Type: Package
Title: Tools for 2D and 3D Plots of Single and Multi-Objective Linear/Integer Programming Models
Version: 1.5.5
URL: https://relund.github.io/gMOIP/, https://github.com/relund/gMOIP/
BugReports: https://github.com/relund/gMOIP/issues
Description: Make 2D and 3D plots of linear programming (LP), integer linear programming (ILP), or mixed integer linear programming (MILP) models with up to three objectives. Plots of both the solution and criterion space are possible. For instance the non-dominated (Pareto) set for bi-objective LP/ILP/MILP programming models (see vignettes for an overview). The package also contains an function for checking if a point is inside the convex hull.
License: GPL (≥ 3)
Language: en-US
Encoding: UTF-8
RoxygenNote: 7.3.2
Depends: R (≥ 4.1.0)
Imports: ggrepel, geometry, ggplot2, rgl, MASS, Matrix, grDevices, stats, Rfast, plyr, tidyselect, tidyr, tibble, purrr, dplyr, rlang, png, sp, moocore
Suggests: tikzDevice, grid, gridExtra, knitr, rmarkdown, roxygen2, ggsci, magrittr, scales, pdftools, testthat (≥ 2.1.0), webshot2
VignetteBuilder: knitr
NeedsCompilation: no
Packaged: 2025-06-23 13:59:30 UTC; au15463
Author: Lars Relund Nielsen ORCID iD [aut, cre]
Maintainer: Lars Relund Nielsen <lars@relund.dk>
Repository: CRAN
Date/Publication: 2025-06-25 12:20:24 UTC

gMOIP: Tools for 2D and 3D Plots of Single and Multi-Objective Linear/Integer Programming Models

Description

Make 2D and 3D plots of linear programming (LP), integer linear programming (ILP), or mixed integer linear programming (MILP) models with up to three objectives. Plots of both the solution and criterion space are possible. For instance the non-dominated (Pareto) set for bi-objective LP/ILP/MILP programming models (see vignettes for an overview). The package also contains an function for checking if a point is inside the convex hull.

Author(s)

Maintainer: Lars Relund Nielsen lars@relund.dk (ORCID)

See Also

plotPolytope(), plotCriterion2D() and plotHull3D().

Check if point input is okay

Description

Check if point input is okay

Usage

.checkPts(pts, p = NULL, warn = FALSE, stopUnique = TRUE, asDF = FALSE)

Arguments

pts

Point input.

p

Desired dimension of points.

warn

Output warnings.

stopUnique

Stop if rows not are unique.

asDF

Return as data frame otherwise as matrix.

Value

Point input converted to a matrix.

Get ranges of the bounding box margins

Description

Get ranges of the bounding box margins

Usage

.getRanges(expand = 1.03, ranges = par3d("bbox"))

Arguments

expand

Expand margins.

ranges

The bounding box.

Value

A list with ranges.

Convert min/max to direction (1/-1)

Description

Convert min/max to direction (1/-1)

Usage

.mToDirection(m, p)

Arguments

m

Min/max vector.

p

Number of objectives.

Value

A direction vector (min = 1 and max = -1)

Estimate 1 em in pixels in the resulting png.

Description

Estimate 1 em in pixels in the resulting png.

Usage

.sizeM(...)

Arguments

...

Arguments parsed on to texToPng.

Value

The width and size of the png.

Add discrete points to a non-dominated set and classify them into extreme supported, non-extreme supported, non-supported.

Description

Add discrete points to a non-dominated set and classify them into extreme supported, non-extreme supported, non-supported.

Usage

addNDSet(
  pts,
  nDSet = NULL,
  crit = "max",
  keepDom = FALSE,
  dubND = FALSE,
  classify = TRUE
)

Arguments

pts

A data frame with points to add (a column for each objective).

nDSet

A data frame with current non-dominated set (NULL if none yet). Column names of the p objectives must be ⁠z1, ..., zp⁠.

crit

A max or min vector. If length one assume all objectives are optimized in the same direction.

keepDom

Keep dominated points in output.

dubND

Duplicated non-dominated points are classified as non-dominated.

classify

Non-dominated points are classified into supported extreme (se), supported non-extreme (sne) and unsupported (us).

Value

A data frame with a column for each objective (z columns) and nd (non-dominated). Moreover if classify then columns se, sne, us and cls.

Author(s)

Lars Relund lars@relund.dk

Examples

nDSet <- data.frame(z1=c(12,14,16,18), z2=c(18,16,12,4))
pts <- data.frame(z1 = c(18,18,14,15,15), z2=c(2,6,14,14,16))
addNDSet(pts, nDSet, crit = "max")
addNDSet(pts, nDSet, crit = "max", keepDom = TRUE)
addNDSet(pts, nDSet, crit = "min")
addNDSet(c(2,2), nDSet, crit = "max")
addNDSet(c(2,2), nDSet, crit = "min")


nDSet <- data.frame(z1=c(12,14,16,18), z2=c(18,16,12,4), z3 = c(1,7,0,6))
pts <- data.frame(z1=c(12,14,16,18), z2=c(18,16,12,4), z3 = c(2,2,2,6))
crit = c("min", "min", "max")
di <- c(1,1,-1)
li <- c(-1,20)
ini3D(argsPlot3d = list(xlim = li, ylim = li, zlim = li))
plotCones3D(nDSet, direction = di, argsPolygon3d = list(color = "green", alpha = 1),
            drawPoint = FALSE)
plotHull3D(nDSet, addRays = TRUE, direction = di)
plotPoints3D(nDSet, argsPlot3d = list(col = "red"), addText = "coord")
plotPoints3D(pts, addText = "coord")
finalize3D()
addNDSet(pts, nDSet, crit, dubND = FALSE)
addNDSet(pts, nDSet, crit, dubND = TRUE)
addNDSet(pts, nDSet, crit, dubND = TRUE, keepDom = TRUE)
addNDSet(pts, nDSet, crit, dubND = TRUE, keepDom = TRUE, classify = FALSE)

Add 2D discrete points to a non-dominated set and classify them into extreme supported, non-extreme supported, non-supported.

Description

Add 2D discrete points to a non-dominated set and classify them into extreme supported, non-extreme supported, non-supported.

Usage

addNDSet2D(pts, nDSet = NULL, crit = "max", keepDom = FALSE)

Arguments

pts

A data frame. It is assumed that z1 and z2 are in the two first columns.

nDSet

A data frame with current non-dominated set (NULL is none yet).

crit

Either max or min.

keepDom

Keep dominated points.

Value

A data frame with columns z1 and z2, nD (non-dominated), ext (extreme), nonExt (non-extreme supported).

Author(s)

Lars Relund lars@relund.dk

Examples

nDSet <- data.frame(z1=c(12,14,16,18), z2=c(18,16,12,4))
pts <- data.frame(z1 = c(18,18,14,15,15), z2=c(2,6,14,14,16))
addNDSet2D(pts, nDSet, crit = "max")
addNDSet2D(pts, nDSet, crit = "max", keepDom = TRUE)
addNDSet2D(pts, nDSet, crit = "min")

Add all points on the bounding box hit by the rays.

Description

Add all points on the bounding box hit by the rays.

Usage

addRays(
  pts,
  m = apply(pts, 2, min) - 5,
  M = apply(pts, 2, max) + 5,
  direction = 1
)

Arguments

pts

A data frame with all points

m

Minimum values of the bounding box.

M

Maximum values of the bounding box.

direction

Ray direction. If i'th entry is positive, consider the i'th column of the pts plus a value greater than on equal zero. If negative, consider the i'th column of the pts minus a value greater than on equal zero.

Value

The points merged with the points on the bounding box. The column pt equals 1 if points from pts and zero otherwise.

Note

Assume that pts has been checked using .checkPts().

Examples

pts <- genNDSet(3,10)[,1:3]
addRays(pts)
addRays(pts, dir = c(1,-1,1))
addRays(pts, dir = c(-1,-1,1), m = c(0,0,0), M = c(100,100,100))
pts <- genSample(5,20)[,1:5]
addRays(pts)

Binary (0-1) points in the feasible region (Ax<=b).

Description

Binary (0-1) points in the feasible region (Ax<=b).

Usage

binaryPoints(A, b)

Arguments

A

Constraint matrix.

b

Right hand side.

Value

A data frame with all binary points inside the feasible region.

Note

Do a simple enumeration of all binary points. Will not work if ncol(A) large.

Author(s)

Lars Relund lars@relund.dk.

Examples

A <- matrix( c(3,-2, 1, 2, 4,-2,-3, 2, 1), nc = 3, byrow = TRUE)
b <- c(10, 12, 3)
binaryPoints(A, b)

A <- matrix(c(9, 10, 2, 4, -3, 2), ncol = 2, byrow = TRUE)
b <- c(90, 27, 3)
binaryPoints(A, b)

Classify a set of nondominated points

Description

Classify a set of nondominated points

Usage

classifyNDSet(pts, direction = 1)

Arguments

pts

A set of non-dominated points. It is assumed that ncol(pts) equals the number of objectives ($p$).

direction

Ray direction. If i'th entry is positive, consider the i'th column of the pts plus a value greater than on equal zero (minimize objective $i$). If negative, consider the i'th column of the pts minus a value greater than on equal zero (maximize objective $i$).

Value

The classification is extreme (se), supported non-extreme (sne) and unsupported us nondominated points. Return the ND set with classification columns se (true/false), sne (true/false), us (true/false) and cls (se, sne or us).

Note

It is assumed that pts are nondominated.

See Also

classifyNDSetExtreme()

Examples


pts <- matrix(c(0,0,1, 0,1,0, 1,0,0, 0.5,0.2,0.5, 0.25,0.5,0.25), ncol = 3, byrow = TRUE)
ini3D(argsPlot3d = list(xlim = c(min(pts[,1])-2,max(pts[,1])+2),
  ylim = c(min(pts[,2])-2,max(pts[,2])+2),
  zlim = c(min(pts[,3])-2,max(pts[,3])+2)))
plotHull3D(pts, addRays = TRUE, argsPolygon3d = list(alpha = 0.5), useRGLBBox = TRUE)
pts <- classifyNDSet(pts[,1:3])
plotPoints3D(pts[pts$se,1:3], argsPlot3d = list(col = "red"))
plotPoints3D(pts[pts$sne,1:3], argsPlot3d = list(col = "black"))
plotPoints3D(pts[pts$us,1:3], argsPlot3d = list(col = "blue"))
plotCones3D(pts[,1:3], rectangle = TRUE, argsPolygon3d = list(alpha = 1))
finalize3D()
pts

pts <- matrix(c(0,0,1, 0,1,0, 1,0,0, 0.2,0.1,0.1, 0.1,0.45,0.45), ncol = 3, byrow = TRUE)
di <- -1 # maximize
ini3D(argsPlot3d = list(xlim = c(min(pts[,1])-1,max(pts[,1])+1),
  ylim = c(min(pts[,2])-1,max(pts[,2])+1),
  zlim = c(min(pts[,3])-1,max(pts[,3])+1)))
plotHull3D(pts, addRays = TRUE, argsPolygon3d = list(alpha = 0.5), direction = di,
           addText = "coord")
pts <- classifyNDSet(pts[,1:3], direction = di)
plotPoints3D(pts[pts$se,1:3], argsPlot3d = list(col = "red"))
plotPoints3D(pts[pts$sne,1:3], argsPlot3d = list(col = "black"))
plotPoints3D(pts[pts$us,1:3], argsPlot3d = list(col = "blue"))
plotCones3D(pts[,1:3], rectangle = TRUE, argsPolygon3d = list(alpha = 1), direction = di)
finalize3D()
pts

pts <- matrix(c(0,0,1, 0,0,1, 0,1,0, 0.5,0.2,0.5, 1,0,0, 0.5,0.2,0.5, 0.25,0.5,0.25), ncol = 3,
              byrow = TRUE)
classifyNDSet(pts)

pts <- genNDSet(3,15)[,1:3]
ini3D(argsPlot3d = list(xlim = c(0,max(pts$z1)+2),
  ylim = c(0,max(pts$z2)+2),
  zlim = c(0,max(pts$z3)+2)))
plotHull3D(pts[, 1:3], addRays = TRUE, argsPolygon3d = list(alpha = 0.5))
pts <- classifyNDSet(pts[,1:3])
plotPoints3D(pts[pts$se,1:3], argsPlot3d = list(col = "red"))
plotPoints3D(pts[pts$sne,1:3], argsPlot3d = list(col = "black"))
plotPoints3D(pts[pts$us,1:3], argsPlot3d = list(col = "blue"))
finalize3D()
pts

pts <- genNDSet(3, 15, keepDom = FALSE, argsSphere = list(below = FALSE, factor = 10))[,1:3]
ini3D(argsPlot3d = list(xlim = c(0,max(pts$z1)+2),
  ylim = c(0,max(pts$z2)+2),
  zlim = c(0,max(pts$z3)+2)))
plotHull3D(pts[, 1:3], addRays = TRUE, argsPolygon3d = list(alpha = 0.5))
pts <- classifyNDSet(pts[,1:3])
plotPoints3D(pts[pts$se,1:3], argsPlot3d = list(col = "red"))
plotPoints3D(pts[pts$sne,1:3], argsPlot3d = list(col = "black"))
plotPoints3D(pts[pts$us,1:3], argsPlot3d = list(col = "blue"))
finalize3D()
pts

Find extreme points of a nondominated set of points

Description

Find extreme points of a nondominated set of points

Usage

classifyNDSetExtreme(pts, direction = 1)

Arguments

pts

A set of non-dominated points. It is assumed that ncol(pts) equals the number of objectives ($p$).

direction

Ray direction. If i'th entry is positive, consider the i'th column of the pts plus a value greater than on equal zero (minimize objective $i$). If negative, consider the i'th column of the pts minus a value greater than on equal zero (maximize objective $i$).

