fastmath.vector — generateme/fastmath 3.0.0-alpha3

Mathematical vector operations.

Types

• Fixed size (custom types):
  • Number - 1d vector
  • Vec2 - 2d vector, creator vec2
  • Vec3 - 3d vector, creator vec3
  • Vec4 - 4d vector, creator vec4
  • ArrayVec - fixed size double array wrapper, n-dimensional, creator array-vec
• Fixed size
  • doubles - double array itself
• Variable size:
  • Clojure's IPersistentVector, creator []
  • Clojure's ISeq

[[VectorProto]] defines most of the functions.

Vectors implements also:

• Sequable
• Sequencial
• IFn
• Counted
• Reversible
• Indexed
• ILookup
• equals and toString from Object
• IPersistentVector
• Associative
• clojure.core.matrix.protocols
• IReduce and IReduceInit

That means that vectors can be destructured, treated as sequence or called as a function. See vec2 for examples.

abs clj

(abs v)

Absolute value of vector elements

acos clj

(acos vector)

Apply acos to vector elements.

acosh clj

(acosh vector)

Apply acosh to vector elements.

acot clj

(acot vector)

Apply acot to vector elements.

acoth clj

(acoth vector)

Apply acoth to vector elements.

acsc clj

(acsc vector)

Apply acsc to vector elements.

acsch clj

(acsch vector)

Apply acsch to vector elements.

add clj

(add v)

(add v1 v2)

Sum of two vectors.

aligned? clj

(aligned? v1 v2)

(aligned? v1 v2 tol)

Are vectors aligned (have the same direction)?

angle-between clj

(angle-between v1 v2)

Angle between two vectors

See also relative-angle-between.

applyf clj deprecated

Same as fmap. Deprecated.

approx clj

(approx v)

(approx v d)

Round to 2 (or d) decimal places

array->vec2 clj

(array->vec2 arr)

Doubles array to Vec2

array->vec3 clj

(array->vec3 arr)

Doubles array to Vec3

array->vec4 clj

(array->vec4 arr)

Doubles array to Vec4

array-vec clj

(array-vec xs)

Make ArrayVec type based on provided sequence xs.

as-vec clj

(as-vec v)

(as-vec v xs)

Create vector from sequence as given type. If there is no sequence fill with 0.0.

asec clj

(asec vector)

Apply asec to vector elements.

asech clj

(asech vector)

Apply asech to vector elements.

asin clj

(asin vector)

Apply asin to vector elements.

asinh clj

(asinh vector)

Apply asinh to vector elements.

atan clj

(atan vector)

Apply atan to vector elements.

atanh clj

(atanh vector)

Apply atanh to vector elements.

average clj

(average v)

(average v weights)

Mean or weighted average of the vector

average-vectors clj

(average-vectors vs)

(average-vectors init vs)

Average / centroid of vectors. Input: initial vector (optional), list of vectors

axis-rotate clj

(axis-rotate v angle axis)

(axis-rotate v angle axis pivot)

Rotate vector. Only for Vec3 types

base-from clj

(base-from v)

List of perpendicular vectors (basis). Works only for Vec2 and Vec3 types.

cb clj

(cb vector)

Apply cb to vector elements.

cbrt clj

(cbrt vector)

Apply cbrt to vector elements.

ceil clj

(ceil vector)

Apply ceil to vector elements.

clamp clj

(clamp v)

(clamp v mn mx)

Clamp elements.

cos clj

(cos vector)

Apply cos to vector elements.

cosh clj

(cosh vector)

Apply cosh to vector elements.

cot clj

(cot vector)

Apply cot to vector elements.

coth clj

(coth vector)

Apply coth to vector elements.

cross clj

(cross v1 v2)

Cross product

csc clj

(csc vector)

Apply csc to vector elements.

csch clj

(csch vector)

Apply csch to vector elements.

degrees clj

(degrees vector)

Apply degrees to vector elements.

delta-eq clj

(delta-eq v1 v2)

(delta-eq v1 v2 abs-tol)

(delta-eq v1 v2 abs-tol rel-tol)

Equality with given absolute (and/or relative) toleance.

dhash-code clj

(dhash-code a)

(dhash-code state a)

double hashcode

dist clj

(dist v1 v2)

Euclidean distance between vectors

dist-abs clj

(dist-abs v1 v2)

Manhattan distance between vectors

dist-ang clj

(dist-ang v1 v2)

Angular distance

dist-canberra clj

(dist-canberra v1 v2)

