Vcalc - vector calculator for HRRs

One ususual aspect of vcalc notation is that functions can have local variables specified in the parameter list, after a semicolon. Thus, the following two examples print the same thing:

> x = {1/2 1/3}
> print(x)
{0.5 0.333}
> print(x; precision=6, brace=false)
0.5 0.333333
> print.precision=6
> print.brace=false
> print(x)
0.5 0.333333

Variables controlling behaviour of vcalc

• var.dim, vector.dim - dimension of newly created vectors
• vector.type - Controls whether vectors are treated as real or complex. Functions and operators behave differently for real and complex vectors. Two possible values:
  • "standard" - vectors of real values. Here's a quick summary of the special features of vcalc:
    • vector by vector multiplication (x*y): circular (wrapped) convolution
    • vector approximate inverse (x'): permute the elements of x (first element stays in place, order of rest is reversed)
  • "circular" - vectors of complex values, stored in polar form, with magnitude then angle. A vector of n elements contains n/2 complex numbers. Here's a quick summary of how complex vectors are treated by various functions and operators.
    • elements of vectors are (r,theta) pairs, theta between -Pi and Pi
    • randvec() gives vectors with thetas uniformly distributed in [-Pi,Pi] and all r = 1 (theta_0 = 0)
    • vector addition: center of gravity in complex plane
    • scalar multiplication: multiply r
    • vector exponent - mutiply theta, exp(r)
    • vector multiplication: addition of angles, multiplication of r
    • vector division: addition of angles, division of r
    • vector inverse - negate theta
    • vector negation - spin theta thru Pi
    • normalization: set r_i=1
    • similarity function (dotProduct) sum xr_i*yr_i*cos(xtheta_i-ytheta_i)
• echo - default "false" (set by command line option)
• store.bitvectors - default "false" (set by command line option)
• match.sim - default "dotProduct"
• match.print - default "true"
• match.filter - default "false"
• match.spread - default 4
• match.precision - default 3
• match.capacity - default 1
• blend.sim - default "dotProduct"
• blend.transfer - default "boundedLinear"
• blend.threshhold - default 0.0
• blend.bias - default 0.0
• blend.weight - default 1
• blend.capacity - default 1
• retrieve.sim - default "dotProduct"
• retrieve.transfer - default "binary"
• retrieve.bias - default 0.0
• retrieve.threshhold - default 0.0
• retrieve.weight - default 1.0
• retrieve.capacity - default 1.0
• rand.seed - default 0 (set by command line option)
• normalize.threshhold - default 0.0
• print.brace - default "true"
• print.level - default 3
• print.precision - default 3
• print.bitspace - default ""
• print.newline - default "true"
• print.flush - default "true"
• bitvec.threshold - default 0
• debug.tree - default "false" (set by command line option)
• debug.addr - default "false" (set by command line option)
• debug.mem - default "false"
• orthogonalize.precision - default 1e-3
• true - constant string value "true"
• false - constant string value "false"
• pi - constant - value of PI

Operators

• x+y
• x*y convolution or scalar multiplication
• x@*y element wise multiplication
• x&*y ??? (unused)
• x@/y element wise multiplication
• x**y
• x^y
• x-y
• x=y
• x==y
• x?=y same as x==y
• x?<y less than (can't use < because we use <x> for normalization)
• x?>y greater than
• x>=y greater than or equals
• x<=y less than or equals
• x!=y
• <x> normalization
• |x|
• x'
• !x
• -x
• x . y dot product. Must have spaces around the dot because a dot is legally part of an identifier.

Functions

<.> - normalization

<x> or equivalently normalize(x) is the normalized version of x

Control:

• type: controls the type of normalization performed. Takes string values among:
  • "logistic" "sigmoid"
  • "tanh"
  • "binary"
  • "symmetric"
  • "nopnorm"
  • "unit"
  • "unitbinary"
  • "power"
  • "linear"
  • "boundedlinear"

Examples:

> y = {1 2 3 4}
> y
{1 2 3 4}
> <y>
{0.183 0.365 0.548 0.73}
> <y;type="nopnorm">
{1 2 3 4}
> normalize.type
unit
> normalize.type="nopnorm"
> normalize(y)
{1 2 3 4}
> normalize(y;type="unit")
{0.183 0.365 0.548 0.73}

cos

cos(x) - the cosine of x

Control:

• ????: controls ... Takes ??? values among:
  • ???

Examples:

sqrt

print

repeat

cons

top

pop

push

randvec

time

randSeed

uniform

rand

bitvec

orthogonalize

match

blend

blend(x,list) - calculates a blend of x among the vectors in list

Control:

• capacity: use this many best matches
• transfer: the function used to compute blend weights from match strengths. Takes string values among:
  • sigmoid or logistic
  • tanh
  • linear
  • boundedlinear: bounded between 0 and 1
• sigmoid.bias: The bias to use with logistic or tanh transfer functions. The weight is computed as sigmoid(sigmoid.bias+sigmoid.weight*matchscore) (or tanh(.)).
• sigmoid.weight: The weight to use with logistic or tanh transfer functions.
• sim: The type of similarity function. Takes string values among:
  • dotproduct
  • cosine

Examples:

> a = <randvec()>
> b = <randvec()>
> c = <randvec()>
> blend.capacity = 2
> match.capacity = 3
> blend.transfer = "boundedlinear"
> store(s, a,b,c)
> x = 2*a + b + c
> match(x, s)
a                    1.80447
b                    0.812107
c                    0.783128
> y = blend(x, s)
> y
{-0.605 -0.0471 0.226 -0.0293 -0.534 0.552 0.705 -0.075}
> a + 0.812107 * b
{-0.605 -0.0471 0.226 -0.0293 -0.534 0.552 0.705 -0.075}