author | penk |
Mon, 10 Feb 2003 17:39:23 +0100 | |
changeset 7019 | 6591ea303fbd |
parent 6500 | d2ce5b0a1a78 |
child 7221 | b38093d749b3 |
permissions | -rw-r--r-- |
3637 | 1 |
" |
2 |
This is a Manchester Goodie. It is distributed freely on condition |
|
3 |
that you observe these conditions in respect of the whole Goodie, and on |
|
4 |
any significant part of it which is separately transmitted or stored: |
|
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parents:
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* You must ensure that every copy includes this notice, and that |
b3b0d0e3ce98
package-definitions fixed/updated
Claus Gittinger <cg@exept.de>
parents:
3637
diff
changeset
|
6 |
source and author(s) of the material are acknowledged. |
b3b0d0e3ce98
package-definitions fixed/updated
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parents:
3637
diff
changeset
|
7 |
* These conditions must be imposed on anyone who receives a copy. |
b3b0d0e3ce98
package-definitions fixed/updated
Claus Gittinger <cg@exept.de>
parents:
3637
diff
changeset
|
8 |
* The material shall not be used for commercial gain without the prior |
b3b0d0e3ce98
package-definitions fixed/updated
Claus Gittinger <cg@exept.de>
parents:
3637
diff
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|
9 |
written consent of the author(s). |
3637 | 10 |
|
11 |
For more information about the Manchester Goodies Library (from which |
|
12 |
this file was distributed) send e-mail: |
|
5287
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Claus Gittinger <cg@exept.de>
parents:
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To: goodies-lib@cs.man.ac.uk |
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package-definitions fixed/updated
Claus Gittinger <cg@exept.de>
parents:
3637
diff
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|
14 |
Subject: help |
3637 | 15 |
|
16 |
This is an additional goody-class, which is NOT covered by the |
|
17 |
ST/X license. It has been packaged with the ST/X distribution to |
|
18 |
make your live easier instead. NO WARRANTY. |
|
19 |
" |
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20 |
||
6500 | 21 |
"{ Package: 'stx:goodies' }" |
22 |
||
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ArithmeticValue subclass:#Complex |
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instanceVariableNames:'real imaginary' |
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classVariableNames:'' |
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poolDictionaries:'' |
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category:'Magnitude-Numbers' |
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! |
29 |
||
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!Complex class methodsFor:'documentation'! |
31 |
||
32 |
copyright |
|
33 |
" |
|
34 |
This is a Manchester Goodie. It is distributed freely on condition |
|
35 |
that you observe these conditions in respect of the whole Goodie, and on |
|
36 |
any significant part of it which is separately transmitted or stored: |
|
5287
b3b0d0e3ce98
package-definitions fixed/updated
Claus Gittinger <cg@exept.de>
parents:
3637
diff
changeset
|
37 |
* You must ensure that every copy includes this notice, and that |
b3b0d0e3ce98
package-definitions fixed/updated
Claus Gittinger <cg@exept.de>
parents:
3637
diff
changeset
|
38 |
source and author(s) of the material are acknowledged. |
b3b0d0e3ce98
package-definitions fixed/updated
Claus Gittinger <cg@exept.de>
parents:
3637
diff
changeset
|
39 |
* These conditions must be imposed on anyone who receives a copy. |
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package-definitions fixed/updated
Claus Gittinger <cg@exept.de>
parents:
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diff
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|
40 |
* The material shall not be used for commercial gain without the prior |
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Claus Gittinger <cg@exept.de>
parents:
3637
diff
changeset
|
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written consent of the author(s). |
3637 | 42 |
|
43 |
For more information about the Manchester Goodies Library (from which |
|
44 |
this file was distributed) send e-mail: |
|
5287
b3b0d0e3ce98
package-definitions fixed/updated
Claus Gittinger <cg@exept.de>
parents:
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diff
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To: goodies-lib@cs.man.ac.uk |
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package-definitions fixed/updated
Claus Gittinger <cg@exept.de>
parents:
3637
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|
46 |
Subject: help |
3637 | 47 |
|
48 |
This is an additional goody-class, which is NOT covered by the |
|
49 |
ST/X license. It has been packaged with the ST/X distribution to |
|
50 |
make your live easier instead. NO WARRANTY. |
|
51 |
" |
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! |
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||
54 |
documentation |
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" |
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This is an implementation of complex numbers. A complex number has real and |
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imaginary parts which must be manipulated simultaneously in any numeric processing. |
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Complex numbers can be used in many of the same places that regular numbers |
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can be used with one major exception of comparisons, since complex numbers cannot |
