5a43f2c6bc
Cleaned up other docs in preparation for alpha-testing announcement Created `math/utils' module for stuff that doesn't go anywhere else (e.g. FFT scaling convention, max-math-threads parameters) Reduced the number of macros that expand to applications of `array-map' Added `flvector-sum', defined `flsum' in terms of it Reduced the number of pointwise `flvector', `flarray' and `fcarray' operations Reworked `inline-build-flvector' and `inline-flvector-map' to be faster and expand to less code in both typed and untyped Racket Redefined conversions like `list->flvector' in terms of for loops (can do it now that TR has working `for/flvector:', etc.)
46 lines
1.8 KiB
Racket
46 lines
1.8 KiB
Racket
#lang scribble/manual
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@(require scribble/eval
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racket/sandbox
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(for-label racket/base racket/future
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math
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(only-in typed/racket/base
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Real Boolean Integer Natural Number Listof
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Positive-Flonum Float-Complex Any List Positive-Integer))
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"utils.rkt")
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@(define untyped-eval (make-untyped-math-eval))
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@title[#:tag "utils"]{Stuff That Doesn't Belong Anywhere Else}
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@(author-neil)
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@defmodule[math/utils]
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@defparam[max-math-threads num Positive-Integer]{
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The maximum number of threads a parallelized @racketmodname[math] function
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will use. The default value is @racket[(max 1 (processor-count))].
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}
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@defparam[dft-convention lst (List Real Real)]{
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A parameter controlling the convention used for scaling discrete Fourier transforms, such as those
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performed by @racket[array-fft]. The default value is @racket['(1 -1)], which represents the convention
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used in signal processing.
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In general, if @racket[lst] is @racket[(list a b)] and @racket[n] is the length of a transformed
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array axis or vector, then
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@itemlist[@item{Each sum is scaled by @racket[(expt n (/ (- a 1) 2))].}
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@item{Each exponential in the sum has its argument scaled by @racket[b].}]
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Conveniently, a Fourier transform with convention @racket[(list (- a) (- b))] is the inverse
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of a Fourier transform with convention @racket[(list a b)].
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See Mathematica's
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@hyperlink["http://reference.wolfram.com/mathematica/tutorial/FourierTransforms.html"]{documentation
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on @tt{Fourier}}, from which this excellent idea was stolen.
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}
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@defproc[(dft-inverse-convention) (List Real Real)]{
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Returns the convention used for inverse Fourier transforms, given the current convention.
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}
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@(close-eval untyped-eval)
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