Title: | 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. |
Authors: | Lars Relund Nielsen [aut, cre] |
Maintainer: | Lars Relund Nielsen <[email protected]> |
License: | GPL (>= 3.3.2) |
Version: | 1.5.4 |
Built: | 2024-10-26 03:36:50 UTC |
Source: | CRAN |
Add discrete points to a non-dominated set and classify them into extreme supported, non-extreme supported, non-supported.
addNDSet( pts, nDSet = NULL, crit = "max", keepDom = FALSE, dubND = FALSE, classify = TRUE )
addNDSet( pts, nDSet = NULL, crit = "max", keepDom = FALSE, dubND = FALSE, classify = TRUE )
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 |
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 ( |
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
.
Lars Relund [email protected]
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)
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 all points on the bounding box hit by the rays.
addRays( pts, m = apply(pts, 2, min) - 5, M = apply(pts, 2, max) + 5, direction = 1 )
addRays( pts, m = apply(pts, 2, min) - 5, M = apply(pts, 2, max) + 5, direction = 1 )
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 |
The points merged with the points on the bounding box. The column pt
equals 1 if
points from pts
and zero otherwise.
Assume that pts
has been checked using .checkPts()
.
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)
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).
binaryPoints(A, b)
binaryPoints(A, b)
A |
Constraint matrix. |
b |
Right hand side. |
A data frame with all binary points inside the feasible region.
Do a simple enumeration of all binary points. Will not work if ncol(A)
large.
Lars Relund [email protected].
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)
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
classifyNDSet(pts, direction = 1)
classifyNDSet(pts, direction = 1)
pts |
A set of non-dominated points. It is assumed that |
direction |
Ray direction. If i'th entry is positive, consider the i'th column of the |
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
).
It is assumed that pts
are nondominated.
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
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
classifyNDSetExtreme(pts, direction = 1)
classifyNDSetExtreme(pts, direction = 1)
pts |
A set of non-dominated points. It is assumed that |
direction |
Ray direction. If i'th entry is positive, consider the i'th column of the |
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
).
It is assumed that pts
are nondominated. This algorithm is faster than classifyNDSet()
,
since only check for extreme points.
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
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.
convexHull( pts, addRays = FALSE, useRGLBBox = FALSE, direction = 1, tol = mean(mean(abs(pts))) * sqrt(.Machine$double.eps) * 2, m = apply(pts, 2, min) - 5, M = apply(pts, 2, max) + 5 )
convexHull( pts, addRays = FALSE, useRGLBBox = FALSE, direction = 1, tol = mean(mean(abs(pts))) * sqrt(.Machine$double.eps) * 2, m = apply(pts, 2, min) - 5, M = apply(pts, 2, max) + 5 )
pts |
A matrix with a point in each row. |
addRays |
Add the ray defined by |
useRGLBBox |
Use the RGL bounding box when add rays. |
direction |
Ray direction. If i'th entry is positive, consider the i'th column of |
tol |
Tolerance on standard deviation if using PCA. |
m |
Minimum values of the bounding box. |
M |
Maximum values of the bounding box. |
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.
## 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()
## 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.
cornerPoints(A, b, type = rep("c", ncol(A)), nonneg = rep(TRUE, ncol(A)))
cornerPoints(A, b, type = rep("c", ncol(A)), nonneg = rep(TRUE, ncol(A)))
A |
Constraint matrix. |
b |
Right hand side. |
type |
A character vector of same length as number of variables. If
entry k is 'i' variable |
nonneg |
A boolean vector of same length as number of variables. If entry k is TRUE then variable k must be non-negative. |
A data frame with a corner point in each row.
Lars Relund [email protected]
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"))
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.
cornerPointsCont(A, b, nonneg = rep(TRUE, ncol(A)))
cornerPointsCont(A, b, nonneg = rep(TRUE, ncol(A)))
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. |
A data frame with a corner point in each row.
