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Merge pull request #200 from chvmvd/update-gaussian-elimination-scripts
2 parents 26ea344 + dc802ad commit ba44b27

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+100
-92
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4 files changed

+100
-92
lines changed

‎static/gaussian-elimination/gauss_jordan_elimination.ipynb‎

Lines changed: 2 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -13,10 +13,12 @@
1313
" for j in range(i + 1, len(a)):\n",
1414
" if abs(a[i][i]) < abs(a[j][i]):\n",
1515
" a[i], a[j] = a[j], a[i]\n",
16+
"\n",
1617
" # pivot倍で行を割る\n",
1718
" pivot = a[i][i]\n",
1819
" for j in range(i, len(a[i])):\n",
1920
" a[i][j] /= pivot\n",
21+
"\n",
2022
" # 掃き出す\n",
2123
" for j in range(len(a)):\n",
2224
" if j != i:\n",

‎static/gaussian-elimination/gaussian_elimination.ipynb‎

Lines changed: 43 additions & 42 deletions
Original file line numberDiff line numberDiff line change
@@ -1,46 +1,47 @@
11
{
2-
"nbformat": 4,
3-
"nbformat_minor": 2,
4-
"metadata": {},
5-
"cells": [
2+
"nbformat": 4,
3+
"nbformat_minor": 2,
4+
"metadata": {},
5+
"cells": [
6+
{
7+
"metadata": {},
8+
"source": [
9+
"def gaussian_elimination(a):\n",
10+
" # 前進消去\n",
11+
" for i in range(len(a)):\n",
12+
" # pivot倍で行を割る\n",
13+
" pivot = a[i][i]\n",
14+
" for j in range(i, len(a[i])):\n",
15+
" a[i][j] /= pivot\n",
16+
"\n",
17+
" # i + 1行目以降を掃き出す\n",
18+
" for j in range(i + 1, len(a)):\n",
19+
" factor = a[j][i]\n",
20+
" for k in range(i, len(a[i])):\n",
21+
" a[j][k] -= factor * a[i][k]\n",
22+
"\n",
23+
" # 後退代入\n",
24+
" x = [0 for _ in range(len(a[0]) - 1)]\n",
25+
" for i in reversed(range(len(a))):\n",
26+
" x[i] = a[i][len(a[i]) - 1]\n",
27+
" for j in range(i):\n",
28+
" a[j][len(a[i]) - 1] -= a[j][i] * x[i]\n",
29+
" return x\n",
30+
"\n",
31+
"\n",
32+
"print(gaussian_elimination([[1, -2, 3, 3], [-1, 3, -2, 1], [1, -1, 6, 11]]))"
33+
],
34+
"cell_type": "code",
35+
"outputs": [
636
{
7-
"metadata": {},
8-
"source": [
9-
"def gaussian_elimination(a):\n",
10-
" # \u524d\u9032\u6d88\u53bb\n",
11-
" for i in range(len(a)):\n",
12-
" # pivot\u500d\u3067\u884c\u3092\u5272\u308b\n",
13-
" pivot = a[i][i]\n",
14-
" for j in range(i, len(a[i])):\n",
15-
" a[i][j] /= pivot\n",
16-
"\n",
17-
" # i+1\u884c\u76ee\u4ee5\u964d\u3092\u6383\u304d\u51fa\u3059\n",
18-
" for j in range(i + 1, len(a)):\n",
19-
" factor = a[j][i]\n",
20-
" for k in range(i, len(a[i])):\n",
21-
" a[j][k] -= factor * a[i][k]\n",
22-
" # \u5f8c\u9000\u4ee3\u5165\n",
23-
" x = [0 for _ in range(len(a[0]) - 1)]\n",
24-
" for i in reversed(range(len(a))):\n",
25-
" x[i] = a[i][len(a[i]) - 1]\n",
26-
" for j in range(i):\n",
27-
" a[j][len(a[i]) - 1] -= a[j][i] * x[i]\n",
28-
" return x\n",
29-
"\n",
30-
"\n",
31-
"print(gaussian_elimination([[1, -2, 3, 3], [-1, 3, -2, 1], [1, -1, 6, 11]]))"
32-
],
33-
"cell_type": "code",
34-
"outputs": [
35-
{
36-
"output_type": "stream",
37-
"name": "stdout",
38-
"text": [
39-
"[1.0, 2.0, 2.0]\n"
40-
]
41-
}
42-
],
43-
"execution_count": null
37+
"output_type": "stream",
38+
"name": "stdout",
39+
"text": [
40+
"[1.0, 2.0, 2.0]\n"
41+
]
4442
}
45-
]
43+
],
44+
"execution_count": null
45+
}
46+
]
4647
}

