[Master Index] [Index for PublicToolbox/regutools]

# Contents

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

### Help Text

     Regularization Tools.
     Version 2.0  16-March-93.
     Copyright (c) 1993 by Per Christian Hansen and UNI-C.

     Demonstration.
       regudemo  - Tutorial introduction to Regularization Tools.

     Test examples.
       baart     - Fredholm integral equation of the first kind.
       deriv2    - Computation of the second derivative.
       foxgood   - Severely ill-posed problem.
       heat      - Inverse heat equation.
       ilaplace  - Inverse Laplace transformation.
       parallax  - Stellar parallax problem with 28 fixed observations.
       phillips  - Philips' "famous" test problem.
       shaw      - One-dimensional image restoration problem.
       spikes    - Test problem with a "spiky" solution.
       ursell    - Integral equation with no square integrable solution.
       wing      - Test problem with a discontinuous solution.

     Regularization routines.
       cgls      - Computes the least squares solution based on k steps
                   of the conjugate gradient algorithm.
       discrep   - Minimizes the solution (semi-)norm subject to an upper
                   bound on the residual norm (discrepancy principle).
       dsvd      - Computes a damped SVD/GSVD solution.
       lsqi      - Minimizes the residual norm subject to an upper bound
                   on the (semi-)norm of the solution.
       lsqr      - Computes the least squares solution based on k steps
                   of the LSQR algorithm (Lanczos bidiagonalization).
       maxent    - Computes the maximum entropy regularized solution.
       mtsvd     - Computes the modified TSVD solution.
       nu        - Computes the solution based on k steps of Brakhage's
                   iterative nu-method.
       pcgls     - Same as cgls, but for general-form regularization.
       plsqr     - Same as lsqr, but for general-form regularization.
       pnu       - Same as nu, but for general-form regularization.
       tgsvd     - Computes the truncated GSVD solution.
       tikhonov  - Computes the Tikhonov regularized solution.
       tsvd      - Computes the truncated SVD solution.
       ttls      - Computes the truncated TLS solution.

     Analysis routines.
       fil_fac   - Computes filter factors for some regularization methods.
       gcv       - Plots the GCV function and computes its minimum.
       l_corner  - Locates the L-shaped corner of the L-curve.
       l_curve   - Computes the L-curve, plots it, and computes its corner.
       lagrange  - Plots the Lagrange function ||Ax-b||^2 + lambda^2*||Lx||^,
                   and its derivative.
       picard    - Plots the (generalized) singular values,
                   the Fourier coefficient for the right-hand side, and a
                   (smoothed curve of) the solution Fourier-coefficients.
       plot_lc   - Plots an L-curve.
       quasiopt  - Plots the quasi-optimality function and computes its minimum.

     Routines for transforming a problem in general form into one in
     standard form, and back again.
       gen_form  - Transforms a standard-form solution back into the
                   general-form setting.
       std_form  - Transforms a general-form problem into one in
                   standard form.

     Utility routines.
       bidiag    - Bidiagonalization of a matrix by Householder transformations.
       bsvd      - Computes the singular values, or the compact SVD,
                   of a bidiagonal matrix stored in compact form.
       csd       - Computes the CS decomposition.
       csvd      - Computes the compact SVD of an m-by-n matrix.
       get_l     - Produces a p-by-n matrix which is the discrete
                   approximation to the d'th order derivative operator.
       gsvd      - Computes the generalized SVD of a matrix pair.
       lanc_b    - Performs k steps of the Lanczos bidiagonalization
                   process with/without reorthogonalization.

     Auxiliary routines required by some of the above routines.
       app_hh_l  - Applies a Householder transformation from the left.
       gen_hh    - Generates a Householder transformation.
       heb_new   - Newton-Raphson iteration with Hebden's rational
                   approximation, used in lsqi.
       heb_new2  - Ditto, used in discrep.
       lsolve    - Inversion with A-weighted generalized inverse of L.
       ltsolve   - Inversion with transposed A-weighted inverse of L.
       mgs       - Modified Gram-Schmidt orthonormalization.
       newton    - Newton-Raphson iteration, used in discrep.
       pinit     - Initialization for treating general-form problems.
       pythag    - Computes sqrt(a^2 + b^2).
       spleval   - Computes points on a spline or spline curve.

     The routine l_corner requires the following routines from the Spline
     Toolbox:
       fnder, ppbrk, ppcut, ppmak, sp2pp, spbrk, spmak.
     If the Spline Toolbox is not available, then dummy functions with these
     names should reside in the same directory as Regularization Tools.

