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core.clj
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(ns hypercomplex.core
(:import
(org.apache.commons.math3.complex
Complex)))
(set! *unchecked-math* true)
(set! *warn-on-reflection* true)
(defprotocol Nion
(init [this])
(c [this])
(times [this other])
(neg [this])
(plus [this other])
(minus [this other])
(valid-idx? [this idx])
(get-idx [this idx])
(set-idx [this idx new-val]))
(defprotocol NionOps
(mag [this])
(scale [this s])
(norm [this])
(inv [this])
(rot [this other]))
(defn- nion-ops-mag
[this]
(->
this
norm
Math/sqrt))
(defn- nion-ops-scale
[this s]
(loop [new-this this
idx (dec (:order this))]
(let [new-new-this (set-idx
new-this
idx
(*
s
(get-idx new-this idx)))]
(if (pos? idx)
(recur new-new-this (dec idx))
new-new-this))))
(defn- nion-ops-norm
[this]
(loop [sum 0.0
idx (dec (:order this))]
(let [new-sum (+
sum
(* (get-idx this idx)
(get-idx this idx)))]
(if (pos? idx)
(recur new-sum (dec idx))
new-sum))))
(defn- nion-ops-inv
[this]
(scale (c this)
(/ 1.0
(norm this))))
(defn- nion-ops-rot
[this other]
(times
(times other
this)
(inv other)))
(defn eq-order?
[a b]
(and
(:order a)
(:order b)
(= (:order a)
(:order b))))
(defrecord Complex2Apache
[a b]
Nion
(init
[this]
(assoc this
:order 2
:obj (Complex. a b)))
(c
[this]
(let [cpx-cnj (.conjugate ^Complex (:obj this))]
(assoc this
:obj cpx-cnj
:a (.getReal cpx-cnj)
:b (.getImaginary cpx-cnj))))
(neg
[this]
(let [cpx-neg (.negate ^Complex (:obj this))]
(assoc this
:obj cpx-neg
:a (.getReal ^Complex cpx-neg)
:b (.getImaginary ^Complex cpx-neg))))
(times
[this other]
(let [cpx-times (.multiply
^Complex (:obj this)
^Complex (:obj other))]
(assoc this
:obj cpx-times
:a (.getReal ^Complex cpx-times)
:b (.getImaginary ^Complex cpx-times))))
(plus
[this other]
(let [cpx-add (.add
^Complex (:obj this)
^Complex (:obj other))]
(assoc this
:obj cpx-add
:a (.getReal ^Complex cpx-add)
:b (.getImaginary ^Complex cpx-add))))
(minus
[this other]
(let [cpx-subtract (.subtract
^Complex (:obj this)
^Complex (:obj other))]
(assoc this
:obj cpx-subtract
:a (.getReal ^Complex cpx-subtract)
:b (.getImaginary ^Complex cpx-subtract))))
(valid-idx?
[this idx]
"Throws exception when index is invalid.
For a Complex2 type, index can only be 0 or 1 (a or b in a+bi)."
(if-not
(and
(contains? #{0 1} idx)
(:order this))
(do
(throw
(ex-info
(str "Complex2 Index must be int 0 or 1: " idx)
{:type :invalid-index-access}))
false)
true))
(get-idx
[this idx]
(when (valid-idx? this idx)
(if (< idx
(/ (:order this)
2))
(:a this)
(:b this))))
(set-idx
[this idx new-val]
(when (valid-idx? this idx)
(if (< idx
(/ (:order this)
2))
(assoc this :a new-val
:obj (Complex. new-val (:b this)))
(assoc this :b new-val
:obj (Complex. (:a this) new-val)))))
NionOps
(mag
[this]
(nion-ops-mag this))
(scale
[this s]
(nion-ops-scale this s))
(norm
[this]
(nion-ops-norm this))
(inv
[this]
(nion-ops-inv this))
(rot
[this other]
(nion-ops-rot this other)))
(defrecord Complex2
[a b]
Nion
(init
[this]
(assoc this :order 2))
(c
[this]
(assoc this :b (* -1
(:b this))))
(neg
[this]
(assoc this :a (* -1
(:a this))
:b (* -1
(:b this))))
(times
[this other]
(assoc this :a (- (* (:a this) (:a other))
(* (:b other) (:b this)))
:b (+ (* (:a this) (:b other))
(* (:a other) (:b this)))))
(plus
[this other]
(assoc this :a (+ (:a this)
(:a other))
:b (+ (:b this)
(:b other))))
(minus
[this other]
(plus this (neg other)))
(valid-idx?
