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GNU Octave Interval Package Summary of important user-visible changes Version 3.0.0 2017-08-19 ======================== This major release introduces support for N-dimensional arrays of intervals. With previous versions, interval objects have been limited to two dimensions. Only scalar values, vectors, and matrices could be created. Now, interval objects can be used with three or more dimensions as well. Binary and ternary operations support broadcasting of singleton dimensions, which can be expanded to produce higher dimensional results. Most work for this version has been accomplished by Joel Dahne during his Google Summer of Code project. The project involved thorough maintenance of all interval functions, which led to improvements and bugfixes beyond the original goal. • Support for N-dimensional arrays of intervals. • Removed interval implementation of ‘meshgrid’, it now falls back on the standard implementation which can output a 3-d grid properly. This no longer automatically converts all input to intervals. For example, it is possible to create a grid for interval X values and non-interval Y values. • dot, prod, sum: Altered how empty input is handled. They are more consistent with the standard sum and prod functions (return zero/one for 0×0 input along the first dimension). For the dot function it is slightly different from how the Octave core function handles it at the moment (bug #51333). • Output of interval matrices may be customized with ‘format compact’ to display more data per page. • nthroot, pownrev: Now supports vectorization of N (for nthroot) and P (for pownrev), broadcasting is fully supported. • Indexing expressions on intervals can now use the ‘end’ keyword and the special operator ‘:’ to select all entries. This affects selection of entries and assignment of entries (bug #49592, bug #50626). • Adjustments to ITF1788 test suite: • Several further unit tests have been derived from libieeep1788 together with the latest version of the interval testing framework. That is, tests with NaN values, NaI values, IEEE 1788 exceptions, and tests for the following functions: numsToInterval, textToInterval, intervalPart, newDev, setDec, decorationPart, and reduction operations. • Unit tests have been reorganized: The source code of test cases has been moved to /src/test/. • The test suite is no longer compiled as separate Octave test files (*.tst). Instead, any interval test library files (*.itl) are stored as loadable test data (itl.mat). The test data is then used by built-in self-tests of the functions. This simplifies testing of functions and saves storage space after package installation. For example, ‘test @infsup/plus’ will run any arithmetic tests on the interval plus function. • Adjustments to the package documentation: • Information about how to create N-dimensional arrays of intervals. • To improve privacy and page loading times, the package manual no longer uses external references for CSS and web fonts. • The package URL has been updated (after Octave Forge has switched to HTTPS). • HTML fonts have been changed and fallback fonts for Windows have been introduced. • Adjustments to code examples to support the latest versions of the doctest package and symbolic package. Bugfixes • Processor support for SSE2 is automatically detected during package installation. This fixes installation problems on devices without SSE2, for example the usual Android phones and tablets (bug #51758). • wid, mig, mag: Fixed wrong return value for NaI (not an interval) values. The functions failed to return NaN (not a number). • diag: With more than one argument the function no longer fails with an error. • dot: Fixed error in identification of dimensions when broadcasting: When the optional dimension argument is missing, the first non-singleton dimension of both arguments is used (before broadcasting applies). • infsupdec: Now creates a warning if the ‘[NaI]’ literal is combined with decoration, e. g. ‘[NaI]_ill’. • infsupdec: No longer produces warnings for mixed parameters with strings and numerics. • verlinineqnn: No longer produces warnings for unverified solutions. • pow: Fixed error when called with vector arguments. The result was only guaranteed to be sharp in the first entry, e. g. ‘pow ([0 0], infsup (0, 1))’ produced the interval [0, 1] for the second entry. • pow2rev: Fixed errors when called with non-scalar arguments in two cases, which could produce wrong results. • ctc_intersect, ctc_union: Fixed runtime errors when the combined contractor function is called with less than two output arguments. • sin: Fixed possible interval representation error, where the upper boundary of the result could become a signed zero (bug #51283). • factorial: Improved result decoration for integer input, since the function is continuous (bug #51783). Version 2.1.0 2016-12-28 ======================== • The speed of some arithmetic operations has been greatly improved. They have previously been computed by multi-precision arithmetic which simulates binary64 floating-point arithmetic (MPFR library). Now, a specialized correctly rounded mathematical library (crlibm) computes identical results 30–100 times faster. There is no accuracy drawback, arithmetic operations will compute