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ode45, ode23, ode113, ode15s, ode23s, ode23t, ode23tb 2-1558 [5] Kahaner, D. , C. Moler, and S. Nash, Numerical Methods and Software, Prentice-Hall, New Jersey, 1989. [6] Shampine, L. F. , Numerical Solution of Ordinary Differential Equations, Chapman & Hall, New York, 1994. [7] Shampine, L. F. and M. K. Gordon, Computer Solution of Ordinary Differential Equations: the Initial Value Problem, W. H. Freeman, San Francisco, 1975. [8] Shampine, L. F. and M. E. Hosea, “Analysis and Implementation of TR-BDF2,” Applied Numerical Mathematics 20, 1996. [9] Shampine, L. F. and M. W. Reichelt, “The MATLAB ODE Suite,” SIAM Journal on Scientific Computing, Vol. 18, 1997, pp 1-22. [10] Shampine, L. F., M. W. Reichelt, and J.A. Kierzenka, “Solving Index-1 DAEs in MATLAB and Simulink,” SIAM Review, Vol. 41, 1999, pp 538-552.
odefile 2odefile Purpose Define a differential equation problem for ordinary differential equation (ODE) solvers Note This reference page describes the odefile and the syntax of the ODE solvers used in MATLAB, Version 5. MATLAB, Version 6, supports the odefile for backward compatibility, however the new solver syntax does not use an ODE file. New functionality is available only with the new syntax. For information about the new syntax, see odeset or any of the ODE solvers. Description odefile is not a command or function. It is a help entry that describes how to create an M-file defining the system of equations to be solved. This definition is the first step in using any of the MATLAB ODE solvers. In MATLAB documentation, this M-file is referred to as an odefile, although you can give your M-file any name you like. You can use the odefile M-file to define a system of differential equations in one of these forms or where: y′ = ft ( , y) Mt ( , y)y′ = ft ( , y)v t is a scalar independent variable, typically representing time. y is a vector of dependent variables. f is a function of t and y returning a column vector the same length as y. Mt ( , y) is a time-and-state-dependent mass matrix. The ODE file must accept the arguments t and y, although it does not have to use them. By default, the ODE file must return a column vector the same length as y. All of the solvers of the ODE suite can solve Mt ( , y)y′ = ft ( , y) , except ode23s, which can only solve problems with constant mass matrices. The ode15s and 2-1559
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Function Reference Volume 2: F - O
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1 Functions — Categorical List De
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Functions — Categorical List 1 Th
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Desktop Tools and Development Envir
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Desktop Tools and Development Envir
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Mathematics Mathematics Functions f
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Operations and Manipulation : (colo
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Matrix Analysis cond Condition numb
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Trigonometric acos Inverse cosine a
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Discrete Math (e.g., Prime Factors)
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Interpolation and Computational Geo
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Ordinary Differential Equations (IV
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Elementary Sparse Matrices spdiags
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Programming and Data Types Programm
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strjust Justify character array str
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Data Type Conversion Numeric double
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Basic Array Information disp Displa
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Arithmetic Operations + Plus - Minu
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Programming in MATLAB “M-File Fun
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Control Flow break Terminate execut
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MEX Programming dbmex Enable MEX-fi
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Opening, Loading, Saving Files impo
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Audio and Audio/Video General audio
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Graphics 2-D graphs, specialized pl
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Area, Bar, and Pie Plots area Area
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Bit-Mapped Images frame2im Convert
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Figure Windows clc Clear figure win
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Color Operations brighten Brighten
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Lighting camlight Cerate or positio
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Deploying User Interfaces guidata S
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Functions — Alphabetical List 2
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2factorial Purpose Factorial functi
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2fclose Purpose Close one or more o
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See Also compass, LineSpec, rose 2
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2ferror Purpose Query MATLAB about
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. . fx = feval(funfcn,x,varargin{:}
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Examples A common use of Fourier tr
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Data Type Support When N is a prime
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2fft2 Purpose Two-dimensional discr
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2fftshift Purpose Shift zero-freque
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2fftw Purpose Interface to the FFTW
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fftw('wisdom', str) loads the strin
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2fgetl Purpose Read line from file,
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2fieldnames Purpose Return field na
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2figflag Purpose This function is O
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2figure Purpose Create a figure gra
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Property Name Property Description
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Modifying Properties Figure Propert
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Children vector of handles Figure P
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Color ColorSpec Figure Properties B
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Figure Properties unless the mouse
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Figure Properties and labels, the c
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InvertHardcopy {on} | off Figure Pr
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Figure Properties This property aff
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PaperType Select a value from the f
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PointerShapeCData 16-by-16 matrix F
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Figure Properties On UNIX systems,
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Or Figure Properties The host compu
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SelectionType {normal} | extend | a
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Units {pixels} | normalized | inche
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Figure Properties and stays above a
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Figure Properties zdepth 24 - indic
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!glxinfo Figure Properties After pr
