MathAction SandBoxLinearProgramming

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fricas

(1) -> <spad>

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)abbrev package LINPROG LinearProgramming
++ Author: Kurt Pagani
++ Date Created: Sun Jun 03 02:05:55 CEST 2018
++ License: BSD
++ References:
++ Description:
++ TODO: description, more in test_linprog, eps, tol    
++ IDEA: linSolve standard method, try LU from jet
++ LINPROG  
++
LinearProgramming() : Exports == Implementation where

  R ==> Float
  PI ==> PositiveInteger
  NNI ==> NonNegativeInteger
  MATR ==> Matrix R
  VECR ==> Vector R
  LI ==> List Integer
  RESR ==> Record(x:VECR,f:R,itn:NNI)
  RESRS ==> Record(X:VECR,objVal:R,Basis:LI)
  RLUP ==> Record(L:MATR,U:MATR,P:MATR)
  RXP ==> Record(X:VECR,P:MATR)

  Exports ==  with

    revisedSimplex : (MATR,VECR,VECR,LI) -> RESRS
    revisedSimplexLU : (MATR,VECR,VECR,LI) -> RESRS
    luDecompose : MATR -> RLUP
    luSolve : (MATR,VECR) -> RXP

  Implementation ==  MATR add 

    eps:R:=0.00001
    zeroTol:R:= 0.00001

    revisedSimplex(A:MATR,b:VECR,c:VECR,B:LI):RESRS ==
      numRows:PI := #b ::PI
      numVars:PI := #c ::PI
      --zeroTol:R:= 0.00001
      N:LI := [i for i in 1..numVars | not member?(i,B)]
      --N:LI:=setDifference([i for i in 1..numVars],B)
      RA:LI:=[i for i in 1..nrows(A)]
      AB:MATR:=A(RA,B) 
      AN:MATR:=A(RA,N)
      numNonbasicVars:=#N
      cN := vector [c.i for i in N]
      cB := vector [c.i for i in B]
      IAB:Union(MATR,"failed"):=inverse(AB)
      if IAB case MATR then
        bBAR:VECR := IAB*b
      else
        error "AB not invertible"
      objVal := dot(cB,bBAR)
      negRedCost := -1.0
      while negRedCost < 0.0 repeat
        IAB:Union(MATR,"failed"):=inverse(AB)
        if IAB case MATR then
          wN:VECR := cN - (cB*IAB)*AN
        else
          error "AB not invertible"
        --
        negRedCostIdx:NNI := 0
        negRedCost := 0.0
        --
        for k in 1..numNonbasicVars repeat
          if wN.k < -zeroTol then
            negRedCost := wN.k
            --record the index
            negRedCostIdx := k
            break
        --
        if negRedCost < 0.0 then
          IAB:Union(MATR,"failed"):=inverse(AB)
          if IAB case MATR then
            aBAR:VECR := IAB*column(AN,negRedCostIdx)
          else
            error "AB not invertible"
          minRatioVal := 1.0/zeroTol --inf
          minRatioIdx := 0
          --
          for k in 1..numRows repeat
            if aBAR.k > zeroTol then
              if bBAR.k / aBAR.k < minRatioVal then
                minRatioVal := bBAR.k / aBAR.k
                --record the index
                minRatioIdx:NNI := k
          --
          bBAR := bBAR - minRatioVal * aBAR
          bBAR.minRatioIdx := minRatioVal
          --
          tmpIdx := B.minRatioIdx
          B.minRatioIdx := N.negRedCostIdx
          N.negRedCostIdx := tmpIdx
          --
          AB:MATR:=A(RA,B) 
          AN:MATR:=A(RA,N)
          cN := vector [c.i for i in N]
          cB := vector [c.i for i in B]
        X:VECR:=zero(numVars)
        for i in 1..numRows repeat
          X.(B.i) := bBAR.i
        objVal := dot(cB,bBAR)
      return [X,objVal,B]

    luDecompose(A:MATR):RLUP ==
      not square?(A)$MATR => error "Input matrix is not square."
      (numRows, numVars) := (nrows A, ncols A)
      U:MATR:=copy A
      LK:MATR:=zero(numRows,numRows)$MATR
      I:MATR:=diagonalMatrix(vector [1 for i in 1..numRows])
      P:MATR:=copy I
      LINV:=copy I
      RA:LI:=[i for i in 1..numRows]  
      for i in 1..numVars repeat
        perm:LI:=[m for m in 1..numRows]   -- don't use RA or i as index!!
        pivotEl := 0$R
        for j in i..numRows repeat
          if abs(U(j,i)) > eps then
            tmp := perm.i
            perm.i := perm.j
            perm.j := tmp
            U:=I(perm,RA)*U
            P:=I(perm,RA)*P
            pivotEl := U(i, i)
            break
        abs(pivotEl) <= eps => error("Matrix is singular")
        LK := I(perm,RA) * LK
        LK(i,i) := 1$R 
        LINVK := copy I
        --
        for k in i+1..numRows repeat
          if U(k, i) ~= 0$R then
            multiplier := U(k, i)/pivotEl
            U(k,RA) := U(k,RA) -  multiplier * U(i,RA)
            LK(k,i) := multiplier
            LINVK(k, i) := - multiplier
        --
        LINV := LINVK*LINV
      return [LK,U,P]