tight interval enclosures as before. The following functions benefit from this: acos, asin, atan, cos, cosh, exp, expm1, log, log10, log1p, log2, sin, sinh, tan. Bugfixes • Fixed indexing expression in interval constructor for illegal intervals of the form ‘[-inf, -inf]’ or ‘[inf, inf]’ • polyval: Fixed unnecessary warnings when evaluated on empty intervals • Fixed compilation errors on FreeBSD 9.3 Version 2.0.0 2016-11-20 ======================== This major release contains fundamental changes to the interval constructors. After a discussion on the P1788 mailing list, it has been revealed that this interval package didn’t implement exceptions from the standard for interval arithmetic correctly: Operations from IEEE Std 1788-2015 which trigger an “exception” shall return a value nonetheless. Conformance has been improved in this new version, but may break compatibility with previous versions. A second big news is that the interval package comprises functions from VERSOFT, a verification software package by Jiří Rohn, who has generously published his work as free software this year. Unfortunately, some of VERSOFT’s functions are encrypted and could not be included yet. • nai: With additional arguments, matrices of NaI (not an interval) values can be constructed. Previously, NaI has been restricted to be of scalar value. • infsup: The bare interval constructor merely triggers a warning instead of an error on illegal input, which creates empty intervals. If input contains legitimate as well as illegal input, only entries with illegal input will carry empty intervals. • infsupdec: The decorated interval constructor may create interval matrices which have NaI (not an interval) as entries. If input contains legitimate as well as illegal input, only entries with illegal input will carry NaI values. • Warning and error identifiers of the constructors have been revised. The warning identifier ‘interval:NaI’ has been removed. Illegal input signals an ‘interval:UndefinedOperation’ warning. If the input is of an illegal data type or of illegal size, the constructors signal an ‘interval:InvalidOperand’ warning. The warning identifier ‘interval:PossiblyUndefinedOperation’ has been renamed to ‘interval:PossiblyUndefined’ to better match the wording in the standard document. Also, previous versions failed to trigger this warning in cases where there is a floating point number between boundaries U < L, which has been fixed. • It is no longer valid to call ‘infsup (+inf, -inf)’ to create an empty interval and the constructor will signal a warning in these cases. This change has been made to better conform to the ‘numsToInterval’ function from the interval standard. You may create empty intervals with either ‘infsup ()’ or ‘infsupdec ()’ or ‘empty ()’. • inf, sup: If the input is NaI (not an interval), these functions return NaN (not a number) values instead of an error. • Output of intervals in hexadecimal form discriminates between subnormal boundaries and normal boundaries. Subnormal numbers start with “0x0.” whereas normal numbers start with “0x1.”. Also, hexadecimal form has been changed to lower case. • resize: New interval elements are initialized with zero instead of empty intervals to better match the corresponding Octave function. • Interval constructors may broadcast column and row vectors. • Performance improvements: factorial on large arguments; plot and plot3 on input that is plotted as a line. • New interval functions: tril, triu, qr • New functions which have been ported from Jiří Rohn’s VERSOFT: chol, vereigback, vereigvec, verintlinineqs, verinvnonneg, verlinineqnn, verlinprog • recip, sqr: The functions have been removed, after they have been deprecated in version 1.4.0. • plot3: Fixed plotting with gnuplot and fixed an issue where the figure did not switch from 2D to 3D after plotting. • expm1: Fixed documentation, the function computes exp (X) - 1 instead of exp (X - 1). • norm: Fixed an error where the Hamming norm of empty intervals was non-empty. Version 1.5.0 2016-05-31 ======================== • norm: Added subordinate matrix norms and the max norm • strictsubset: New interval comparison function • Package documentation: Added new example (Cameleon problem), and the growing list of examples has been split into several web pages. • Package documentation: Updated recommendations to install and load the package. The autoload feature will be removed in Octave 4.2.0. (patch #8981, thanks to juanpi) • Support package installation in Octave 4.1.0+ (bug #47288) Version 1.4.1 2016-02-13 ======================== • Fixed a compile error for 32-bit systems during package installation (bug #47100) Version 1.4.0 2016-02-09 ======================== • mpower: Improved accuracy and speed. The interval matrix square can now be computed without dependency errors and with tightest accuracy. • factorial: New interval arithmetic operation • expm, norm: New interval matrix operations • The functions recip and sqr have been deprecated and will be removed in a future release. Please use ‘1 ./ X’ and ‘X .