public static BigTableau F22c(double[][] A, double[] b, double[] c,
int[] ik, double[] beta, Action<string, object> notify)
{
int m = A.Length;
int n = A[0].Length;
int k = ik.Length;
int m2 = m + k;
int n2 = n + m + k;
double[] b2 = new double[m2];
Array.Copy(b, b2, m);
double[] c2 = new double[n2];
Array.Copy(c, c2, n);
double[][] A2 = new double[m2][];
for (int i = 0; i < m2; i++) {
A2[i] = new double[n2];
}
for (int i = 0; i < m; i++) {
Array.Copy(A[i], A2[i], n);
A2[i][n + i] = 1;
}
for (int i = 0; i < k; i++) {
A2[m + i][ik[i]] = 1;
A2[m + i][n + m + i] = -1;
b2[m + i] = beta[i];
}
EqSimplexProblem p = new EqSimplexProblem(true, A2, b2, c2);
if (notify != null) {
notify("Without artificial variables:", p);
}
return SolveArtificial(p, notify);
}
public static BigTableau SolveArtificial(EqSimplexProblem p,
Action<string, object> notify)
{
ArtEqSimplexProblem p2 = CreateWithArtificialVariables(p);
BigTableau bt = CreateBigTableau(p2, notify);
SolveBig(bt);
if (notify != null) {
notify("Final tableau:", bt);
}
if (Math.Abs(bt.t[bt.m][bt.n]) > 0) {
throw new InfeasibleProblemException();
}
BigTableau bt2 = EliminateArtificials(bt, p2, p);
if (notify != null) {
notify("After eliminating:", bt2);
}
SolveBig(bt2);
return bt2;
}
public static BigTableau EliminateArtificials(BigTableau bt,
ArtEqSimplexProblem p, EqSimplexProblem pOrig)
{
int nVars = bt.n - bt.m;
int n2 = bt.n - p.art.Length;
double[][] t = new double[bt.m + 1][];
for (int i = 0; i <= bt.m; i++) {
t[i] = new double[n2 + 1];
}
int k = 0;
for (int j = 0; j < bt.n; j++) {
if (j >= nVars && p.baseVar[j - nVars] == -1) {
continue;
}
for (int i = 0; i < bt.m; i++) {
t[i][k] = bt.t[i][j];
}
k++;
}
// Copy RHS.
for (int i = 0; i < bt.m; i++) {
t[i][n2] = bt.t[i][bt.n];
}
// Restoring the indices.
int[] ind = (int[])bt.ind.Clone();
for (int i = 0; i < ind.Length; i++) {
if (ind[i] >= nVars) {
ind[i] = p.baseVar[ind[i] - nVars];
}
}
bool[] nonBase = NonBase2(ind, n2);
// Solving the new objective function.
for (int j = 0; j <= n2; j++) {
if (!nonBase[j]) {
continue;
}
for (int i = 0; i < bt.m; i++) {
Console.WriteLine(j + " " + i + " ::: " + ind[i] + " " + t[i][j] + " " + pOrig.c[ind[i]]);
t[bt.m][j] += t[i][j] * pOrig.c[ind[i]];
}
}
return new BigTableau(bt.m, n2, t, ind);
}
public static ArtEqSimplexProblem CreateWithArtificialVariables(
EqSimplexProblem p)
{
int m = p.A.Length;
int[] baseVar = new int[m]; // -1 == needs an artificial one.
int nArtificial = 0;
// Find the base variable for each constraint.
for (int i = 0; i < m; i++) {
baseVar[i] = CalcBaseVar(p.A, p.c, i);
if (baseVar[i] == -1) {
nArtificial++;
}
}
bool[] nonBase = CalcNonBase(baseVar, m, p.c.Length);
int n = p.c.Length + nArtificial;
int nVar = n - m;
double[][] A = new double[m][];
for (int i = 0; i < m; i++) {
A[i] = new double[n];
}
int k = 0;
for (int j = 0; j < p.c.Length; j++) {
if (nonBase[j]) {
for (int i = 0; i < m; i++) {
A[i][k] = p.A[i][j];
}
k++;
}
}
double[] c = new double[n];
for (int i = 0; i < m; i++) {
A[i][nVar + i] = 1;
if (baseVar[i] == -1) {
c[nVar + i] = -1;
}
}
foreach (var item in c) {
Console.Write(item.ToString() + " ");
}
Console.WriteLine();
int[] art = new int[nArtificial];
k = 0;
for (int i = 0; i < m; i++) {
if (baseVar[i] == -1) {
art[k] = nVar + i;
k++;
}
}
return new ArtEqSimplexProblem(p.max, A, p.b, c, art, baseVar);
}
// TODO: All these printing things need to be simplified. And these
// functions especially need to be removed because of all the
// duplication.
private string Print(EqSimplexProblem p)
{
int m = p.A.Length;
int n = p.A[0].Length;
StringBuilder sb = new StringBuilder();
sb.Append("<table class='simplex-problem'>");
sb.AppendFormat("<tr><td class='first'>{0} ",
p.max ? "max" : "min");
string comp = "=";
string name = p.max ? "x" : "y";
bool first = true;
for (int j = 0; j < n; j++) {
AddX(sb, name, p.c[j], j, ref first);
}
sb.Append("</td></tr>");
for (int i = 0; i < m; i++) {
sb.Append("<tr><td class='first'>");
first = true;
for (int j = 0; j < n; j++) {
AddX(sb, name, p.A[i][j], j, ref first);
}
sb.AppendFormat("</td><td>=</td><td>{1:0.###}</td></tr>",
comp, p.b[i]);
}
sb.Append("<tr><td class='first'>");
for (int j = 0; j < n; j++) {
if (j > 0) {
sb.Append(",");
}
sb.AppendFormat("{0}<sub>{1}</sub>", name, j + 1);
}
sb.Append("</td><td>ā„</td><td>0</td></tr>");
sb.Append("</table>");
return sb.ToString();
}
public ArtEqSimplexProblem simplexArtEq(EqSimplexProblem p)
{
return Simplex.CreateWithArtificialVariables(p);
}
public double[] simplex3(EqSimplexProblem p)
{
BigTableau bt = Simplex.SolveArtificial(p, notify);
return bt.MakeSolutionAll();
}