Lars Relund [email protected]
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.
criterionPoints(pts, obj, crit, labels = "coord")
criterionPoints(pts, obj, crit, labels = "coord")
pts |
A data frame with a column for each variable in the solution
space (can also be a |
obj |
A p x n matrix(one row for each criterion). |
crit |
Either |
labels |
If |
A data frame with columns x1, ..., xn, z1, ..., zp, lbl (label), nD (non-dominated), ext (extreme), nonExt (non-extreme supported)
.
Lars Relund [email protected]
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")
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.
df2String(df, round = 2)
df2String(df, round = 2)
df |
Data frame. |
round |
How many digits to round |
A vector of strings.
Return the dimension of the convex hull of a set of points.
dimFace(pts, dim = NULL)
dimFace(pts, dim = NULL)
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. |
The dimension of the object.
## 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,)
## 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.
finalize3D(...)
finalize3D(...)
... |
Further arguments passed on the the RGL plotting functions. This must be done as lists. Currently the following arguments are supported:
|
The RGL object (using rgl::highlevel()
).
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"))
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"))
Generate a sample of nondominated points.
genNDSet( p, n, range = c(1, 100), random = FALSE, sphere = TRUE, planes = FALSE, box = FALSE, keepDom = FALSE, crit = "min", dubND = FALSE, classify = FALSE, ... )
genNDSet( p, n, range = c(1, 100), random = FALSE, sphere = TRUE, planes = FALSE, box = FALSE, keepDom = FALSE, crit = "min", dubND = FALSE, classify = FALSE, ... )
p |
Dimension of the points. |
n |
Number nondominated points generated. |
range |
The range of the points in each dimension (a vector or matrix with |
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 ( |
... |
Further arguments passed on to |
A data frame with p+1
columns (last one indicate if dominated or not).
## 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$nd,], argsPlot3d = list(col = "red", size = 10)) rgl::planes3d(planeC[1],planeC[2],planeC[3],planeC[4], alpha = 0.5, col = "red") finalize3D()
## Random range <- matrix(c(1,100, 50, 100, 10, 50), ncol = 2, byrow = TRUE) pts <- genNDSet(3, 5, range = range, random = TRUE, keepDom = TRUE) head(pts) Rfast::colMinsMaxs(as.matrix(pts[, 1:3])) ini3D(FALSE, argsPlot3d = list(xlim = c(min(pts[,1])-2,max(pts[,1])+10), ylim = c(min(pts[,2])-2,max(pts[,2])+10), zlim = c(min(pts[,3])-2,max(pts[,3])+10))) plotPoints3D(pts[,1:3]) plotPoints3D(pts[pts$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 $p$.
genSample( p, n, range = c(1, 100), random = FALSE, sphere = TRUE, planes = FALSE, box = FALSE, ... )
genSample( p, n, range = c(1, 100), random = FALSE, sphere = TRUE, planes = FALSE, box = FALSE, ... )
p |
Dimension of the points. |
n |
Number of samples generated. |
range |
The range of the points in each dimension (a vector or matrix with |
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:
|
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.
A matrix with p
columns.
### 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))
### 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.
getTexture(pch = 16, cex = 10, ...)
getTexture(pch = 16, cex = 10, ...)
pch |
Point number/symbol. |
cex |
Point size |
... |
Further arguments passed to |
The file name.
# 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()
# 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()
ggplot
theme for the packageThe ggplot
theme for the package
gMOIPTheme(...)
gMOIPTheme(...)
... |
Further arguments parsed to |
The theme object.
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]))
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]))
Find segments (lines) of a face.
hullSegment( vertices, hull = geometry::convhulln(vertices), tol = mean(mean(abs(vertices))) * sqrt(.Machine$double.eps) )
hullSegment( vertices, hull = geometry::convhulln(vertices), tol = mean(mean(abs(vertices))) * sqrt(.Machine$double.eps) )
vertices |
A |
hull |
Tessellation (or triangulation) generated by |
tol |
Tolerance on the tests for inclusion in the convex hull. You can
think of
In higher dimensions, the numerical issues of floating point arithmetic
will probably suggest a larger value of |
A matrix with segments.
