Annotation of OpenXM/src/asir-doc/parts/builtin/array.texi, Revision 1.6
1.6 ! noro 1: @comment $OpenXM: OpenXM/src/asir-doc/parts/builtin/array.texi,v 1.5 2002/08/08 05:24:37 noro Exp $
1.2 noro 2: \BJP
1.1 noro 3: @node $BG[Ns(B,,, $BAH$_9~$_H!?t(B
4: @section $BG[Ns(B
1.2 noro 5: \E
6: \BEG
7: @node Arrays,,, Built-in Function
8: @section Arrays
9: \E
1.1 noro 10:
11: @menu
12: * newvect::
1.4 noro 13: * newbytearray::
1.1 noro 14: * vtol::
15: * newmat::
16: * size::
1.5 noro 17: * det invmat::
1.1 noro 18: * qsort::
19: @end menu
20:
1.2 noro 21: \JP @node newvect,,, $BG[Ns(B
22: \EG @node newvect,,, Arrays
1.1 noro 23: @subsection @code{newvect}
24: @findex newvect
25:
26: @table @t
27: @item newvect(@var{len}[,@var{list}])
1.2 noro 28: \JP :: $BD9$5(B @var{len} $B$N%Y%/%H%k$r@8@.$9$k(B.
29: \EG :: Creates a new vector object with its length @var{len}.
1.1 noro 30: @end table
31:
32: @table @var
33: @item return
1.2 noro 34: \JP $B%Y%/%H%k(B
35: \EG vector
1.1 noro 36: @item len
1.2 noro 37: \JP $B<+A3?t(B
38: \EG non-negative integer
1.1 noro 39: @item list
1.2 noro 40: \JP $B%j%9%H(B
41: \EG list
1.1 noro 42: @end table
43:
44: @itemize @bullet
1.2 noro 45: \BJP
1.1 noro 46: @item
47: $BD9$5(B @var{len} $B$N%Y%/%H%k$r@8@.$9$k(B. $BBh(B 2 $B0z?t$,$J$$>l9g(B,
48: $B3F@.J,$O(B 0 $B$K=i4|2=$5$l$k(B. $BBh(B 2 $B0z?t$,$"$k>l9g(B,
49: $B%$%s%G%C%/%9$N>.$5$$@.J,$+$i(B, $B%j%9%H$N(B
50: $B3FMWAG$K$h$j=i4|2=$5$l$k(B. $B3FMWAG$O(B, $B@hF,$+$i=g$K(B
51: $B;H$o$l(B, $BB-$j$J$$J,$O(B 0 $B$,Kd$a$i$l$k(B.
52: @item
53: $B%Y%/%H%k$N@.J,$O(B, $BBh(B 0 $B@.J,$+$iBh(B @var{len}-1 $B@.J,$H$J$k(B.
54: ($BBh(B 1 $B@.J,$+$i$G$O$J$$;v$KCm0U(B. )
55: @item
56: $B%j%9%H$O3F@.J,$,(B, $B%]%$%s%?$rC)$k;v$K$h$C$F%7!<%1%s%7%c%k$K(B
57: $B8F$S=P$5$l$k$N$KBP$7(B, $B%Y%/%H%k$O3F@.J,$,(B
58: $BBh0l@.J,$+$i$N%a%b%j>e$N(B displacement ($BJQ0L(B)$B$K$h$C$F%i%s%@%`%"%/%;%9$G(B
59: $B8F$S=P$5$l(B, $B$=$N7k2L(B, $B@.J,$N%"%/%;%9;~4V$KBg$-$J:9$,=P$F$/$k(B.
60: $B@.J,%"%/%;%9$O(B, $B%j%9%H$G$O(B, $B@.J,$NNL$,A}$($k$K=>$C$F(B
61: $B;~4V$,$+$+$k$h$&$K$J$k$,(B, $B%Y%/%H%k$G$O(B, $B@.J,$NNL$K0MB8$;$:$[$\0lDj$G$"$k(B.