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2fileattrib Purpose Set or get attr
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Examples Get Attributes of File To
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fileattrib The operation was succes
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filebrowser 2filebrowser Purpose Di
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File Format Extension File Content
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2fileparts Purpose Return filename
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2fill Purpose Filled two-dimensiona
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See Also axis, caxis, colormap, Col
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If you specify color using C, fill3
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2filter Purpose Filter data with an
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The operation of filter at sample m
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2find Purpose Find indices and valu
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x = [11 0 33 0 55]'; find(x) ans =
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2findall Purpose Find handles of al
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2findobj Purpose Locate graphics ob
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'-and','-not',{'Color','red','-or',
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2finish Purpose MATLAB termination
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fitsinfo The tables that follow sho
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Fields of the BinaryTable Structure
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Fields of the Unknown Structure Arr
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key = S.AsciiTable.Keywords ans = '
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Example Read FITS file tst0012.fits
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2flipdim Purpose Flip array along a
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2flipud Purpose Flip matrices up-do
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2floor Purpose Round towards minus
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2flow Purpose A simple function of
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1 fminbnd converged to a solution x
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fminbnd Limitations The function to
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TolFun Termination tolerance on the
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function f = myfun(x,a) f = x(1)^2
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current directory. If it is not fou
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2for Purpose Repeat statements a sp
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2format Purpose Control display for
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get(0,'Format') ans = long Set the
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2fplot Purpose Plot a function betw
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1 0.8 0.6 0.4 0.2 0 −0.2 −0.4
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100 80 60 40 20 0 0 0.1 0.2 0.3 0.4
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fprintf Flags You can control the a
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Character Description \'' or '' (tw
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It's Friday. The commands B = [8.8
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2frameedit Purpose Create and edit
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frameedit Printing Simulink Block D
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machineformat argument from the out
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Specifying Output Precision By defa
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Remarks If the input stream is byte
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In the example, the fread command a
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2freqspace Purpose Determine freque
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2fscanf Purpose Read formatted data
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fscanf Mixing character and numeric
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'eof' 1: End of file status A retur
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2ftp Purpose Connect to FTP server,
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2full Purpose Convert sparse matrix
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2func2str Purpose Construct a funct
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2function Purpose Function M-files
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2function_handle (@) Purpose MATLAB
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To execute the sqr function defined
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f = functions(@floor) f = function:
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2funm Purpose Evaluate general matr
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[F, exitflag, output] = funm(...) r
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2fwrite Purpose Write binary data t
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[x,fval,exitflag] = fzero(...) retu
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Purpose Test matrices Syntax [A,B,C
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C = gallery('chebvand',m,p) where m
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Argument k defaults to round(n/4),
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(n,n+1-abs(j)) position, and zeros
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kahan—Upper trapezoidal matrix A
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gallery with the same diagonal entr
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pei—Pei matrix gallery A = galler
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andhess—Random, orthogonal upper
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iemann—Matrix associated with the
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toeppen—Pentadiagonal Toeplitz ma
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n = 5 hilb(6)(1:5,2:6)*1.8144. A sy
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gamma, gammainc, gammaln Y = gammal
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2gcbf Purpose Get handle of figure
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2gcd Purpose Greatest common diviso
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2gcf Purpose Get current figure han
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2genpath Purpose Generate a path st
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See Also addpath, path, pathdef, pa
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genvarname If the str input contain
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k time_elapsed time_elapsed2 time_e
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object property names and whose fie
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2get (timer) Purpose Display or get
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2getappdata Purpose Get value of ap
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2getfield Purpose Get field of stru
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2getframe Purpose Get movie frame S
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getplottool 2getplottool Purpose Ut
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2global Purpose Define a global var
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2gmres Purpose Generalized Minimum
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Examples Example 1. A = gallery('wi
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gmres References [1] Barrett, R., M
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See Also LineSpec, sparse, spy 1 0.