Value

The classification is extreme (se), supported non-extreme (sne) and unsupported us nondominated points. Return the ND set with classification columns se (true/false), sne (true/false), us (true/false) and cls (se, sne or us).

Note

It is assumed that pts are nondominated. This algorithm is faster than classifyNDSet(), since only check for extreme points.

See Also

classifyNDSet()

Examples


pts <- matrix(c(0,0,1, 0,1,0, 1,0,0, 0.5,0.2,0.5, 0.25,0.5,0.25), ncol = 3, byrow = TRUE)
ini3D(argsPlot3d = list(xlim = c(min(pts[,1])-2,max(pts[,1])+2),
  ylim = c(min(pts[,2])-2,max(pts[,2])+2),
  zlim = c(min(pts[,3])-2,max(pts[,3])+2)))
plotHull3D(pts, addRays = TRUE, argsPolygon3d = list(alpha = 0.5), useRGLBBox = TRUE)
pts <- classifyNDSetExtreme(pts[,1:3])
plotPoints3D(pts[pts$se,1:3], argsPlot3d = list(col = "red"))  # extreme
plotPoints3D(pts[is.na(pts$cls),1:3], argsPlot3d = list(col = "yellow"))  # unclassified
finalize3D()
pts

pts <- matrix(c(0,0,1, 0,1,0, 1,0,0, 0.2,0.1,0.1, 0.1,0.45,0.45), ncol = 3, byrow = TRUE)
di <- -1 # maximize
ini3D(argsPlot3d = list(xlim = c(min(pts[,1])-1,max(pts[,1])+1),
  ylim = c(min(pts[,2])-1,max(pts[,2])+1),
  zlim = c(min(pts[,3])-1,max(pts[,3])+1)))
plotHull3D(pts, addRays = TRUE, argsPolygon3d = list(alpha = 0.5), direction = di,
           addText = "coord")
pts <- classifyNDSetExtreme(pts[,1:3], direction = di)
plotPoints3D(pts[pts$se,1:3], argsPlot3d = list(col = "red"))
plotPoints3D(pts[is.na(pts$cls),1:3], argsPlot3d = list(col = "yellow"))  # unclassified
finalize3D()
pts

pts <- matrix(c(0,0,1, 0,0,1, 0,1,0, 0.5,0.2,0.5, 1,0,0, 0.5,0.2,0.5, 0.25,0.5,0.25), ncol = 3,
              byrow = TRUE)
classifyNDSetExtreme(pts)

pts <- genNDSet(3,15)[,1:3]
ini3D(argsPlot3d = list(xlim = c(0,max(pts$z1)+2),
  ylim = c(0,max(pts$z2)+2),
  zlim = c(0,max(pts$z3)+2)))
plotHull3D(pts[, 1:3], addRays = TRUE, argsPolygon3d = list(alpha = 0.5))
pts <- classifyNDSetExtreme(pts[,1:3])
plotPoints3D(pts[pts$se,1:3], argsPlot3d = list(col = "red"))
plotPoints3D(pts[is.na(pts$cls),1:3], argsPlot3d = list(col = "yellow"))  # unclassified
finalize3D()
pts

pts <- genNDSet(3, 15, keepDom = FALSE, argsSphere = list(below = FALSE, factor = 10))[,1:3]
ini3D(argsPlot3d = list(xlim = c(0,max(pts$z1)+2),
  ylim = c(0,max(pts$z2)+2),
  zlim = c(0,max(pts$z3)+2)))
plotHull3D(pts[, 1:3], addRays = TRUE, argsPolygon3d = list(alpha = 0.5))
pts <- classifyNDSetExtreme(pts[,1:3])
plotPoints3D(pts[pts$se,1:3], argsPlot3d = list(col = "red"))
plotPoints3D(pts[is.na(pts$cls),1:3], argsPlot3d = list(col = "yellow"))  # unclassified
finalize3D()
pts

Find the convex hull of a set of points.

Description

Find the convex hull of a set of points.

Usage

convexHull(
  pts,
  addRays = FALSE,
  useRGLBBox = FALSE,
  direction = 1,
  tol = mean(mean(abs(pts))) * sqrt(.Machine$double.eps) * 2,
  m = apply(pts, 2, min) - 5,
  M = apply(pts, 2, max) + 5
)

Arguments

pts

A matrix with a point in each row.

addRays

Add the ray defined by direction.

useRGLBBox

Use the RGL bounding box when add rays.

direction

Ray direction. If i'th entry is positive, consider the i'th column of pts plus a value greater than on equal zero (minimize objective $i$). If negative, consider the i'th column of pts minus a value greater than on equal zero (maximize objective $i$).

tol

Tolerance on standard deviation if using PCA.

m

Minimum values of the bounding box.

M

Maximum values of the bounding box.

Value

A list with hull equal a matrix with row indices of the vertices defining each facet in the hull and pts equal the input points (and dummy points) and columns: pt, true if a point in the original input; false if a dummy point (a point on a ray). vtx, TRUE if a vertex in the hull.

Examples

## 1D
pts<-matrix(c(1,2,3), ncol = 1, byrow = TRUE)
dimFace(pts) # a line
convexHull(pts)
convexHull(pts, addRays = TRUE)

## 2D
pts<-matrix(c(1,1, 2,2), ncol = 2, byrow = TRUE)
dimFace(pts) # a line
convexHull(pts)
plotHull2D(pts, drawPoints = TRUE)
convexHull(pts, addRays = TRUE)
plotHull2D(pts, addRays = TRUE, drawPoints = TRUE)
pts<-matrix(c(1,1, 2,2, 0,1), ncol = 2, byrow = TRUE)
dimFace(pts) # a polygon
convexHull(pts)
plotHull2D(pts, drawPoints = TRUE)
convexHull(pts, addRays = TRUE, direction = c(-1,1))
plotHull2D(pts, addRays = TRUE, direction = c(-1,1), addText = "coord")

## 3D
pts<-matrix(c(1,1,1), ncol = 3, byrow = TRUE)
dimFace(pts) # a point
convexHull(pts)
pts<-matrix(c(0,0,0,1,1,1,2,2,2,3,3,3), ncol = 3, byrow = TRUE)
dimFace(pts) # a line
convexHull(pts)
pts<-matrix(c(0,0,0,0,1,1,0,2,2,0,0,2), ncol = 3, byrow = TRUE)
dimFace(pts) # a polygon
convexHull(pts)
convexHull(pts, addRays = TRUE)
pts<-matrix(c(1,0,0,1,1,1,1,2,2,3,1,1), ncol = 3, byrow = TRUE)
dimFace(pts) # a polygon
convexHull(pts) # a polyhedron
pts<-matrix(c(1,1,1,2,2,1,2,1,1,1,1,2), ncol = 3, byrow = TRUE)
dimFace(pts) # a polytope (polyhedron)
convexHull(pts)

ini3D(argsPlot3d = list(xlim = c(0,3), ylim = c(0,3), zlim = c(0,3)))
pts<-matrix(c(1,1,1,2,2,1,2,1,1,1,1,2), ncol = 3, byrow = TRUE)
plotPoints3D(pts)
plotHull3D(pts, argsPolygon3d = list(color = "red"))
convexHull(pts)
plotHull3D(pts, addRays = TRUE)
convexHull(pts, addRays = TRUE)
finalize3D()

Calculate the corner points for the polytope Ax<=b.

Description

Calculate the corner points for the polytope Ax<=b.

Usage

cornerPoints(A, b, type = rep("c", ncol(A)), nonneg = rep(TRUE, ncol(A)))

Arguments

A

Constraint matrix.

b

Right hand side.

type

A character vector of same length as number of variables. If entry k is 'i' variable k must be integer and if 'c' continuous.

nonneg

A boolean vector of same length as number of variables. If entry k is TRUE then variable k must be non-negative.

Value

A data frame with a corner point in each row.

Author(s)

Lars Relund lars@relund.dk

Examples

A <- matrix( c(3,-2, 1, 2, 4,-2,-3, 2, 1), nc = 3, byrow = TRUE)
b <- c(10, 12, 3)
cornerPoints(A, b, type = c("c", "c", "c"))
cornerPoints(A, b, type = c("i", "i", "i"))
cornerPoints(A, b, type = c("i", "c", "c"))

Calculate the corner points for the polytope Ax<=b assuming all variables are continuous.

Description

Calculate the corner points for the polytope Ax<=b assuming all variables are continuous.

Usage

cornerPointsCont(A, b, nonneg = rep(TRUE, ncol(A)))

Arguments

A

Constraint matrix.

b

Right hand side.

nonneg

A boolean vector of same length as number of variables. If entry k is TRUE then variable k must be non-negative.

Value

A data frame with a corner point in each row.

Author(s)

Lars Relund lars@relund.dk

Calculate the criterion points of a set of points and ranges to find the set of non-dominated points (Pareto points) and classify them into extreme supported, non-extreme supported, non-supported.

Description

Calculate the criterion points of a set of points and ranges to find the set of non-dominated points (Pareto points) and classify them into extreme supported, non-extreme supported, non-supported.

Usage

criterionPoints(pts, obj, crit, labels = "coord")

Arguments

pts

A data frame with a column for each variable in the solution space (can also be a rangePoints).

obj

A p x n matrix(one row for each criterion).

crit

Either max or min.

labels

If NULL or "n" don't add any labels (empty string). If equals coord, labels are the solution space coordinates. Otherwise number all points from one based on the solution space points.

Value

A data frame with columns ⁠x1, ..., xn, z1, ..., zp, lbl (label), nD (non-dominated), ext (extreme), nonExt (non-extreme supported)⁠.

Author(s)

Lars Relund lars@relund.dk

Examples

A <- matrix( c(3, -2, 1, 2, 4, -2, -3, 2, 1), nc = 3, byrow = TRUE)
b <- c(10,12,3)
pts <- integerPoints(A, b)
obj <- matrix( c(1,-3,1,-1,1,-1), byrow = TRUE, ncol = 3 )
criterionPoints(pts, obj, crit = "max", labels = "numb")

Convert each row to a string.

Description

Convert each row to a string.

Usage

df2String(df, round = 2)

Arguments

df

Data frame.

round

How many digits to round

Value

A vector of strings.

Return the dimension of the convex hull of a set of points.

Description

Return the dimension of the convex hull of a set of points.

Usage

dimFace(pts, dim = NULL)

Arguments

pts

A matrix/data frame/vector that can be converted to a matrix with a row for each point.

dim

The dimension of the points, i.e. assume that column 1-dim specify the points. If NULL assume that the dimension are the number of columns.

Value

The dimension of the object.

Examples

## In 1D
pts <- matrix(c(3), ncol = 1, byrow = TRUE)
dimFace(pts)
pts <- matrix(c(1,3,4), ncol = 1, byrow = TRUE)
dimFace(pts)

## In 2D
pts <- matrix(c(3,3,6,3,3,6), ncol = 2, byrow = TRUE)
dimFace(pts)
pts <- matrix(c(1,1,2,2,3,3), ncol = 2, byrow = TRUE)
dimFace(pts)
pts <- matrix(c(0,0), ncol = 2, byrow = TRUE)
dimFace(pts)

## In 3D
pts <- c(3,3,3,6,3,3,3,6,3,6,6,3)
dimFace(pts, dim = 3)
pts <- matrix( c(1,1,1), ncol = 3, byrow = TRUE)
dimFace(pts)
pts <- matrix( c(1,1,1,2,2,2), ncol = 3, byrow = TRUE)
dimFace(pts)
pts <- matrix(c(2,2,2,3,2,2), ncol=3, byrow= TRUE)
dimFace(pts)
pts <- matrix(c(0,0,0,0,1,1,0,2,2,0,5,2,0,6,1), ncol = 3, byrow = TRUE)
dimFace(pts)
pts <- matrix(c(0,0,0,0,1,1,0,2,2,0,0,2,1,1,1), ncol = 3, byrow = TRUE)
dimFace(pts)

## In 4D
pts <- matrix(c(2,2,2,3,2,2,3,4,1,2,3,4), ncol=4, byrow= TRUE)
dimFace(pts,)

Finalize the RGL window.

Description

Finalize the RGL window.

Usage

finalize3D(...)

Arguments

...

Further arguments passed on the the RGL plotting functions. This must be done as lists. Currently the following arguments are supported:

Value

The RGL object (using rgl::highlevel()).

Examples


ini3D()
pts<-matrix(c(1,1,1,5,5,5), ncol = 3, byrow = TRUE)
plotPoints3D(pts)
finalize3D()

ini3D()
pts<-matrix(c(1,1,1,5,5,5), ncol = 3, byrow = TRUE)
plotPoints3D(pts)
finalize3D(argsAxes3d = list(edges = "bbox"))

The ggplot theme for the package

Description

The ggplot theme for the package

Usage

gMOIPTheme(...)

Arguments

...

Further arguments parsed to ggplot2::theme().

Value

The theme object.

Examples

pts <- matrix(c(1,1), ncol = 2, byrow = TRUE)
plotHull2D(pts)
pts1 <- matrix(c(2,2, 3,3), ncol = 2, byrow = TRUE)
pts2 <- matrix(c(1,1, 2,2, 0,1), ncol = 2, byrow = TRUE)
ggplot2::ggplot() +
  plotHull2D(pts2, drawPoints = TRUE, addText = "coord", drawPlot = FALSE) +
  plotHull2D(pts1, drawPoints = TRUE, drawPlot = FALSE) +
  gMOIPTheme() +
  ggplot2::xlab(expression(x[1])) +
  ggplot2::ylab(expression(x[2]))

Generate a sample of nondominated points.

Description

Generate a sample of nondominated points.

