api-tensor-CPNTensor-sliceTensor

Sub-tensor of a normalized CP tensor, sliced by equation (row) and rank (column).

Syntax

sub = obj.sliceTensor()
sub = obj.sliceTensor(equationIndex)
sub = obj.sliceTensor(equationIndex, columnIndex)

Description

sliceTensor returns a CPNTensor holding only the selected equations and rank-1 terms. Both slicing axes preserve the CPN form — dropping parameter-matrix rows drops whole equations, and dropping columns drops whole rank-1 terms — so the result is a valid smaller tensor that can be evaluated or differentiated on its own, and is mathematically equivalent to the corresponding sub-block of the original.

The intended use is to build the slice once and reuse it across operating points, rather than re-slicing on every evaluation. jacobian uses it exactly this way, folding its equation and column selection into a slice before calling computeJacobian.

When columnIndex is omitted, the columns are inferred: only the rank-1 terms that the selected equations actually reference are kept, since terms with no weight in any selected equation contribute nothing. Restricting equationIndex alone therefore already narrows the tensor on both axes.

The structure matrix keeps every row

Structure-matrix rows are never dropped, even for signals that no surviving monomial reads. This is deliberate: the row space is the signal space, so keeping it intact means v and variableIndex still index the full signal vector downstream, and no re-mapping is needed between the slice and its parent.

There is, correspondingly, no variable axis on this method. Selecting variables is a selection on the columns of the Jacobian, not a sub-tensor: dropping structure-matrix rows would silently corrupt the factor products of every monomial that reads those signals. Use jacobian’s variableIndex, which post-slices the result columns, instead.

Input arguments

Output arguments

Example

Argument	Description
`obj`	`CPNTensor` to slice.
`equationIndex`	(default `[]`) Parameter-matrix rows to keep. Empty means all equations.
`columnIndex`	(default `[]`) Rank-1 columns to keep. Empty means only the columns the selected equations use.

Output	Description
`sub`	`CPNTensor` with the selected equations and rank terms, and all structure-matrix rows retained.

%      x1  x2  x1x2
S = [   1   0    1     % x1
        0   1    1 ];  % x2
P = [ -10  10    0     % dx1 = -10*x1 + 10*x2
        0   0    1 ];  % dx2 = x1*x2

T = CPNTensor(S,P);

whole = T.sliceTensor();          % 2 equations, R = 3
eq2   = T.sliceTensor(2);         % 1 equation,  R = 1 - only the x1x2 term
size(eq2.structureMatrixTrue,1)   % 2 - both signal rows kept