\section{ldmat Class Reference}
\label{classldmat}\index{ldmat@{ldmat}}
Matrix stored in LD form, (typically known as UD).  


{\tt \#include $<$libDC.h$>$}

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\subsection*{Public Member Functions}
\begin{CompactItemize}
\item 
{\bf ldmat} (const mat \&{\bf L}, const vec \&{\bf D})\label{classldmat_968113788422e858da23a477e98fd3a1}

\begin{CompactList}\small\item\em Construct by copy of L and D. \item\end{CompactList}\item 
{\bf ldmat} (const mat \&V)\label{classldmat_5f21785358072d36892d538eed1d1ea5}

\begin{CompactList}\small\item\em Construct by decomposition of full matrix V. \item\end{CompactList}\item 
{\bf ldmat} (vec D0)\label{classldmat_abe16e0f86668ef61a9a4896c8565dee}

\begin{CompactList}\small\item\em Construct diagonal matrix with diagonal D0. \item\end{CompactList}\item 
{\bf ldmat} ()\label{classldmat_a12dda6f529580b0377cc45226b43303}

\begin{CompactList}\small\item\em Default constructor. \item\end{CompactList}\item 
{\bf ldmat} (const int dim0)\label{classldmat_163ee002a7858d104da1c59dd11f016d}

\begin{CompactList}\small\item\em Default initialization with proper size. \item\end{CompactList}\item 
virtual {\bf $\sim$ldmat} ()\label{classldmat_1e2734c0164ce5233c4d709679555138}

\begin{CompactList}\small\item\em Destructor for future use;. \item\end{CompactList}\item 
void {\bf opupdt} (const vec \&v, double w)
\item 
mat {\bf to\_\-mat} ()\label{classldmat_5b0515da8dc2293d9e4360b74cc26c9e}

\begin{CompactList}\small\item\em Conversion to full matrix. \item\end{CompactList}\item 
void {\bf mult\_\-sym} (const mat \&C)
\begin{CompactList}\small\item\em Inplace symmetric multiplication by a SQUARE matrix $C$, i.e. $V = C*V*C'$. \item\end{CompactList}\item 
void {\bf mult\_\-sym\_\-t} (const mat \&C)
\begin{CompactList}\small\item\em Inplace symmetric multiplication by a SQUARE transpose of matrix $C$, i.e. $V = C'*V*C$. \item\end{CompactList}\item 
void {\bf add} (const {\bf ldmat} \&ld2, double w=1.0)\label{classldmat_a60f2c7e4f3c6a7738eaaaab81ffad20}

\begin{CompactList}\small\item\em Add another matrix in LD form with weight w. \item\end{CompactList}\item 
double {\bf logdet} () const \label{classldmat_2b42750ba4962d439aa52a77ae12949b}

\begin{CompactList}\small\item\em Logarithm of a determinant. \item\end{CompactList}\item 
double {\bf qform} (const vec \&v) const \label{classldmat_d64f331b781903e913cb2ee836886f3f}

\begin{CompactList}\small\item\em Evaluates quadratic form $x= v'*V*v$;. \item\end{CompactList}\item 
double {\bf invqform} (const vec \&v) const \label{classldmat_d876c5f83e02b3e809b35c9de5068f14}

\begin{CompactList}\small\item\em Evaluates quadratic form $x= v'*inv(V)*v$;. \item\end{CompactList}\item 
void {\bf clear} ()\label{classldmat_4d6e401de9607332305c27e67972a07a}

\begin{CompactList}\small\item\em Clearing matrix so that it corresponds to zeros. \item\end{CompactList}\item 
int {\bf cols} () const \label{classldmat_0fceb6b5b637cec89bb0a3d2e6be1306}

\begin{CompactList}\small\item\em access function \item\end{CompactList}\item 
int {\bf rows} () const \label{classldmat_96dfb21865db4f5bd36fa70f9b0b1163}

\begin{CompactList}\small\item\em access function \item\end{CompactList}\item 
vec {\bf sqrt\_\-mult} (const vec \&v) const 
\begin{CompactList}\small\item\em Multiplies square root of $V$ by vector $x$. \item\end{CompactList}\item 
virtual void {\bf inv} ({\bf ldmat} \&Inv) const 
\begin{CompactList}\small\item\em Matrix inversion preserving the chosen form. \item\end{CompactList}\item 
void {\bf mult\_\-sym} (const mat \&C, {\bf ldmat} \&U) const 
\begin{CompactList}\small\item\em Symmetric multiplication of $U$ by a general matrix $C$, result of which is stored in the current class. \item\end{CompactList}\item 
void {\bf mult\_\-sym\_\-t} (const mat \&C, {\bf ldmat} \&U) const 
\begin{CompactList}\small\item\em Symmetric multiplication of $U$ by a transpose of a general matrix $C$, result of which is stored in the current class. \item\end{CompactList}\item 
void {\bf ldform} (const mat \&A, const vec \&D0)
\begin{CompactList}\small\item\em Transforms general $A'D0 A$ into pure $L'DL$. \item\end{CompactList}\item 
void {\bf setD} (const vec \&nD)\label{classldmat_0884a613b94fde61bfc84288e73ce57f}