Canberra distance

dist-cheb clj

(dist-cheb v1 v2)

Chebyshev distance between 2d vectors

dist-discrete clj

(dist-discrete v1 v2)

Discrete distance between 2d vectors

dist-emd clj

(dist-emd v1 v2)

Earth Mover's Distance

dist-sq clj

(dist-sq v1 v2)

Squared Euclidean distance between vectors

distances clj

div clj

(div v1)

(div v1 v)

Vector division or reciprocal.

dot clj

(dot v1 v2)

Dot product of two vectors.

econstrain clj

(econstrain v mn mx)

Element-wise constrain

edelta-eq clj

(edelta-eq v1 v2)

(edelta-eq v1 v2 abs-tol)

(edelta-eq v1 v2 abs-tol rel-tol)

Element-wise equality with given absolute (and/or relative) toleance.

ediv clj

(ediv v1 v2)

Element-wise division of two vectors.

einterpolate clj

(einterpolate v1 v2 v)

(einterpolate v1 v2 v f)

Interpolate vector selement-wise, optionally set interpolation fn (default: lerp)

emn clj

(emn v1 v2)

Element-wise min from two vectors.

emult clj

(emult v1 v2)

Element-wise vector multiplication (Hadamard product).

emx clj

(emx v1 v2)

Element-wise max from two vectors.

exp clj

(exp vector)

Apply exp to vector elements.

expm1 clj

(expm1 vector)

Apply expm1 to vector elements.

faceforward clj

(faceforward n v)

Flip normal n to match the same direction as v.

floor clj

(floor vector)

Apply floor to vector elements.

fmap clj

(fmap v f)

Apply function to all vector values (like map but returns the same type).

frac clj

(frac vector)

Apply frac to vector elements.

from-polar clj

(from-polar v)

From polar coordinates (2d, 3d only)

generate-vec2 clj

(generate-vec2 f)

(generate-vec2 f1 f2)

Generate Vec2 with fn(s)

generate-vec3 clj

(generate-vec3 f)

(generate-vec3 f1 f2 f3)

Generate Vec3 with fn(s)

generate-vec4 clj

(generate-vec4 f)

(generate-vec4 f1 f2 f3 f4)

Generate Vec4 with fn(s)

heading clj

(heading v)

Angle between vector and unit vector [1,0,...]

interpolate clj

(interpolate v1 v2 t)

(interpolate v1 v2 t f)

Interpolate vectors, optionally set interpolation fn (default: lerp)

is-near-zero? clj

(is-near-zero? v)

(is-near-zero? v abs-tol)

(is-near-zero? v abs-tol rel-tol)

Equality to zero 0 with given absolute (and/or relative) toleance.

is-zero? clj

(is-zero? v)

Is vector zero?

lerp clj

(lerp v1 v2 t)

Linear interpolation of vectors

limit clj

(limit v len)

Limit length of the vector by given value

ln clj

(ln vector)

Apply ln to vector elements.

log clj

(log vector)

Apply log to vector elements.

log10 clj

(log10 vector)

Apply log10 to vector elements.

log1mexp clj

(log1mexp vector)

Apply log1mexp to vector elements.

log1p clj

(log1p vector)

Apply log1p to vector elements.

log1pexp clj

(log1pexp vector)

Apply log1pexp to vector elements.

log1pmx clj

(log1pmx vector)

Apply log1pmx to vector elements.

log1psq clj

(log1psq vector)

Apply log1psq to vector elements.

log2 clj

(log2 vector)

Apply log2 to vector elements.

logexpm1 clj

(logexpm1 vector)

Apply logexpm1 to vector elements.

logit clj

(logit vector)

Apply logit to vector elements.

logmeanexp clj

(logmeanexp v)

logmxp1 clj

(logmxp1 vector)

Apply logmxp1 to vector elements.

logsoftmax clj

(logsoftmax v)

logsumexp clj

(logsumexp v)

mag clj

(mag v)

Length of the vector.

magsq clj

(magsq v)

Length of the vector squared.

make-vector clj

(make-vector dims)

(make-vector dims xs)

Returns fixed size vector for given number of dimensions.