60 |
be directly compared for size (except through lengths of vectors (see absolute |
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value)). |
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||
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Instance variables: |
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real <Number> the part of the number which can be expressed as a Real number |
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imaginary <Number> the part of the number which, in terms of how the number behaves, |
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has been multiplied by 'i' (-1 sqrt) |
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Author: Kurt Hebel (hebel@uinova.cerl.uiuc.edu) |
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" |
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! |
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||
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example |
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" |
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(5 % 7) real |
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(5 % 7) imaginary |
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(5 % 7) = 5 |
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(5 % 0) = 5 |
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(5.0 % 0) = 5 |
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" |
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! ! |
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!Complex class methodsFor:'instance creation'! |
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fromReal: aNumber |
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"Create a new complex number from the given real number." |
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^ self basicNew setReal: aNumber setImaginary: 0 |
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! |
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|
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real: u imaginary: v |
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"Create a new complex number with the given real and imaginary parts. If the |
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imaginary part is zero, return the real part of the number." |
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^v = 0 ifTrue: [u] |
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ifFalse: [self basicNew setReal: u setImaginary: v] |
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! ! |
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95 |
|
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!Complex class methodsFor:'constants access'! |
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|
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unity |
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"Answer the value which allows, for any given arithmetic value, the following to be true |
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aNumber * aNumber class unity = aNumber |
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|
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This must be true regardless of how a given subclass chooses to define #*" |
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|
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^self fromReal: 1 |
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! |
107 |
||
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zero |
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"Answer the value which allows, for any given arithmetic value, the following to be true |
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|
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aNumber + aNumber class zero = aNumber |
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|
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This must be true regardless of how a given subclass chooses to define #+" |
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|
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^self fromReal: 0 |
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! ! |
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|
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!Complex class methodsFor:'exception handling'! |
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|
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trapImaginary: aBlock |
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"Complex trapImaginary: [-27 sqrt]" |
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|
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| send | |
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|
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^Number domainErrorSignal handle: [ :ex | |
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send := ex parameter. |
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(send selector = #sqrt or: [send selector = #sqrtTruncated]) ifTrue: [ |
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128 |
send receiver: send receiver asComplex. |
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ex proceedWith: send value |
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] ifFalse: [ |
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ex reject |
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] |
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] do: aBlock |
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! ! |
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|
