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Data representation for machine learning
a factorial code of the data, i.e., a new vector-valued representation of each data vector such that it gets uniquely encoded by the resulting code vector
Factorial_code
Numeral system in combinatorics
the factorial number system (also known as factoradic), is a mixed radix numeral system adapted to numbering permutations. It is also called factorial base
Factorial_number_system
Product of numbers from 1 to n
In mathematics, the factorial of a non-negative integer n {\displaystyle n} , denoted by n ! {\displaystyle n!} , is the product of all positive integers
Factorial
Topics referred to by the same term
{\displaystyle n} . Factorial may also refer to: Factorial experiment, a statistical experiment over all combinations of values Factorial code, data representation
Factorial_(disambiguation)
Experimental design in statistics
In statistics, a factorial experiment (also known as full factorial experiment) investigates how multiple factors influence a specific outcome, called
Factorial_experiment
Subroutine call performed as final action of a procedure
factorial of the factorial: function factorial(n::Integer)::Integer if n == 0 return 1 else return n * factorial(n - 1) end end Indeed, n * factorial(n
Tail_call
Method of data analysis
Expectation–maximization algorithm Exploratory factor analysis (Wikiversity) Factorial code Functional principal component analysis Geometric data analysis Independent
Principal_component_analysis
Statistical experimental design approach
statistics, a fractional factorial design is a way to conduct experiments with fewer experimental runs than a full factorial design. Instead of testing
Fractional_factorial_design
Object-oriented programming language
second "factorial" message, yielding 3628800. 3628800 then receives "between:and:", answering false. Because the meaning of binary messages is not coded into
Smalltalk
Ordering of binary values, used for positioning and error correction
related to inverse Gray code Ryser formula Steinhaus–Johnson–Trotter algorithm – an algorithm that generates Gray codes for the factorial number system By applying
Gray_code
Metaprogramming technique
return n == 0 ? 1 : n * factorial(n - 1); } // Usage examples: // factorial(0) would yield 1; // factorial(4) would yield 24. The code above will execute at
Template_metaprogramming
Functional programming language
Function (fix) factorial = fix fac where fac f x | x < 2 = 1 | otherwise = x * f (x - 1) As the Integer type has arbitrary-precision, this code will compute
Haskell
Signal processing computational method
a factorial code of the data, i.e., a new vector-valued representation of each data vector such that it gets uniquely encoded by the resulting code vector
Independent component analysis
Independent_component_analysis
Statically typed functional programming language
optimization: pub fn factorial(x: Int) -> Int { // The public function calls the private tail recursive function factorial_loop(x, 1) } fn factorial_loop(x: Int
Gleam_(programming_language)
Multi-paradigm system programming language
using code that is similar to that of the function above: template Factorial(ulong n) { static if (n < 2) { enum Factorial = 1; } else { enum Factorial =
D_(programming_language)
Programming language family
notation. For example, to evaluate a number's factorial: (defun factorial (n) (if (zerop n) 1 (* n (factorial (1- n))))) An alternative implementation takes
Lisp_(programming_language)
Use of functions that call themselves
this can be mitigated by a wrapper function. The box shows C code to shortcut factorial cases 0 and 1. Short-circuiting is primarily a concern when many
Recursion_(computer_science)
analysis Factor regression model Factor graph Factorial code Factorial experiment Factorial moment Factorial moment generating function Failure rate Fair
List_of_statistics_articles
Scheme for numbering permutations
signifies a right-to-left maximum, and that the Lehmer code of σ coincides with the factorial number system representation of its position in the list
Lehmer_code
Punctuation mark (!)