Proper type is used.

maxdim clj

(maxdim v)

Index of maximum value.

mindim clj

(mindim v)

Index of minimum value.

mn clj

(mn v)

Minimum value of vector elements

mult clj

(mult v x)

Multiply vector by number x.

mx clj

(mx v)

Maximum value of vector elements

near-zero? clj

(near-zero? v)

(near-zero? v abs-tol)

(near-zero? v abs-tol rel-tol)

Equality to zero 0 with given absolute (and/or relative) toleance.

nonzero-count clj

(nonzero-count v)

Count non zero velues in vector

normalize clj

(normalize v)

Normalize vector (set length = 1.0)

orthogonal-polynomials clj

(orthogonal-polynomials xs)

Creates orthogonal list of vectors based on xs, starting from degree 1

orthonormal-polynomials clj

(orthonormal-polynomials xs)

Creates orthonormal list of vector based on xs, starting from degree 1

permute clj

(permute v idxs)

Permute vector elements with given indices.

perpendicular clj

(perpendicular v)

(perpendicular v1 v2)

Perpendicular vector. Only for Vec2 and Vec3 types.

prod clj

(prod v)

Product of elements

project clj

(project v1 v2)

Project v1 onto v2

radians clj

(radians vector)

Apply radians to vector elements.

reciprocal clj

(reciprocal v)

Reciprocal of elements.

relative-angle-between clj

(relative-angle-between v1 v2)

Angle between two vectors relative to each other.

See also angle-between.

rint clj

(rint vector)

Apply rint to vector elements.

rotate clj

(rotate v angle)

(rotate v angle-x angle-y angle-z)

Rotate vector. Only for Vec2 and Vec3 types.

round clj

(round vector)

Apply round to vector elements.

safe-sqrt clj

(safe-sqrt vector)

Apply safe-sqrt to vector elements.

sec clj

(sec vector)

Apply sec to vector elements.

sech clj

(sech vector)

Apply sech to vector elements.

seq->vec2 clj

(seq->vec2 xs)

Any seq to Vec2

seq->vec3 clj

(seq->vec3 xs)

Any seq to Vec3

seq->vec4 clj

(seq->vec4 xs)

Any seq to Vec4

set-mag clj

(set-mag v len)

Set length of the vector

sfrac clj

(sfrac vector)

Apply sfrac to vector elements.

sgn clj

(sgn vector)

Apply sgn to vector elements.

shift clj

(shift v)

(shift v x)

Add value to every vector element.

sigmoid clj

(sigmoid vector)

Apply sigmoid to vector elements.

signum clj

(signum vector)

Apply signum to vector elements.

sim-cos clj

(sim-cos v1 v2)

Cosine similarity

sin clj

(sin vector)

Apply sin to vector elements.

sinc clj

(sinc vector)

Apply sinc to vector elements.

sinh clj

(sinh vector)

Apply sinh to vector elements.

size clj

(size v)

Length of the vector.

softmax clj

(softmax v)

sq clj

(sq vector)

Apply sq to vector elements.

sqrt clj

(sqrt vector)

Apply sqrt to vector elements.

sub clj

(sub v)

(sub v1 v2)

Subtraction of two vectors.

sum clj

(sum v)

Sum of elements

tan clj

(tan vector)

Apply tan to vector elements.

tanh clj

(tanh vector)

Apply tanh to vector elements.

to-polar clj

(to-polar v)

To polar coordinates (2d, 3d only), first element is length, the rest angle.

to-vec clj deprecated

Same as vec->Vec. Deprecated.

transform clj

(transform v o vx vy)

(transform v o vx vy vz)

Transform vector; map point to coordinate system defined by origin, vx and vy (as bases), Only for Vec2 and Vec3 types.

triple-product clj

(triple-product a b c)

a o (b x c)

trunc clj

(trunc vector)

Apply trunc to vector elements.

vec->array clj

(vec->array v)

Convert to double array

vec->RealVector clj

(vec->RealVector v)

Convert to Apache Commons Math RealVector

vec->seq clj

(vec->seq v)

Convert to sequence (same as seq)

vec->Vec clj

(vec->Vec v)

Convert to Clojure primitive vector Vec.

vec2 clj

(vec2)

(vec2 [x y])

(vec2 x y)

Make 2d vector.

vec3 clj

(vec3)

(vec3 [x y z])

(vec3 v z)

(vec3 x y z)

Make Vec2 vector

vec4 clj

(vec4)

(vec4 [x y z w])

(vec4 v w)

(vec4 v z w)

(vec4 x y z w)

Make Vec4 vector

xlogx clj

(xlogx vector)

Apply xlogx to vector elements.

zero-count clj

(zero-count v)

Count zeros in vector

zero? clj

(zero? v)

Is vector zero?