62: @item
63: @b{Asir} $B$G$O(B, $B=D%Y%/%H%k(B, $B2#%Y%/%H%k$N6hJL$O$J$$(B.
64: $B9TNs$r:8$+$i3]$1$l$P=D%Y%/%H%k$H$_$J$5$l$k$7(B, $B1&$+$i3]$1$l$P2#%Y%/%H%k$H(B
65: $B$_$J$5$l$k(B.
66: @item
67: $B%Y%/%H%k$ND9$5$O(B @code{size()} $B$K$h$C$FF@$i$l$k(B.
68: @item
69: $BH!?t$N0z?t$H$7$F%Y%/%H%k$rEO$7$?>l9g(B, $BEO$5$l$?H!?t$O(B, $B$=$N%Y%/%H%k$N@.J,(B
70: $B$r=q$-49$($k$3$H$,$G$-$k(B.
1.2 noro 71: \E
72: \BEG
73: @item
74: Creates a new vector object with its length @var{len} and its elements
75: all cleared to value 0.
76: If the second argument, a list, is given, the vector is initialized by
77: the list elements.
78: Elements are used from the first through the last.
79: If the list is short for initializing the full vector,
80: 0's are filled in the remaining vector elements.
81: @item
82: Elements are indexed from 0 through @var{len}-1. Note that the first
83: element has not index 1.
84: @item
85: List and vector are different types in @b{Asir}.
86: Lists are conveniently used for representing many data objects whose
87: size varies dynamically as computation proceeds.
88: By its flexible expressive power, it is also conveniently used to
89: describe initial values for other structured objects as you see
90: for vectors.
91: Access for an element of a list is performed by following pointers to
92: next elements. By this, access costs for list elements differ for
93: each element.
94: In contrast to lists, vector elements can be accessed in a same time,
95: because they are accessed by computing displacements from the top memory
96: location of the vector object.
97:
98: Note also, in @b{Asir}, modification of an element of a vector causes
99: modification of the whole vector itself,
100: while modification of a list element does not cause the modification
101: of the whole list object.
102:
103: By this, in @b{Asir} language,
104: a vector element designator can be a left value of
105: assignment statement, but a list element designator can NOT be a left
106: value of assignment statement.
107:
108: @item
109: No distinction of column vectors and row vectors in @b{Asir}.
110: If a matrix is applied to a vector from left, the vector shall be taken
111: as a column vector, and if from right it shall be taken as a row vector.
112: @item
113: The length (or size or dimension) of a vector is given by function
114: @code{size()}.
115: @item
116: When a vector is passed to a function as its argument
117: (actual parameter), the vector element can be modified in that
118: function.
119:
120: @item
121: A vector is displayed in a similar format as for a list.
122: Note, however, there is a distinction: Elements of a vector are
123: separated simply by a `blank space', while those of a list by a `comma.'
124: \E
1.1 noro 125: @end itemize
126:
127: @example
128: [0] A=newvect(5);
129: [ 0 0 0 0 0 ]
130: [1] A=newvect(5,[1,2,3,4,[5,6]]);
131: [ 1 2 3 4 [5,6] ]
132: [2] A[0];
133: 1
134: [3] A[4];
135: [5,6]
136: [4] size(A);
137: [5]
138: [5] def afo(V) @{ V[0] = x; @}
139: [6] afo(A)$
140: [7] A;
141: [ x 2 3 4 [5,6] ]
142: @end example
143:
144: @table @t
1.2 noro 145: \JP @item $B;2>H(B
146: \EG @item References
1.3 takayama 147: @fref{newmat}, @fref{size}, @fref{vtol}.
1.1 noro 148: @end table
149:
1.2 noro 150: \JP @node vtol,,, $BG[Ns(B
151: \EG @node vtol,,, Arrays
1.1 noro 152: @subsection @code{vtol}
153: @findex vtol
154:
155: @table @t
156: @item vtol(@var{vect})
1.2 noro 157: \JP :: $B%Y%/%H%k$r%j%9%H$KJQ49$9$k(B.
