public void Smooth(ref double[,] inputValues)
{
// TODO: Using the matrix works, but does a lot of data accesses. Can improve by working out all the data access myself? I might be able to cut down on number of data accesses, but not sure.
var inputMatrix = new DenseMatrix(inputValues.GetLength(0), inputValues.GetLength(1));
for (int i = 0; i < inputMatrix.RowCount; i++)
{
inputMatrix.SetRow(i, Smooth(inputMatrix.Row(i).ToArray()));
}
for (int i = 0; i < inputMatrix.ColumnCount; i++)
{
inputMatrix.SetColumn(i, Smooth(inputMatrix.Column(i).ToArray()));
}
inputValues = inputMatrix.ToArray();
}
/// <summary>
/// Run example
/// </summary>
public void Run()
{
// Format vector output to console
var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone();
formatProvider.TextInfo.ListSeparator = " ";
// Create new empty square matrix
var matrix = new DenseMatrix(10);
Console.WriteLine(@"Empty matrix");
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 1. Fill matrix by data using indexer []
var k = 0;
for (var i = 0; i < matrix.RowCount; i++)
{
for (var j = 0; j < matrix.ColumnCount; j++)
{
matrix[i, j] = k++;
}
}
Console.WriteLine(@"1. Fill matrix by data using indexer []");
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 2. Fill matrix by data using At. The element is set without range checking.
for (var i = 0; i < matrix.RowCount; i++)
{
for (var j = 0; j < matrix.ColumnCount; j++)
{
matrix.At(i, j, k--);
}
}
Console.WriteLine(@"2. Fill matrix by data using At");
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 3. Clone matrix
var clone = matrix.Clone();
Console.WriteLine(@"3. Clone matrix");
Console.WriteLine(clone.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 4. Clear matrix
clone.Clear();
Console.WriteLine(@"4. Clear matrix");
Console.WriteLine(clone.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 5. Copy matrix into another matrix
matrix.CopyTo(clone);
Console.WriteLine(@"5. Copy matrix into another matrix");
Console.WriteLine(clone.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 6. Get submatrix into another matrix
var submatrix = matrix.SubMatrix(2, 2, 3, 3);
Console.WriteLine(@"6. Copy submatrix into another matrix");
Console.WriteLine(submatrix.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 7. Get part of the row as vector. In this example: get 4 elements from row 5 starting from column 3
var row = matrix.Row(5, 3, 4);
Console.WriteLine(@"7. Get part of the row as vector");
Console.WriteLine(row.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 8. Get part of the column as vector. In this example: get 3 elements from column 2 starting from row 6
var column = matrix.Column(2, 6, 3);
Console.WriteLine(@"8. Get part of the column as vector");
Console.WriteLine(column.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 9. Get columns using column enumerator. If you need all columns you may use ColumnEnumerator without parameters
Console.WriteLine(@"9. Get columns using column enumerator");
foreach (var keyValuePair in matrix.ColumnEnumerator(2, 4))
{
Console.WriteLine(@"Column {0}: {1}", keyValuePair.Item1, keyValuePair.Item2.ToString("#0.00\t", formatProvider));
}
Console.WriteLine();
// 10. Get rows using row enumerator. If you need all rows you may use RowEnumerator without parameters
Console.WriteLine(@"10. Get rows using row enumerator");
foreach (var keyValuePair in matrix.RowEnumerator(4, 3))
{
Console.WriteLine(@"Row {0}: {1}", keyValuePair.Item1, keyValuePair.Item2.ToString("#0.00\t", formatProvider));
}
Console.WriteLine();
// 11. Convert matrix into multidimensional array
var data = matrix.ToArray();
Console.WriteLine(@"11. Convert matrix into multidimensional array");
for (var i = 0; i < data.GetLongLength(0); i++)
{
for (var j = 0; j < data.GetLongLength(1); j++)
{
Console.Write(data[i, j].ToString("#0.00\t"));
}
