author | Claus Gittinger <cg@exept.de> |
Tue, 26 Oct 1999 20:45:29 +0200 | |
changeset 4944 | e06f2428c0a4 |
parent 3637 | 2b4d733c9a01 |
child 5287 | b3b0d0e3ce98 |
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: |
|
5 |
* You must ensure that every copy includes this notice, and that |
|
6 |
source and author(s) of the material are acknowledged. |
|
7 |
* These conditions must be imposed on anyone who receives a copy. |
|
8 |
* The material shall not be used for commercial gain without the prior |
|
9 |
written consent of the author(s). |
|
10 |
||
11 |
For more information about the Manchester Goodies Library (from which |
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this file was distributed) send e-mail: |
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To: goodies-lib@cs.man.ac.uk |
|
14 |
Subject: help |
|
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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||
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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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! |
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||
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!Complex class methodsFor:'documentation'! |
29 |
||
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copyright |
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" |
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This is a Manchester Goodie. It is distributed freely on condition |
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33 |
that you observe these conditions in respect of the whole Goodie, and on |
|
34 |
any significant part of it which is separately transmitted or stored: |
|
35 |
* You must ensure that every copy includes this notice, and that |
|
36 |
source and author(s) of the material are acknowledged. |
|
37 |
* These conditions must be imposed on anyone who receives a copy. |
|
38 |
* The material shall not be used for commercial gain without the prior |
|
39 |
written consent of the author(s). |
|
40 |
||
41 |
For more information about the Manchester Goodies Library (from which |
|
42 |
this file was distributed) send e-mail: |
|
43 |
To: goodies-lib@cs.man.ac.uk |
|
44 |
Subject: help |
|
45 |
||
46 |
This is an additional goody-class, which is NOT covered by the |
|
47 |
ST/X license. It has been packaged with the ST/X distribution to |
|
48 |
make your live easier instead. NO WARRANTY. |
|
49 |
" |
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! |
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||
52 |
documentation |
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53 |
" |
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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. |
56 |
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 |
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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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!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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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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!Complex class methodsFor:'constants access'! |
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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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This must be true regardless of how a given subclass chooses to define #*" |
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^self fromReal: 1 |
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! |
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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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aNumber + aNumber class zero = aNumber |
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This must be true regardless of how a given subclass chooses to define #+" |
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^self fromReal: 0 |
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! ! |
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105 |
|
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!Complex class methodsFor:'exception handling'! |
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107 |
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trapImaginary: aBlock |
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"Complex trapImaginary: [-27 sqrt]" |
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| send | |
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112 |
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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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send receiver: send receiver asComplex. |
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117 |
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'! |
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imaginary |
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"Return the imaginary part of the complex number." |
128 |
^ imaginary |
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! |
130 |
||
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real |
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"Return the real part of the complex number." |
133 |
^ real |
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! ! |
135 |
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!Complex methodsFor:'arithmetic'! |
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* aNumber |
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"Return the product of the receiver and the argument." |
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141 |
