dimensions = [d1, ..., dn]

This option controls the dimensions of $X$. Its value needs to be a list of $n$ positive integers, giving the dimensions of $X$. For example, when constructing a sparse Vector, the value should be a list containing a single positive integer, and for a Matrix it should be a list of two positive integers. If the option is not specified, Maple uses the maximal value in the $i$th index vector $\mathrm{Ai}$ as the $i$th dimension.

scan = true or scan = false

This option determines whether or not $B$ is scanned for zeroes. If scan = true, the default, then $B$ is scanned to test if it contains any entries that are equal to 0. If this is the case, the operation is aborted with an error message: such entries are not allowed. If you are certain that there are no entries equal to 0, you can save a little bit of processing time by disabling this scan by passing scan = false to the procedure. Use this option with extreme caution.

The FromSplitForm function constructs a sparse rtable $X$ from its split form, performing the opposite function to SplitForm.

The split form of an $n$-dimensional rtable $X$ with $k$ nonzero entries consists of $n+1$ Vectors, $\mathrm{A1}$, $\mathrm{A2}$, ..., $\mathrm{An}$, and $B$, each with $k$ entries: for every nonzero entry $X_{\mathrm{a1},\mathrm{a2},\mathrm{...},\mathrm{an}}=b$, there is an index $i$ such that ${\mathrm{A1}}_i=\mathrm{a1}$, ${\mathrm{A2}}_i=\mathrm{a2}$, ..., ${\mathrm{An}}_i=\mathrm{an}$, and $B_i=b$. (If $X$ is a Vector, then $n=1$; if $X$ is a Matrix, then $n=2$.)

The Vectors $\mathrm{Aj}$ need to be of word-size integer data type; that is, on 32-bit platforms they will have data type ${\mathrm{integer}}_4$ and on 64-bit platforms data type ${\mathrm{integer}}_8$. The Vector $B$ needs to have a data type compatible with NAG-sparse rtables; that is, the datatype of $B$ as returned by rtable_options needs to be one of these values:

$\mathrm{sfloat},\mathrm{complex}\left(\mathrm{sfloat}\right),{\mathrm{integer}}_1,{\mathrm{integer}}_2,{\mathrm{integer}}_4,{\mathrm{integer}}_8,{\mathrm{float}}_4,{\mathrm{float}}_8,{\mathrm{complex}}_8$

$\mathrm{with}\left(\mathrm{LinearAlgebra}\right)\:$

$m≔\mathrm{Matrix}\left(5\,6\,\left\{\left(1\,2\right)=-81\,\left(2\,3\right)=-55\,\left(2\,4\right)=-15\,\left(3\,1\right)=-46\,\left(3\,3\right)=-17\,\left(3\,4\right)=99\,\left(3\,5\right)=-61\,\left(4\,2\right)=18\,\left(4\,5\right)=-78\,\left(5\,6\right)=22\right\}\,\mathrm{datatype}=\mathrm{integer}\left[4\right]\right)$

$m≔\left[\begin{array}{cccccc}0& \mathrm{-81}& 0& 0& 0& 0\\ 0& 0& \mathrm{-55}& \mathrm{-15}& 0& 0\\ \mathrm{-46}& 0& \mathrm{-17}& 99& \mathrm{-61}& 0\\ 0& 18& 0& 0& \mathrm{-78}& 0\\ 0& 0& 0& 0& 0& 22\end{array}\right]$

$\mathrm{ai},b≔\mathrm{SplitForm}\left(m\right)$

$\mathrm{ai},b≔\left[\left[\begin{array}{c}1\\ 2\\ 2\\ 3\\ 3\\ 3\\ 3\\ 4\\ 4\\ 5\end{array}\right]\,\left[\begin{array}{c}2\\ 3\\ 4\\ 1\\ 3\\ 4\\ 5\\ 2\\ 5\\ 6\end{array}\right]\right],\left[\begin{array}{c}\mathrm{-81}\\ \mathrm{-55}\\ \mathrm{-15}\\ \mathrm{-46}\\ \mathrm{-17}\\ 99\\ \mathrm{-61}\\ 18\\ \mathrm{-78}\\ 22\end{array}\right]$

$\mathrm{FromSplitForm}\left(\mathrm{ai}\,b\right)$

$\left[\begin{array}{cccccc}0& \mathrm{-81}& 0& 0& 0& 0\\ 0& 0& \mathrm{-55}& \mathrm{-15}& 0& 0\\ \mathrm{-46}& 0& \mathrm{-17}& 99& \mathrm{-61}& 0\\ 0& 18& 0& 0& \mathrm{-78}& 0\\ 0& 0& 0& 0& 0& 22\end{array}\right]$

$\mathrm{FromSplitForm}\left(\left[\mathrm{ai}\left[2\right]\,\mathrm{ai}\left[1\right]\right]\,b\right)$