Lars Relund [email protected]
Efficient test for points inside a convex hull in p dimensions.
inHull( pts, vertices, hull = NULL, tol = mean(mean(abs(as.matrix(vertices)))) * sqrt(.Machine$double.eps) )
inHull( pts, vertices, hull = NULL, tol = mean(mean(abs(as.matrix(vertices)))) * sqrt(.Machine$double.eps) )
pts |
A |
vertices |
A |
hull |
Tessellation (or triangulation) generated by |
tol |
Tolerance on the tests for inclusion in the convex hull. You can think of |
An integer vector of length with values 1 (inside hull), -1 (outside hull) or 0
(on hull to precision indicated by
tol
).
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 then PCA may be used to check (a
warning will be given).
Lars Relund [email protected]
## 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)
## 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.
ini3D(new = TRUE, clear = FALSE, ...)
ini3D(new = TRUE, clear = FALSE, ...)
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:
|
NULL (invisible).
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()
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).
integerPoints(A, b, nonneg = rep(TRUE, ncol(A)))
integerPoints(A, b, nonneg = rep(TRUE, ncol(A)))
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. |
A data frame with all integer points inside the feasible region.
Do a simple enumeration of all integer points between min and max values found using the continuous polytope.
Lars Relund [email protected].
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)
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
loadView( fname = "view.RData", v = NULL, clear = TRUE, close = FALSE, zoom = 1, ... )
loadView( fname = "view.RData", v = NULL, clear = TRUE, close = FALSE, zoom = 1, ... )
fname |
The file name of the view. |
v |
The view matrix. |
clear |
Call |
close |
Call |
zoom |
Zoom level. |
... |
Additional parameters passed to |
Lars Relund [email protected]
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
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
mergeLists(a, b)
mergeLists(a, b)
a |
First list. |
b |
Second list. |
The cones are defined as the point plus/minus rays of R2.
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, ... )
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, ... )
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 |
rectangle |
Draw the cone as a rectangle. |
drawPlot |
Draw the |
m |
Minimum values of the bounding box. |
M |
Maximum values of the bounding box. |
... |
Further arguments passed to plotHull2D |
A ggplot
object
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()
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()
The cones are defined as the point plus R3+.
plotCones3D( pts, drawPoint = TRUE, drawLines = TRUE, drawPolygons = TRUE, direction = 1, rectangle = FALSE, useRGLBBox = TRUE, ... )
plotCones3D( pts, drawPoint = TRUE, drawLines = TRUE, drawPolygons = TRUE, direction = 1, rectangle = FALSE, useRGLBBox = TRUE, ... )
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 |
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:
|
Object ids (invisible).
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
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
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 )
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 )
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 |
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 |
latex |
If true make latex math labels for TikZ. |
labels |
If |
The ggplot
object.
Currently only points are checked for dominance. That is, for MILP models some nondominated points may in fact be dominated by a segment.
Lars Relund [email protected]
### 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")
### 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.
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, ... )
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, ... )
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 |
addRays |
Add the ray defined by |
direction |
Ray direction. If i'th entry is positive, consider the i'th column of |
drawPlot |
Draw the |
drawBBoxHull |
If |
m |
Minimum values of the bounding box. |
M |
Maximum values of the bounding box. |
... |
Further arguments passed on the the
|
The ggplot
object if drawPlot = TRUE
; otherwise, a list of ggplot
components.
