質問編集履歴
2
アルゴリズムの修正。説明を追加。作り直したソースコードを張りました。
test
CHANGED
|
File without changes
|
test
CHANGED
|
@@ -6,17 +6,109 @@
|
|
|
6
6
|
|
|
7
7
|
プログラムの流れは、
|
|
8
8
|
|
|
9
|
-
1.行列の行数、列数を入力
|
|
9
|
+
1.行列の行数(lnum)、列数(cnum)を入力
|
|
10
10
|
|
|
11
11
|
2.行列の各成分を入力、格納。
|
|
12
12
|
|
|
13
|
+
3．行列の走査（matsearch）を行う。
|
|
14
|
+
|
|
15
|
+
走査範囲は初めは1列目の全行であるとする。
|
|
16
|
+
|
|
17
|
+
１列目から順に
|
|
18
|
+
|
|
19
|
+
特定の列の走査範囲内の要素をを上から順に確認
|
|
20
|
+
|
|
21
|
+
→すべて0 ⇒ 走査範囲はそのままで次の列に
|
|
22
|
+
|
|
23
|
+
|
|
24
|
+
|
|
13
|
-
|
|
25
|
+
→上端が非0かつ上端以外はすべて0 ⇒ 走査範囲を一つ縮める（元の走査範囲から上端の行を抜いたもの）。そして走査範囲は次の列へ
|
|
26
|
+
|
|
27
|
+
|
|
28
|
+
|
|
14
|
-
|
|
29
|
+
→上端以外に非0が存在
|
|
30
|
+
|
|
31
|
+
⇒ その列が基本変形対象範囲最重要列J₀
|
|
32
|
+
|
|
33
|
+
かつ
|
|
34
|
+
|
|
15
|
-
|
|
35
|
+
その走査範囲の上端の行は基本変形対象範囲開始行I₀。
|
|
36
|
+
|
|
16
|
-
|
|
37
|
+
for行ループ → break
|
|
38
|
+
|
|
39
|
+
for列ループ → break
|
|
40
|
+
|
|
41
|
+
matsearch → 終了
|
|
42
|
+
|
|
43
|
+
|
|
44
|
+
|
|
45
|
+
最終的に…matsearchの返却値は
|
|
46
|
+
|
|
47
|
+
①J=cnumですべてその列の成分が０
|
|
48
|
+
|
|
49
|
+
→ -2
|
|
50
|
+
|
|
51
|
+
②（I₀，J₀）＝０かつbreak
|
|
52
|
+
|
|
53
|
+
→ I₀
|
|
54
|
+
|
|
55
|
+
③（I₀，J₀）≠０かつbreak
|
|
56
|
+
|
|
57
|
+
→ -1
|
|
58
|
+
|
|
59
|
+
4.行基本変形
|
|
60
|
+
|
|
61
|
+
①：
|
|
62
|
+
|
|
63
|
+
rank計算へ
|
|
64
|
+
|
|
65
|
+
|
|
66
|
+
|
|
67
|
+
②：
|
|
68
|
+
|
|
69
|
+
（I, J₀）成分のうち、I₀≦I≦lnumの範囲で
|
|
70
|
+
|
|
71
|
+
非0となっている成分について考える。
|
|
72
|
+
|
|
73
|
+
このような成分のうち、最小行番号をもつ成分の行番号
|
|
74
|
+
|
|
75
|
+
をI₁とする。（I₀＜I₁≦lnum）
|
|
76
|
+
|
|
77
|
+
|
|
78
|
+
|
|
17
|
-
|
|
79
|
+
2-2-1.1：（I₁，J）成分でI₁行成分をすべて割る。
|
|
80
|
+
|
|
18
|
-
|
|
81
|
+
2-2-1.2：（I₀，J）成分に
|
|
82
|
+
|
|
83
|
+
「（I₀，J）成分 + （I₁，J）成分」
|
|
84
|
+
|
|
85
|
+
の演算結果を代入する。
|
|
86
|
+
|
|
87
|
+
2-2-1.3：
|
|
88
|
+
|
|
89
|
+
（I，J）成分に（I＞I₀）
|
|
90
|
+
|
|
91
|
+
「（I，J）成分 -｛（I，J）成分*（I₀，J）｝」
|
|
92
|
+
|
|
93
|
+
の演算結果を代入する。
|
|
94
|
+
|
|
95
|
+
そのまま③へ
|
|
96
|
+
|
|
97
|
+
|
|
98
|
+
|
|
99
|
+
③：
|
|
100
|
+
|
|
101
|
+
操作2-1
|
|
102
|
+
|
|
19
|
-
|
|
103
|
+
2-1.1：（I₀ , J₀）成分でI₀行成分をすべて割る。
|
|
104
|
+
|
|
105
|
+
2-1.2：（I，J）成分に（I＞I₀）
|
|
106
|
+
|
|
107
|
+
「（I，J）成分 -｛（I，J）成分*（I₀，J）｝」
|
|
108
|
+
|
|
109
|
+
の演算結果を代入する。
|
|
110
|
+
|
|
111
|
+
|
|
20
112
|
|
|
21
113
|
|
|
22
114
|
|
|
@@ -28,25 +120,7 @@
|
|
|
28
120
|
|
|
29
121
|
###発生している問題・エラーメッセージ
|
|
30
122
|
|
|
31
|
-
例えば、計算過程で
|
|
32
|
-
|
|
33
|
-
| 1.00 2.00 3.00 |
|
|
34
|
-
|
|
35
|
-
| 0.00 1.00 2.00 |
|
|
36
|
-
|
|
37
|
-
| 0.00 0.00 0.00 |
|
|
38
|
-
|
|
39
|
-
こ
|
|
123
|
+
計算過程でループが終了せずどこが間違っているのかがわからないです。
|
|
40
|
-
|
|
41
|
-
次の手順後には
|
|
42
|
-
|
|
43
|
-
| 1.00 2.00 3.00 |
|
|
44
|
-
|
|
45
|
-
| 0.00 1.00 2.00 |
|
|
46
|
-
|
|
47
|
-
| 0.00 0.00 1.00 |
|
|
48
|
-
|
|
49
|
-
と訳の分からないことをしています。
|
|
50
124
|
|
|
51
125
|
|
|
52
126
|
|
|
@@ -54,105 +128,277 @@
|
|
|
54
128
|
|
|
55
129
|
###該当のソースコード
|
|
56
130
|
|
|
57
|
-
```
|
|
131
|
+
```
|
|
58
132
|
|
|
59
133
|
#include <stdio.h>
