/// <summary>
///
/// </summary>
/// <param name="A"></param>
/// <param name="indexes"></param>
/// <param name="work"></param>
/// <returns></returns>
public static DoubleMatrix1D Permute(DoubleMatrix1D A, int[] indexes, double[] work)
{
// check validity
int size = A.Size;
if (indexes.Length != size)
{
throw new IndexOutOfRangeException("invalid permutation");
}
/*
* int i=size;
* int a;
* while (--i >= 0 && (a=indexes[i])==i) if (a < 0 || a >= size) throw new IndexOutOfRangeException("invalid permutation");
* if (i<0) return; // nothing to permute
*/
if (work == null || size > work.Length)
{
work = A.ToArray();
}
else
{
A.ToArray(ref work);
}
for (int i = size; --i >= 0;)
{
A[i] = work[indexes[i]];
}
return(A);
}
/// <summary>
/// Update the SVD with the addition of a new column.
/// </summary>
/// <param name="c">
/// The new column.
/// </param>
/// <param name="wantV">
/// Whether the matrix V is needed.
/// </param>
public void Update(DoubleMatrix1D c, bool wantV)
{
int nRows = c.Size - _m;
if (nRows > 0)
{
_u = DoubleFactory2D.Dense.AppendRows(_u, new SparseDoubleMatrix2D(nRows, _n));
_m = c.Size;
}
else if (nRows < 0)
{
c = DoubleFactory1D.Sparse.AppendColumns(c, DoubleFactory1D.Sparse.Make(-nRows));
}
var d = DoubleFactory2D.Dense.Make(c.ToArray(), c.Size);
// l = U'd is the eigencoding of d
var l = _u.ViewDice().ZMult(d, null);
////var uu = _u.ZMult(_u.ViewDice(), null);
// Ul = UU'd
////var ul = uu.ZMult(d, null);
var ul = _u.ZMult(l, null);
// h = d - UU'd = d - Ul is the component of d orthogonal to the subspace spanned by U
////var h = d.Copy().Assign(uu.ZMult(d, null), BinaryFunctions.Minus);
////var h = d.Copy().Assign(ul, BinaryFunctions.Minus);
// k is the projection of d onto the subspace othogonal to U
var k = Math.Sqrt(d.Aggregate(BinaryFunctions.Plus, a => a * a) - (2 * l.Aggregate(BinaryFunctions.Plus, a => a * a)) + ul.Aggregate(BinaryFunctions.Plus, a => a * a));
// truncation
if (k == 0 || double.IsNaN(k))
{
return;
}
_n++;
// j = d - UU'd = d - Ul is an orthogonal basis for the component of d orthogonal to the subspace spanned by U
////var j = h.Assign(UnaryFunctions.Div(k));
var j = d.Assign(ul, BinaryFunctions.Minus).Assign(UnaryFunctions.Div(k));
// Q = [ S, l; 0, ||h||]
var q =
DoubleFactory2D.Sparse.Compose(
new[] { new[] { S, l }, new[] { null, DoubleFactory2D.Dense.Make(1, 1, k) } });
var svdq = new SingularValueDecomposition(q, true, wantV, true);
_u = DoubleFactory2D.Dense.AppendColumns(_u, j).ZMult(svdq.U, null);
_s = svdq.SingularValues;
if (wantV)
{
_v = DoubleFactory2D.Dense.ComposeDiagonal(_v, DoubleFactory2D.Dense.Identity(1)).ZMult(
svdq.V, null);
}
}
/// <summary>
/// 3-d OLAP cube operator; Fills all cells of the given vectors into the given histogram.
/// If you use Hep.Aida.Ref.Converter.ToString(histo) on the result, the OLAP cube of x-"column" vsd y-"column" vsd z-"column", summing the weights "column" will be printed.
/// For example, aggregate sales by product by region by time.
/// <p>
/// Computes the distinct values of x and y and z, yielding histogram axes that capture one distinct value per bin.
/// Then fills the histogram.
/// </summary>
/// <param name="x"></param>
/// <param name="y"></param>
/// <param name="z"></param>
/// <param name="weights"></param>
/// <returns>the histogram containing the cube.</returns>
/// <excption cref="ArgumentException">if <i>x.Count != y.Count || x.Count != z.Count || x.Count != weights.Count</i>.</excption>
public static Hep.Aida.IHistogram3D cube(DoubleMatrix1D x, DoubleMatrix1D y, DoubleMatrix1D z, DoubleMatrix1D weights)
{
if (x.Size != y.Size || x.Size != z.Size || x.Size != weights.Size)
{
throw new ArgumentException("vectors must have same size");
}
var epsilon = 1.0E-9;
var distinct = new DoubleArrayList();
var vals = new double[x.Size];
var sorted = new DoubleArrayList(vals);
// compute distinct values of x
vals = x.ToArray(); // copy x into vals
sorted.Sort();
Cern.Jet.Stat.Descriptive.Frequencies(sorted, distinct, null);
// since bins are right-open [from,to) we need an additional dummy bin so that the last distinct value does not fall into the overflow bin
if (distinct.Count > 0)
{
distinct.Add(distinct[distinct.Count - 1] + epsilon);
}
distinct.TrimToSize();
Hep.Aida.IAxis xaxis = new Hep.Aida.Ref.VariableAxis(distinct.ToArray());
// compute distinct values of y
vals = y.ToArray();
sorted.Sort();
Cern.Jet.Stat.Descriptive.Frequencies(sorted, distinct, null);
// since bins are right-open [from,to) we need an additional dummy bin so that the last distinct value does not fall into the overflow bin
if (distinct.Count > 0)
{
distinct.Add(distinct[distinct.Count - 1] + epsilon);
}
distinct.TrimToSize();
Hep.Aida.IAxis yaxis = new Hep.Aida.Ref.VariableAxis(distinct.ToArray());
// compute distinct values of z
vals = z.ToArray();
sorted.Sort();
Cern.Jet.Stat.Descriptive.Frequencies(sorted, distinct, null);
// since bins are right-open [from,to) we need an additional dummy bin so that the last distinct value does not fall into the overflow bin
if (distinct.Count > 0)
{
distinct.Add(distinct[distinct.Count - 1] + epsilon);
}
distinct.TrimToSize();
Hep.Aida.IAxis zaxis = new Hep.Aida.Ref.VariableAxis(distinct.ToArray());
Hep.Aida.IHistogram3D histo = new Hep.Aida.Ref.Histogram3D("Cube", xaxis, yaxis, zaxis);
return(Histogram(histo, x, y, z, weights));
}
/// <summary>
/// Initializes a new instance of the <see cref="SingularValueDecomposition"/> class with a vector (the first column).
/// </summary>
/// <param name="arg">
/// A vector.
/// </param>
/// <exception cref="ArgumentException">
/// If <code>a.Rows < a.Columns</code>.
/// </exception>
public SingularValueDecomposition(DoubleMatrix1D arg)
{
BatchSVD(DoubleFactory2D.Dense.Make(arg.ToArray(), arg.Size), true, true, true);
}