public static string SixPapFormat(SimplexProblem p)
{
int m = p.A.Length;
int n = p.A[0].Length;
StringBuilder sb = new StringBuilder();
sb.AppendFormat("objective: MAX\nm: {0}\ns: {1}\n", m, n);
sb.Append("C(j):");
for (var j = 0; j < n; j++) {
sb.Append(" " + p.c[j]);
}
sb.Append("\nconstraints:\n");
for (var i = 0; i < m; i++) {
sb.AppendFormat("({0}):", i + 1);
for (var j = 0; j < n; j++) {
sb.Append(" " + p.A[i][j]);
}
sb.AppendFormat(" < {0}\n", p.b[i]);
}
return sb.ToString();
}
public static CompactTableau CreateInfeasibleTableau(SimplexProblem p)
{
int m = p.A.Length;
int nOrig = p.A[0].Length;
int n = nOrig + 1;
double[][] t = new double[m + 1][];
for (int i = 0; i < m; i++) {
t[i] = new double[n + 1];
Array.Copy(p.A[i], t[i], nOrig);
t[i][nOrig] = -1;
t[i][n] = p.b[i];
}
t[m] = new double[n + 1];
t[m][nOrig] = -1;
int[] ind = new int[n + m];
for (int i = 0; i < nOrig; i++) {
ind[i] = i;
}
ind[nOrig] = ind.Length - 1;
for (int i = 0; i < m; i++) {
ind[n + i] = nOrig + i;
}
return new CompactTableau(m, n, t, ind, true);
}
public static CompactTableau CreateTableau(SimplexProblem p,
Action<string, object> notify)
{
CompactTableau ct;
if (notify != null) {
notify("Problem:", p);
}
if (p.IsInitiallyFeasible()) {
ct = CreateFeasibleTableau(p);
if (notify != null) {
notify("Created feasible tableau:", ct);
}
return ct;
}
ct = CreateInfeasibleTableau(p);
if (notify != null) {
notify("Created infeasible tableau:", ct);
}
PivotInfeasibleTableau(ct);
if (notify != null) {
notify("Pivoted infeasible tableau:", ct);
}
SolveFeasible(ct, notify);
TransformToFeasible(ct, p.c);
if (notify != null) {
notify("Removed column:", ct);
}
return 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 CompactTableau CreateFeasibleTableau(SimplexProblem p)
{
int m = p.A.Length;
int n = p.A[0].Length;
double[][] t = new double[m + 1][];
for (int i = 0; i < m; i++) {
t[i] = new double[n + 1];
Array.Copy(p.A[i], t[i], n);
t[i][n] = p.b[i];
}
t[m] = new double[n + 1];
Array.Copy(p.c, t[m], n);
int[] ind = new int[n + m];
for (int i = 0; i < ind.Length; i++) {
ind[i] = i;
}
return new CompactTableau(m, n, t, ind, false);
}
public static BigTableau CreateBigRestartedTableau(BigTableau bt,
SimplexProblem p)
{
int m = bt.m;
int n = bt.n;
int nVar = n - m;
double[][] t1 = bt.t;
double[][] t2 = new double[m + 1][];
// Allocating new matrix and setting the middle S* and y*T.
for (int i = 0; i <= m; i++) {
t2[i] = new double[n + 1];
Array.Copy(t1[i], nVar, t2[i], nVar, m);
}
// Setting S*b.
double sum;
for (int i = 0; i < m; i++) {
sum = 0.0;
for (int j = 0; j < m; j++) {
sum += t1[i][nVar + j] * p.b[j];
}
t2[i][n] = sum;
}
// Setting y*Tb.
sum = 0.0;
for (int j = 0; j < m; j++) {
sum += t1[m][nVar + j] * p.b[j];
}
t2[m][n] = sum;
// Setting S*A.
for (int i = 0; i < m; i++) {
for (int j = 0; j < nVar; j++) {
sum = 0.0;
for (int k = 0; k < nVar; k++) {
sum += t1[i][nVar + k] * p.A[k][j];
}
t2[i][j] = sum;
}
}
// Setting y*TA-cT.
for (int j = 0; j < nVar; j++) {
sum = 0.0;
for (int i = 0; i < m; i++) {
sum += t1[m][nVar + i] * p.A[i][j];
}
t2[m][j] = sum - p.c[j];
}
// Copying the labels.
int[] ind = new int[m];
Array.Copy(bt.ind, ind, m);
return new BigTableau(m, n, t2, ind);
}
public static BigTableau CreateBigTableau(SimplexProblem p,
Action<string, object> notify)
{
if (notify != null) {
notify("Problem:", p);
}
int m = p.A.Length;
int nVars = p.A[0].Length;
int n = m + nVars;
double[][] t = new double[m + 1][];
for (int i = 0; i < m; i++) {
t[i] = new double[n + 1];
Array.Copy(p.A[i], t[i], nVars);
t[i][nVars + i] = 1;
t[i][n] = p.b[i];
}
t[m] = new double[n + 1];
for (int i = 0; i < nVars; i++) {
t[m][i] = -p.c[i];
}
int[] ind = new int[m];
for (int i = 0; i < ind.Length; i++) {
ind[i] = nVars + i;
}
BigTableau bt = new BigTableau(m, n, t, ind);
if (notify != null) {
notify("Created tableau:", bt);
}
return bt;
}
public double[] simplex2(SimplexProblem p)
{
return simplex2(simplex2Tableau(p));
}
private string Print(SimplexProblem 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 = p.max ? "≤" : "≥";
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>{0}</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>≥</td><td>0</td></tr>");
sb.Append("</table>");
return sb.ToString();
}
public CompactTableau simplexTableau(SimplexProblem p)
{
return Simplex.CreateTableau(p, notify);
}
public double[] simplexDual(SimplexProblem p)
{
return simplexDual(simplexDualTableau(p));
}
public BigTableau simplex2TableauSolved(SimplexProblem p)
{
BigTableau bt = simplex2Tableau(p);
Simplex.SolveBig(bt, notify);
return bt;
}
public BigTableau simplex2Tableau(SimplexProblem p)
{
return Simplex.CreateBigTableau(p, notify);
}
public double[] simplex2Restart(BigTableau old, SimplexProblem p)
{
BigTableau bt2 = Simplex.CreateBigRestartedTableau(old, p);
if (notify != null) {
notify("Before pivoting:", bt2);
}
Simplex.FixBigRestartedTableau(bt2, notify);
return bt2.MakeSolution();
}