Usage

genNDSet(
  p,
  n,
  range = c(1, 100),
  random = FALSE,
  sphere = TRUE,
  planes = FALSE,
  box = FALSE,
  keepDom = FALSE,
  crit = "min",
  dubND = FALSE,
  classify = FALSE,
  ...
)

Arguments

p

Dimension of the points.

n

Number nondominated points generated.

range

The range of the points in each dimension (a vector or matrix with p rows).

random

Random sampling.

sphere

Generate points on a sphere.

planes

Generate points between two planes.

box

Generate points in boxes.

keepDom

Keep dominated points also.

crit

Criteria used (a vector of min/max).

dubND

Should duplicated non-dominated points be considered as non-dominated.

classify

Non-dominated points are classified into supported extreme (se), supported non-extreme (sne) and unsupported (us)

...

Further arguments passed on to genSample.

Value

A data frame with p+1 columns (last one indicate if dominated or not).

Examples


## Random
range <- matrix(c(1,100, 50, 100, 10, 50), ncol = 2, byrow = TRUE)
pts <- genNDSet(3, 5, range = range, random = TRUE, keepDom = TRUE)
head(pts)
Rfast::colMinsMaxs(as.matrix(pts[, 1:3]))
ini3D(FALSE, argsPlot3d = list(xlim = c(min(pts[,1])-2,max(pts[,1])+10),
  ylim = c(min(pts[,2])-2,max(pts[,2])+10),
  zlim = c(min(pts[,3])-2,max(pts[,3])+10)))
plotPoints3D(pts[,1:3])
plotPoints3D(pts[pts$nd,1:3], argsPlot3d = list(col = "red", size = 10))
plotCones3D(pts[pts$nd,1:3], argsPolygon3d = list(alpha = 1))
finalize3D()


## Between planes
range <- matrix(c(1,10000, 1,10000), ncol = 2, byrow = TRUE)
pts <- genNDSet(2, 50, range = range, planes = TRUE, classify = TRUE)
head(pts)
Rfast::colMinsMaxs(as.matrix(pts[, 1:2]))
plot(pts[, 1:2])

range <- matrix(c(1,100, 50,100, 10, 50), ncol = 2, byrow = TRUE)
center <- rowMeans(range)
planeU <- c(rep(1, 3), -1.2*sum(rowMeans(range)))
planeL <- c(rep(1, 3), -0.8*sum(rowMeans(range)))
pts <- genNDSet(3, 50, range = range, planes = TRUE, keepDom = TRUE, classify = TRUE,
   argsPlanes = list(center = center, planeU = planeU, planeL = planeL))
head(pts)
Rfast::colMinsMaxs(as.matrix(pts[, 1:3]))
ini3D(FALSE, argsPlot3d = list(xlim = c(min(pts[,1])-2,max(pts[,1])+10),
  ylim = c(min(pts[,2])-2,max(pts[,2])+10),
  zlim = c(min(pts[,3])-2,max(pts[,3])+10),
  box = TRUE, axes = TRUE))
plotPoints3D(pts[,1:3])
plotPoints3D(pts[pts$nd,1:3], argsPlot3d = list(col = "red", size = 10))
rgl::planes3d(planeL[1], planeL[2], planeL[3], planeL[4], alpha = 0.5)
rgl::planes3d(planeU[1], planeU[2], planeU[3], planeU[4], alpha = 0.5)
finalize3D()


## On a sphere
ini3D()
range <- c(1,100)
cent <- rep(range[1] + (range[2]-range[1])/2, 3)
pts <- genNDSet(3, 20, range = range, sphere = TRUE, keepDom = TRUE,
       argsSphere = list(center = cent))
rgl::spheres3d(cent, radius=49.5, color = "grey100", alpha=0.1)
plotPoints3D(pts)
plotPoints3D(pts[pts$nd,], argsPlot3d = list(col = "red", size = 10))
rgl::planes3d(cent[1],cent[2],cent[3],-sum(cent^2), alpha = 0.5, col = "red")
finalize3D()

ini3D()
cent <- c(100,100,100)
r <- 75
planeC <- c(cent+r/3)
planeC <- c(planeC, -sum(planeC^2))
pts <- genNDSet(3, 20, keepDom = TRUE,
  argsSphere = list(center = cent, radius = r, below = FALSE, plane = planeC, factor = 6))
rgl::spheres3d(cent, radius=r, color = "grey100", alpha=0.1)
plotPoints3D(pts)
plotPoints3D(pts[pts$nd,], argsPlot3d = list(col = "red", size = 10))
rgl::planes3d(planeC[1],planeC[2],planeC[3],planeC[4], alpha = 0.5, col = "red")
finalize3D()

Generate a sample of points in dimension $p$.

Description

Generate a sample of points in dimension $p$.

Usage

genSample(
  p,
  n,
  range = c(1, 100),
  random = FALSE,
  sphere = TRUE,
  planes = FALSE,
  box = FALSE,
  ...
)

Arguments

p

Dimension of the points.

n

Number of samples generated.

range

The range of the points in each dimension (a vector or matrix with p rows).

random

Random sampling.

sphere

Generate points on a sphere.

planes

Generate points between two planes.

box

Generate points in boxes.

...

Further arguments passed on to the method for generating points. This must be done as lists (see examples). Currently the following arguments are supported:

  • argsPlanes: A list of arguments for generating points between planes and in the cube defined by the range:

    • center: A point between the planes (default rowMeans(range)).

    • planeU: The upper plane (default c(rep(1, p), -1.2*sum(center))).

    • planeL: The lower plane (default c(rep(1, p), -0.8*sum(center))).

  • argsSphere: A list of arguments for generating points on a sphere:

    • radius: The radius of the sphere.

    • center: The center of the sphere.

    • plane: The plane used.

    • below: Either true (generate points below the plane), false (generate points above the plane) or NULL (generated on the whole sphere).

    • factor: If using a plane. Then the factor to multiply n with, so generate enough points below/above the plane.

    • closeToPlane: If TRUE only return points close to the plane.

  • argsBox: A list of arguments for generating points inside boxes:

    • intervals: Number of intervals to split the length of the range into. That is, each range is divided into intervals (sub)intervals and only the lowest/highest subrange is used.

    • cor: How to correlate indices. If 'idxAlt' then alternate the intervals (high/low) for each dimension. For instance if p = 3 and the first dimension is in the high interval range then the second will be in the low interval range and third in the high interval range again. If idxRand then choose the low/high interval range for each dimension based on prHigh. If idxSplit then select floor(p/2):ceiling(p/2) dimensions for the high interval range and the other for the low interval range.

    • prHigh: Probability for choosing the high interval range in each dimension.

Details

Note having ranges with different length when using the sphere method, doesn't make sense. The best option is properly to use a center and radius here. Moreover, as for higher p you may have to use a larger radius than half of the desired interval range.

Value

A matrix with p columns.

Examples

### Using random
## p = 2
range <- matrix(c(1,100, 50,100), ncol = 2, byrow = TRUE )
pts <- genSample(2, 1000, range = range, random = TRUE)
head(pts)
Rfast::colMinsMaxs(as.matrix(pts))
plot(pts)


## p = 3
range <- matrix(c(1,100, 50,100, 10,50), ncol = 2, byrow = TRUE )
ini3D()
pts <- genSample(3, 1000, range = range, random = TRUE)
head(pts)
Rfast::colMinsMaxs(as.matrix(pts))
plotPoints3D(pts)
finalize3D()


## other p
p <- 10
range <- c(1,100)
pts <- genSample(p, 1000, range = range, random = TRUE)
head(pts)
Rfast::colMinsMaxs(as.matrix(pts))


### Using planes
## p = 2
range <- matrix(c(1,100, 50,100), ncol = 2, byrow = TRUE )
center <- rowMeans(range)
planeU <- c(rep(1, 2), -1.5*sum(rowMeans(range)))
planeL <- c(rep(1, 2), -0.7*sum(rowMeans(range)))
pts <- genSample(2, 1000, range = range, planes = TRUE,
   argsPlanes = list(center = center, planeU = planeU, planeL = planeL))
head(pts)
Rfast::colMinsMaxs(as.matrix(pts))
plot(pts)


## p = 3
range <- matrix(c(1,100, 50,100, 10, 50), ncol = 2, byrow = TRUE )
center <- rowMeans(range)
planeU <- c(rep(1, 3), -1.2*sum(rowMeans(range)))
planeL <- c(rep(1, 3), -0.6*sum(rowMeans(range)))
pts <- genSample(3, 1000, range = range, planes = TRUE,
   argsPlanes = list(center = center, planeU = planeU, planeL = planeL))
head(pts)
Rfast::colMinsMaxs(as.matrix(pts))
ini3D(argsPlot3d = list(box = TRUE, axes = TRUE))
plotPoints3D(pts)
rgl::planes3d(planeL[1], planeL[2], planeL[3], planeL[4], alpha = 0.5)
rgl::planes3d(planeU[1], planeU[2], planeU[3], planeU[4], alpha = 0.5)
finalize3D()



### Using sphere
## p = 2
range <- c(1,100)
cent <- rep(range[1] + (range[2]-range[1])/2, 2)
pts <- genSample(2, 1000, range = range)
dim(pts)
Rfast::colMinsMaxs(as.matrix(pts))
plot(pts, asp=1)
abline(sum(cent^2)/cent[1], -cent[2]/cent[1])

cent <- c(100,100)
r <- 75
planeC <- c(cent+r/3)
planeC <- c(planeC, -sum(planeC^2))
pts <- genSample(2, 100,
  argsSphere = list(center = cent, radius = r, below = FALSE, plane = planeC, factor = 6))
dim(pts)
Rfast::colMinsMaxs(as.matrix(pts))
plot(pts, asp=1)
abline(-planeC[3]/planeC[1], -planeC[2]/planeC[1])

pts <- genSample(2, 100, argsSphere = list(center = cent, radius = r, below = NULL))
dim(pts)
Rfast::colMinsMaxs(as.matrix(pts))
plot(pts, asp=1)


## p = 3
ini3D()
range <- c(1,100)
cent <- rep(range[1] + (range[2]-range[1])/2, 3)
pts <- genSample(3, 1000, range = range)
dim(pts)
Rfast::colMinsMaxs(as.matrix(pts))
rgl::spheres3d(cent, radius=49.5, color = "grey100", alpha=0.1)
plotPoints3D(pts)
rgl::planes3d(cent[1],cent[2],cent[3],-sum(cent^2), alpha = 0.5, col = "red")
finalize3D()

ini3D()
cent <- c(100,100,100)
r <- 75
planeC <- c(cent+r/3)
planeC <- c(planeC, -sum(planeC^2))
pts <- genSample(3, 100,
  argsSphere = list(center = cent, radius = r, below = FALSE, plane = planeC, factor = 6))
rgl::spheres3d(cent, radius=r, color = "grey100", alpha=0.1)
plotPoints3D(pts)
rgl::planes3d(planeC[1],planeC[2],planeC[3],planeC[4], alpha = 0.5, col = "red")
finalize3D()

ini3D()
pts <- genSample(3, 10000, argsSphere = list(center = cent, radius = r, below = NULL))
Rfast::colMinsMaxs(as.matrix(pts))
rgl::spheres3d(cent, radius=r, color = "grey100", alpha=0.1)
plotPoints3D(pts)
finalize3D()


## Other p
p <- 10
cent <- rep(0,p)
r <- 100
pts <- genSample(p, 100000, argsSphere = list(center = cent, radius = r, below = NULL))
head(pts)
Rfast::colMinsMaxs(as.matrix(pts))
apply(pts,1, function(x){sqrt(sum((x-cent)^2))}) # test should be approx. equal to radius


### Using box
## p = 2
range <- matrix(c(1,100, 50,100), ncol = 2, byrow = TRUE )
pts <- genSample(2, 1000, range = range, box = TRUE, argsBox = list(cor = "idxAlt"))
head(pts)
Rfast::colMinsMaxs(as.matrix(pts))
plot(pts)

pts <- genSample(2, 1000, range = range, box = TRUE, argsBox = list(cor = "idxAlt",
                 intervals = 6))
plot(pts)

pts <- genSample(2, 1000, range = range, box = TRUE, argsBox = list(cor = "idxRand"))
plot(pts)
pts <- genSample(2, 1000, range = range, box = TRUE,
                 argsBox = list(cor = "idxRand", prHigh = c(0.1,0.6)))
points(pts, pch = 3, col = "red")
pts <- genSample(2, 1000, range = range, box = TRUE,
                 argsBox = list(cor = "idxRand", prHigh = c(0,0)))
points(pts, pch = 4, col = "blue")

pts <- genSample(2, 1000, range = range, box = TRUE, argsBox = list(cor = "idxSplit"))
plot(pts)


## p = 3
range <- matrix(c(1,100, 1,200, 1,50), ncol = 2, byrow = TRUE )
ini3D(argsPlot3d = list(box = TRUE, axes = TRUE))
pts <- genSample(3, 1000, range = range, box = TRUE, , argsBox = list(cor = "idxAlt"))
head(pts)
Rfast::colMinsMaxs(as.matrix(pts))
plotPoints3D(pts)
finalize3D()

ini3D(argsPlot3d = list(box = TRUE, axes = TRUE))
pts <- genSample(3, 1000, range = range, box = TRUE, ,
                 argsBox = list(cor = "idxAlt", intervals = 6))
plotPoints3D(pts)
finalize3D()

ini3D(argsPlot3d = list(box = TRUE, axes = TRUE))
pts <- genSample(3, 1000, range = range, box = TRUE, , argsBox = list(cor = "idxRand"))
plotPoints3D(pts)
pts <- genSample(3, 1000, range = range, box = TRUE, ,
                 argsBox = list(cor = "idxRand", prHigh = c(0.1,0.6,0.1)))
plotPoints3D(pts, argsPlot3d = list(col="red"))
finalize3D()

ini3D(argsPlot3d = list(box = TRUE, axes = TRUE))
pts <- genSample(3, 1000, range = range, box = TRUE, , argsBox = list(cor = "idxSplit"))
plotPoints3D(pts)
finalize3D()


## other p
p <- 10
range <- c(1,100)
pts <- genSample(p, 1000, range = range, box = TRUE, argsBox = list(cor = "idxSplit"))
head(pts)
Rfast::colMinsMaxs(as.matrix(pts))

Save a point symbol as a temporary file.

