Annotation of OpenXM/src/asir-doc/parts/builtin/array.texi, Revision 1.9
1.9 ! ohara 1: @comment $OpenXM: OpenXM/src/asir-doc/parts/builtin/array.texi,v 1.8 2003/10/19 07:21:57 takayama 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::
1.9 ! ohara 13: * ltov::
! 14: * vtol::
1.4 noro 15: * newbytearray::
1.1 noro 16: * newmat::
17: * size::
1.5 noro 18: * det invmat::
1.1 noro 19: * qsort::
20: @end menu
21:
1.2 noro 22: \JP @node newvect,,, $BG[Ns(B
23: \EG @node newvect,,, Arrays
1.1 noro 24: @subsection @code{newvect}
25: @findex newvect
26:
27: @table @t
28: @item newvect(@var{len}[,@var{list}])
1.2 noro 29: \JP :: $BD9$5(B @var{len} $B$N%Y%/%H%k$r@8@.$9$k(B.
30: \EG :: Creates a new vector object with its length @var{len}.
1.1 noro 31: @end table
32:
33: @table @var
34: @item return
1.2 noro 35: \JP $B%Y%/%H%k(B
36: \EG vector
1.1 noro 37: @item len
1.2 noro 38: \JP $B<+A3?t(B
39: \EG non-negative integer
1.1 noro 40: @item list
1.2 noro 41: \JP $B%j%9%H(B
42: \EG list
1.1 noro 43: @end table
44:
45: @itemize @bullet
1.2 noro 46: \BJP
1.1 noro 47: @item
48: $BD9$5(B @var{len} $B$N%Y%/%H%k$r@8@.$9$k(B. $BBh(B 2 $B0z?t$,$J$$>l9g(B,
49: $B3F@.J,$O(B 0 $B$K=i4|2=$5$l$k(B. $BBh(B 2 $B0z?t$,$"$k>l9g(B,
50: $B%$%s%G%C%/%9$N>.$5$$@.J,$+$i(B, $B%j%9%H$N(B
51: $B3FMWAG$K$h$j=i4|2=$5$l$k(B. $B3FMWAG$O(B, $B@hF,$+$i=g$K(B
52: $B;H$o$l(B, $BB-$j$J$$J,$O(B 0 $B$,Kd$a$i$l$k(B.
53: @item
54: $B%Y%/%H%k$N@.J,$O(B, $BBh(B 0 $B@.J,$+$iBh(B @var{len}-1 $B@.J,$H$J$k(B.
55: ($BBh(B 1 $B@.J,$+$i$G$O$J$$;v$KCm0U(B. )
56: @item
57: $B%j%9%H$O3F@.J,$,(B, $B%]%$%s%?$rC)$k;v$K$h$C$F%7!<%1%s%7%c%k$K(B
58: $B8F$S=P$5$l$k$N$KBP$7(B, $B%Y%/%H%k$O3F@.J,$,(B
59: $BBh0l@.J,$+$i$N%a%b%j>e$N(B displacement ($BJQ0L(B)$B$K$h$C$F%i%s%@%`%"%/%;%9$G(B
60: $B8F$S=P$5$l(B, $B$=$N7k2L(B, $B@.J,$N%"%/%;%9;~4V$KBg$-$J:9$,=P$F$/$k(B.
61: $B@.J,%"%/%;%9$O(B, $B%j%9%H$G$O(B, $B@.J,$NNL$,A}$($k$K=>$C$F(B
62: $B;~4V$,$+$+$k$h$&$K$J$k$,(B, $B%Y%/%H%k$G$O(B, $B@.J,$NNL$K0MB8$;$:$[$\0lDj$G$"$k(B.
63: @item
64: @b{Asir} $B$G$O(B, $B=D%Y%/%H%k(B, $B2#%Y%/%H%k$N6hJL$O$J$$(B.
65: $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
66: $B$_$J$5$l$k(B.
67: @item
68: $B%Y%/%H%k$ND9$5$O(B @code{size()} $B$K$h$C$FF@$i$l$k(B.
