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Highlights from
Chebfun

• A greedy algorithm for choosi...
• A keyhole contour integral
• A parameter dependent ODE wit...
• A periodic ODE system
• A wiggly function and its bes...
• ANGLE, UNWRAP, and branches o...
• Abscissa of the linearized Vl...
• Absolute value approximations...
• Advection-diffusion equation ...
• An Allen-Cahn equation with c...
• An ellipse rolling around ano...
• Approximation of piecewise li...
• Area and centroid of a 2D reg...
• Automatic differentiation in ...
• Battery test of Chebfun as an...
• Best approximation with the R...
• Birthday cards and analytic f...
• Blowup equation (Frank-Kamene...
• Bouncing photon, Sinai billia...
• Boundary layer for advection-...
• CHEBFUN GUIDE 10: NONLINEAR O...
• CHEBFUN GUIDE 1: GETTING STAR...
• CHEBFUN GUIDE 2: INTEGRATION ...
• CHEBFUN GUIDE 3: ROOTFINDING ...
• CHEBFUN GUIDE 4: CHEBFUN AND ...
• CHEBFUN GUIDE 5: COMPLEX CHEB...
• CHEBFUN GUIDE 6: QUASIMATRICE...
• CHEBFUN GUIDE 7: LINEAR DIFFE...
• CHEBFUN GUIDE 8: CHEBFUN PREF...
• CHEBFUN GUIDE 9: INFINITE INT...
• CHEBFUN GUIDE: INDEX
• Can one hear the shape of a c...
• Carrier equation
• Chebyshev Coefficients
• Chebyshev interpolation of os...
• Chebyshev polynomials as plot...
• Complex roots near the real a...
• Computing The Complex Singula...
• Condition numbers of various ...
• Convergence rates for interpo...
• Coupled system of reaction-di...
• Double-well Schrödinger ...
• Dual points, lines, polygons ...
• Eigenstates of the Schroeding...
• Eigenvalue level repulsion
• Eigenvalues of the Fox-Li int...
• Exact solutions of some ODEs
• Extrema of a complicated func...
• Field of values and numerical...
• Fractional calculus in Chebfun
• Frequencies of a drum
• Gauss and Clenshaw-Curtis qua...
• Gauss quadrature nodes and we...
• Generalized Polynomial Chaos
• Gravitational force between t...
• Half-wave rectifier
• Halphen's constant for approx...
• Happy Valentines Day!
• Heat equation via EXPM
• Histogram from function or da...
• Jump Conditions in BVPS
• Lane-Emden equation from astr...
• Least-squares data fitting an...
• Lebesgue functions and Lebesg...
• Linear EXP initial-value prob...
• Linear sine/cosine initial-va...
• Lissajous curves
• Local complexity of a function
• Matched asymptotics and bound...
• MathJax Introduction
• Maxwell's equations
• Mercer's theorem and the Karh...
• Merry Christmas!
• Model of a quantum dot array ...
• Multiple BVP solutions by sol...
• Nonlinear ODE modeling solar ...
• Nonnormality quiz from Trefet...
• Nonstandard 'Boundary' Condit...
• Optimization of a parameteris...
• Orbiting around fixed stars
• Orr-Sommerfeld eigenvalues
• Orthogonal polynomials via th...
• Orthogonal polynomials via th...
• Parameter-dependent ODEs: Thr...
• Perimeter of an ellipse
• Piecewise Operators Demo
• Polynomial basis for Hermite ...
• Polynomial eigenproblems with...
• Procrustes shape analysis
• Rational interpolation, robus...
• Resampling of random variables
• Resolvent norm on the imagina...
• Roots of a Bessel function
• Roots of a complex function v...
• Roots of a secular equation w...
• Roots of random polynomials
• Schwarz-Christoffel toolbox a...
• Simple computations with prob...
• Singular Value Decomposition ...
• Spike integral
• Stability Regions of ODE Form...
• Stability of a thermoelastic ...
• Stochastic collocation for Bu...
• System of two nonlinear BVPs
• The Dixon-Szego function in 2...
• The FFT in Chebfun
• The Mystery of Bernoulli Poly...
• The Nullspace of Linear Opera...
• The Rosenbrock function in 2D...
• The gamma function and its po...
• The white curves of Ortiz and...
• Time independent Black-Schole...
• Time-dependent integro-differ...
• Time-independent Schrödi...
• Transient Growth
• Wave equation with decay band
• Wikipedia ODE examples
• Wikipedia integro-differentia...
