Plot Linear Equations in 3D — plotEqn3d • matlib

Shows what matrices \(A, b\) look like as the system of linear equations, \(A x = b\) with three unknowns, x1, x2, and x3, by plotting a plane for each equation.

Usage

plotEqn3d(
  A,
  b,
  vars,
  xlim = c(-2, 2),
  ylim = c(-2, 2),
  zlim,
  col = 2:(nrow(A) + 1),
  alpha = 0.9,
  labels = FALSE,
  solution = TRUE,
  axes = TRUE,
  lit = FALSE
)

Arguments

A: either the matrix of coefficients of a system of linear equations, or the matrix cbind(A,b) The A matrix must have three columns.
b: if supplied, the vector of constants on the right hand side of the equations, of length matching the number of rows of A.
vars: a numeric or character vector of names of the variables. If supplied, the length must be equal to the number of unknowns in the equations. The default is paste0("x", 1:ncol(A).
xlim: axis limits for the first variable
ylim: axis limits for the second variable
zlim: horizontal axis limits for the second variable; if missing, zlim is calculated from the range of the set of equations over the xlim and ylim
col: scalar or vector of colors for the lines, recycled as necessary
alpha: transparency applied to each plane
labels: logical, or a vector of character labels for the equations; not yet implemented.
solution: logical; should the solution point for all equations be marked (if possible)
axes: logical; whether to frame the plot with coordinate axes
lit: logical, specifying if lighting calculation should take place on geometry; see rgl.material

Value

nothing; used for the side effect of making a plot

References

Fox, J. and Friendly, M. (2016). "Visualizing Simultaneous Linear Equations, Geometric Vectors, and Least-Squares Regression with the matlib Package for R". useR Conference, Stanford, CA, June 27 - June 30, 2016.

Author

Michael Friendly, John Fox

Examples

# three consistent equations in three unknowns
A <- matrix(c(13, -4, 2, -4, 11, -2, 2, -2, 8), 3,3)
b <- c(1,2,4)
plotEqn3d(A,b)
3D plot