[Master Index] [Index for PublicToolbox/regutools]

# pinit

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

### Function Synopsis

    [NAA,x_0] = pinit(W,A,b)

### Help Text

    PINIT Utility init.-procedure for "preconditioned" iterative methods.

     NAA = pinit(W,A)
     [NAA,x_0] = pinit(W,A,b)

     Initialization for `preconditioning' of general-form problems.
     Here, W holds a basis for the null space of L.

     Determines the matrix NAA needed in the iterative routines for
     treating regularization problems in general form.

     If b is also specified then x_0, the component of the solution in
     the null space of L, is also computed.

### Cross-Reference Information

This function calls

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

This function is called by

    pcgls                              C:\BrainStorm_2001\PublicToolbox\regutools\pcgls.m
    plsqr                              C:\BrainStorm_2001\PublicToolbox\regutools\plsqr.m
    pnu                                C:\BrainStorm_2001\PublicToolbox\regutools\pnu.m
    std_form                           C:\BrainStorm_2001\PublicToolbox\regutools\std_form.m

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

    function [NAA,x_0] = pinit(W,A,b)
    %PINIT Utility init.-procedure for "preconditioned" iterative methods.
    %
    % NAA = pinit(W,A)
    % [NAA,x_0] = pinit(W,A,b)
    %
    % Initialization for `preconditioning' of general-form problems.
    % Here, W holds a basis for the null space of L.
    %
    % Determines the matrix NAA needed in the iterative routines for
    % treating regularization problems in general form.
    %
    % If b is also specified then x_0, the component of the solution in
    % the null space of L, is also computed.

    % Reference: M. Hanke, "Regularization with differential operators.
    % An iterative approach", J. Numer. Funct. Anal. Optim. 13 (1992),
    % 523-540.

    % Per Christian Hansen, UNI-C, and Martin Hanke, Institut fuer
    % Praktische Mathematik, Universitaet Karlsruhe, 05/26/93.

    % Initialization.
    [n,nu] = size(W);

    % Special treatment of square L.
    if (nu==0), NAA = []; x_0 = zeros(n,1); return, end

    % Compute NAA.
    T = pinv(A*W);
    NAA = T*A;

    % If required, also compute x_0.
    if (nargin==3), x_0 = W*(T*b); end

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