[Master Index] [Index for PublicToolbox/regutools]

# get_l

## (PublicToolbox/regutools/get_l.m in BrainStorm 2.0 (Alpha))

### Function Synopsis

    [L,W] = get_l(n,d)

### Help Text

    GET_L Compute discrete derivative operators.

     [L,W] = get_l(n,d)

     Computes the discrete approximation L to the derivative operator
     of order d on a regular grid with n points, i.e. L is (n-d)-by-n.

     L is stored as a sparse matrix.

     Also computes W, an orthonormal basis for the null space of L.

### Cross-Reference Information

This function calls

    mgs                                C:\BrainStorm_2001\PublicToolbox\regutools\mgs.m

This function is called by

    regudemo                           C:\BrainStorm_2001\PublicToolbox\regutools\regudemo.m

### Listing of function C:\BrainStorm_2001\PublicToolbox\regutools\get_l.m

    function [L,W] = get_l(n,d)
    %GET_L Compute discrete derivative operators.
    %
    % [L,W] = get_l(n,d)
    %
    % Computes the discrete approximation L to the derivative operator
    % of order d on a regular grid with n points, i.e. L is (n-d)-by-n.
    %
    % L is stored as a sparse matrix.
    %
    % Also computes W, an orthonormal basis for the null space of L.

    % Per Christian Hansen, UNI-C, 05/26/93.

    % Initialization.
    if (d<1), error ('Order d must be positive'), end
    nd = n-d;

    % Compute L.
    c = [1,-1,zeros(1,d-1)];
    for i=2:d, c = [c(1:d),0] - [0,c(1:d)]; end
    L = sparse(nd,n);
    for i=1:d+1
      L = L + sparse(1:nd,[1:nd]+i-1,c(i)*ones(1,nd),nd,n);
    end

    % If required, compute the null vectors W.
    if (nargout==2)
      W = zeros(n,d);
      W(:,1) = ones(n,1);
      for i=2:d, W(:,i) = W(:,i-1).*[1:n]'; end
      W = mgs(W);
    end

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