Description

Save a point symbol as a temporary file.

Usage

getTexture(pch = 16, cex = 10, ...)

Arguments

pch

Point number/symbol.

cex

Point size

...

Further arguments passed to plot.

Value

The file name.

Examples


# Pch shapes
generateRPointShapes<-function(){
   oldPar<-par()
   par(font=2, mar=c(0.5,0,0,0))
   y=rev(c(rep(1,6),rep(2,5), rep(3,5), rep(4,5), rep(5,5)))
   x=c(rep(1:5,5),6)
   plot(x, y, pch = 0:25, cex=1.5, ylim=c(1,5.5), xlim=c(1,6.5),
        axes=FALSE, xlab="", ylab="", bg="blue")
   text(x, y, labels=0:25, pos=3)
   par(mar=oldPar$mar,font=oldPar$font )
}
generateRPointShapes()

getTexture()

Find segments (lines) of a face.

Description

Find segments (lines) of a face.

Usage

hullSegment(
  vertices,
  hull = geometry::convhulln(vertices),
  tol = mean(mean(abs(vertices))) * sqrt(.Machine$double.eps)
)

Arguments

vertices

A ⁠m x p⁠ array of vertices of the convex hull, as used by geometry::convhulln().

hull

Tessellation (or triangulation) generated by geometry::convhulln() If hull is left empty or not supplied, then it will be generated.

tol

Tolerance on the tests for inclusion in the convex hull. You can think of tol as the distance a point may possibly lie outside the hull, and still be perceived as on the surface of the hull. Because of numerical slop nothing can ever be done exactly here. I might guess a semi-intelligent value of tol to be

⁠tol = 1.e-13*mean(abs(vertices(:)))⁠

In higher dimensions, the numerical issues of floating point arithmetic will probably suggest a larger value of tol.

Value

A matrix with segments.

Author(s)

Lars Relund lars@relund.dk

Efficient test for points inside a convex hull in p dimensions.

Description

Efficient test for points inside a convex hull in p dimensions.

Usage

inHull(
  pts,
  vertices,
  hull = NULL,
  tol = mean(mean(abs(as.matrix(vertices)))) * sqrt(.Machine$double.eps)
)

Arguments

pts

A nxp array to test, n data points, in dimension p. If you have many points to test, it is most efficient to call this function once with the entire set.

vertices

A mxp array of vertices of the convex hull. May contain redundant (non-vertex) points.

hull

Tessellation (or triangulation) generated by convhulln (only works if the dimension of the hull is p). If hull is NULL, then it will be generated.

tol

Tolerance on the tests for inclusion in the convex hull. You can think of tol as the difference a point value may be different from the values of the hull, and still be perceived as on the surface of the hull. Because of numerical slop nothing can ever be done exactly here. In higher dimensions, the numerical issues of floating point arithmetic will probably suggest a larger value of tol. tol is not used if the dimension of the hull is larger than one and not equal p.

Value

An integer vector of length n with values 1 (inside hull), -1 (outside hull) or 0 (on hull to precision indicated by tol).

Note

Some of the code are inspired by the Matlab code by John D'Errico and how to find a point inside a hull. If the dimension of the hull is below p then PCA may be used to check (a warning will be given).

Author(s)

Lars Relund lars@relund.dk

Examples

## In 1D
vertices <- matrix(4, ncol = 1)
pt <- matrix(c(2,4), ncol = 1, byrow = TRUE)
inHull(pt, vertices)
vertices <- matrix(c(1,4), ncol = 1)
pt <- matrix(c(1,3,4,5), ncol = 1, byrow = TRUE)
inHull(pt, vertices)

## In 2D
vertices <- matrix(c(2,4), ncol = 2)
pt <- matrix(c(2,4, 1,1), ncol = 2, byrow = TRUE)
inHull(pt, vertices)
vertices <- matrix(c(0,0, 3,3), ncol = 2, byrow = TRUE)
pt <- matrix(c(0,0, 1,1, 2,2, 3,3, 4,4), ncol = 2, byrow = TRUE)
inHull(pt, vertices)
vertices <- matrix(c(0,0, 0,3, 3,0), ncol = 2, byrow = TRUE)
pt <- matrix(c(0,0, 1,1, 4,4), ncol = 2, byrow = TRUE)
inHull(pt, vertices)


## in 3D
vertices <- matrix(c(2,2,2), ncol = 3, byrow = TRUE)
pt <- matrix(c(1,1,1, 3,3,3, 2,2,2, 3,3,2), ncol = 3, byrow = TRUE)
inHull(pt, vertices)

vertices <- matrix(c(2,2,2, 4,4,4), ncol = 3, byrow = TRUE)
ini3D()
plotHull3D(vertices)
pt <- matrix(c(1,1,1, 2,2,2, 3,3,3, 4,4,4, 3,3,2), ncol = 3, byrow = TRUE)
plotPoints3D(pt, addText = TRUE)
finalize3D()
inHull(pt, vertices)

vertices <- matrix(c(1,0,0, 1,1,0, 1,0,1), ncol = 3, byrow = TRUE)
ini3D()
plotHull3D(vertices)
pt <- matrix(c(1,0.1,0.2, 3,3,2), ncol = 3, byrow = TRUE)
plotPoints3D(pt, addText = TRUE)
finalize3D()
inHull(pt, vertices)

vertices <- matrix(c(2,2,2, 2,4,4, 2,2,4, 4,4,2, 4,2,2, 2,4,2, 4,2,4, 4,4,4), ncol = 3,
            byrow = TRUE)
ini3D()
plotHull3D(vertices)
pt <- matrix(c(1,1,1, 3,3,3, 2,2,2, 3,3,2), ncol = 3, byrow = TRUE)
plotPoints3D(pt, addText = TRUE)
finalize3D()
inHull(pt, vertices)


## In 5D
vertices <- matrix(c(4,0,0,0,0, 0,4,0,0,0, 0,0,4,0,0, 0,0,0,4,0, 0,0,0,0,4, 0,0,0,0,0),
            ncol = 5, byrow = TRUE)
pt <- matrix(c(0.1,0.1,0.1,0.1,0.1, 3,3,3,3,3, 2,0,0,0,0), ncol = 5, byrow = TRUE)
inHull(pt, vertices)

Initialize the RGL window.

Description

Initialize the RGL window.

Usage

ini3D(new = TRUE, clear = FALSE, ...)

Arguments

new

A new window is opened (otherwise the current is cleared).

clear

Clear the current RGL window.

...

Further arguments passed on the the RGL plotting functions. This must be done as lists. Currently the following arguments are supported:

Value

NULL (invisible).

Examples


ini3D()
pts<-matrix(c(1,1,1,5,5,5), ncol = 3, byrow = TRUE)
plotPoints3D(pts)
finalize3D()

lim <- c(-1, 7)
ini3D(argsPlot3d = list(xlim = lim, ylim = lim, zlim = lim))
plotPoints3D(pts)
finalize3D()

Integer points in the feasible region (Ax<=b).

Description

Integer points in the feasible region (Ax<=b).

Usage

integerPoints(A, b, nonneg = rep(TRUE, ncol(A)))

Arguments

A

Constraint matrix.

b

Right hand side.

nonneg

A boolean vector of same length as number of variables. If entry k is TRUE then variable k must be non-negative.

Value

A data frame with all integer points inside the feasible region.

Note

Do a simple enumeration of all integer points between min and max values found using the continuous polytope.

Author(s)

Lars Relund lars@relund.dk.

Examples

A <- matrix( c(3,-2, 1, 2, 4,-2,-3, 2, 1), nc = 3, byrow = TRUE)
b <- c(10, 12, 3)
integerPoints(A, b)

A <- matrix(c(9, 10, 2, 4, -3, 2), ncol = 2, byrow = TRUE)
b <- c(90, 27, 3)
integerPoints(A, b)

Help function to load the view angle for the RGL 3D plot from a file or matrix

Description

Help function to load the view angle for the RGL 3D plot from a file or matrix

Usage

loadView(
  fname = "view.RData",
  v = NULL,
  clear = TRUE,
  close = FALSE,
  zoom = 1,
  ...
)

Arguments

fname

The file name of the view.

v

The view matrix.

clear

Call rgl::clear3d().

close

Call rgl::close3d().

zoom

Zoom level.

...

Additional parameters passed to rgl::view3d().

Author(s)

Lars Relund lars@relund.dk

Examples


view <- matrix( c(-0.412063330411911, -0.228006735444069, 0.882166087627411, 0,
0.910147845745087, -0.0574885793030262, 0.410274744033813, 0, -0.042830865830183,
0.97196090221405, 0.231208890676498, 0, 0, 0, 0, 1), nc = 4)

loadView(v = view)
A <- matrix( c(3, 2, 5, 2, 1, 1, 1, 1, 3, 5, 2, 4), nc = 3, byrow = TRUE)
b <- c(55, 26, 30, 57)
obj <- c(20, 10, 15)
plotPolytope(A, b, plotOptimum = TRUE, obj = obj, labels = "coord")

# Try to modify the angle in the RGL window
saveView(print = TRUE)  # get the view angle to insert into R code

Merge two lists to one

Description

Merge two lists to one

Usage

mergeLists(a, b)

Arguments

a

First list.

b

Second list.

Plot a cone defined by a point in 2D.

Description

The cones are defined as the point plus/minus rays of R2.

Usage

plotCones2D(
  pts,
  drawPoint = TRUE,
  drawLines = TRUE,
  drawPolygons = TRUE,
  direction = 1,
  rectangle = FALSE,
  drawPlot = TRUE,
  m = apply(pts, 2, min) - 5,
  M = apply(pts, 2, max) + 5,
  ...
)

Arguments

pts

A matrix with a point in each row.

drawPoint

Draw the points defining the cone.

drawLines

Draw lines of the cone.

drawPolygons

Draw polygons of the cone.

direction

Ray direction. If i'th entry is positive, consider the i'th column of pts plus a value greater than on equal zero (minimize objective $i$). If negative, consider the i'th column of pts minus a value greater than on equal zero (maximize objective $i$).

rectangle

Draw the cone as a rectangle.

drawPlot

Draw the ggplot. Set to FALSE if you want to combine hulls in a single plot.

m

Minimum values of the bounding box.

M

Maximum values of the bounding box.

...

Further arguments passed to plotHull2D

Value

A ggplot object

Examples

library(ggplot2)
plotCones2D(c(4,4), drawLines = FALSE, drawPoint = TRUE,
           argsGeom_point = list(col = "red", size = 10),
           argsGeom_polygon = list(alpha = 0.5), rectangle = TRUE)
plotCones2D(c(1,1), rectangle = FALSE)
plotCones2D(matrix(c(3,3,2,2), ncol = 2, byrow = TRUE))

## The Danish flag
lst <- list(argsGeom_polygon = list(alpha = 0.85, fill = "red"),
            drawPlot = FALSE, drawPoint = FALSE, drawLines = FALSE)
p1 <- do.call(plotCones2D, args = c(list(c(2,4), direction = 1), lst))
p2 <- do.call(plotCones2D, args = c(list(c(1,2), direction = -1), lst))
p3 <- do.call(plotCones2D, args = c(list(c(2,2), direction = c(1,-1)), lst))
p4 <- do.call(plotCones2D, args = c(list(c(1,4), direction = c(-1,1)), lst))
ggplot() + p1 + p2 + p3 + p4 + theme_void()

Plot a cone defined by a point in 3D.

Description

The cones are defined as the point plus R3+.

Usage

plotCones3D(
  pts,
  drawPoint = TRUE,
  drawLines = TRUE,
  drawPolygons = TRUE,
  direction = 1,
  rectangle = FALSE,
  useRGLBBox = TRUE,
  ...
)

Arguments

pts

A matrix with a point in each row.

drawPoint

Draw the points defining the cone.

drawLines

Draw lines of the cone.

drawPolygons

Draw polygons of the cone.

direction

Ray direction. If i'th entry is positive, consider the i'th column of pts plus a value greater than on equal zero (minimize objective $i$). If negative, consider the i'th column of pts minus a value greater than on equal zero (maximize objective $i$).

rectangle

Draw the cone as a rectangle.

useRGLBBox

Use the RGL bounding box as ray limits for the cone.

...

Further arguments passed on the the RGL plotting functions. This must be done as lists (see examples). Currently the following arguments are supported:

Value

Object ids (invisible).

Examples


ini3D(argsPlot3d = list(xlim = c(0,6), ylim = c(0,6), zlim = c(0,6)))
plotCones3D(c(4,4,4), drawLines = FALSE, drawPoint = TRUE,
           argsPlot3d = list(col = "red", size = 10),
           argsPolygon3d = list(alpha = 1), rectangle = TRUE)
plotCones3D(c(1,1,1), rectangle = FALSE)
plotCones3D(matrix(c(3,3,3,2,2,2), ncol = 3, byrow = TRUE))
finalize3D()

ini3D(argsPlot3d = list(xlim = c(0,6), ylim = c(0,6), zlim = c(0,6)))
plotCones3D(c(4,4,4), direction = 1)
plotCones3D(c(2,2,2), direction = -1)
plotCones3D(c(4,2,2), direction = c(1,-1,-1))
ids <- plotCones3D(c(2,2,4), direction = c(-1,-1,1))
finalize3D()
# pop3d(id = ids) # remove last cone

Create a plot of the criterion space of a bi-objective problem

Description

Create a plot of the criterion space of a bi-objective problem

Usage

plotCriterion2D(
  A,
  b,
  obj,
  type = rep("c", ncol(A)),
  nonneg = rep(TRUE, ncol(A)),
  crit = "max",
  addTriangles = FALSE,
  addHull = TRUE,
  plotFeasible = TRUE,
  latex = FALSE,
  labels = NULL
)

Arguments

A

The constraint matrix.

b

Right hand side.

obj

A p x n matrix(one row for each criterion).

type

A character vector of same length as number of variables. If entry k is 'i' variable k must be integer and if 'c' continuous.

nonneg

A boolean vector of same length as number of variables. If entry k is TRUE then variable k must be non-negative.

crit

Either max or min (only used if add the iso-profit line).

addTriangles

Add search triangles defined by the non-dominated extreme points.

addHull

Add the convex hull and the rays.

plotFeasible

If True then plot the criterion points/slices.

latex

If true make latex math labels for TikZ.

labels

If NULL don't add any labels. If 'n' no labels but show the points. If equal coord add coordinates to the points. Otherwise number all points from one.

