Print Functions for Simplex in Gauss-Jordan Form

This file contains functions to print a Simplex scheme in Gauss-Jordan form. I.e. we print only the columns of M|b that are not in the basis J. The columns in the basis J must contains the identity matrix.

This is nice if the problem starts with Ax<=b, and the scheme is M=A|I.

The target function is printed underneath the scheme as in

>A=[1,4,3;4,5,1]; b=[5,3]'; c=[1,2,3]; >fraction simplex(A,b,c,>max) 4/11 0 17/11 >M=(A|id(2)|b)_c; J=[4,5]; >load pivp; >pivp(M,J,8) 1 2 3

4 1 4 3 5 5 4 5 1 3

1 2 3 0 >piv(M,2,1,J,8) 2 3 5

4 11/4 11/4 -1/4 17/4 1 5/4 1/4 1/4 3/4

3/4 11/4 -1/4 -3/4 >piv(M,2,2,J,8) 1 3 5

4 -11/5 11/5 -4/5 13/5 2 4/5 1/5 1/5 3/5

-3/5 13/5 -2/5 -6/5 >piv(M,1,3,J,8) 1 4 5

3 -1 5/11 -4/11 13/11 2 1 -1/11 3/11 4/11

2 -13/11 6/11 -47/11 >piv(M,2,1,J,8) 2 4 5

3 1 4/11 -1/11 17/11 1 1 -1/11 3/11 4/11

-2 -1 0 -5 >fraction pivsol(M,J)' 4/11 0 17/11 0 0 >

Load with "load hondt".

function pfrac (x,n)

  Print a row vector in fractional format.
  
  n : Number of digits for each element.

function pivp (H,b,l=6)

  Print the Simplex scheme in Gauss-Jordan fractional Form
  
  H : Scheme Mx=b with a target function in last row.
  b : Indices of Basis columns (must contain identity matrix)
  l : length of element output
  
  >A=[1,4,3;4,5,1]; b=[5,3]'; c=[1,2,3];
  >fraction simplex(A,b,c,>max)
  4/11
  0
  17/11
  >M=(A|id(2)|b)_c; J=[4,5];
  >load pivp;
  >pivp(M,J,8)
  1       2       3
  
  4       1       4       3       5
  5       4       5       1       3
  
  1       2       3       0
  
  See: 
  pivsol (Print Functions for Simplex in Gauss-Jordan Form)

function piv (H,i,j,b,l=6)

  Pivotize Simplex Scheme in Gauss-Jordan form
  
  H : Scheme Mx=b with a target function in last row.
  b : Indices of Basis columns (must contain identity matrix)
  i : Basis element to be excluded (row of H)
  j : Basis element to be included (column of H)
  l : length of element output
  
  >pivp(M,J,8)
  1       2       3
  
  4       1       4       3       5
  5       4       5       1       3
  
  1       2       3       0
  >piv(M,2,1,J,8)
  2       3       5
  
  4    11/4    11/4    -1/4    17/4
  1     5/4     1/4     1/4     3/4
  
  3/4    11/4    -1/4    -3/4
  
  See: 
  pivp (Print Functions for Simplex in Gauss-Jordan Form), 
  pivsol (Print Functions for Simplex in Gauss-Jordan Form), 
  addcut (Print Functions for Simplex in Gauss-Jordan Form)

function pivsol (M,b)

  Compute the solution from Gauss-Jordan form
  
  M : Scheme Mx=b with a target function in last row.
  b : Indices of Basis columns (must contain identity matrix)
  
  >piv(M,2,1,J,8)
  2       4       5
  
  3       1    4/11   -1/11   17/11
  1       1   -1/11    3/11    4/11
  
  -2      -1       0      -5
  >fraction pivsol(M,J)'
  4/11
  0
  17/11
  0
  0
  
  See: 
  pivp (Print Functions for Simplex in Gauss-Jordan Form)

function addcut (M,b,c)

  Add a Gomory Cut to the Simplex in Gauss-Jordan form
  
  M : Scheme Mx=b with a target function in last row.
  b : Indices of Basis columns (must contain identity matrix)
  
  The cut is derived from the c-th row of the scheme and added
  as one line of M.
  
  See: 
  piv (Print Functions for Simplex in Gauss-Jordan Form), 
  pivp (Print Functions for Simplex in Gauss-Jordan Form), 
  pivsol (Print Functions for Simplex in Gauss-Jordan Form)

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