text without emotion. Other uses include: In mathematics, it denotes the factorial operation and shriek maps. Several computer languages use ! at the beginning
Exclamation_mark
Traditional first example of a computer programming language
programming languages, such as Lisp, ML, and Haskell, tend to substitute a factorial program for "Hello, world", as functional programming emphasizes recursive
Hello,_world
General-purpose programming language
ValueError('You must enter a non-negative integer') factorial = 1 for i in range(2, n + 1): factorial *= i print(factorial) Python's large standard library is commonly
Python_(programming_language)
section of code. For example: The result of a factorial is always an integer and greater than or equal to 1. So a program that calculates the factorial of an
Postcondition
General-purpose functional programming language
used for abstraction. The factorial function can be expressed as follows: fun factorial n = if n = 0 then 1 else n * factorial (n - 1) An SML compiler must
Standard_ML
Programming language
Sachs, Nintendo, AdRoll, Grindr, BT Mobile, Samsung, OpenX, and SITA. A factorial algorithm implemented in Erlang: -module(fact). % This is the file 'fact
Erlang_(programming_language)
Number of subsets of a given size
\cdots \times (n-k+1)}{k\times (k-1)\times \cdots \times 1}},} which using factorial notation can be compactly expressed as ( n k ) = n ! k ! ( n − k ) !
Binomial_coefficient
Feature of some compilers
Factorial<0>::VALUE; // == 1 int y = Factorial<4>::VALUE; // == 24 } Using compile-time function evaluation, code used to compute the factorial would be similar to what
Compile-time function execution
Compile-time_function_execution
Microsoft programming language
languages is the factorial function for non-negative 32-bit integers, here shown in F#: /// Using pattern matching expression let rec factorial n = match n
F Sharp (programming language)
F_Sharp_(programming_language)
Books. pp. 222–227. Schmidhuber, Jürgen (November 1992). "Learning Factorial Codes by Predictability Minimization". Neural Computation. 4 (6): 863–879
History of artificial neural networks
History_of_artificial_neural_networks
Features in Haskell programming language
the factorial function for non-negative integers, shown in Haskell: factorial :: Integer -> Integer factorial 0 = 1 factorial n = n * factorial (n-1)
Haskell_features
Computer programming concept
The factorial function is only defined where its parameter is an integer greater than or equal to zero. So an implementation of the factorial function
Precondition
Software programming optimization technique
memoized version of factorial using the above strategy, rather than calling factorial directly, code invokes memoized-call(factorial)(n). Each such call
Memoization
Programming language
factorial, are most naturally represented in a purely functional form. The following recursive, purely functional Caml function implements factorial:
Caml
British vision scientist (1921–2020)
in the field of factorial codes. The goal was to encode images with statistically redundant components or pixels such that the code components are statistically
Horace_Barlow
Wiki-based programming chrestomathy
(draw) Dot product Dragon curve Egyptian fractions Eight queens puzzle Factorials Fibonacci sequence FizzBuzz Galton box (bean box) animation Gamma function
Rosetta_Code
Experimental design in statistical mathematics
three-level factorial experiment. After the designed experiment is performed, linear regression is used, sometimes iteratively, to obtain results. Coded variables
Central_composite_design
Separation of a set of source signals from a set of mixed signals
filtering Celemony Software#Direct Note Access Colin Cherry Deconvolution Factorial codes Infomax principle Segmentation (image processing) Speech segmentation
Signal_separation
Programming style in which control is passed explicitly
global transformation. The direct-style factorial takes, as might be expected, a single argument; the CPS factorial& takes two: the argument and a continuation
Continuation-passing_style
6,909 known living languages.) Mathematics: 7! = 5,040 is the largest factorial that is also a highly composite number. Culture: 5,040 is mentioned by
Orders_of_magnitude_(numbers)