‎static/gaussian-elimination/gaussian_elimination_error.ipynb‎

Lines changed: 48 additions & 47 deletions
Original file line numberDiff line numberDiff line change
@@ -1,51 +1,52 @@
11
{
2-
"nbformat": 4,
3-
"nbformat_minor": 2,
4-
"metadata": {},
5-
"cells": [
2+
"nbformat": 4,
3+
"nbformat_minor": 2,
4+
"metadata": {},
5+
"cells": [
6+
{
7+
"metadata": {},
8+
"source": [
9+
"def gaussian_elimination(a):\n",
10+
" # 前進消去\n",
11+
" for i in range(len(a)):\n",
12+
" # pivot倍で行を割る\n",
13+
" pivot = a[i][i]\n",
14+
" for j in range(i, len(a[i])):\n",
15+
" a[i][j] /= pivot\n",
16+
"\n",
17+
" # i + 1行目以降を掃き出す\n",
18+
" for j in range(i + 1, len(a)):\n",
19+
" factor = a[j][i]\n",
20+
" for k in range(i, len(a[i])):\n",
21+
" a[j][k] -= factor * a[i][k]\n",
22+
"\n",
23+
" # 後退代入\n",
24+
" x = [0 for _ in range(len(a[0]) - 1)]\n",
25+
" for i in reversed(range(len(a))):\n",
26+
" x[i] = a[i][len(a[i]) - 1]\n",
27+
" for j in range(i):\n",
28+
" a[j][len(a[i]) - 1] -= a[j][i] * x[i]\n",
29+
" return x\n",
30+
"\n",
31+
"\n",
32+
"print(gaussian_elimination([[0, -2, 3, 2], [-1, 3, -2, 1], [1, -1, 6, 11]]))"
33+
],
34+
"cell_type": "code",
35+
"outputs": [
636
{
7-
"metadata": {},
8-
"source": [
9-
"def gaussian_elimination(a):\n",
10-
" # \u524d\u9032\u6d88\u53bb\n",
11-
" for i in range(len(a)):\n",
12-
" # pivot\u500d\u3067\u884c\u3092\u5272\u308b\n",
13-
" pivot = a[i][i]\n",
14-
" for j in range(i, len(a[i])):\n",
15-
" a[i][j] /= pivot\n",
16-
"\n",
17-
" # i+1\u884c\u76ee\u4ee5\u964d\u3092\u6383\u304d\u51fa\u3059\n",
18-
" for j in range(i + 1, len(a)):\n",
19-
" factor = a[j][i]\n",
20-
" for k in range(i, len(a[i])):\n",
21-
" a[j][k] -= factor * a[i][k]\n",
22-
" # \u5f8c\u9000\u4ee3\u5165\n",
23-
" x = [0 for _ in range(len(a[0]) - 1)]\n",
24-
" for i in reversed(range(len(a))):\n",
25-
" x[i] = a[i][len(a[i]) - 1]\n",
26-
" for j in range(i):\n",
27-
" a[j][len(a[i]) - 1] -= a[j][i] * x[i]\n",
28-
" return x\n",
29-
"\n",
30-
"\n",
31-
"print(gaussian_elimination([[0, -2, 3, 2], [-1, 3, -2, 1], [1, -1, 6, 11]]))"
32-
],
33-
"cell_type": "code",
34-
"outputs": [
35-
{
36-
"output_type": "error",
37-
"ename": "ZeroDivisionError",
38-
"evalue": "division by zero",
39-
"traceback": [
40-
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
41-
"\u001b[0;31mZeroDivisionError\u001b[0m Traceback (most recent call last)",
42-
"Cell \u001b[0;32mIn [1], line 23\u001b[0m\n\u001b[1;32m 19\u001b[0m a[j][\u001b[39mlen\u001b[39m(a[i]) \u001b[39m-\u001b[39m \u001b[39m1\u001b[39m] \u001b[39m-\u001b[39m\u001b[39m=\u001b[39m a[j][i] \u001b[39m*\u001b[39m x[i]\n\u001b[1;32m 20\u001b[0m \u001b[39mreturn\u001b[39;00m x\n\u001b[0;32m---> 23\u001b[0m \u001b[39mprint\u001b[39m(gaussian_elimination([[\u001b[39m0\u001b[39m, \u001b[39m-\u001b[39m\u001b[39m2\u001b[39m, \u001b[39m3\u001b[39m, \u001b[39m2\u001b[39m], [\u001b[39m-\u001b[39m\u001b[39m1\u001b[39m, \u001b[39m3\u001b[39m, \u001b[39m-\u001b[39m\u001b[39m2\u001b[39m, \u001b[39m1\u001b[39m], [\u001b[39m1\u001b[39m, \u001b[39m-\u001b[39m\u001b[39m1\u001b[39m, \u001b[39m6\u001b[39m, \u001b[39m11\u001b[39m]]))\n",
43-
"Cell \u001b[0;32mIn [1], line 7\u001b[0m, in \u001b[0;36mgaussian_elimination\u001b[0;34m(a)\u001b[0m\n\u001b[1;32m 5\u001b[0m pivot \u001b[39m=\u001b[39m a[i][i]\n\u001b[1;32m 6\u001b[0m \u001b[39mfor\u001b[39;00m j \u001b[39min\u001b[39;00m \u001b[39mrange\u001b[39m(i, \u001b[39mlen\u001b[39m(a[i])):\n\u001b[0;32m----> 7\u001b[0m a[i][j] \u001b[39m/\u001b[39m\u001b[39m=\u001b[39m pivot\n\u001b[1;32m 9\u001b[0m \u001b[39m# i+1\u884c\u76ee\u4ee5\u964d\u3092\u6383\u304d\u51fa\u3059\u001b[39;00m\n\u001b[1;32m 10\u001b[0m \u001b[39mfor\u001b[39;00m j \u001b[39min\u001b[39;00m \u001b[39mrange\u001b[39m(i \u001b[39m+\u001b[39m \u001b[39m1\u001b[39m, \u001b[39mlen\u001b[39m(a)):\n",
44-
"\u001b[0;31mZeroDivisionError\u001b[0m: division by zero"
45-
]
46-
}
47-
],
48-
"execution_count": null
37+
"output_type": "error",
38+
"ename": "ZeroDivisionError",
39+
"evalue": "division by zero",
40+
"traceback": [
41+
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
42+
"\u001b[0;31mZeroDivisionError\u001b[0m Traceback (most recent call last)",
43+
"Cell \u001b[0;32mIn [1], line 24\u001b[0m\n\u001b[1;32m 20\u001b[0m a[j][\u001b[39mlen\u001b[39m(a[i]) \u001b[39m-\u001b[39m \u001b[39m1\u001b[39m] \u001b[39m-\u001b[39m\u001b[39m=\u001b[39m a[j][i] \u001b[39m*\u001b[39m x[i]\n\u001b[1;32m 21\u001b[0m \u001b[39mreturn\u001b[39;00m x\n\u001b[0;32m---> 24\u001b[0m \u001b[39mprint\u001b[39m(gaussian_elimination([[\u001b[39m0\u001b[39m, \u001b[39m-\u001b[39m\u001b[39m2\u001b[39m, \u001b[39m3\u001b[39m, \u001b[39m2\u001b[39m], [\u001b[39m-\u001b[39m\u001b[39m1\u001b[39m, \u001b[39m3\u001b[39m, \u001b[39m-\u001b[39m\u001b[39m2\u001b[39m, \u001b[39m1\u001b[39m], [\u001b[39m1\u001b[39m, \u001b[39m-\u001b[39m\u001b[39m1\u001b[39m, \u001b[39m6\u001b[39m, \u001b[39m11\u001b[39m]]))\n",
44+
"Cell \u001b[0;32mIn [1], line 7\u001b[0m, in \u001b[0;36mgaussian_elimination\u001b[0;34m(a)\u001b[0m\n\u001b[1;32m 5\u001b[0m pivot \u001b[39m=\u001b[39m a[i][i]\n\u001b[1;32m 6\u001b[0m \u001b[39mfor\u001b[39;00m j \u001b[39min\u001b[39;00m \u001b[39mrange\u001b[39m(i, \u001b[39mlen\u001b[39m(a[i])):\n\u001b[0;32m----> 7\u001b[0m a[i][j] \u001b[39m/\u001b[39m\u001b[39m=\u001b[39m pivot\n\u001b[1;32m 9\u001b[0m \u001b[39m# i + 1行目以降を掃き出す\u001b[39;00m\n\u001b[1;32m 10\u001b[0m \u001b[39mfor\u001b[39;00m j \u001b[39min\u001b[39;00m \u001b[39mrange\u001b[39m(i \u001b[39m+\u001b[39m \u001b[39m1\u001b[39m, \u001b[39mlen\u001b[39m(a)):\n",
45+
"\u001b[0;31mZeroDivisionError\u001b[0m: division by zero"
46+
]
4947
}
50-
]
48+
],
49+
"execution_count": null
50+
}
51+
]
5152
}