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!Complex methodsFor:'accessing'! |
265 | 137 |
|
138 |
imaginary |
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"Return the imaginary part of the complex number." |
140 |
^ imaginary |
|
265 | 141 |
! |
142 |
||
143 |
real |
|
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"Return the real part of the complex number." |
145 |
^ real |
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! ! |
147 |
||
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!Complex methodsFor:'arithmetic'! |
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|
150 |
* aNumber |
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"Return the product of the receiver and the argument." |
265 | 152 |
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| u v r i | |
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aNumber isComplex ifTrue:[ |
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u := aNumber real. |
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v := aNumber imaginary. |
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r := (real * u) - (imaginary * v). |
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i := (real * v) + (imaginary * u). |
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i = 0 ifTrue:[ ^ r ]. |
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^ Complex real:r imaginary:i |
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]. |
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^ self retry: #* coercing: aNumber |
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|
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"Modified: / 8.7.1998 / 12:12:37 / cg" |
265 | 166 |
! |
167 |
||
168 |
+ aNumber |
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"Return the sum of the receiver and the argument." |
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171 |
| r i | |
265 | 172 |
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aNumber isComplex ifTrue: [ |
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174 |
r := aNumber real + real. |
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175 |
i := aNumber imaginary + imaginary. |
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i = 0 ifTrue:[ ^ r ]. |
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^ Complex real:r imaginary:i |
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178 |
]. |
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^ self retry: #+ coercing: aNumber |
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181 |
"Modified: / 8.7.1998 / 12:15:42 / cg" |
265 | 182 |
! |
183 |
||
184 |
- aNumber |
|
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185 |
"Return the difference of the receiver and the argument." |
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186 |
|
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187 |
| r i | |
265 | 188 |
|
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189 |
aNumber isComplex ifTrue: [ |
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|
190 |
r := real - aNumber real. |
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191 |
i := imaginary - aNumber imaginary. |
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|
192 |
i = 0 ifTrue:[ ^ r ]. |
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193 |
^ Complex real:r imaginary:i. |
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194 |
]. |
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195 |
^ self retry: #- coercing: aNumber |
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|
196 |
|
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197 |
"Modified: / 8.7.1998 / 12:15:38 / cg" |
265 | 198 |
! |
199 |
||
200 |
/ aNumber |
|
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201 |
"Return the quotient of the receiver and the argument." |
265 | 202 |
|
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|
203 |
| denom u v r i | |
265 | 204 |
|
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205 |
aNumber isComplex ifTrue:[ |
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206 |
u := aNumber real. |
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|
207 |
v := aNumber imaginary. |
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|
208 |
denom := u * u + (v * v). |
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|
209 |
r := u * real + (v * imaginary) / denom. |
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|
210 |
i := u * imaginary - (v * real) / denom. |
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|
211 |
i = 0 ifTrue:[ ^ r ]. |
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|
212 |
^ Complex real:r imaginary:i |
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|
213 |
]. |
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|
214 |
^ self retry: #/ coercing: aNumber |
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|
215 |
|
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|
216 |
"Modified: / 8.7.1998 / 12:15:34 / cg" |
265 | 217 |
! |
218 |
||
219 |
abs |
|
1944 | 220 |
"Return the magnitude (or absolute value) of the complex number." |
265 | 221 |
|
1944 | 222 |
^ (real * real + (imaginary * imaginary)) sqrt |
265 | 223 |
! |
224 |
||
225 |
conjugated |
|
1944 | 226 |
"Return the complex conjugate of this complex number." |
265 | 227 |
|
1944 | 228 |
^ Complex real: real imaginary: imaginary negated |
265 | 229 |
! ! |
230 |
||
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|
231 |
!Complex methodsFor:'coercing'! |
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|
232 |
|
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233 |