|
|
60
134
|
|
|
61
|
-
|
|
135
|
+
#define NA 7
|
|
62
|
-
|
|
136
|
+
|
|
63
|
-
#define
|
|
137
|
+
#define NB 3
|
|
64
|
-
|
|
65
|
-
|
|
138
|
+
|
|
66
|
-
|
|
67
|
-
#define
|
|
139
|
+
#define PLUS 0
|
|
68
|
-
|
|
140
|
+
|
|
69
|
-
#define
|
|
141
|
+
#define MINUS 1
|
|
70
|
-
|
|
71
|
-
|
|
72
|
-
|
|
73
|
-
|
|
142
|
+
|
|
74
|
-
|
|
75
|
-
#in
|
|
143
|
+
#define ERROR_R 1.000000e-15
|
|
76
|
-
|
|
77
|
-
|
|
78
|
-
|
|
144
|
+
|
|
145
|
+
|
|
146
|
+
|
|
147
|
+
|
|
148
|
+
|
|
79
|
-
|
|
149
|
+
int zerojudgef(double a)
|
|
80
150
|
|
|
81
151
|
{
|
|
82
152
|
|
|
83
|
-
double dst;
|
|
84
|
-
|
|
85
|
-
|
|
86
|
-
|
|
87
|
-
dst = src * pow(10, -n - 1); /*処理を行う桁を10-1 の位にする*/
|
|
88
|
-
|
|
89
|
-
dst = (double)(int)(dst + 0.5);
|
|
90
|
-
|
|
91
|
-
|
|
92
|
-
|
|
93
|
-
|
|
153
|
+
return ((a < ERROR_R) & (a > (-1)*ERROR_R) ? 0 : 1);
|
|
94
154
|
|
|
95
155
|
}
|
|
96
156
|
|
|
97
157
|
|
|
98
158
|
|
|
99
|
-
|
|
100
|
-
|
|
101
|
-
|
|
102
|
-
|
|
103
|
-
|
|
104
|
-
|
|
105
|
-
|
|
106
|
-
|
|
107
|
-
|
|
108
|
-
|
|
109
|
-
|
|
110
|
-
|
|
111
|
-
|
|
159
|
+
int matsearchf(double mat[][NA][NA], int lnum, int cnum, int keylinenum, int keycolumnnum, int rank)
|
|
160
|
+
|
|
161
|
+
/*
|
|
162
|
+
|
|
163
|
+
keylinenum : the number of line that is the start point of elementary row operation. Exactly, in the column of key-column number, and below the line of the start line of elemntary row operation ,there may exists the element that is not zero which has the smallest number of line. The line number of such elements is defined as keylinenum.
|
|
164
|
+
|
|
165
|
+
That is, if the start line of elementary row operation is not the exactly defined keyline number, the start line of elementray row operation is linebreak.
|
|
166
|
+
|
|
167
|
+
|
|
168
|
+
|
|
169
|
+
keycolumnnum : the number of column that is the key-column of elementary row op
|
|
170
|
+
|
|
171
|
+
ertion.
|
|
172
|
+
|
|
173
|
+
*/
|
|
112
174
|
|
|
113
175
|
{
|
|
114
176
|
|
|
115
|
-
|
|
177
|
+
int i, j;
|
|
178
|
+
|
|
179
|
+
int linebreak = 0;
|
|
180
|
+
|
|
181
|
+
for(j=0; j<cnum; j++){
|
|
182
|
+
|
|
183
|
+
int k = 0;
|
|
184
|
+
|
|
185
|
+
int notzero = 0;
|
|
186
|
+
|
|
187
|
+
int keynum_for_count = 0;
|
|
188
|
+
|
|
189
|
+
for(i=linebreak; i<lnum; i++){
|
|
190
|
+
|
|
191
|
+
|
|
192
|
+
|
|
193
|
+
if(zerojudgef(mat[0][i][j])){
|
|
194
|
+
|
|
195
|
+
notzero++;
|
|
196
|
+
|
|
197
|
+
}/*for-for-if*/
|
|
198
|
+
|
|
199
|
+
}/*for-for*/
|
|
200
|
+
|
|
201
|
+
/*Finding out the key-line number
|
|
202
|
+
|
|
203
|
+
In the column of key-column number, and below the line of key-line number, there may exists the element that is not zero which has the smallest number of line. The line number of such elements is defined as keylinenum, and in this function, for the purpose of counting the key-line number, a variable 'keynum_for_count' is defined.
