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Display matrix scaling information

Description
This example shows how to use the mmxprs subroutine 'getscale' to retrieve summary scaling information for matrix coefficients, RHS values and/or objective coefficients. The information is displayed in textual form and as an SVG bar chart.

scalestats.zip[download all files]

Source Files





scalestats.mos

(!******************************************************
   Mosel Example Problems
   ======================

   file scalestats.mos 
   ```````````````````
   Retrieving ranging information with graphical display.
 
   (c) 2020 Fair Isaac Corporation
       author: Z.Csizmadia, S.Heipcke Nov 2020
*******************************************************!)
model "test_scaleinfo"
 uses "mmxprs", "mmsystem", "mmsvg"
 parameters
   N = 30000          ! Number of variables
   M = 1000           ! Number of constraints
   L = 5              ! Limit value for display (must be in [5,...,20])
   SEL = 1+2+4        ! 1 - matrix coefficients, 2 - RHS, 4 - objective
 end-parameters

 declarations
   J = 1..N
   I = 1..M
   x,y: mpvar
   vars: dynamic array(J) of mpvar
   Rows: dynamic array(I) of linctr
   Buckets: set of integer
   Scaling: dynamic array(Buckets) of integer
   starttime: real
   procedure drawrange(CB: array(integer) of integer, limit: integer, fname: string)
 end-declarations

 starttime:= gettime
 setparam("xprs_matrixtol", 0.0)

! Constraint with coefficients in 'middle' buckets
 0.1 * x + y <= 6

! Constraints with extremely small and extremely large coefficients
 10^(-21) * x + 10 ^ 21 * y <= 6
 10^(-101) * x + 10 ^ 110 * y <= 6

! Generate further variables and constraints
 forall(j in J) create(vars(j))
 forall(i in I) do
   Rows(i):= sum(j in J) i*j*vars(j) <= i
   sum(j in J) 1.0/(i*j) * vars(j) <= 1 / i
 end-do
 
 writeln("Building time: ", gettime-starttime)

 setparam("xprs_verbose", true)
 starttime:= gettime
 loadprob(5)
 writeln("Loading time: ", gettime-starttime)

 starttime:= gettime
! SEL: range coeff selection: 1 - matrix coefficients, 2 - RHS, 4 - objective
 getscale(SEL, Scaling)

 writeln("Scale check time: ", gettime-starttime)

 forall (b in Buckets | exists(Scaling(b)))
   if (b > 20) then
     writeln( "[10^20, inf[ ", Scaling(b) )
   elif (b <= -19) then
     writeln( "[0, 10^(-20)[ ", Scaling(b) )
   else
     writeln( "[", 10^(b-1), ", ", 10^b, "[ ", Scaling(b) )
   end-if

 drawrange(Scaling, L, "coefrng.svg")

!**********************************
 !@doc.descr Configure and draw the range graphic
 !@doc.param CB the array of scaling bucket values
 !@doc.param limit value range to be displayed (value between 5 and 20)
 procedure drawrange(CB: array(DR:set of integer) of integer, limit: integer, fname: string)
  declarations
    CR: range
    pids: array(CR) of string
    ypos: dynamic array(CR) of real
  end-declarations

  LIM:=if(limit>20, 20, if(limit<5,5,limit)); TOFFSET:=10/LIM
  LFAC:=255/LIM; SCALE:= 5; YFAC:=minlist(2,15/LIM)
  MAXV:= maxlist(max(b in DR) CB(b),
    sum(i in DR | exists(CB(i)) and i>=LIM) CB(i),
    sum(i in DR | exists(CB(i)) and i<=-LIM) CB(i) )
  XFAC:= 150/MAXV; ct:=0  
  forall(b in -LIM..LIM, ct as counter) do 
    pids(b):="g"+b
    col:=svgcolor(round(abs(b)*LFAC),0,round(255-(abs(b)*LFAC)))
    ypos(b):=ct*5*YFAC
    if b = LIM then
      intervtxt:="[10E,"+(LIM-1)+" inf["
      totb:=sum(i in DR | exists(CB(i)) and i>=LIM) CB(i)
    elif b = -LIM then
      intervtxt:="[0, 10E-"+LIM+"["
      totb:=sum(i in DR | exists(CB(i)) and i<=-LIM) CB(i)
    else
      intervtxt:="[10E"+(b-1)+ ", 10E"+b+"["
      totb:=CB(b)
    end-if    
    svgaddgroup(pids(b), intervtxt, col)
    svgsetstyle(SVG_FILL, SVG_CURRENT)
    svgsetstyle(SVG_STROKE, col)
    svgsetstyle(SVG_FONTSIZE, 4*SCALE*minlist(1.25,YFAC))
    svgaddtext(0, ypos(b)+TOFFSET, intervtxt)   !text("10E")+b)
    if totb>0 then
      svgaddrectangle(40, ypos(b), totb*XFAC, 4*YFAC)
      svgaddtext(40+totb*XFAC+2,ypos(b)+TOFFSET,text(totb))
    end-if
  end-do
  svgaddgroup("msg", "", SVG_BLACK)
  svgsetstyle(SVG_FONTSIZE, 7*SCALE*minlist(1.25,YFAC))
  svgaddtext(0,150+20,"Coefficient ranges")
  XRANGE:=220; YRANGE:=150+32
  svgsetgraphviewbox(0,0,XRANGE,YRANGE)
  svgsetgraphscale(SCALE)
  svgsetgraphsize(XRANGE*SCALE,YRANGE*SCALE)

 ! Draw the graph
  svgrefresh

 ! Optionally save graphic to a file
  if fname<>"" then svgsave(fname); end-if

 ! Wait for display window to close
  svgwaitclose("Close browser window to terminate model execution.", 1)

 end-procedure
end-model

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