158: \EG :: Converts a vector into a list.
1.1 noro 159: @end table
160:
161: @table @var
162: @item return
1.2 noro 163: \JP $B%j%9%H(B
164: \EG list
1.1 noro 165: @item vect
1.2 noro 166: \JP $B%Y%/%H%k(B
167: \EG vector
1.1 noro 168: @end table
169:
170: @itemize @bullet
1.2 noro 171: \BJP
1.1 noro 172: @item
173: $BD9$5(B @var{n} $B$N%Y%/%H%k(B @var{vect} $B$r(B
174: @code{[@var{vect}[0],...,@var{vect}[@var{n}-1]]} $B$J$k%j%9%H$KJQ49$9$k(B.
175: @item
176: $B%j%9%H$+$i%Y%/%H%k$X$NJQ49$O(B @code{newvect()} $B$G9T$&(B.
1.2 noro 177: \E
178: \BEG
179: @item
180: Converts a vector @var{vect} of length @var{n} into
181: a list @code{[@var{vect}[0],...,@var{vect}[@var{n}-1]]}.
182: @item
183: A conversion from a list to a vector is done by @code{newvect()}.
184: \E
1.1 noro 185: @end itemize
186:
187: @example
188: [3] A=newvect(3,[1,2,3]);
189: [ 1 2 3 ]
190: [4] vtol(A);
191: [1,2,3]
1.4 noro 192: @end example
193:
194: @table @t
195: \JP @item $B;2>H(B
196: \EG @item References
197: @fref{newvect}.
198: @end table
199:
200: \JP @node newbytearray,,, $BG[Ns(B
201: \EG @node newbytearray,,, Arrays
202: @subsection @code{newbytearray}
203: @findex newbytearray
204:
205: @table @t
206: @item newbytearray(@var{len},[@var{listorstring}])
207: \JP :: $BD9$5(B @var{len} $B$N(B byte array $B$r@8@.$9$k(B.
208: \EG :: Creates a new byte array.
209: @end table
210:
211: @table @var
212: @item return
213: byte array
214: @item len
215: \JP $B<+A3?t(B
216: \EG non-negative integer
217: @item listorstring
218: \JP $B%j%9%H$^$?$OJ8;zNs(B
219: \EG list or string
220: @end table
221:
222: @itemize @bullet
223: @item
224: \JP @code{newvect} $B$HF1MM$K$7$F(B byte array $B$r@8@.$9$k(B.
225: \EG This function generates a byte array. The specification is
226: similar to that of @code{newvect}.
227: @item
228: \JP $BJ8;zNs$G=i4|CM$r;XDj$9$k$3$H$b2DG=$G$"$k(B.
229: \EG The initial value can be specified by a character string.
230: @item
231: \JP byte array $B$NMWAG$N%"%/%;%9$OG[Ns$HF1MM$G$"$k(B.
232: \EG One can access elements of a byte array just as an array.
233: @end itemize
234:
235: @example
236: [182] A=newbytearray(3);
237: |00 00 00|
238: [183] A=newbytearray(3,[1,2,3]);
239: |01 02 03|
240: [184] A=newbytearray(3,"abc");
241: |61 62 63|
242: [185] A[0];
243: 97
244: [186] A[1]=123;
245: 123
246: [187] A;
247: |61 7b 63|
1.1 noro 248: @end example
249:
250: @table @t
1.2 noro 251: \JP @item $B;2>H(B
252: \EG @item References
1.1 noro 253: @fref{newvect}.
254: @end table
255:
1.2 noro 256: \JP @node newmat,,, $BG[Ns(B
257: \EG @node newmat,,, Arrays
1.1 noro 258: @subsection @code{newmat}
259: @findex newmat
260:
261: @table @t
1.6 ! noro 262: @item newmat(@var{row},@var{col} [,[[@var{a},@var{b},...],[@var{c},@var{d},...],...]])