|
|
204
|
+
|
|
205
|
+
*/
|
|
206
|
+
|
|
207
|
+
do{
|
|
208
|
+
|
|
209
|
+
keynum_for_count = (zerojudgef(mat[0][k][j]) != 0 ? k : -1);//ここは最悪k+linebreakでもok
|
|
210
|
+
|
|
211
|
+
k++;
|
|
212
|
+
|
|
213
|
+
}while( (keynum_for_count < 0) & (k != (NA-1) ) );//matのイランとこは全部0で初期化が条件
|
|
214
|
+
|
|
215
|
+
|
|
216
|
+
|
|
217
|
+
if(zerojudgef(notzero)){/*There exist at least one element that is not equal to zero.*/
|
|
218
|
+
|
|
219
|
+
|
|
220
|
+
|
|
221
|
+
if(zerojudgef(mat[0][linebreak][j])){/*The top elements in the scope of line-searching is not equal to zero.*/
|
|
222
|
+
|
|
223
|
+
if(notzero > 1){/*There exists not-zero elemnet at the top of the scope of line searching, and exists not-zero elements below the elements at the top. break roop*/
|
|
224
|
+
|
|
225
|
+
keylinenum = keynum_for_count;
|
|
226
|
+
|
|
227
|
+
keycolumnnum = j;
|
|
228
|
+
|
|
229
|
+
return -1;
|
|
230
|
+
|
|
231
|
+
break;
|
|
232
|
+
|
|
233
|
+
}else{
|
|
234
|
+
|
|
235
|
+
/*There exists not-zero element only at the top of the searching range, and elements below it is all equal to zero. continue roop*/
|
|
236
|
+
|
|
237
|
+
linebreak++;
|
|
238
|
+
|
|
239
|
+
|
|
240
|
+
|
|
241
|
+
}/*for-if-if-if*/
|
|
242
|
+
|
|
243
|
+
}else{/*The top elements in the scope of line-searching is equal to zero, but there exist at least one elements that is not equal to zero. break roop*/
|
|
244
|
+
|
|
245
|
+
keylinenum = keynum_for_count;
|
|
246
|
+
|
|
247
|
+
keycolumnnum = j;
|
|
248
|
+
|
|
249
|
+
return linebreak;
|
|
250
|
+
|
|
251
|
+
break;
|
|
252
|
+
|
|
253
|
+
}/*for-if-if*/
|
|
254
|
+
|
|
255
|
+
}else{/*There exist only elements that is equal to zero. continue roop*/
|
|
256
|
+
|
|
257
|
+
|
|
258
|
+
|
|
259
|
+
}/*for-if*/
|
|
260
|
+
|
|
261
|
+
}/*for*/
|
|
262
|
+
|
|
263
|
+
|
|
264
|
+
|
|
265
|
+
rank = linebreak;
|
|
266
|
+
|
|
267
|
+
return -2;
|
|
268
|
+
|
|
269
|
+
|
|
270
|
+
|
|
271
|
+
/*Finally, the result is classified into 3 types.
|
|
272
|
+
|
|
273
|
+
1:All the elemnets in the last column of the scope is equal to zero.
|
|
274
|
+
|
|
275
|
+
output = -2
|
|
276
|
+
|
|
277
|
+
2:The (keylinenum, keycolumnnum) elemnet is equal to zero.
|
|
278
|
+
|
|
279
|
+
output = linebreak
|
|
280
|
+
|
|
281
|
+
3:The (keylinenum, keycolumnnum) elemnet is not equal to zero.
|
|
282
|
+
|
|
283
|
+
output = -1
|
|
284
|
+
|
|
285
|
+
*/
|
|
116
286
|
|
|
117
287
|
}
|
|
118
288
|
|
|
119
289
|
|
|
120
290
|
|
|
121
|
-
void
|
|
291
|
+
void divf(int divdo, int divdonel, int cnum, double mat[][NA][NA])
|
|
122
292
|
|
|
123
293
|
{
|
|
124
294
|
|
|
295
|
+
/*
|
|
296
|
+
|
|
125
|
-
|
|
297
|
+
divdo :割る数の要素の列番号
|
|
126
|
-
|
|
298
|
+
|
|
127
|
-
|
|
299
|
+
divdonel :割られる数の要素が存在する行番号
|
|
300
|
+
|
|
128
|
-
|
|
301
|
+
cnum :割り算実行される行の列数
|
|
302
|
+
|
|
303
|
+
*/
|
|
304
|
+
|
|
305
|
+
double divisor = mat[0][divdonel][divdo];
|
|
306
|
+
|
|
307
|
+
|
|
308
|
+
|
|
129
|
-
int
|
|
309
|
+
int i;
|
|
130
|
-
|
|
131
|
-
|
|
310
|
+
|
|
132
|
-
|
|
133
|
-
for(
|
|
311
|
+
for(i=0; i<cnum; i++){
|
|
134
|
-
|
|
135
|
-
|
|
312
|
+
|
|
136
|
-
|
|
137
|
-
|
|
313
|
+
mat[0][divdonel][i] /= divisor;
|
|
138
314
|
|
|
139
315
|
}
|
|
140
316
|
|
|
141
317
|
|
|
142
318
|
|
|
319
|
+
/**/
|
|
320
|
+
|
|
321
|
+
int line, column;
|
|
322
|
+
|
|
323
|
+
puts("divf");
|
|
324
|
+
|
|
325
|
+
printf("\n");
|
|
326
|
+
|
|
327
|
+
for(line=0; line<NA; line++){
|
|
328
|
+
|
|
329
|
+
printf("|");
|
|
330
|
+
|
|
331
|
+
for(column=0; column<NA; column++){
|
|
332
|
+
|
|
333
|
+
printf("%5.2f", mat[0][line][column]);
|
|
334
|
+
|
|
335
|
+
}
|
|
336
|
+
|
|
337
|
+
printf(" |\n");
|
|
338
|
+
|
|
339
|
+
}
|
|
340
|
+
|
|
341
|
+
printf("\n\n");
|
|
342
|
+
|
|
343
|
+
|
|
344
|
+
|
|
345
|
+
|
|
346
|
+
|
|
143
347
|
/**/
|
|
144
348
|
|
|
349
|
+
|
|
350
|
+
|
|
351
|
+
}
|
|
352
|
+
|
|
353
|
+
|
|
354
|
+
|
|
355
|
+
void subtraf(int p, int q, int r, int cnum, double mat[][NA][NA], double coeff)
|
|
356
|
+
|
|
357
|
+
{
|
|
358
|
+
|
|
359
|
+
/*
|
|
360
|
+
|
|
361
|
+
This function operates the line p ± the line q.
