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190 <strong>GNU</strong> <strong>Octave</strong>lsode options (opt, val)Loadable FunctionWhen called with two arguments, this function allows you set options parameters forthe function lsode. Given one argument, lsode_options returns the value of thecorresponding option. If no arguments are supplied, the names of all the availableoptions and their current values are displayed.Options include"absolute tolerance"Absolute tolerance. May be either vector or scalar. If a vector, it mustmatch the dimension of the state vector."relative tolerance"Relative tolerance parameter. Unlike the absolute tolerance, this parametermay only be a scalar.The local error test applied at each integration step isabs (local error in x(i))
Chapter 23: Differential Equations 191function xdot = f (x, t)xdot = zeros (3,1);xdot(1) = 77.27 * (x(2) - x(1)*x(2) + x(1) \- 8.375e-06*x(1)^2);xdot(2) = (x(3) - x(1)*x(2) - x(2)) / 77.27;xdot(3) = 0.161*(x(1) - x(3));endfunctionand the initial condition x0 = [ 4; 1.1; 4 ], the set of equations can be integrated usingthe commandt = linspace (0, 500, 1000);y = lsode ("f", x0, t);If you try this, you will see that the value of the result changes dramatically between t= 0 and 5, and again around t = 305. A more efficient set of output points might bet = [0, logspace (-1, log10(303), 150), \logspace (log10(304), log10(500), 150)];See Alan C. Hindmarsh, ODEPACK, A Systematized Collection of ODE Solvers, inScientific Computing, R. S. Stepleman, editor, (1983) for more information about the innerworkings of lsode.23.2 Differential-Algebraic EquationsThe function daspk can be used to solve DAEs of the form0 = f(ẋ, x, t), x(t = 0) = x 0 , ẋ(t = 0) = ẋ 0using Petzold’s DAE solver Daspk.[x, xdot, istate, msg] = daspk (fcn, x 0, xdot 0, t, t crit)Solve the set of differential-algebraic equationsLoadable Function0 = f(x, ẋ, t)withx(t 0 ) = x 0 , ẋ(t 0 ) = ẋ 0The solution is returned in the matrices x and xdot, with each row in the resultmatrices corresponding to one of the elements in the vector t. The first element of tshould be t 0 and correspond to the initial state of the system x 0 and its derivativexdot 0, so that the first row of the output x is x 0 and the first row of the outputxdot is xdot 0.The first argument, fcn, is a string that names the function to call to compute thevector of residuals for the set of equations. It must have the form
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GNU OctaveA high-level interactive
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iTable of ContentsPreface . . . . .
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10 Expressions . . . . . . . . . .
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19 Arithmetic . . . . . . . . . . .
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Appendix A Tips and Standards . . .
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Preface 1PrefaceOctave was original
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Preface 3• Tony Richardson richar
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Chapter 1: A Brief Introduction to
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Chapter 2: Getting Started 132 Gett
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Chapter 2: Getting Started 15argvBu
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Chapter 2: Getting Started 17helpCo
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Chapter 2: Getting Started 19clc ()
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Chapter 2: Getting Started 21C-rC-s
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Chapter 2: Getting Started 23‘\h
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Chapter 2: Getting Started 25Anothe
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Chapter 2: Getting Started 27usage:
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Chapter 3: Data Types 293 Data Type
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Chapter 3: Data Types 31size (a, n)
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Chapter 4: Numeric Data Types 334 N
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Chapter 4: Numeric Data Types 35war
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Chapter 4: Numeric Data Types 37Emp
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Chapter 5: Strings 395 StringsA str
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Chapter 5: Strings 41string fill ch
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Chapter 5: Strings 435.3 String Con
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Chapter 5: Strings 45toupper (s)Bui
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Chapter 6: Data Structures 476 Data
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Chapter 6: Data Structures 49octave
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Chapter 7: Containers 517 Container
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Chapter 8: I/O Streams 538 I/O Stre
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Chapter 9: Variables 559 VariablesV
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Chapter 9: Variables 57persistent p
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Chapter 9: Variables 59exist (name,
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Chapter 9: Variables 61default_save
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Chapter 9: Variables 63warn_divide_
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Chapter 10: Expressions 6510 Expres
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Chapter 10: Expressions 67sqrt (arg
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Chapter 10: Expressions 69x - ySubt
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Chapter 10: Expressions 7110.5.1 El
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Chapter 10: Expressions 73z = 1Afte
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Chapter 10: Expressions 75++x--xThi
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Chapter 11: Evaluation 7711 Evaluat
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Chapter 12: Statements 7912 Stateme
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Chapter 12: Statements 81warn assig
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Chapter 12: Statements 83while (con
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Chapter 12: Statements 85for [ val,