| u v r i | |
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aNumber isComplex ifTrue:[ |
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144 |
u := aNumber real. |
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145 |
v := aNumber imaginary. |
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146 |
r := (real * u) - (imaginary * v). |
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i := (real * v) + (imaginary * u). |
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148 |
i = 0 ifTrue:[ ^ r ]. |
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149 |
^ Complex real:r imaginary:i |
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150 |
]. |
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151 |
^ self retry: #* coercing: aNumber |
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152 |
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"Modified: / 8.7.1998 / 12:12:37 / cg" |
265 | 154 |
! |
155 |
||
156 |
+ aNumber |
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157 |
"Return the sum of the receiver and the argument." |
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158 |
|
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159 |
| r i | |
265 | 160 |
|
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161 |
aNumber isComplex ifTrue: [ |
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162 |
r := aNumber real + real. |
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163 |
i := aNumber imaginary + imaginary. |
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164 |
i = 0 ifTrue:[ ^ r ]. |
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165 |
^ Complex real:r imaginary:i |
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166 |
]. |
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^ self retry: #+ coercing: aNumber |
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168 |
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"Modified: / 8.7.1998 / 12:15:42 / cg" |
265 | 170 |
! |
171 |
||
172 |
- aNumber |
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173 |
"Return the difference of the receiver and the argument." |
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174 |
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175 |
| r i | |
265 | 176 |
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177 |
aNumber isComplex ifTrue: [ |
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178 |
r := real - aNumber real. |
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179 |
i := imaginary - aNumber imaginary. |
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i = 0 ifTrue:[ ^ r ]. |
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181 |
^ Complex real:r imaginary:i. |
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182 |
]. |
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183 |
^ self retry: #- coercing: aNumber |
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184 |
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185 |
"Modified: / 8.7.1998 / 12:15:38 / cg" |
265 | 186 |
! |
187 |
||
188 |
/ aNumber |
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189 |
"Return the quotient of the receiver and the argument." |
265 | 190 |
|
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191 |
| denom u v r i | |
265 | 192 |
|
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193 |
aNumber isComplex ifTrue:[ |
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|
194 |
u := aNumber real. |
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|
195 |
v := aNumber imaginary. |
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|
196 |
denom := u * u + (v * v). |
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|
197 |
r := u * real + (v * imaginary) / denom. |
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198 |
i := u * imaginary - (v * real) / denom. |
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|
199 |
i = 0 ifTrue:[ ^ r ]. |
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|
200 |
^ Complex real:r imaginary:i |
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|
201 |
]. |
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|
202 |
^ self retry: #/ coercing: aNumber |
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|
203 |
|
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|
204 |
"Modified: / 8.7.1998 / 12:15:34 / cg" |
265 | 205 |
! |
206 |
||
207 |
abs |
|
1944 | 208 |
"Return the magnitude (or absolute value) of the complex number." |
265 | 209 |
|
1944 | 210 |
^ (real * real + (imaginary * imaginary)) sqrt |
265 | 211 |
! |
212 |
||
213 |
conjugated |
|
1944 | 214 |
"Return the complex conjugate of this complex number." |
265 | 215 |
|
1944 | 216 |
^ Complex real: real imaginary: imaginary negated |
265 | 217 |
! ! |
218 |
||
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|
219 |
!Complex methodsFor:'coercing'! |
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|
220 |
|
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|
221 |
coerce: aNumber |
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|
222 |
|
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223 |
^aNumber asComplex |
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|
224 |
! |
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|
225 |
|
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|
226 |
generality |
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|
227 |
|
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|
228 |
^150 |
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|
229 |
! ! |
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|
230 |
|
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|
231 |
