#include <Matrix.h>
Inheritance diagram for UTRRealMatrix:
Subscripting speed is crucial. For this reason upper triangular matrices often stand in for symmetric matrices which have a slower subscripting operator. The upper triangular matrix then represents the symmetric matrix of which it is the upper half. This expalains why we implement operations for upper triangular matrics which make sense for symmetric matrices (eigen value analysis, pseudo square roots,...).
Definition at line 1335 of file Matrix.h.
Public Member Functions  
UTRRealMatrix (int d, int b=0)  
template<int n>  UTRRealMatrix (Real A[n][n], int b=0) 
RealMatrix &  symmetricCompletion () const 
UTRRealMatrix &  inverse () const 
LTRRealMatrix &  ltrRoot () const 
UTRRealMatrix &  utrRoot () const 
RealMatrix &  rankReducedRoot (int r) const 
UTRRealMatrix &  exp () const 
RealMatrix &  matrixFunction (Real(*f)(Real)) 
void  analyseFactors (int r) const 
void  testFactorization (int r, string message="") const 

Constructor, initializes all components with zeroes.
Definition at line 1343 of file Matrix.h. References Matrix< Real, UpperTriangular< Real > >::b, and Real. 

Construct from data array, only upper triangular half is used.
Definition at line 1351 of file Matrix.h. References Matrix< Real, UpperTriangular< Real > >::b, and Real. 

The symmetric matrix of which this is the upper half. Return by value is deliberate. 

The matrix inverse. This is upper triangular of the same size. 

Cholesky root L (lower triangular, LL'=A where A is the symmetric matrix with upper half 

Upper triangular root U of A, where A is the symmetric matrix of which 

Let C be the symmetric matrix with upper half The row index base remains the same, columns of the root are indexed from zero. 

Matrix exponential. Reimplemented from Matrix< Real, UpperTriangular< Real > >. 

Computes the function f(A) of the symmetric matrix A of which is the diagonal matrix with the eigenvalues of A on the diagonal the columns of U are associated eigenvectors. Set (f is applied to each eigenvalue). Then


Matrix is interpreted as the upper half of a multinormal covariance matrix. This method prints how much variability is captured by the r largest eigenvalues of C. 

Let C be the symmetric matrix with upper half