69: @item
70: $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
71: $B$r=q$-49$($k$3$H$,$G$-$k(B.
1.2 noro 72: \E
73: \BEG
74: @item
75: Creates a new vector object with its length @var{len} and its elements
76: all cleared to value 0.
77: If the second argument, a list, is given, the vector is initialized by
78: the list elements.
79: Elements are used from the first through the last.
80: If the list is short for initializing the full vector,
81: 0's are filled in the remaining vector elements.
82: @item
83: Elements are indexed from 0 through @var{len}-1. Note that the first
84: element has not index 1.
85: @item
86: List and vector are different types in @b{Asir}.
87: Lists are conveniently used for representing many data objects whose
88: size varies dynamically as computation proceeds.
89: By its flexible expressive power, it is also conveniently used to
90: describe initial values for other structured objects as you see
91: for vectors.
92: Access for an element of a list is performed by following pointers to
93: next elements. By this, access costs for list elements differ for
94: each element.
95: In contrast to lists, vector elements can be accessed in a same time,
96: because they are accessed by computing displacements from the top memory
97: location of the vector object.
98:
99: Note also, in @b{Asir}, modification of an element of a vector causes
100: modification of the whole vector itself,
101: while modification of a list element does not cause the modification
102: of the whole list object.
103:
104: By this, in @b{Asir} language,
105: a vector element designator can be a left value of
106: assignment statement, but a list element designator can NOT be a left
107: value of assignment statement.
108:
109: @item
110: No distinction of column vectors and row vectors in @b{Asir}.
111: If a matrix is applied to a vector from left, the vector shall be taken
112: as a column vector, and if from right it shall be taken as a row vector.
113: @item
114: The length (or size or dimension) of a vector is given by function
115: @code{size()}.
116: @item
117: When a vector is passed to a function as its argument
118: (actual parameter), the vector element can be modified in that
119: function.
120:
121: @item
122: A vector is displayed in a similar format as for a list.
123: Note, however, there is a distinction: Elements of a vector are
124: separated simply by a `blank space', while those of a list by a `comma.'
125: \E
1.1 noro 126: @end itemize
127:
128: @example
129: [0] A=newvect(5);
130: [ 0 0 0 0 0 ]
131: [1] A=newvect(5,[1,2,3,4,[5,6]]);
132: [ 1 2 3 4 [5,6] ]
133: [2] A[0];
134: 1
135: [3] A[4];
136: [5,6]
137: [4] size(A);
138: [5]
139: [5] def afo(V) @{ V[0] = x; @}
140: [6] afo(A)$
141: [7] A;
142: [ x 2 3 4 [5,6] ]
143: @end example
144:
145: @table @t
1.2 noro 146: \JP @item $B;2>H(B
147: \EG @item References
1.9 ! ohara 148: @fref{newmat}, @fref{size}, @fref{ltov}, @fref{vtol}.
! 149: @end table
! 150:
! 151: \JP @node ltov,,, $BG[Ns(B
! 152: \EG @node ltov,,, Arrays
! 153: @subsection @code{ltov}
! 154: @findex ltov
! 155:
! 156: @table @t
! 157: @item ltov(@var{list})
! 158: \JP :: $B%j%9%H$r%Y%/%H%k$KJQ49$9$k(B.
! 159: \EG :: Converts a list into a vector.
! 160: @end table
! 161:
! 162: @table @var
! 163: @item return
! 164: \JP $B%Y%/%H%k(B
! 165: \EG vector
! 166: @item list
! 167: \JP $B%j%9%H(B
! 168: \EG list
! 169: @end table
! 170:
! 171: @itemize @bullet
! 172: \BJP
! 173: @item
! 174: $B%j%9%H(B @var{list} $B$rF1$8D9$5$N%Y%/%H%k$KJQ49$9$k(B.
! 175: @item
! 176: $B$3$N4X?t$O(B @code{newvect(length(@var{list}), @var{list})} $B$KEy$7$$(B.