|
|
362
|
+
|
|
363
|
+
Judge by whether r = 0 or 1
|
|
364
|
+
|
|
365
|
+
-r＝０→addition＋
|
|
366
|
+
|
|
367
|
+
-r＝１→subtractionー
|
|
368
|
+
|
|
369
|
+
cnum = The total number of line
|
|
370
|
+
|
|
371
|
+
coeff = the coefficient of the number that subtacts any numbers
|
|
372
|
+
|
|
373
|
+
*/
|
|
374
|
+
|
|
375
|
+
int pm = (r == 1 ? (-1) : 1);
|
|
376
|
+
|
|
377
|
+
int i;
|
|
378
|
+
|
|
379
|
+
for(i=0; i<cnum; i++){
|
|
380
|
+
|
|
381
|
+
mat[0][p][i] += (coeff * pm * mat[0][q][i]);
|
|
382
|
+
|
|
383
|
+
}
|
|
384
|
+
|
|
385
|
+
|
|
386
|
+
|
|
387
|
+
/**/
|
|
388
|
+
|
|
389
|
+
int line, column;
|
|
390
|
+
|
|
145
|
-
puts("sub
|
|
391
|
+
puts("subtraf");
|
|
146
392
|
|
|
147
393
|
printf("\n");
|
|
148
394
|
|
|
149
|
-
for(line=0; line<
|
|
395
|
+
for(line=0; line<NA; line++){
|
|
150
396
|
|
|
151
397
|
printf("|");
|
|
152
398
|
|
|
153
|
-
for(column=0; column<
|
|
399
|
+
for(column=0; column<NA; column++){
|
|
154
|
-
|
|
400
|
+
|
|
155
|
-
printf("%
|
|
401
|
+
printf("%5.2f", mat[0][line][column]);
|
|
156
402
|
|
|
157
403
|
}
|
|
158
404
|
|
|
@@ -164,75 +410,177 @@
|
|
|
164
410
|
|
|
165
411
|
|
|
166
412
|
|
|
167
|
-
for(line=0; line<numb; line++)
|
|
168
|
-
|
|
169
|
-
printf("n[%d] %5d\n", line, n[line]);
|
|
170
|
-
|
|
171
413
|
|
|
172
414
|
|
|
173
415
|
/**/
|
|
174
416
|
|
|
417
|
+
|
|
418
|
+
|
|
419
|
+
|
|
420
|
+
|
|
175
421
|
}
|
|
176
422
|
|
|
177
423
|
|
|
178
424
|
|
|
179
|
-
void
|
|
425
|
+
void erowoperatef(double mat[][NA][NA], int lnum, int cnum, int keylinenum, int keycolumnnum)
|
|
180
426
|
|
|
181
427
|
{
|
|
182
428
|
|
|
183
|
-
|
|
184
|
-
|
|
185
|
-
|
|
186
|
-
|
|
187
|
-
|
|
188
|
-
|
|
189
|
-
|
|
190
|
-
|
|
191
|
-
|
|
192
|
-
|
|
193
|
-
|
|
194
|
-
|
|
195
|
-
|
|
196
|
-
|
|
197
|
-
in
|
|
198
|
-
|
|
199
|
-
f
|
|
200
|
-
|
|
201
|
-
|
|
202
|
-
|
|
203
|
-
|
|
429
|
+
int rank = 0;
|
|
430
|
+
|
|
431
|
+
int i, j, k;
|
|
432
|
+
|
|
433
|
+
int breakjudge = 0;
|
|
434
|
+
|
|
435
|
+
for(i=0; i<NA; i++){
|
|
436
|
+
|
|
437
|
+
k = ( ( matsearchf(mat, lnum, cnum, keylinenum, keycolumnnum, rank) < 0 ) ? matsearchf(mat, lnum, cnum, keylinenum, keycolumnnum, rank) : 1 );
|
|
438
|
+
|
|
439
|
+
switch(k){
|
|
440
|
+
|
|
441
|
+
case 1:{
|
|
442
|
+
|
|
443
|
+
divf(keycolumnnum, keylinenum, cnum, mat);
|
|
444
|
+
|
|
445
|
+
subtraf( matsearchf(mat, lnum, cnum, keylinenum, keycolumnnum, rank), keylinenum, PLUS, cnum, mat, 1);
|
|
446
|
+
|
|
447
|
+
}/*for-switch-case0*/
|
|
448
|
+
|
|
449
|
+
case -1:{
|
|
450
|
+
|
|
451
|
+
divf(keycolumnnum, keylinenum, cnum, mat);
|
|
452
|
+
|
|
453
|
+
if(i = keylinenum){
|
|
454
|
+
|
|
455
|
+
}else{
|
|
456
|
+
|
|
457
|
+
for(j=0; j<lnum; j++){
|
|
458
|
+
|
|
459
|
+
subtraf( j, keylinenum, MINUS, cnum, mat , mat[0][j][keycolumnnum]);
|
|
460
|
+
|
|
461
|
+
}/*for-switch-case-1-if-for*/
|
|
462
|
+
|
|
463
|
+
}/*for-switch-case-1-if*/
|
|
464
|
+
|
|
465
|
+
break;
|
|
466
|
+
|
|
467
|
+
}/*for-switch-case1*/
|
|
468
|
+
|
|
469
|
+
case -2:{
|
|
470
|
+
|
|
471
|
+
breakjudge = 1;
|
|
472
|
+
|
|
473
|
+
break;
|
|
474
|
+
|
|
475
|
+
}/*for-switch-case-1*/
|
|
476
|
+
|
|
477
|
+
}/*switch*/
|
|
478
|
+
|
|
479
|
+
if(breakjudge == 1){
|
|
480
|
+
|
|
481
|
+
break;
|
|
482
|
+
|
|
483
|
+
}/*for-if*/
|
|
484
|
+
|
|
485
|
+
}/*for*/
|
|
486
|
+
|
|
487
|
+
|
|
488
|
+
|
|
489
|
+
}
|
|
490
|
+
|
|
491
|
+
|
|
492
|
+
|
|
493
|
+
int rankcaloperatef(double mat[][NA][NA], int lnum, int cnum)
