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Gauß-Jordan Scheme

This files provices routines for the Gauß-Jordan scheme.

Some functions for the demonstration of the Gauß-Jordan algorithm. These functions can be used for linear systems or for the simplex algorithm.

Load the functions with "load gaussjordan".

function gjprint (A : real, n : positive integer vector,
    v : string vector, digits:nonnegative integer=none,
    length:index=none)

  Print the matrix A in Gauß-Jordan form.
  
  The scheme A is printed in the form
  
  x  y ...
  a  1  2 ...
  b  3  4 ...
  ...
  
  n : index vector with a permumatin of the variables
  v : variable names with the column variables first
  digits : number of digits for each number
  length : output length of each number
  
  File: gaussjordan
  
  See: 
gjstep (Gauß-Jordan Scheme)
function gjstep (A:numerical, i:index, j:index,
    n:positive integer vector=none,
    v:string vector=none, digits:nonnegative integer=none,
    length:index=none)

  Make A[i,j]=1 and all other elements in column j equal to 0.
  
  The function is using elementary operations on the rows of A. Use
  this functions for the demonstration of the Gauss algorithm.
  
  The function modifies A and n.
  
  n : A row vector of indices, the function assumes the Gauß-Jordan
  form. n contains the indices of the variables, first the indices of
  the variables in the rows, and then the indices of the variables in
  the columns. The row variable i is exchanged with the column
  variable j. This is the same as makeing the j-th column to an
  canonical vector e[i], and inserting in the j-th column the result
  of this operation applied to e[i].
  
  If n is present, you can add a vector v of strings, which contains
  the names of the variables. The problem will then be printed using
  gjprint.
  
  File: gaussjordan
  
  See: 
pivotize (Linear Algebra),
gjprint (Gauß-Jordan Scheme)
function gjsolution (M : real, n : positive integer vector)

  Read the values of the solution from the Gauß-Jordan scheme.
  
  For this, we assume that the last column contains the values, and
  the variables in the top row are set to zero.
  
  See: 
gjstep (Gauß-Jordan Scheme)
function gjvars (M : real, simplex=false)

  Generate variable names for M
  
  simplex : If true the last row variable will be named ""
  and the last column will name will be missing.
  
  Returns {v,n}
  where n=1:(rows+cols), v=["s1"...,"x1",...]
  
  See: 
gjprint (Gauß-Jordan Scheme)
function gjaddcondition (M : real,
    n:positive integer vector, v:string vector,
    line:real vector, varname:string)

  Add a condition to the Gauß-Jordan Form
  
  The line for the condition (left side <= right side) and the
  variable name must be provided. The condition uses the current top
  row variables.
  
  Return {M,n,v}

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