^ 2’ instead. Bugfixes • bitunpack, interval_bitpack: The order of inf/sup/dec parts has been fixed. The function documentation describes how the functions behave on little-endian and big-endian systems. Version 1.3.0 2015-12-22 ======================== • postpad, prepad, subsasgn: Implicit new elements during subscript assignment and padding have been initialized with empty intervals before this release. This behavior has changed. Now, the implicit new element are initialized with zero to make a correct interval extension of the corresponding built-in function. • fsolve: New function to solve (systems of) equations and compute the inverse of a set under a function • ctc_intersect, ctc_union: Utility functions for contractors and the fsolve function • det, prod, recip: New interval arithmetic functions • diag: New utility function to create diagonal matrices or extract vectors from diagonals of matrices • decorationpart: Choose between different return types with a second parameter • For several functions it is now possible to broadcast row vectors against column vectors or vectors against matrices. • The user manual has been restructured for better accessibility by new users. A bunch of usage examples demonstrates the package’s capabilities. Bugfixes • sum, sumabs, sumsq: Fixed result for matrices of size zero • powrev1, powrev2: Fixed indexing for vectors Version 1.2.0 2015-10-01 ======================== • The output format for intervals has been changed. The number of decimal places now respects what has been set by the user with the ‘format short’ or ‘format long’ command, and is much shorter by default. Also it is possible to use ‘format hex’. The old format can be accessed with the ‘intervaltotext’ function. • fminsearch: New optimizer function for finding the minimum value of a function over interval constraints using the Skelboe-Moore algorithm • fzero: Changed function parameters to support optimset options • power: Improved speed of the general interval power function and monomials with the notation x .^ n • plot, plot3: Added support for colormaps Bugfixes • mldivide: Fixed algorithm to handle more matrices without error • bisect: Fixed an error during bisection of singleton intervals (thanks to Helmut for finding this during OctConf 2015) Version 1.1.0 2015-08-03 ======================== • meshgrid, mince: New utility functions to help plotting of interval functions • linspace: New interval arithmetic function • intersect, max, min, union: Allow evaluation as aggregate functions within an interval matrix along a common dimension • Improvements to the documentation • Added cross-references between package documentation and function reference • Extended information about interval arithmetic in general • Extended information about implemented IEEE Std 1788-2015 functions and fixed references to the standard document • Added information about plotting intervals • Simplified package description • Graphics with higher resolutions, demo of interval sombrero function plot on first page, and minor style fixes Bugfixes • plot3: Fixed plotting of interval edges when plotting several intervals at once using matrices Version 1.0.0 2015-06-13 ======================== • IEEE Std 1788-2015, IEEE standard for interval arithmetic, was approved on June 11. To mark the occasion, the major version number has been raised. • All interval constructors have been extended to create interval matrices from a single string. Commas or spaces may be used as a column separator (consecutive separators are trimmed). Semicolon and new line characters can be used as a row separator. • hdist, idist, sdist, smig: New interval numeric functions • User manual: Relicensed under GPL, added examples from the former Octave SIMP package, and various minor improvements. Bugfixes • mtimes: Fixed matrix-vector multiplication of decorated intervals • Fixed a linking error in mkoctfile that could prevent package installation (bug #45280) Version 0.2.1 2015-05-30 ======================== • plot, plot3: New interval plotting functions. Pay attention to the included examples, which can be executed with ‘demo @infsup/plot’ and ‘demo @infsup/plot3’ respectively. • polyval: New interval arithmetic algorithm • bisect: New set operation for bisecting algorithms • sinrev, cosrev, tanrev, atan2rev1, atan2rev2: Now allow non-scalar arguments • Simplified licensing: Relicensed parts of the software that were not under GPL • Updated information for citation of the package Bugfixes • Fixed generation of the manual in PDF format • subsasgn: Fixed cases where decoration could be lost (bug #42735) Version 0.2.0 2015-05-03 ======================== • User manual included in the package, see doc/manual.texinfo • New utility functions: cat, postpad, prepad, reshape, resize • and, or: Removed deprecated functions • Improved display output for cell arrays and new function: disp • Minor performance improvements (all decorated interval functions, horzcat, vertcat) Bugfixes • issquare, isrow, iscolumn: Fixed compatibility issues with GNU Octave 4.0 • cbrt: Allow negative values as parameter • cot: Fixed accuracy for x = 0 • cos, csc, sec, sin: Fixed correctness in certain cases • Prevent multibyte characters in Microsoft Windows console Version 0.1.5 2015-04-06 ======================== • Implicit decoration of bare intervals triggers a warning now and can be allowed or forbidden by the user. Implicit decoration of bare interval literals is not affected. • newdec: New operation for explicit promotion of