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-rw-r--r--stdlib/source/test/lux/math/number/complex.lux288
1 files changed, 144 insertions, 144 deletions
diff --git a/stdlib/source/test/lux/math/number/complex.lux b/stdlib/source/test/lux/math/number/complex.lux
index a705bbb0e..d2e2d152a 100644
--- a/stdlib/source/test/lux/math/number/complex.lux
+++ b/stdlib/source/test/lux/math/number/complex.lux
@@ -50,20 +50,20 @@
[real ..dimension
imaginary ..dimension]
(all _.and
- (_.cover [/.complex]
- (and (let [r+i (/.complex real imaginary)]
- (and (f.= real (the /.#real r+i))
- (f.= imaginary (the /.#imaginary r+i))))
- (let [r+i (/.complex real)]
- (and (f.= real (the /.#real r+i))
- (f.= +0.0 (the /.#imaginary r+i))))))
- (_.cover [/.approximately?]
- (/.approximately? ..margin_of_error
- (/.complex real imaginary)
- (/.complex real imaginary)))
- (_.cover [/.not_a_number?]
- (and (/.not_a_number? (/.complex f.not_a_number imaginary))
- (/.not_a_number? (/.complex real f.not_a_number))))
+ (_.coverage [/.complex]
+ (and (let [r+i (/.complex real imaginary)]
+ (and (f.= real (the /.#real r+i))
+ (f.= imaginary (the /.#imaginary r+i))))
+ (let [r+i (/.complex real)]
+ (and (f.= real (the /.#real r+i))
+ (f.= +0.0 (the /.#imaginary r+i))))))
+ (_.coverage [/.approximately?]
+ (/.approximately? ..margin_of_error
+ (/.complex real imaginary)
+ (/.complex real imaginary)))
+ (_.coverage [/.not_a_number?]
+ (and (/.not_a_number? (/.complex f.not_a_number imaginary))
+ (/.not_a_number? (/.complex real f.not_a_number))))
)))
(def: constant
@@ -72,20 +72,20 @@
[sample ..random
dimension ..dimension]
(all _.and
- (_.cover [/.zero]
- (/.= /.zero (/.* /.zero sample)))
- (_.cover [/.+one]
- (/.= sample (/.* /.+one sample)))
- (_.cover [/.-one]
- (and (/.= /.zero
- (/.+ sample
- (/.* /.-one sample)))
- (/.= sample (/.* /.-one (/.* /.-one sample)))))
- (_.cover [/.i]
- (and (/.= (/.complex +0.0 dimension)
- (/.* /.i (/.complex dimension)))
- (/.= (/.* /.-one sample)
- (/.* /.i (/.* /.i sample)))))
+ (_.coverage [/.zero]
+ (/.= /.zero (/.* /.zero sample)))
+ (_.coverage [/.+one]
+ (/.= sample (/.* /.+one sample)))
+ (_.coverage [/.-one]
+ (and (/.= /.zero
+ (/.+ sample
+ (/.* /.-one sample)))
+ (/.= sample (/.* /.-one (/.* /.-one sample)))))
+ (_.coverage [/.i]
+ (and (/.= (/.complex +0.0 dimension)
+ (/.* /.i (/.complex dimension)))
+ (/.= (/.* /.-one sample)
+ (/.* /.i (/.* /.i sample)))))
)))
(def: absolute_value&argument
@@ -94,32 +94,32 @@
[real ..dimension
imaginary ..dimension]
(all _.and
- (_.cover [/.abs]
- (let [normal!
- (let [r+i (/.complex real imaginary)]
- (and (f.>= (f.abs real) (/.abs r+i))
- (f.>= (f.abs imaginary) (/.abs r+i))))
+ (_.coverage [/.abs]
+ (let [normal!
+ (let [r+i (/.complex real imaginary)]
+ (and (f.>= (f.abs real) (/.abs r+i))
+ (f.>= (f.abs imaginary) (/.abs r+i))))
- not_a_number!
- (and (f.not_a_number? (/.abs (/.complex f.not_a_number imaginary)))
- (f.not_a_number? (/.abs (/.complex real f.not_a_number))))
+ not_a_number!
+ (and (f.not_a_number? (/.abs (/.complex f.not_a_number imaginary)))
+ (f.not_a_number? (/.abs (/.complex real f.not_a_number))))
- infinity!
- (and (f.= f.positive_infinity (/.abs (/.complex f.positive_infinity imaginary)))
- (f.= f.positive_infinity (/.abs (/.complex real f.positive_infinity)))
- (f.= f.positive_infinity (/.abs (/.complex f.negative_infinity imaginary)))
- (f.= f.positive_infinity (/.abs (/.complex real f.negative_infinity))))]
- (and normal!
- not_a_number!
- infinity!)))
+ infinity!
+ (and (f.= f.positive_infinity (/.abs (/.complex f.positive_infinity imaginary)))
+ (f.= f.positive_infinity (/.abs (/.complex real f.positive_infinity)))
+ (f.= f.positive_infinity (/.abs (/.complex f.negative_infinity imaginary)))
+ (f.= f.positive_infinity (/.abs (/.complex real f.negative_infinity))))]
+ (and normal!
