Contents

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

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 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

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.