Branch of discrete mathematics
complexity theory. Coding theory started as a part of design theory with early combinatorial constructions of error-correcting codes. The main idea of
Combinatorics
Higher-order function Y for which Y f = f (Y f)
<- \(f) { g <- \(x) f(x(x)) g(g) } This can then be used to implement factorial as follows: fact <- \(f) \(n) if (n == 0) 1 else n * f(n - 1) Y(fact)(5)
Fixed-point_combinator
Programming language
arithmetic. As the factorial function grows very rapidly, it quickly overflows machine-precision numbers (typically 32- or 64-bits). Thus, factorial is a suitable
OCaml
Text in computer source code that is generally ignored by a compiler/interpreter
embedded in source code that a translator (compiler or interpreter) ignores. Generally, a comment is an annotation intended to make the code easier for a programmer
Comment (computer programming)
Comment_(computer_programming)
Collection of statistical models
accepted by the emerging field of psychology which developed strong (full factorial) experimental methods to which randomization and blinding were soon added
Analysis_of_variance
Multi-paradigm programming language
1415927d0; A factorial function: define function factorial (n :: <integer>) => (n! :: <integer>) case n < 0 => error("Can't take factorial of negative
Dylan_(programming_language)
Assembly language and bytecode for web browsers
The table below shows an example of a factorial function written in C and its corresponding WebAssembly code after compiling, shown both in .wat text
WebAssembly
Experimental designs for response surface methodology
proficient and more powerful than other designs such as the three-level full factorial design, central composite design (CCD) and Doehlert design, despite its
Box–Behnken_design
Statistical method
acceptable mathematically. But different factorial theories proved to differ as much in terms of the orientations of factorial axes for a given solution as in
Factor_analysis
Type of numeral systems
lexicographic order, which uses the factorial representation of the integer, followed by an interpretation as a Lehmer code. The above equation is a particular
Mixed_radix
Computer programming language
factorial(x) // Getting function which is factorial, then getting value which is x { if (x <= 1) { // if x is less than 1 return 1; // then the code will
Squirrel (programming language)
Squirrel_(programming_language)
Mapping arbitrary data to fixed-size values
algorithmic way of constructing such a function—searching for one is a factorial function of the number of keys to be mapped versus the number of table
Hash_function
Generic type features in C++
Induction template <unsigned int N> struct Factorial { static constexpr unsigned int value = N * Factorial<N - 1>::value; }; // Base case via template
Template_(C++)
Natural number
so that 1 is also the identity for any power semigroup. 1 is its own factorial 1 ! = 1 {\displaystyle 1!=1} . Moreover, the empty product, that is the
1
General-purpose programming language
the factorial definition. For instance, the recursive version of the factorial: def factorial(n: Int): Int = if n == 0 then 1 else n * factorial(n - 1)
Scala_(programming_language)
Programming language derived from Perl
say 'Hello, world'; — though there is more than one way to do it. The factorial function in Raku, defined in a few different ways: # Using recursion (with
Raku_(programming_language)
Recursive integer sequence
triangle Catalan–Mersenne number Delannoy number Fuss–Catalan number List of factorial and binomial topics Lobb numbers Motzkin number Narayana number Narayana
Catalan_number
Method of writing text on seven-segment displays
other punctuation. In some calculators that use dot matrix displays, a factorial product sign ("!") can be used to add emphasis. For example, "B00B1E5
Calculator_spelling
Universal code which encodes positive integers into binary code words
mathematics and computing, Fibonacci coding is a universal code which encodes positive integers into binary code words. It is one example of representations
Fibonacci_coding
Program function without side effects
and Code Brevity. SpringerLink : Bücher. Apress. p. 109. ISBN 978-1-4842-2958-3. Retrieved 2024-02-04. "I've got an incorrect output for 13 factorial,how
Pure_function
