Merge pull request #282 from PolyMathOrg/refactor-quaternions-pt2

Refactor Quaternion Natural Log

Author: SergeStinckwich

src/Math-Quaternion/PMQuaternion.class.st

@@ -348,25 +348,21 @@ PMQuaternion >> k [
 
 { #category : #'mathematical functions' }
 PMQuaternion >> ln [
-	"Answer the receiver natural logarithm"
+
+	"Compute the natural logarithm."
 
 	| z |
 	z := self unreal abs.
-	^z isZero 
-		ifTrue: 
-			[self species 
-				qr: self abs ln
-				qi: (z arcTan: qr)
-				qj: 0
-				qk: 0]
-		ifFalse: 
-			[| theta |
-			theta := (z arcTan: qr) / z.
-			self species 
-				qr: self abs ln
-				qi: qi * theta
-				qj: qj * theta
-				qk: qk * theta]
+	^ z isZero
+		  ifTrue: [ 
+			  | vectorPart |
+			  vectorPart := 0 + (z arcTan: qr) i + qj j + qk k.
+			  self abs ln + vectorPart ]
+		  ifFalse: [ 
+			  | theta vectorPart |
+			  theta := (z arcTan: qr) / z.
+			  vectorPart := theta * (0 + qi i + qj j + qk k).
+			  self abs ln + vectorPart ]
 ]
 
 { #category : #'mathematical functions' }

src/Math-Tests-Quaternion/PMQuaternionTest.class.st

@@ -137,13 +137,6 @@ PMQuaternionTest >> testHash [
 	self assert: 1 k k hash equals: -1 hash
 ]
 
-{ #category : #running }
-PMQuaternionTest >> testLn [
-	| eps |
-	eps := 1.0e-6.
-	self assert: ((1 + 2 i) ln - (1 + 2 j k) ln) abs < eps
-]
-
 { #category : #running }
 PMQuaternionTest >> testLog [
 
@@ -160,6 +153,67 @@ PMQuaternionTest >> testLog [
 	self assert: (qln qk closeTo: qlg10ln qk)
 ]
 
+{ #category : #running }
+PMQuaternionTest >> testNaturalLogOfQuaternion [
+
+	"See https://en.wikipedia.org/wiki/Quaternion#cite_note-Särkkä2007-39 for more detail"
+
+	| quaternion naturalLogOfQuaternion expected vectorPartOfQuaternion |
+	quaternion := 3 + 4 i + 5 j + 6 k.
+	naturalLogOfQuaternion := quaternion ln.
+
+	vectorPartOfQuaternion := PMQuaternion
+		                      qr: 0
+		                      qi: 4
+		                      qj: 5
+		                      qk: 6.
+	expected := 86 sqrt ln
+	            + (vectorPartOfQuaternion / 77 sqrt * (3 / 86 sqrt) arcCos).
+
+	self assert: naturalLogOfQuaternion qr equals: expected qr.
+	self assert: naturalLogOfQuaternion qi equals: expected qi.
+	self assert: naturalLogOfQuaternion qj closeTo: expected qj.
+	self assert: naturalLogOfQuaternion qk equals: expected qk
+]
+
+{ #category : #running }
+PMQuaternionTest >> testNaturalLogOfQuaternionWithNoVectorPart [
+	| expected naturalLogOfQuaternion quaternionWithNoVector |
+	
+	quaternionWithNoVector := 5 + 0 i + 0 j + 0 k.
+	
+	naturalLogOfQuaternion := quaternionWithNoVector ln.
+	
+	expected := 5 ln + 0 i + 0 j + 0 k.
+	self assert: naturalLogOfQuaternion qr equals: expected qr.
+	self assert: naturalLogOfQuaternion qi equals: 0.
+	self assert: naturalLogOfQuaternion qj equals: 0.
+	self assert: naturalLogOfQuaternion qk equals: 0.
+]
+
+{ #category : #tests }
+PMQuaternionTest >> testNaturalLogOfQuaternionWithOnlyVectorPart [
+
+	"See https://en.wikipedia.org/wiki/Quaternion#cite_note-Särkkä2007-39 for more detail"
+
+	| quaternion naturalLogOfQuaternion expected expectedVectorPart |
+	quaternion := 0 + 7 i - 10 j + 23 k.
+	naturalLogOfQuaternion := quaternion ln.
+	expectedVectorPart := PMQuaternion
+		                      qr: 0
+		                      qi: 7
+		                      qj: -10
+		                      qk: 23.
+
+
+	expected := 678 sqrt ln + ((expectedVectorPart / 678 sqrt) * ((0 / 678 sqrt) arcCos)).
+
+	self assert: naturalLogOfQuaternion qr equals: expected qr.
+	self assert: naturalLogOfQuaternion qi equals: expected qi.
+	self assert: naturalLogOfQuaternion qj closeTo: expected qj.
+	self assert: naturalLogOfQuaternion qk equals: expected qk
+]
+
 { #category : #running }
 PMQuaternionTest >> testOne [
 	self assert: PMQuaternion one unreal isZero.
@@ -264,6 +318,15 @@ PMQuaternionTest >> testSinh [
 	self assert: ((1 + 2 i) sinh - (1 + 2 j k) sinh) abs < eps
 ]
 
+{ #category : #running }
+PMQuaternionTest >> testSquareOfQuaternion [
+| q expected |
+	q := 1 + 2 i - 3 j - 4 k.
+	expected := -28 + 4 i - 6 j - 8 k.
+
+	self assert: q squared equals: expected
+]
+
 { #category : #running }
 PMQuaternionTest >> testSubtractPolynomial [
 	| poly |