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## Copyright (c) Eduardo Julian. All rights reserved.
## This Source Code Form is subject to the terms of the Mozilla Public License, v. 2.0.
## If a copy of the MPL was not distributed with this file,
## You can obtain one at http://mozilla.org/MPL/2.0/.
(;module:
lux
(lux [math]
(control eq
[ord]
number
codec
monad)
(data [number "r:" Number<Real> Codec<Text,Real>]
[text "Text/" Monoid<Text>]
error
maybe
(struct [list "List/" Monad<List>]))
[compiler]
(macro [ast]
["s" syntax #+ syntax: Syntax])))
## Based on org.apache.commons.math4.complex.Complex
(type: #export Complex
{#real Real
#imaginary Real})
(syntax: #export (complex real {?imaginary (s;opt s;any)})
(wrap (list (` {#;;real (~ real)
#;;imaginary (~ (default (` 0.0)
?imaginary))}))))
(def: #export i Complex (complex 0.0 1.0))
(def: #export one Complex (complex 1.0 0.0))
(def: #export zero Complex (complex 0.0 0.0))
(def: #export (c= param input)
(-> Complex Complex Bool)
(and (=. (get@ #real param)
(get@ #real input))
(=. (get@ #imaginary param)
(get@ #imaginary input))))
(do-template [<name> <op>]
[(def: #export (<name> param input)
(-> Complex Complex Complex)
{#real (<op> (get@ #real param)
(get@ #real input))
#imaginary (<op> (get@ #imaginary param)
(get@ #imaginary input))})]
[c+ +.]
[c- -.]
)
(struct: #export _ (Eq Complex)
(def: = c=))
(def: #export negate
(-> Complex Complex)
(|>. (update@ #real r:negate)
(update@ #imaginary r:negate)))
(def: #export signum
(-> Complex Complex)
(|>. (update@ #real r:signum)
(update@ #imaginary r:signum)))
(def: #export conjugate
(-> Complex Complex)
(update@ #imaginary r:negate))
(def: #export (c*' param input)
(-> Real Complex Complex)
{#real (*. param
(get@ #real input))
#imaginary (*. param
(get@ #imaginary input))})
(def: #export (c* param input)
(-> Complex Complex Complex)
{#real (-. (*. (get@ #imaginary param)
(get@ #imaginary input))
(*. (get@ #real param)
(get@ #real input)))
#imaginary (+. (*. (get@ #real param)
(get@ #imaginary input))
(*. (get@ #imaginary param)
(get@ #real input)))})
(def: #export (c/ (^slots [#real #imaginary]) input)
(-> Complex Complex Complex)
(if (<. (r:abs imaginary)
(r:abs real))
(let [quot (/. imaginary real)
denom (|> real (*. quot) (+. imaginary))]
{#real (|> (get@ #real input) (*. quot) (+. (get@ #imaginary input)) (/. denom))
#imaginary (|> (get@ #imaginary input) (*. quot) (-. (get@ #real input)) (/. denom))})
(let [quot (/. real imaginary)
denom (|> imaginary (*. quot) (+. real))]
{#real (|> (get@ #imaginary input) (*. quot) (+. (get@ #real input)) (/. denom))
#imaginary (|> (get@ #imaginary input) (-. (*. quot (get@ #real input))) (/. denom))})))
(def: #export (c/' param (^slots [#real #imaginary]))
(-> Real Complex Complex)
{#real (/. param real)
#imaginary (/. param imaginary)})
(def: #export (cos (^slots [#real #imaginary]))
(-> Complex Complex)
{#real (*. (math;cosh imaginary)
(math;cos real))
#imaginary (*. (math;sinh imaginary)
(r:negate (math;sin real)))})
(def: #export (cosh (^slots [#real #imaginary]))
(-> Complex Complex)
{#real (*. (math;cos imaginary)
(math;cosh real))
#imaginary (*. (math;sin imaginary)
(math;sinh real))})
(def: #export (sin (^slots [#real #imaginary]))
(-> Complex Complex)
{#real (*. (math;cosh imaginary)
(math;sin real))
#imaginary (*. (math;sinh imaginary)
(math;cos real))})
(def: #export (sinh (^slots [#real #imaginary]))
(-> Complex Complex)
{#real (*. (math;cos imaginary)
(math;sinh real))
#imaginary (*. (math;sin imaginary)
(math;cosh real))})
(def: #export (tan (^slots [#real #imaginary]))