    luSolve(A:MATR,b:VECR):RXP ==
      not square?(A)$MATR => error "Input matrix is not square."
      (numRows, numVars) := (nrows A, ncols A)
      r:RLUP:=luDecompose(A)
      U:=copy r.U
      L:=copy r.L
      P:=copy r.P
      Y:=vector [0$R for m in 1..numRows]
      X:=vector [0$R for m in 1..numRows]
      rhs:VECR := P*b
      for i in 1..numVars repeat
        Y.i := rhs.i
        rhs := rhs - Y.i * column(L,i)
      for i in numVars..1 by -1 repeat
        X.i := Y.i / U(i,i)
        Y := Y - X.i * column(U,i)      
      return [X,P]

    revisedSimplexLU(A:MATR,b:VECR,c:VECR,B:LI):RESRS ==
      numRows:PI := #b ::PI
      numVars:PI := #c ::PI
      --zeroTol:R:= 0.00001
      N:LI := [i for i in 1..numVars | not member?(i,B)]
      --N:LI:=setDifference([i for i in 1..numVars],B)
      RA:LI:=[i for i in 1..nrows(A)]
      AB:MATR:=A(RA,B) 
      AN:MATR:=A(RA,N)
      numNonbasicVars:=#N
      cN := vector [c.i for i in N]
      cB := vector [c.i for i in B]
      --
      bBAR:VECR := luSolve(AB,b).X ---- luSolve
      objVal := dot(cB,bBAR)
      negRedCost := -1.0
      while negRedCost < 0.0 repeat
        u:VECR:= luSolve(transpose(AB),cB).X
        wN:VECR := cN - u*AN
        --
        negRedCostIdx:NNI := 0
        negRedCost := 0.0
        --
        for k in 1..numNonbasicVars repeat
          if wN.k < -zeroTol then
            negRedCost := wN.k
            --record the index
            negRedCostIdx := k
            break
        --
        if negRedCost < 0.0 then

          aBAR:VECR := luSolve(AB,column(AN,negRedCostIdx)).X
          minRatioVal := 1.0/zeroTol --inf
          minRatioIdx := 0
          --
          for k in 1..numRows repeat
            if aBAR.k > zeroTol then
              if bBAR.k / aBAR.k < minRatioVal then
                minRatioVal := bBAR.k / aBAR.k
                --record the index
                minRatioIdx:NNI := k
          --
          bBAR := bBAR - minRatioVal * aBAR
          bBAR.minRatioIdx := minRatioVal
          --
          tmpIdx := B.minRatioIdx
          B.minRatioIdx := N.negRedCostIdx
          N.negRedCostIdx := tmpIdx
          --
          AB:MATR:=A(RA,B) 
          AN:MATR:=A(RA,N)
          cN := vector [c.i for i in N]
          cB := vector [c.i for i in B]
        X:VECR:=zero(numVars)
        for i in 1..numRows repeat
          X.(B.i) := bBAR.i
        objVal := dot(cB,bBAR)
      return [X,objVal,B]</spad>

fricas

Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/5717432969159631359-25px001.spad
      using old system compiler.
   LINPROG abbreviates package LinearProgramming 
------------------------------------------------------------------------
   initializing NRLIB LINPROG for LinearProgramming 
   compiling into NRLIB LINPROG 
   compiling exported revisedSimplex : (Matrix Float,Vector Float,Vector Float,List Integer) -> Record(X: Vector Float,objVal: Float,Basis: List Integer)
Local variable minRatioIdx type redefined: (NonNegativeInteger) to (Float)
Time: 0.04 SEC.

   compiling exported luDecompose : Matrix Float -> Record(L: Matrix Float,U: Matrix Float,P: Matrix Float)
Time: 0.02 SEC.

   compiling exported luSolve : (Matrix Float,Vector Float) -> Record(X: Vector Float,P: Matrix Float)
Time: 0.01 SEC.

   compiling exported revisedSimplexLU : (Matrix Float,Vector Float,Vector Float,List Integer) -> Record(X: Vector Float,objVal: Float,Basis: List Integer)
Local variable minRatioIdx type redefined: (NonNegativeInteger) to (Float)
Time: 0.02 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |LinearProgramming| REDEFINED

;;;     ***       |LinearProgramming| REDEFINED
Time: 0 SEC.

