=Paper= {{Paper |id=Vol-1490/paper48 |storemode=property |title=The concept of «range» used in experimental calculations |pdfUrl=https://ceur-ws.org/Vol-1490/paper48.pdf |volume=Vol-1490 }} ==The concept of «range» used in experimental calculations== https://ceur-ws.org/Vol-1490/paper48.pdf

Data Mining and Big Data

The concept of "range" used in experimental calculations

Yablokova L.V.

Samara State Aerospace University

Abstract. In article considered the concept of range, as main design tool and
implementation of algorithms of processing of the big data sets used in
experimental calculations of mathematical physics.

Keywords: the range concept, algorithms, first, last, interval function

Citation: Yablokova L.V. The concept of "range" used in experimental
calculations. Proceedings of Information Technology and Nanotechnology
(ITNT-2015), CEUR Workshop Proceedings, 2015; 1490: 402-405. DOI:
10.18287/1613-0073-2015-1490-402-405

Wise use of modern computer technology is unthinkable without the skillful use of
the approximate and numerical analysis. This explains the extremely increased
interest in methods for approximate computation and analysis of experimental data
containing a big volume of information. Like no other branch of science, numerical
methods, as the main tool of mathematical physics, is closely intertwined with many
software applications, as a means or an object of research. At the same time the
problems solved by modern science and modern technology, much more complex,
and the way to solve them is not limited to general questions. Numerical methods and
algorithms for processing big data sets, as a means to successfully meet the new
challenges, are utilized in areas such as numerical solution of Maxwell's equations
and d’Alambert's equation. As a rule, that to create complex mathematical computer
model from the specialist require not only an impeccable mathematical background,
but a basic knowledge of modern, high-performance algorithms, as well as effective
methods for their use for big data. Currently, the bulk of the library for scientific
calculations includes the implementation of the set of basic algorithms. However,
manual implementation of simple variants of the basic algorithms it allows for better
understanding and, consequently, more efficient using and configuring more
advanced version of the library. Another important fact to re-implement the basic
algorithms, is the fact that we are often faced with new computing environments with
their new properties, which cannot be well involved in older implementations.
Realizing basis versions of algorithms, more fitted to specific objectives, and, not
based on system subprograms, specialist’s researchers can achieve bigger portability
and more long save relevance, applied in the course of the decision, algorithms and
data structures. Besides, despite the enhancements which are built in program libraries
for scientific computations, the mechanisms used to sharing of programs aren't always
rather powerful that library functions could be adjusted easily for effective

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implementation within a specific objective. For example, the imperative programming
paradigm with which use codes of the print_array programs (Fig. 1) and print_array_1
(Fig. 2) bringing array contents to the console provides to the developer of means of
the description of sequence of commands and logical transitions which the computer
is going to execute. It is very similar to the orders expressed by an imperative mood in
natural languages, and the basic syntax concept supporting this paradigm is the
operator. Within this it is quite enough simple, provided in examples, tasks, language
tools, means supported by the selected coding style and the used idioms for
implementation of the decision. But similar approach can be hardly conceptually
widespread on more complex problems where the abstractions used in design process
shall be already higher level.
program print_array
implicit none
integer, parameter :: n = 10
integer :: i, arr(n) = (/1, 2, 3, 4, 5, 6, 7, 8, 9, 10/)
do i = 1, n
print *, arr(i)
end do
end program
Fig. 1. – The output to console with using a subscript operator

program print_array_1
implicit none
integer, target :: i, arr(10) = (/(i, i = 1,10)/)
integer, pointer :: p_arr(:)
p_arr => arr(:)
print "(i4)", (p_arr(i), i = 1, size(p_arr))
end program
Fig. 2. – The output to console with using a pointer

Provision of the most effective implementation of the specific algorithm directed
on operation with a big data set will allow to use it for the solution of complex
challenges of computing character and repeatedly. In an example of print_array_2
(Fig. 3), procedural and operator programming style which is development of an
imperative paradigm is applied and allows to use concept the range for
implementation of subprograms.
We will assume that there is a sequence which elements shall be processed by any
algorithm. In the course of such processing there is an appeal to all elements of
sequence, beginning from the first and finishing last. The similar situation meets in
implementation process of algorithms so often that for processed elements of
sequence there is a special notation: the range. For example, the range [first, last)
consists of all elements from first to last, but not including the last. Such asymmetric
form of record is used to focus attention that [first, last) is a half-open interval which
includes all elements, since first, but not last. The range [first, last) is admissible if to
all its elements, excepting last, it is possible to get access and if the element facing
last is achievable from first namely if sequentially being moved, since first, on all line

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Information Technology and Nanotechnology (ITNT-2015)
Data Mining and Big Data Yablokova L.V. The concept of "range" used in…

items of the range a finite number of times it is possible to get to a line item the
previous last. For example, the range [0, N) is valid. The empty range [0,0) also is
valid, and here the range [N-1,0) is invalid as the element in a line item of N-1 appears
after an element in a line item 0. Therefore it doesn't make sense to speak about
elements in line items from N-1 to 0 as about tolerance range.
program print_array_2
implicit none
integer, parameter :: n = 100000
integer :: arr(n)
! .....
! array initialization
! .....
call print(loc(arr(1)), loc(arr(n)))
end program
subroutine print(first, last)
integer :: first, last, val
pointer(first, val)
do while(first <= last)
print *, val
first = first + sizeof(integer)
end do
end subroutine
Fig. 3. – The output to console with using the range concept

Generally, the ranges satisfy the following properties:
1. id range.
2. For any element in i line items, the range [i, i) is a valIf [i, N) is a valid range, then
[i+1, N) is also a valid range.
3. If [i, N) is a valid range, and an element in a line item of k is achievable from an
element in i line item, and the element in a line item of N-1 is achievable from an
element in k line items, the ranges [i, k) and [k, N) are both valid ranges.
4. If both ranges [i, k) and [k, N) are both valid ranges, the range [i, N) is also a valid
range.
From the fundamental point of view the ranges are defined thus because their
asymmetric form helps to avoid errors, the so-called, lost unit, i.e. the quantity of
elements in the range [i, N) is equal to N-i, namely it is exactly so much, how many it
is expected.
Using the concept of the range it is possible to pass to other more general concept
of interval function. The concept of interval function provides possibility of creation
of algorithms capable to process any data structures of the elements supporting
concept of one-dimensional sequence, for example one-dimensional arrays in the
FORTRAN and similar languages. Besides, writing of a code of the program with use
of interval functions requires smaller efforts, and decisions with their application
usually look more visually and logically.

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