November 2018
Intermediate to advanced
272 pages
6h 51m
Japanese
book
エレガントなSciPy ―Pythonによる科学技術計算
by Juan Nunez-Iglesias, Stéfan van der Walt, Harriet Dashnow, 山崎 邦子, 山崎 康宏
Content preview from エレガントなSciPy ―Pythonによる科学技術計算
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151
例えば、
3
×
3
の回転行列
R
を任意の
3
次元ベクトル
p
に掛けると、
p
は
z
軸の周りを
30
度回
転します。
R
は、
z
軸上にあるベクトル以外のすべてのベクトルを回転させます。
z
軸上にあるベ
クトルは、何の影響も受けません。すなわち、固有値がλ ＝
1
の場合に
Rp
＝
p
（つまり、
Rp = λp
）となります。
6.2.1
演習：回転行列
以下の回転行列を考えます。
R =
cos θ − sin θ 0
sin θ cos θ 0
0 0 1
R
を
3
次元の列ベクトル
p = [x y z]
T
に掛け合わせると、その結果得られるベクトル
Rp
は、
z
軸を中心にθ度回転します。
問題
1.
θ＝
45º
の場合に、行列
R
によってベクトルが
z
軸を中心に回転することを、いく
つかのベクトルで試して確かめましょう。なお
Python
の行列の掛け算は
@
で記さ
れることを思い出してください。
問題
2.
行列
S = RR
は何をするものでしょうか。
Python
を使って確かめましょう。
問題
3.
R
を掛けても、ベクトル
[0 0 1]
T
が不変であることを確かめましょう。言い換える
と、
Rp
＝
1p
であり、つまり
p
は
R
の固有値が
1
である場合の固有ベクトルです。
問題
4.
np.linalg.eig
を使って
R
の固有値と固有ベクトルを求め、
[0 0 1]
T
が固有ベクトル
の
1
つであり、固有値
1
に対応することを確かめましょう。
さて、ラプラシアンの話に戻りましょう。ネットワーク解析で起きがちなのは、可視化に関する
問題です。ノードとエッジをどのように描いたら、
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I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.Addison B.
I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.Amir M.
I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.