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Examples The statements gradient di
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2graymon Purpose Set default figure
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2griddata Purpose Data gridding Syn
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0.5 0 −0.5 2 1 0 See Also delauna
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griddata3 [2] National Science and
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griddatan Reference [1] Barber, C.
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Examples Example 1. The matrices ha
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A = B = The statement 1 4 7 10 13 2
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2gtext Purpose Mouse placement of t
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% save the structure guidata(figure
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Purpose Hadamard matrix Syntax H =
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2hdf Purpose HDF interface Syntax h
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2hdf5 Purpose HDF5 data type classe
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The following are the methods of th
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Methods Description Syntax setData
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h5vlen The HDF5 h5vlen class associ
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Data: {[] [] []} MemberNames: {'tem
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2hdf5info Purpose Return informatio
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2hdf5read Purpose Read data from an
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2hdf5write Purpose Write a Hierarch
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hdf5write If the data in the worksp
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2hdfinfo Purpose Return information
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hdfinfo Fields Common to Returned S
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Fields of the Vdata Structure Field
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See Also hdfread, hdf fileinfo = hd
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hdfread If a parameter requires mul
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Parameter Description Required Para
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hdfread Subsetting Parameters for H
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Parameter Description Optional Para
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ans = 16 ans = 5 hdfread Using hdfr
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2hdftool Purpose Browse and import
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help classname.methodname displays
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help datafeed displays help for the
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Tabs in Help Navigator pane provide
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2helpdlg Purpose Create a help dial
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2helpwin Purpose Provide access to
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See Also eig, qz, schur Matrix A Ro
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2hex2num Purpose Convert IEEE hexad
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2hggroup Purpose Create hggroup obj
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Modifying Properties Hggroup Proper
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Hggroup Properties MATLAB executes
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Hggroup Properties potentially dama
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Hggroup Properties When you want to
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2hgsave Purpose Saves a Handle Grap
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More Information The references in
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h(1) = surface(x,y,z,'FaceColor','r
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Hgtransform Properties ButtonDownFc
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Hgtransform Properties none — Do
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Interruptible {on} | off Hgtransfor
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Hgtransform Properties the child ob
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2hilb Purpose Hilbert matrix Syntax
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The histogram’s x-axis reflects t
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2histc Purpose Histogram count Synt
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hold off sets the NextPlot property
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2horzcat Purpose Horizontal concate
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2hostid Purpose Return MATLAB serve
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Purpose Imaginary unit Syntax i a+b
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Remarks Nonscalar Expressions If th
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2ifft Purpose Inverse discrete Four
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2ifft2 Purpose Two-dimensional inve
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2ifftn Purpose Multidimensional inv
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2ifftshift Purpose Inverse FFT shif
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2im2java Purpose Convert image to J
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2imag Purpose Imaginary part of a c
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image(x,y,C,'PropertyName',Property
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The order of the operations must be
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Modifying Properties Image Properti
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Image Properties ButtonDownFcn stri
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0.5 1 1.5 2 2.5 3 3.5 4 4.5 0.5 1 1
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Image Properties slowest. The other
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Image Properties See Objects That C