• Writing a message in 3D
• chebguiedit(varargin) CHEBGUIEDIT MATLAB code for chebguiedit.fig
• chebguiwindow(varargin) CHEBGUIWINDOW Driver file for Chebfun's CHEBGUI
• absTest
• ad_basic Tests basic AD functionality:
• ad_basic2 This test checks that Automatic Differentiation is working.
• ad_qmdiff Check if automatic differentiation of a quasimatrix with respect
• ad_systems Checks whether AD works correctly for multiple variables
• ad_vs_diff_special A test that compares derivatives obtained via AD to derivatives obtained
• ad_vs_diff_trig A test that compares derivatives obtained via AD to derivatives obtained
• ad_vs_diff_trig_deg A test that compares derivatives obtained via AD to derivatives obtained
• airy_extrema Verifies that the extrema of the airy function on [-15,0] are found
• aliasing Tests for aliasing: Check if the constructor accurately re-constructs the
• arithtest Test some basic arithmetic operators, i.e. plus, minus, times,
• bary(x,gvals,xk,ek) BARY Barycentric interpolation with arbitrary weights/nodes.
• bary_weights(xk) W = BARY_WEIGHTS(XK)
• barymat(M,N,map,w) BARYMAT Barycentric Interpolation Matrix
• barytest Test the evaluation of a chebfun using barycentric interpolation.
• besseljextrema Check if the extrema of the BesselJ function on [0,100] are recovered
• besseljroots Checks if the roots of the BesselJ function on [0,100] are recovered
• blowup(on_off) BLOWUP CHEBFUN blowup option
• blowup_exps Build a series of chebfuns with different non-integer exponents and check
• blowup_scale Tests scale invariance for functions with blowups (integer exponents
• blowup_splitting Check if blowups and splitting play well together.
• booltest Test boolean operators on chebfuns and quasimatrices.
• breakpoints Check if splitting works, with or without breakpoints.
• bvp45ctest This routine tests the chebfun wrappers for the BVP solvers
• callpref Check if options passed to the constructor are handled correctly.
• cftest Test CF approximation in various ways.
• chebbench(varargin) CHEBBENCH Chebfun Benchmark
• chebdomain Tests the chebfun constructor using the domain class.
• chebfunpref(varargin) CHEBFUNPREF Settings for Chebfun.
• chebfunpreftest Tests the chebfunpref options by getting and setting them
• cheblogo Chebfun logo.
• chebop_bc Solve two simple linear BVPs, check the solution vs. the exact
• chebop_bc2 Test nonseperable boundary conditions and other supplementary conditions
• chebop_cumsum Check if the indefinite integral chebop works.
• chebop_diff Checks if the differentiation chebop is equivalent to differentiating
• chebop_different_syntaxes Checks whether different allowed syntaxes for chebops work
• chebop_eigs Test the chebop eigs method.
• chebop_ellipjode Test to check that the chebfun command for
• chebop_expm Test the chebop expm method.
• chebop_feval Test various combinations of inputs to chebop/feval.
• chebop_fitbcs Create chebops, convert them to linops, and obtain chebfuns which satisfy
• chebop_gmrestest Test the Chebfun implementation of GMRES for solving Lu = f,
• chebop_intops Test integral operators
• chebop_ivp This tests solves a linear IVP using chebop and checks
• chebop_linop Test the chebop linop method.
• chebop_polyeigs Test the chebop polyeigs method.
• chebop_pwintops This test checks the construction of the piecewise fred and volt
• chebop_pwlinear This test constructs a piecewise-linear chebop and checks
• chebop_scalingtest This tests solves a nonlinear pendulum BVP with
• chebop_simplify This test has a purpose: to make sure that the
• chebop_svds Test the chebop svds method.
• chebop_systemeig Eigenvalue test, inspired by Maxwell's equation.
• chebop_systemexpm Exponential test, inspired by Maxwell's equation
• chebop_systemsolve1
• chebop_systemsolve2 Test solution of a 2x2 system
• chebop_v4tests Test a few things concerning the version 4 chebops (i.e.
• chebop_vs_linop Chebtest CHEBOP_VS_LINOP
• cheboppref(varargin) CHEBOPPREF Settings for chebops.
• chebpadetest Test the chebpade function against some examples.
• chebpoly(n,d,kind) CHEBPOLY Chebyshev polynomial of degree n.
• chebpolytest Tests chebpoly with integer and chebfun arguments.
• chebpolyval(c,kind) CHEBPOLYVAL maps Chebyshev coefficients to values at Chebyshev points
• chebpts(n,d,kind)
• chebsnake(nodes,alpha) CHEBSNAKE Chebfun snake game.
• chebtest(dirname) CHEBTEST Probe Chebfun against standard test files.
• circplate Use a linear chebop to compute the deflection of a circular plate.
