private static void Pivot(CompactTableau ct, int k, int l)
{
double[][] t = ct.t;
for (int i = 0; i <= ct.m; i++) {
if (i == k) {
continue;
}
for (int j = 0; j <= ct.n; j++) {
if (j == l) {
continue;
}
t[i][j] = (t[i][j] * t[k][l] - t[i][l] * t[k][j]) / t[k][l];
}
}
for (int i = 0; i <= ct.m; i++) {
if (i != k) {
t[i][l] = -t[i][l] / t[k][l];
}
}
for (int j = 0; j <= ct.n; j++) {
if (j != l) {
t[k][j] /= t[k][l];
}
}
t[k][l] = 1 / t[k][l];
// Change indices.
int tmp = ct.ind[ct.n + k];
ct.ind[ct.n + k] = ct.ind[l];
ct.ind[l] = tmp;
}
private static int ChooseRow(CompactTableau ct, int l)
{
int k = -1;
double tkmin = double.MaxValue;
double[][] t = ct.t;
for (int i = 0; i < ct.m; i++) {
if (t[i][l] > 0) {
double tk = t[i][ct.n] / t[i][l];
if (tk < tkmin) {
tkmin = tk;
k = i;
}
}
}
return k;
}
private static int ChooseRowBlandDual(CompactTableau ct)
{
for (int i = 0; i < ct.m; i++) {
if (ct.t[i][ct.n] < 0) {
return i;
}
}
return -1;
}
private static int ChooseColumnDual(CompactTableau ct, int k)
{
int l = -1;
double tlmin = double.MaxValue;
double[][] t = ct.t;
for (int j = 0; j < ct.n; j++) {
if (t[k][j] < 0) {
double tl = t[ct.m][j] / t[k][j];
if (tl < tlmin) {
tlmin = tl;
l = j;
}
}
}
return l;
}
// Use this if you like infinite loops.
private static int ChooseColumnMax(CompactTableau ct)
{
int l = 0;
double max = Double.MinValue;
double tmj;
for (int j = 0; j < ct.n; j++) {
tmj = ct.t[ct.m][j];
if (tmj > 0 && tmj > max) {
max = tmj;
l = j;
}
}
return l;
}
public static void SolveDual(CompactTableau ct)
{
SolveDual(ct, null);
}
public double[] simplex(CompactTableau ct)
{
Simplex.SolveFeasible(ct, notify);
return ct.MakeSolution();
}
private string XNumber(CompactTableau ct, int j)
{
if (ct.hasU && ct.ind[j] == ct.ind.Length - 1) {
return "u";
}
return "x<sub>" + (ct.ind[j] + 1) + "</sub>";
}
public static void SolveFeasible(CompactTableau ct)
{
SolveFeasible(ct, null);
}
private void PrintSimplexHeader(StringBuilder sb, CompactTableau ct)
{
sb.Append("<tr class='header'>");
for (int j = 0; j < ct.n; j++) {
sb.AppendFormat("<td>" + XNumber(ct, j) + "</td>");
}
sb.Append("<td class='rhs'>-1</td>");
sb.Append("<td> </td>");
sb.Append("</tr>");
}
private string PrintSimplexTableau(CompactTableau ct)
{
StringBuilder sb = new StringBuilder();
sb.Append("<table class='simplex-tableau'>");
PrintSimplexHeader(sb, ct);
for (int i = 0; i < ct.m; i++) {
sb.Append("<tr>");
for (int j = 0; j < ct.n; j++) {
sb.AppendFormat("<td>{0:0.###}</td>", ct.t[i][j]);
}
sb.AppendFormat("<td class='rhs'>{0:0.###}</td>",
ct.t[i][ct.n]);
sb.AppendFormat("<td class='last'>= -{0}</td>",
XNumber(ct, ct.n + i));
sb.Append("</tr>");
}
PrintSimplexFooter(sb, ct);
sb.Append("</table>");
return sb.ToString();
}
private void PrintSimplexFooter(StringBuilder sb, CompactTableau ct)
{
sb.Append("<tr class='footer'>");
for (int j = 0; j < ct.n; j++) {
sb.AppendFormat("<td>{0:0.###}</td>", ct.t[ct.m][j]);
}
sb.AppendFormat("<td class='rhs'>{0:0.###}</td>",
ct.t[ct.m][ct.n]);
sb.Append("<td class='last'>= z</td>");
sb.Append("</tr>");
}
private string PrintDualTableau(CompactTableau ct)
{
StringBuilder sb = new StringBuilder();
sb.Append("<table class='simplex-dual-tableau'>");
for (int i = 0; i < ct.m; i++) {
sb.Append("<tr>");
sb.AppendFormat("<td class='first'>y<sub>{0}</sub></td>",