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2imagesc Purpose Scale data and dis
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See Also image “Bit-Mapped Images
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Information Returned Format File Ty
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See Also imformats, imread, imwrite
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Field Value alpha Returns 1 if the
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2importdata Purpose Load data from
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Supported Formats [...] = imread(fi
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imread Note By default, Microsoft W
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[...] = imread(...,'Back','none');
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This example reads an ICO image, ap
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Supported Formats imwrite This tabl
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JPEG-Specific Parameters This table
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Parameter Values Default 'Transpare
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RAS-Specific Parameters This table
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imwrite L*a*b* Color Data For TIFF
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2ind2rgb Purpose Convert an indexed
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IND = [3 4 5 6] s = [3,3]; [I,J] =
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2Inf Purpose Infinity Syntax Inf In
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2info Purpose Display Release Notes
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g(t) = t^2 You can convert the resu
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2inmem Purpose Return functions in
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2inpolygon Purpose Detect points in
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2input Purpose Request user input S
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2inputname Purpose Input argument n
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Check this field in the MATLAB comm
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2int8, int16, int32, int64 Purpose
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2interp1 Purpose One-dimensional da
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y = sin(x); xi = 0:.25:10; yi = int
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interp1 For the 'spline' method, in
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interp2 spacing is handled by mappi
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2interp3 Purpose Three-dimensional
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2interpft Purpose One-dimensional i
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interpn Discussion All the interpol
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interpstreamspeed coordinates for U
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See Also stream2, stream3, streamli
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2intmax Purpose Return largest poss
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2intwarning Purpose Control state o
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Examples Check the initial state of
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2inv Purpose Matrix inverse Syntax
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See Also det, lu, rref Inputs of Ty
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2ipermute Purpose Inverse permute t
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See Also isa islogical Determine if
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To check for a sparse array, use is
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2iscell Purpose Determine if input
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2ischar Purpose Determine if input
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2isempty Purpose Test if array is e
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f2: 50 B.f2 = 50; B.f1 = 25 B = f2:
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2isfield Purpose Determine if input
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2isfloat Purpose Detect floating-po
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2ishandle Purpose Determines if val
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2isinf Purpose Detect infinite elem
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2iskeyword Purpose Determine if inp
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2isletter Purpose Detect array elem
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2ismember Purpose Detect members of
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2ismethod Purpose Determine if inpu
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2isnumeric Purpose Determine if inp
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2isocaps Purpose Compute isosurface
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“Volume Visualization” for rela
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isonormals(x,y,z,data,p); isocolors
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See Also isosurface, isocaps, smoot
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isonormals Draw an isosurface from
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isosurface(...) with no output argu
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2ispc Purpose Determine if PC (Wind
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2isprop Purpose Determine if input
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This expression detects strictly re
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2issorted Purpose Determine if set
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2isspace Purpose Detect space chara
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2isstr Purpose Determine if input i
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Category Description isstrprop wspa
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2isstruct Purpose Determine if inpu