Console.WriteLine();
}
Console.WriteLine();
// 12. Convert matrix into row-wise array
var rowwise = matrix.ToRowWiseArray();
Console.WriteLine(@"12. Convert matrix into row-wise array");
for (var i = 0; i < matrix.RowCount; i++)
{
for (var j = 0; j < matrix.ColumnCount; j++)
{
Console.Write(rowwise[(i * matrix.ColumnCount) + j].ToString("#0.00\t"));
}
Console.WriteLine();
}
Console.WriteLine();
// 13. Convert matrix into column-wise array
var columnise = matrix.ToColumnWiseArray();
Console.WriteLine(@"13. Convert matrix into column-wise array");
for (var i = 0; i < matrix.RowCount; i++)
{
for (var j = 0; j < matrix.ColumnCount; j++)
{
Console.Write(columnise[(j * matrix.RowCount) + i].ToString("#0.00\t"));
}
Console.WriteLine();
}
Console.WriteLine();
// 14. Get matrix diagonal as vector
var diagonal = matrix.Diagonal();
Console.WriteLine(@"14. Get matrix diagonal as vector");
Console.WriteLine(diagonal.ToString("#0.00\t", formatProvider));
Console.WriteLine();
}
private void optimize(DenseMatrix coefficients, DenseVector objFunValues, bool artifical)
{
//for calculations on the optimal solution row
int cCounter,
width = coefficients.ColumnCount;
DenseVector cBVect = new DenseVector(basics.Count);
//Sets up the b matrix
DenseMatrix b = new DenseMatrix(basics.Count, 1);
//basics will have values greater than coefficients.ColumnCount - 1 if there are still artificial variables
//or if Nathan is bad and didn't get rid of them correctly
foreach (int index in basics)
{
b = (DenseMatrix)b.Append(DenseVector.OfVector(coefficients.Column(index)).ToColumnMatrix());
}
// removes the first column
b = (DenseMatrix)b.SubMatrix(0, b.RowCount, 1, b.ColumnCount - 1);
double[] cPrimes = new double[width];
double[] rhsOverPPrime;
DenseMatrix[] pPrimes = new DenseMatrix[width];
DenseMatrix bInverse;
int newEntering, exitingRow;
bool optimal = false;
if(artifical)
{
rhsOverPPrime = new double[numConstraints + 1];
}
else
{
rhsOverPPrime = new double[numConstraints];
}
while (!optimal)
{
//calculates the inverse of b for this iteration
bInverse = (DenseMatrix)b.Inverse();
//updates the C vector with the most recent basic variables
cCounter = 0;
foreach (int index in basics)
{
cBVect[cCounter++] = objFunValues.At(index);
}
//calculates the pPrimes and cPrimes
for (int i = 0; i < coefficients.ColumnCount; i++)
{
if (!basics.Contains(i))
{
pPrimes[i] = (DenseMatrix)bInverse.Multiply((DenseMatrix)coefficients.Column(i).ToColumnMatrix());
//c' = objFunVals - cB * P'n
//At(0) to turn it into a double
cPrimes[i] = objFunValues.At(i) - (pPrimes[i].LeftMultiply(cBVect)).At(0);
}
else
{
pPrimes[i] = null;
}
}
//RHS'
xPrime = (DenseMatrix)bInverse.Multiply((DenseMatrix)rhsValues.ToColumnMatrix());
//Starts newEntering as the first nonbasic
newEntering = -1;
int iter = 0;
while(newEntering == -1)
{
if(!basics.Contains(iter))
{
newEntering = iter;
}
iter++;
}
//new entering becomes the small cPrime that corresponds to a non-basic value
for (int i = 0; i < cPrimes.Length; i++)
{
if (cPrimes[i] < cPrimes[newEntering] && !basics.Contains(i))
{
newEntering = i;
}
}
//if the smallest cPrime is >= 0, ie they are all positive
if (cPrimes[newEntering] >= 0)
{
optimal = true;
}
else
{
//fix me to deal with if all these values are negative
exitingRow = 0;
for (int i = 0; i < xPrime.RowCount; i++)
{
double[,] pPrime = pPrimes[newEntering].ToArray();
rhsOverPPrime[i] = xPrime.ToArray()[i, 0] / pPrime[i, 0];
if (rhsOverPPrime[i] < rhsOverPPrime[exitingRow] && rhsOverPPrime[i] > 0 )
{
exitingRow = i;
}
}
//translates from the index in the basics list to the actual row
exitingRow = basics[exitingRow];
//make sure you're not being stupid here!!!!
int tempIndex = basics.IndexOf(exitingRow);
basics.Remove(exitingRow);
basics.Insert(tempIndex, newEntering);
b.SetColumn(basics.IndexOf(newEntering), coefficients.Column(newEntering));
}
}
}