title: ÐÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½ÑÐµ ÑÑÐµÐ´ÑÑÐ²Ð° Ð¼ÐµÑÑÐ¾Ð»Ð¾Ð³Ð¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð°Ð²ÑÐ¾ÑÐ¾Ð¿ÑÐ¾Ð²Ð¾Ð¶Ð´ÐµÐ½Ð¸Ñ Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ð¹ Ñ Ð½ÐµÑÐ¾ÑÐ½ÑÐ¼Ð¸ Ð´Ð°Ð½Ð½ÑÐ¼Ð¸ Ð½Ð° ÑÐ·ÑÐºÐµ Java
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Software tools for metrological auto-tracking of calculations with inaccurate data in Java
Creators: name: ÐÐ°Ð»ÑÑÐµÐ², ÐÐ°Ð²ÐµÐ»
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2021
Subjects: Ð¾ÑÐµÐ½ÐºÐ° Ð¿Ð¾Ð³ÑÐµÑÐ½Ð¾ÑÑÐ¸
Ð°Ð²ÑÐ¾Ð¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
ÑÐµÐ¿Ð½Ð¾Ðµ Ð¿ÑÐ°Ð²Ð¸Ð»Ð¾
Ð¿ÑÑÐ¼Ð¾Ð¹ Ð¼ÐµÑÐ¾Ð´
Ð¾Ð±ÑÐ°ÑÐ½ÑÐ¹ Ð¼ÐµÑÐ¾Ð´
java
Ð¿ÐµÑÐµÐ³ÑÑÐ·ÐºÐ° Ð¾Ð¿ÐµÑÐ°ÑÐ¾ÑÐ¾Ð²
error estimation
automatic differentiation
chain rule
forward mode
backward mode
operator overloading

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° ÑÐ¾Ð·Ð´Ð°Ð½Ð¸Ñ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½ÑÑ ÑÑÐµÐ´ÑÑÐ² Ð¾ÑÐµÐ½ÐºÐ¸ Ð¿Ð¾Ð³ÑÐµÑÐ½Ð¾ÑÑÐ¸ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² ÐºÐ¾ÑÐ²ÐµÐ½Ð½ÑÑ Ð¸Ð·Ð¼ÐµÑÐµÐ½Ð¸Ð¹ Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ Ð¼ÐµÑÐ¾Ð´Ð° Ð°Ð²ÑÐ¾Ð¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ. ÐÐ°Ð½Ð½ÑÐ¹ Ð¼ÐµÑÐ¾Ð´ Ð¿Ð¾Ð·Ð²Ð¾Ð»ÑÐµÑ Ð¾ÑÐµÐ½Ð¸Ð²Ð°ÑÑ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ðµ Ð¿ÑÐ¾Ð¸Ð·Ð²Ð¾Ð´Ð½ÑÑ Ð²ÑÑÐ¸ÑÐ»ÑÐµÐ¼ÑÑ ÑÑÐ½ÐºÑÐ¸Ð¹, Ð¾ÑÐ½Ð¾Ð²Ð°Ð½ Ð½Ð° ÑÐµÐ¿Ð½Ð¾Ð¼ Ð¿ÑÐ°Ð²Ð¸Ð»Ðµ Ð¸ Ð¿ÑÐµÐ´ÑÑÐ°Ð²Ð»ÐµÐ½ Ð´Ð²ÑÐ¼Ñ ÑÐµÐ¶Ð¸Ð¼Ð°Ð¼Ð¸ ÑÐ°Ð±Ð¾ÑÑ â Ð¿ÑÑÐ¼ÑÐ¼ Ð¸ Ð¾Ð±ÑÐ°ÑÐ½ÑÐ¼. ÐÐ±Ð° ÑÐµÐ¶Ð¸Ð¼Ð° Ð±ÑÐ»Ð¸ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ñ Ð² Ð±Ð¸Ð±Ð»Ð¸Ð¾ÑÐµÐºÐµ Ð½Ð° ÑÐ·ÑÐºÐµ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Java. ÐÐ°Ð´Ð°ÑÐ¸, ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐµÑÐ°Ð»Ð¸ÑÑ Ð² ÑÐ¾Ð´Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ: 1. Ð¸Ð·ÑÑÐµÐ½Ð¸Ðµ Ð¿ÑÐ¸Ð½ÑÐ¸Ð¿Ð¾Ð² ÑÐ°Ð±Ð¾ÑÑ Ð°Ð²ÑÐ¾Ð¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ, ÐµÐ³Ð¾ Ð¿ÑÑÐ¼Ð¾Ð³Ð¾ Ð¸ Ð¾Ð±ÑÐ°ÑÐ½Ð¾Ð³Ð¾ ÑÐµÐ¶Ð¸Ð¼Ð¾Ð², 2. ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ° Ð±Ð¸Ð±Ð»Ð¸Ð¾ÑÐµÐºÐ¸ Ð½Ð° ÑÐ·ÑÐºÐµ Java, 3. Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ð¸Ðµ ÑÐµÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ, 4. ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ Ñ ÑÑÑÐµÑÑÐ²ÑÑÑÐ¸Ð¼Ð¸ Ð±Ð¸Ð±Ð»Ð¸Ð¾ÑÐµÐºÐ°Ð¼Ð¸. ÐÑÐ¸ ÑÐ¾Ð·Ð´Ð°Ð½Ð¸Ð¸ ÑÑÑÑÐºÑÑÑÑ ÑÐ°Ð·ÑÐ°Ð±Ð°ÑÑÐ²Ð°ÐµÐ¼Ð¾Ð¹ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½Ð¾Ð¹ Ð±Ð¸Ð±Ð»Ð¸Ð¾ÑÐµÐºÐ¸ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð»Ð°ÑÑ Ð¿ÐµÑÐµÐ³ÑÑÐ·ÐºÐ° Ð¾Ð¿ÐµÑÐ°ÑÐ¾ÑÐ¾Ð² Ð´Ð»Ñ Ð¼ÐµÑÐ¾Ð´Ð¾Ð², ÑÐµÐ°Ð»Ð¸Ð·ÑÑÑÐ¸Ñ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ°ÑÐ½ÑÐµ Ð°ÑÐ¸ÑÐ¼ÐµÑÐ¸ÑÐµÑÐºÐ¸Ðµ Ð¾Ð¿ÐµÑÐ°ÑÐ¸Ð¸, Ð´Ð»Ñ ÐºÐ¾ÑÐ¾ÑÑÑ Ð±ÑÐ» ÑÐ¾Ð·Ð´Ð°Ð½ ÑÐ¿ÐµÑÐ¸Ð°Ð»ÑÐ½ÑÐ¹ ÐºÐ»Ð°ÑÑ-ÑÐµÑÑÐ¸ÑÐ¾Ð²ÑÐ¸Ðº. ÐÑÐ¾Ð²ÐµÐ´ÐµÐ½Ñ Ð°Ð½Ð°Ð»Ð¸Ð· Ð¸ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ Ñ Ð´ÑÑÐ³Ð¸Ð¼Ð¸ ÑÑÑÐµÑÑÐ²ÑÑÑÐ¸Ð¼Ð¸ Ð±Ð¸Ð±Ð»Ð¸Ð¾ÑÐµÐºÐ°Ð¼Ð¸. ÐÑÐ¼ÐµÑÐµÐ½Ñ Ð¿ÑÐµÐ¸Ð¼ÑÑÐµÑÑÐ²Ð° ÑÐµÐ°Ð»Ð¸Ð·Ð¾Ð²Ð°Ð½Ð½Ð¾Ð¹ Ð±Ð¸Ð±Ð»Ð¸Ð¾ÑÐµÐºÐ¸ Ð¿Ð¾ Ð·Ð°Ð½Ð¸Ð¼Ð°ÐµÐ¼Ð¾Ð¹ Ð¿Ð°Ð¼ÑÑÐ¸, Ð·Ð°ÑÑÐ°ÑÐ¸Ð²Ð°ÐµÐ¼Ð¾Ð¼Ñ Ð²ÑÐµÐ¼ÐµÐ½Ð¸ Ð½Ð° ÐºÐ¾Ð¼Ð¿Ð¸Ð»ÑÑÐ¸Ñ, Ð¾Ð±ÑÐµÐ¼Ñ ÐºÐ¾Ð´Ð° Ð¸ Ð¿ÑÐ¾ÑÑÐ¾ÑÑ Ð¿Ð¾Ð½Ð¸Ð¼Ð°Ð½Ð¸Ñ Ð¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°ÑÐµÐ»ÐµÐ¼.
description: This work is devoted to the development of a tool for software evaluation of the measurement resultsâ error using the method called automatic differentiation. This method is based on the chain rule of derivatives calculations and is represented by two modes â forward and backward. Both modes were developed in a library using programming language Java. The research contained the following goals: 1. the study of the automatic differentiation, its forward and backward modes, 2. Java library development, 3. testing, 4. comparison with existing libraries. When creating classes, operator overloading was used for implementing the elementary arithmetic operations, for which a special tester class was created. Analysis and comparison with other existing libraries was carried out. As a result, the advantages of the implemented library were marked: the volume of occupied memory, the time spent on compilation, the amount of code and simplicity for user.