семинарпоинтервальнымвычислениямнаjava

семинарпоинтервальнымвычислениямнаjava内容摘要：

subdifferential Newton, NonNeg, Shaidurov  “Rational bounds” branch: – Interval bounds: smart rational/double, arbitrary precision, rounding policies, contexts – IA: setbased – Interval elementary functions, vectors, matrices  Generic interfaces on top of branches Барнаул, 28 Июня 2020 МАК 2020 31 / 60 JInterval (Boyhood): Type Hierarchy Барнаул, 28 Июня 2020 МАК 2020 32 / 60 Interval ClassicRealInterval ComplexInterval RealInterval DoubleInterval RationalInterval ComplexIntervalCircle ComplexIntervalRectangle ComplexIntervalPolar ComplexIntervalRing JInterval (Boyhood): Lessons Learned Барнаул, 28 Июня 2020 МАК 2020 33 / 60 Problem Possible Solution Java syntax is not expressive enough for calculations Developing Scala API for a new JInterval implementation JInterval is not pliant with the project of interval standard IEEE P1788 Redesign the library according to IEEE P1788 Low performance Using optional plugins for native code of high precision arithmetic and interval linear algebra algorithms through JNA Java r = ((z))。 Scala r = x + y*z ARCHITECTURE JInterval Library: Principles, Development, and Perspectives Барнаул, 28 Июня 2020 МАК 2020 34 / 60 Class Diagram (package ) Барнаул, 28 Июня 2020 МАК 2020 35 / 60 Keyrole Interfaces Барнаул, 28 Июня 2020 МАК 2020 36 / 60  Types graph follows the flavor structure of P1788  Java interfaces: – Interval Common methods for all flavors – SetInterval Extends Interval with methods for flavor ‘Set Interval’ – KaucherInterval Extends Interval with methods for flavor ‘Kaucher interval’ – ClassicInterval Extends all flavors, because can be mapped to related flavor intervals Interface Interval: mon methods of all flavors Барнаул, 28 Июня 2020 МАК 2020 37 / 60  Interval defines mon methods of all interval flavors  Defines numerical and boolean operations only IntervalContext: interval operations interface Барнаул, 28 Июня 2020 МАК 2020 38 / 60  Generic interface IntervalContext defines signature for intervalvalued methods KaucherIntervalContext: interval flavor interface Барнаул, 28 Июня 2020 МАК 2020 39 / 60  KaucherIntervalContext extends IntervalContext and binds type variable I to Kaucher interval flavor Implementation of interval contexts  There may be several implementations for flavor contexts – SetIntervalContextInfSupBase and SetIntervalContextInfSup are two tightest implementations of set interval operations and functions (P1788 Level 2, InfSup_F). Барнаул, 28 Июня 2020 МАК 2020 40 / 60 Factory classes for interval contexts Барнаул, 28 Июня 2020 МАК 2020 41 / 60  Factory classes create particular instances of interval contexts – SetIntervalContexts – KaucherIntervalContexts Exact context Барнаул, 28 Июня 2020 МАК 2020 42 / 60  Static method getExact() creates the exact context  All operations in the exact context return intervals with rational bounds – P1788 Level 1 results or throw IrrationalException InfSup_F contexts Барнаул, 28 Июня 2020 МАК 2020 43 / 60  Static method getInfSup(BinaryValueSet numberFormat) creates the InfsSup_F contexts with binary floatingpoint interval representations (BINARY32, BINARY64, BINARY128, …, BINARY1024) jinterval Aggregator of JInterval Core Module Dependencies Graph Барнаул, 28 Июня 2020 МАК 2020 44 / 60 jintervalir Interval regression solver jintervalils Interval linear equation system solver jintervalintervaljava Intervals, IAs, interval elem. functions jintervalrationaljava Rational numbers fortressrounding Rounding class from Fortress boehmcreals Boehm’s constructive reals mpfradapter JNA adapter for native GNU MPFR monsmath3 Apache Commons Math lpsolve Java port of lp_solve jna Java access to native libraries largetestjava JInterval tests monspress Apache Commons Compress External dependencies JInterval packages FUNCTIONALITY AND EXAMPLES JInterval Library: Principles, Development, and Perspectives Барнаул, 28 Июня 2020 МАК 2020 45 / 60 Functionality of JInterval (Youth)  Rational arithmetic – flexible inner representation (rational, binary32, binary64, binary128,…) – exact and approximate operations  Extended Rational arithmetic – Rational + {∞ , +∞}  Interval Arithmetic – Setbased – Kaucher  Elementary Functions – According to P1788  Dense Vectors and Matrices – Rational, extended rational – Interval  Solvers – ILS Solvers • HansenBliekRohnNingKearfott enclo。