• complexrotation This code makes sure a few things are ok if you make them complex,
• composetest Test composition of chebfuns with chebfuns and chebfuns
• convTest
• convspline Generates piecewise polynomial cardinal B-splines by a process
• ctortest Test the chebfun constructor for vectorized and non-vectorized
• cumsum_fracexps Tests CUMSUM for Chebfuns with fractional exponents. This situation
• cumsum_infint Check CUMSUM on for functions which diverge over an infnite
• cumsum_oscillate Compute the indefinite integral of an oscillatory function
• cumsummat(N) CUMSUMMAT Chebyshev integration matrix.
• cumsumunbnd Test CUMSUM for chebfuns that have negative, and possibly
• diff_matrices Test the construction of differentiation matrices
• diffexp Tests the computation of derivatives using DIFF
• diffinf Tests the computation of derivatives using DIFF when the
• diffmat(N,k) DIFFMAT Chebyshev differentiation matrix
• difforder Check to see whether difforder of systems are computed correctly.
• diffsingmaps Tests the computation of derivatives using DIFF when the
• diffsingmaps Tests the computation of derivatives using DIFF when the
• elementary Check that computations of elementary functions
• ellipjtest Test the accuracy of the Chebfun overload of the
• evalcomplex Check that a chebfun evaluates correctly for complex arguments.
• exact_endpoints Test whether endpoints are interpolated (exactly):
• exps_ctor Tests construction with exps
• exps_cumsum Tests cumsum with exponents
• exps_diff Tests diff with exponents
• exps_sum Tests SUM for Chebfuns with exponents
• extracting_roots Test extracting roots with and without maps
• falknerskan Solves the Falkner-Skan equation and checks the result.
• findexps_test Tests automatic exponent computation for functions
• fov(A) FOV Field of values (numerical range) of matrix A
• fovtest Tests the FOV (field of values) function.
• fraccalctest Perform some tests for fractional derivatives
• funscale Check that fun scales have been correctly updated after
• fzerotest Tests the fzero wrapper.
• grammatrix Construct the Gram matrix with chebfuns and
• guide2tests Perform various tests from chapter 2 of the Chebfun Guide.
• hermpoly(n,type) HERMPOLY Hermite polynomial of degree n.
• hermpts(n,varargin) HERMPTS Hermite points and Gauss-Hermite Quadrature Weights.
• infimps Check that imps are properly set in computations involving exps
• interp1test Check that the Chebfun-overloaded INTERP1
• inverseq This test checks roots and the vectorise preference
• invtest This test constructs two chebfuns and uses inv to invert them. It checks
• isequaltest Check if chebfun/isequal works by comparing a chebfun with itself
• ivp_test This test solves the Van der Pol ODEs in Chebfun with ode113. It checks
• ivp_testcomplex Nick Trefethen March 2009
• ivp_ty_test This test solves the Van der Pol ODE in
• jacpoly(N,a,b,d,flag) JACPOLY Jacobi polynomials.
• jacpts(n,alpha,beta,varargin) JACPTS Gauss-Jacobi Abscissae and Quadrature Weights.
• jacptstest This test computes Legrendre points with Gauss quadrature weights. It
• lagpoly(n) LAGPOLY Laguerre polynomial of degree n.
• lagpts(n,int,meth) LAGPTS Laguerre points and Gauss-Laguerre Quadrature Weights.
• lebesgue(x,varargin)
• lebesguetest This tests computes the Lebesgue function and Lebesgue constant
• legpoly(n,d,normalize,method) LEGPOLY Legendre polynomials.
• legpts(n,int,meth) LEGPTS Legendre points and Gauss Quadrature Weights.
• legptstest This tests checks legpts and the accuracy of the method GW and FAST
• lexerParserTest This test ensures that the chebgui string parser is doing the correct
• linop_bcchange Check if changing the boundary conditions of a chebop that has already
• linop_diag Check if multiplication with a pointwise multiplication operator
• linop_eye Checks the 10 by 10 realization of the identity operator.
• linop_feval_lr Check that left/right evaluation with linops behaves as expected.
• linop_functionals Tests the construction and applciation of the Chebfun/Chebop
• linop_operarith This test checks basic arithmetric operations of linops
• linop_systemapply Test 2x2 systems applied to functions.
• linopzerotest Checks whether iszero information for linear chebops is being passed and
• mapends_nan_inf Tests for rounding errors on mapped endpoints and NaN and inf error
• mappref(varargin) MAPPREF fun map preferences
• mappreftest Tests the mappref options by getting and setting them
• maps(varargin) CHEBFUN MAPS
• mathieu This test computes periodic Mathieu functions and eigenvalues for the
• matrixnorms This test constructs a matrix with chebfuns as columns and computes
• max_and_imps Tests if max introduces small jumps when computing the maximum
• max_min Tests max and min of functions.
