDHR", walk_step = 100, N=num_of_points)
int<-0
Expand Down Expand Up @@ -337,7 +369,7 @@ We can approximate this number by the following code.
```r
A = matrix(c(-1,0,1,0,0,0,-1,1,0,0,0,-1,0,1,0,0,0,0,-1,1,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,-1,0,0,0,0,0,-1,0,0,0,0,0,-1,0,0,0,0,0,-1,0,0,0,0,0,-1), ncol=5, nrow=14, byrow=TRUE)
b = c(0,0,0,0,0,0,0,0,0,1,1,1,1,1)
P = Hpolytope$new(A, b)
P = make_h_polytope(A, b)
volume(P,error=0.2)*factorial(5)
```

Expand All @@ -347,7 +379,7 @@ volume(P,error=0.2)*factorial(5)
For a specific set of assets in a stock market, portfolios are characterized by their return and their risk which is the variance of the portfolios’ returns (volatility). Copulas are approximations of the bivariate joint distribution of return and volatility.

```r
#install.packages('plotly')
install.packages('plotly')
library('plotly')
```

Expand Down
84 changes: 84 additions & 0 deletions external/lpsolve/lpsolve-master/CMakeLists.txt
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@@ -0,0 +1,84 @@
# Copyright (C) 2014 Tai Chi Minh Ralph Eastwood.
# Redistribution and use of this file is allowed according to the terms of the MIT license.
# For details see the COPYRIGHT file distributed with Flymir LuaDist.
# Please note that the package source code is licensed under its own license.

project(lpsolve C)
cmake_minimum_required(VERSION 2.8)

include (cmake/dist.cmake)
include (cmake/lpsolve.cmake)

include_directories(${PROJECT_SOURCE_DIR})
include_directories(${PROJECT_SOURCE_DIR}/shared)
include_directories(${PROJECT_SOURCE_DIR}/bfp)
include_directories(${PROJECT_SOURCE_DIR}/bfp/bfp_LUSOL)
include_directories(${PROJECT_SOURCE_DIR}/bfp/bfp_LUSOL/LUSOL)
include_directories(${PROJECT_SOURCE_DIR}/colamd)

add_definitions(-DYY_NEVER_INTERACTIVE -DPARSER_LP -DINVERSE_ACTIVE=INVERSE_LUSOL -DRoleIsExternalInvEngine)
add_definitions(-DLLONG=long)

set(LPSOLVE_SOURCES
lp_MDO.c
shared/commonlib.c
shared/mmio.c
shared/myblas.c
ini.c
fortify.c
colamd/colamd.c
lp_rlp.c
lp_crash.c
bfp/bfp_LUSOL/lp_LUSOL.c
bfp/bfp_LUSOL/LUSOL/lusol.c
lp_Hash.c
lp_lib.c
lp_wlp.c
lp_matrix.c
lp_mipbb.c
lp_MPS.c
lp_params.c
lp_presolve.c
lp_price.c
lp_pricePSE.c
lp_report.c
lp_scale.c
lp_simplex.c
lp_SOS.c
lp_utils.c
yacc_read.c
)

set(LPSOLVE_HEADERS
lp_bit.h
lp_crash.h
lp_explicit.h
lp_fortify.h
lp_Hash.h
lp_lib.h
lp_matrix.h
lp_MDO.h
lp_mipbb.h
lp_MPS.h
lp_presolve.h
lp_price.h
lp_pricePSE.h
lp_report.h
lp_rlp.h
lp_scale.h
lp_simplex.h
lp_solveDLL.h
lp_SOS.h
lp_types.h
lp_utils.h
lp_wlp.h
)

add_library(lpsolve55 ${LPSOLVE_SOURCES})
target_link_libraries(lpsolve55 m dl)

add_executable(lp_solve ${LPSOLVE_SOURCES} lp_solve/lp_solve.c)
target_link_libraries(lp_solve m dl)

install(TARGETS lpsolve55 DESTINATION lib)
install(FILES ${LPSOLVE_HEADERS} DESTINATION include)
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