SmartInv

Large sparse matrix inversion. Returns block diagonal, tridiagonal or pentadiagonal elements.

Returns block mono, tri or penta diagonal elements of the inverse of a symetric square matrix.

Useful for large sparse matrix which LU decomposition is easy to compute for. Not the fastest way to compute inverse matrix, but avoid memory problem of a full matrix storage.

Optional progressive diagonal computation display. Useful to quickly observe an important modification on the diagonal.

% Q = smartinv(N) returns the N^-1. N is a square symetric matrix n x n.
%
% Q = smartinv(N,blocksize) returns the block (blocksize x blocksize)
% diagonal elements of N^-1.
%
% Q = smartinv(N,blocksize,type) returns the block type-diagonal
% elements of N^-1 type can be mono, tri or penta. The type
% determines the inclusion of diagonal block computation,
% i.e there is redundancy for tri (25%) and for penta (~45%).
%
% Q = smartinv(N,blocksize,position) returns the block diagonal elements
% of N^-1 at position. Q is blocksize x blocksize if position
% is a single value or n x n if posistion is a vector. If
% position is not set, the block values will be computed in an
% order so the curve shape will appear progressively (if graph
% displaymode is used).
%
% Q = smartinv(N,blocksize,...,'displaymode',displaymodevalue) specifies
% process graphical display: none, waitbar (default), graph.
% If position exists and is scalar, no display is set up at all.
% Graph mode will draw a curve for each diagonal element of block
% (i.e. a block represents an epoch, and each element of a block
% a variable to display).
%
% Q = smartinv(N,blocksize,...,'linelegend',linelegendvalue) where
% linelegendvalue is a cell array of string specifying legend
% strings to display for each block element (used for graph
% display mode).
%
% Q = smartinv(N,blocksize,...,'linecolor',linecolorvalue) where
% linecolorvalue is a cell array of color string or RGB value
% to display for each block element (used for graph display mode).
%
% Q = smartinv(N,blocksize,...,'linefunction',linefunctionname) where
% linefunctionname is a function called to display value in
% graph displaymode. linefunctionname can be a string (the same
% function will be used for each element in the block) or a cell
% array of strings of blocksize length.