/// <summary>
/// Run example
/// </summary>
/// <seealso cref="http://en.wikipedia.org/wiki/Matrix_norm">Matrix norm</seealso>
public void Run()
{
// Format matrix output to console
var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone();
formatProvider.TextInfo.ListSeparator = " ";
// Create square matrix
var matrix = new DenseMatrix(new[,] { { 1.0, 2.0, 3.0 }, { 6.0, 5.0, 4.0 }, { 8.0, 9.0, 7.0 } });
Console.WriteLine(@"Initial square matrix");
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 1. 1-norm of the matrix
Console.WriteLine(@"1. 1-norm of the matrix");
Console.WriteLine(matrix.L1Norm());
Console.WriteLine();
// 2. 2-norm of the matrix
Console.WriteLine(@"2. 2-norm of the matrix");
Console.WriteLine(matrix.L2Norm());
Console.WriteLine();
// 3. Frobenius norm of the matrix
Console.WriteLine(@"3. Frobenius norm of the matrix");
Console.WriteLine(matrix.FrobeniusNorm());
Console.WriteLine();
// 4. Infinity norm of the matrix
Console.WriteLine(@"4. Infinity norm of the matrix");
Console.WriteLine(matrix.InfinityNorm());
Console.WriteLine();
// 5. Normalize matrix columns
Console.WriteLine(@"5. Normalize matrix columns: before normalize");
foreach (var keyValuePair in matrix.ColumnEnumerator())
{
Console.WriteLine(@"Column {0} 2-nd norm is: {1}", keyValuePair.Item1, keyValuePair.Item2.Norm(2));
}
Console.WriteLine();
var normalized = matrix.NormalizeColumns(2);
Console.WriteLine(@"5. Normalize matrix columns: after normalize");
foreach (var keyValuePair in normalized.ColumnEnumerator())
{
Console.WriteLine(@"Column {0} 2-nd norm is: {1}", keyValuePair.Item1, keyValuePair.Item2.Norm(2));
}
Console.WriteLine();
// 6. Normalize matrix columns
Console.WriteLine(@"6. Normalize matrix rows: before normalize");
foreach (var keyValuePair in matrix.RowEnumerator())
{
Console.WriteLine(@"Row {0} 2-nd norm is: {1}", keyValuePair.Item1, keyValuePair.Item2.Norm(2));
}
Console.WriteLine();
normalized = matrix.NormalizeRows(2);
Console.WriteLine(@"6. Normalize matrix rows: after normalize");
foreach (var keyValuePair in normalized.RowEnumerator())
{
Console.WriteLine(@"Row {0} 2-nd norm is: {1}", keyValuePair.Item1, keyValuePair.Item2.Norm(2));
}
}
/// <summary>
/// Adaptive Cross Approximation (ACA) matrix compression
/// the result is stored in U and V matrices like U*V
/// </summary>
/// <param name="acaThres">Relative error threshold to stop adding rows and columns in ACA iteration</param>
/// <param name="m">Row indices of Z submatrix to compress</param>
/// <param name="n">Column indices of Z submatrix to compress</param>
/// <param name="U">to store result</param>
/// <param name="V">to store result</param>
/// <returns>pair with matrix U and V</returns>
public static Tuple<Matrix, Matrix> Aca(double acaThres, List<int> m, List<int> n, Matrix U, Matrix V)
{
int M = m.Count;
int N = n.Count;
int Min = Math.Min(M, N);
U = new DenseMatrix(Min, Min);
V = new DenseMatrix(Min, Min);
//if Z is a vector, there is nothing to compress
if (M == 1 || N == 1)
{
U = UserImpedance(m, n);
V = new DenseMatrix(1, 1);
V[0, 0] = 1.0;
return new Tuple<Matrix,Matrix>(U,V);
}
//Indices of columns picked up from Z
//Vector J = new DenseVector(N);
//List<int> J = new List<int>(N);
List<int> J = new List<int>(new int [N]);
//int[] J = new int[N];
//Indices of rows picked up from Z
//Vector I = new DenseVector(M);
List<int> I = new List<int>(new int [M]);
//int[] I = new int[M];