1.2 noro 263: \JP :: @var{row} $B9T(B @var{col} $BNs$N9TNs$r@8@.$9$k(B.
264: \EG :: Creates a new matrix with @var{row} rows and @var{col} columns.
1.1 noro 265: @end table
266:
267: @table @var
268: @item return
1.2 noro 269: \JP $B9TNs(B
270: \EG matrix
1.6 ! noro 271: @item row col
1.2 noro 272: \JP $B<+A3?t(B
273: \EG non-negative integer
1.6 ! noro 274: @item a b c d
1.2 noro 275: \JP $BG$0U(B
276: \EG arbitrary
1.1 noro 277: @end table
278:
279: @itemize @bullet
1.2 noro 280: \BJP
1.1 noro 281: @item
282: @var{row} $B9T(B @var{col} $BNs$N9TNs$r@8@.$9$k(B. $BBh(B 3 $B0z?t$,$J$$>l9g(B,
283: $B3F@.J,$O(B 0 $B$K=i4|2=$5$l$k(B. $BBh(B 3 $B0z?t$,$"$k>l9g(B,
284: $B%$%s%G%C%/%9$N>.$5$$@.J,$+$i(B, $B3F9T$,(B, $B%j%9%H$N(B
285: $B3FMWAG(B ($B$3$l$O$^$?%j%9%H$G$"$k(B) $B$K$h$j=i4|2=$5$l$k(B. $B3FMWAG$O(B, $B@hF,$+$i=g$K(B
286: $B;H$o$l(B, $BB-$j$J$$J,$O(B 0 $B$,Kd$a$i$l$k(B.
287: @item
288: $B9TNs$N%5%$%:$O(B @code{size()} $B$GF@$i$l$k(B.
289: @item
290: @code{M} $B$,9TNs$N$H$-(B, @code{M[I]} $B$K$h$jBh(B @code{I} $B9T$r%Y%/%H%k$H$7$F(B
291: $B<h$j=P$9$3$H$,$G$-$k(B. $B$3$N%Y%/%H%k$O(B, $B$b$H$N9TNs$H@.J,$r6&M-$7$F$*$j(B,
292: $B$$$:$l$+$N@.J,$r=q$-49$($l$P(B, $BB>$NBP1~$9$k@.J,$b=q$-49$o$k$3$H$K$J$k(B.
293: @item
294: $BH!?t$N0z?t$H$7$F9TNs$rEO$7$?>l9g(B, $BEO$5$l$?H!?t$O(B, $B$=$N9TNs$N@.J,(B
295: $B$r=q$-49$($k$3$H$,$G$-$k(B.
1.2 noro 296: \E
297: \BEG
298: @item
299: If the third argument, a list, is given, the newly created matrix
300: is initialized so that each element of the list (again a list)
301: initializes each of the rows of the matrix.
302: Elements are used from the first through the last.
303: If the list is short, 0's are filled in the remaining matrix elements.
304: If no third argument is given all the elements are cleared to 0.
305: @item
306: The size of a matrix is given by function @code{size()}.
307: @item
308: Let @code{M} be a program variable assigned to a matrix.
309: Then, @code{M[I]} denotes a (row) vector which corresponds with
310: the @code{I}-th row of the matrix.
311: Note that the vector shares its element with the original matrix.
312: Subsequently, if an element of the vector is modified, then the
313: corresponding matrix element is also modified.
314: @item
315: When a matrix is passed to a function as its argument
316: (actual parameter), the matrix element can be modified within that
317: function.
318: \E
1.1 noro 319: @end itemize
320:
321: @example
322: [0] A = newmat(3,3,[[1,1,1],[x,y],[x^2]]);
323: [ 1 1 1 ]
324: [ x y 0 ]
325: [ x^2 0 0 ]
326: [1] det(A);
327: -y*x^2
328: [2] size(A);
329: [3,3]
330: [3] A[1];
331: [ x y 0 ]
332: [4] A[1][3];
333: getarray : Out of range
334: return to toplevel
335: @end example
336:
337: @table @t
1.2 noro 338: \JP @item $B;2>H(B
339: \EG @item References
1.5 noro 340: @fref{newvect}, @fref{size}, @fref{det invmat}.