|
|
494
|
+
|
|
495
|
+
{
|
|
496
|
+
|
|
497
|
+
int keylinenum = 0;
|
|
498
|
+
|
|
499
|
+
int keycolumnnum = 0;
|
|
500
|
+
|
|
501
|
+
erowoperatef(mat, lnum, cnum, keylinenum, keycolumnnum);
|
|
502
|
+
|
|
503
|
+
int rank = 0;
|
|
504
|
+
|
|
505
|
+
int empty = matsearchf(mat, lnum, cnum, keylinenum, keycolumnnum, rank);
|
|
506
|
+
|
|
507
|
+
return rank;
|
|
508
|
+
|
|
509
|
+
}
|
|
510
|
+
|
|
511
|
+
|
|
512
|
+
|
|
513
|
+
int main(void)
|
|
514
|
+
|
|
515
|
+
{
|
|
516
|
+
|
|
517
|
+
double mat[NB][NA][NA] = {};
|
|
518
|
+
|
|
519
|
+
int lnum, cnum;
|
|
520
|
+
|
|
521
|
+
/*mat[kind of matrix][line number][column number] */
|
|
522
|
+
|
|
523
|
+
puts("\nWe will calculate the rank of a matrix.\nPlease enter the scale of matrix.");
|
|
524
|
+
|
|
525
|
+
printf("The number of lines (under %d) = ", NA);
|
|
526
|
+
|
|
527
|
+
scanf("%d", &lnum);
|
|
528
|
+
|
|
529
|
+
printf("The number of columns (under %d) = ", NA);
|
|
530
|
+
|
|
531
|
+
scanf("%d", &cnum);
|
|
532
|
+
|
|
533
|
+
puts("Please enter the elements of the matrix.");
|
|
534
|
+
|
|
535
|
+
puts("'mat[i][j]' represents the (i,j) elements of the matrix.");
|
|
536
|
+
|
|
537
|
+
int i, j;
|
|
538
|
+
|
|
539
|
+
for(i=0; i<lnum; i++){
|
|
540
|
+
|
|
541
|
+
for(j=0; j<cnum; j++){
|
|
542
|
+
|
|
543
|
+
printf("mat[%d][%d] = ", i+1, j+1);
|
|
544
|
+
|
|
545
|
+
scanf("%lf", &mat[0][i][j]);
|
|
546
|
+
|
|
547
|
+
mat[1][i][j] = mat[0][i][j];
|
|
548
|
+
|
|
549
|
+
}
|
|
204
550
|
|
|
205
551
|
}
|
|
206
552
|
|
|
207
|
-
|
|
208
|
-
|
|
209
|
-
|
|
553
|
+
/*mat[1]にはもともと行列が保存される。*/
|
|
554
|
+
|
|
210
|
-
|
|
555
|
+
int Rank = rankcaloperatef(mat, lnum, cnum);
|
|
556
|
+
|
|
557
|
+
int r;
|
|
558
|
+
|
|
211
|
-
|
|
559
|
+
for(r=0; r<2; r++){
|
|
212
|
-
|
|
560
|
+
|
|
213
|
-
|
|
561
|
+
printf("\n");
|
|
214
|
-
|
|
562
|
+
|
|
215
|
-
|
|
563
|
+
for(i=0; i<lnum; i++){
|
|
216
|
-
|
|
564
|
+
|
|
217
|
-
|
|
565
|
+
printf("|");
|
|
218
|
-
|
|
566
|
+
|
|
219
|
-
|
|
567
|
+
for(j=0; j<cnum; j++){
|
|
220
|
-
|
|
568
|
+
|
|
221
|
-
|
|
569
|
+
printf("%5.f", mat[r][i][j]);
|
|
222
|
-
|
|
223
|
-
}
|
|
224
|
-
|
|
225
|
-
printf(" |\n");
|
|
226
570
|
|
|
227
571
|
}
|
|
228
572
|
|
|
573
|
+
printf(" |\n");
|
|
574
|
+
|
|
575
|
+
}
|
|
576
|
+
|
|
229
|
-
|
|
577
|
+
printf("\n\n");
|
|
578
|
+
|
|
230
|
-
|
|
579
|
+
}
|
|
580
|
+
|
|
231
|
-
|
|
581
|
+
printf("\nThe rank of this matrix is %d.\n", Rank);
|
|
232
|
-
|
|
233
|
-
|
|
234
|
-
|
|
582
|
+
|
|
235
|
-
|
|
583
|
+
return 0;
|
|
236
584
|
|
|
237
585
|
|
|
238
586
|
|
|
@@ -240,519 +588,7 @@
|
|
|
240
588
|
|
|
241
589
|
|
|
242
590
|
|
|
243
|
-
|
|
591
|
+
|
|
244
|
-
|
|
245
|
-
{
|
|
246
|
-
|
|
247
|
-
/*
|
|
248
|
-
|
|
249
|
-
p行 ± q行 を行う。
|
|
250
|
-
|
|
251
|
-
r = 0 or 1 で
|
|
252
|
-
|
|
253
|
-
-r＝０→足し算＋
|
|
254
|
-
|
|
255
|
-
-r＝１→引き算ー
|
|
256
|
-
|
|
257
|
-
cnum = 行列の総列数
|
|
258
|
-
|
|
259
|
-
*/
|
|
260
|
-
|
|
261
|
-
int pm = (r == 1 ? (-1) : 1);
|
|
262
|
-
|
|
263
|
-
int i;
|
|
264
|
-
|
|
265
|
-
for(i=0; i<cnum; i++){
|
|
266
|
-
|
|
267
|
-
mat[0][p][i] += (pm * mat[0][q][i]);
|
|
268
|
-
|
|
269
|
-
}
|
|
270
|
-
|
|
271
|
-
|
|
272
|
-
|
|
273
|
-
/**/
|
|
274
|
-
|
|
275
|
-
puts("subtraf");
|
|
276
|
-
|
|
277
|
-
printf("\n");
|
|
278
|
-
|
|
279
|
-
for(line=0; line<numb; line++){
|
|
280
|
-
|
|
281
|
-
printf("|");
|
|
282
|
-
|
|
283
|
-
for(column=0; column<numb; column++){
|
|
284
|
-
|