$\left[\begin{array}{ccccc}0& 0& \mathrm{-46}& 0& 0\\ \mathrm{-81}& 0& 0& 18& 0\\ 0& \mathrm{-55}& \mathrm{-17}& 0& 0\\ 0& \mathrm{-15}& 99& 0& 0\\ 0& 0& \mathrm{-61}& \mathrm{-78}& 0\\ 0& 0& 0& 0& 22\end{array}\right]$

$\mathrm{m1}≔\mathrm{Matrix}\left(\left[\left[0\,1\,0\right]\,\left[2\,0\,0\right]\,\left[3\,0\,4\right]\right]\,'\mathrm{datatype}=\mathrm{float}'\right)$

$\mathrm{m1}≔\left[\begin{array}{ccc}0.& 1.& 0.\\ 2.& 0.& 0.\\ 3.& 0.& 4.\end{array}\right]$

$\mathrm{m2}≔\mathrm{Matrix}\left(\left[\left[0\,1\,0\right]\,\left[2\,0\,0\right]\,\left[3\,0\,4\right]\,\left[0\,0\,0\right]\right]\,'\mathrm{datatype}=\mathrm{float}'\right)$

$\mathrm{m2}≔\left[\begin{array}{ccc}0.& 1.& 0.\\ 2.& 0.& 0.\\ 3.& 0.& 4.\\ 0.& 0.& 0.\end{array}\right]$

$\mathrm{ai1},\mathrm{b1}≔\mathrm{SplitForm}\left(\mathrm{m1}\right)$

$\mathrm{ai1},\mathrm{b1}≔\left[\left[\begin{array}{c}1\\ 2\\ 3\\ 3\end{array}\right]\,\left[\begin{array}{c}2\\ 1\\ 1\\ 3\end{array}\right]\right],\left[\begin{array}{c}1.\\ 2.\\ 3.\\ 4.\end{array}\right]$

$\mathrm{ai2},\mathrm{b2}≔\mathrm{SplitForm}\left(\mathrm{m2}\right)$

$\mathrm{ai2},\mathrm{b2}≔\left[\left[\begin{array}{c}1\\ 2\\ 3\\ 3\end{array}\right]\,\left[\begin{array}{c}2\\ 1\\ 1\\ 3\end{array}\right]\right],\left[\begin{array}{c}1.\\ 2.\\ 3.\\ 4.\end{array}\right]$

$\mathrm{FromSplitForm}\left(\mathrm{ai2}\,\mathrm{b2}\right)$

$\left[\begin{array}{ccc}0.& 1.& 0.\\ 2.& 0.& 0.\\ 3.& 0.& 4.\end{array}\right]$

$\mathrm{FromSplitForm}\left(\mathrm{ai2}\,\mathrm{b2}\,'\mathrm{dimensions}'=\left[4\,3\right]\right)$

$\left[\begin{array}{ccc}0.& 1.& 0.\\ 2.& 0.& 0.\\ 3.& 0.& 4.\\ 0.& 0.& 0.\end{array}\right]$

$\mathrm{dt}≔'\mathrm{integer}'\left[\frac{\mathrm{kernelopts}\left('\mathrm{wordsize}'\right)}{8}\right]$

$\mathrm{dt}≔{\mathrm{integer}}_8$

$\mathrm{A1}≔\mathrm{Vector}\left(\left[5\,4\,3\,2\,1\right]\,'\mathrm{datatype}'=\mathrm{dt}\right)$

$\mathrm{A1}≔\left[\begin{array}{c}5\\ 4\\ 3\\ 2\\ 1\end{array}\right]$

$\mathrm{A2}≔\mathrm{Vector}\left(\left[3\,2\,1\,2\,3\right]\,'\mathrm{datatype}'=\mathrm{dt}\right)$

$\mathrm{A2}≔\left[\begin{array}{c}3\\ 2\\ 1\\ 2\\ 3\end{array}\right]$

$\mathrm{A3}≔\mathrm{Vector}\left(\left[2\,1\,5\,4\,3\right]\,'\mathrm{datatype}'=\mathrm{dt}\right)$

$\mathrm{A3}≔\left[\begin{array}{c}2\\ 1\\ 5\\ 4\\ 3\end{array}\right]$

$B≔\mathrm{Vector}\left(\left[\mathrm{I}\,2+\mathrm{I}\,\mathrm{I}-3\,-2-\mathrm{I}\,-\mathrm{I}\right]\,'\mathrm{datatype}'='\mathrm{complex}\left[8\right]'\right)$

$B≔\left[\begin{array}{c}0.+\mathrm{I}\\ 2.+\mathrm{I}\\ \mathrm{-3.}+\mathrm{I}\\ \mathrm{-2.}-\mathrm{I}\\ 0.-\mathrm{I}\end{array}\right]$

$\mathrm{FromSplitForm}\left(\left[\mathrm{A1}\,\mathrm{A2}\,\mathrm{A3}\right]\,B\right)$

The LinearAlgebra[FromSplitForm] command was introduced in Maple 17.

For more information on Maple 17 changes, see Updates in Maple 17.