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nlevp.m
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nlevp.m
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function varargout = nlevp(name,varargin)
%NLEVP Collection of nonlinear eigenvalue problems.
% [COEFFS,FUN,OUT3,OUT4,...] = NLEVP(NAME,ARG1,ARG2,...)
% generates the matrices and functions defining the problem specified by
% NAME (a case insensitive string).
% ARG1, ARG2,... are problem-specific input arguments.
% All problems are of the form
% T(lambda)*x = 0
% where
% T(lambda)= f0(lambda)*A0 + f1(lambda)*A1 + ... + fk(lambda)*Ak.
% The matrices A0, A1, ..., Ak are returned in a cell array:
% COEFFS = {A0,...,Ak}.
% FUN is a function handle that can be used to evaluate the functions
% f1(lambda),...,fk(lambda). For a scalar lambda,
% F = FUN(lambda) returns a row vector containing
% F = [f1(lambda), f2(lambda), ..., fk(lambda)].
% If lambda is a column vector, FUN(lambda) returns a row per element in
% lambda.
% [F,FP] = FUN(lambda) also returns the derivatives
% FP = [f1'(lambda), f2'(lambda), ..., fk'(lambda)].
% [F,FP,FPP,FPPP,...] = FUN(lambda) also returns higher derivatives.
% OUT3, OUT4, ... are additional problem-specific output arguments.
% See the list below for the available problems.
%
% PROBLEMS = NLEVP('query','problems') or NLEVP QUERY PROBLEMS
% returns a cell array containing the names of all problems
% in the collection.
% NLEVP('help','name') or NLEVP HELP NAME
% gives additional information on problem NAME, including number and
% meaning of input/output arguments.
% NLEVP('query','name') or NLEVP QUERY NAME
% returns a cell array containing the properties of the problem NAME.
% PROPERTIES = NLEVP('query','properties') or NLEVP QUERY PROPERTIES
% returns the properties used to classify problems in the collection.
% NLEVP('query',property1,property2,...) or NLEVP QUERY PROPERTY1 ...
% lists the names of all problems having all the specified properties.
%
% [T,TP,TPP,...] = NLEVP('eval',NAME,LAMBDA,ARG1,ARG2,...)
% evaluates the matrix function T and its derivatives TP, TPP,...
% for problem NAME at the scalar LAMBDA.
%
% NLEVP('version') or NLEVP VERSION
% prints version, release date, and number of problems
% of the installed NLEVP collection.
% V = NLEVP('version')
% returns a structure V containing version information.
% V consists of the fields v.number, v.date, and v.problemcount.
%
% Available problems:
%
% acoustic_wave_1d Acoustic wave problem in 1 dimension.
% acoustic_wave_2d Acoustic wave problem in 2 dimensions.
% bcc_traffic QEP from stability analysis of chain of non-identical cars.
% under bilateral cruise control.
% bent_beam 6-by-6 NEP from a bent beam model.
% bicycle 2-by-2 QEP from the Whipple bicycle model.
% bilby 5-by-5 QEP from Bilby population model.
% buckling_plate 3-by-3 NEP from a buckling plate model.
% butterfly Quartic matrix polynomial with T-even structure.
% canyon_particle NEP from the Schrödinger equation on a canyon-like shape.
% cd_player QEP from model of CD player.
% circular_piston Sparse QEP from model of circular piston.
% clamped_beam_1d NEP from 1D clamped beam model with delayed feedback control.
% closed_loop 2-by-2 QEP associated with closed-loop control system.
% concrete Sparse QEP from model of a concrete structure.
% damped_beam QEP from simply supported beam damped in the middle.
% damped_gyro QEP of a damped gyroscopic system.
% deformed_consensus n-by-n QEP from multi-agent systems theory.
% dirac QEP from Dirac operator.
% disk_brake100 100-by-100 QEP from a disk brake model.
% disk_brake4669 4669-by-4669 QEP from a disk brake model.
% distributed_delay1 3-by-3 NEP from distributed delay system.
% elastic_deform QEP from elastic deformation of anisotropic material.
% fiber NEP from fiber optic design.
% foundation Sparse QEP from model of machine foundations.
% gen_hyper2 Hyperbolic QEP constructed from prescribed eigenpairs.
% gen_tantipal2 T-anti-palindromic QEP with eigenvalues on the unit
% circle.
% gen_tpal2 T-palindromic QEP with prescribed eigenvalues on the
% unit circle.
% gun NEP from model of a radio-frequency gun cavity.
% hadeler NEP due to Hadeler.
% hospital QEP from model of Los Angeles Hospital building.
% intersection 10-by-10 QEP from intersection of three surfaces.
% loaded_string REP from finite element model of a loaded vibrating
% string.
% metal_strip QEP related to stability of electronic model of metal
% strip.
% mirror Quartic PEP from calibration of cadioptric vision system.
% mobile_manipulator QEP from model of 2-dimensional 3-link mobile manipulator.
% nep1 2-by-2 basic NEP example.
% nep2 3-by-3 basic NEP example.