\begin{CompactList}\small\item\em Access functions. \item\end{CompactList}\item 
void {\bf setD} (const vec \&nD, int i)\label{classldmat_7619922b4de18830ce5351c6b5667e60}

\begin{CompactList}\small\item\em Access functions. \item\end{CompactList}\item 
void {\bf setL} (const vec \&nL)\label{classldmat_32ff66296627ff5341d7c0b973249614}

\begin{CompactList}\small\item\em Access functions. \item\end{CompactList}\item 
const vec \& {\bf \_\-D} () const \label{classldmat_282c879f50aa9ef934e7f46d86881582}

\begin{CompactList}\small\item\em Access functions. \item\end{CompactList}\item 
const mat \& {\bf \_\-L} () const \label{classldmat_5f44f100248c6627314afaa653b9e5bd}

\begin{CompactList}\small\item\em Access functions. \item\end{CompactList}\item 
{\bf ldmat} \& {\bf operator+=} (const {\bf ldmat} \&ldA)
\begin{CompactList}\small\item\em add another \doxyref{ldmat}{p.}{classldmat} matrix \item\end{CompactList}\item 
{\bf ldmat} \& {\bf operator-=} (const {\bf ldmat} \&ldA)
\begin{CompactList}\small\item\em subtract another \doxyref{ldmat}{p.}{classldmat} matrix \item\end{CompactList}\item 
{\bf ldmat} \& {\bf operator$\ast$=} (double x)\label{classldmat_875b7e6dcf73ae7001329099019fdb1d}

\begin{CompactList}\small\item\em multiply by a scalar \item\end{CompactList}\end{CompactItemize}
\subsection*{Protected Attributes}
\begin{CompactItemize}
\item 
vec {\bf D}\label{classldmat_4cce04824539c4a8d062d9a36d6e014e}

\begin{CompactList}\small\item\em Positive vector $D$. \item\end{CompactList}\item 
mat {\bf L}\label{classldmat_f74a64b99fe58a75ebd37bb679e121ea}

\begin{CompactList}\small\item\em Lower-triangular matrix $L$. \item\end{CompactList}\end{CompactItemize}
\subsection*{Friends}
\begin{CompactItemize}
\item 
std::ostream \& {\bf operator$<$$<$} (std::ostream \&os, const {\bf ldmat} \&sq)\label{classldmat_eaaa0baa6026b84cfcbced41c84599d1}

\begin{CompactList}\small\item\em print both {\tt L} and {\tt D} \item\end{CompactList}\end{CompactItemize}


\subsection{Detailed Description}
Matrix stored in LD form, (typically known as UD). 

Matrix is decomposed as follows: \[M = L'DL\] where only $L$ and $D$ matrices are stored. All inplace operations modifies only these and the need to compose and decompose the matrix is avoided. 

\subsection{Member Function Documentation}
\index{ldmat@{ldmat}!opupdt@{opupdt}}
\index{opupdt@{opupdt}!ldmat@{ldmat}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}void ldmat::opupdt (const vec \& {\em v}, \/  double {\em w})\hspace{0.3cm}{\tt  [virtual]}}\label{classldmat_0f0f6e083e6d947cf58097ffce3ccd1a}


Perfroms a rank-1 update by outer product of vectors: $V = V + w v v'$. \begin{Desc}
\item[Parameters:]
\begin{description}
\item[{\em v}]Vector forming the outer product to be added \item[{\em w}]weight of updating; can be negative\end{description}
\end{Desc}
BLAS-2b operation. 

Implements {\bf sqmat} \doxyref{}{p.}{classsqmat_b223484796661f2dadb5607a86ce0581}.

References D, sqmat::dim, and L.

Referenced by add(), ARX::bayes(), and inv().\index{ldmat@{ldmat}!mult\_\-sym@{mult\_\-sym}}
\index{mult\_\-sym@{mult\_\-sym}!ldmat@{ldmat}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}void ldmat::mult\_\-sym (const mat \& {\em C})\hspace{0.3cm}{\tt  [virtual]}}\label{classldmat_e967b9425007f0cb6cd59b845f9756d8}


Inplace symmetric multiplication by a SQUARE matrix $C$, i.e. $V = C*V*C'$. 

\begin{Desc}
\item[Parameters:]
\begin{description}
\item[{\em C}]multiplying matrix, \end{description}
\end{Desc}


Implements {\bf sqmat} \doxyref{}{p.}{classsqmat_60fbbfa9e483b8187c135f787ee53afa}.

References D, L, and ldform().\index{ldmat@{ldmat}!mult\_\-sym\_\-t@{mult\_\-sym\_\-t}}
\index{mult\_\-sym\_\-t@{mult\_\-sym\_\-t}!ldmat@{ldmat}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}void ldmat::mult\_\-sym\_\-t (const mat \& {\em C})\hspace{0.3cm}{\tt  [virtual]}}\label{classldmat_4fd155f38eb6dd5af4bdf9c98a7999a9}


Inplace symmetric multiplication by a SQUARE transpose of matrix $C$, i.e. $V = C'*V*C$. 

\begin{Desc}
\item[Parameters:]
\begin{description}
\item[{\em C}]multiplying matrix, \end{description}
\end{Desc}


Implements {\bf sqmat} \doxyref{}{p.}{classsqmat_6909e906da17725b1b80f3cae7cf3325}.