ct.ind[ct.n + i] + 1);
for (int j = 0; j < ct.n; j++) {
sb.AppendFormat("<td>{0:0.###}</td>", ct.t[i][j]);
}
sb.AppendFormat("<td class='last'>{0:0.###}</td>",
ct.t[i][ct.n]);
sb.Append("</tr>");
}
sb.Append("<tr>");
sb.Append("<td class='vals first'>-1</td>");
for (int j = 0; j < ct.n; j++) {
sb.AppendFormat("<td class='vals'>{0:0.###}</td>",
ct.t[ct.m][j]);
}
sb.AppendFormat("<td class='vals last'>{0:0.###}</td>",
ct.t[ct.m][ct.n]);
sb.Append("</tr>");
sb.Append("<tr>");
sb.Append("<td class='first'> </td>");
for (int j = 0; j < ct.n; j++) {
sb.AppendFormat("<td>= y<sub>{0}</sub></td>", ct.ind[j] + 1);
}
sb.AppendFormat("<td class='last'>= w</td>");
sb.Append("</tr>");
sb.Append("</table>");
return sb.ToString();
}
private string Print(CompactTableau ct)
{
return ct.dual ? PrintDualTableau(ct) : PrintSimplexTableau(ct);
}
public static CompactTableau CreateDualTableau(SimplexProblem p,
Action<string, object> notify)
{
if (notify != null) {
notify("Problem:", p);
}
int m = p.A[0].Length;
int n = p.A.Length;
double[][] t = new double[m + 1][];
for (int i = 0; i < m; i++) {
t[i] = new double[n + 1];
for (int j = 0; j < n; j++) {
t[i][j] = p.A[j][i];
}
t[i][n] = p.c[i];
}
t[m] = new double[n + 1];
Array.Copy(p.b, t[m], n);
int[] ind = new int[n + m];
for (int j = 0; j < n; j++) {
ind[j] = m + j;
}
for (int i = 0; i < m; i++) {
ind[n + i] = i;
}
CompactTableau ct = new CompactTableau(m, n, t, ind, false);
ct.dual = true;
if (notify != null) {
notify("Created dual tableau:", ct);
}
return ct;
}
public static void TransformToFeasible(CompactTableau ct, double[] c)
{
ct.n--;
double[][] t = ct.t;
int[] ind = ct.ind;
int m = ct.m;
int n = ct.n;
int uIndex = ind.Length - 1;
// Checking the position of the u in the columns.
int uPos = -1;
for (int i = 0; i <= n; i++) {
if (ind[i] == uIndex) {
uPos = i;
break;
}
}
if (uPos == -1) {
throw new InfeasibleProblemException();
}
// Removing the column.
for (int i = 0; i < m; i++) {
for (int j = uPos; j <= n; j++) {
t[i][j] = t[i][j + 1];
}
}
// Removing the extra index.
for (int j = uPos; j < uIndex; j++) {
ind[j] = ind[j + 1];
}
// Solving the new objective function.
for (int j = 0; j < n; j++) {
t[m][j] = (ind[j] < n) ? c[ind[j]] : 0;
}
t[m][n] = 0;
for (int i = 0; i < m; i++) {
if (ind[n + i] < n) {
for (int j = 0; j <= n; j++) {
t[m][j] -= c[ind[n + i]] * t[i][j];
}
}
}
ct.hasU = false;
}
public static void PivotInfeasibleTableau(CompactTableau ct)
{
int iMin = 0;
double iValMin = ct.t[iMin][ct.n];
for (int i = 1; i < ct.m; i++) {
if (ct.t[i][ct.n] < iValMin) {
iValMin = ct.t[i][ct.n];
iMin = i;
}
}
Pivot(ct, iMin, ct.n - 1);
}
private static int ChooseColumnBland(CompactTableau ct)
{
for (int j = 0; j < ct.n; j++) {
if (ct.t[ct.m][j] > 0) {
return j;
}
}
return -1;
}
public static void SolveDual(CompactTableau ct,
Action<string, object> notify)
{
int iter = 1;
while (true) {
int k = ChooseRowBlandDual(ct);
if (k == -1) {
break; // The optimal solution was found.
}
int l = ChooseColumnDual(ct, k);
if (l == -1) {
throw new UnboundedProblemException();
}
Pivot(ct, k, l);
if (notify != null) {
notify("After iteration " + iter + ":", ct);
}
iter++;
}
}
public double[] simplexDual(CompactTableau ct)
{
Simplex.SolveDual(ct, notify);
return ct.MakeDualSolution();
}