! 177: \E
! 178: \BEG
! 179: @item
! 180: Converts a list @var{list} into a vector of same length.
! 181: See also @code{newvect()}.
! 182: \E
! 183: @end itemize
! 184:
! 185: @example
! 186: [3] A=[1,2,3];
! 187: [4] ltov(A);
! 188: [ 1 2 3 ]
! 189: @end example
! 190:
! 191: @table @t
! 192: \JP @item $B;2>H(B
! 193: \EG @item References
! 194: @fref{newvect}, @fref{vtol}.
1.1 noro 195: @end table
196:
1.2 noro 197: \JP @node vtol,,, $BG[Ns(B
198: \EG @node vtol,,, Arrays
1.1 noro 199: @subsection @code{vtol}
200: @findex vtol
201:
202: @table @t
203: @item vtol(@var{vect})
1.2 noro 204: \JP :: $B%Y%/%H%k$r%j%9%H$KJQ49$9$k(B.
205: \EG :: Converts a vector into a list.
1.1 noro 206: @end table
207:
208: @table @var
209: @item return
1.2 noro 210: \JP $B%j%9%H(B
211: \EG list
1.1 noro 212: @item vect
1.2 noro 213: \JP $B%Y%/%H%k(B
214: \EG vector
1.1 noro 215: @end table
216:
217: @itemize @bullet
1.2 noro 218: \BJP
1.1 noro 219: @item
220: $BD9$5(B @var{n} $B$N%Y%/%H%k(B @var{vect} $B$r(B
221: @code{[@var{vect}[0],...,@var{vect}[@var{n}-1]]} $B$J$k%j%9%H$KJQ49$9$k(B.
222: @item
223: $B%j%9%H$+$i%Y%/%H%k$X$NJQ49$O(B @code{newvect()} $B$G9T$&(B.
1.2 noro 224: \E
225: \BEG
226: @item
227: Converts a vector @var{vect} of length @var{n} into
228: a list @code{[@var{vect}[0],...,@var{vect}[@var{n}-1]]}.
229: @item
230: A conversion from a list to a vector is done by @code{newvect()}.
231: \E
1.1 noro 232: @end itemize
233:
234: @example
235: [3] A=newvect(3,[1,2,3]);
236: [ 1 2 3 ]
237: [4] vtol(A);
238: [1,2,3]
1.4 noro 239: @end example
240:
241: @table @t
242: \JP @item $B;2>H(B
243: \EG @item References
1.9 ! ohara 244: @fref{newvect}, @fref{ltov}.
1.4 noro 245: @end table
246:
247: \JP @node newbytearray,,, $BG[Ns(B
248: \EG @node newbytearray,,, Arrays
249: @subsection @code{newbytearray}
250: @findex newbytearray
251:
252: @table @t
253: @item newbytearray(@var{len},[@var{listorstring}])
254: \JP :: $BD9$5(B @var{len} $B$N(B byte array $B$r@8@.$9$k(B.
255: \EG :: Creates a new byte array.
256: @end table
257:
258: @table @var
259: @item return
260: byte array
261: @item len
262: \JP $B<+A3?t(B
263: \EG non-negative integer
264: @item listorstring
265: \JP $B%j%9%H$^$?$OJ8;zNs(B
266: \EG list or string
267: @end table
268:
269: @itemize @bullet
270: @item
271: \JP @code{newvect} $B$HF1MM$K$7$F(B byte array $B$r@8@.$9$k(B.
272: \EG This function generates a byte array. The specification is
273: similar to that of @code{newvect}.
274: @item
275: \JP $BJ8;zNs$G=i4|CM$r;XDj$9$k$3$H$b2DG=$G$"$k(B.
276: \EG The initial value can be specified by a character string.
277: @item
278: \JP byte array $B$NMWAG$N%"%/%;%9$OG[Ns$HF1MM$G$"$k(B.
279: \EG One can access elements of a byte array just as an array.