|
285
|
-
printf("%5.2f", mat[0][line][column]);
|
|
286
|
-
|
|
287
|
-
}
|
|
288
|
-
|
|
289
|
-
printf(" |\n");
|
|
290
|
-
|
|
291
|
-
}
|
|
292
|
-
|
|
293
|
-
printf("\n\n");
|
|
294
|
-
|
|
295
|
-
|
|
296
|
-
|
|
297
|
-
|
|
298
|
-
|
|
299
|
-
/**/
|
|
300
|
-
|
|
301
|
-
|
|
302
|
-
|
|
303
|
-
|
|
304
|
-
|
|
305
|
-
}
|
|
306
|
-
|
|
307
|
-
|
|
308
|
-
|
|
309
|
-
|
|
310
|
-
|
|
311
|
-
void divjudgef(int e, int k, int cnum, int lnum, double mat[0][numb][numb], int n[])
|
|
312
|
-
|
|
313
|
-
{
|
|
314
|
-
|
|
315
|
-
/*
|
|
316
|
-
|
|
317
|
-
e :行基本変形の対象範囲の左上角の成分の行番号
|
|
318
|
-
|
|
319
|
-
k :行基本変形対象範囲の左上角の成分の列番号
|
|
320
|
-
|
|
321
|
-
cnum :行列の総行数
|
|
322
|
-
|
|
323
|
-
lnum :行列の総列数
|
|
324
|
-
|
|
325
|
-
*/
|
|
326
|
-
|
|
327
|
-
|
|
328
|
-
|
|
329
|
-
int u = 0;/*e以降のeに対する相対的な行番号e+uはa_e_k以降初めての非0の成分の存在する業番号を表す。*/
|
|
330
|
-
|
|
331
|
-
|
|
332
|
-
|
|
333
|
-
switch(n[e] == 0){
|
|
334
|
-
|
|
335
|
-
/*１:The pattern of A_e_k = 0*/
|
|
336
|
-
|
|
337
|
-
case 1:{
|
|
338
|
-
|
|
339
|
-
while(n[e+u] == 0){
|
|
340
|
-
|
|
341
|
-
u++;
|
|
342
|
-
|
|
343
|
-
if((e+u) == lnum){
|
|
344
|
-
|
|
345
|
-
break;
|
|
346
|
-
|
|
347
|
-
}/*switch-case1-while-if*/
|
|
348
|
-
|
|
349
|
-
break;
|
|
350
|
-
|
|
351
|
-
}/*switch-case1-while*/
|
|
352
|
-
|
|
353
|
-
|
|
354
|
-
|
|
355
|
-
switch((e+u) == lnum){
|
|
356
|
-
|
|
357
|
-
|
|
358
|
-
|
|
359
|
-
/*The pattern of １－１：A_e_* = 0(All zero)*/
|
|
360
|
-
|
|
361
|
-
case 1:{
|
|
362
|
-
|
|
363
|
-
e -= 1;
|
|
364
|
-
|
|
365
|
-
printf("%d\n", e);
|
|
366
|
-
|
|
367
|
-
break;
|
|
368
|
-
|
|
369
|
-
}/*switch-case1-switch-case1*/
|
|
370
|
-
|
|
371
|
-
|
|
372
|
-
|
|
373
|
-
/*The pattern of １－２：There exists at least one elemnets such as A_e_* ≠ 0*/
|
|
374
|
-
|
|
375
|
-
case 0:{
|
|
376
|
-
|
|
377
|
-
divf(k, e+u, cnum, mat);
|
|
378
|
-
|
|
379
|
-
subtraf(e, e+u, plus, cnum, mat);
|
|
380
|
-
|
|
381
|
-
break;
|
|
382
|
-
|
|
383
|
-
}/*switch-case1-switch-case0*/
|
|
384
|
-
|
|
385
|
-
}/*switch-case1-switch*/
|
|
386
|
-
|
|
387
|
-
break;
|
|
388
|
-
|
|
389
|
-
}/*switch-case1*/
|
|
390
|
-
|
|
391
|
-
|
|
392
|
-
|
|
393
|
-
/*The pattern of ２：A_e_k ≠ 0*/
|
|
394
|
-
|
|
395
|
-
case 0:{
|
|
396
|
-
|
|
397
|
-
for(u=0; u<lnum; u++){
|
|
398
|
-
|
|
399
|
-
switch(n[e+u] == 1){
|
|
400
|
-
|
|
401
|
-
|
|
402
|
-
|
|
403
|
-
/*The pattern of ２－２：A_e_p ≠ 0*/
|
|
404
|
-
|
|
405
|
-
case 1:{
|
|
406
|
-
|
|
407
|
-
divf(k, e+u, cnum, mat);
|
|
408
|
-
|
|
409
|
-
break;
|
|
410
|
-
|
|
411
|
-
}/*switch-case0-for-switch-case1*/
|
|
412
|
-
|
|
413
|
-
|
|
414
|
-
|
|
415
|
-
/*The pattern of ２－１：A_e_p = 0*/
|
|
416
|
-
|
|
417
|
-
case 0:{
|
|
418
|
-
|
|
419
|
-
break;
|
|
420
|
-
|
|
421
|
-
}/*switch-case0-for-switch-case0*/
|
|
422
|
-
|
|
423
|
-
}/*switch-case0-for-switch*/
|
|
424
|
-
|
|
425
|
-
}/*switch-case0-for*/
|
|
426
|
-
|
|
427
|
-
|
|
428
|
-
|
|
429
|
-
break;
|
|
430
|
-
|
|
431
|
-
}/*switch-case0*/
|
|
432
|
-
|
|
433
|
-
|
|
434
|
-
|
|
435
|
-
}/*switch*/
|
|
436
|
-
|
|
437
|
-
|
|
438
|
-
|
|
439
|
-
/**/
|
|
440
|
-
|
|
441
|
-
puts("divjudgef");
|
|
442
|
-
|
|
443
|
-
printf("\n");
|
|
444
|
-
|
|
445
|
-
for(line=0; line<numb; line++){
|
|
446
|
-
|
|
447
|
-
printf("|");
|
|
448
|
-
|
|
449
|
-
for(column=0; column<numb; column++){
|
|
450
|
-
|
|
451
|
-
printf("%5.2f", mat[0][line][column]);
|
|
452
|
-
|
|
453
|
-
}
|
|
454
|
-
|
|
455
|
-
printf(" |\n");
|
|
456
|
-
|
|
457
|
-
}