+ not_a_number!
+ infinity!)))
... https://en.wikipedia.org/wiki/Argument_(complex_analysis)#Identities
- (_.cover [/.argument]
- (let [sample (/.complex real imaginary)]
- (or (/.= /.zero sample)
- (/.approximately? ..margin_of_error
- sample
- (/.*' (/.abs sample)
- (/.exp (/.* /.i (/.complex (/.argument sample)))))))))
+ (_.coverage [/.argument]
+ (let [sample (/.complex real imaginary)]
+ (or (/.= /.zero sample)
+ (/.approximately? ..margin_of_error
+ sample
+ (/.*' (/.abs sample)
+ (/.exp (/.* /.i (/.complex (/.argument sample)))))))))
)))
(def: number
@@ -129,40 +129,40 @@
y ..random
factor ..dimension]
(all _.and
- (_.cover [/.+]
- (let [z (/.+ y x)]
- (and (/.= z
- (/.complex (f.+ (the /.#real y)
- (the /.#real x))
- (f.+ (the /.#imaginary y)
- (the /.#imaginary x)))))))
- (_.cover [/.-]
- (let [normal!
- (let [z (/.- y x)]
- (and (/.= z
- (/.complex (f.- (the /.#real y)
- (the /.#real x))
- (f.- (the /.#imaginary y)
- (the /.#imaginary x))))))
+ (_.coverage [/.+]
+ (let [z (/.+ y x)]
+ (and (/.= z
+ (/.complex (f.+ (the /.#real y)
+ (the /.#real x))
+ (f.+ (the /.#imaginary y)
+ (the /.#imaginary x)))))))
+ (_.coverage [/.-]
+ (let [normal!
+ (let [z (/.- y x)]
+ (and (/.= z
+ (/.complex (f.- (the /.#real y)
+ (the /.#real x))
+ (f.- (the /.#imaginary y)
+ (the /.#imaginary x))))))
- inverse!
- (and (|> x (/.+ y) (/.- y) (/.approximately? ..margin_of_error x))
- (|> x (/.- y) (/.+ y) (/.approximately? ..margin_of_error x)))]
- (and normal!
- inverse!)))
- (_.cover [/.* /./]
- (|> x (/.* y) (/./ y) (/.approximately? ..margin_of_error x)))
- (_.cover [/.*' /./']
- (|> x (/.*' factor) (/./' factor) (/.approximately? ..margin_of_error x)))
- (_.cover [/.%]
- (let [rem (/.% y x)
- quotient (|> x (/.- rem) (/./ y))
- floored (|> quotient
- (revised /.#real f.floor)
- (revised /.#imaginary f.floor))]
- (/.approximately? +0.000000000001
- x
- (|> quotient (/.* y) (/.+ rem)))))
+ inverse!
+ (and (|> x (/.+ y) (/.- y) (/.approximately? ..margin_of_error x))
+ (|> x (/.- y) (/.+ y) (/.approximately? ..margin_of_error x)))]
+ (and normal!
+ inverse!)))
+ (_.coverage [/.* /./]
+ (|> x (/.* y) (/./ y) (/.approximately? ..margin_of_error x)))
+ (_.coverage [/.*' /./']
+ (|> x (/.*' factor) (/./' factor) (/.approximately? ..margin_of_error x)))
+ (_.coverage [/.%]
+ (let [rem (/.% y x)
+ quotient (|> x (/.- rem) (/./ y))
+ floored (|> quotient
+ (revised /.#real f.floor)
+ (revised /.#imaginary f.floor))]
+ (/.approximately? +0.000000000001
+ x
+ (|> quotient (/.* y) (/.+ rem)))))
)))
(def: conjugate&reciprocal&signum&negation
@@ -170,38 +170,38 @@
(do random.monad
[x ..random]
(all _.and
- (_.cover [/.conjugate]
- (let [cx (/.conjugate x)]
- (and (f.= (the /.#real x)
- (the /.#real cx))
- (f.= (f.opposite (the /.#imaginary x))
- (the /.#imaginary cx)))))
- (_.cover [/.reciprocal]
- (let [reciprocal!
- (|> x (/.* (/.reciprocal x)) (/.approximately? ..margin_of_error /.+one))
-
- own_inverse!
- (|> x /.reciprocal /.reciprocal (/.approximately? ..margin_of_error x))]
- (and reciprocal!
- own_inverse!)))
- (_.cover [/.signum]
- ... Absolute value of signum is always root_2(2), 1 or 0.
- (let [signum_abs (|> x /.signum /.abs)]
- (or (f.= +0.0 signum_abs)
- (f.= +1.0 signum_abs)
- (f.= (f.pow +0.5 +2.0) signum_abs))))
- (_.cover [/.opposite]
- (let [own_inverse!
- (let [there (/.opposite x)
- back_again (/.opposite there)]
- (and (not (/.= there x))
- (/.= back_again x)))
+ (_.coverage [/.conjugate]
+ (let [cx (/.conjugate x)]
+ (and (f.= (the /.#real x)
+ (the /.#real cx))
+ (f.= (f.opposite (the /.#imaginary x))
+ (the /.#imaginary cx)))))
+ (_.coverage [/.reciprocal]
+ (let [reciprocal!