coerce: aNumber |
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|
234 |
|
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|
235 |
^aNumber asComplex |
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|
236 |
! |
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|
237 |
|
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|
238 |
generality |
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|
239 |
|
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|
240 |
^150 |
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|
241 |
! ! |
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|
242 |
|
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|
243 |
!Complex methodsFor:'comparing'! |
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|
244 |
|
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|
245 |
< aNumber |
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|
246 |
^Number |
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|
247 |
raise: #unorderedSignal |
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|
248 |
receiver: self |
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|
249 |
selector: #< |
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|
250 |
arg: aNumber |
6500 | 251 |
errorString: 'Complex numbers are not well ordered' |
252 |
! |
|
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|
253 |
|
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|
254 |
= aNumber |
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|
255 |
^ (aNumber real = real) and:[aNumber imaginary = imaginary] |
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|
256 |
! |
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|
257 |
|
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|
258 |
hash |
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|
259 |
"Hash is implemented because equals is implemented." |
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|
260 |
|
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|
261 |
^ real hash |
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|
262 |
! ! |
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|
263 |
|
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|
264 |
!Complex methodsFor:'converting'! |
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1944
diff
changeset
|
265 |
|
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|
266 |
asComplex |
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|
267 |
|
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|
268 |
^self |
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|
269 |
! |
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|
270 |
|
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|
271 |
asFloat |
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|
272 |
|
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|
273 |
imaginary = 0 ifTrue: [^real asFloat]. |
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|
274 |
^Number |
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|
275 |
raise: #coercionErrorSignal |
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|
276 |
receiver: self |
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|
277 |
selector: #asFloat |
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|
278 |
errorString: 'Can''t coerce an instance of Complex to a Float' |
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|
279 |
! |
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|
280 |
|
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|
281 |
asInteger |
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|
282 |
|
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|
283 |
imaginary = 0 ifTrue: [^real asInteger]. |
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|
284 |
^Number |
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|
285 |
raise: #coercionErrorSignal |
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|
286 |
receiver: self |
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|
287 |
selector: #asInteger |
89f1f31527f4
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changeset
|
288 |
errorString: 'Can''t coerce an instance of Complex to an Integer' |
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|
289 |
! |
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changeset
|
290 |
|
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|
291 |
asPoint |
89f1f31527f4
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parents:
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diff
changeset
|
292 |
"Return the complex number as a point." |
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|
293 |
^ real @ imaginary |
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|
294 |
! |
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|
295 |
|
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|
296 |
reduceGeneralityIfPossible |
89f1f31527f4
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diff
changeset
|
297 |
"Answer the receiver transformed to a lower generality, if such a |
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|
298 |
transformation is possible without losing information. If not, answer |
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|
299 |
the receiver" |
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|
300 |
|
89f1f31527f4
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changeset
|
301 |
imaginary isZero |
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|
302 |
ifTrue: [^real] |
89f1f31527f4
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|
303 |