//Row indices to search for maximum in R
//Vector i = new DenseVector(M);
List<int> i = new List<int>();
//int[] i = new int[M];
//Column indices to search for maximum in R
//Vector j = new DenseVector(N);
List<int> j = new List<int>();
//int[] j = new int[N];
for (int k = 1; k < M; k++)
{
i.Add(k);
}
for (int k = 0; k < N; k++)
{
j.Add(k);
}
//Initialization
//Initialize the 1st row index I(1) = 1
I[0] = 0;
//Initialize the 1st row of the approximate error matrix
List<int> m0 = new List<int>();
m0.Add(m[I[0]]);
Matrix Rik = UserImpedance(m0, n);
//Find the 1st column index J(0)
double max = -1.0;
int col = 0;
foreach (int ind in j)
{
if (Math.Abs(Rik[0, ind]) > max)
{
max = Math.Abs(Rik[0, ind]);
col = ind;
}
}
//J[0] = j[col];
J[0] = col;
j.Remove(J[0]);
//First row of V
V = new DenseMatrix(1, Rik.ColumnCount);
V.SetRow(0, Rik.Row(0).Divide(Rik[0, J[0]]));
//Initialize the 1st column of the approximate error matrix
List<int> n0 = new List<int>();
n0.Add(n[J[0]]);
Matrix Rjk = UserImpedance(m, n0);
//First column of U
U = new DenseMatrix(Rjk.RowCount, 1);
U.SetColumn(0, Rjk.Column(0));
// Norm of (approximate) Z, to test error
double d1 = U.L2Norm();
double d2 = V.L2Norm();
double normZ = d1 * d1 * d2 * d2;
//Find 2nd row index I(2)
int row = 0;
max = -1.0;
foreach (int ind in i)
{
if (Math.Abs(Rjk[ind, 0]) > max)
{
max = Math.Abs(Rjk[ind, 0]);
row = ind;
}
}
//I[1] = i[row];
I[1] = row;
i.Remove(I[1]);
//Iteration
for (int k = 1; k < Math.Min(M, N); k++)
{
//Update (Ik)th row of the approximate error matrix:
List<int> t1 = new List<int>();
t1.Add(m[I[k]]);
Rik = (Matrix)(UserImpedance(t1, n) - U.SubMatrix(I[k], 1, 0, U.ColumnCount).Multiply(V));
//CHECKED OK all code before works fine
//Find kth column index Jk
max = -1.0;
col = 0;
foreach (int ind in j)
{
if (Math.Abs(Rik[0, ind]) > max)
{
max = Math.Abs(Rik[0, ind]);
col = ind;
}
}
J[k] = col;
j.Remove(J[k]);
//Terminate if R(I(k),J(k)) == 0
if (Rik[0, J[k]] == 0)
{
break;
}
//Set k-th row of V equal to normalized error
Matrix Vk = (Matrix)Rik.Divide(Rik[0, J[k]]);
//Update (Jk)th column of the approximate error matrix
List<int> n1 = new List<int>();
n1.Add(n[J[k]]);
Rjk = (Matrix)(UserImpedance(m, n1) - U.Multiply(V.SubMatrix(0, V.RowCount, J[k], 1)));
// Set k-th column of U equal to updated error
Matrix Uk = Rjk;
//Norm of approximate Z
//Matrix s = (Matrix)(U.Transpose().Multiply(Uk)).Multiply((Vk.Multiply(V.Transpose())).Transpose());
//Matrix s = (Matrix)((U.Transpose()).Multiply(Uk)).Multiply(((Vk.Multiply(V.Transpose())).Transpose()));
Matrix a = (Matrix)U.Transpose().Multiply(Uk);
Matrix b = (Matrix)Vk.Multiply(V.Transpose()).Transpose();
Matrix s = (Matrix)a.PointwiseMultiply(b);
double sum = 0;
for (int i1 = 0; i1 < s.RowCount; i1++)
{
for (int j1 = 0; j1 < s.ColumnCount; j1++)
{
sum += s[i1, j1];
}
}
d1 = Uk.L2Norm();
d2 = Vk.L2Norm();
normZ += 2 * sum + d1 * d1 * d2 * d2;
//Update U and V
//U.SetColumn(U.ColumnCount - 1, Uk.Column(0));
//V.SetRow(V.RowCount - 1, Vk.Row(0));
U = AddColumn(U, (Vector)Uk.Column(0));
//U.SetColumn(k, Uk.Column(0));
V = AddRow(V, (Vector)Vk.Row(0));
//V.SetRow(k, Vk.Row(0));
if (d1 * d2 <= acaThres * Math.Sqrt(normZ))
{
break;
}
if (k == Math.Min(N, M) - 1)
{
break;
}
max = -1;
row = 0;
foreach (int ind in i)
{
if (Math.Abs(Rjk[ind, 0]) > max)
{
max = Math.Abs(Rjk[ind, 0]);
row = ind;
}
}
I[k + 1] = row;
//i = removeIndex(i,I[k+1]);
i.Remove(I[k + 1]);
}
return new Tuple<Matrix, Matrix>(U, V);
}
