6.15 Subtypes

6.15.1 Flonum Arrays

syntax
FlArray

The type of flonum arrays, a subtype of (Settable-Array Flonum) that stores its elements in an FlVector. A flonum array is always strict.

syntax
(flarray #[#[...] ...])

Like array, but creates flonum arrays. The listed elements must be real numbers, and may be exact.

Examples:

> (flarray 0.0)
- : FlArray
(flarray 0.0)
> (flarray #['x])
eval:312:0: Type Checker: type mismatch
  expected: Real
  given: 'x
  in: #((quote x))
> (flarray #[#[1 2] #[3 4]])
- : FlArray
(flarray #[#[1.0 2.0] #[3.0 4.0]])

procedure
(array->flarray arr) → FlArray
arr : (Array Real)

Returns a flonum array that has approximately the same elements as arr. Exact elements will likely lose precision during conversion.

procedure
(flarray-data arr) → FlVector
arr : FlArray

Returns the elements of arr in a flonum vector, in row-major order.

Example:

> (flarray-data (flarray #[#[1 2] #[3 4]]))
- : FlVector
(flvector 1.0 2.0 3.0 4.0)

procedure
(flarray-map f arrs ...) → FlArray
f : (Flonum ... -> Flonum)
arrs : FlArray

Maps the function f over the arrays arrs. If the arrays do not have the same shape, they are broadcast first. If the arrays do have the same shape, this operation can be quite fast.

The function f is meant to accept the same number of arguments as the number of its following flonum array arguments. However, a current limitation in Typed Racket requires f to accept any number of arguments. To map a single-arity function such as fl+, for now, use inline-flarray-map or array-map.

syntax
(inline-flarray-map f arrs ...)

f : (Flonum ... -> Flonum)
arrs : FlArray

Like inline-array-map, but for flonum arrays.

This is currently unavailable in untyped Racket.

procedure
(flarray+ arr0 arr1) → FlArray
  arr0 : FlArray
  arr1 : FlArray
procedure
(flarray* arr0 arr1) → FlArray
  arr0 : FlArray
  arr1 : FlArray
procedure
(flarray- arr) → FlArray
  arr : FlArray
(flarray- arr0 arr1) → FlArray
  arr0 : FlArray
  arr1 : FlArray
procedure
(flarray/ arr) → FlArray
  arr : FlArray
(flarray/ arr0 arr1) → FlArray
  arr0 : FlArray
  arr1 : FlArray
procedure
(flarray-min arr0 arr1) → FlArray
  arr0 : FlArray
  arr1 : FlArray
procedure
(flarray-max arr0 arr1) → FlArray
  arr0 : FlArray
  arr1 : FlArray
procedure
(flarray-scale arr x) → FlArray
  arr : FlArray
  x : Flonum
procedure
(flarray-abs arr) → FlArray
  arr : FlArray
procedure
(flarray-sqr arr) → FlArray
  arr : FlArray
procedure
(flarray-sqrt arr) → FlArray
  arr : FlArray

Arithmetic lifted to flonum arrays.

6.15.2 Float-Complex Arrays

syntax
FCArray

The type of float-complex arrays, a subtype of (Settable-Array Float-Complex) that stores its elements in a pair of FlVectors. A float-complex array is always strict.

syntax
(fcarray #[#[...] ...])

Like array, but creates float-complex arrays. The listed elements must be numbers, and may be exact.

Examples:

> (fcarray 0.0)
- : FCArray
(fcarray 0.0+0.0i)
> (fcarray #['x])
eval:316:0: Type Checker: type mismatch
  expected: Number
  given: 'x
  in: #((quote x))
> (fcarray #[#[1 2+1i] #[3 4+3i]])
- : FCArray
(fcarray #[#[1.0+0.0i 2.0+1.0i] #[3.0+0.0i 4.0+3.0i]])

procedure
(array->fcarray arr) → FCArray
arr : (Array Number)

Returns a float-complex array that has approximately the same elements as arr. Exact elements will likely lose precision during conversion.

procedure
(fcarray-real-data arr) → FlVector
arr : FCArray
procedure
(fcarray-imag-data arr) → FlVector
arr : FCArray

Return the real and imaginary parts of arr’s elements in flonum vectors, in row-major order.

Examples:

> (define arr (fcarray #[#[1 2+1i] #[3 4+3i]]))
> (fcarray-real-data arr)
- : FlVector
(flvector 1.0 2.0 3.0 4.0)
> (fcarray-imag-data arr)
- : FlVector
(flvector 0.0 1.0 0.0 3.0)

procedure
(fcarray-map f arrs ...) → FCArray
f : (Float-Complex ... -> Float-Complex)
arrs : FCArray

Maps the function f over the arrays arrs. If the arrays do not have the same shape, they are broadcast first. If the arrays do have the same shape, this operation can be quite fast.

The function f is meant to accept the same number of arguments as the number of its following float-complex array arguments. However, a current limitation in Typed Racket requires f to accept any number of arguments. To map a single-arity function, for now, use inline-fcarray-map or array-map.

syntax
(inline-fcarray-map f arrs ...)

f : (Float-Complex ... -> Float-Complex)
arrs : FCArray

Like inline-array-map, but for float-complex arrays.

This is currently unavailable in untyped Racket.

procedure
(fcarray+ arr0 arr1) → FCArray
  arr0 : FCArray
  arr1 : FCArray
procedure
(fcarray* arr0 arr1) → FCArray
  arr0 : FCArray
  arr1 : FCArray
procedure
(fcarray- arr) → FCArray
  arr : FCArray
(fcarray- arr0 arr1) → FCArray
  arr0 : FCArray
  arr1 : FCArray
procedure
(fcarray/ arr) → FCArray
  arr : FCArray
(fcarray/ arr0 arr1) → FCArray
  arr0 : FCArray
  arr1 : FCArray
procedure
(fcarray-scale arr z) → FCArray
  arr : FCArray
  z : Float-Complex
procedure
(fcarray-sqr arr) → FCArray
  arr : FCArray
procedure
(fcarray-sqrt arr) → FCArray
  arr : FCArray
procedure
(fcarray-conjugate arr) → FCArray
  arr : FCArray

Arithmetic lifted to float-complex arrays.

procedure
(fcarray-real-part arr) → FlArray
  arr : FCArray
procedure
(fcarray-imag-part arr) → FlArray
  arr : FCArray
procedure
(fcarray-make-rectangular arr0 arr1) → FCArray
  arr0 : FlArray
  arr1 : FlArray
procedure
(fcarray-magnitude arr) → FlArray
  arr : FCArray
procedure
(fcarray-angle arr) → FlArray
  arr : FCArray
procedure
(fcarray-make-polar arr0 arr1) → FCArray
  arr0 : FlArray
  arr1 : FlArray

Conversions to and from complex numbers, lifted to flonum and float-complex arrays.

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1	Constants and Elementary Functions
2	Flonums
3	Special Functions
4	Number Theory
5	Arbitrary-Precision Floating-Point Numbers (Bigfloats)
6	Arrays
7	Matrices and Linear Algebra
8	Statistics Functions
9	Probability Distributions
10	Stuff That Doesn’t Belong Anywhere Else

6.1	Quick Start
6.2	Definitions
6.3	Broadcasting
6.4	Slicing
6.5	Nonstrict Arrays
6.6	Types, Predicates and Accessors
6.7	Construction
6.8	Conversion
6.9	Comprehensions and Sequences
6.10	Pointwise Operations
6.11	Indexing and Slicing
6.12	Transformations
6.13	Folds, Reductions and Expansions
6.14	Other Array Operations
6.15	Subtypes
6.16	Strictness