   Warnings: 
      [1] revisedSimplex:  negRedCostIdx has no value
      [2] revisedSimplex:  minRatioIdx has no value
      [3] revisedSimplex:  bBAR has no value
      [4] revisedSimplex:  X has no value
      [5] luDecompose:  U has no value
      [6] luDecompose:  LK has no value
      [7] luDecompose:  P has no value
      [8] luSolve:  U has no value
      [9] luSolve:  L has no value
      [10] luSolve:  P has no value
      [11] revisedSimplexLU:  negRedCostIdx has no value
      [12] revisedSimplexLU:  minRatioIdx has no value
      [13] revisedSimplexLU:  bBAR has no value
      [14] revisedSimplexLU:  X has no value

   Cumulative Statistics for Constructor LinearProgramming
      Time: 0.09 seconds

--------------non extending category----------------------
.. LinearProgramming of cat 
(CATEGORY |package|
 (SIGNATURE |revisedSimplex|
  ((|Record| (|:| X (|Vector| (|Float|))) (|:| |objVal| (|Float|))
             (|:| |Basis| (|List| (|Integer|))))
   (|Matrix| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|))
   (|List| (|Integer|))))
 (SIGNATURE |revisedSimplexLU|
  ((|Record| (|:| X (|Vector| (|Float|))) (|:| |objVal| (|Float|))
             (|:| |Basis| (|List| (|Integer|))))
   (|Matrix| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|))
   (|List| (|Integer|))))
 (SIGNATURE |luDecompose|
  ((|Record| (|:| L (|Matrix| (|Float|))) (|:| U (|Matrix| (|Float|)))
             (|:| P (|Matrix| (|Float|))))
   (|Matrix| (|Float|))))
 (SIGNATURE |luSolve|
  ((|Record| (|:| X (|Vector| (|Float|))) (|:| P (|Matrix| (|Float|))))
   (|Matrix| (|Float|)) (|Vector| (|Float|)))))   has no 
(|MatrixCategory| (|Float|) (|Vector| (|Float|)) (|Vector| (|Float|)))    finalizing NRLIB LINPROG 
   Processing LinearProgramming for Browser database:
--------constructor---------
--->-->LinearProgramming((revisedSimplex ((Record (: X (Vector (Float))) (: objVal (Float)) (: Basis (List (Integer)))) (Matrix (Float)) (Vector (Float)) (Vector (Float)) (List (Integer))))): Not documented!!!!
--->-->LinearProgramming((revisedSimplexLU ((Record (: X (Vector (Float))) (: objVal (Float)) (: Basis (List (Integer)))) (Matrix (Float)) (Vector (Float)) (Vector (Float)) (List (Integer))))): Not documented!!!!
--->-->LinearProgramming((luDecompose ((Record (: L (Matrix (Float))) (: U (Matrix (Float))) (: P (Matrix (Float)))) (Matrix (Float))))): Not documented!!!!
--->-->LinearProgramming((luSolve ((Record (: X (Vector (Float))) (: P (Matrix (Float)))) (Matrix (Float)) (Vector (Float))))): Not documented!!!!
; compiling file "/var/aw/var/LatexWiki/LINPROG.NRLIB/LINPROG.lsp" (written 15 MAR 2025 05:43:16 AM):

; wrote /var/aw/var/LatexWiki/LINPROG.NRLIB/LINPROG.fasl
; compilation finished in 0:00:00.428
------------------------------------------------------------------------
   LinearProgramming is now explicitly exposed in frame initial 
   LinearProgramming will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/LINPROG.NRLIB/LINPROG

Test flavours

fricas -- Unittest .....: Package LinearProgramming

Author .......: Kurt Pagani -- Date .........: Sun Jun 17 02:14:10 CEST 2018

fricas

)set break resume

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)expose UnittestCount UnittestAux Unittest

   UnittestCount is now explicitly exposed in frame initial 
   UnittestAux is now explicitly exposed in frame initial 
   Unittest is now explicitly exposed in frame initial 

--)co linprog

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)expose LINPROG

   LinearProgramming is already explicitly exposed in frame initial 

-- Test Suite
testsuite "Package: LinearProgramming"

   All user variables and function definitions have been cleared.
   WARNING: string for testsuite should have less than 15 characters!

Type: Void

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-- Cases
testcase "revisedSimplex"

   All user variables and function definitions have been cleared.

Type: Void

fricas

-- testEquals("", "")

A:=matrix [[0.7,1.0,1.0,0.0,0.0,0.0],[0.5,(5/6)::Float,0.0,1.0,0.0,0.0],
           [1.0,(2/3)::Float,0.0,0.0,1.0,0.0],[0.1,0.25,0.0,0.0,0.0,1.0]]

$\label{eq1}\left[ \begin{array}{cccccc} {0.7}&{1.0}&{1.0}&{0.0}&{0.0}&{0.0} \ {0.5}&{0.8333333333 \ 3333333333}&{0.0}&{1.0}&{0.0}&{0.0} \ {1.0}&{0.6666666666 \ 6666666667}&{0.0}&{0.0}&{1.0}&{0.0} \ {0.1}&{0.25}&{0.0}&{0.0}&{0.0}&{1.0}$

(1)

Type: Matrix(Float)

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c:=vector [-10.0,-9.0,0.0,0.0,0.0,0.0]

$\label{eq2}\left[ -{10.0}, \: -{9.0}, \:{0.0}, \:{0.0}, \:{0.0}, \:{0.0}\right]$

(2)

Type: Vector(Float)

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b:=vector [630.0,600.0,708.0,135.0]

$\label{eq3}\left[{630.0}, \:{600.0}, \:{708.0}, \:{135.0}\right]$

(3)

Type: Vector(Float)

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B:=[3,4,5,6]

$\label{eq4}\left[ 3, \: 4, \: 5, \: 6 \right]$

(4)

Type: List(PositiveInteger?)