Value

The ggplot object.

Note

Currently only points are checked for dominance. That is, for MILP models some nondominated points may in fact be dominated by a segment.

Author(s)

Lars Relund lars@relund.dk

Examples

### Set up 2D plot
# Function for plotting the solution and criterion space in one plot (two variables)
plotBiObj2D <- function(A, b, obj,
   type = rep("c", ncol(A)),
   crit = "max",
   faces = rep("c", ncol(A)),
   plotFaces = TRUE,
   plotFeasible = TRUE,
   plotOptimum = FALSE,
   labels = "numb",
   addTriangles = TRUE,
   addHull = TRUE)
{
   p1 <- plotPolytope(A, b, type = type, crit = crit, faces = faces, plotFaces = plotFaces,
                      plotFeasible = plotFeasible, plotOptimum = plotOptimum, labels = labels)
   p2 <- plotCriterion2D(A, b, obj, type = type, crit = crit, addTriangles = addTriangles,
                         addHull = addHull, plotFeasible = plotFeasible, labels = labels)
   gridExtra::grid.arrange(p1, p2, nrow = 1)
}


### Bi-objective problem with two variables
A <- matrix(c(-3,2,2,4,9,10), ncol = 2, byrow = TRUE)
b <- c(3,27,90)

## LP model
obj <- matrix(
   c(7, -10, # first criterion
     -10, -10), # second criterion
   nrow = 2)
plotBiObj2D(A, b, obj, addTriangles = FALSE)


## ILP models with different criteria (maximize)
obj <- matrix(c(7, -10, -10, -10), nrow = 2)
plotBiObj2D(A, b, obj, type = rep("i", ncol(A)))
obj <- matrix(c(3, -1, -2, 2), nrow = 2)
plotBiObj2D(A, b, obj, type = rep("i", ncol(A)))
obj <- matrix(c(-7, -1, -5, 5), nrow = 2)
plotBiObj2D(A, b, obj, type = rep("i", ncol(A)))
obj <- matrix(c(-1, -1, 2, 2), nrow = 2)
plotBiObj2D(A, b, obj, type = rep("i", ncol(A)))

## ILP models with different criteria (minimize)
obj <- matrix(c(7, -10, -10, -10), nrow = 2)
plotBiObj2D(A, b, obj, type = rep("i", ncol(A)), crit = "min")
obj <- matrix(c(3, -1, -2, 2), nrow = 2)
plotBiObj2D(A, b, obj, type = rep("i", ncol(A)), crit = "min")
obj <- matrix(c(-7, -1, -5, 5), nrow = 2)
plotBiObj2D(A, b, obj, type = rep("i", ncol(A)), crit = "min")
obj <- matrix(c(-1, -1, 2, 2), nrow = 2)
plotBiObj2D(A, b, obj, type = rep("i", ncol(A)), crit = "min")


# More examples
## MILP model (x1 integer) with different criteria (maximize)
obj <- matrix(c(7, -10, -10, -10), nrow = 2)
plotBiObj2D(A, b, obj, type = c("i", "c"))
obj <- matrix(c(3, -1, -2, 2), nrow = 2)
plotBiObj2D(A, b, obj, type = c("i", "c"))
obj <- matrix(c(-7, -1, -5, 5), nrow = 2)
plotBiObj2D(A, b, obj, type = c("i", "c"))
obj <- matrix(c(-1, -1, 2, 2), nrow = 2)
plotBiObj2D(A, b, obj, type = c("i", "c"))

## MILP model (x2 integer) with different criteria (minimize)
obj <- matrix(c(7, -10, -10, -10), nrow = 2)
plotBiObj2D(A, b, obj, type = c("c", "i"), crit = "min")
obj <- matrix(c(3, -1, -2, 2), nrow = 2)
plotBiObj2D(A, b, obj, type = c("c", "i"), crit = "min")
obj <- matrix(c(-7, -1, -5, 5), nrow = 2)
plotBiObj2D(A, b, obj, type = c("c", "i"), crit = "min")
obj <- matrix(c(-1, -1, 2, 2), nrow = 2)
plotBiObj2D(A, b, obj, type = c("c", "i"), crit = "min")


### Set up 3D plot

# Function for plotting the solution and criterion space in one plot (three variables)
plotBiObj3D <- function(A, b, obj,
                        type = rep("c", ncol(A)),
                        crit = "max",
                        faces = rep("c", ncol(A)),
                        plotFaces = TRUE,
                        plotFeasible = TRUE,
                        plotOptimum = FALSE,
                        labels = "numb",
                        addTriangles = TRUE,
                        addHull = TRUE)
{
   plotPolytope(A, b, type = type, crit = crit, faces = faces, plotFaces = plotFaces,
                plotFeasible = plotFeasible, plotOptimum = plotOptimum, labels = labels)
   plotCriterion2D(A, b, obj, type = type, crit = crit, addTriangles = addTriangles,
                   addHull = addHull, plotFeasible = plotFeasible, labels = labels)
}

### Bi-objective problem with three variables
loadView <- function(fname = "view.RData", v = NULL) {
   if (!is.null(v)) {
      rgl::view3d(userMatrix = v)
   } else {
      if (file.exists(fname)) {
         load(fname)
         rgl::view3d(userMatrix = view)
      } else {
         warning(paste0("Can'TRUE load view in file ", fname, "!"))
      }
   }
}

## Ex
view <- matrix( c(-0.452365815639496, -0.446501553058624, 0.77201122045517, 0, 0.886364221572876,
                  -0.320795893669128, 0.333835482597351, 0, 0.0986008867621422, 0.835299551486969,
                  0.540881276130676, 0, 0, 0, 0, 1), nc = 4)
loadView(v = view)
Ab <- matrix( c(
   1, 1, 2, 5,
   2, -1, 0, 3,
   -1, 2, 1, 3,
   0, -3, 5, 2
), nc = 4, byrow = TRUE)
A <- Ab[,1:3]
b <- Ab[,4]
obj <- matrix(c(1, -6, 3, -4, 1, 6), nrow = 2)

# LP model
plotBiObj3D(A, b, obj, crit = "min", addTriangles = FALSE)

# ILP model
plotBiObj3D(A, b, obj, type = c("i","i","i"), crit = "min")

# MILP model
plotBiObj3D(A, b, obj, type = c("c","i","i"), crit = "min")
plotBiObj3D(A, b, obj, type = c("i","c","i"), crit = "min")
plotBiObj3D(A, b, obj, type = c("i","i","c"), crit = "min")
plotBiObj3D(A, b, obj, type = c("i","c","c"), crit = "min")
plotBiObj3D(A, b, obj, type = c("c","i","c"), crit = "min")
plotBiObj3D(A, b, obj, type = c("c","c","i"), crit = "min")


## Ex
view <- matrix( c(0.976349174976349, -0.202332556247711, 0.0761845782399178, 0, 0.0903248339891434,
                  0.701892614364624, 0.706531345844269, 0, -0.196427255868912, -0.682940244674683,
                  0.703568696975708, 0, 0, 0, 0, 1), nc = 4)
loadView(v = view)
A <- matrix( c(
   -1, 1, 0,
   1, 4, 0,
   2, 1, 0,
   3, -4, 0,
   0, 0, 4
), nc = 3, byrow = TRUE)
b <- c(5, 45, 27, 24, 10)
obj <- matrix(c(1, -6, 3, -4, 1, 6), nrow = 2)

# LP model
plotBiObj3D(A, b, obj, crit = "min", addTriangles = FALSE, labels = "coord")

# ILP model
plotBiObj3D(A, b, obj, type = c("i","i","i"))

# MILP model
plotBiObj3D(A, b, obj, type = c("c","i","i"))
plotBiObj3D(A, b, obj, type = c("i","c","i"), plotFaces = FALSE)
plotBiObj3D(A, b, obj, type = c("i","i","c"))
plotBiObj3D(A, b, obj, type = c("i","c","c"), plotFaces = FALSE)
plotBiObj3D(A, b, obj, type = c("c","i","c"), plotFaces = FALSE)
plotBiObj3D(A, b, obj, type = c("c","c","i"))


## Ex
view <- matrix( c(-0.812462985515594, -0.029454167932272, 0.582268416881561, 0, 0.579295456409454,
                  -0.153386667370796, 0.800555109977722, 0, 0.0657325685024261, 0.987727105617523,
                  0.14168381690979, 0, 0, 0, 0, 1), nc = 4)
loadView(v = view)
A <- matrix( c(
   1, 1, 1,
   3, 0, 1
), nc = 3, byrow = TRUE)
b <- c(10, 24)
obj <- matrix(c(1, -6, 3, -4, 1, 6), nrow = 2)

# LP model
plotBiObj3D(A, b, obj, crit = "min", addTriangles = FALSE, labels = "coord")

# ILP model
plotBiObj3D(A, b, obj, type = c("i","i","i"), crit = "min", labels = "n")

# MILP model
plotBiObj3D(A, b, obj, type = c("c","i","i"), crit = "min")
plotBiObj3D(A, b, obj, type = c("i","c","i"), crit = "min")
plotBiObj3D(A, b, obj, type = c("i","i","c"), crit = "min")
plotBiObj3D(A, b, obj, type = c("i","c","c"), crit = "min")
plotBiObj3D(A, b, obj, type = c("c","i","c"), crit = "min", plotFaces = FALSE)
plotBiObj3D(A, b, obj, type = c("c","c","i"), crit = "min", plotFaces = FALSE)


## Ex
view <- matrix( c(-0.412063330411911, -0.228006735444069, 0.882166087627411, 0, 0.910147845745087,
                  -0.0574885793030262, 0.410274744033813, 0, -0.042830865830183, 0.97196090221405,
                  0.231208890676498, 0, 0, 0, 0, 1), nc = 4)
loadView(v = view)
A <- matrix( c(
3, 2, 5,
2, 1, 1,
1, 1, 3,
5, 2, 4
), nc = 3, byrow = TRUE)
b <- c(55, 26, 30, 57)
obj <- matrix(c(1, -6, 3, -4, 1, -1), nrow = 2)

# LP model
plotBiObj3D(A, b, obj, crit = "min", addTriangles = FALSE, labels = "coord")

# ILP model
plotBiObj3D(A, b, obj, type = c("i","i","i"), crit = "min", labels = "n")

# MILP model
plotBiObj3D(A, b, obj, type = c("c","i","i"), crit = "min", labels = "n")
plotBiObj3D(A, b, obj, type = c("i","c","i"), crit = "min", labels = "n", plotFaces = FALSE)
plotBiObj3D(A, b, obj, type = c("i","i","c"), crit = "min", labels = "n")
plotBiObj3D(A, b, obj, type = c("i","c","c"), crit = "min", labels = "n")
plotBiObj3D(A, b, obj, type = c("c","i","c"), crit = "min", labels = "n", plotFaces = FALSE)
plotBiObj3D(A, b, obj, type = c("c","c","i"), crit = "min", labels = "n")

Plot the convex hull of a set of points in 2D.

Description

Plot the convex hull of a set of points in 2D.

Usage

plotHull2D(
  pts,
  drawPoints = FALSE,
  drawLines = TRUE,
  drawPolygons = TRUE,
  addText = FALSE,
  addRays = FALSE,
  direction = 1,
  drawPlot = TRUE,
  drawBBoxHull = FALSE,
  m = apply(pts, 2, min) - 5,
  M = apply(pts, 2, max) + 5,
  ...
)

Arguments

pts

A matrix with a point in each row.

drawPoints

Draw the points.

drawLines

Draw lines of the facets.

drawPolygons

Fill the hull.

addText

Add text to the points. Currently coord (coordinates), rownames (rownames) and both supported or a vector with text.

addRays

Add the ray defined by direction.

direction

Ray direction. If i'th entry is positive, consider the i'th column of pts plus a value greater than on equal zero (minimize objective $i$). If negative, consider the i'th column of pts minus a value greater than on equal zero (maximize objective $i$).

drawPlot

Draw the ggplot. Set to FALSE if you want to combine hulls in a single plot.

drawBBoxHull

If addRays then draw the hull areas hitting the bounding box also.

m

Minimum values of the bounding box.

M

Maximum values of the bounding box.

...

Further arguments passed on the the ggplot plotting functions. This must be done as lists. Currently the following arguments are supported:

Value

The ggplot object if drawPlot = TRUE; otherwise, a list of ggplot components.