### Cross-Reference Information

This is called by

    bst_splashscreen                   C:\BrainStorm_2001\Toolbox\bst_splashscreen.m
    bst_static_taskbar                 C:\BrainStorm_2001\Toolbox\bst_static_taskbar.m
    help_manager                       C:\BrainStorm_2001\Toolbox\help_manager.m

### Listing of C:\BrainStorm_2001\PublicToolbox\regutools\Contents.m

    % Regularization Tools.
    % Version 2.0  16-March-93.
    % Copyright (c) 1993 by Per Christian Hansen and UNI-C.
    %
    % Demonstration.
    %   regudemo  - Tutorial introduction to Regularization Tools.
    %
    % Test examples.
    %   baart     - Fredholm integral equation of the first kind.
    %   deriv2    - Computation of the second derivative.
    %   foxgood   - Severely ill-posed problem.
    %   heat      - Inverse heat equation.
    %   ilaplace  - Inverse Laplace transformation.
    %   parallax  - Stellar parallax problem with 28 fixed observations.
    %   phillips  - Philips' "famous" test problem.
    %   shaw      - One-dimensional image restoration problem.
    %   spikes    - Test problem with a "spiky" solution.
    %   ursell    - Integral equation with no square integrable solution.
    %   wing      - Test problem with a discontinuous solution.
    %
    % Regularization routines.
    %   cgls      - Computes the least squares solution based on k steps
    %               of the conjugate gradient algorithm.
    %   discrep   - Minimizes the solution (semi-)norm subject to an upper
    %               bound on the residual norm (discrepancy principle).
    %   dsvd      - Computes a damped SVD/GSVD solution.
    %   lsqi      - Minimizes the residual norm subject to an upper bound
    %               on the (semi-)norm of the solution.
    %   lsqr      - Computes the least squares solution based on k steps
    %               of the LSQR algorithm (Lanczos bidiagonalization).
    %   maxent    - Computes the maximum entropy regularized solution.
    %   mtsvd     - Computes the modified TSVD solution.
    %   nu        - Computes the solution based on k steps of Brakhage's
    %               iterative nu-method.
    %   pcgls     - Same as cgls, but for general-form regularization.
    %   plsqr     - Same as lsqr, but for general-form regularization.
    %   pnu       - Same as nu, but for general-form regularization.
    %   tgsvd     - Computes the truncated GSVD solution.
    %   tikhonov  - Computes the Tikhonov regularized solution.
    %   tsvd      - Computes the truncated SVD solution.
    %   ttls      - Computes the truncated TLS solution.
    %
    % Analysis routines.
    %   fil_fac   - Computes filter factors for some regularization methods.
    %   gcv       - Plots the GCV function and computes its minimum.
    %   l_corner  - Locates the L-shaped corner of the L-curve.
    %   l_curve   - Computes the L-curve, plots it, and computes its corner.
    %   lagrange  - Plots the Lagrange function ||Ax-b||^2 + lambda^2*||Lx||^,
    %               and its derivative.
    %   picard    - Plots the (generalized) singular values,
    %               the Fourier coefficient for the right-hand side, and a
    %               (smoothed curve of) the solution Fourier-coefficients.
    %   plot_lc   - Plots an L-curve.
    %   quasiopt  - Plots the quasi-optimality function and computes its minimum.
    %
    % Routines for transforming a problem in general form into one in
    % standard form, and back again.
    %   gen_form  - Transforms a standard-form solution back into the
    %               general-form setting.
    %   std_form  - Transforms a general-form problem into one in
    %               standard form.
    %
    % Utility routines.
    %   bidiag    - Bidiagonalization of a matrix by Householder transformations.
    %   bsvd      - Computes the singular values, or the compact SVD,
    %               of a bidiagonal matrix stored in compact form.
    %   csd       - Computes the CS decomposition.
    %   csvd      - Computes the compact SVD of an m-by-n matrix.
    %   get_l     - Produces a p-by-n matrix which is the discrete
    %               approximation to the d'th order derivative operator.
    %   gsvd      - Computes the generalized SVD of a matrix pair.
    %   lanc_b    - Performs k steps of the Lanczos bidiagonalization
    %               process with/without reorthogonalization.
    %
    % Auxiliary routines required by some of the above routines.
    %   app_hh_l  - Applies a Householder transformation from the left.
    %   gen_hh    - Generates a Householder transformation.
    %   heb_new   - Newton-Raphson iteration with Hebden's rational
    %               approximation, used in lsqi.
    %   heb_new2  - Ditto, used in discrep.
    %   lsolve    - Inversion with A-weighted generalized inverse of L.
    %   ltsolve   - Inversion with transposed A-weighted inverse of L.
    %   mgs       - Modified Gram-Schmidt orthonormalization.
    %   newton    - Newton-Raphson iteration, used in discrep.
    %   pinit     - Initialization for treating general-form problems.
    %   pythag    - Computes sqrt(a^2 + b^2).
    %   spleval   - Computes points on a spline or spline curve.
    %
    % The routine l_corner requires the following routines from the Spline
    % Toolbox:
    %   fnder, ppbrk, ppcut, ppmak, sp2pp, spbrk, spmak.
    % If the Spline Toolbox is not available, then dummy functions with these
    % names should reside in the same directory as Regularization Tools.

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