function for computing the factorial of a number, written in E. Functions are defined using the def keyword. def factorial(n :int) :int { if (n == 1)
E_(programming_language)
Topics referred to by the same term
Division Half-factorial domain, an atomic domain Half flux diameter, a measure of star size in astronomical images Halfords, UK retailer, LSE code Hardware
HFD
Data serialization format
Program code can be written in S-expressions, usually using prefix notation. Example in Common Lisp: (defun factorial (x) (if (zerop x) 1 (* x (factorial (-
S-expression
High-level computer programming language
calculate a factorial. % Accepts a number and calculates its factorial function factorial (n: int) : real if n = 0 then result 1 else result n * factorial (n -
Turing_(programming_language)
Programming language
ballerina/http; service on new http:Listener(9090) { resource function post factorial(@http:Payload string payload) returns http:Ok|http:BadRequest { int|error
Ballerina (programming language)
Ballerina_(programming_language)
Lightweight programming language
comment --[[ Multi-line comment --]] The factorial function is implemented in this example: function factorial(n) local x = 1 for i = 2, n do x = x * i
Lua
Natural number
second Lucas prime), the second Sophie Germain prime, and the second factorial prime. 3 is the second and only prime triangular number, and Carl Friedrich
3
Programming language
IN THISFORM.Controls MESSAGEBOX(oControl.Name) ENDFOR f = Factorial(10) FUNCTION Factorial(n) LOCAL i, r r = 1 FOR i = n TO 1 STEP -1 r = r * i NEXT &&
Visual_FoxPro
Large number defined as ten to the 100th power
≈ 1.1979 × 10 100 {\displaystyle 70!\approx 1.1979\times 10^{100}} (factorial of 70). Using an integral, binary numeral system, one would need 333 bits
Googol
Multi-paradigm computer programming language
START and WRITEF must be changed to lower case to avoid errors. Print factorials: GET "LIBHDR" LET START() = VALOF $( FOR I = 1 TO 5 DO WRITEF("%N! = %I4*N"
BCPL
Mathematical version of an order change
RNA sequences. The number of permutations of n distinct objects is n factorial, usually written as n!, which means the product of all positive integers
Permutation
Number that is the product of factorials
the numbers that can be obtained by multiplying together one or more factorials, not required to be distinct from each other. For instance, 480 {\displaystyle
Jordan–Pólya_number
Natural number
prime. It is also a Newman–Shanks–Williams prime, a Woodall prime, a factorial prime, a Harshad number, a lucky prime, a happy number (happy prime),
7
Number expressed in the base-2 numeral system
Balanced ternary Bitwise operation Binary code Binary-coded decimal Binary non positional code Finger binary Gray code IEEE 754 Linear-feedback shift register
Binary_number
used in code as any other fudget. factorialF = stdoutF >==< mapF (show . factorial . read) >==< stdinF factorial :: Integer -> Integer factorial n = product
Fudgets
Type of mathematical array
qualitative. In a full factorial experiment all combinations of levels of the factors need to be tested. In a fractional factorial design only a subset
Orthogonal_array
Process of repeating items in a self-similar way
recursion is the definition of the factorial function, given here in Python code: def factorial(n): if n > 0: return n * factorial(n - 1) else: return 1 The function
Recursion
Study of programming languages via mathematical objects
be defined in code as follows (using Map<int,int> for N ⇀ N {\displaystyle \mathbb {N} \rightharpoonup \mathbb {N} } ): int factorial_nonrecursive(Map<int
Denotational_semantics
Programming language
comprehension. A factorial procedure definition: procedure factorial(n); -- calculates the factorial n! return if n = 1 then 1 else n * factorial(n - 1) end
SETL
Natural number
Thus it is the order of the symmetric group on four symbols, and is the factorial of 4. This is the full symmetry group of the regular tetrahedron, and
24_(number)
Lisp dialect
be written in different dialects of Racket. Here is an example of the factorial program in Typed Racket, a statically typed dialect of Racket: #lang typed/racket
Racket_(programming_language)
Mathematical sequences in combinatorics