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"))
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.
plotHull3D( pts, drawPoints = FALSE, drawLines = TRUE, drawPolygons = TRUE, addText = FALSE, addRays = FALSE, useRGLBBox = TRUE, direction = 1, drawBBoxHull = TRUE, ... )
plotHull3D( pts, drawPoints = FALSE, drawLines = TRUE, drawPolygons = TRUE, addText = FALSE, addRays = FALSE, useRGLBBox = TRUE, direction = 1, drawBBoxHull = TRUE, ... )
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 |
addRays |
Add the ray defined by |
useRGLBBox |
Use the RGL bounding box when add rays. |
direction |
Ray direction. If i'th entry is positive, consider the i'th column of |
drawBBoxHull |
If |
... |
Further arguments passed on the the RGL plotting functions. This must be done as lists (see examples). Currently the following arguments are supported:
|
A list with hull, pts
classified and object ids (invisible).
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$z)+10))) plotHull3D(pts, drawPoints = TRUE, addRays = TRUE) finalize3D() pts <- matrix(c( 0, 4, 8, 0, 8, 4, 8, 4, 0, 4, 8, 0, 4, 0, 8, 8, 0, 4, 4, 4, 4, 6, 6, 6 ), ncol = 3, byrow = TRUE) ini3D(FALSE, argsPlot3d = list(xlim = c(min(pts[,1])-2,max(pts[,1])+10), ylim = c(min(pts[,2])-2,max(pts[,2])+10), zlim = c(min(pts[,3])-2,max(pts[,3])+10))) plotHull3D(pts, drawPoints = TRUE, addText = "coord") plotHull3D(pts, addRays = TRUE) finalize3D() pts <- genNDSet(3, 100, dubND = FALSE) pts <- as.data.frame(pts[,1:3]) ini3D(argsPlot3d = list( xlim = c(0,max(pts[,1])+10), ylim = c(0,max(pts[,2])+10), zlim = c(0,max(pts[,3])+10))) plotHull3D(pts, drawPoints = TRUE, addRays = TRUE) finalize3D() ini3D(argsPlot3d = list( xlim = c(0,max(pts[,1])+10), ylim = c(0,max(pts[,2])+10), zlim = c(0,max(pts[,3])+10))) plotHull3D(pts, drawPoints = TRUE, drawPolygons = TRUE, addText = "coord", addRays = TRUE) finalize3D() ini3D(argsPlot3d = list( xlim = c(0,max(pts[,1])+10), ylim = c(0,max(pts[,2])+10), zlim = c(0,max(pts[,3])+10))) plotHull3D(pts, drawPoints = TRUE, drawLines = FALSE, argsPolygon3d = list(alpha = 1), addRays = TRUE) finalize3D() ini3D(argsPlot3d = list( xlim = c(0,max(pts[,1])+10), ylim = c(0,max(pts[,2])+10), zlim = c(0,max(pts[,3])+10))) plotHull3D(pts, drawPoints = TRUE, argsPolygon3d = list(color = "red"), addRays = TRUE) plotCones3D(pts, argsPolygon3d = list(alpha = 1), rectangle = TRUE) finalize3D()
ini3D() pts<-matrix(c(0,0,0), ncol = 3, byrow = TRUE) plotHull3D(pts) # a point pts<-matrix(c(1,1,1,2,2,2,3,3,3), ncol = 3, byrow = TRUE) plotHull3D(pts, drawPoints = TRUE) # a line pts<-matrix(c(1,0,0,1,1,1,1,2,2,3,1,1,3,3,3), ncol = 3, byrow = TRUE) plotHull3D(pts, drawLines = FALSE, argsPolygon3d = list(alpha=0.6)) # a polygon pts<-matrix(c(5,5,5,10,10,5,10,5,5,5,5,10), ncol = 3, byrow = TRUE) lst <- plotHull3D(pts, argsPolygon3d = list(alpha=0.9), argsSegments3d = list(color="red")) finalize3D() # pop3d(id = lst$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)
plotLines2D(A, b, nonneg = rep(TRUE, ncol(A)), latex = FALSE, ...)
plotLines2D(A, b, nonneg = rep(TRUE, ncol(A)), latex = FALSE, ...)
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 |
... |
Further arguments passed on the the
|
A ggplot
object.
In general you will properly use plotPolytope()
instead of this function.