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2isunix Purpose Determine if UNIX v
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2isvarname Purpose Determine if inp
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Purpose Imaginary unit Syntax j x+y
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2kron Purpose Kronecker tensor prod
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lasterr catch errmsg = lasterr; if(
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catch do_cleanup rethrow(lasterror)
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lastwarn Use lastwarn to determine
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2ldivide, rdivide Purpose Left or r
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legend(string_matrix) adds a legend
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Obsolete Location Values Obsolete S
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See Also LineSpec, plot In this exa
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m m Nn ( x) = ( - 1) legendre m Des
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2length Purpose Length of vector Sy
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license Image Processing Toolbox. T
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2light Purpose Create a light objec
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Modifying Properties Light Property
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HandleVisibility {on} | callback |
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Light Properties to define object h
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2lighting Purpose Select the lighti
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2line Purpose Create line object Sy
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Finally, pop the first line to the
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Line Properties queue — Queue the
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Line Properties color with that of
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Line Properties Marker character (s
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Line Properties Type string (read o
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Lineseries Properties routine as a
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Lineseries Properties obtain greate
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Lineseries Properties Marker charac
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Lineseries Properties Type string (
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Lineseries Properties MATLAB reeval
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Specifier Marker Type 'square' or s
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1 0.8 0.6 0.4 0.2 0 −0.2 −0.4
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2linkaxes Purpose Synchronize limit
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2linkprop Purpose Keep same value f
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The property linking code is in ste
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2linsolve Purpose Solve a linear sy
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opts.UT = true; opts.TRANSA = true;
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2listdlg Purpose Create list select
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2load Purpose Load workspace variab
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Example 2 — Loading From an ASCII
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See Also load, save, saveobj loadob
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2log1p Purpose Compute log(1+x) acc
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2log10 Purpose Common (base 10) log
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2loglog Purpose Log-log scale plot
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2logm Purpose Matrix logarithm Synt
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2logspace Purpose Generate logarith
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2lower Purpose Convert string to lo
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2lscov Purpose Least squares soluti
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Reference [1] Strang, G., Introduct
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[x,resnorm,residual,exitflag] = lsq
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2lsqr Purpose LSQR implementation o
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[x,flag,relres,iter,resvec] = lsqr(
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2lu Purpose LU matrix factorization
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P Row permutation matrix satisfying
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The determinant of the example matr
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2luinc Purpose Incomplete LU matrix
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thresh is the pivot threshold betwe
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0 100 200 300 400 0 100 200 300 400
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Purpose Magic square Syntax M = mag
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350 300 250 200 150 100 50 n = 18 0
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2mat2cell Purpose Divide matrix int
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2mat2str Purpose Convert a matrix i
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2material Purpose Controls the refl
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2matlab (UNIX) Purpose Start MATLAB
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Values for archOption Option Descri
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matlab (UNIX) separated list of lic
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matlab (UNIX) The following table l
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Variable Definition and Standard As
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Variable Definition and Standard As
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2matlab (Windows) Purpose Start MAT
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matlab (Windows) matlab mgrOption s
