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(1)  標準入力から実数 a と b を読み込み、その和、差、積、商を標準出力に出力。 

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(1)

1

計算物理学2  第2回演習 

ver. 2018/4/19    以下の例題を Fortran もしくは C 言語を用いてプログラム化せよ。 

 

四則演算 

 

(1)  標準入力から実数 a と b を読み込み、その和、差、積、商を標準出力に出力。 

  ・b にゼロを代入するとどうなりますか。 

 

DO ループ 

 

(2)    および の N=1 から 30 までの値。 

 

(3) N! (階乗)の値(N が 1 から 30 まで) 

  ・N がいくつまで正確に計算できますか。 

 

(4)  整数 N=1,...30 に対して単精度と倍精度で N の値を出力(sqrt(x)関数を使う)。 

 

配列 

 

(5)  行列 A(1:3,1:3)と B(1:3,1:3)の積の計算(Fortran の場合は MATMUL を使う場合と 使わない場合二通り)。 

ただし A の行列要素 a

ij

は    b

ij

は とする。 

 

(6) n が 5 までのルジャンドル多項式の直交性を以下の方法で評価しなさい。 

まず区間[-1,1]を N-1 等分し、それぞれの座標を要素数 N の配列 x(1:N)にセットする。端 点を x(1)=-1, x(N)=1 として残りの点 x(2), x(3), ...., x(N)も求めて値を配列にセット。 

配 列 P(1:N,0:5) を 用 意 し 、 同 じ [-1,1] 区 間 で ル ジ ャ ン ド ル 多 項 式   P

0

(x),  P

1

(x),  P

2

(x),P

3

(x),P

4

(x),P

5

(x)の値をセット。(例えば x=x(i)でのルジャンドル多項式 P

2

(x(i))の値 を配列 P(i,2)に代入)  ただし n=0,1,2,3,4,5 のルジャンドル多項式は以下で与えられる。 

X

N k=1

k

2

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X

N

k=1

k

3

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a

ij

= e

|i j|

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b

ij

= e

|i j|

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(2)

2

 

  ルジャンドル多項式の配列を用いて、区分求積法で次の積分を計算する。 

  Δx は N から計算できる。I

nm

を 6x6 の行列として出力。 

  ・N の値を 100, 1000,10000 と変えるとどうなるか。 

  ・区分求積の和を N-1 までにした時と N までにした時で何が変わるか。 

 

(7)  標準入力から2つの角度 a と b を実数で読み取り(単位:度)、cos(a+b)と sin(a+b) を 3 通りの方法で計算。 

  1. cos(a+b), sin(a+b)をそのまま出力(ラジアンに変換)。 

  2.  角度 a 回転させる 2 次元の行列、角度 b 回転させる行列を配列を使って作 り、それらの行列の積を計算して cos(a+b)と sin(a+b)に対応する成分を出力。ただし角

度θ回転させる回転行列は で与えられる。 

   

  3.  複素数 e

ia

と e

ib

の積を計算し、その実部と虚部から出力。 

   

P0(x) =1 P1(x) =x P2(x) =1

2(3x2 1) P3(x) =1

2(5x3 3x) P4(x) =1

8(35x4 30x2+ 3) P5(x) =1

8(63x5 70x3+ 15x)

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Inm = Z 1

1

Pn(x)Pm(x)dx⇠

NX1 i=1

Pn(x(i))Pm(x(i)) x

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✓cos✓ sin✓ sin✓ cos✓

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参照

関連したドキュメント

① 要求仕様固め 1)入出力:入力電圧範囲、出力電圧/精度 2)負荷:電流、過渡有無(スリープ/ウェイクアップ含む)

(2)

夏場以降、日米の金融政策格差を巡るドル高圧力

理由:ボイラー MCR範囲内の 定格出力超過出 力は技術評価に て問題なしと確 認 済 み で あ る が、複数の火力

機排水口の放出管理目標値を示す。 画においては1号機排水口~4号機排水口の放出管理目標値を設定していない。.. 福島第二原子力発電所 )

基準の電力は,原則として次のいずれかを基準として決定するも

Dual I/O リードコマンドは、SI/SIO0、SO/SIO1 のピン機能が入出力に切り替わり、アドレス入力 とデータ出力の両方を x2

(2)燃料GMは,定格熱出力一定運転にあたり,原子炉熱出力について運転管理目標を