280: @end itemize
281:
282: @example
283: [182] A=newbytearray(3);
284: |00 00 00|
285: [183] A=newbytearray(3,[1,2,3]);
286: |01 02 03|
287: [184] A=newbytearray(3,"abc");
288: |61 62 63|
289: [185] A[0];
290: 97
291: [186] A[1]=123;
292: 123
293: [187] A;
294: |61 7b 63|
1.1 noro 295: @end example
296:
297: @table @t
1.2 noro 298: \JP @item $B;2>H(B
299: \EG @item References
1.1 noro 300: @fref{newvect}.
301: @end table
302:
1.2 noro 303: \JP @node newmat,,, $BG[Ns(B
304: \EG @node newmat,,, Arrays
1.1 noro 305: @subsection @code{newmat}
306: @findex newmat
307:
308: @table @t
1.6 noro 309: @item newmat(@var{row},@var{col} [,[[@var{a},@var{b},...],[@var{c},@var{d},...],...]])
1.2 noro 310: \JP :: @var{row} $B9T(B @var{col} $BNs$N9TNs$r@8@.$9$k(B.
311: \EG :: Creates a new matrix with @var{row} rows and @var{col} columns.
1.1 noro 312: @end table
313:
314: @table @var
315: @item return
1.2 noro 316: \JP $B9TNs(B
317: \EG matrix
1.6 noro 318: @item row col
1.2 noro 319: \JP $B<+A3?t(B
320: \EG non-negative integer
1.6 noro 321: @item a b c d
1.2 noro 322: \JP $BG$0U(B
323: \EG arbitrary
1.1 noro 324: @end table
325:
326: @itemize @bullet
1.2 noro 327: \BJP
1.1 noro 328: @item
329: @var{row} $B9T(B @var{col} $BNs$N9TNs$r@8@.$9$k(B. $BBh(B 3 $B0z?t$,$J$$>l9g(B,
330: $B3F@.J,$O(B 0 $B$K=i4|2=$5$l$k(B. $BBh(B 3 $B0z?t$,$"$k>l9g(B,
331: $B%$%s%G%C%/%9$N>.$5$$@.J,$+$i(B, $B3F9T$,(B, $B%j%9%H$N(B
332: $B3FMWAG(B ($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
333: $B;H$o$l(B, $BB-$j$J$$J,$O(B 0 $B$,Kd$a$i$l$k(B.
334: @item
335: $B9TNs$N%5%$%:$O(B @code{size()} $B$GF@$i$l$k(B.
336: @item
337: @code{M} $B$,9TNs$N$H$-(B, @code{M[I]} $B$K$h$jBh(B @code{I} $B9T$r%Y%/%H%k$H$7$F(B
338: $B<h$j=P$9$3$H$,$G$-$k(B. $B$3$N%Y%/%H%k$O(B, $B$b$H$N9TNs$H@.J,$r6&M-$7$F$*$j(B,
339: $B$$$:$l$+$N@.J,$r=q$-49$($l$P(B, $BB>$NBP1~$9$k@.J,$b=q$-49$o$k$3$H$K$J$k(B.
340: @item
341: $BH!?t$N0z?t$H$7$F9TNs$rEO$7$?>l9g(B, $BEO$5$l$?H!?t$O(B, $B$=$N9TNs$N@.J,(B
342: $B$r=q$-49$($k$3$H$,$G$-$k(B.
1.2 noro 343: \E
344: \BEG
345: @item
346: If the third argument, a list, is given, the newly created matrix
347: is initialized so that each element of the list (again a list)
348: initializes each of the rows of the matrix.
349: Elements are used from the first through the last.
350: If the list is short, 0's are filled in the remaining matrix elements.
351: If no third argument is given all the elements are cleared to 0.
352: @item
353: The size of a matrix is given by function @code{size()}.
354: @item
355: Let @code{M} be a program variable assigned to a matrix.
356: Then, @code{M[I]} denotes a (row) vector which corresponds with
357: the @code{I}-th row of the matrix.
358: Note that the vector shares its element with the original matrix.
359: Subsequently, if an element of the vector is modified, then the
360: corresponding matrix element is also modified.