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X1:Vector Float:= vector [540.0,252.0,0.0,120.0,0.0,18.0]

$\label{eq5}\left[{540.0}, \:{252.0}, \:{0.0}, \:{120.0}, \:{0.0}, \:{18.0}\right]$

(5)

Type: Vector(Float)

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objVal1:Float:= - 7668.0

$\label{eq6}-{7668.0}$

(6)

Type: Float

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Basis1:List Integer:= [2,4,1,6]

$\label{eq7}\left[ 2, \: 4, \: 1, \: 6 \right]$

(7)

Type: List(Integer)

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eps:=0.0000000001

$\label{eq8}0.1 E - 9$

(8)

Type: Float

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floatNull(v:Vector Float):Boolean == sqrt dot(v,v) <= eps 

   Function declaration floatNull : Vector(Float) -> Boolean has been 
      added to workspace.

Type: Void

fricas

r1:=revisedSimplex( A, b, c, B)

   >> System error:
   The value
  (0 . 0)
is not of type
  UNSIGNED-BYTE

   Continuing to read the file...

testEquals("floatNull(r1.X-X1)", "true")

   There are no library operations named r1 
      Use HyperDoc Browse or issue
                                 )what op r1
      to learn if there is any operation containing " r1 " in its name.

   Cannot find a definition or applicable library operation named r1 
      with argument type(s) 
                                 Variable(X)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

Type: Void

fricas

testEquals("abs(r1.objVal-objVal1)<eps", "true")

   There are no library operations named r1 
      Use HyperDoc Browse or issue
                                 )what op r1
      to learn if there is any operation containing " r1 " in its name.

   Cannot find a definition or applicable library operation named r1 
      with argument type(s) 
                              Variable(objVal)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

Type: Void

fricas

testEquals("r1.Basis", "Basis1")

   There are no library operations named r1 
      Use HyperDoc Browse or issue
                                 )what op r1
      to learn if there is any operation containing " r1 " in its name.

   Cannot find a definition or applicable library operation named r1 
      with argument type(s) 
                               Variable(Basis)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

Type: Void

fricas

r1lu:=revisedSimplexLU( A, b, c, B)

   >> System error:
   The value
  (0 . 0)
is not of type
  UNSIGNED-BYTE

   Continuing to read the file...

testEquals("floatNull(r1lu.X-X1)", "true")

   There are no library operations named r1lu 
      Use HyperDoc Browse or issue
                                )what op r1lu
      to learn if there is any operation containing " r1lu " in its 
      name.

   Cannot find a definition or applicable library operation named r1lu 
      with argument type(s) 
                                 Variable(X)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

Type: Void

fricas

testEquals("abs(r1lu.objVal-objVal1)<eps", "true")

   There are no library operations named r1lu 
      Use HyperDoc Browse or issue
                                )what op r1lu
      to learn if there is any operation containing " r1lu " in its 
      name.

   Cannot find a definition or applicable library operation named r1lu 
      with argument type(s) 
                              Variable(objVal)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

Type: Void

fricas

testEquals("r1lu.Basis", "Basis1")

   There are no library operations named r1lu 
      Use HyperDoc Browse or issue
                                )what op r1lu
      to learn if there is any operation containing " r1lu " in its 
      name.

   Cannot find a definition or applicable library operation named r1lu 
      with argument type(s) 
                               Variable(Basis)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

Type: Void

fricas

--

---
A2 := matrix [[0,1,-1,0,0,0], [1,1,0,-1,0,0], 
               [-0.5,1,0,0,1,0],[-1,1,0,0,0,1]]

$\label{eq9}\left[ \begin{array}{cccccc} {0.0}&{1.0}& -{1.0}&{0.0}&{0.0}&{0.0} \ {1.0}&{1.0}&{0.0}& -{1.0}&{0.0}&{0.0} \ -{0.5}&{1.0}&{0.0}&{0.0}&{1.0}&{0.0} \ -{1.0}&{1.0}&{0.0}&{0.0}&{0.0}&{1.0}$

(9)

Type: Matrix(Float)

fricas

c2 := vector [2,-3,0,0,0,0]

$\label{eq10}\left[ 2, \: - 3, \: 0, \: 0, \: 0, \: 0 \right]$

(10)

Type: Vector(Integer)

fricas

b2 := vector [1,2,8,6]

$\label{eq11}\left[ 1, \: 2, \: 8, \: 6 \right]$

(11)

Type: Vector(PositiveInteger?)