that many use for falling factorials is used in special functions for rising factorials.) Similarly, the rising factorial, defined as x ( n ) =
Stirling_number
In programming languages, the object or class the currently running code belongs to
recursion, with static dispatch. For example, in the following Perl code for the factorial, the token __SUB__ is a reference to the current function: use feature
This_(computer_programming)
Prototype-based programming language
creates a new, empty object named "A" A simple non-recursive factorial function, in Io: factorial := method(n, if(n == 0, return 1) res := 1 Range 1 to(n)
Io_(programming_language)
mathematics, negafibonacci coding is a universal code which encodes nonzero integers into binary code words. It is similar to Fibonacci coding, except that it allows
Negafibonacci_coding
Programmable calculator produced by Texas Instruments
not have the factorial function built-in, but do support it through the software module which was delivered with the calculator. Op-code Comment LBL A
TI-59_/_TI-58
Size of a mathematical ball
recurrence relation. Closed-form expressions involve the gamma, factorial, or double factorial function. The volume can also be expressed in terms of A n {\displaystyle
Volume_of_an_n-ball
Stack-oriented programming language
graphical listener). The factorial function n ! {\displaystyle n!} can be implemented in Factor in the following way: : factorial ( n -- n! ) dup 1 > [ [1
Factor_(programming_language)
Third letter of the Greek alphabet
written as Γ {\displaystyle \Gamma } -function) is an extension of the factorial to complex numbers In mathematics, the upper incomplete gamma function
Gamma
Base five numeral system
Units of currencies are commonly partially or wholly biquinary. Bi-quinary coded decimal is a variant of biquinary that was used on a number of early computers
Quinary
Sigmoid shape special function
\end{aligned}}} where ( 2 n − 1 ) ! ! {\displaystyle (2n-1)!!} is the double factorial of 2 n − 1 {\displaystyle 2n-1} , i.e. the product of all odd numbers
Error_function
number, the more likely the email is considered spam. [citation needed] Factorial number system {1, 2, 3, 4, 5, 6, ...} Primorial number system {2, 3, 5
List_of_numeral_systems
Audio programming language
their indices [1, 2, 5, 10, -3].collect { |elem, idx| elem * idx }; // Factorial function f = { |x| if(x == 0) { 1 } { f.(x-1) * x } }; // «Pan Sonic emulation
SuperCollider
Base-8 numeral representation
aircraft transmit a "squawk" code, expressed as a four-octal-digit number, when interrogated by ground radar. This code is used to distinguish different
Octal
Intravenous medication used in general anaesthesia
Endoscopy: Protocol for a Randomized, Double-Blind, Controlled Trial With Factorial Design". Frontiers in Pharmacology. 13 821691. doi:10.3389/fphar.2022
Cipepofol
Method for representing or encoding numbers
× 33 + 0 × 32 − 1 × 31 + 1 × 30 = 25. The factorial number system uses a varying radix, giving factorials as place values; they are related to Chinese
Positional_notation
Natural number
Leyland number 134,340 = Pluto's minor planet designation 135,135 = double factorial of 13 135,137 = Markov number 142,129 = 3772, square number, dodecagonal
100,000
Natural number
divisible by 23, a property shared by few other numbers. It is the fifth factorial prime, and since 14! + 1 is a multiple of 23, but 23 is not one more than
23_(number)
Recursive function
following: factorial 5 = 5 * (factorial 4) = 120 factorial 4 = 4 * (factorial 3) = 24 factorial 3 = 3 * (factorial 2) = 6 factorial 2 = 2 * (factorial 1) =
Hylomorphism (computer science)
Hylomorphism_(computer_science)
such a classification, such as list of exponential topics and list of factorial and binomial topics, which may surprise the reader with the diversity
Lists_of_mathematics_topics
Functional programming language
included in the Clean distribution. Hello world: Start = "Hello, world!" Factorial: Fibonacci sequence: Infix operator: (^) infixr 8 :: Int Int -> Int (^)
Clean_(programming_language)
FACTORIAL CODE
FACTORIAL CODE
Girl/Female
Tamil
Code
Boy/Male
American, Anglo, Australian, British, English, Irish
Cushion; Helpful; Pillow
Boy/Male
American, British, English, Irish
Helpful
Surname or Lastname
English
English : variant spelling of Coad.
Boy/Male
Irish American English
Helpful.