361: @item
362: When a matrix is passed to a function as its argument
363: (actual parameter), the matrix element can be modified within that
364: function.
365: \E
1.1 noro 366: @end itemize
367:
368: @example
369: [0] A = newmat(3,3,[[1,1,1],[x,y],[x^2]]);
370: [ 1 1 1 ]
371: [ x y 0 ]
372: [ x^2 0 0 ]
373: [1] det(A);
374: -y*x^2
375: [2] size(A);
376: [3,3]
377: [3] A[1];
378: [ x y 0 ]
379: [4] A[1][3];
380: getarray : Out of range
381: return to toplevel
382: @end example
383:
384: @table @t
1.2 noro 385: \JP @item $B;2>H(B
386: \EG @item References
1.5 noro 387: @fref{newvect}, @fref{size}, @fref{det invmat}.
1.1 noro 388: @end table
389:
1.2 noro 390: \JP @node size,,, $BG[Ns(B
391: \EG @node size,,, Arrays
1.1 noro 392: @subsection @code{size}
393: @findex size
394:
395: @table @t
396: @item size(@var{vect|mat})
1.2 noro 397: \JP :: @code{[@var{vect} $B$ND9$5(B]} $B$^$?$O(B @code{[@var{mat} $B$N9T?t(B,@var{mat} $B$NNs?t(B]}.
398: \BEG
399: :: A list containing the number of elements of the given vector,
400: @code{[size of @var{vect}]},
401: or a list containing row size and column size of the given matrix,
402: @code{[row size of @var{mat}, column size of @var{mat}]}.
403: \E
1.1 noro 404: @end table
405:
406: @table @var
407: @item return
1.2 noro 408: \JP $B%j%9%H(B
409: \EG list
1.1 noro 410: @item vect
1.2 noro 411: \JP $B%Y%/%H%k(B
412: \EG vector
1.1 noro 413: @item mat
1.2 noro 414: \JP $B9TNs(B
415: \EG matrix
1.1 noro 416: @end table
417:
418: @itemize @bullet
1.2 noro 419: \BJP
1.1 noro 420: @item
1.9 ! ohara 421: @var{vect} $B$ND9$5(B, $B$^$?$O(B @var{mat} $B$NBg$-$5$r%j%9%H$G=PNO$9$k(B.
! 422: @item
! 423: @var{vect} $B$ND9$5$O(B @code{length()} $B$G5a$a$k$3$H$b$G$-$k(B.
1.1 noro 424: @item
1.9 ! ohara 425: @var{list} $B$ND9$5$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 426: \E
427: \BEG
428: @item
429: Return a list consisting of the dimension of the vector @var{vect},
430: or a list consisting of the row size and column size of the matrix
431: @var{matrix}.
432: @item
433: Use @code{length()} for the size of @var{list}, and
434: @code{nmono()} for the number of monomials with non-zero coefficients
435: in a rational expression.
436: \E
1.1 noro 437: @end itemize
438:
439: @example
440: [0] A = newvect(4);
441: [ 0 0 0 0 ]
442: [1] size(A);
443: [4]
1.9 ! ohara 444: [2] length(A);
! 445: 4
! 446: [3] B = newmat(2,3,[[1,2,3],[4,5,6]]);
1.1 noro 447: [ 1 2 3 ]
448: [ 4 5 6 ]
1.9 ! ohara 449: [4] size(B);
1.1 noro 450: [2,3]
451: @end example
452:
453: @table @t
1.2 noro 454: \JP @item $B;2>H(B
455: \EG @item References
1.1 noro 456: @fref{car cdr cons append reverse length}, @fref{nmono}.
457: @end table
458:
1.5 noro 459: \JP @node det invmat,,, $BG[Ns(B
460: \EG @node det invmat,,, Arrays
461: @subsection @code{det},@code{invmat}
1.1 noro 462: @findex det
1.5 noro 463: @findex invmat
1.1 noro 464:
465: @table @t
466: @item det(@var{mat}[,@var{mod}])
1.2 noro 467: \JP :: @var{mat} $B$N9TNs<0$r5a$a$k(B.