Examples

library(ggplot2)
pts<-matrix(c(1,1), ncol = 2, byrow = TRUE)
plotHull2D(pts)
pts1<-matrix(c(2,2, 3,3), ncol = 2, byrow = TRUE)
plotHull2D(pts1, drawPoints = TRUE)
plotHull2D(pts1, drawPoints = TRUE, addRays = TRUE, addText = "coord")
plotHull2D(pts1, drawPoints = TRUE, addRays = TRUE, addText = "coord", drawBBoxHull = TRUE)
plotHull2D(pts1, drawPoints = TRUE, addRays = TRUE, direction = -1, addText = "coord")
pts2<-matrix(c(1,1, 2,2, 0,1), ncol = 2, byrow = TRUE)
plotHull2D(pts2, drawPoints = TRUE, addText = "coord")
plotHull2D(pts2, drawPoints = TRUE, addRays = TRUE, addText = "coord")
plotHull2D(pts2, drawPoints = TRUE, addRays = TRUE, direction = -1, addText = "coord")
## Combine hulls
ggplot() +
  plotHull2D(pts2, drawPoints = TRUE, addText = "coord", drawPlot = FALSE) +
  plotHull2D(pts1, drawPoints = TRUE, drawPlot = FALSE) +
  gMOIPTheme() +
  xlab(expression(x[1])) +
  ylab(expression(x[2]))

# Plotting an LP
A <- matrix(c(-3,2,2,4,9,10), ncol = 2, byrow = TRUE)
b <- c(3,27,90)
obj <- c(7.75, 10)
pts3 <- cornerPoints(A, b)
plotHull2D(pts3, drawPoints = TRUE, addText = "coord", argsGeom_polygon = list(fill = "red"))

Plot the convex hull of a set of points in 3D.

Description

Plot the convex hull of a set of points in 3D.

Usage

plotHull3D(
  pts,
  drawPoints = FALSE,
  drawLines = TRUE,
  drawPolygons = TRUE,
  addText = FALSE,
  addRays = FALSE,
  useRGLBBox = TRUE,
  direction = 1,
  drawBBoxHull = TRUE,
  ...
)

Arguments

pts

A matrix with a point in each row.

drawPoints

Draw the points.

drawLines

Draw lines of the facets.

drawPolygons

Fill the facets.

addText

Add text to the points. Currently coord (coordinates), rownames (rownames) and both supported or a vector with text.

addRays

Add the ray defined by direction.

useRGLBBox

Use the RGL bounding box when add rays.

direction

Ray direction. If i'th entry is positive, consider the i'th column of pts plus a value greater than on equal zero (minimize objective $i$). If negative, consider the i'th column of pts minus a value greater than on equal zero (maximize objective $i$).

drawBBoxHull

If addRays then draw the hull areas hitting the bounding box also.

...

Further arguments passed on the the RGL plotting functions. This must be done as lists (see examples). Currently the following arguments are supported:

Value

A list with hull, pts classified and object ids (invisible).

Examples


ini3D()
pts<-matrix(c(0,0,0), ncol = 3, byrow = TRUE)
plotHull3D(pts) # a point
pts<-matrix(c(1,1,1,2,2,2,3,3,3), ncol = 3, byrow = TRUE)
plotHull3D(pts, drawPoints = TRUE) # a line
pts<-matrix(c(1,0,0,1,1,1,1,2,2,3,1,1,3,3,3), ncol = 3, byrow = TRUE)
plotHull3D(pts, drawLines = FALSE, argsPolygon3d = list(alpha=0.6)) # a polygon
pts<-matrix(c(5,5,5,10,10,5,10,5,5,5,5,10), ncol = 3, byrow = TRUE)
lst <- plotHull3D(pts, argsPolygon3d = list(alpha=0.9), argsSegments3d = list(color="red"))
finalize3D()
# pop3d(id = lst$ids) # remove last hull

## Using addRays
pts <- data.frame(x = c(1,3), y = c(1,3), z = c(1,3))
ini3D(argsPlot3d = list(xlim = c(0,max(pts$x)+10),
  ylim = c(0,max(pts$y)+10),
  zlim = c(0,max(pts$z)+10)))
plotHull3D(pts, drawPoints = TRUE, addRays = TRUE, , drawBBoxHull = FALSE)
plotHull3D(c(4,4,4), drawPoints = TRUE, addRays = TRUE)
finalize3D()

pts <- data.frame(x = c(4,2.5,1), y = c(1,2.5,4), z = c(1,2.5,4))
ini3D(argsPlot3d = list(xlim = c(0,max(pts$x)+10),
  ylim = c(0,max(pts$y)+10),
  zlim = c(0,max(pts$z)+10)))
plotHull3D(pts, drawPoints = TRUE, addRays = TRUE)
finalize3D()

pts <- matrix(c(
  0, 4, 8,
  0, 8, 4,
  8, 4, 0,
  4, 8, 0,
  4, 0, 8,
  8, 0, 4,
  4, 4, 4,
  6, 6, 6
  ), ncol = 3, byrow = TRUE)
ini3D(FALSE, argsPlot3d = list(xlim = c(min(pts[,1])-2,max(pts[,1])+10),
  ylim = c(min(pts[,2])-2,max(pts[,2])+10),
  zlim = c(min(pts[,3])-2,max(pts[,3])+10)))
plotHull3D(pts, drawPoints = TRUE, addText = "coord")
plotHull3D(pts, addRays = TRUE)
finalize3D()

pts <- genNDSet(3, 100, dubND = FALSE)
pts <- as.data.frame(pts[,1:3])

ini3D(argsPlot3d = list(
  xlim = c(0,max(pts[,1])+10),
  ylim = c(0,max(pts[,2])+10),
  zlim = c(0,max(pts[,3])+10)))
plotHull3D(pts, drawPoints = TRUE, addRays = TRUE)
finalize3D()

ini3D(argsPlot3d = list(
  xlim = c(0,max(pts[,1])+10),
  ylim = c(0,max(pts[,2])+10),
  zlim = c(0,max(pts[,3])+10)))
plotHull3D(pts, drawPoints = TRUE, drawPolygons = TRUE, addText = "coord", addRays = TRUE)
finalize3D()

ini3D(argsPlot3d = list(
  xlim = c(0,max(pts[,1])+10),
  ylim = c(0,max(pts[,2])+10),
  zlim = c(0,max(pts[,3])+10)))
plotHull3D(pts, drawPoints = TRUE, drawLines = FALSE,
  argsPolygon3d = list(alpha = 1), addRays = TRUE)
finalize3D()

ini3D(argsPlot3d = list(
  xlim = c(0,max(pts[,1])+10),
  ylim = c(0,max(pts[,2])+10),
  zlim = c(0,max(pts[,3])+10)))
plotHull3D(pts, drawPoints = TRUE, argsPolygon3d = list(color = "red"), addRays = TRUE)
plotCones3D(pts, argsPolygon3d = list(alpha = 1), rectangle = TRUE)
finalize3D()

Plot the lines of a linear mathematical program (Ax = b)

Description

Plot the lines of a linear mathematical program (Ax = b)

Usage

plotLines2D(A, b, nonneg = rep(TRUE, ncol(A)), latex = FALSE, ...)

Arguments

A

The constraint matrix.

b

Right hand side.

nonneg

A boolean vector of same length as number of variables. If entry k is TRUE then variable k must be non-negative and the line is plotted too.

latex

If True make latex math labels for TikZ.

...

Further arguments passed on the the ggplot plotting functions. This must be done as lists. Currently the following arguments are supported:

Value

A ggplot object.

Note

In general you will properly use plotPolytope() instead of this function.

Author(s)

Lars Relund lars@relund.dk

See Also

plotPolytope().

Plot TeX in the margin

Description

Plot TeX in the margin

Usage

plotMTeX3D(tex, edge, line = 0, at = NULL, pos = NA, ...)

Arguments

tex

TeX string

edge

The position at which to draw the axis or text.

line

The “line” of the plot margin to draw the label on.

at

The value of a coordinate at which to draw the axis.

pos

The position at which to draw the axis or text.

...

Further arguments passed to plotTeX3D().

Value

The object IDs of objects added to the scene.

Create a plot of a discrete non-dominated set.

Description

Create a plot of a discrete non-dominated set.

Usage

plotNDSet2D(
  points,
  crit,
  addTriangles = FALSE,
  addHull = TRUE,
  latex = FALSE,
  labels = NULL
)

Arguments

points

Data frame with non-dominated points.

crit

Either max or min (only used if add the iso-profit line). A vector is currently not supported.

addTriangles

Add search triangles defined by the non-dominated extreme points.

addHull

Add the convex hull and the rays.

latex

If true make latex math labels for TikZ.

labels

If NULL don't add any labels. If 'n' no labels but show the points. If equal coord add coordinates to the points. Otherwise number all points from one.

Value

The ggplot object.

Note

Currently only points are checked for dominance. That is, for MILP models some nondominated points may in fact be dominated by a segment.

Author(s)

Lars Relund lars@relund.dk

Examples

dat <- data.frame(z1=c(12,14,16,18,18,18,14,15,15), z2=c(18,16,12,4,2,6,14,14,16))
points <- addNDSet(dat, crit = "min", keepDom = TRUE)
plotNDSet2D(points, crit = "min", addTriangles = TRUE)
plotNDSet2D(points, crit = "min", addTriangles = FALSE)
plotNDSet2D(points, crit = "min", addTriangles = TRUE, addHull = FALSE)
points <- addNDSet(dat, crit = "max", keepDom = TRUE)
plotNDSet2D(points, crit = "max", addTriangles = TRUE)
plotNDSet2D(points, crit = "max", addHull = FALSE)

Plot a plane in 3D.

Description

Plot a plane in 3D.

Usage

plotPlane3D(
  normal,
  point = NULL,
  offset = 0,
  useShade = TRUE,
  useLines = FALSE,
  usePoints = FALSE,
  ...
)

Arguments

normal

Normal to the plane.

point

A point on the plane.

offset

The offset of the plane (only used if point = NULL).

useShade

Plot shade of the plane.

useLines

Plot lines inside the plane.

usePoints

Plot point shapes inside the plane.

...

Further arguments passed on the the RGL plotting functions. This must be done as lists (see examples). Currently the following arguments are supported:

  • argsPlanes3d: A list of arguments for rgl::planes3d() used when useShade = TRUE.

  • argsLines: A list of arguments for rgl::persp3d() when useLines = TRUE. Moreover, the list may contain lines: number of lines.

Value

NULL (invisible)

Examples


ini3D(argsPlot3d = list(xlim = c(-1,10), ylim = c(-1,10), zlim = c(-1,10)) )
plotPlane3D(c(1,1,1), point = c(1,1,1))
plotPoints3D(c(1,1,1))
plotPlane3D(c(1,2,1), point = c(2,2,2), argsPlanes3d = list(color="red"))
plotPoints3D(c(2,2,2))
plotPlane3D(c(2,1,1), offset = -6, argsPlanes3d = list(color="blue"))
plotPlane3D(c(2,1,1), argsPlanes3d = list(color="green"))
finalize3D()

ini3D(argsPlot3d = list(xlim = c(-1,10), ylim = c(-1,10), zlim = c(-1,10)) )
plotPlane3D(c(1,1,1), point = c(1,1,1), useLines = TRUE, useShade = TRUE)
ids <- plotPlane3D(c(1,2,1), point = c(2,2,2), argsLines = list(col="blue", lines = 100),
            useLines = TRUE)
finalize3D()
# pop3d(id = ids) # remove last plane

Plot points in 3D.

Description

Plot points in 3D.

Usage

plotPoints3D(pts, addText = FALSE, ...)

Arguments

pts

A vector or matrix with the points.

addText

Add text to the points. Currently coord (coordinates), rownames (rownames) and both supported or a vector with the text.

...

Further arguments passed on the the RGL plotting functions. This must be done as lists (see examples). Currently the following arguments are supported:

Value

Object ids (invisible).

Examples


ini3D()
pts<-matrix(c(1,1,1,5,5,5), ncol = 3, byrow = TRUE)
plotPoints3D(pts)
plotPoints3D(c(2,3,3), argsPlot3d = list(col = "red", size = 10))
plotPoints3D(c(3,2,3), argsPlot3d = list(col = "blue", size = 10, type="p"))
plotPoints3D(c(1.5,1.5,1.5), argsPlot3d = list(col = "blue", size = 10, type="p"))
plotPoints3D(c(2,2,2, 1,1,1), addText = "coord")
ids <- plotPoints3D(c(3,3,3, 4,4,4), addText = "rownames")
finalize3D()
rgl::rglwidget()
# pop3d(ids) # remove the last again

Plot a polygon.

Description

Plot a polygon.

Usage

plotPolygon3D(
  pts,
  useShade = TRUE,
  useLines = FALSE,
  usePoints = FALSE,
  useFrame = TRUE,
  ...
)

Arguments

pts

Vertices.

useShade

Plot shade of the polygon.

useLines

Plot lines inside the polygon.

usePoints

Plot point shapes inside the polygon.

useFrame

Plot a frame around the polygon.

...

Further arguments passed on the RGL plotting functions. This must be done as lists (see examples). Currently the following arguments are supported:

  • argsShade: A list of arguments for rgl::polygon3d (n > 4 vertices), rgl::triangles3d() (n = 3 vertices) and rgl::quads3d() (n = 4 vertices) if useShade = TRUE.

  • argsFrame: A list of arguments for rgl::lines3d if useFrame = TRUE.

  • argsPoints: A list of arguments for rgl::shade3d if usePoints = TRUE. It is important to give a texture using texture. A texture can be set using getTexture().

  • argsLines: A list of arguments for rgl::persp3d() when useLines = TRUE. Moreover, the list may contain lines: number of lines.

Value

Object ids (invisible).

