gaussianElimination: Gaussian Elimination

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

Gaussian Elimination

Description

gaussianElimination demonstrates the algorithm of row reduction used for solving systems of linear equations of the form A x = B. Optional arguments verbose and fractions may be used to see how the algorithm works.

Usage

gaussianElimination(
  A,
  B,
  tol = sqrt(.Machine$double.eps),
  verbose = FALSE,
  latex = FALSE,
  fractions = FALSE
)

## S3 method for class 'enhancedMatrix'
print(x, ...)

Arguments

A	coefficient matrix
B	right-hand side vector or matrix. If B is a matrix, the result gives solutions for each column as the right-hand side of the equations with coefficients in A.
tol	tolerance for checking for 0 pivot
verbose	logical; if TRUE, print intermediate steps
latex	logical; if TRUE, and verbose is TRUE, print intermediate steps using LaTeX equation outputs rather than R output
fractions	logical; if TRUE, try to express non-integers as rational numbers, 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)).
x	matrix to print
...	arguments to pass down

Value

If B is absent, returns the reduced row-echelon form of A. If B is present, returns the reduced row-echelon form of A, with the same operations applied to B.

Author(s)

John Fox

Examples

  A <- matrix(c(2, 1, -1,
               -3, -1, 2,
               -2,  1, 2), 3, 3, byrow=TRUE)
  b <- c(8, -11, -3)
  gaussianElimination(A, b)
  gaussianElimination(A, b, verbose=TRUE, fractions=TRUE)
  gaussianElimination(A, b, verbose=TRUE, fractions=TRUE, latex=TRUE)

  # determine whether matrix is solvable
  gaussianElimination(A, numeric(3))

  # find inverse matrix by elimination: A = I -> A^-1 A = A^-1 I -> I = A^-1
  gaussianElimination(A, diag(3))
  inv(A)

  # works for 1-row systems (issue # 30)
  A2 <- matrix(c(1, 1), nrow=1)
  b2 = 2
  gaussianElimination(A2, b2)
  showEqn(A2, b2)
  # plotEqn works for this case
  plotEqn(A2, b2)

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