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B2 := [1,2,5,6]

$\label{eq12}\left[ 1, \: 2, \: 5, \: 6 \right]$

(12)

Type: List(PositiveInteger?)

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X2:= [4.0,10.0,9.0,12.0,0.0,0.0]

$\label{eq13}\left[{4.0}, \:{10.0}, \:{9.0}, \:{12.0}, \:{0.0}, \:{0.0}\right]$

(13)

Type: List(Float)

fricas

objVal2:= - 22.0

$\label{eq14}-{22.0}$

(14)

Type: Float

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Basis2:= [3,2,1,4]

$\label{eq15}\left[ 3, \: 2, \: 1, \: 4 \right]$

(15)

Type: List(PositiveInteger?)

fricas

r2:=revisedSimplex( A2, b2, c2, B2)

   >> System error:
   The value
  (0 . 0)
is not of type
  UNSIGNED-BYTE

   Continuing to read the file...

testEquals("floatNull(r2.X-X2)", "true")

   There are no library operations named r2 
      Use HyperDoc Browse or issue
                                 )what op r2
      to learn if there is any operation containing " r2 " in its name.

   Cannot find a definition or applicable library operation named r2 
      with argument type(s) 
                                 Variable(X)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

Type: Void

fricas

testEquals("abs(r2.objVal-objVal2)<eps", "true")

   There are no library operations named r2 
      Use HyperDoc Browse or issue
                                 )what op r2
      to learn if there is any operation containing " r2 " in its name.

   Cannot find a definition or applicable library operation named r2 
      with argument type(s) 
                              Variable(objVal)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

Type: Void

fricas

testEquals("r2.Basis", "Basis2")

   There are no library operations named r2 
      Use HyperDoc Browse or issue
                                 )what op r2
      to learn if there is any operation containing " r2 " in its name.

   Cannot find a definition or applicable library operation named r2 
      with argument type(s) 
                               Variable(Basis)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

Type: Void

fricas

r2lu:=revisedSimplexLU( A2, b2, c2, B2)

   >> System error:
   The value
  (0 . 0)
is not of type
  UNSIGNED-BYTE

   Continuing to read the file...

testEquals("floatNull(r2lu.X-X2)", "true")

   There are no library operations named r2lu 
      Use HyperDoc Browse or issue
                                )what op r2lu
      to learn if there is any operation containing " r2lu " in its 
      name.

   Cannot find a definition or applicable library operation named r2lu 
      with argument type(s) 
                                 Variable(X)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

Type: Void

fricas

testEquals("abs(r2lu.objVal-objVal2)<eps", "true")

   There are no library operations named r2lu 
      Use HyperDoc Browse or issue
                                )what op r2lu
      to learn if there is any operation containing " r2lu " in its 
      name.

   Cannot find a definition or applicable library operation named r2lu 
      with argument type(s) 
                              Variable(objVal)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

Type: Void

fricas

testEquals("r2lu.Basis", "Basis2")

   There are no library operations named r2lu 
      Use HyperDoc Browse or issue
                                )what op r2lu
      to learn if there is any operation containing " r2lu " in its 
      name.

   Cannot find a definition or applicable library operation named r2lu 
      with argument type(s) 
                               Variable(Basis)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

Type: Void

fricas

--

A3 := matrix [[0.4,0.5,1,0,0],[0,0.2,0,1,0],[0.6,0.3,0,0,1]]

$\label{eq16}\left[ \begin{array}{ccccc} {0.4}&{0.5}&{1.0}&{0.0}&{0.0} \ {0.0}&{0.2}&{0.0}&{1.0}&{0.0} \ {0.6}&{0.3}&{0.0}&{0.0}&{1.0}$

(16)

Type: Matrix(Float)

fricas

c3 := vector [-40,-30,0,0,0]

$\label{eq17}\left[ -{40}, \: -{30}, \: 0, \: 0, \: 0 \right]$

(17)

Type: Vector(Integer)

fricas

b3 := vector [20,5,21]

$\label{eq18}\left[{20}, \: 5, \:{21}\right]$

(18)

Type: Vector(PositiveInteger?)

fricas

B3 := [3,4,5]

$\label{eq19}\left[ 3, \: 4, \: 5 \right]$

(19)

Type: List(PositiveInteger?)

fricas

X3:= [25.0,20.0,0.0,1.0,0.0]

$\label{eq20}\left[{25.0}, \:{20.0}, \:{0.0}, \:{1.0}, \:{0.0}\right]$

(20)

Type: List(Float)

fricas

objVal3:= - 1600.0

$\label{eq21}-{1600.0}$

(21)

Type: Float

fricas

Basis3:= [2,4,1]

$\label{eq22}\left[ 2, \: 4, \: 1 \right]$

(22)

Type: List(PositiveInteger?)

fricas

r3:=revisedSimplex(A3, b3, c3, B3)

   >> System error:
   The value
  (0 . 0)
is not of type
  UNSIGNED-BYTE

   Continuing to read the file...

testEquals("floatNull(r3.X-X3)", "true")

   There are no library operations named r3 
      Use HyperDoc Browse or issue
                                 )what op r3
      to learn if there is any operation containing " r3 " in its name.

