intlab 5.5 matlab下的工具包

A short overview how to use INTLAB (see also file FAQ): ======================================================= INTLAB was started with the introduction of an operation concept in Matlab. It is continuously developed since the first version in 1998. The only developer is Siegfried M. Rump, head of the Institue for Reliable Computing at the Hamburg University of Technology. As a reference to INTLAB please use S.M. Rump. INTLAB - INTerval LABoratory. In Tibor Csendes, editor, Developments in Reliable Computing, pages 77?104. Kluwer Academic Publishers, Dordrecht, 1999. @incollection{Ru99a, author = {Rump, {S.M.}}, title = {{INTLAB - INTerval LABoratory}}, editor = {Tibor Csendes}, booktitle = {{Developments~in~Reliable Computing}}, publisher = {Kluwer Academic Publishers}, address = {Dordrecht}, pages = {77--104}, year = {1999}, url = {http://www.ti3.tu-harburg.de/rump/} } ===> If you used INTLAB before with an older Matlab version, you had to set the system variable BLAS_VERSION: ===> Please delete this system variable. It was necessary to avoid IMKL, now with new rounding routines the Intel Math Kernel Library (IMKL), which is the default and very fast, can safely be used (thanks to Dr. Takeshi Ogita from Tokyo). The easiest way to start is create a file startup.m (or to replace the content of the existing one) in the Matlab path \toolbox\local by cd ... insert the INTLAB path ... startintlab Then the startintlab.m file is started and should do the rest. For some user-specific options you may adjust the file startintlab.m . INTLAB is successfully tested under Matlab versions 5.3, 6.0.0, 6.5.0, 6.5.1, 7.0, 7.0.1 (SP1), 7.0.4 (SP2), 7.1 (SP3), 7.2 (R2006a), 7.3 (R2006b), 7.4 (R2007a), R2007b, R2008a. The Matlab version 7.0.4 (R14) Service Pack 2, however, is not very stable, sometimes a segmentation violation may occur. There are some problems in Matlab version 7.2 (R2006a). For example, const*sparse for larger dimension can be slow: >> n=1e4, a=sparse([],[],[],n,n), tic,b=2*a,toc, tic,c=a/2,toc n = 10000 a = All zero sparse: 10000-by-10000 b = All zero sparse: 10000-by-10000 Elapsed time is 3.101008 seconds. c = All zero sparse: 10000-by-10000 Elapsed time is 0.000131 seconds. >> or, still in Matlab version 7.2 (R2006a) under Windows XP, >> m=1e6, n=1e4, I=100, J=300, A=sparse(I,J,NaN,m,n), sqrt(-1)*A the last multiplication produces an infinite loop. Matlab Version R2006b produces sometimes a core dump with segment violation. For Matlab Version 5.3 and higher on PCs and Windows, INTLAB is entirely written in Matlab. There is no system dependency. This is because the Mathworks company was so kind to add into the routine "system_dependent" a possibility to change the rounding mode (my dear thanks to Cleve). For other platforms or Matlab Version 5.3-, INTLAB is written entirely in Matlab language except one routine setround for switching rounding mode. A corresponding C-routine together with a dll-file is in directory \setround. This routine is the only portability constraint (see also function "setround"). The file setround.dll is put in a separate path "setround". If rounding does not work properly, this path is removed. So INTLAB should detect automatically whether a rounding routine is necessary. If not, for some reason, ===> and you are using Matlab Version 5.3+ on a PC under Windows, **delete** ===> the file "setround.dll" . ===> Prerequisite for INTLAB is the possibility to switch the processor ===> permanently into a specific rounding mode "downwards", "upwards" and ===> "to nearest". This is always checked when starting INTLAB under Matlab. ===> If the check fails, INTLAB will be terminated not to produce incorrect results! The progress in the different INTLAB versions can be viewed using help, for example help Version5_3 Note that '_' is used rather than a dot, otherwise the help function does not work. INTLAB supports - interval scalars, vectors and matrices, real and complex, - full and sparse matrices, - interval standard functions, real and complex, - and a number of toolboxes for intervals, gradients, hessians, slopes, polynomials, multi-precision arithmetic and more. There are some demo-routines to get acquainted with INTLAB such as demointlab demointval demogradient demohessian demoslope demopolynom demolong Call "demos" and access the INTLAB-demos. INTLAB results are verified to be correct including I/O and standard functions. Interval input is rigorous when using string constants, see help intval . Interval output is always rigorous. For details, try e.g. "help intval\display" and "demointval". You may switch your display permanently to infimum/supremum notation, or midpoint/radius, or display using "_" for uncertainties; see "help intvalinit" for more information. For example format long, x = midrad(pi,1e-14); infsup(x) midrad(x) disp_(x) produces intval x = [ 3.14159265358978, 3.14159265358981] intval x = < 3.14159265358979, 0.00000000000002> intval x = 3.1415926535898_ Display with uncertainties represents the interval produces by subtracting and adding 1 from and to the last displayed digit of the mantissa. Note that the output is written in a way that "what you see is correct". For example, midrad(4.99993,0.0004) produces intval ans = < 4.9999, 0.0005> in "format short" and mid-rad representation. Due to non-representable real numbers this is about the best what can be done with four decimal places after the decimal point. A possible trap is for example >> Z=[1,2]+i*[-1,1] Z = 1.0000 - 1.0000i 2.0000 + 1.0000i The brackets in the definition of Z might lead to the conclusion that Z is a complex interval (rectangle) with lower left endpoint 1-i and upper right endpoint 2+i. This is not the case. The above statement is a standard Matlab statement defining a (row) vector of length 2. It cannot be an interval: Otherwise Z would be preceded in the output by "intval". Standard functions are rigorous. This includes trigonometric functions with large argument. For example, x=2^500; sin(x), sin(intval(x)) produces ans = 3.273390607896142e+150 intval ans = 0.42925739234243 the latter being correct to the last digit. For real interval input causing an exception for a real standard function, one may switch between changing to complex standard functions with or without warning or, to stay with real standard functions causing NaN result. For example, intvalinit('DisplayMidRad') intvalinit('RealStdFctsExcptnAuto'), sqrt(infsup(-3,-2)) produces ===> Complex interval stdfct used automatically for real interval input out of range (without warning) intval ans = < 0.0000 + 1.5811i, 0.1670> whereas intvalinit('RealStdFctsExcptnWarn'), sqrt(infsup(-3,-2)) produces ===> Complex interval stdfct used automatically for real interval input out of range, but with warning Warning: SQRT: Real interval input out of range changed to be complex > In c:\matlab_v5.1\toolbox\intlab\intval\@intval\sqrt.m at line 81 intval ans = < 0.0000 + 1.5811i, 0.1670> and intvalinit('RealStdFctsExcptnNaN'), sqrt(infsup(-3,-2)) gives ===> Result NaN for real interval input out of range intval ans = < NaN, NaN> All functions support vector and matrix input to minimize interpretation overhead. Pure floating point standard functions (not rigorous) are still faster; therefore those are still in INTLAB (for details, see help intvalinit). Sometimes it is useful to ignore input data