(-> Complex Complex)
(let [r2 (*. 2.0 real)
i2 (*. 2.0 imaginary)
d (+. (math;cos r2) (math;cosh i2))]
{#real (/. d (math;sin r2))
#imaginary (/. d (math;sinh i2))}))
(def: #export (tanh (^slots [#real #imaginary]))
(-> Complex Complex)
(let [r2 (*. 2.0 real)
i2 (*. 2.0 imaginary)
d (+. (math;cosh r2) (math;cos i2))]
{#real (/. d (math;sinh r2))
#imaginary (/. d (math;sin i2))}))
(def: #export (abs (^slots [#real #imaginary]))
(-> Complex Real)
(if (<. (r:abs imaginary)
(r:abs real))
(if (=. 0.0 imaginary)
(r:abs real)
(let [q (/. imaginary real)]
(*. (math;sqrt (+. 1.0 (*. q q)))
(r:abs imaginary))))
(if (=. 0.0 real)
(r:abs imaginary)
(let [q (/. real imaginary)]
(*. (math;sqrt (+. 1.0 (*. q q)))
(r:abs real))))
))
(def: #export (exp (^slots [#real #imaginary]))
(-> Complex Complex)
(let [r-exp (math;exp real)]
{#real (*. r-exp (math;cos imaginary))
#imaginary (*. r-exp (math;sin imaginary))}))
(def: #export (log (^@ input (^slots [#real #imaginary])))
(-> Complex Complex)
{#real (math;log (abs input))
#imaginary (math;atan2 real imaginary)})
(do-template [<name> <type> <op>]
[(def: #export (<name> param input)
(-> <type> Complex Complex)
(|> input log (<op> param) exp))]
[pow Complex c*]
[pow' Real c*']
)
(def: (copy-sign sign magnitude)
(-> Real Real Real)
(*. (r:signum sign) magnitude))
(def: #export (sqrt (^@ input (^slots [#real #imaginary])))
(-> Complex Complex)
(let [t (|> input abs (+. (r:abs real)) (/. 2.0) math;sqrt)]
(if (>=. 0.0 real)
{#real t
#imaginary (/. (*. 2.0 t)
imaginary)}
{#real (/. (*. 2.0 t)
(r:abs imaginary))
#imaginary (*. t (copy-sign imaginary 1.0))})))
(def: #export (sqrt-1z input)
(-> Complex Complex)
(|> (complex 1.0) (c- (c* input input)) sqrt))
(def: #export (reciprocal (^slots [#real #imaginary]))
(-> Complex Complex)
(if (<. (r:abs imaginary)
(r:abs real))
(let [q (/. imaginary real)
scale (/. (|> real (*. q) (+. imaginary))
1.0)]
{#real (*. q scale)
#imaginary (r:negate scale)})
(let [q (/. real imaginary)
scale (/. (|> imaginary (*. q) (+. real))
1.0)]
{#real scale
#imaginary (|> scale r:negate (*. q))})))
(def: #export (acos input)
(-> Complex Complex)
(|> input
(c+ (|> input sqrt-1z (c* i)))
log
(c* (negate i))))
(def: #export (asin input)
(-> Complex Complex)
(|> input
sqrt-1z
(c+ (c* i input))
log
(c* (negate i))))
(def: #export (atan input)
(-> Complex Complex)
(|> input
(c+ i)
(c/ (c- input i))
log
(c* (c/ (complex 2.0) i))))
(def: #export (argument (^slots [#real #imaginary]))
(-> Complex Real)
(math;atan2 real imaginary))
(def: #export (nth-root nth input)
(-> Nat Complex (List Complex))
(if (=+ +0 nth)
(list)
(let [r-nth (|> nth nat-to-int int-to-real)
nth-root-of-abs (math;pow (/. r-nth 1.0)
(abs input))
nth-phi (|> input argument (/. r-nth))
slice (|> math;pi (*. 2.0) (/. r-nth))]
(|> (list;range+ +0 (dec+ nth))
(List/map (lambda [nth']
(let [inner (|> nth' nat-to-int int-to-real
(*. slice)
(+. nth-phi))
real (*. nth-root-of-abs
(math;cos inner))
imaginary (*. nth-root-of-abs
(math;sin inner))]
{#real real
#imaginary imaginary})))))))
(struct: #export _ (Codec Text Complex)
(def: (encode (^slots [#real #imaginary]))
($_ Text/append "(" (r:encode real) ", " (r:encode imaginary) ")"))
(def: (decode input)
(case (do Monad<Maybe>
[input' (text;sub +1 (-+ +1 (text;size input)) input)]
(text;split-with "," input'))
#;None
(#;Left (Text/append "Wrong syntax for complex numbers: " input))
(#;Some [r' i'])
(do Monad<Error>
[r (r:decode (text;trim r'))
i (r:decode (text;trim i'))]
(wrap {#real r
#imaginary i}))
)))
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