Examples


pts <- data.frame(x = c(1,0,0,0.4), y = c(0,1,0,0.3), z = c(0,0,1,0.3))
pts <- data.frame(x = c(1,0,0), y = c(0,1,0), z = c(0,0,1))

ini3D()
plotPolygon3D(pts)
finalize3D()

ini3D()
plotPolygon3D(pts, argsShade = list(color = "red", alpha = 1))
finalize3D()

ini3D()
plotPolygon3D(pts, useFrame = TRUE, argsShade = list(color = "red", alpha = 0.5),
              argsFrame = list(color = "green"))
finalize3D()

ini3D()
plotPolygon3D(pts, useFrame = TRUE, useLines = TRUE, useShade = TRUE,
              argsShade = list(color = "red", alpha = 0.2),
              argsLines = list(color = "blue"))
finalize3D()

ini3D()
ids <- plotPolygon3D(pts, usePoints = TRUE, useFrame = TRUE,
              argsPoints = list(texture = getTexture(pch = 16, cex = 20)))
finalize3D()
# pop3d(id = ids) # remove object again

# In general you have to finetune size and numbers when you use textures
# Different pch
for (i in 0:3) {
  fname <- getTexture(pch = 15+i, cex = 30)
  ini3D(TRUE)
  plotPolygon3D(pts, usePoints = TRUE, argsPoints = list(texture = fname))
  finalize3D()
}

# Size of pch
for (i in 1:4) {
  fname <- getTexture(pch = 15+i, cex = 10 * i)
  ini3D(TRUE)
  plotPolygon3D(pts, usePoints = TRUE, argsPoints = list(texture = fname))
  finalize3D()
}

# Number of pch
fname <- getTexture(pch = 16, cex = 20)
for (i in 1:4) {
  ini3D(TRUE)
  plotPolygon3D(pts, usePoints = TRUE,
                argsPoints = list(texture = fname, texcoords = rbind(pts$x, pts$y, pts$z)*5*i))
  finalize3D()
}

Plot the polytope (bounded convex set) of a linear mathematical program (Ax <= b)

Description

This is a wrapper function calling plotPolytope2D() (2D graphics) and plotPolytope3D() (3D graphics).

Usage

plotPolytope(
  A,
  b,
  obj = NULL,
  type = rep("c", ncol(A)),
  nonneg = rep(TRUE, ncol(A)),
  crit = "max",
  faces = type,
  plotFaces = TRUE,
  plotFeasible = TRUE,
  plotOptimum = FALSE,
  latex = FALSE,
  labels = NULL,
  ...
)

Arguments

A

The constraint matrix.

b

Right hand side.

obj

A vector with objective coefficients.

type

A character vector of same length as number of variables. If entry k is 'i' variable k must be integer and if 'c' continuous.

nonneg

A boolean vector of same length as number of variables. If entry k is TRUE then variable k must be non-negative.

crit

Either max or min (only used if add the iso-profit line)

faces

A character vector of same length as number of variables. If entry k is 'i' variable k must be integer and if 'c' continuous. Useful if e.g. want to show the linear relaxation of an IP.

plotFaces

If True then plot the faces.

plotFeasible

If True then plot the feasible points/segments (relevant for IPLP/MILP).

plotOptimum

Show the optimum corner solution point (if alternative solutions only one is shown) and add the iso-profit line.

latex

If True make latex math labels for TikZ.

labels

If NULL don't add any labels. If 'n' no labels but show the points. If equal coord add coordinates to the points. Otherwise number all points from one.

...

If 2D, further arguments passed on the the ggplot plotting functions. This must be done as lists. Currently the following arguments are supported:

If 3D further arguments passed on the the RGL plotting functions. This must be done as lists. Currently the following arguments are supported:

  • argsAxes3d: A list of arguments for rgl::axes3d.

  • argsPlot3d: A list of arguments for rgl::plot3d to open the RGL window.

  • argsTitle3d: A list of arguments for rgl::title3d.

  • argsFaces: A list of arguments for plotHull3D.

  • argsFeasible: A list of arguments for RGL functions:

  • argsLabels: A list of arguments for RGL functions:

  • argsOptimum: A list of arguments for RGL functions:

Value

If 2D a ggplot object. If 3D a RGL window with the 3D plot.

Note

The feasible region defined by the constraints must be bounded (i.e. no extreme rays) otherwise you may see strange results.

Author(s)

Lars Relund lars@relund.dk

Examples

#### 2D examples ####
# Define the model max/min coeff*x st. Ax<=b, x>=0
A <- matrix(c(-3,2,2,4,9,10), ncol = 2, byrow = TRUE)
b <- c(3,27,90)
obj <- c(7.75, 10)

## LP model
# The polytope with the corner points
plotPolytope(
   A,
   b,
   obj,
   type = rep("c", ncol(A)),
   crit = "max",
   faces = rep("c", ncol(A)),
   plotFaces = TRUE,
   plotFeasible = TRUE,
   plotOptimum = FALSE,
   labels = NULL,
   argsFaces = list(argsGeom_polygon = list(fill = "red"))
)
# With optimum and labels:
plotPolytope(
   A,
   b,
   obj,
   type = rep("c", ncol(A)),
   crit = "max",
   faces = rep("c", ncol(A)),
   plotFaces = TRUE,
   plotFeasible = TRUE,
   plotOptimum = TRUE,
   labels = "coord",
   argsOptimum = list(lty="solid")
)
# Minimize:
plotPolytope(
   A,
   b,
   obj,
   type = rep("c", ncol(A)),
   crit = "min",
   faces = rep("c", ncol(A)),
   plotFaces = TRUE,
   plotFeasible = TRUE,
   plotOptimum = TRUE,
   labels = "n"
)
# Note return a ggplot so can e.g. add other labels on e.g. the axes:
p <- plotPolytope(
   A,
   b,
   obj,
   type = rep("c", ncol(A)),
   crit = "max",
   faces = rep("c", ncol(A)),
   plotFaces = TRUE,
   plotFeasible = TRUE,
   plotOptimum = TRUE,
   labels = "coord"
)
p + ggplot2::xlab("x") + ggplot2::ylab("y")

# More examples

## LP-model with no non-negativity constraints
A <- matrix(c(-3, 2, 2, 4, 9, 10, 1, -2), ncol = 2, byrow = TRUE)
b <- c(3, 27, 90, 2)
obj <- c(7.75, 10)
plotPolytope(
   A,
   b,
   obj,
   type = rep("c", ncol(A)),
   nonneg = rep(FALSE, ncol(A)),
   crit = "max",
   faces = rep("c", ncol(A)),
   plotFaces = TRUE,
   plotFeasible = TRUE,
   plotOptimum = FALSE,
   labels = NULL
)



## The package don't plot feasible regions that are unbounded e.g if we drop the 2 and 3 constraint
A <- matrix(c(-3,2), ncol = 2, byrow = TRUE)
b <- c(3)
obj <- c(7.75, 10)
# Wrong plot
plotPolytope(
   A,
   b,
   obj,
   type = rep("c", ncol(A)),
   crit = "max",
   faces = rep("c", ncol(A)),
   plotFaces = TRUE,
   plotFeasible = TRUE,
   plotOptimum = FALSE,
   labels = NULL
)
# One solution is to add a bounding box and check if the bounding box is binding
A <- rbind(A, c(1,0), c(0,1))
b <- c(b, 10, 10)
plotPolytope(
   A,
   b,
   obj,
   type = rep("c", ncol(A)),
   crit = "max",
   faces = rep("c", ncol(A)),
   plotFaces = TRUE,
   plotFeasible = TRUE,
   plotOptimum = FALSE,
   labels = NULL
)


## ILP model
A <- matrix(c(-3,2,2,4,9,10), ncol = 2, byrow = TRUE)
b <- c(3,27,90)
obj <- c(7.75, 10)
# ILP model with LP faces:
plotPolytope(
   A,
   b,
   obj,
   type = rep("i", ncol(A)),
   crit = "max",
   faces = rep("c", ncol(A)),
   plotFaces = TRUE,
   plotFeasible = TRUE,
   plotOptimum = TRUE,
   labels = "coord",
   argsLabels = list(size = 4, color = "blue"),
   argsFeasible = list(color = "red", size = 3)
)
#ILP model with IP faces:
plotPolytope(
   A,
   b,
   obj,
   type = rep("i", ncol(A)),
   crit = "max",
   faces = rep("i", ncol(A)),
   plotFaces = TRUE,
   plotFeasible = TRUE,
   plotOptimum = TRUE,
   labels = "coord"
)


## MILP model
A <- matrix(c(-3,2,2,4,9,10), ncol = 2, byrow = TRUE)
b <- c(3,27,90)
obj <- c(7.75, 10)
# Second coordinate integer
plotPolytope(
   A,
   b,
   obj,
   type = c("c", "i"),
   crit = "max",
   faces = c("c", "i"),
   plotFaces = FALSE,
   plotFeasible = TRUE,
   plotOptimum = TRUE,
   labels = "coord",
   argsFeasible = list(color = "red")
)
# First coordinate integer and with LP faces:
plotPolytope(
   A,
   b,
   obj,
   type = c("i", "c"),
   crit = "max",
   faces = c("c", "c"),
   plotFaces = TRUE,
   plotFeasible = TRUE,
   plotOptimum = TRUE,
   labels = "coord"
)
# First coordinate integer and with LP faces:
plotPolytope(
   A,
   b,
   obj,
   type = c("i", "c"),
   crit = "max",
   faces = c("i", "c"),
   plotFaces = TRUE,
   plotFeasible = TRUE,
   plotOptimum = TRUE,
   labels = "coord"
)




#### 3D examples ####

# Ex 1
view <- matrix( c(-0.412063330411911, -0.228006735444069, 0.882166087627411, 0, 0.910147845745087,
                  -0.0574885793030262, 0.410274744033813, 0, -0.042830865830183, 0.97196090221405,
                  0.231208890676498, 0, 0, 0, 0, 1), nc = 4)
loadView(v = view)
A <- matrix( c(
   3, 2, 5,
   2, 1, 1,
   1, 1, 3,
   5, 2, 4
), nc = 3, byrow = TRUE)
b <- c(55, 26, 30, 57)
obj <- c(20, 10, 15)
# LP model
plotPolytope(A, b, plotOptimum = TRUE, obj = obj, labels = "coord")
plotPolytope(A, b, plotOptimum = TRUE, obj = obj, labels = "coord",
             argsFaces = list(drawLines = FALSE, argsPolygon3d = list(alpha = 0.95)),
             argsLabels = list(points3d = list(color = "blue")))
# ILP model
plotPolytope(A, b, faces = c("c","c","c"), type = c("i","i","i"), plotOptimum = TRUE, obj = obj)
# MILP model
plotPolytope(A, b, faces = c("c","c","c"), type = c("i","c","i"), plotOptimum = TRUE, obj = obj)
plotPolytope(A, b, faces = c("c","c","c"), type = c("c","i","i"), plotOptimum = TRUE, obj = obj)
plotPolytope(A, b, faces = c("c","c","c"), type = c("i","i","c"), plotOptimum = TRUE, obj = obj)
plotPolytope(A, b, faces = c("c","c","c"), type = c("i","i","c"), plotFaces = FALSE)
plotPolytope(A, b, type = c("i","c","c"), plotOptimum = TRUE, obj = obj, plotFaces = FALSE)
plotPolytope(A, b, type = c("c","i","c"), plotOptimum = TRUE, obj = obj, plotFaces = FALSE)
plotPolytope(A, b, type = c("c","c","i"), plotOptimum = TRUE, obj = obj, plotFaces = FALSE)

# Ex 2
view <- matrix( c(-0.812462985515594, -0.029454167932272, 0.582268416881561, 0, 0.579295456409454,
                  -0.153386667370796, 0.800555109977722, 0, 0.0657325685024261, 0.987727105617523,
                  0.14168381690979, 0, 0, 0, 0, 1), nc = 4)
loadView(v = view)
A <- matrix( c(
   1, 1, 1,
   3, 0, 1
), nc = 3, byrow = TRUE)
b <- c(10, 24)
obj <- c(20, 10, 15)
plotPolytope(A, b, plotOptimum = TRUE, obj = obj, labels = "coord")
# ILP model
plotPolytope(A, b, faces = c("c","c","c"), type = c("i","i","i"), plotOptimum = TRUE, obj = obj)
# MILP model
plotPolytope(A, b, faces = c("c","c","c"), type = c("i","c","i"), plotOptimum = TRUE, obj = obj)
plotPolytope(A, b, faces = c("c","c","c"), type = c("c","i","i"), plotOptimum = TRUE, obj = obj)
plotPolytope(A, b, faces = c("c","c","c"), type = c("i","i","c"), plotOptimum = TRUE, obj = obj)
plotPolytope(A, b, faces = c("c","c","c"), type = c("i","i","c"), plotFaces = FALSE)
plotPolytope(A, b, type = c("i","c","c"), plotOptimum = TRUE, obj = obj, plotFaces = FALSE)
plotPolytope(A, b, type = c("c","i","c"), plotOptimum = TRUE, obj = obj, plotFaces = FALSE)
plotPolytope(A, b, type = c("c","c","i"), plotOptimum = TRUE, obj = obj, plotFaces = FALSE)

# Ex 3
view <- matrix( c(0.976349174976349, -0.202332556247711, 0.0761845782399178, 0, 0.0903248339891434,
                  0.701892614364624, 0.706531345844269, 0, -0.196427255868912, -0.682940244674683,
                  0.703568696975708, 0, 0, 0, 0, 1), nc = 4)
loadView(v = view)
A <- matrix( c(
   -1, 1, 0,
   1, 4, 0,
   2, 1, 0,
   3, -4, 0,
   0, 0, 4
), nc = 3, byrow = TRUE)
b <- c(5, 45, 27, 24, 10)
obj <- c(5, 45, 15)
plotPolytope(A, b, plotOptimum = TRUE, obj = obj, labels = "coord")
# ILP model
plotPolytope(A, b, faces = c("c","c","c"), type = c("i","i","i"), plotOptimum = TRUE, obj = obj)
# MILP model
plotPolytope(A, b, faces = c("c","c","c"), type = c("i","c","i"), plotOptimum = TRUE, obj = obj)
plotPolytope(A, b, faces = c("c","c","c"), type = c("c","i","i"), plotOptimum = TRUE, obj = obj)
plotPolytope(A, b, faces = c("c","c","c"), type = c("i","i","c"), plotOptimum = TRUE, obj = obj)
plotPolytope(A, b, faces = c("c","c","c"), type = c("i","i","c"), plotFaces = FALSE)
plotPolytope(A, b, type = c("i","c","c"), plotOptimum = TRUE, obj = obj, plotFaces = FALSE)
plotPolytope(A, b, type = c("c","i","c"), plotOptimum = TRUE, obj = obj, plotFaces = FALSE)
plotPolytope(A, b, type = c("c","c","i"), plotOptimum = TRUE, obj = obj, plotFaces = FALSE)