|
|
458
|
-
|
|
459
|
-
printf("\n\n");
|
|
460
|
-
|
|
461
|
-
|
|
462
|
-
|
|
463
|
-
|
|
464
|
-
|
|
465
|
-
/**/
|
|
466
|
-
|
|
467
|
-
|
|
468
|
-
|
|
469
|
-
|
|
470
|
-
|
|
471
|
-
}
|
|
472
|
-
|
|
473
|
-
|
|
474
|
-
|
|
475
|
-
|
|
476
|
-
|
|
477
|
-
|
|
478
|
-
|
|
479
|
-
|
|
480
|
-
|
|
481
|
-
int rankcalf(double mat[0][numb][numb], int lnum, int cnum)
|
|
482
|
-
|
|
483
|
-
{
|
|
484
|
-
|
|
485
|
-
|
|
486
|
-
|
|
487
|
-
int rank = 0;
|
|
488
|
-
|
|
489
|
-
int i,j;
|
|
490
|
-
|
|
491
|
-
for(i=0; i<lnum; i++){
|
|
492
|
-
|
|
493
|
-
for(j=0; j<numb; j++){
|
|
494
|
-
|
|
495
|
-
if(mat[0][i][j] == 1){
|
|
496
|
-
|
|
497
|
-
if(j != numb-1){
|
|
498
|
-
|
|
499
|
-
rank++;
|
|
500
|
-
|
|
501
|
-
break;
|
|
502
|
-
|
|
503
|
-
}/*'j = numb-1' means the last column number of the matrix and its elements is a sentinel.*/
|
|
504
|
-
|
|
505
|
-
|
|
506
|
-
|
|
507
|
-
}
|
|
508
|
-
|
|
509
|
-
}
|
|
510
|
-
|
|
511
|
-
}
|
|
512
|
-
|
|
513
|
-
|
|
514
|
-
|
|
515
|
-
/**/
|
|
516
|
-
|
|
517
|
-
puts("rankcalf");
|
|
518
|
-
|
|
519
|
-
printf("\n");
|
|
520
|
-
|
|
521
|
-
for(line=0; line<numb; line++){
|
|
522
|
-
|
|
523
|
-
printf("|");
|
|
524
|
-
|
|
525
|
-
for(column=0; column<numb; column++){
|
|
526
|
-
|
|
527
|
-
printf("%5.2f", mat[0][line][column]);
|
|
528
|
-
|
|
529
|
-
}
|
|
530
|
-
|
|
531
|
-
printf(" |\n");
|
|
532
|
-
|
|
533
|
-
}
|
|
534
|
-
|
|
535
|
-
printf("\n\n");
|
|
536
|
-
|
|
537
|
-
|
|
538
|
-
|
|
539
|
-
|
|
540
|
-
|
|
541
|
-
/**/
|
|
542
|
-
|
|
543
|
-
|
|
544
|
-
|
|
545
|
-
|
|
546
|
-
|
|
547
|
-
return rank;
|
|
548
|
-
|
|
549
|
-
|
|
550
|
-
|
|
551
|
-
}
|
|
552
|
-
|
|
553
|
-
|
|
554
|
-
|
|
555
|
-
int rankopf(double mat[0][numb][numb], int lnum, int cnum, int n[])
|
|
556
|
-
|
|
557
|
-
{
|
|
558
|
-
|
|
559
|
-
/*
|
|
560
|
-
|
|
561
|
-
We'll use substif and then use for sentence to apply dvijudgef to each column.
|
|
562
|
-
|
|
563
|
-
In the for sentence, operation continues as follows.:
|
|
564
|
-
|
|
565
|
-
After applying divjudgef to a particular column, the situation will be A or B.
|
|
566
|
-
|
|
567
|
-
The element that is located in the upper-left side in the scope of elementary rows operations
|
|
568
|
-
|
|
569
|
-
is
|
|
570
|
-
|
|
571
|
-
A : 1
|
|
572
|
-
|
|
573
|
-
B : 0.
|
|
574
|
-
|
|
575
|
-
subtraf operation will be applied to the type A.
|
|
576
|
-
|
|
577
|
-
nothing will be done to the type B.
|
|
578
|
-
|
|
579
|
-
*/
|
|
580
|
-
|
|
581
|
-
int i = 0;/*for controling line row*/
|
|
582
|
-
|
|
583
|
-
int j = 0;/*for controling column row*/
|
|
584
|
-
|
|
585
|
-
for(i=0; i<lnum; i++){
|
|
586
|
-
|
|
587
|
-
int detallzero = i;
|
|
588
|
-
|
|
589
|
-
substif(n, mat, j, lnum);
|
|
590
|
-
|
|
591
|
-
divjudgef(i, j, cnum, lnum, mat, n);
|
|
592
|
-
|
|
593
|
-
if(detallzero == i){
|
|
594
|
-
|
|
595
|
-
int k;
|
|
596
|
-
|
|
597
|
-
for(k=i+1; k<lnum; k++){
|
|
598
|
-
|
|
599
|
-
if(n[k] != 0){
|
|
600
|
-
|
|
601
|
-
subtraf(k, i, minus, cnum, mat);
|
|
602
|
-
|
|
603
|
-
}/*for-if-for-if*/
|
|
604
|
-
|
|
605
|
-
}/*for-if-for*/
|
|
606
|
-
|
|
607
|
-
}/*for-if*/
|
|
608
|
-
|
|
609
|
-
j++;
|
|
610
|
-
|
|
611
|
-
}/*for*/
|
|
612
|
-
|
|
613
|
-
|
|
614
|
-
|
|
615
|
-
/*The operation above are all 'Elementary rows operations of matrix',
|
|
616
|
-
|
|
617
|
-
and then, we will calculate the rank of the matrix.*/
|
|
618
|
-
|
|
619
|
-
|
|
620
|
-
|
|
621
|
-
/**/
|
|
622
|
-
|
|
623
|