Surname or Lastname
English
English : nickname for a person who insisted on a strict code of social behavior.German : topographic name for someone who lived on or by a hill, from Middle High German stickel ‘hill’, ‘slope’ + the suffix -er denoting an inhabitant; in the south an occupational name for someone who shapes and sets stakes in vineyards.
Girl/Female
American, Australian, British, English, Irish
Cushion; Helpful
Female
Japanese
(1-儀, 2-典, 3-則, 4-法) Japanese unisex name NORI means 1) "ceremony, regalia," 2) "code, precedent," 3) "model, rule, standard," 4) "law, rule."
Surname or Lastname
English
English : occupational name for a watchman or guard, from Old English weard ‘guard’ (used as both an agent noun and an abstract noun).Irish : reduced form of McWard, an Anglicized form of Gaelic Mac an Bhaird ‘son of the poet’. The surname occurs throughout Ireland, where three different branches of the family are known as professional poets.Surname adopted by bearers of the Jewish surname Warshawski, Warshawsky or some other Jewish name bearing some similarity to the English name.Americanized form of French Guerin.The surname Ward was brought to North America from England independently by several different bearers in the 17th and 18th centuries. Nathaniel Ward (1578–1652), author of the MA legal code, was born in Haverhill, Suffolk, England, and emigrated to Agawam (Ipswich, MA) in 1633. William Ward was one of the original settlers of Sudbury, MA, in about 1638. Miles Ward came from England to Salem, MA, in about 1639. Thomas Ward (d. 1689) settled in Newport, RI, in 1671; among his descendants were two governors of colonial RI.
Girl/Female
Hindu
Code
Boy/Male
Arabic, Muslim
Rockstar
FACTORIAL CODE
FACTORIAL CODE
Girl/Female
Biblical
Grace, or gift, of God.
Boy/Male
Muslim/Islamic
Consoler Comforter, restorer
Boy/Male
Tamil
Dhanunjaya | தாநà¯à®‚நà¯à®œà®¾à®¯à®¾Â
Partha, Arjun, Agni God, Fire
Male
Hungarian
Hungarian form of Greek Theodoros, TÓDOR means "gift of God."
Boy/Male
Indian, Punjabi, Sikh
Victory of the Ruler
Male
Czechoslovakian
, here comes glory.
Boy/Male
Indian, Tamil
Flawless Gem
Girl/Female
Danish, Finnish, French, German, Hebrew, Swedish
Jewish; Praise; From Judea
Girl/Female
Australian, Indonesian
Beautiful
Girl/Female
Indian
A smile
FACTORIAL CODE
FACTORIAL CODE
FACTORIAL CODE
FACTORIAL CODE
FACTORIAL CODE
n.
The pictorial aspect of a country.
n.
A name given to the factors of a continued product when the former are derivable from one and the same function F(x) by successively imparting a constant increment or decrement h to the independent variable. Thus the product F(x).F(x + h).F(x + 2h) . . . F[x + (n-1)h] is called a factorial term, and its several factors take the name of factorials.
a.
Related to factorials.
p. pr. & vb. n.
of Factorize
a.
Pictorial.
a.
Adapted for sucking; living by sucking; as, the humming birds are suctorial birds.
imp. & p. p.
of Factorize
a.
Suctorial.
a.
Raptorial.
n.
A large pictorial sketch, as in a journal or magazine; esp. a pictorial caricature; as, the cartoons of "Puck."
a.
Capable of adhering by suction; as, the suctorial fishes.
a.
Of or pertaining to covering; -- applied to a membrane immediately over the organ of Corti in the internal ear.
a.
Of or pertaining to a tailor or his work.
a.
Of or pertaining to the sartorius muscle.
n.
A sectorial, or carnassial, tooth.
a.
Of or pertaining to a factory.
a.
Of or pertaining to pictures; illustrated by pictures; forming pictures; representing with the clearness of a picture; as, a pictorial dictionary; a pictorial imagination.
n.
The product of the consecutive numbers from unity up to any given number.
a.
Adapted for cutting.
a.
Pictorial.