• max_min_unbnd Tests max and min of unbounded functions.
• maxdegree Tests if the maxdegree is working in resampling on and off modes.
• maxdoubleroots
• maxtest This test checks max when the difference between the functions
• mfun_integrate This test computes the integrals of blow-up functions
• minsamples_adapt Test for minsaples in adaptive mode on an infinite domain (unbounded maps)
• misclnttests1 This tests the chebfun constructor with different syntax, sum and norm.
• nanavoidance This test check that NaNs are avoided on point evaluations
• normtests This test checks that norm of a chebfun is working correctly
• orrsommerfeld Orr-Sommerfeld eigenvalues for plane Poiseuille flow (just barely
• orthosincos This test constructs a system of chebfuns and checks they have been
• outerprod This test checks that the outer product of a system of chebfuns is
• paramODE Test solving a parameter dependent ODE.
• pdeset(varargin) PDESET Set options for pde15s
• plotrow This test checks that row chebfuns can be plotted
• plusquasimatrix This test checks that quasimatrices of different sizes cannot be added.
• pointevals This test checks that point evaluations are working.
• pole_construct Test to check if Chebfun operations on the basic chebfun 'x'
• polyfittest This test checks that the polyfit commmandis working correctly.
• polytest This test check that poly and ployval are working correctly.
• qrTest
• qrtest Tests QR factorization of Chebfun quasimatrices.
• quadtest Tests sum and quad over bounded domains.
• ratinterp( f , varargin ) RATINTERP computes a robust rational interpolation or approximation.
• ratinterptest Check a few basics with ratinterp
• remeztest The REMEZ command constructs infinity-norm
• resampletest Test if the resampling option is working by counting the number of
• resampling(on_off) RESAMPLING CHEBFUN resample option
• residuetest Tests the Chebfun residue command.
• restrict_roots Test restriction from one interval to another with { }.
• restrictimps Test handling of the imps matrix by restrict
• restrictscl This function tests the retrict function (problem related to a bug report
• rootsTest
• rootspol Check behavior of roots of a perturbed polynomial
• scale Tests for scale invariance.
• scaleinvariance This code makes sure a few things are scale-invariant.
• scaleinvariance2 Modification of scaleinvariance.m
• schrodinger_sqwell Tests eigs with piecewise constant coefficient, on a Schrodinger
• scribble.m
• scribbleTest
• scribbleio Tests that scribble responds to the expected input and output
• scribbles scribbles.m - uses "scribble" to test various things
• sing(str,bpm) SING - A basic keyboard for MATLAB using chebfuns
• sinx (by Rodrigo Platte)
• smallintervals Tests of operations on small intervals
• splitting(on_off) SPLITTING CHEBFUN splitting option
• splittingtest A collection of tests for exact jump detection
• sqrt_test Tests representations of the square root
• std_test Check that std of a complex chebfun gives the correct real result.
• stringinput Makes sure that the Chebfun constructor accepts
• subspacetest test the subspace function (angle between subspaces). Also calls vander.m
• sumcos20x Tests a couple of simple integrals, real and complex.
• suminftest Test a few things involving sum applied to
• sumtest Tests various integrals over unbounded domains.
• test_ratinterp ( ) Test the ratinterp function with different input types
• unbndpolys Tests both the construction of Laguerre and Hermite polynomials on unbounded
• unboundednorms Tests norm for unbounded domains and subtraction of chebfuns.
• vectornorms Sets up a chebfun with two pieces and
• webexamples Test the examples that are on the front page of the Chebfun website
• anon ANON constructor for the anon class, which is used to work with AD
• chebconst
• chebfun CHEBFUN Constructor for chebfuns.
• chebgui INTRODUCTION TO CHEBGUI
• fun FUN Class definition for funs
• oparray OPARRAY Array of function handles.
• varmat VARMAT Variable-sized matrix object constructor.
• {?double}) chebop CHEBOP Construct an operator on chebfuns.
• {?double}) domain DOMAIN Domain object constructor.
• {?double}) linop function A = linop(varargin)
• ATAPformats.m
• Contents.m
• ExampleTemplate.m
• LevinIntegrate.m
• guidedefaults.m
• Chebfun
• Chebfun Examples
• approx.html
• complex.html
• fun.html
• geom.html
• integro.html
• linalg.html
• ode-eig.html
• ode.html
• opt.html
• pde.html
• quad.html
• roots.html
• stats.html
• View all files