TRIUNPACK - Unpack the non-redundant representation of a triangular or symmetric matrix.

Contents

Description

Build the square (lower or upper) triangular or symmetric matrix whose non redundant entries are given in a representation vector.

Syntax

     u = TRIUNPACK(p);
     u = TRIUNPACK(p, x, 'l'/'u'/'s');

Inputs

p : unpacked vector data storing the x(x+1)/2 (see below) distinct components of a (lower or upper) triangular or symmetric matrix of size (x,x) to be output.

x : (optional) size of the output (square) matrix to rebuild; default: x is estimated as the solution (>0) of the quadratic system x(x+1)=numel(p).

flag : (optional) string stating if the upper ('u'), the lower ('l') or both ('s') parts (thus, the output matrix will be symmetric) must be filled with the unpacked data; default: flag='s'.

Outputs

u : the square matrix with its lower, upper or both triangular parts (depending on the variable flag, see above) are filled with the packed representation stored in p.

Example

a = rand(4,4);
b = nonzeros(triu(a));
triunpack(b)
triunpack(b, [], 'u')
triunpack(b, [], 'l')

See also

Requires: TRIU, TRIL, DIAG, OR.

Function implementation

%--------------------------------------------------------------------------
function u = triunpack(p, x, flag)

check/set the input variables

if ~isnumeric(p) || nb_dims(p)>1
    error('triunpack:inputerror', ...
        'input unpacked data must be a numeric vector');
elseif mod(numel(p),2)
    error('triunpack:inputerror', ...
        'input unpacked data must be of odd size');
end

if nargin<3,  flag = 's';  end
if nargin<2 || isempty(x),  x = (-1 + sqrt(1+8*numel(p))) / 2;  end

if numel(p)~=x*(x+1)/2
    error('triunpack:inputerror', ...
        'incompatible unpacked data and output matrix size');
end

create the output

u = zeros(x, x);

create the handle function

if any(strcmpi(flag,{'u','upper','s','symm'}))
    fhandle = @triu;
elseif any(strcmpi(flag,{'l','lower'}))
    fhandle = @tril;
else
    error('triunpack:inputerror', 'unreckognized flag')
end

fill the output

i = true(x,x);
u(fhandle(i)) = p;

complete in symmetric case

if any(strcmpi(flag,{'s','symm'}))
    u(tril(i)) = p;
end

end % end of triunpack

Published with MATLAB® 7.14