!Complex methodsFor:'comparing'! |
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changeset
|
232 |
|
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|
233 |
< aNumber |
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|
234 |
^Number |
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|
235 |
raise: #unorderedSignal |
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|
236 |
receiver: self |
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|
237 |
selector: #< |
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parents:
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changeset
|
238 |
arg: aNumber |
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diff
changeset
|
239 |
errorString: 'Complex numbers are not well ordered'! |
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parents:
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changeset
|
240 |
|
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changeset
|
241 |
= aNumber |
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parents:
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diff
changeset
|
242 |
^ (aNumber real = real) and:[aNumber imaginary = imaginary] |
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changeset
|
243 |
! |
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changeset
|
244 |
|
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changeset
|
245 |
hash |
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parents:
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diff
changeset
|
246 |
"Hash is implemented because equals is implemented." |
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changeset
|
247 |
|
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diff
changeset
|
248 |
^ real hash |
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diff
changeset
|
249 |
! ! |
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diff
changeset
|
250 |
|
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parents:
1944
diff
changeset
|
251 |
!Complex methodsFor:'converting'! |
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parents:
1944
diff
changeset
|
252 |
|
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changeset
|
253 |
asComplex |
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parents:
1944
diff
changeset
|
254 |
|
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parents:
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diff
changeset
|
255 |
^self |
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parents:
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diff
changeset
|
256 |
! |
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diff
changeset
|
257 |
|
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parents:
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diff
changeset
|
258 |
asFloat |
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parents:
1944
diff
changeset
|
259 |
|
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parents:
1944
diff
changeset
|
260 |
imaginary = 0 ifTrue: [^real asFloat]. |
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parents:
1944
diff
changeset
|
261 |
^Number |
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parents:
1944
diff
changeset
|
262 |
raise: #coercionErrorSignal |
89f1f31527f4
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parents:
1944
diff
changeset
|
263 |
receiver: self |
89f1f31527f4
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parents:
1944
diff
changeset
|
264 |
selector: #asFloat |
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
265 |
errorString: 'Can''t coerce an instance of Complex to a Float' |
89f1f31527f4
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parents:
1944
diff
changeset
|
266 |
! |
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
267 |
|
89f1f31527f4
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parents:
1944
diff
changeset
|
268 |
asInteger |
89f1f31527f4
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parents:
1944
diff
changeset
|
269 |
|
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
270 |
imaginary = 0 ifTrue: [^real asInteger]. |
89f1f31527f4
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parents:
1944
diff
changeset
|
271 |
^Number |
89f1f31527f4
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parents:
1944
diff
changeset
|
272 |
raise: #coercionErrorSignal |
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
273 |
receiver: self |
89f1f31527f4
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parents:
1944
diff
changeset
|
274 |
selector: #asInteger |
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
275 |
errorString: 'Can''t coerce an instance of Complex to an Integer' |
89f1f31527f4
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parents:
1944
diff
changeset
|
276 |
! |
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
277 |
|
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
278 |
asPoint |
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
279 |
"Return the complex number as a point." |
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
280 |
^ real @ imaginary |
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
281 |
! |
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
282 |
|
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
283 |
reduceGeneralityIfPossible |
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
284 |
"Answer the receiver transformed to a lower generality, if such a |
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
285 |
transformation is possible without losing information. If not, answer |
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
286 |
the receiver" |
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
