Return to the 'interval' package
GNU Octave Interval Package
Summary of important user-visible changes
Version 3.2.1 2022-01-28
========================
This bugfix release fixes compatibility issues with new versions of GNU
Octave.
• The minimum required Octave version has been increased from 3.8.0
to 4.2.0.
• subsref: Access to interval properties using field syntax, e. g.,
‘x.inf’ and ‘x.sup’, has been fixed for Octave 5.1 and later on
Windows (bug #59334).
• disp: Fix runtime errors in Octave 6 and later, when the function
parameter is not a named variable (bug #59334).
• numel: Fix runtime warnings in Octave 6 and later, when the
function is called with only one parameter.
• Syntax errors caused by increment and decrement operators in
Octave 7 and later have been fixed (bug #59334).
• Interval constants for ‘pi’ and ‘e’ in Octave 7 and later have been
fixed. This also fixes several trigonometric functions, which have
produced wrong results in Octave 7.
• Compilation errors during package installation with Octave 8 and
later have been fixed (bug #61568).
•
Version 3.2.0 2018-07-01
========================
• Fixed a regression where decorated intervals could no longer be
used in Octave 4.4 (bug #53331).
• intervaltotext: A change in Octave 4.4 has removed the possibility
to increase Octave’s output precision beyond 16 decimal digits (bug
#53456), which has made it impossible to output intervals with a
higher accuracy. The function ‘intervaltotext’ has been
reimplemented with several new format options to customize the
format and accuracy of the interval literal. All recommended
conversion specifiers from IEEE Std 1788-2015 are now supported,
e. g., intervals can be printed in uncertain form.
• printf, fprintf, sprintf: New functions to produce formatted output
with interval literals.
• numel: Added support for additional arguments to compute the number
of elements after indexing an interval array. This allows combined
indexing expressions of the form ‘x(1:2).inf’.
• Fixed several warnings during package installation.
Version 3.1.0 2017-12-21
========================
This minor release introduces two new functions and fixes severe bugs.
• mod, rem: Two new interval arithmetic functions to compute the
remainder of a floored division or truncated division respectively.
• plot: Fixed a regression with plotting 2D rectangles in the
upcoming Octave 4.4.
• The internal function ‘__print_mesa__’ for off-screen mesa
rendering has been removed, because the upstream mesa project no
longer supports off-screen and on-screen rendering in a single
executable (Debian bug #877149). It is recommended to use Octave’s
‘print’ function instead, which has greatly been improved in
Octave 4.2 regarding the output of rectangles and boxes.
• A package installation error on 32-bit systems could be fixed
(bug #51857).
• During package installation, FPU control has not be activated on
x86-32 platforms. Thus, the crlibm library could not disable
80-bit floating-point arithmetic and produced wrong results. This
has been detected by the interval package, which fell back on the
slower mpfr library instead (Debian bug #874135). After fixing
compiler options, x86-32 platforms can now use crlibm
correctly—even without 64-bit SSE registers.
• Source code for interval arithmetic tests from the ITF1788 project
have been removed from this package, since the loadable test data
‘itl.mat’ can be edited and processed with Octave easily. If unit
test code for other interval arithmetic libraries shall be
generated, find the project at <https://github.com/oheim/ITF1788>.
• Thanks to Olaf Till, this package obtains a configure script (patch
#9518). It checks for available libraries during package
installation and can help to identify missing dependencies.
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