1.1 noro 341: @end table
342:
1.2 noro 343: \JP @node size,,, $BG[Ns(B
344: \EG @node size,,, Arrays
1.1 noro 345: @subsection @code{size}
346: @findex size
347:
348: @table @t
349: @item size(@var{vect|mat})
1.2 noro 350: \JP :: @code{[@var{vect} $B$ND9$5(B]} $B$^$?$O(B @code{[@var{mat} $B$N9T?t(B,@var{mat} $B$NNs?t(B]}.
351: \BEG
352: :: A list containing the number of elements of the given vector,
353: @code{[size of @var{vect}]},
354: or a list containing row size and column size of the given matrix,
355: @code{[row size of @var{mat}, column size of @var{mat}]}.
356: \E
1.1 noro 357: @end table
358:
359: @table @var
360: @item return
1.2 noro 361: \JP $B%j%9%H(B
362: \EG list
1.1 noro 363: @item vect
1.2 noro 364: \JP $B%Y%/%H%k(B
365: \EG vector
1.1 noro 366: @item mat
1.2 noro 367: \JP $B9TNs(B
368: \EG matrix
1.1 noro 369: @end table
370:
371: @itemize @bullet
1.2 noro 372: \BJP
1.1 noro 373: @item
374: @var{vect} $BKt$O(B, @var{mat} $B$N%5%$%:$r%j%9%H$G=PNO$9$k(B.
375: @item
376: @var{list} $B$N%5%$%:$O(B @code{length()}$B$r(B, $BM-M}<0$K8=$l$kC19`<0$N?t$O(B @code{nmono()} $B$rMQ$$$k(B.
1.2 noro 377: \E
378: \BEG
379: @item
380: Return a list consisting of the dimension of the vector @var{vect},
381: or a list consisting of the row size and column size of the matrix
382: @var{matrix}.
383: @item
384: Use @code{length()} for the size of @var{list}, and
385: @code{nmono()} for the number of monomials with non-zero coefficients
386: in a rational expression.
387: \E
1.1 noro 388: @end itemize
389:
390: @example
391: [0] A = newvect(4);
392: [ 0 0 0 0 ]
393: [1] size(A);
394: [4]
395: [2] B = newmat(2,3,[[1,2,3],[4,5,6]]);
396: [ 1 2 3 ]
397: [ 4 5 6 ]
398: [3] size(B);
399: [2,3]
400: @end example
401:
402: @table @t
1.2 noro 403: \JP @item $B;2>H(B
404: \EG @item References
1.1 noro 405: @fref{car cdr cons append reverse length}, @fref{nmono}.
406: @end table
407:
1.5 noro 408: \JP @node det invmat,,, $BG[Ns(B
409: \EG @node det invmat,,, Arrays
410: @subsection @code{det},@code{invmat}
1.1 noro 411: @findex det
1.5 noro 412: @findex invmat
1.1 noro 413:
414: @table @t
415: @item det(@var{mat}[,@var{mod}])
1.2 noro 416: \JP :: @var{mat} $B$N9TNs<0$r5a$a$k(B.
417: \EG :: Determinant of @var{mat}.
1.5 noro 418: @item invmat(@var{mat})
419: \JP :: @var{mat} $B$N9TNs<0$r5a$a$k(B.
420: \EG :: Inverse matrix of @var{mat}.