   Cannot find a definition or applicable library operation named r3 
      with argument type(s) 
                                 Variable(X)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

Type: Void

fricas

testEquals("abs(r3.objVal-objVal3)<eps", "true")

   There are no library operations named r3 
      Use HyperDoc Browse or issue
                                 )what op r3
      to learn if there is any operation containing " r3 " in its name.

   Cannot find a definition or applicable library operation named r3 
      with argument type(s) 
                              Variable(objVal)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

Type: Void

fricas

testEquals("r3.Basis", "Basis3")

   There are no library operations named r3 
      Use HyperDoc Browse or issue
                                 )what op r3
      to learn if there is any operation containing " r3 " in its name.

   Cannot find a definition or applicable library operation named r3 
      with argument type(s) 
                               Variable(Basis)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

Type: Void

fricas

r3lu:=revisedSimplexLU(A3, b3, c3, B3)

   >> System error:
   The value
  (0 . 0)
is not of type
  UNSIGNED-BYTE

   Continuing to read the file...

testEquals("floatNull(r3lu.X-X3)", "true")

   There are no library operations named r3lu 
      Use HyperDoc Browse or issue
                                )what op r3lu
      to learn if there is any operation containing " r3lu " in its 
      name.

   Cannot find a definition or applicable library operation named r3lu 
      with argument type(s) 
                                 Variable(X)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

Type: Void

fricas

testEquals("abs(r3lu.objVal-objVal3)<eps", "true")

   There are no library operations named r3lu 
      Use HyperDoc Browse or issue
                                )what op r3lu
      to learn if there is any operation containing " r3lu " in its 
      name.

   Cannot find a definition or applicable library operation named r3lu 
      with argument type(s) 
                              Variable(objVal)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

Type: Void

fricas

testEquals("r3lu.Basis", "Basis3")

   There are no library operations named r3lu 
      Use HyperDoc Browse or issue
                                )what op r3lu
      to learn if there is any operation containing " r3lu " in its 
      name.

   Cannot find a definition or applicable library operation named r3lu 
      with argument type(s) 
                               Variable(Basis)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

Type: Void

fricas

--
A4 := matrix [[1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],_
              [0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0],_
              [0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0],_
              [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0],_
              [3, 0, 6, 0, 5, 0, 7, 0, 1, 0, 0, 0, 0, 0, 1, 0],_
              [0, 2, 0, 4, 0, 10, 0, 4, 0, 1, 0, 0, 0, 0, 0, 1]]

$\label{eq23}\left[ \begin{array}{cccccccccccccccc} 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \ 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \ 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \ 3 & 0 & 6 & 0 & 5 & 0 & 7 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \ 0 & 2 & 0 & 4 & 0 &{10}& 0 & 4 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1$

(23)

Type: Matrix(NonNegativeInteger?)

fricas

b4 := vector [1, 1, 1, 1, 13, 10]

$\label{eq24}\left[ 1, \: 1, \: 1, \: 1, \:{13}, \:{10}\right]$

(24)

Type: Vector(PositiveInteger?)

fricas

c4 := vector [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1]

$\label{eq25}\left[ 0, \: 0, \: 0, \: 0, \: 0, \: 0, \: 0, \: 0, \: 0, \: 0, \: 1, \: 1, \: 1, \: 1, \: 1, \: 1 \right]$

(25)

Type: Vector(NonNegativeInteger?)

fricas

B4 := [11, 12, 13, 14, 15, 16]

$\label{eq26}\left[{11}, \:{12}, \:{13}, \:{14}, \:{15}, \:{16}\right]$

(26)

Type: List(PositiveInteger?)

fricas

X4:= [1.0, 0.0, 0.25, 0.7500000000_0000000001, 0.3, 0.7, 1.0, 0.0, 0.0, 0.0,
      0.0, 0.0, 0.0, 0.0, 0.0, 0.0]

$\label{eq27}\begin{array}{@{}l} \displaystyle \left[{1.0}, \:{0.0}, \:{0.25}, \:{0.7500000000 \_ 0000000001}, \:{0.3}, \:{0.7}, \:{1.0}, \:{0.0}, \:{0.0}, \right. \ \ \displaystyle \left.\:{0.0}, \:{0.0}, \:{0.0}, \:{0.0}, \:{0.0}, \:{0.0}, \:{0.0}\right]$

(27)

Type: List(Float)

fricas

objVal4:= 0.0

$\label{eq28}0.0$

(28)

Type: Float

fricas

Basis4:= [1,3,6,5,7,4]

$\label{eq29}\left[ 1, \: 3, \: 6, \: 5, \: 7, \: 4 \right]$

(29)

Type: List(PositiveInteger?)

fricas

r4 := revisedSimplex( A4, b4, c4, B4)

   >> System error:
   The value
  (0 . 0)
is not of type
  UNSIGNED-BYTE

   Continuing to read the file...

testEquals("floatNull(r4.X-X4)", "true")

   There are no library operations named r4 
      Use HyperDoc Browse or issue
                                 )what op r4
      to learn if there is any operation containing " r4 " in its name.