Lars Relund [email protected]
Plot TeX in the margin
plotMTeX3D(tex, edge, line = 0, at = NULL, pos = NA, ...)
plotMTeX3D(tex, edge, line = 0, at = NULL, pos = NA, ...)
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 |
The object IDs of objects added to the scene.
Create a plot of a discrete non-dominated set.
plotNDSet2D( points, crit, addTriangles = FALSE, addHull = TRUE, latex = FALSE, labels = NULL )
plotNDSet2D( points, crit, addTriangles = FALSE, addHull = TRUE, latex = FALSE, labels = NULL )
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 |
The ggplot
object.
Currently only points are checked for dominance. That is, for MILP models some nondominated points may in fact be dominated by a segment.
Lars Relund [email protected]
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)
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.
plotPlane3D( normal, point = NULL, offset = 0, useShade = TRUE, useLines = FALSE, usePoints = FALSE, ... )
plotPlane3D( normal, point = NULL, offset = 0, useShade = TRUE, useLines = FALSE, usePoints = FALSE, ... )
normal |
Normal to the plane. |
point |
A point on the plane. |
offset |
The offset of the plane (only used if |
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:
|
NULL (invisible)
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
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.
plotPoints3D(pts, addText = FALSE, ...)
plotPoints3D(pts, addText = FALSE, ...)
pts |
A vector or matrix with the points. |
addText |
Add text to the points. Currently |
... |
Further arguments passed on the the RGL plotting functions. This must be done as lists (see examples). Currently the following arguments are supported:
|
Object ids (invisible).
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
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.
plotPolygon3D( pts, useShade = TRUE, useLines = FALSE, usePoints = FALSE, useFrame = TRUE, ... )
plotPolygon3D( pts, useShade = TRUE, useLines = FALSE, usePoints = FALSE, useFrame = TRUE, ... )
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:
|
Object ids (invisible).
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$z)*5*i)) finalize3D() }
pts <- data.frame(x = c(1,0,0,0.4), y = c(0,1,0,0.3), z = c(0,0,1,0.3)) pts <- data.frame(x = c(1,0,0), y = c(0,1,0), z = c(0,0,1)) ini3D() plotPolygon3D(pts) finalize3D() ini3D() plotPolygon3D(pts, argsShade = list(color = "red", alpha = 1)) finalize3D() ini3D() plotPolygon3D(pts, useFrame = TRUE, argsShade = list(color = "red", alpha = 0.5), argsFrame = list(color = "green")) finalize3D() ini3D() plotPolygon3D(pts, useFrame = TRUE, useLines = TRUE, useShade = TRUE, argsShade = list(color = "red", alpha = 0.2), argsLines = list(color = "blue")) finalize3D() ini3D() ids <- plotPolygon3D(pts, usePoints = TRUE, useFrame = TRUE, argsPoints = list(texture = getTexture(pch = 16, cex = 20))) finalize3D() # pop3d(id = ids) # remove object again # In general you have to finetune size and numbers when you use textures # Different pch for (i in 0:3) { fname <- getTexture(pch = 15+i, cex = 30) ini3D(TRUE) plotPolygon3D(pts, usePoints = TRUE, argsPoints = list(texture = fname)) finalize3D() } # Size of pch for (i in 1:4) { fname <- getTexture(pch = 15+i, cex = 10 * i) ini3D(TRUE) plotPolygon3D(pts, usePoints = TRUE, argsPoints = list(texture = fname)) finalize3D() } # Number of pch fname <- getTexture(pch = 16, cex = 20) for (i in 1:4) { ini3D(TRUE) plotPolygon3D(pts, usePoints = TRUE, argsPoints = list(texture = fname, texcoords = rbind(pts$x, pts$y, pts$z)*5*i)) finalize3D() }
This is a wrapper function calling plotPolytope2D()
(2D graphics) and
plotPolytope3D()
(3D graphics).