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Chapter 12: Statements 87# print el
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Chapter 12: Statements 89For contin
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Chapter 13: Functions and Script Fi
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Chapter 14: Error Handling 10514 Er
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Chapter 15: Debugging 10715 Debuggi
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Chapter 16: Input and Output 10916
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Chapter 16: Input and Output 111for
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Chapter 16: Input and Output 113bit
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Chapter 16: Input and Output 115-ma
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Chapter 16: Input and Output 117The
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Chapter 16: Input and Output 119‘
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Chapter 16: Input and Output 121Thi
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Chapter 16: Input and Output 123‘
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Chapter 16: Input and Output 12516.
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Chapter 16: Input and Output 127max
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Chapter 16: Input and Output 129[nr
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Chapter 16: Input and Output 131Con
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Chapter 16: Input and Output 133SEE
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Chapter 17: Plotting 13517 Plotting
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Chapter 17: Plotting 137hold argsBu
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Chapter 29: Control Theory 241[zer,
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Chapter 29: Control Theory 243Examp
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Chapter 29: Control Theory 245A mat
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Chapter 29: Control Theory 247clstu
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Chapter 29: Control Theory 249_____
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Chapter 29: Control Theory 25529.5
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Chapter 29: Control Theory 257dlyap
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Chapter 29: Control Theory 25929.6
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Chapter 29: Control Theory 261retva
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Chapter 29: Control Theory 263sysef
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Chapter 29: Control Theory 265d2c (
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Chapter 29: Control Theory 267[y, t
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Chapter 29: Control Theory 273[k, p
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Chapter 29: Control Theory 275gmaxg
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Chapter 29: Control Theory 279[rlda
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Chapter 29: Control Theory 281[a, b
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Chapter 30: Signal Processing 28330
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Chapter 30: Signal Processing 285wh
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Chapter 30: Signal Processing 287[1
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Chapter 30: Signal Processing 289hu
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Chapter 31: Image Processing 29131
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Chapter 31: Image Processing 293hsv
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Chapter 32: Audio Processing 29532
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Chapter 33: Quaternions 29733 Quate
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Chapter 34: System Utilities 29934
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Chapter 34: System Utilities 301asc
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Chapter 34: System Utilities 303eti
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Chapter 34: System Utilities 305[er
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Chapter 34: System Utilities 307fnm
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Chapter 34: System Utilities 309in
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Chapter 34: System Utilities 311[er
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Chapter 34: System Utilities 31334.
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Chapter 34: System Utilities 315isi
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Appendix A: Tips and Standards 317A
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Appendix A: Tips and Standards 319
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Appendix A: Tips and Standards 321i
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Appendix B: Known Causes of Trouble
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Appendix C: Installing Octave 329Ap
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Appendix C: Installing Octave 331On
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Appendix C: Installing Octave 333gc
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Appendix D: Emacs Octave Support 33
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Appendix E: Grammar 343Appendix E G
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Appendix F: GNU GENERAL PUBLIC LICE
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Concept Index 351Concept Index#‘#
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Concept Index 353Iif statement . .
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Variable Index 355Variable IndexAan
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Function Index 357Function Index(([
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Function Index 359errorbar . . . .
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Function Index 361isnumeric . . . .
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Function Index 363qzval . . . . . .
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Function Index 365vertcat. . . . .
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Operator Index 367Operator Index!!.
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