‎static/gaussian-elimination/gaussian_elimination_revised.ipynb‎

Lines changed: 7 additions & 3 deletions
Original file line numberDiff line numberDiff line change
@@ -10,19 +10,23 @@
1010
" # 前進消去\n",
1111
" for i in range(len(a)):\n",
1212
" # 部分ピボット選択\n",
13+
" max_index = i\n",
1314
" for j in range(i + 1, len(a)):\n",
14-
" if abs(a[i][i]) < abs(a[j][i]):\n",
15-
" a[i], a[j] = a[j], a[i]\n",
15+
" if abs(a[max_index][i]) < abs(a[j][i]):\n",
16+
" max_index = j\n",
17+
" a[i], a[max_index] = a[max_index], a[i]\n",
18+
"\n",
1619
" # pivot倍で行を割る\n",
1720
" pivot = a[i][i]\n",
1821
" for j in range(i, len(a[i])):\n",
1922
" a[i][j] /= pivot\n",
2023
"\n",
21-
" # i+1行目以降を掃き出す\n",
24+
" # i + 1行目以降を掃き出す\n",
2225
" for j in range(i + 1, len(a)):\n",
2326
" factor = a[j][i]\n",
2427
" for k in range(i, len(a[i])):\n",
2528
" a[j][k] -= factor * a[i][k]\n",
29+
"\n",
2630
" # 後退代入\n",
2731
" x = [0 for _ in range(len(a[0]) - 1)]\n",
2832
" for i in reversed(range(len(a))):\n",

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