% nep3 NEP with weighted norm coefficients.
% neuron_dde 2-by-2 NEP from a neural-network DDE.
% omnicam1 9-by-9 QEP from model of omnidirectional camera.
% omnicam2 15-by-15 QEP from model of omnidirectional camera.
% orr_sommerfeld Quartic PEP arising from Orr-Sommerfeld equation.
% pdde_stability QEP from stability analysis of discretized PDDE.
% pdde_symmetric n-by-n NEP from a partial delay differential equation.
% photonic_crystal REP from dG-FEM of wave propagation in a periodic
% medium.
% pillbox_cavity 170562-by-170562 NEP from a RF pillbox cavity.
% pillbox_small 20-by-20 NEP from a RF pillbox cavity.
% planar_waveguide Quartic PEP from planar waveguide.
% plasma_drift Cubic PEP arising in Tokamak reactor design.
% power_plant 8-by-8 QEP from simplified nuclear power plant problem.
% qep1 3-by-3 QEP with known eigensystem.
% qep2 3-by-3 QEP with known, nontrivial Jordan structure.
% qep3 3-by-3 parametrized QEP with known eigensystem.
% qep4 3-by-4 QEP with known, nontrivial Jordan structure.
% qep5 3-by-3 nonregular QEP with known Smith form.
% railtrack QEP from study of vibration of rail tracks.
% railtrack_rep REP from study of vibration of rail tracks.
% railtrack2 Palindromic QEP from model of rail tracks.
% railtrack2_rep REP from model of rail tracks.
% relative_pose_5pt Cubic PEP from relative pose problem in computer vision.
% relative_pose_6pt QEP from relative pose problem in computer vision.
% sandwich_beam NEP from model of a clamped sandwich beam.
% schrodinger QEP from Schrodinger operator.
% schrodinger_abc NEP from Schrodinger equation with absorbing boundary condition.
% shaft QEP from model of a shaft on bearing supports with a
% damper.
% sign1 QEP from rank-1 perturbation of sign operator.
% sign2 QEP from rank-1 perturbation of 2*sin(x) + sign(x)
% operator.
% sleeper QEP modelling a railtrack resting on sleepers.
% speaker_box QEP from finite element model of speaker box.
% spring QEP from finite element model of damped mass-spring
% system.
% spring_dashpot QEP from model of spring/dashpot configuration.
% square_root Square root of a skew-symmetric matrix.
% surveillance 27-by-20 QEP from surveillance camera callibration.
% time_delay 3-by-3 NEP from a time-delay system.
% time_delay2 2-by-2 NEP from a time-delay system.
% time_delay3 NEP with high-variance-norm coefficients.
% utrecht1331 QEP 1331-by-1331 QEP with singular A1.
% wing 3-by-3 QEP from analysis of oscillations of a wing in
% an airstream.
% wiresaw1 Gyroscopic system from vibration analysis of wiresaw.
% wiresaw2 QEP from vibration analysis of wiresaw with viscous
% damping.
%
% Examples:
% coeffs = nlevp('railtrack')
% generates the matrices defining the railtrack problem.
% nlevp('help','railtrack')
% prints the help text of the railtrack problem.
% nlevp('query','railtrack')
% prints the properties of the railtrack problem.
%
% For example code to solve all polynomial eigenvalue problems (PEPs)
% in this collection of dimension < 500 with MATLAB's POLYEIG
% see NLEVP_EXAMPLE.M.
% Reference:
% T. Betcke, N. J. Higham, V. Mehrmann, C. Schroeder, and F. Tisseur.
% NLEVP: A Collection of Nonlinear Eigenvalue Problems,
% ACM Transactions on Mathematical Software, 39(2), pp7:1-7:28, 2013.
% Check inputs
if nargin < 1, error('Not enough input arguments'); end
if ~ischar(name), error('NAME must be a string'); end
name = lower(name);
if strcmp(name,'query')
if nargin == 1
error('Not enough input arguments')
end
[varargout{1:nargout}] = nlevp_query(varargin{:});
return
end
if strcmp('string',name)
name = 'spring';
warning('NLEVP:string_renamed','Problem string has been renamed spring.')
end
if strcmp('version',name)
[varargout{1:nargout}] = nlevp_version(varargin{:});
return
end
switch name
case 'help'
nlevp_home = which('nlevp');
nlevp_home = strrep(nlevp_home, 'nlevp.m', '');
if nargin < 2
help nlevp
else
if ~nlevp_isoctave
% some nlevp are shadowed by MATLAB functions. This fixes it
if ispc % we need to see if we are on Windows or not
help(sprintf('%sprivate\\%s', nlevp_home, varargin{1}))
else
help(sprintf('%sprivate/%s', nlevp_home, varargin{1}))
end
else
% Uglier code necessary for Octave.
eval(['help ', varargin{1}]);
end
end
case 'eval'
[varargout{1:max(nargout,1)}] = nlevp_eval(varargin{:});
otherwise
[varargout{1:nargout}] = feval(name,varargin{:});
end
end