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/* split free variables
*
* PCx 1.1 11/97
*
* Authors: Joe Czyzyk, Sanjay Mehrotra, Michael Wagner, Steve Wright.
*
* (C) 1996 University of Chicago. See COPYRIGHT in main directory.
*/
#include <stdio.h>
#include <string.h>
#include <math.h>
#include "memory.h"
#include "main.h"
int SplitFreeVars(LP)
LPtype *LP;
{
int col, NextCol, FreeCounter, NextEnt, entry, NumberFree,
NewCols, NewEnts, MoreEnts, NextBound, NewBounds;
LPtype *MakeTranspose();
/* count number of free variables */
for (col = 0, NumberFree = 0, MoreEnts = 0; col < LP->Cols; col++)
if (LP->VarType[col] == FREE) {
NumberFree++;
MoreEnts += (LP->A.pEndRow[col] - LP->A.pBeginRow[col] + 1);
}
/* Reallocate memory to allow for larger vectors, etc. */
NewEnts = LP->Ents + MoreEnts;
NewCols = LP->Cols + NumberFree;
if (LP->FreePlus) Free((char *) LP->FreePlus);
LP->FreePlus = NewInt(NumberFree, "LP->FreePlus");
if (LP->FreeMinus) Free((char *) LP->FreeMinus);
LP->FreeMinus = NewInt(NumberFree, "LP->FreeMinus");
LP->c = (double *)
Realloc(LP->c, NewCols * sizeof(double), "LP->c");
LP->VarType = (int *)
Realloc(LP->VarType, NewCols * sizeof(int), "LP->VarType");
LP->UpBound = (double *)
Realloc(LP->UpBound, NewCols * sizeof(double), "LP->UpBound");
LP->A.pBeginRow = (int *)
Realloc(LP->A.pBeginRow, NewCols * sizeof(int), "LP->A.pBeginRow");
LP->A.pEndRow = (int *)
Realloc(LP->A.pEndRow, NewCols * sizeof(int), "LP->A.pEndRow");
LP->A.Row = (int *)
Realloc(LP->A.Row, NewEnts * sizeof(int), "LP->A.Row");
LP->A.Value = (double *)
Realloc(LP->A.Value, NewEnts * sizeof(double), "LP->A.Value");
LP->A.NumCols = NewCols; LP->A.Nonzeros = NewEnts;
/* LP->A.transpose already has the right number of columns, so just
allocate extra space for its additional nonzeros */
LP->Atranspose.Row = (int *)
Realloc(LP->Atranspose.Row, NewEnts * sizeof(int),
"LP->Atranspose.Row");
LP->Atranspose.Value = (double *)
Realloc(LP->Atranspose.Value, NewEnts * sizeof(double),
"LP->Atranspose.Value");
LP->Atranspose.NumRows = NewCols; LP->Atranspose.Nonzeros = NewEnts;
NextCol = LP->Cols; NextEnt = LP->Ents;
for (col = 0, FreeCounter = 0; col < LP->Cols; col++)
if (LP->VarType[col] == FREE) {
/* reset this column to NORMAL */
LP->VarType[col] = NORMAL;
LP->FreePlus[FreeCounter] = col;
/* make additional variable such that x = x^+ - x^- */
LP->VarType[NextCol] = NORMAL; /* add new split variable at end */
LP->FreeMinus[FreeCounter] = NextCol;
/* copy constraint matrix elements from original variable - flip signs */
LP->A.pBeginRow[NextCol] = NextEnt + 1;
for (entry = LP->A.pBeginRow[col] - 1; entry <= LP->A.pEndRow[col] - 1; entry++) {
LP->A.Row[NextEnt] = LP->A.Row[entry];
LP->A.Value[NextEnt] = -LP->A.Value[entry];
NextEnt++;
}
LP->A.pEndRow[NextCol] = NextEnt;
LP->c[NextCol] = -LP->c[col];
NextCol++;
FreeCounter++;
}
LP->Cols = NewCols;
LP->A.NumCols = NewCols;
LP->Ents = NewEnts;
LP->A.Nonzeros = NewEnts;
LP->NumberFree = 0;
