showEqn: Show Matrices (A, b) as Linear Equations

In matlib: Matrix Functions for Teaching and Learning Linear Algebra and Multivariate Statistics

Show Matrices (A, b) as Linear Equations

Description

Shows what matrices \\mathbf{A}, \\mathbf{b} look like as the system of linear equations, \\mathbf{A x} = \\mathbf{b}, but written out as a set of equations.

Usage

showEqn(
  A,
  b,
  vars,
  simplify = FALSE,
  reduce = FALSE,
  fractions = FALSE,
  latex = FALSE
)

Arguments

A	either the matrix of coefficients of a system of linear equations, or the matrix cbind(A,b). The matrix can be numeric or character. Alternatively, can be of class 'lm' to print the equations for the design matrix in a linear regression model
b	if supplied, the vector of constants on the right hand side of the equations. When omitted the values b1, b2, ..., bn will be used as placeholders
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).
simplify	logical; try to simplify the equations?
reduce	logical; only show the unique linear equations
fractions	logical; express numbers as rational fractions, using the fractions function; if you require greater accuracy, you can set the cycles (default 10) and/or max.denominator (default 2000) arguments to fractions as a global option, e.g., options(fractions=list(cycles=100, max.denominator=10^4)).
latex	logical; print equations in a form suitable for LaTeX output?

Value

a one-column character matrix, one row for each equation

Author(s)

Michael Friendly, John Fox, and Phil Chalmers

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.

See Also

plotEqn, plotEqn3d, latexMatrix

Examples

  A <- matrix(c(2, 1, -1,
               -3, -1, 2,
               -2,  1, 2), 3, 3, byrow=TRUE)
  b <- c(8, -11, -3)
  showEqn(A, b)
  # show numerically
  x <- solve(A, b)
  showEqn(A, b, vars=x)

  showEqn(A, b, simplify=TRUE)
  showEqn(A, b, latex=TRUE)


 # lower triangle of equation with zeros omitted (for back solving)
  A <- matrix(c(2, 1, 2,
               -3, -1, 2,
               -2,  1, 2), 3, 3, byrow=TRUE)
  U <- LU(A)$U
  showEqn(U, simplify=TRUE, fractions=TRUE)
  showEqn(U, b, simplify=TRUE, fractions=TRUE)

 ####################
 # Linear models Design Matricies
  data(mtcars)
  ancova <- lm(mpg ~ wt + vs, mtcars)
  summary(ancova)
  showEqn(ancova)
  showEqn(ancova, simplify=TRUE)
  showEqn(ancova, vars=round(coef(ancova),2))
  showEqn(ancova, vars=round(coef(ancova),2), simplify=TRUE)

  twoway_int <- lm(mpg ~ vs * am, mtcars)
  summary(twoway_int)
  car::Anova(twoway_int)
  showEqn(twoway_int)
  showEqn(twoway_int, reduce=TRUE)
  showEqn(twoway_int, reduce=TRUE, simplify=TRUE)

  # Piece-wise linear regression
  x <- c(1:10, 13:22)
  y <- numeric(20)
  y[1:10] <- 20:11 + rnorm(10, 0, 1.5)
  y[11:20] <- seq(11, 15, len=10) + rnorm(10, 0, 1.5)
  plot(x, y, pch = 16)

  x2 <- as.numeric(x > 10)
  mod <- lm(y ~ x + I((x - 10) * x2))
  summary(mod)
  lines(x, fitted(mod))
  showEqn(mod)
  showEqn(mod, vars=round(coef(mod),2))
  showEqn(mod, simplify=TRUE)

matlib documentation built on Oct. 3, 2024, 1:09 a.m.