bare intervals into decorated intervals (without warning). • Decorated interval literals with illegal decoration are no longer allowed and produce NaIs. • hull: In contrast to the union function, the interval constructor is no longer considered a set operation and can create intervals with a non-trivial decoration. • setdiff, setxor: New set operations • intersect, union: Renamed set operations; the old function names (and, or) are hereby deprecated and are going to be removed in the next release. • intervaltotext, intervaltoexact: Decimal fractions no longer omit zero before the point, and unnecessary trailing decimal places can be omitted more consistently and in more cases than before (also affects console output). Improved accuracy and performance with support for interval matrices. Bugfixes • mtimes, mldivide: Support for broadcasting of scalar parameters • nextout: Support for decorated intervals • An error in GNU Octave core, which could lead to lost or wrong interval decorations, no longer affects decorated intervals (bug #42735) • Some errors in the function documentation have been fixed (thanks to doctest-for-matlab and Colin’s texinfo compatibility patches) • Fixed interval field access on Windows Version 0.1.4 2015-03-15 ======================== • New interval constructors: hull, midrad • New interval arithmetic functions: cbrt, cot, coth, csc, csch, dilog, ei, erf, erfc, gamma, gammaln, psi, rsqrt, sec, sech • mtimes: Support for fast, less accurate evaluation using BLAS routines • mldivide, mrdivide, inv: Improved performance by using faster mtimes • infsup, infsupdec: Enabled broadcasting of scalar boundaries • rad: May compute mid and rad simultaneously • subsref: Access to interval properties using field syntax: x.inf and x.sup Version 0.1.3 2015-02-24 ======================== • Fixed a compile error that could possibly occur during package installation Version 0.1.2 2015-02-22 ======================== • New interval arithmetic functions: nthroot, hypot, log1p, expm1 • lu: New operation for LU(P) decomposition of interval matrices • nai: New decorated interval constant • mldivide, mrdivide, inv: Greatly improved accuracy and performance of the linear solver • Improved accuracy of vector sums, dot products, pownrev, and powrev2 • powrev1, powrev2, pownrev, mulrev: Now allow non-scalar arguments • overlap: Renamed one overlapping state from equal to equals • mulrevtopair: No longer available, use mulrev with two output parameters for two-output division • setdec: No longer available, use infsupdec instead • Small performance improvements Bugfixes • Compatibility with GNU Octave 4.0 (bug #43925) • Build problems during package installation with environment variables • iscommoninterval: The decorated variant must return true for common intervals without com decoration • eq: The decorated variant must not consider the decoration value • Several decorated functions: When evaluated on a subset of the function’s domain, the result’s decoration must be dac if the function’s restriction to that subset is continuous • Decorated boolean functions: Must return false when evaluated on NaI input • Interval constructors: A PossibleUndefined warning must be issued if an interval is created from two very close decimal numbers (which can not be separated in the floating-point context) where the lower boundary is greater than the upper boundary when compared with infinite precision • Interval constructors: NaNs must produce empty intervals • Decorated interval constructor: Illegal decorations for empty intervals must be adjusted to trv, and illegal decoration com for unbounded intervals must be adjusted to dac. • cancelminus/cancelplus: The functions returned wrong results if the interval widths could not be compared in double-precision • cos: Accuracy for x = [0] improved • pow, powrev1, powrev2: The function must be defined for x = 0 and y > 0 • All reverse operations: Must return a trivial decoration information at best (the only exception is mulrev) Version 0.1.1 2015-02-01 ======================== • Increased speed of computation for large matrices • Improved performance for fma and dot • mpfr_vector_dot_d: Changed syntax for faster computation on intervals • Decorated versions of mtimes, mldivide, mpower, inv and reduction operations sum, dot, subabs, subsquare • Renamed function sumsquare to sumsq in accordance with GNU Octave function names • New function: fzero for finding all roots of an interval arithmetic function Bugfixes • nextout: Function returned wrong results • exacttointerval: Now produces bare intervals instead of decorated intervals in conformance with IEEE P1788 • atanh: Function returned wrong results for ±1 • dot: Function returned wrong results for some inputs • fma: Function returned wrong results for some inputs • infsup: Function returned wrong interval boundaries for decimal numbers, function failed on mixed numerical and string boundaries in single cell array parameter • mulrevtopair: Fixed order of operands in conformance with IEEE P1788 and wrong results when evaluated on intervals that contain zero Version 0.1.0 2015-01-21 ======================== • Initial release version, which already contains all required operations of the preliminary standard document IEEE P1788.

Package: interval