LP->NumberSplit = NumberFree;
if (NextEnt != NewEnts) {
printf("Error splitting free variables: ");
printf("NextEnt (%d) != NewEnts (%d)\n", NextEnt, NewEnts);
}
if (NextCol != NewCols) {
printf("Error splitting free variables: ");
printf("NextCol (%d) != NewCols (%d)\n", NextCol, NewCols);
}
if (FreeCounter != NumberFree) {
printf("Error splitting free variables: ");
printf("FreeCounter (%d) != NumberFree (%d)\n", FreeCounter, NumberFree);
}
LP = MakeTranspose(LP);
return 0;
}
int UnSplitFreeVars(LP, Solution)
LPtype *LP;
solution *Solution;
{
int i, plus, minus;
for (i = 0; i < LP->NumberSplit; i++) {
plus = LP->FreePlus[i];
minus = LP->FreeMinus[i];
Solution->x[plus] = Solution->x[plus] - Solution->x[minus];
Solution->DualLower[plus] = 0.0;
LP->VarType[plus] = FREE;
}
LP->Cols -= LP->NumberSplit;
LP->A.NumCols -= LP->NumberSplit;
Solution->Columns -= LP->NumberSplit;
return 0;
}
/* Implement the split-shift heuristic for dealing with free vars */
int ShiftSplitVariables(LP, Current)
LPtype *LP;
Iterate *Current;
{
int i, im, ip;
int NumCols, NumBounds;
double mutemp=0.0, splitshift, xmax, xmin,
goal, avx, sxmax=0.0, smin=10.e0, smax=100.e0;
NumCols = LP->Cols;
NumBounds = LP->NumberBounds;
mutemp = 0.0; avx = 0.0;
for (i = 0; i < NumCols; i++) {
mutemp += Current->x[i] * Current->s[i];
avx += Current->x[i];
}
for (i = 0; i < NumBounds; i++) {
mutemp += Current->w[i] * Current->r[i];
avx += Current->w[i];
}
/* Shifts each split-variable pair so that the smaller of the two takes on
* the value MID(smin, larger-smaller, smax). Adjusts the s components
* accordingly. */
for (i = 0; i < LP->NumberSplit; i++) {
im = LP->FreeMinus[i];
ip = LP->FreePlus[i];
mutemp -= ( Current->x[ip] * Current->s[ip] +
Current->x[im] * Current->s[im]);
avx -= (Current->x[ip] + Current->x[im]);
sxmax = MAX(Current->x[ip], Current->x[im]);
}
mutemp /= (NumCols + NumBounds - 2*LP->NumberSplit);
avx /= (NumCols + NumBounds - 2*LP->NumberSplit);
for (i = 0; i < LP->NumberSplit; i++) {
im = LP->FreeMinus[i];
ip = LP->FreePlus[i];
xmax = MAX(Current->x[ip], Current->x[im]);
xmin = MIN(Current->x[ip], Current->x[im]);
/* shift so that the geometric mean of the shifted var equals avx */
splitshift = (xmax-xmin)*(xmax-xmin) + 4.0*avx*avx;
splitshift = sqrt(splitshift) - (xmax-xmin);
splitshift/= 2.0;
if (splitshift > smax) splitshift = smax;
if (splitshift < smin) splitshift = smin;
splitshift = xmin - splitshift;
Current->x[ip] -= splitshift;
Current->x[im] -= splitshift;
}
/* finally, adjust duals so that the average pairwise product is
achieved by the split vars */
goal = 1.e-2;
for (i = 0; i < LP->NumberSplit; i++) {
im = LP->FreeMinus[i];
ip = LP->FreePlus[i];
if (Current->s[im] * Current->x[im] < goal*mutemp)
Current->s[im] = goal * mutemp / Current->x[im];
if (Current->s[ip] * Current->x[ip] < goal*mutemp)
Current->s[ip] = goal * mutemp / Current->x[ip];
}
return 0;
}
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