+ (|> x (/.* (/.reciprocal x)) (/.approximately? ..margin_of_error /.+one))
+
+ own_inverse!
+ (|> x /.reciprocal /.reciprocal (/.approximately? ..margin_of_error x))]
+ (and reciprocal!
+ own_inverse!)))
+ (_.coverage [/.signum]
+ ... Absolute value of signum is always root_2(2), 1 or 0.
+ (let [signum_abs (|> x /.signum /.abs)]
+ (or (f.= +0.0 signum_abs)
+ (f.= +1.0 signum_abs)
+ (f.= (f.pow +0.5 +2.0) signum_abs))))
+ (_.coverage [/.opposite]
+ (let [own_inverse!
+ (let [there (/.opposite x)
+ back_again (/.opposite there)]
+ (and (not (/.= there x))
+ (/.= back_again x)))
- absolute!
- (f.= (/.abs x)
- (/.abs (/.opposite x)))]
- (and own_inverse!
- absolute!)))
+ absolute!
+ (f.= (/.abs x)
+ (/.abs (/.opposite x)))]
+ (and own_inverse!
+ absolute!)))
)))
(def: (trigonometric_symmetry forward backward angle)
@@ -214,30 +214,30 @@
(do [! random.monad]
[angle ..angle]
(all _.and
- (_.cover [/.sin /.asin]
- (trigonometric_symmetry /.sin /.asin angle))
- (_.cover [/.cos /.acos]
- (trigonometric_symmetry /.cos /.acos angle))
- (_.cover [/.tan /.atan]
- (trigonometric_symmetry /.tan /.atan angle)))))
+ (_.coverage [/.sin /.asin]
+ (trigonometric_symmetry /.sin /.asin angle))
+ (_.coverage [/.cos /.acos]
+ (trigonometric_symmetry /.cos /.acos angle))
+ (_.coverage [/.tan /.atan]
+ (trigonometric_symmetry /.tan /.atan angle)))))
(def: hyperbolic
Test
(do [! random.monad]
[angle ..angle]
(all _.and
- (_.cover [/.sinh]
- (/.approximately? ..margin_of_error
- (|> angle (/.* /.i) /.sin (/.* /.i) (/.* /.-one))
- (/.sinh angle)))
- (_.cover [/.cosh]
- (/.approximately? ..margin_of_error
- (|> angle (/.* /.i) /.cos)
- (/.cosh angle)))
- (_.cover [/.tanh]
- (/.approximately? ..margin_of_error
- (|> angle (/.* /.i) /.tan (/.* /.i) (/.* /.-one))
- (/.tanh angle)))
+ (_.coverage [/.sinh]
+ (/.approximately? ..margin_of_error
+ (|> angle (/.* /.i) /.sin (/.* /.i) (/.* /.-one))
+ (/.sinh angle)))
+ (_.coverage [/.cosh]
+ (/.approximately? ..margin_of_error
+ (|> angle (/.* /.i) /.cos)
+ (/.cosh angle)))
+ (_.coverage [/.tanh]
+ (/.approximately? ..margin_of_error
+ (|> angle (/.* /.i) /.tan (/.* /.i) (/.* /.-one))
+ (/.tanh angle)))
)))
(def: exponentiation&logarithm
@@ -245,12 +245,12 @@
(do random.monad
[x ..random]
(all _.and
- (_.cover [/.pow /.root_2]
- (|> x (/.pow (/.complex +2.0)) /.root_2 (/.approximately? ..margin_of_error x)))
- (_.cover [/.pow']
- (|> x (/.pow' +2.0) (/.pow' +0.5) (/.approximately? ..margin_of_error x)))
- (_.cover [/.log /.exp]
- (|> x /.log /.exp (/.approximately? ..margin_of_error x)))
+ (_.coverage [/.pow /.root_2]
+ (|> x (/.pow (/.complex +2.0)) /.root_2 (/.approximately? ..margin_of_error x)))
+ (_.coverage [/.pow']
+ (|> x (/.pow' +2.0) (/.pow' +0.5) (/.approximately? ..margin_of_error x)))
+ (_.coverage [/.log /.exp]
+ (|> x /.log /.exp (/.approximately? ..margin_of_error x)))
)))
(def: root
@@ -258,11 +258,11 @@
(do [! random.monad]
[sample ..random
degree (|> random.nat (# ! each (|>> (n.max 1) (n.% 5))))]
- (_.cover [/.roots]
- (|> sample
- (/.roots degree)
- (list#each (/.pow' (|> degree .int int.frac)))
- (list.every? (/.approximately? ..margin_of_error sample))))))
+ (_.coverage [/.roots]
+ (|> sample
+ (/.roots degree)
+ (list#each (/.pow' (|> degree .int int.frac)))
+ (list.every? (/.approximately? ..margin_of_error sample))))))
(def: .public test
Test
generated by cgit v1.2.3 (git 2.25.1) at 2024-08-25 07:31:32 +0000