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2matlabcolon (matlab:) Purpose Run
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and depending on which link is clic
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2matlabrc Purpose MATLAB startup M-
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2max Purpose Maximum elements of an
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2median Purpose Median value of arr
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2menu Purpose Generate a menu of ch
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2mesh, meshc, meshz Purpose Mesh pl
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5 0 −5 −10 3 2 1 0 −1 −2 Ge
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mesh, meshc, meshz meshc assumes th
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Y = 10 10 10 11 11 11 12 12 12 13 1
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GetBSTR GetVariantVector addpropert
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2mex Purpose Compile MEX-function f
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2mexext Purpose Return the MEX-file
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2mget (ftp) Purpose Download file f
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2minres Purpose Minimum Residual me
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Examples Example 1. n = 100; on = o
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2mislocked Purpose True if M-file o
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s = 1 mess = '' messid = '' mkdir I
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2mkpp Purpose Make a piecewise poly
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See Also ppval, spline, unmkpp mkpp
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mldivide \, mrdivide / Note Matrix
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-0.0321 mldivide \, mrdivide / The
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mldivide \, mrdivide / forward subs
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X = U\(L\B) mldivide \, mrdivide /
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2mlint Purpose Check M-files for po
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2mlintrpt Purpose Run mlint for fil
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See Also mlint mlintrpt For more in
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2mmfileinfo Purpose Information abo
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audio_data = Format: 'MPEGLAYER3' N
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2more Purpose Display Command Windo
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If the current directory is project
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2movegui Purpose Move GUI figure to
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2movie Purpose Play recorded movie
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2movie2avi Purpose Create an Audio/
Page 817 and 818:
2mput (ftp) Purpose Upload file or
Page 819 and 820:
2mtimes Purpose Matrix multiplicati
Page 821 and 822:
while the third column of B is B(:,
Page 823 and 824:
2multibandread Purpose Read band in
Page 825 and 826:
Subsetting Parameters multibandread
Page 827 and 828:
2multibandwrite Purpose Write multi
Page 829 and 830:
Band Column Row C C C C C B B B B B
Page 831 and 832: 2munlock Purpose Allow M-file or ME
Page 833 and 834: Purpose Return maximum identifier l
Page 835 and 836: See Also Inf, isnan unique([1 1 NaN
Page 837 and 838: error(nargchk(2, 4, nargin, 'struct
Page 839 and 840: end See Also inputname, varargin, v
Page 841 and 842: error(nargoutchk(2, 4, nargout, 'st
Page 843 and 844: 2ndgrid Purpose Generate arrays for
Page 845 and 846: 2ndims Purpose Number of array dime
Page 847 and 848: First, newplot reads the current fi
Page 849 and 850: 2nextpow2 Purpose Next power of two
Page 851 and 852: 2noanimate Purpose Change EraseMode
Page 853 and 854: 2norm Purpose Vector and matrix nor
Page 855 and 856: 2normest Purpose 2-norm estimate Sy
Page 857 and 858: 2now Purpose Current date and time
Page 859 and 860: 2null Purpose Null space of a matri
Page 861 and 862: 2num2cell Purpose Convert a numeric
Page 863 and 864: 2num2str Purpose Number to string c
Page 865 and 866: 2numel Purpose Number of elements i
Page 867 and 868: Purpose Solve fully implicit differ
Page 869 and 870: sol.x Steps chosen by the solver. I
Page 871 and 872: [y0,yp0] = decic(@weissinger,t0,y0,
Page 873 and 874: ode45, ode23, ode113, ode15s, ode23
Page 881: ode45, ode23, ode113, ode15s, ode23
Page 885 and 886: options = < Insert options = odeset
Page 887 and 888: 3 2 1 0 −1 −2 −3 0 2 4 6 8 10
Page 889 and 890: 2odeget Purpose Extract properties
Page 891 and 892: Solver output Jacobian matrix Event
Page 893 and 894: Jacobian Matrix Properties (for ode
Page 895 and 896: Step Size Properties Property Value
Page 897 and 898: odextend Note To extend solutions o
Page 899 and 900: 2open Purpose Open files based on e
Page 901 and 902: Example 4 — Opening a MAT-File Th
Page 903 and 904: figure_handle = openfig(...) return
Page 905 and 906: openvar 2openvar Purpose Open works
Page 907 and 908: 2optimset Purpose Create or edit an
Page 909 and 910: Option Value Description optimset O
Page 911 and 912: c: 3 a: 1 snew = orderfields(s) sne
Page 913 and 914: 2ordschur Purpose Reorder eigenvalu
Page 915 and 916: See Also print, set the orient port
Page 917 and 918: 2otherwise Purpose Default part of
Page 919 and 920: Symbols $matlabroot 2-1430 @ 2-915
Page 921 and 922: COM object methods inspect 2-1184 i
Page 923 and 924: equal arrays detecting 2-1228, 2-12
Page 925 and 926: format precision when writing 2-890
Page 927 and 928: appending to when saving (WriteMode
Page 929 and 930: one-dimensional 2-1189 two-dimensio
Page 931 and 932: lighting 2-1315 Line creating 2-131
Page 933 and 934:
M-files checking for problems 2-147
Page 935 and 936:
elational 2-1368 symbols 2-1050 opt
Page 937 and 938:
R range space 2-1592 RAS files para
Page 939 and 940:
tensor, Kronecker product 2-1283 te
Page 941:
Line property 2-1331 lineseries pro
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