[this idx]
(if-not
(and
(contains? #{0 1} idx)
(:order this))
(do
(throw
(ex-info
(str
"Complex2 Index must be int 0 or 1: "
idx)
{:type :invalid-index-access}))
false)
true))
(get-idx
[this idx]
(when (valid-idx? this idx)
(if (< idx
(/ (:order this)
2))
(:a this)
(:b this))))
(set-idx
[this idx new-val]
(when (valid-idx? this idx)
(if (< idx
(/ (:order this)
2))
(assoc this :a new-val)
(assoc this :b new-val))))
NionOps
(mag
[this]
(nion-ops-mag this))
(scale
[this s]
(nion-ops-scale this s))
(norm
[this]
(nion-ops-norm this))
(inv
[this]
(nion-ops-inv this))
(rot
[this other]
(nion-ops-rot this other)))
(defrecord Construction
[a b]
Nion
(init
[this]
(if-not (eq-order? a b)
(throw
(ex-info
(str
"Orders of a and b must match to init hypercomplex: "
a b)
{:type :orders-mismatch}))
(assoc this
:order (* 2 (:order a)))))
(c
[this]
(assoc this :a (c (:a this))
:b (neg (:b this))))
(times
[this other]
(if-not (eq-order? this other)
(throw
(ex-info
(str
"Orders of this and other must match to multiply hypercomplex: "
this other)
{:type :orders-mismatch}))
(assoc this :a (minus
(times (:a this) (:a other))
(times (c (:b other)) (:b this)))
:b (plus
(times (:b other) (:a this))
(times (:b this) (c (:a other)))))))
(neg
[this]
(assoc this :a (neg (:a this))
:b (neg (:b this))))
(plus
[this other]
(if-not (eq-order? this other)
(throw
(ex-info
(str
"Orders of this and other must match to add hypercomplex: "
this other)
{:type :orders-mismatch}))
(assoc this :a (plus (:a this)
(:a other))
:b (plus (:b this)
(:b other)))))
(minus
[this other]
(plus this (neg other)))
(valid-idx?
[this idx]
(if-not (and
(:order this)
(= idx
(int idx))
(>= idx 0)
(<= idx (:order this)))
(do
(throw
(ex-info
(str
"Construction index must be less than order: "
idx (:order this))
{:type :invalid-index-access}))
false)
true))
(get-idx
[this idx]
(when (valid-idx? this idx)
(let [half-order (/ (:order this)
2)
new-idx (rem idx half-order)
retval (if (< idx half-order)
(get-idx (:a this) new-idx)
(get-idx (:b this) new-idx))]
retval)))
(set-idx
[this idx new-val]
(when (valid-idx? this idx)
(let [half-order (/ (:order this)
2)
new-idx (rem idx half-order)]
(if (< idx half-order)
(update-in this [:a] set-idx new-idx new-val)
(update-in this [:b] set-idx new-idx new-val)))))
NionOps
(mag
[this]
(nion-ops-mag this))
(scale
[this s]
(nion-ops-scale this s))
(norm
[this]
(nion-ops-norm this))
(inv
[this]
(nion-ops-inv this))
(rot
[this other]
(nion-ops-rot this other)))
(defn init-complex2
[a b impl]
(case impl
:plain (init
(->Complex2 a b))
:apache (init
(->Complex2Apache a b))))
(defn init-construction
[a b]
(init
(->Construction a b)))