   Cannot find a definition or applicable library operation named r4 
      with argument type(s) 
                                 Variable(X)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

Type: Void

fricas

testEquals("abs(r4.objVal-objVal4)<eps", "true")

   There are no library operations named r4 
      Use HyperDoc Browse or issue
                                 )what op r4
      to learn if there is any operation containing " r4 " in its name.

   Cannot find a definition or applicable library operation named r4 
      with argument type(s) 
                              Variable(objVal)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

Type: Void

fricas

testEquals("r4.Basis", "Basis4")

   There are no library operations named r4 
      Use HyperDoc Browse or issue
                                 )what op r4
      to learn if there is any operation containing " r4 " in its name.

   Cannot find a definition or applicable library operation named r4 
      with argument type(s) 
                               Variable(Basis)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

Type: Void

fricas

r4lu := revisedSimplexLU( A4, b4, c4, B4)

   >> System error:
   The value
  (0 . 0)
is not of type
  UNSIGNED-BYTE

   Continuing to read the file...

testEquals("floatNull(r4lu.X-X4)", "true")

   There are no library operations named r4lu 
      Use HyperDoc Browse or issue
                                )what op r4lu
      to learn if there is any operation containing " r4lu " in its 
      name.

   Cannot find a definition or applicable library operation named r4lu 
      with argument type(s) 
                                 Variable(X)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

Type: Void

fricas

testEquals("abs(r4lu.objVal-objVal4)<eps", "true")

   There are no library operations named r4lu 
      Use HyperDoc Browse or issue
                                )what op r4lu
      to learn if there is any operation containing " r4lu " in its 
      name.

   Cannot find a definition or applicable library operation named r4lu 
      with argument type(s) 
                              Variable(objVal)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

Type: Void

fricas

testEquals("r4lu.Basis", "Basis4")

   There are no library operations named r4lu 
      Use HyperDoc Browse or issue
                                )what op r4lu
      to learn if there is any operation containing " r4lu " in its 
      name.

   Cannot find a definition or applicable library operation named r4lu 
      with argument type(s) 
                               Variable(Basis)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

Type: Void

fricas

--
A5 := matrix [[1, -1, 1, 0, 0], [4, 9, 0, 1, 0], [-2, 4, 0, 0, 1]]

$\label{eq30}\left[ \begin{array}{ccccc} 1 & - 1 & 1 & 0 & 0 \ 4 & 9 & 0 & 1 & 0 \ - 2 & 4 & 0 & 0 & 1$

(30)

Type: Matrix(Integer)

fricas

c5 := vector [-1, -1, 0, 0, 0]

$\label{eq31}\left[ - 1, \: - 1, \: 0, \: 0, \: 0 \right]$

(31)

Type: Vector(Integer)

fricas

b5 := vector [2, 18, 4]

$\label{eq32}\left[ 2, \:{18}, \: 4 \right]$

(32)

Type: Vector(PositiveInteger?)

fricas

B5 := vector [3, 4, 5]

$\label{eq33}\left[ 3, \: 4, \: 5 \right]$

(33)

Type: Vector(PositiveInteger?)

fricas

X5 := [2.7692307692_307692308, 0.7692307692_3076923077, 0.0, 0.0,
       6.4615384615_384615385]

$\label{eq34}\begin{array}{@{}l} \displaystyle \left[{2.7692307692 \ 307692308}, \:{0.7692307692 \ 3076923 077}, \:{0.0}, \: \right. \ \ \displaystyle \left.{0.0}, \:{6.4615384615 \_ 384615385}\right]$

(34)

Type: List(Float)

fricas

objVal5:= - 3.5384615384_615384615

$\label{eq35}-{3.5384615384 \ 615384615}$

(35)

Type: Float

fricas

Basis5:= [1,2,5]

$\label{eq36}\left[ 1, \: 2, \: 5 \right]$

(36)

Type: List(PositiveInteger?)

fricas

r5 := revisedSimplex( A5, b5, c5, B5)

   >> System error:
   The value
  (0 . 0)
is not of type
  UNSIGNED-BYTE

   Continuing to read the file...

testEquals("floatNull(r5.X-X5)", "true")

   There are no library operations named r5 
      Use HyperDoc Browse or issue
                                 )what op r5
      to learn if there is any operation containing " r5 " in its name.

   Cannot find a definition or applicable library operation named r5 
      with argument type(s) 
                                 Variable(X)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

Type: Void

fricas

testEquals("abs(r5.objVal-objVal5)<eps", "true")

   There are no library operations named r5 
      Use HyperDoc Browse or issue
                                 )what op r5
      to learn if there is any operation containing " r5 " in its name.