References D, L, and ldform().\index{ldmat@{ldmat}!sqrt\_\-mult@{sqrt\_\-mult}}
\index{sqrt\_\-mult@{sqrt\_\-mult}!ldmat@{ldmat}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}vec ldmat::sqrt\_\-mult (const vec \& {\em v}) const\hspace{0.3cm}{\tt  [virtual]}}\label{classldmat_fc380626ced6f9244fb58c5f0231174d}


Multiplies square root of $V$ by vector $x$. 

Used e.g. in generating normal samples. 

Implements {\bf sqmat} \doxyref{}{p.}{classsqmat_6b79438b5d7544a9c8e110a145355d8f}.

References D, sqmat::dim, and L.\index{ldmat@{ldmat}!inv@{inv}}
\index{inv@{inv}!ldmat@{ldmat}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}void ldmat::inv ({\bf ldmat} \& {\em Inv}) const\hspace{0.3cm}{\tt  [virtual]}}\label{classldmat_2c160cb123c1102face7a50ec566a031}


Matrix inversion preserving the chosen form. 

\begin{Desc}
\item[Parameters:]
\begin{description}
\item[{\em Inv}]a space where the inverse is stored. \end{description}
\end{Desc}


References clear(), D, sqmat::dim, L, and opupdt().\index{ldmat@{ldmat}!mult\_\-sym@{mult\_\-sym}}
\index{mult\_\-sym@{mult\_\-sym}!ldmat@{ldmat}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}void ldmat::mult\_\-sym (const mat \& {\em C}, \/  {\bf ldmat} \& {\em U}) const}\label{classldmat_e7207748909325bb0f99b43f090a2b7e}


Symmetric multiplication of $U$ by a general matrix $C$, result of which is stored in the current class. 

\begin{Desc}
\item[Parameters:]
\begin{description}
\item[{\em C}]matrix to multiply with \item[{\em U}]a space where the inverse is stored. \end{description}
\end{Desc}


References D, L, and ldform().\index{ldmat@{ldmat}!mult\_\-sym\_\-t@{mult\_\-sym\_\-t}}
\index{mult\_\-sym\_\-t@{mult\_\-sym\_\-t}!ldmat@{ldmat}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}void ldmat::mult\_\-sym\_\-t (const mat \& {\em C}, \/  {\bf ldmat} \& {\em U}) const}\label{classldmat_f94dc3a233f3d40fc853d8d4ac3b8eab}


Symmetric multiplication of $U$ by a transpose of a general matrix $C$, result of which is stored in the current class. 

\begin{Desc}
\item[Parameters:]
\begin{description}
\item[{\em C}]matrix to multiply with \item[{\em U}]a space where the inverse is stored. \end{description}
\end{Desc}


References D, L, and ldform().\index{ldmat@{ldmat}!ldform@{ldform}}
\index{ldform@{ldform}!ldmat@{ldmat}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}void ldmat::ldform (const mat \& {\em A}, \/  const vec \& {\em D0})}\label{classldmat_f291faa073e7bc8dfafc7ae93daa2506}


Transforms general $A'D0 A$ into pure $L'DL$. 

The new decomposition fullfills: $A'*diag(D)*A = self.L'*diag(self.D)*self.L$ \begin{Desc}
\item[Parameters:]
\begin{description}
\item[{\em A}]general matrix \item[{\em D0}]general vector \end{description}
\end{Desc}


References D, sqmat::dim, and L.

Referenced by ldmat(), mult\_\-sym(), and mult\_\-sym\_\-t().\index{ldmat@{ldmat}!operator+=@{operator+=}}
\index{operator+=@{operator+=}!ldmat@{ldmat}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}{\bf ldmat} \& ldmat::operator+= (const {\bf ldmat} \& {\em ldA})\hspace{0.3cm}{\tt  [inline]}}\label{classldmat_ca445ee152a56043af946ea095b2d8f8}


add another \doxyref{ldmat}{p.}{classldmat} matrix 

Operations: mapping of add operation to operators \index{ldmat@{ldmat}!operator-=@{operator-=}}
\index{operator-=@{operator-=}!ldmat@{ldmat}}
\subsubsection{\setlength{\rightskip}{0pt plus 5cm}{\bf ldmat} \& ldmat::operator-= (const {\bf ldmat} \& {\em ldA})\hspace{0.3cm}{\tt  [inline]}}\label{classldmat_e3f4d2d85ab1ba384c852329aa31d0fb}


subtract another \doxyref{ldmat}{p.}{classldmat} matrix 

mapping of negative add operation to operators 

The documentation for this class was generated from the following files:\begin{CompactItemize}
\item 
work/mixpp/bdm/math/{\bf libDC.h}\item 
work/mixpp/bdm/math/libDC.cpp\end{CompactItemize}