1.1 noro 421: @end table
422:
423: @table @var
424: @item return
1.5 noro 425: \JP @code{det}: $B<0(B, @code{invmat}: $B%j%9%H(B
426: \EG @code{det}: expression, @code{invmat}: list
1.1 noro 427: @item mat
1.2 noro 428: \JP $B9TNs(B
429: \EG matrix
1.1 noro 430: @item mod
1.2 noro 431: \JP $BAG?t(B
432: \EG prime
1.1 noro 433: @end table
434:
435: @itemize @bullet
1.2 noro 436: \BJP
1.1 noro 437: @item
1.5 noro 438: @code{det} $B$O9TNs(B @var{mat} $B$N9TNs<0$r5a$a$k(B.
439: @code{invmat} $B$O9TNs(B @var{mat} $B$N5U9TNs$r5a$a$k(B. $B5U9TNs$O(B @code{[$BJ,Jl(B, $BJ,;R(B]}
440: $B$N7A$GJV$5$l(B, @code{$BJ,Jl(B}$B$,9TNs(B, @code{$BJ,Jl(B/$BJ,;R(B} $B$,5U9TNs$H$J$k(B.
1.1 noro 441: @item
442: $B0z?t(B @var{mod} $B$,$"$k;~(B, GF(@var{mod}) $B>e$G$N9TNs<0$r5a$a$k(B.
443: @item
444: $BJ,?t$J$7$N%,%&%9>C5nK!$K$h$C$F$$$k$?$a(B, $BB?JQ?tB?9`<0$r@.J,$H$9$k(B
445: $B9TNs$KBP$7$F$O>.9TNs<0E83+$K$h$kJ}K!$N$[$&$,8zN($,$h$$>l9g$b$"$k(B.
1.2 noro 446: \E
447: \BEG
448: @item
1.5 noro 449: @code{det} computes the determinant of matrix @var{mat}.
450: @code{invmat} computes the inverse matrix of matrix @var{mat}.
451: @code{invmat} returns a list @code{[num,den]}, where @code{num}
452: is a matrix and @code{num/den} represents the inverse matrix.
1.2 noro 453: @item
454: The computation is done over GF(@var{mod}) if @var{mod} is specitied.
455: @item
456: The fraction free Gaussian algorithm is employed. For matrices with
457: multi-variate polynomial entries, minor expansion algorithm sometimes
458: is more efficient than the fraction free Gaussian algorithm.
459: \E
1.1 noro 460: @end itemize
461:
462: @example
463: [91] A=newmat(5,5)$
464: [92] V=[x,y,z,u,v];
465: [x,y,z,u,v]
466: [93] for(I=0;I<5;I++)for(J=0,B=A[I],W=V[I];J<5;J++)B[J]=W^J;
467: [94] A;
468: [ 1 x x^2 x^3 x^4 ]
469: [ 1 y y^2 y^3 y^4 ]
470: [ 1 z z^2 z^3 z^4 ]
471: [ 1 u u^2 u^3 u^4 ]
472: [ 1 v v^2 v^3 v^4 ]
473: [95] fctr(det(A));
474: [[1,1],[u-v,1],[-z+v,1],[-z+u,1],[-y+u,1],[y-v,1],[-y+z,1],[-x+u,1],[-x+z,1],
475: [-x+v,1],[-x+y,1]]
1.5 noro 476: [96] A = newmat(3,3)$
477: [97] for(I=0;I<3;I++)for(J=0,B=A[I],W=V[I];J<3;J++)B[J]=W^J;
478: [98] A;
479: [ 1 x x^2 ]
480: [ 1 y y^2 ]
481: [ 1 z z^2 ]
482: [99] invmat(A);
483: [[ -z*y^2+z^2*y z*x^2-z^2*x -y*x^2+y^2*x ]
484: [ y^2-z^2 -x^2+z^2 x^2-y^2 ]
485: [ -y+z x-z -x+y ],(-y+z)*x^2+(y^2-z^2)*x-z*y^2+z^2*y]
486: [100] A*B[0];
487: [ (-y+z)*x^2+(y^2-z^2)*x-z*y^2+z^2*y 0 0 ]
488: [ 0 (-y+z)*x^2+(y^2-z^2)*x-z*y^2+z^2*y 0 ]
489: [ 0 0 (-y+z)*x^2+(y^2-z^2)*x-z*y^2+z^2*y ]
490: [101] map(red,A*B[0]/B[1]);
491: [ 1 0 0 ]
492: [ 0 1 0 ]
493: [ 0 0 1 ]
1.1 noro 494: @end example
495:
496: @table @t
1.2 noro 497: \JP @item $B;2>H(B
498: \EG @item References
1.1 noro 499: @fref{newmat}.
