/// <summary>
/// Performs a principal component analysis of the data.
/// </summary>
/// <returns>The result of the principal component analysis.</returns>
/// <exception cref="InsufficientDataException">The number of data entries (<see cref="Count"/>) is
/// less than the number of variables (<see cref="Dimension"/>).</exception>
/// <seealso cref="PrincipalComponentAnalysis"/>
public PrincipalComponentAnalysis PrincipalComponentAnalysis()
{
if (Count < Dimension)
{
throw new InsufficientDataException();
}
// construct a (Count X Dimension) matrix of mean-centered data
double[] store = MatrixAlgorithms.AllocateStorage(Count, Dimension);
int i = 0;
for (int c = 0; c < Dimension; c++)
{
double mu = storage[c].Mean;
for (int r = 0; r < Count; r++)
{
store[i] = storage[c][r] - mu;
i++;
}
}
// bidiagonalize it
double[] a, b;
MatrixAlgorithms.Bidiagonalize(store, Count, Dimension, out a, out b);
// form the U and V matrices
double[] left = MatrixAlgorithms.AccumulateBidiagonalU(store, Count, Dimension);
double[] right = MatrixAlgorithms.AccumulateBidiagonalV(store, Count, Dimension);
// find the singular values of the bidiagonal matrix
MatrixAlgorithms.ExtractSingularValues(a, b, left, right, Count, Dimension);
// sort them
MatrixAlgorithms.SortValues(a, left, right, Count, Dimension);
PrincipalComponentAnalysis pca = new PrincipalComponentAnalysis(left, a, right, Count, Dimension);
return(pca);
}
/// <summary>
/// Performs a principal component analysis of the multivariate sample.
/// </summary>
/// <returns>The result of the principal component analysis.</returns>
/// <param name="columns">The set of columns to analyze.</param>
/// <exception cref="ArgumentNullException"><paramref name="columns"/> or one of its members is <see langword="null"/>.</exception>
/// <exception cref="DimensionMismatchException">The columns do not all have the same number of entries.</exception>
/// <exception cref="InsufficientDataException">The number of entries is less than the number of columns.</exception>
/// <remarks>
/// <para>For background on principal component analysis, see the remarks at <see cref="Meta.Numerics.Statistics.PrincipalComponentAnalysis"/>.</para>
/// <para>Note that the <paramref name="columns"/> argument is column-oriented, i.e. it is a list of columns,
/// not row-oriented, i.e. a list of rows. Either of these would match the method signature, but only
/// column-oriented inputs will produce correct results.</para>
/// </remarks>
/// <exception cref="ArgumentNullException"><paramref name="columns"/>, or one of the columns in it, is <see langword="null"/>.</exception>
/// <exception cref="DimensionMismatchException">Not all of the columns in <paramref name="columns"/> have the same length.</exception>
/// <exception cref="InsufficientDataException">There are fewer rows than columns.</exception>
/// <seealso href="https://en.wikipedia.org/wiki/Principal_component_analysis"/>
public static PrincipalComponentAnalysis PrincipalComponentAnalysis(this IReadOnlyList <IReadOnlyList <double> > columns)
{
if (columns == null)
{
throw new ArgumentNullException(nameof(columns));
}
int dimension = columns.Count;
int count = -1;
for (int c = 0; c < dimension; c++)
{
IReadOnlyList <double> column = columns[c];
if (column == null)
{
throw new ArgumentNullException(nameof(columns));
}
if (count < 0)
{
count = column.Count;
}
else
{
if (column.Count != count)
{
throw new DimensionMismatchException();
}
}
}
if (count < dimension)
{
throw new InsufficientDataException();
}
// construct a (Count X Dimension) matrix of mean-centered data
double[] store = MatrixAlgorithms.AllocateStorage(count, dimension);
int i = 0;
for (int c = 0; c < dimension; c++)
{
IReadOnlyList <double> column = columns[c];
double mu = column.Mean();
for (int r = 0; r < count; r++)
{
store[i] = column[r] - mu;
i++;
}
}
// bidiagonalize it
double[] a, b;
MatrixAlgorithms.Bidiagonalize(store, count, dimension, out a, out b);
// form the U and V matrices
double[] left = MatrixAlgorithms.AccumulateBidiagonalU(store, count, dimension);
double[] right = MatrixAlgorithms.AccumulateBidiagonalV(store, count, dimension);
// find the singular values of the bidiagonal matrix
MatrixAlgorithms.ExtractSingularValues(a, b, left, right, count, dimension);
// sort them
MatrixAlgorithms.SortValues(a, left, right, count, dimension);
PrincipalComponentAnalysis pca = new PrincipalComponentAnalysis(left, a, right, count, dimension);
return(pca);
}