// see https://www.youtube.com/watch?v=Axg9OhJ4cjg (german) bottom row is negative unlike in the video
// see http://de.slideshare.net/itsmedv91/special-cases-in-simplex special cases
// TODO< handle other special cases >
public Result iterate()
{
setupVariables();
// for now we use a iteration counter to protect us from infinite loops
// TODO< implement loop detection scheme, basic idea
// * we manage a fixed sized array as a sliding window or the hashes of the operations
// * if we detect a loop we apply bland's rule to resolve it (is the rule detection realy neccesary?)
//
//
// * every operation (pivot column, pivot row, number of pivot element itself) gets an hash
// * at each iteration we subtract the previous hash and add the current hash
// * if the hash doesn't change in n iteration(where n == 2 for the simple loop) we are looping
// >
// TODO< implement https://en.wikipedia.org/wiki/Bland's_rule >
uint iterationCounter = 0;
const uint MaximalIterationCounter = 128;
for (;;)
{
iterationCounter++;
if (iterationCounter > MaximalIterationCounter)
{
return(new Result(Result.EnumSolverState.TOOMANYITERATIONS));
}
bool foundMaximumColumn;
int pivotColumnIndex = searchMinimumColumn(out foundMaximumColumn);
// all values in the target value row are < 0.0, done
if (!foundMaximumColumn)
{
return(new Result(Result.EnumSolverState.FOUNDSOLUTION));
}
//std.cout << "min column " << pivotColumnIndex << std.endl;
if (areAllEntriesOfPivotColumnNegativeOrZero(pivotColumnIndex))
{
// solution is unbounded
return(new Result(Result.EnumSolverState.UNBOUNDEDSOLUTION));
}
// divide numbers of pivot column with right side and store in temporary vector
Matrix minRatioVector = divideRightSideWithPivotColumnWhereAboveZero(pivotColumnIndex);
//std.cout << "temporary vector" << std.endl;
//std.cout << minRatioVector << std.endl;
int minIndexOfTargetFunctionCoefficient = getMinIndexOfMinRatioVector(minRatioVector);
bool positiveMinRatioExists = doesPositiveMinRatioExist(minRatioVector);
if (!positiveMinRatioExists)
{
// solution is unbounded
return(new Result(Result.EnumSolverState.UNBOUNDEDSOLUTION));
}
int pivotRowIndex = minIndexOfTargetFunctionCoefficient;
//std.cout << "pivotRowIndex " << pivotRowIndex << std.endl;
// C++ code was matrix(pivotRowIndex, pivotColumnIndex)
double pivotElement = matrix[pivotRowIndex, pivotColumnIndex];
// divide the pivot row with the pivot element
MatrixUtilities.block(matrix, (uint)pivotRowIndex, 0, 1, matrix.columns).div(pivotElement);
// TODO< assert that pivot elemnt is roughtly 1.0 >
// do pivot operation
for (int pivotRowIteration = 0; pivotRowIteration < matrix.rows; pivotRowIteration++)
{
if (pivotRowIteration == pivotRowIndex)
{
continue;
}
double iterationElementAtPivotColumn = matrix[pivotRowIteration, pivotColumnIndex];
//matrix.block(pivotRowIteration, 0, 1, matrix.columns) -= (matrix.block(pivotRowIndex, 0, 1, matrix.columns) * iterationElementAtPivotColumn);
MatrixUtilities.block(matrix, (uint)pivotRowIteration, 0, 1, matrix.columns).subEqual(
MatrixUtilities.block(matrix, (uint)pivotRowIndex, 0, 1, matrix.columns).scaleAndDeref(iterationElementAtPivotColumn)
);
}
// set the variable identifier that we know which row of the matrix is for which variable
variables[pivotRowIndex] = new Variable(Variable.EnumType.NAMEME, pivotColumnIndex);
//std.cout << matrix << std.endl;
}
}