500: @end table
501:
1.2 noro 502: \JP @node qsort,,, $BG[Ns(B
503: \EG @node qsort,,, Arrays
1.1 noro 504: @subsection @code{qsort}
505: @findex qsort
506:
507: @table @t
508: @item qsort(@var{array}[,@var{func}])
1.2 noro 509: \JP :: $B0l<!85G[Ns(B @var{array} $B$r%=!<%H$9$k(B.
510: \EG :: Sorts an array @var{array}.
1.1 noro 511: @end table
512:
513: @table @var
514: @item return
1.2 noro 515: \JP @var{array} ($BF~NO$HF1$8(B; $BMWAG$N$_F~$lBX$o$k(B)
516: \EG @var{array} (The same as the input; Only the elements are exchanged.)
1.1 noro 517: @item array
1.2 noro 518: \JP $B0l<!85G[Ns(B
519: \EG array
1.1 noro 520: @item func
1.2 noro 521: \JP $BHf3SMQ4X?t(B
522: \EG function for comparison
1.1 noro 523: @end table
524:
525: @itemize @bullet
1.2 noro 526: \BJP
1.1 noro 527: @item
528: $B0l<!85G[Ns$r(B quick sort $B$G%=!<%H$9$k(B.
529: @item
530: $BHf3SMQ4X?t$,;XDj$5$l$F$$$J$$>l9g(B, $B%*%V%8%'%/%H$I$&$7$NHf3S7k2L$G(B
531: $B=g=x$,2<$N$b$N$+$i=g$KJB$Y49$($i$l$k(B.
532: @item
533: 0, 1, -1 $B$rJV$9(B 2 $B0z?t4X?t$,(B @var{func} $B$H$7$FM?$($i$l$?>l9g(B,
534: @code{@var{func}(A,B)=1} $B$N>l9g$K(B @code{A<B} $B$H$7$F(B, $B=g=x$,2<$N(B
535: $B$b$N$+$i=g$KJB$Y49$($i$l$k(B.
536: @item
537: $BG[Ns$O?7$?$K@8@.$5$l$:(B, $B0z?t$NG[Ns$NMWAG$N$_F~$lBX$o$k(B.
1.2 noro 538: \E
539: \BEG
540: @item
541: This function sorts an array by @var{quick sort}.
542: @item
543: If @var{func} is not specified, the built-in comparison function
544: is used and the array is sorted in increasing order.
545: @item
546: If a function of two arguments @var{func} which returns 0, 1, or -1
547: is provided, then an ordering is detemined so that
548: @code{A<B} if @code{@var{func}(A,B)=1} holds, and
549: the array is sorted in increasing order with respect to the ordering.
550: @item
551: The returned array is the same as the input. Only the elements
552: are exchanged.
553: \E
1.1 noro 554: @end itemize
555:
556: @example
557: [0] qsort(newvect(10,[1,4,6,7,3,2,9,6,0,-1]));
558: [ -1 0 1 2 3 4 6 6 7 9 ]
559: [1] def rev(A,B) @{ return A>B?-1:(A<B?1:0); @}
560: [2] qsort(newvect(10,[1,4,6,7,3,2,9,6,0,-1]),rev);
561: [ 9 7 6 6 4 3 2 1 0 -1 ]
562: @end example
563:
564: @table @t
1.2 noro 565: \JP @item $B;2>H(B
566: \EG @item References
1.1 noro 567: @fref{ord}, @fref{vars}.
568: @end table
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