Changeset 79 for doc/latex/classldmat.tex
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- 04/18/08 14:03:19 (16 years ago)
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doc/latex/classldmat.tex (modified) (12 diffs)
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doc/latex/classldmat.tex
r33 r79 47 47 \begin{CompactList}\small\item\em Conversion to full matrix. \item\end{CompactList}\item 48 48 void {\bf mult\_\-sym} (const mat \&C) 49 \begin{CompactList}\small\item\em Inplace symmetric multiplication by a SQUARE matrix \$C\$, i.e. \$V = C$\ast$V$\ast$C'\$. \item\end{CompactList}\item49 \begin{CompactList}\small\item\em Inplace symmetric multiplication by a SQUARE matrix $C$, i.e. $V = C*V*C'$. \item\end{CompactList}\item 50 50 void {\bf mult\_\-sym\_\-t} (const mat \&C) 51 \begin{CompactList}\small\item\em Inplace symmetric multiplication by a SQUARE transpose of matrix \$C\$, i.e. \$V = C'$\ast$V$\ast$C\$. \item\end{CompactList}\item51 \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 52 52 void {\bf add} (const {\bf ldmat} \&ld2, double w=1.0)\label{classldmat_a60f2c7e4f3c6a7738eaaaab81ffad20} 53 53 … … 58 58 double {\bf qform} (const vec \&v) const \label{classldmat_d64f331b781903e913cb2ee836886f3f} 59 59 60 \begin{CompactList}\small\item\em Evaluates quadratic form \$x= v'$\ast$V$\ast$v\$;. \item\end{CompactList}\item 60 \begin{CompactList}\small\item\em Evaluates quadratic form $x= v'*V*v$;. \item\end{CompactList}\item 61 double {\bf invqform} (const vec \&v) const \label{classldmat_d876c5f83e02b3e809b35c9de5068f14} 62 63 \begin{CompactList}\small\item\em Evaluates quadratic form $x= v'*inv(V)*v$;. \item\end{CompactList}\item 61 64 void {\bf clear} ()\label{classldmat_4d6e401de9607332305c27e67972a07a} 62 65 … … 69 72 \begin{CompactList}\small\item\em access function \item\end{CompactList}\item 70 73 vec {\bf sqrt\_\-mult} (const vec \&v) const 71 \begin{CompactList}\small\item\em Multiplies square root of \$V\$ by vector \$x\$. \item\end{CompactList}\item74 \begin{CompactList}\small\item\em Multiplies square root of $V$ by vector $x$. \item\end{CompactList}\item 72 75 virtual void {\bf inv} ({\bf ldmat} \&Inv) const 73 76 \begin{CompactList}\small\item\em Matrix inversion preserving the chosen form. \item\end{CompactList}\item 74 77 void {\bf mult\_\-sym} (const mat \&C, {\bf ldmat} \&U) const 75 \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}\item78 \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 76 79 void {\bf mult\_\-sym\_\-t} (const mat \&C, {\bf ldmat} \&U) const 77 \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}\item80 \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 78 81 void {\bf ldform} (const mat \&A, const vec \&D0) 79 \begin{CompactList}\small\item\em Transforms general \$A'D0 A\$ into pure \$L'DL\$. \item\end{CompactList}\item82 \begin{CompactList}\small\item\em Transforms general $A'D0 A$ into pure $L'DL$. \item\end{CompactList}\item 80 83 void {\bf setD} (const vec \&nD)\label{classldmat_0884a613b94fde61bfc84288e73ce57f} 81 84 … … 99 102 vec {\bf D}\label{classldmat_4cce04824539c4a8d062d9a36d6e014e} 100 103 101 \begin{CompactList}\small\item\em Positive vector \$D\$. \item\end{CompactList}\item104 \begin{CompactList}\small\item\em Positive vector $D$. \item\end{CompactList}\item 102 105 mat {\bf L}\label{classldmat_f74a64b99fe58a75ebd37bb679e121ea} 103 106 104 \begin{CompactList}\small\item\em Lower-triangular matrix \$L\$. \item\end{CompactList}\end{CompactItemize}107 \begin{CompactList}\small\item\em Lower-triangular matrix $L$. \item\end{CompactList}\end{CompactItemize} 105 108 \subsection*{Friends} 106 109 \begin{CompactItemize} … … 114 117 Matrix stored in LD form, (typically known as UD). 115 118 116 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.119 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. 117 120 118 121 \subsection{Member Function Documentation} … … 122 125 123 126 124 Perfroms a rank-1 update by outer product of vectors: \$V = V + w v v'\$. \begin{Desc}127 Perfroms a rank-1 update by outer product of vectors: $V = V + w v v'$. \begin{Desc} 125 128 \item[Parameters:] 126 129 \begin{description} … … 134 137 135 138 136 Inplace symmetric multiplication by a SQUARE matrix \$C\$, i.e. \$V = C$\ast$V$\ast$C'\$.139 Inplace symmetric multiplication by a SQUARE matrix $C$, i.e. $V = C*V*C'$. 137 140 138 141 \begin{Desc} … … 148 151 149 152 150 Inplace symmetric multiplication by a SQUARE transpose of matrix \$C\$, i.e. \$V = C'$\ast$V$\ast$C\$.153 Inplace symmetric multiplication by a SQUARE transpose of matrix $C$, i.e. $V = C'*V*C$. 151 154 152 155 \begin{Desc} … … 162 165 163 166 164 Multiplies square root of \$V\$ by vector \$x\$.167 Multiplies square root of $V$ by vector $x$. 165 168 166 169 Used e.g. in generating normal samples. … … 183 186 184 187 185 Symmetric multiplication of \$U\$ by a general matrix \$C\$, result of which is stored in the current class.188 Symmetric multiplication of $U$ by a general matrix $C$, result of which is stored in the current class. 186 189 187 190 \begin{Desc} … … 195 198 196 199 197 Symmetric multiplication of \$U\$ by a transpose of a general matrix \$C\$, result of which is stored in the current class.200 Symmetric multiplication of $U$ by a transpose of a general matrix $C$, result of which is stored in the current class. 198 201 199 202 \begin{Desc} … … 207 210 208 211 209 Transforms general \$A'D0 A\$ into pure \$L'DL\$.210 211 The new decomposition fullfills: \$A'$\ast$diag(D)$\ast$A = self.L'$\ast$diag(self.D)$\ast$self.L\$ \begin{Desc}212 Transforms general $A'D0 A$ into pure $L'DL$. 213 214 The new decomposition fullfills: $A'*diag(D)*A = self.L'*diag(self.D)*self.L$ \begin{Desc} 212 215 \item[Parameters:] 213 216 \begin{description}