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, ... )
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, ... )
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 |
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 |
plotFaces |
If |
plotFeasible |
If |
plotOptimum |
Show the optimum corner solution point (if alternative solutions only one is shown) and add the iso-profit line. |
latex |
If |
labels |
If |
... |
If 2D, further arguments passed on the the
If 3D further arguments passed on the the RGL plotting functions. This must be done as lists. Currently the following arguments are supported:
|
If 2D a ggplot
object. If 3D a RGL window with the 3D plot.
The feasible region defined by the constraints must be bounded (i.e. no extreme rays) otherwise you may see strange results.
Lars Relund [email protected]
#### 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)
#### 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
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, ... )
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, ... )
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 |
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 |
plotFaces |
If |
plotFeasible |
If |
plotOptimum |
Show the optimum corner solution point (if alternative solutions only one is shown) and add the iso-profit line. |
latex |
If |
labels |
If |
... |
Further arguments passed on the the
|
A ggplot
object.
In general use plotPolytope()
instead of this function. The feasible region defined by the constraints must be bounded otherwise you may see
strange results.
Lars Relund [email protected]
plotPolytope()
for examples.
Plot the polytope (bounded convex set) of a linear mathematical program
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, ... )
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, ... )
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 |
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 |
plotFaces |
If |
plotFeasible |
If |
plotOptimum |
Show the optimum corner solution point (if alternative solutions only one is shown) and add the iso-profit line. |
latex |
If |
labels |
If |
... |
Further arguments passed on the the RGL plotting functions. This must be done as lists. Currently the following arguments are supported:
|
A RGL window with 3D plot.
In general use plotPolytope()
instead of this function. The feasible region defined by the constraints must be bounded otherwise you may see
strange results.
Lars Relund [email protected]
plotPolytope()
for examples.
The rectangle is defined by {x|a <= x <= b} where a is the minimum values and b is the maximum values.
plotRectangle3D(a, b, ...)
plotRectangle3D(a, b, ...)
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:
|
Object ids (invisible).
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
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.
plotTeX3D( x, y, z, tex, cex = graphics::par("cex"), fixedSize = FALSE, size = 480, ... )
plotTeX3D( x, y, z, tex, cex = graphics::par("cex"), fixedSize = FALSE, size = 480, ... )
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 |
The shape ID of the displayed object is returned.
## 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)
## 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.
plotTitleTeX3D( main = NULL, sub = NULL, xlab = NULL, ylab = NULL, zlab = NULL, line = NA, ... )
plotTitleTeX3D( main = NULL, sub = NULL, xlab = NULL, ylab = NULL, zlab = NULL, line = NA, ... )
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 |
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.
The object IDs of objects added to the scene.
## 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)
## 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.
pngSize(png)
pngSize(png)
png |
Png file name. |
A list with width and height.
Help function to save the view angle for the RGL 3D plot
saveView(fname = "view.RData", overwrite = FALSE, print = FALSE)
saveView(fname = "view.RData", overwrite = FALSE, print = FALSE)
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). |
NULL (invisible).
Only save if the file name don't exists.
Lars Relund [email protected]
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
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.
slices( A, b, type = rep("c", ncol(A)), nonneg = rep(TRUE, ncol(A)), collapse = FALSE )
slices( A, b, type = rep("c", ncol(A)), nonneg = rep(TRUE, ncol(A)), collapse = FALSE )
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 |
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. |
A list with the corner points (one entry for each slice).
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)
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
texToPng( tex, width = NULL, height = NULL, dpi = 72, viewPng = FALSE, fontsize = 12, calcM = FALSE, crop = FALSE )
texToPng( tex, width = NULL, height = NULL, dpi = 72, viewPng = FALSE, fontsize = 12, calcM = FALSE, crop = FALSE )
tex |
TeX string. Remember to escape backslash with \. |
width |
Width of the png. |
height |
Height of the png ( |
dpi |
Dpi of the png. Not used if |
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 |
The filename of the png or a list if calcM = TRUE
.
## 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)
## 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)