function

LinearAlgebra.covarianceRoot

Lower triangular covariance root from factor columns

Public declarations

Explicit source declarations; dimensions, modifications and defaults are shown as written, without evaluation.

Role	Name	Type	Dimensions / attributes / default	Description
input	`columns`	`Real`	`[:, :]`
output	`root`	`Real`	`[size(columns, 1), size(columns, 1)]`

Modelica declarations and implementation

Show parameters, interfaces and source

Parameters, inputs, outputs, defaults and equations from the source file.

function covarianceRoot "Lower triangular covariance root from factor columns"
  input Real columns[:, :];
  output Real root[size(columns, 1), size(columns, 1)];
protected
  Real work[size(columns, 2), size(columns, 1)];
  Real upperRow[size(columns, 1)];
  Real scale;
  Real radius;
  Real cosine;
  Real sine;
algorithm
  work := transpose(columns);
  for column in 1:size(columns, 1) loop
    for row in (column + 1):size(work, 1) loop
      scale := max(abs(work[column, column]), abs(work[row, column]));
      if scale > 0.0 then
        radius := sqrt((work[column, column] / scale)^2
          + (work[row, column] / scale)^2);
        cosine := (work[column, column] / scale) / radius;
        sine := (work[row, column] / scale) / radius;
        upperRow := {work[column, entry] for entry in 1:size(columns, 1)};
        work[column, :] := cosine * upperRow + sine * work[row, :];
        work[row, :] := -sine * upperRow + cosine * work[row, :];
        work[column, column] := scale * radius;
        work[row, column] := 0.0;
      end if;
    end for;
  end for;
  for row in 1:size(columns, 1) loop
    root[:, row] := if row > size(work, 1) then zeros(size(columns, 1))
      elseif work[row, row] < 0.0 then -work[row, :] else work[row, :];
  end for;
end covarianceRoot;