-
puts("rankopf");
|
|
624
|
-
|
|
625
|
-
printf("\n");
|
|
626
|
-
|
|
627
|
-
for(line=0; line<numb; line++){
|
|
628
|
-
|
|
629
|
-
printf("|");
|
|
630
|
-
|
|
631
|
-
for(column=0; column<numb; column++){
|
|
632
|
-
|
|
633
|
-
printf("%5.2f", mat[0][line][column]);
|
|
634
|
-
|
|
635
|
-
}
|
|
636
|
-
|
|
637
|
-
printf(" |\n");
|
|
638
|
-
|
|
639
|
-
}
|
|
640
|
-
|
|
641
|
-
printf("\n\n");
|
|
642
|
-
|
|
643
|
-
|
|
644
|
-
|
|
645
|
-
|
|
646
|
-
|
|
647
|
-
/**/
|
|
648
|
-
|
|
649
|
-
|
|
650
|
-
|
|
651
|
-
|
|
652
|
-
|
|
653
|
-
|
|
654
|
-
|
|
655
|
-
return rankcalf(mat, lnum, cnum);
|
|
656
|
-
|
|
657
|
-
}
|
|
658
|
-
|
|
659
|
-
|
|
660
|
-
|
|
661
|
-
int main(void)
|
|
662
|
-
|
|
663
|
-
{
|
|
664
|
-
|
|
665
|
-
|
|
666
|
-
|
|
667
|
-
int lnum, cnum;
|
|
668
|
-
|
|
669
|
-
/*mat[kind of matrix][line number][column number] */
|
|
670
|
-
|
|
671
|
-
|
|
672
|
-
|
|
673
|
-
puts("\nWe will calculate the rank of a matrix.\nPlease enter the scale of matrix.");
|
|
674
|
-
|
|
675
|
-
printf("The number of lines (under %d) = ", numb);
|
|
676
|
-
|
|
677
|
-
scanf("%d", &lnum);
|
|
678
|
-
|
|
679
|
-
printf("The number of columns (under %d) = ", numb);
|
|
680
|
-
|
|
681
|
-
scanf("%d", &cnum);
|
|
682
|
-
|
|
683
|
-
|
|
684
|
-
|
|
685
|
-
puts("Please enter the elements of the matrix.");
|
|
686
|
-
|
|
687
|
-
puts("'mat[i][j]' represents the (i,j) elements of the matrix.");
|
|
688
|
-
|
|
689
|
-
|
|
690
|
-
|
|
691
|
-
int i, j;
|
|
692
|
-
|
|
693
|
-
for(i=0; i<numb; i++){
|
|
694
|
-
|
|
695
|
-
mat[0][i][numb-1] = 1;
|
|
696
|
-
|
|
697
|
-
}/*Rendering mat[0][i][numb-1] sentinel for the rank calcularation.*/
|
|
698
|
-
|
|
699
|
-
|
|
700
|
-
|
|
701
|
-
for(i=0; i<lnum; i++){
|
|
702
|
-
|
|
703
|
-
for(j=0; j<cnum; j++){
|
|
704
|
-
|
|
705
|
-
printf("mat[0][%d][%d] = ", i+1, j+1);
|
|
706
|
-
|
|
707
|
-
scanf("%lf", &mat[0][i][j]);
|
|
708
|
-
|
|
709
|
-
mat[1][i][j] = mat[0][i][j];
|
|
710
|
-
|
|
711
|
-
}
|
|
712
|
-
|
|
713
|
-
}
|
|
714
|
-
|
|
715
|
-
/*mat[1]にはもともと行列が保存される。*/
|
|
716
|
-
|
|
717
|
-
int n[numb];
|
|
718
|
-
|
|
719
|
-
int rank = rankopf(mat, lnum, cnum, n);
|
|
720
|
-
|
|
721
|
-
|
|
722
|
-
|
|
723
|
-
int r;
|
|
724
|
-
|
|
725
|
-
for(r=0; r<2; r++){
|
|
726
|
-
|
|
727
|
-
printf("\n");
|
|
728
|
-
|
|
729
|
-
for(i=0; i<lnum; i++){
|
|
730
|
-
|
|
731
|
-
printf("|");
|
|
732
|
-
|
|
733
|
-
for(j=0; j<cnum; j++){
|
|
734
|
-
|
|
735
|
-
printf("%5.f", mat[r][i][j]);
|
|
736
|
-
|
|
737
|
-
}
|
|
738
|
-
|
|
739
|
-
printf(" |\n");
|
|
740
|
-
|
|
741
|
-
}
|
|
742
|
-
|
|
743
|
-
printf("\n\n");
|
|
744
|
-
|
|
745
|
-
}
|
|
746
|
-
|
|
747
|
-
|
|
748
|
-
|
|
749
|
-
printf("\nThe rank of this matrix is %d.\n", rank);
|
|
750
|
-
|
|
751
|
-
|
|
752
|
-
|
|
753
|
-
return 0;
|
|
754
|
-
|
|
755
|
-
}
|
|
756
592
|
|
|
757
593
|
|
|
758
594
|
|
|
@@ -765,3 +601,7 @@
|
|
|
765
601
|
###試したこと
|
|
766
602
|
|
|
767
603
|
上のソースコードのなかで、２つの/**/で挟まれたprintf …の部分は演算過程を見るために付け加えたものです。いくつかのデバッグは自己解決できたのですが、これに関してはわからないです。
|
|
604
|
+
|
|
605
|
+
|
|
606
|
+
|
|
607
|
+
又、初めのアルゴリズムでは欠陥があったので、少し変えて作り直しました。
|
1
「試したこと」を記入しました。
test
CHANGED
|
File without changes
|
test
CHANGED
|
@@ -757,3 +757,11 @@
|
|
|
757
757
|
|
|
758
758
|
|
|
759
759
|
```
|
|
760
|
+
|
|
761
|
+
|
|
762
|
+
|
|
763
|
+
|
|
764
|
+
|
|
765
|
+
###試したこと
|
|
766
|
+
|
|
767
|
+
上のソースコードのなかで、２つの/**/で挟まれたprintf …の部分は演算過程を見るために付け加えたものです。いくつかのデバッグは自己解決できたのですが、これに関してはわからないです。
|