vsa.funcs: Generic algebraic operations and functions for VSA vectors

In vsa: Vector Symbol Architectures for AI & CogSci

Description

Generic functions for working with VSA vectors. Functions for all standard algebraic operations on vectors: multiplication, addition, superposition, scaling, powers (including inverses), approximate inverse, similarity.

Usage

vsaprod(e1, e2, method = c("fft", "outer"))
appinv(e1)
!e1

add(e1, ...)
vnorm(e1)
addnorm(...)
dot(e1, e2)
e1 %.% e2
equiv(e1, e2, tol)
e1 %==% e2
cosine(e1, e2, mag1=NULL, mag2=NULL)
e1 %cos% e2
mag(e1, actual=NULL)
vsapower(e1, e2)
vsascale(e1, e2)
e1 * e2
e1 + e2
e1 / e2
e1 - e2
e1 ^ e2

Arguments

e1	a vsa vector – a subclass of vsa
e2	a vsa vector for vsaprod, dot, equiv, cosine, and add, or a scalar (a numeric vector of length 1) for vsapower and vsascale
method	computational method for convolution (vsaprod)
tol	numerical tolerance for equiv
mag1,mag2	precomputed magnitudes for e1 and e2
actual	work with data values from this object (in this mode of invocation e1 is a template holding the class)
...	addtional vsa vectors for add or addnorm

Details

All of these functions take as arguments one or more VSA vectors, and possibily a scalar. A VSA vector is a subclass of vsa (e.g., realhrr). The result is a VSA vector, or a scalar with class simval. To catch some errors due to misunderstanding of R's precedence, a "simval" scalar cannot be supplied as the argument of one of these functions (to do, remove the simval class using the function scalar).

• mag computes the magnitude of a vector (scalar value)

• vnorm normalizes a vector so that its magnitude is 1 (vector value)

• vsaprod and its synonym * compute the vector product of two vectors (vector value)

• appinv and its synonym ! computes an approximate inverse of a vector. The expression x / y where x and y are vectors computes x * appinv(y). (vector value)

• vsascale and its synonym * multiple a vector by a scalar (vector value)

• add computes the vector superposition of a collection of vectors (supplied as arguments). Need not be associative (if it always was, a two-argument addition function would suffice). x + y is a synonym for add(x, y). x - y is a synonym for add(x, vsascale(y, -1)). (vector value)

• addnorm computes the vector superposition of a collection of vectors (supplied as arguments) and normalizes the result.

• vsapower and its synonym ^ compute the power of a vector. Negative powers are allowed (vector value)

• equiv compares two vectors for approximate relative equality (to a quite strict tolerance) (logical value)

• cosine and its synonym %cos% compute the normalized similarity of two vectors and return a scalar value with class simval

• dot and its synonym %.% compute the unnormalized similarity of two vectors and return a scalar value with class simval

Value

vsaprod, appinv, add, vnorm, vsapower, vsascale return a vsa object of the same class as their argument.

mag, dot and cosine return a scalar value with class simval

Author(s)

Tony Plate [e-mail]

References

http://www.d-reps.org

See Also

vsa, vsa.mem, for operator precedence: Syntax

Examples

library(vsa)
a <- newVec()
a
b <- newVec()
b
dot(a, b)
a 
elts(a)[1:10]
x <- a * b
(!a)
(!a * x) 
((!a) * x) 
(appinv(a) * x) 
(x / a) 
c <- newVec()
d <- newVec()
e <- newVec()
f <- newVec()
x <- vnorm(a * b + c * d + e * f)
mem <- vsamem(a, b, c, d, e, f)
cosmem(mem, a)
dotmem(mem, x / b)
cosmem(mem, x / b)
cosmem(mem, x / c)
cosmem(mem, x / f)
bestmatch(mem, x / b, cos=TRUE)
bestmatch(mem, x / b, cos=FALSE)

vsa documentation built on May 2, 2019, 4:53 p.m.