ifFalse: [^self] |
89f1f31527f4
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|
304 |
! ! |
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changeset
|
305 |
|
89f1f31527f4
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Claus Gittinger <cg@exept.de>
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changeset
|
306 |
!Complex methodsFor:'double dispatching'! |
265 | 307 |
|
308 |
differenceFromFloat: argument |
|
1944 | 309 |
^ argument asComplex - self |
265 | 310 |
! |
311 |
||
312 |
differenceFromFraction: argument |
|
1944 | 313 |
^ argument asComplex - self |
265 | 314 |
! |
315 |
||
316 |
differenceFromInteger: argument |
|
1944 | 317 |
^ argument asComplex - self |
265 | 318 |
! |
319 |
||
320 |
productFromFloat: argument |
|
1944 | 321 |
^ argument asComplex * self |
265 | 322 |
! |
323 |
||
324 |
productFromFraction: argument |
|
1944 | 325 |
^ argument asComplex * self |
265 | 326 |
! |
327 |
||
328 |
productFromInteger: argument |
|
1944 | 329 |
^ argument asComplex * self |
265 | 330 |
! |
331 |
||
332 |
quotientFromFloat: argument |
|
1944 | 333 |
^ argument asComplex / self |
265 | 334 |
! |
335 |
||
336 |
quotientFromFraction: argument |
|
1944 | 337 |
^ argument asComplex / self |
265 | 338 |
! |
339 |
||
340 |
quotientFromInteger: argument |
|
1944 | 341 |
^ argument asComplex / self |
265 | 342 |
! |
343 |
||
344 |
sumFromFloat: argument |
|
1944 | 345 |
^ argument asComplex + self |
265 | 346 |
! |
347 |
||
348 |
sumFromFraction: argument |
|
1944 | 349 |
^ argument asComplex + self |
265 | 350 |
! |
351 |
||
352 |
sumFromInteger: argument |
|
1944 | 353 |
^ argument asComplex + self |
265 | 354 |
! ! |
355 |
||
3633
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
356 |
!Complex methodsFor:'mathematical functions'! |
265 | 357 |
|
358 |
angle |
|
1944 | 359 |
"Return the radian angle for this Complex number." |
265 | 360 |
|
1944 | 361 |
real < 0 ifTrue: [ |
362 |
imaginary < 0 ifTrue: [ |
|
363 |
^ (imaginary / real) arcTan - Float pi |
|
364 |
]. |
|
365 |
^ Float pi + (imaginary / real) arcTan |
|
366 |
]. |
|
367 |
^ (imaginary / real) arcTan |
|
265 | 368 |
! |
369 |
||
370 |
exp |
|
1944 | 371 |
"Return the complex exponential of the receiver." |
265 | 372 |
|
1944 | 373 |
^ imaginary cos % imaginary sin * real exp |
265 | 374 |
! |
375 |
||
376 |
sqrt |
|
1944 | 377 |
"Return the square root of the receiver" |
265 | 378 |
|
1944 | 379 |
| u v | |
380 |
(imaginary = 0 and: [real >= 0]) ifTrue: [^real sqrt]. |
|
381 |
v := (self abs - real / 2) sqrt. |
|
382 |
u := imaginary / 2 / v. |
|
383 |
^Complex real: u imaginary: v |
|
265 | 384 |
|
1944 | 385 |
"-4 asComplex sqrt" |
386 |
"-4 asComplex sqrt squared" |
|
265 | 387 |
! ! |
388 |
||
3633
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
389 |
!Complex methodsFor:'printing'! |
265 | 390 |
|
3633
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
391 |
printOn: aStream |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
392 |
aStream nextPut: $(. |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
393 |
real storeOn: aStream. |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
394 |
aStream nextPutAll: '%'. |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
395 |
imaginary storeOn: aStream. |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
396 |
aStream nextPut: $). |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
397 |
! |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
398 |
|
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
399 |
printString |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
400 |
^ '(' , real printString, '%', imaginary printString, ')' |
265 | 401 |
! |
402 |
||
3633
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
403 |
storeOn: aStream |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
404 |
aStream nextPut: $(. |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
405 |
real storeOn: aStream. |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
406 |
aStream nextPutAll: '%'. |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
407 |
imaginary storeOn: aStream. |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
408 |
aStream nextPut: $). |
265 | 409 |
! ! |
410 |
||
3633
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
411 |
!Complex methodsFor:'private'! |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
412 |
|
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
413 |
setReal: u setImaginary: v |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
414 |
real := u. |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
415 |
imaginary := v. |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
416 |
! ! |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
417 |
|
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
418 |
!Complex methodsFor:'testing'! |
265 | 419 |
|
420 |
isComplex |
|
421 |
||
1944 | 422 |
^true |
265 | 423 |
! |
424 |
||
425 |
isReal |
|
1944 | 426 |
"Return true if this Complex number has a zero imaginary part." |
427 |
^ imaginary = 0 |
|
265 | 428 |
! |
429 |
||
430 |
isZero |
|
1944 | 431 |
"Answer whether 'self = self class zero'. We can't use #= because |
432 |
#= is defined in terms of #isZero" |
|
265 | 433 |
|
1944 | 434 |
^real isZero and: [imaginary isZero] |
265 | 435 |
! |
436 |
||
437 |
sign |
|
438 |
||
1944 | 439 |
^Complex real: real sign imaginary: imaginary sign |
265 | 440 |
! ! |
441 |
||
3637 | 442 |
!Complex class methodsFor:'documentation'! |
443 |
||
444 |
version |
|
6500 | 445 |
^ '$Header: /cvs/stx/stx/libbasic/Complex.st,v 1.6 2002-04-11 14:03:42 cg Exp $' |
3637 | 446 |
! ! |