# Ex 4
view <- matrix( c(-0.452365815639496, -0.446501553058624, 0.77201122045517, 0, 0.886364221572876,
                  -0.320795893669128, 0.333835482597351, 0, 0.0986008867621422, 0.835299551486969,
                  0.540881276130676, 0, 0, 0, 0, 1), nc = 4)
loadView(v = view)
Ab <- matrix( c(
   1, 1, 2, 5,
   2, -1, 0, 3,
   -1, 2, 1, 3,
   0, -3, 5, 2
   #   0, 1, 0, 4,
   #   1, 0, 0, 4
), nc = 4, byrow = TRUE)
A <- Ab[,1:3]
b <- Ab[,4]
obj = c(1,1,3)
plotPolytope(A, b, plotOptimum = TRUE, obj = obj, labels = "coord")
# ILP model
plotPolytope(A, b, faces = c("c","c","c"), type = c("i","i","i"), plotOptimum = TRUE, obj = obj)
# MILP model
plotPolytope(A, b, faces = c("c","c","c"), type = c("i","c","i"), plotOptimum = TRUE, obj = obj)
plotPolytope(A, b, faces = c("c","c","c"), type = c("c","i","i"), plotOptimum = TRUE, obj = obj)
plotPolytope(A, b, faces = c("c","c","c"), type = c("i","i","c"), plotOptimum = TRUE, obj = obj)
plotPolytope(A, b, faces = c("c","c","c"), type = c("i","i","c"), plotFaces = FALSE)
plotPolytope(A, b, type = c("i","c","c"), plotOptimum = TRUE, obj = obj, plotFaces = FALSE)
plotPolytope(A, b, type = c("c","i","c"), plotOptimum = TRUE, obj = obj, plotFaces = FALSE)
plotPolytope(A, b, faces = c("c","c","c"), type = c("c","c","i"), plotOptimum = TRUE, obj = obj)

Plot the polytope (bounded convex set) of a linear mathematical program

Description

Plot the polytope (bounded convex set) of a linear mathematical program

Usage

plotPolytope2D(
  A,
  b,
  obj = NULL,
  type = rep("c", ncol(A)),
  nonneg = rep(TRUE, ncol(A)),
  crit = "max",
  faces = rep("c", ncol(A)),
  plotFaces = TRUE,
  plotFeasible = TRUE,
  plotOptimum = FALSE,
  latex = FALSE,
  labels = NULL,
  ...
)

Arguments

A

The constraint matrix.

b

Right hand side.

obj

A vector with objective coefficients.

type

A character vector of same length as number of variables. If entry k is 'i' variable k must be integer and if 'c' continuous.

nonneg

A boolean vector of same length as number of variables. If entry k is TRUE then variable k must be non-negative.

crit

Either max or min (only used if add the iso-profit line)

faces

A character vector of same length as number of variables. If entry k is 'i' variable k must be integer and if 'c' continuous. Useful if e.g. want to show the linear relaxation of an IP.

plotFaces

If True then plot the faces.

plotFeasible

If True then plot the feasible points/segments (relevant for ILP/MILP).

plotOptimum

Show the optimum corner solution point (if alternative solutions only one is shown) and add the iso-profit line.

latex

If True make latex math labels for TikZ.

labels

If NULL don't add any labels. If 'n' no labels but show the points. If equal coord add coordinates to the points. Otherwise number all points from one.

...

Further arguments passed on the the ggplot plotting functions. This must be done as lists. Currently the following arguments are supported:

Value

A ggplot object.

Note

In general use plotPolytope() instead of this function. The feasible region defined by the constraints must be bounded otherwise you may see strange results.

Author(s)

Lars Relund lars@relund.dk

See Also

plotPolytope() for examples.

Plot the polytope (bounded convex set) of a linear mathematical program

Description

Plot the polytope (bounded convex set) of a linear mathematical program

Usage

plotPolytope3D(
  A,
  b,
  obj = NULL,
  type = rep("c", ncol(A)),
  nonneg = rep(TRUE, ncol(A)),
  crit = "max",
  faces = rep("c", ncol(A)),
  plotFaces = TRUE,
  plotFeasible = TRUE,
  plotOptimum = FALSE,
  latex = FALSE,
  labels = NULL,
  ...
)

Arguments

A

The constraint matrix.

b

Right hand side.

obj

A vector with objective coefficients.

type

A character vector of same length as number of variables. If entry k is 'i' variable k must be integer and if 'c' continuous.

nonneg

A boolean vector of same length as number of variables. If entry k is TRUE then variable k must be non-negative.

crit

Either max or min (only used if add the iso-profit line)

faces

A character vector of same length as number of variables. If entry k is 'i' variable k must be integer and if 'c' continuous. Useful if e.g. want to show the linear relaxation of an IP.

plotFaces

If True then plot the faces.

plotFeasible

If True then plot the feasible points/segments (relevant for ILP/MILP).

plotOptimum

Show the optimum corner solution point (if alternative solutions only one is shown) and add the iso-profit line.

latex

If True make latex math labels for TikZ.

labels

If NULL don't add any labels. If 'n' no labels but show the points. If equal coord add coordinates to the points. Otherwise number all points from one.

...

Further arguments passed on the the RGL plotting functions. This must be done as lists. Currently the following arguments are supported:

  • argsAxes3d: A list of arguments for rgl::axes3d.

  • argsPlot3d: A list of arguments for rgl::plot3d to open the RGL window.

  • argsTitle3d: A list of arguments for rgl::title3d.

  • argsFaces: A list of arguments for plotHull3D.

  • argsFeasible: A list of arguments for RGL functions:

  • argsLabels: A list of arguments for RGL functions:

  • argsOptimum: A list of arguments for RGL functions:

Value

A RGL window with 3D plot.

Note

In general use plotPolytope() instead of this function. The feasible region defined by the constraints must be bounded otherwise you may see strange results.

Author(s)

Lars Relund lars@relund.dk

See Also

plotPolytope() for examples.

Plot a rectangle defined by two corner points.

Description

The rectangle is defined by {x|a <= x <= b} where a is the minimum values and b is the maximum values.

Usage

plotRectangle3D(a, b, ...)

Arguments

a

A vector of length 3.

b

A vector of length 3.

...

Further arguments passed on the the RGL plotting functions. This must be done as lists (see examples). Currently the following arguments are supported:

Value

Object ids (invisible).

Examples


ini3D()
plotRectangle3D(c(0,0,0), c(1,1,1))
plotRectangle3D(c(1,1,1), c(4,4,3), drawPoints = TRUE, drawLines = FALSE,
           argsPlot3d = list(size=2, type="s", alpha=0.3))
ids <- plotRectangle3D(c(2,2,2), c(3,3,2.5), argsPolygon3d = list(alpha = 1) )
finalize3D()
# pop3d(id = ids) remove last object

Plot TeX at a position.

Description

Plot TeX at a position.

Usage

plotTeX3D(
  x,
  y,
  z,
  tex,
  cex = graphics::par("cex"),
  fixedSize = FALSE,
  size = 480,
  ...
)

Arguments

x

Coordinate.

y

Coordinate.

z

Coordinate.

tex

TeX string.

cex

Expansion factor (you properly have to fine tune it).

fixedSize

Fix the size of the object (no scaling when zoom).

size

Size of the generated png.

...

Arguments passed on to rgl::sprites3d() and texToPng().

Value

The shape ID of the displayed object is returned.

Examples

## Not run: 
tex0 <- "$\\mathbb{R}_{\\geqq}$"
tex1 <- "\\LaTeX"
tex2 <- "This is a title"
ini3D(argsPlot3d = list(xlim = c(0, 2), ylim = c(0, 2), zlim = c(0, 2)))
plotTeX3D(0.75,0.75,0.75, tex0)
plotTeX3D(0.5,0.5,0.5, tex0, cex = 2)
plotTeX3D(1,1,1, tex2)
finalize3D()
ini3D(new = TRUE, argsPlot3d = list(xlim = c(0, 200), ylim = c(0, 200), zlim = c(0, 200)))
plotTeX3D(75,75,75, tex0)
plotTeX3D(50,50,50, tex1)
plotTeX3D(100,100,100, tex2)
finalize3D()

## End(Not run)

Draw boxes, axes and other text outside the data using TeX strings.

Description

Draw boxes, axes and other text outside the data using TeX strings.

Usage

plotTitleTeX3D(
  main = NULL,
  sub = NULL,
  xlab = NULL,
  ylab = NULL,
  zlab = NULL,
  line = NA,
  ...
)

Arguments

main

The main title for the plot.

sub

The subtitle for the plot.

xlab

The axis labels for the plot .

ylab

The axis labels for the plot .

zlab

The axis labels for the plot .

line

The “line” of the plot margin to draw the label on.

...

Additional parameters which are passed to plotMTeX3D().

Details

The rectangular prism holding the 3D plot has 12 edges. They are identified using 3 character strings. The first character (⁠x', ⁠y', or ⁠z') selects the direction of the axis. The next two characters are each ⁠-' or ⁠+', selecting the lower or upper end of one of the other coordinates. If only one or two characters are given, the remaining characters default to ⁠-'. For example edge = 'x+' draws an x-axis at the high level of y and the low level of z.

By default, rgl::axes3d() uses the rgl::bbox3d() function to draw the axes. The labels will move so that they do not obscure the data. Alternatively, a vector of arguments as described above may be used, in which case fixed axes are drawn using rgl::axis3d().

If pos is a numeric vector of length 3, edge determines the direction of the axis and the tick marks, and the values of the other two coordinates in pos determine the position. See the examples.

Value

The object IDs of objects added to the scene.

Examples

## Not run: 
ini3D(argsPlot3d = list(xlim = c(0, 2), ylim = c(0, 2), zlim = c(0, 2)))
plotTitleTeX3D(main = "\\LaTeX", sub = "subtitle $\\alpha$",
               xlab = "$x^1_2$", ylab = "$\\beta$", zlab = "$x\\cdot y$")
finalize3D()

## End(Not run)

To size of the png file.

Description

To size of the png file.

Usage

pngSize(png)

Arguments

png

Png file name.

Value

A list with width and height.

Help function to save the view angle for the RGL 3D plot

Description

Help function to save the view angle for the RGL 3D plot

Usage

saveView(fname = "view.RData", overwrite = FALSE, print = FALSE)

Arguments

fname

The file name of the view.

overwrite

Overwrite existing file.

print

Print the view so can be copied to R code (no file is saved).

Value

NULL (invisible).

Note

Only save if the file name don't exists.

Author(s)

Lars Relund lars@relund.dk

Examples


view <- matrix( c(-0.412063330411911, -0.228006735444069, 0.882166087627411, 0,
0.910147845745087, -0.0574885793030262, 0.410274744033813, 0, -0.042830865830183,
0.97196090221405, 0.231208890676498, 0, 0, 0, 0, 1), nc = 4)

loadView(v = view)
A <- matrix( c(3, 2, 5, 2, 1, 1, 1, 1, 3, 5, 2, 4), nc = 3, byrow = TRUE)
b <- c(55, 26, 30, 57)
obj <- c(20, 10, 15)
plotPolytope(A, b, plotOptimum = TRUE, obj = obj, labels = "coord")

# Try to modify the angle in the RGL window
saveView(print = TRUE)  # get the view angle to insert into R code

Find all corner points in the slices define for each fixed integer combination.

Description

Find all corner points in the slices define for each fixed integer combination.

Usage

slices(
  A,
  b,
  type = rep("c", ncol(A)),
  nonneg = rep(TRUE, ncol(A)),
  collapse = FALSE
)

Arguments

A

The constraint matrix.

b

Right hand side.

type

A character vector of same length as number of variables. If entry k is 'i' variable k must be integer and if 'c' continuous.

nonneg

A boolean vector of same length as number of variables. If entry k is TRUE then variable k must be non-negative.

collapse

Collapse list to a data frame with unique points.

Value

A list with the corner points (one entry for each slice).

Examples

A <- matrix( c(3, -2, 1,2, 4, -2,-3, 2, 1), nc = 3, byrow = TRUE)
b <- c(10,12,3)
slices(A, b, type=c("i","c","i"))

A <- matrix(c(9,10,2,4,-3,2), ncol = 2, byrow = TRUE)
b <- c(90,27,3)
slices(A, b, type=c("c","i"), collapse = TRUE)

Convert LaTeX to a png file

Description

Convert LaTeX to a png file

Usage

texToPng(
  tex,
  width = NULL,
  height = NULL,
  dpi = 72,
  viewPng = FALSE,
  fontsize = 12,
  calcM = FALSE,
  crop = FALSE
)

Arguments

tex

TeX string. Remember to escape backslash with \.

width

Width of the png.

height

Height of the png (width are ignored).

dpi

Dpi of the png. Not used if width or height are specified.

viewPng

View the result in the plots window.

fontsize

Front size used in the LaTeX document.

calcM

Estimate 1 em in pixels in the resulting png.

crop

Call command line program pdfcrop (must be installed).

Value

The filename of the png or a list if calcM = TRUE.

Examples

## Not run: 
tex <- "$\\mathbb{R}_{\\geqq}$"
texToPng(tex, viewPng = TRUE)
texToPng(tex, fontsize = 20, viewPng = TRUE)
texToPng(tex, height = 50, fontsize = 10, viewPng = TRUE)
texToPng(tex, height = 50, fontsize = 50, viewPng = TRUE)
tex <- "MMM"
texToPng(tex, dpi=72, calcM = TRUE)
texToPng(tex, width = 100, calcM = TRUE)
f <- texToPng(tex, dpi=300)
pngSize(f)

## End(Not run)