Octave メモ2015年9月4日 | |
はじめにプログラミング言語 GNU Octave のメモ。 ベクトル定義>> a = [ 1 2 3 ] a = 1 2 3 成分>> a = [1, 2, 3]' >> a(2) ans = 2 >> a(2:3) ans = 2 3 代入>> a = [1, 2, 3]' >> b = a b = 1 2 3 スカラーとの和・差>> a = [1, 2, 3]'; >> a + 1 ans = 2 3 4 >> a - 1 ans = 0 1 2 スカラーとの積・除算>> a = [1, 2, 3]'; >> a*2 ans = 2 4 6 >> a/2 ans = 0.50000 1.00000 1.50000 ベクトルどうしの和・差>> a = [1, 2, 3]'; >> b = [4, 5, 6]'; >> a + b ans = 5 7 9 >> b - a ans = 3 3 3 ベクトルの成分どうしの積・除算
>> a = [1, 2, 3]';
>> b = [4, 5, 6]';
>> a .* b
ans =
4
10
18
>> b ./ a
ans =
4.0000
2.5000
2.0000
ノルム>> a = [1, 2, 3]'; >> norm(a) ans = 3.7417 内積>> a = [1, 2, 3]'; >> b = [4, 5, 6]'; >> dot(a, b) ans = 32 外積>> a = [1, 2, 3]'; >> b = [4, 5, 6]'; >> cross(a, b) ans = -3 6 -3 総和>> a = [1, 2, 3]'; >> sum(a) ans = 6 最大・最小>> a = [1, 2, 3]'; >> max(a) ans = 3 >> min(a) ans = 1 行列定義>> A = [ 1, 2, 3 4, 5, 6 7, 8, 9 ] A = 1 2 3 4 5 6 7 8 9 成分>> A = [1, 2, 3; 4, 5, 6; 7, 8, 9]; >> A(2, 3) ans = 6 >> A(:, 2) ans = 2 5 8 >> A(1:2, 2:3) ans = 2 3 5 6 >> A(:, [1, 3]) ans = 1 3 4 6 7 9 代入>> A = [1, 2, 3; 4, 5, 6; 7, 8, 9]; >> B = A B = 1 2 3 4 5 6 7 8 9 スカラーとの和・差
>> A = [1, 2, 3; 4, 5, 6; 7, 8, 9];
>> A + 1
ans =
2 3 4
5 6 7
8 9 10
>> A - 1
ans =
0 1 2
3 4 5
6 7 8
スカラーとの積/除算
>> A = [1, 2, 3; 4, 5, 6; 7, 8, 9];
>> A*2
ans =
2 4 6
8 10 12
14 16 18
>> A/2
ans =
0.50000 1.00000 1.50000
2.00000 2.50000 3.00000
3.50000 4.00000 4.50000
行列どうしの和・差>> A = [1, 2, 3; 4, 5, 6; 7, 8, 9]; >> B = [10, 11, 12; 13, 14, 15; 16, 17, 18]; >> A + B ans = 11 13 15 17 19 21 23 25 27 >> B - A ans = 9 9 9 9 9 9 9 9 9 行列の成分どうしの積・除算
>> A = [1, 2, 3; 4, 5, 6; 7, 8, 9];
>> B = [10, 11, 12; 13, 14, 15; 16, 17, 18];
>> A .* B
ans =
10 22 36
52 70 90
112 136 162
>> B ./ A
ans =
10.0000 5.5000 4.0000
3.2500 2.8000 2.5000
2.2857 2.1250 2.0000
行列の積
>> A = [1, 2, 3; 4, 5, 6; 7, 8, 9];
>> B = [10, 11, 12; 13, 14, 15; 16, 17, 18];
>> A*B
ans =
84 90 96
201 216 231
318 342 366
行列とベクトルの積>> a = [1, 2, 3]'; >> A = [1, 2, 3; 4, 5, 6; 7, 8, 9]; >> A*a ans = 14 32 50 行列の累乗
>> A = [1, 2, 3; 4, 5, 6; 7, 8, 9];
>> A^2
ans =
30 36 42
66 81 96
102 126 150
転置>> A = [1, 2, 3; 4, 5, 6; 7, 8, 9]; >> A' ans = 1 4 7 2 5 8 3 6 9 トレース>> A = [1, 2, 3; 4, 5, 6; 7, 8, 9]; >> trace(A) ans = 15 対角成分>> A = [1, 2, 3; 4, 5, 6; 7, 8, 9]; >> diag(A) ans = 1 5 9 >> sum(diag(A)) ans = 15 行列式>> A = [1, 2, 3; 4, 5, 6; 7, 8, 10]; >> det(A) ans = -3.0000 逆行列>> A = [1, 2, 3; 4, 5, 6; 7, 8, 10]; >> inv(A) ans = -0.66667 -1.33333 1.00000 -0.66667 3.66667 -2.00000 1.00000 -2.00000 1.00000 >> A*inv(A) ans = 1.00000 0.00000 -0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 1.00000 連立方程式の解>> A = [1, 2, 3; 4, 5, 6; 7, 8, 10]; >> b = [1, 2, 3]'; >> x = A \ b x = -0.33333 0.66667 -0.00000 >> A*x ans = 1.00000 2.00000 3.00000 単位行列>> eye(3) ans = Diagonal Matrix 1 0 0 0 1 0 0 0 1 >> A = [1, 2, 3; 4, 5, 6; 7, 8, 9]; >> eye(3)*A ans = 1 2 3 4 5 6 7 8 9 ゼロ行列>> zeros(3) ans = 0 0 0 0 0 0 0 0 0 >> zeros(2, 3) ans = 0 0 0 0 0 0 固有値・固有ベクトル
>> A = [1, 2, 3; 4, 5, 6; 7, 8, 10];
>> [P, lambda] = eig(A)
P =
-0.223513 -0.865846 0.278296
-0.503946 0.085651 -0.831847
-0.834314 0.492925 0.480190
lambda =
Diagonal Matrix
16.70749 0 0
0 -0.90574 0
0 0 0.19825
>> inv(P)*A*P
ans =
16.70749 -0.00000 -0.00000
0.00000 -0.90574 -0.00000
0.00000 -0.00000 0.19825
非線形方程式非線形方程式を解く>> function r = f(x) r = x^2 - 2; end >> fsolve(@f, 1) ans = 1.4142 最小化>> fminsearch(@(x) abs(x^2 - 2), 1) ans = 1.4142 表示結果の表示桁数を増やす>> sqrt(2) ans = 1.4142 >> format long >> sqrt(2) ans = 1.41421356237310 >> format short >> sqrt(2) ans = 1.4142 表示
>> a = 1
>> printf("a = %d\n", a)
a = 1
| |
| PENGUINITIS | |