   Cannot find a definition or applicable library operation named r5 
      with argument type(s) 
                              Variable(objVal)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

Type: Void

fricas

testEquals("r5.Basis", "Basis5") 

   There are no library operations named r5 
      Use HyperDoc Browse or issue
                                 )what op r5
      to learn if there is any operation containing " r5 " in its name.

   Cannot find a definition or applicable library operation named r5 
      with argument type(s) 
                               Variable(Basis)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

Type: Void

fricas

r5lu := revisedSimplexLU( A5, b5, c5, B5)

   >> System error:
   The value
  (0 . 0)
is not of type
  UNSIGNED-BYTE

   Continuing to read the file...

testEquals("floatNull(r5lu.X-X5)", "true")

   There are no library operations named r5lu 
      Use HyperDoc Browse or issue
                                )what op r5lu
      to learn if there is any operation containing " r5lu " in its 
      name.

   Cannot find a definition or applicable library operation named r5lu 
      with argument type(s) 
                                 Variable(X)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

Type: Void

fricas

testEquals("abs(r5lu.objVal-objVal5)<eps", "true")

   There are no library operations named r5lu 
      Use HyperDoc Browse or issue
                                )what op r5lu
      to learn if there is any operation containing " r5lu " in its 
      name.

   Cannot find a definition or applicable library operation named r5lu 
      with argument type(s) 
                              Variable(objVal)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

Type: Void

fricas

testEquals("r5lu.Basis", "Basis5") 

   There are no library operations named r5lu 
      Use HyperDoc Browse or issue
                                )what op r5lu
      to learn if there is any operation containing " r5lu " in its 
      name.

   Cannot find a definition or applicable library operation named r5lu 
      with argument type(s) 
                               Variable(Basis)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

Type: Void

fricas

-- Results/Statistics

fricas

)set output algebra on

fricas

)version

"FriCAS 1.3.10 compiled at Wed 10 Jan 02:19:45 CET 2024"

fricas

)lisp (lisp-implementation-type)

   Your user access level is compiler and this command is therefore not
      available. See the )set userlevel command for more information.

fricas

)lisp (lisp-implementation-version)

   Your user access level is compiler and this command is therefore not
      available. See the )set userlevel command for more information.

statistics()

   =============================================================================
   General WARNINGS:
   * do not use ')clear completely' before having used 'statistics()'
     It clears the statistics without warning!
   * do not forget to pass the arguments of the testXxxx functions as Strings!
     Otherwise, the test will fail and statistics() will not notice!

   =============================================================================
   Testsuite: Package: LinearProgramming
     failed (total): 1 (1)

     failed testcases were:
     ---------------------------------------------------------------------------
     Testcase: revisedSimplex
       failed (total): 30 (30)

     fatal tests were:

         1: EQUL: (floatNull(r1.X-X1), true)

         2: EQUL: (abs(r1.objVal-objVal1)<eps, true)

         3: EQUL: (r1.Basis, Basis1)

         4: EQUL: (floatNull(r1lu.X-X1), true)

         5: EQUL: (abs(r1lu.objVal-objVal1)<eps, true)

         6: EQUL: (r1lu.Basis, Basis1)

         7: EQUL: (floatNull(r2.X-X2), true)

         8: EQUL: (abs(r2.objVal-objVal2)<eps, true)

         9: EQUL: (r2.Basis, Basis2)

         10: EQUL: (floatNull(r2lu.X-X2), true)

         11: EQUL: (abs(r2lu.objVal-objVal2)<eps, true)

         12: EQUL: (r2lu.Basis, Basis2)

         13: EQUL: (floatNull(r3.X-X3), true)

         14: EQUL: (abs(r3.objVal-objVal3)<eps, true)

         15: EQUL: (r3.Basis, Basis3)

         16: EQUL: (floatNull(r3lu.X-X3), true)

         17: EQUL: (abs(r3lu.objVal-objVal3)<eps, true)

         18: EQUL: (r3lu.Basis, Basis3)

         19: EQUL: (floatNull(r4.X-X4), true)

         20: EQUL: (abs(r4.objVal-objVal4)<eps, true)

         21: EQUL: (r4.Basis, Basis4)

         22: EQUL: (floatNull(r4lu.X-X4), true)

         23: EQUL: (abs(r4lu.objVal-objVal4)<eps, true)

         24: EQUL: (r4lu.Basis, Basis4)

         25: EQUL: (floatNull(r5.X-X5), true)

         26: EQUL: (abs(r5.objVal-objVal5)<eps, true)

         27: EQUL: (r5.Basis, Basis5)

         28: EQUL: (floatNull(r5lu.X-X5), true)

         29: EQUL: (abs(r5lu.objVal-objVal5)<eps, true)

         30: EQUL: (r5lu.Basis, Basis5)

   =============================================================================
   testsuite | testcases: failed (total) | tests: failed (total)
   Package: LinearProgramming    1     (1)              30    (30)
   =============================================================================
   File summary.
   unexpected failures: 30
   expected failures: 0
   unexpected passes: 0
   total tests: 30

Type: Void