468: \EG :: Determinant of @var{mat}.
1.5 noro 469: @item invmat(@var{mat})
1.8 takayama 470: \JP :: @var{mat} $B$N5U9TNs$r5a$a$k(B.
1.5 noro 471: \EG :: Inverse matrix of @var{mat}.
1.1 noro 472: @end table
473:
474: @table @var
475: @item return
1.5 noro 476: \JP @code{det}: $B<0(B, @code{invmat}: $B%j%9%H(B
477: \EG @code{det}: expression, @code{invmat}: list
1.1 noro 478: @item mat
1.2 noro 479: \JP $B9TNs(B
480: \EG matrix
1.1 noro 481: @item mod
1.2 noro 482: \JP $BAG?t(B
483: \EG prime
1.1 noro 484: @end table
485:
486: @itemize @bullet
1.2 noro 487: \BJP
1.1 noro 488: @item
1.5 noro 489: @code{det} $B$O9TNs(B @var{mat} $B$N9TNs<0$r5a$a$k(B.
490: @code{invmat} $B$O9TNs(B @var{mat} $B$N5U9TNs$r5a$a$k(B. $B5U9TNs$O(B @code{[$BJ,Jl(B, $BJ,;R(B]}
491: $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 492: @item
493: $B0z?t(B @var{mod} $B$,$"$k;~(B, GF(@var{mod}) $B>e$G$N9TNs<0$r5a$a$k(B.
494: @item
495: $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
496: $B9TNs$KBP$7$F$O>.9TNs<0E83+$K$h$kJ}K!$N$[$&$,8zN($,$h$$>l9g$b$"$k(B.
1.2 noro 497: \E
498: \BEG
499: @item
1.5 noro 500: @code{det} computes the determinant of matrix @var{mat}.
501: @code{invmat} computes the inverse matrix of matrix @var{mat}.
502: @code{invmat} returns a list @code{[num,den]}, where @code{num}
503: is a matrix and @code{num/den} represents the inverse matrix.
1.2 noro 504: @item
505: The computation is done over GF(@var{mod}) if @var{mod} is specitied.
506: @item
507: The fraction free Gaussian algorithm is employed. For matrices with
508: multi-variate polynomial entries, minor expansion algorithm sometimes
509: is more efficient than the fraction free Gaussian algorithm.
510: \E
1.1 noro 511: @end itemize
512:
513: @example
514: [91] A=newmat(5,5)$
515: [92] V=[x,y,z,u,v];
516: [x,y,z,u,v]
517: [93] for(I=0;I<5;I++)for(J=0,B=A[I],W=V[I];J<5;J++)B[J]=W^J;
518: [94] A;
519: [ 1 x x^2 x^3 x^4 ]
520: [ 1 y y^2 y^3 y^4 ]
521: [ 1 z z^2 z^3 z^4 ]
522: [ 1 u u^2 u^3 u^4 ]
523: [ 1 v v^2 v^3 v^4 ]
524: [95] fctr(det(A));
1.7 noro 525: [[1,1],[u-v,1],[-z+v,1],[-z+u,1],[-y+u,1],[y-v,1],[-y+z,1],[-x+u,1],
526: [-x+z,1],[-x+v,1],[-x+y,1]]
1.5 noro 527: [96] A = newmat(3,3)$
528: [97] for(I=0;I<3;I++)for(J=0,B=A[I],W=V[I];J<3;J++)B[J]=W^J;
529: [98] A;
530: [ 1 x x^2 ]
531: [ 1 y y^2 ]
532: [ 1 z z^2 ]
533: [99] invmat(A);
534: [[ -z*y^2+z^2*y z*x^2-z^2*x -y*x^2+y^2*x ]
535: [ y^2-z^2 -x^2+z^2 x^2-y^2 ]
536: [ -y+z x-z -x+y ],(-y+z)*x^2+(y^2-z^2)*x-z*y^2+z^2*y]
537: [100] A*B[0];
538: [ (-y+z)*x^2+(y^2-z^2)*x-z*y^2+z^2*y 0 0 ]
539: [ 0 (-y+z)*x^2+(y^2-z^2)*x-z*y^2+z^2*y 0 ]
540: [ 0 0 (-y+z)*x^2+(y^2-z^2)*x-z*y^2+z^2*y ]
541: [101] map(red,A*B[0]/B[1]);
542: [ 1 0 0 ]
543: [ 0 1 0 ]
544: [ 0 0 1 ]
1.1 noro 545: @end example
546:
547: @table @t
1.2 noro 548: \JP @item $B;2>H(B
549: \EG @item References
1.1 noro 550: @fref{newmat}.
