plot_decomposition: Graphically Display the Orthogonal Decomposition of a...

In ryan-heslin/matador: Linear Algebra Visualization

Description

This function produces plots illustrating the transformation of a pair of linearly independent two-dimensional vectors into an orthogonal basis (the Q of the QR decomposition). The algorithm, which can be found in any linear algebra textbook, scales the first vector to unit length, then extracts the component of the second vector orthogonal to the first and normalizes it. The plots are based on those found on pp. 218-219 of Otto Bretscher's Linear Algebra with Applications (5th ed.).

Usage

plot_decomposition(
  m,
  color_par = "blue",
  color_perp = "red",
  color_text = "red4",
  output = "plot",
  fix_coords = FALSE
)

Arguments

m	A 2 x 2 numeric matrix of full rank, one whose columns provide a valid basis for the two-dimensional plane. If m has different dimensions, a different type, or does not have full rank, an error is thrown.
color_par	Color for the second vector's parallel component.
color_perp	Color for the second vector's orthogonal component.
color_text	Color for the text of the equations.
output	Output mode. If "plot", a single gridExtra multiplot featuring the plots side by side. If "list", a list containing the plots. Defaults to "plot."
fix_coords	Logical determining whether to draw the plots with fixed aspect ratio. Defaults to FALSE.

Value

If output is "plot", a multiplot featuring the six decomposition plots; otherwise a list containing them.

Examples

plot_decomposition(square(1, 4, 7, 2))
# With custom colors
plot_decomposition(square(1:4), color_par = "green", color_perp = "orange")
# Already orthogonal vectors: only scaling necessary
plot_decomposition(square(30, 20, 2, -3))

ryan-heslin/matador documentation built on Dec. 22, 2021, 8:17 p.m.