287 |
|
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
288 |
imaginary isZero |
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
289 |
ifTrue: [^real] |
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
290 |
ifFalse: [^self] |
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
291 |
! ! |
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
292 |
|
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
293 |
!Complex methodsFor:'double dispatching'! |
265 | 294 |
|
295 |
differenceFromFloat: argument |
|
1944 | 296 |
^ argument asComplex - self |
265 | 297 |
! |
298 |
||
299 |
differenceFromFraction: argument |
|
1944 | 300 |
^ argument asComplex - self |
265 | 301 |
! |
302 |
||
303 |
differenceFromInteger: argument |
|
1944 | 304 |
^ argument asComplex - self |
265 | 305 |
! |
306 |
||
307 |
productFromFloat: argument |
|
1944 | 308 |
^ argument asComplex * self |
265 | 309 |
! |
310 |
||
311 |
productFromFraction: argument |
|
1944 | 312 |
^ argument asComplex * self |
265 | 313 |
! |
314 |
||
315 |
productFromInteger: argument |
|
1944 | 316 |
^ argument asComplex * self |
265 | 317 |
! |
318 |
||
319 |
quotientFromFloat: argument |
|
1944 | 320 |
^ argument asComplex / self |
265 | 321 |
! |
322 |
||
323 |
quotientFromFraction: argument |
|
1944 | 324 |
^ argument asComplex / self |
265 | 325 |
! |
326 |
||
327 |
quotientFromInteger: argument |
|
1944 | 328 |
^ argument asComplex / self |
265 | 329 |
! |
330 |
||
331 |
sumFromFloat: argument |
|
1944 | 332 |
^ argument asComplex + self |
265 | 333 |
! |
334 |
||
335 |
sumFromFraction: argument |
|
1944 | 336 |
^ argument asComplex + self |
265 | 337 |
! |
338 |
||
339 |
sumFromInteger: argument |
|
1944 | 340 |
^ argument asComplex + self |
265 | 341 |
! ! |
342 |
||
3633
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
343 |
!Complex methodsFor:'mathematical functions'! |
265 | 344 |
|
345 |
angle |
|
1944 | 346 |
"Return the radian angle for this Complex number." |
265 | 347 |
|
1944 | 348 |
real < 0 ifTrue: [ |
349 |
imaginary < 0 ifTrue: [ |
|
350 |
^ (imaginary / real) arcTan - Float pi |
|
351 |
]. |
|
352 |
^ Float pi + (imaginary / real) arcTan |
|
353 |
]. |
|
354 |
^ (imaginary / real) arcTan |
|
265 | 355 |
! |
356 |
||
357 |
exp |
|
1944 | 358 |
"Return the complex exponential of the receiver." |
265 | 359 |
|
1944 | 360 |
^ imaginary cos % imaginary sin * real exp |
265 | 361 |
! |
362 |
||
363 |
sqrt |
|
1944 | 364 |
"Return the square root of the receiver" |
265 | 365 |
|
1944 | 366 |
| u v | |
367 |
(imaginary = 0 and: [real >= 0]) ifTrue: [^real sqrt]. |
|
368 |
v := (self abs - real / 2) sqrt. |
|
369 |
u := imaginary / 2 / v. |
|
370 |
^Complex real: u imaginary: v |
|
265 | 371 |
|
1944 | 372 |
"-4 asComplex sqrt" |
373 |
"-4 asComplex sqrt squared" |
|
265 | 374 |
! ! |
375 |
||
3633
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
376 |
!Complex methodsFor:'printing'! |
265 | 377 |
|
3633
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
378 |
printOn: aStream |
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
379 |
aStream nextPut: $(. |
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
380 |
real storeOn: aStream. |
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
381 |
aStream nextPutAll: '%'. |
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
382 |
imaginary storeOn: aStream. |
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
383 |
aStream nextPut: $). |
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
384 |
! |
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
385 |
|
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
386 |
printString |
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
387 |
^ '(' , real printString, '%', imaginary printString, ')' |
265 | 388 |
! |
389 |
||
3633
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
390 |
storeOn: aStream |
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
391 |
aStream nextPut: $(. |
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
392 |
real storeOn: aStream. |
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
393 |
aStream nextPutAll: '%'. |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
394 |
imaginary storeOn: aStream. |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
395 |
aStream nextPut: $). |
265 | 396 |
! ! |
397 |
||
3633
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
398 |
!Complex methodsFor:'private'! |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
399 |
|
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
400 |
setReal: u setImaginary: v |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
401 |
real := u. |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
402 |
imaginary := v. |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
403 |
! ! |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
404 |
|
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
405 |
!Complex methodsFor:'testing'! |
265 | 406 |
|
407 |
isComplex |
|
408 |
||
1944 | 409 |
^true |
265 | 410 |
! |
411 |
||
412 |
isReal |
|
1944 | 413 |
"Return true if this Complex number has a zero imaginary part." |
414 |
^ imaginary = 0 |
|
265 | 415 |
! |
416 |
||
417 |
isZero |
|
1944 | 418 |
"Answer whether 'self = self class zero'. We can't use #= because |
419 |
#= is defined in terms of #isZero" |
|
265 | 420 |
|
1944 | 421 |
^real isZero and: [imaginary isZero] |
265 | 422 |
! |
423 |
||
424 |
sign |
|
425 |
||
1944 | 426 |
^Complex real: real sign imaginary: imaginary sign |
265 | 427 |
! ! |
428 |
||
3637 | 429 |
!Complex class methodsFor:'documentation'! |
430 |
||
431 |
version |
|
432 |
^ '$Header: /cvs/stx/stx/libbasic/Complex.st,v 1.4 1998-07-09 08:25:14 cg Exp $' |
|
433 |
! ! |