551: @end table
552:
1.2 noro 553: \JP @node qsort,,, $BG[Ns(B
554: \EG @node qsort,,, Arrays
1.1 noro 555: @subsection @code{qsort}
556: @findex qsort
557:
558: @table @t
559: @item qsort(@var{array}[,@var{func}])
1.2 noro 560: \JP :: $B0l<!85G[Ns(B @var{array} $B$r%=!<%H$9$k(B.
561: \EG :: Sorts an array @var{array}.
1.1 noro 562: @end table
563:
564: @table @var
565: @item return
1.2 noro 566: \JP @var{array} ($BF~NO$HF1$8(B; $BMWAG$N$_F~$lBX$o$k(B)
567: \EG @var{array} (The same as the input; Only the elements are exchanged.)
1.1 noro 568: @item array
1.2 noro 569: \JP $B0l<!85G[Ns(B
570: \EG array
1.1 noro 571: @item func
1.2 noro 572: \JP $BHf3SMQ4X?t(B
573: \EG function for comparison
1.1 noro 574: @end table
575:
576: @itemize @bullet
1.2 noro 577: \BJP
1.1 noro 578: @item
579: $B0l<!85G[Ns$r(B quick sort $B$G%=!<%H$9$k(B.
580: @item
581: $BHf3SMQ4X?t$,;XDj$5$l$F$$$J$$>l9g(B, $B%*%V%8%'%/%H$I$&$7$NHf3S7k2L$G(B
582: $B=g=x$,2<$N$b$N$+$i=g$KJB$Y49$($i$l$k(B.
583: @item
584: 0, 1, -1 $B$rJV$9(B 2 $B0z?t4X?t$,(B @var{func} $B$H$7$FM?$($i$l$?>l9g(B,
585: @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
586: $B$b$N$+$i=g$KJB$Y49$($i$l$k(B.
587: @item
588: $BG[Ns$O?7$?$K@8@.$5$l$:(B, $B0z?t$NG[Ns$NMWAG$N$_F~$lBX$o$k(B.
1.2 noro 589: \E
590: \BEG
591: @item
592: This function sorts an array by @var{quick sort}.
593: @item
594: If @var{func} is not specified, the built-in comparison function
595: is used and the array is sorted in increasing order.
596: @item
597: If a function of two arguments @var{func} which returns 0, 1, or -1
598: is provided, then an ordering is detemined so that
599: @code{A<B} if @code{@var{func}(A,B)=1} holds, and
600: the array is sorted in increasing order with respect to the ordering.
601: @item
602: The returned array is the same as the input. Only the elements
603: are exchanged.
604: \E
1.1 noro 605: @end itemize
606:
607: @example
608: [0] qsort(newvect(10,[1,4,6,7,3,2,9,6,0,-1]));
609: [ -1 0 1 2 3 4 6 6 7 9 ]
610: [1] def rev(A,B) @{ return A>B?-1:(A<B?1:0); @}
611: [2] qsort(newvect(10,[1,4,6,7,3,2,9,6,0,-1]),rev);
612: [ 9 7 6 6 4 3 2 1 0 -1 ]
613: @end example
614:
615: @table @t
1.2 noro 616: \JP @item $B;2>H(B
617: \EG @item References
1.1 noro 618: @fref{ord}, @fref{vars}.
619: @end table
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