matlab and numerical analysisbml.pusan.ac.kr/lectureframe/lecture/undergraduates... ·...
TRANSCRIPT
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MATLAB and Numerical Analysis
Radiological Imaging SciencesSchool of Mechanical Engineering
Pusan National University
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MATLAB and Numerical Analysis
Radiological Imaging Sciences
Review
무명함수
>> fun = @(x,y) x^2 + y^2; % 𝑓𝑓 𝑥𝑥, 𝑦𝑦 = 𝑥𝑥2 + 𝑦𝑦2
>> fun(3,4)
>> ans
= 25
If문
>> if a == b
>> c=d;
>> end
만약 a=b 라면, c=d로계산하시오
for문
>> for i = 1:5
>> x(i+1)=x(i)+1;
>> end
순서도와동일
시작
x=x+1
i=5
출력
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MATLAB and Numerical Analysis
Radiological Imaging Sciences
Review
nlinfit
>> fun = @(p,x) I(1)*exp(-p*x); 𝑓𝑓 𝑡𝑡 = 𝐼𝐼 0 × 𝑒𝑒−𝜇𝜇𝑡𝑡
>> t = [0:2:10];
>> I = [0.9726 0.8001 0.6582 0.5415 0.4455 0.3665];
>> b0 = 1;
>> mu = nlinfit(t,I,fun,b0);
>> figure,plot(t,I,’ob’); hold on;
>> plot(t,fun(mu,t),’r’);
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MATLAB and Numerical Analysis
Radiological Imaging Sciences
Bisection
2ul
rxx
x+
=
추정된근의값
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MATLAB and Numerical Analysis
Radiological Imaging Sciences
Bisection
다음의방법들을사용하여 𝑓𝑓 𝑥𝑥 = 𝑒𝑒−𝑥𝑥 − 𝑥𝑥의근을구하고, 참백분율상대오차를하나의그래프에함께그려비교하시오. 반복횟수에따른오차의특성을살피고, 각방법들간의차이점에대해논하시오.
참값으로 0.56714329를사용.
𝑓𝑓 𝑥𝑥 = 𝑒𝑒−𝑥𝑥 − 𝑥𝑥
𝑥𝑥𝑙𝑙 = 0, 𝑥𝑥𝑢𝑢 = 1
𝑦𝑦𝑙𝑙 = 𝑓𝑓(𝑥𝑥𝑙𝑙),𝑦𝑦𝑢𝑢 = 𝑓𝑓(𝑥𝑥𝑢𝑢)
함수및초기치설정 𝑥𝑥𝑥𝑥𝑖𝑖 =𝑥𝑥𝑥𝑥𝑖𝑖 + 𝑥𝑥𝑥𝑥𝑖𝑖
2
iteration
𝑦𝑦𝑥𝑥𝑖𝑖 = 𝑓𝑓(𝑥𝑥𝑥𝑥𝑖𝑖)
만약 𝑦𝑦𝑥𝑥𝑖𝑖 × 𝑦𝑦𝑥𝑥𝑖𝑖 < 0이면,
𝑥𝑥𝑥𝑥𝑖𝑖+1 = 𝑥𝑥𝑥𝑥𝑖𝑖만약 𝑦𝑦𝑥𝑥𝑖𝑖 × 𝑦𝑦𝑥𝑥𝑖𝑖 > 0이면,
𝑥𝑥𝑥𝑥𝑖𝑖+1 = 𝑥𝑥𝑥𝑥𝑖𝑖
𝑥𝑥𝑥𝑥𝑖𝑖+1 = 𝑥𝑥𝑥𝑥𝑖𝑖
𝑥𝑥𝑥𝑥𝑖𝑖+1 = 𝑥𝑥𝑥𝑥𝑖𝑖
𝑒𝑒𝑡𝑡𝑖𝑖 = 100 ×𝑥𝑥𝑡𝑡𝑡𝑡𝑢𝑢𝑡𝑡 − 𝑥𝑥𝑥𝑥𝑖𝑖𝑥𝑥𝑡𝑡𝑡𝑡𝑢𝑢𝑡𝑡
𝑥𝑥𝑡𝑡𝑡𝑡𝑢𝑢𝑡𝑡 = 0.56714329최종결과
𝑥𝑥𝑥𝑥𝑡𝑡𝑒𝑒𝑒𝑒, 𝑒𝑒𝑡𝑡𝑡𝑡𝑒𝑒𝑒𝑒 획득
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MATLAB and Numerical Analysis
Radiological Imaging Sciences
Bisection coding
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MATLAB and Numerical Analysis
Radiological Imaging Sciences
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MATLAB and Numerical Analysis
Radiological Imaging Sciences
False position
다음의방법들을사용하여 𝑓𝑓 𝑥𝑥 = 𝑒𝑒−𝑥𝑥 − 𝑥𝑥의근을구하고, 참백분율상대오차를하나의그래프에함께그려비교하시오. 반복횟수에따른오차의특성을살피고, 각방법들간의차이점에대해논하시오.
참값으로 0.56714329를사용.
𝑓𝑓 𝑥𝑥 = 𝑒𝑒−𝑥𝑥 − 𝑥𝑥
𝑥𝑥𝑙𝑙 = 0, 𝑥𝑥𝑢𝑢 = 1
𝑦𝑦𝑙𝑙 = 𝑓𝑓(𝑥𝑥𝑙𝑙),𝑦𝑦𝑢𝑢 = 𝑓𝑓(𝑥𝑥𝑢𝑢)
함수및초기치설정 𝑥𝑥𝑥𝑥𝑖𝑖 = 𝑥𝑥𝑥𝑥𝑖𝑖 − 𝑦𝑦𝑥𝑥𝑖𝑖 ×𝑥𝑥𝑥𝑥𝑖𝑖 − 𝑥𝑥𝑥𝑥𝑖𝑖𝑦𝑦𝑥𝑥𝑖𝑖 − 𝑦𝑦𝑥𝑥𝑖𝑖
iteration
𝑦𝑦𝑥𝑥𝑖𝑖 = 𝑓𝑓(𝑥𝑥𝑥𝑥𝑖𝑖)
만약 𝑦𝑦𝑥𝑥𝑖𝑖 × 𝑦𝑦𝑥𝑥𝑖𝑖 < 0이면,
𝑥𝑥𝑥𝑥𝑖𝑖+1 = 𝑥𝑥𝑥𝑥𝑖𝑖만약 𝑦𝑦𝑥𝑥𝑖𝑖 × 𝑦𝑦𝑥𝑥𝑖𝑖 > 0이면,
𝑥𝑥𝑥𝑥𝑖𝑖+1 = 𝑥𝑥𝑥𝑥𝑖𝑖
𝑥𝑥𝑥𝑥𝑖𝑖+1 = 𝑥𝑥𝑥𝑥𝑖𝑖
𝑥𝑥𝑥𝑥𝑖𝑖+1 = 𝑥𝑥𝑥𝑥𝑖𝑖
𝑒𝑒𝑡𝑡𝑖𝑖 = 100 ×𝑥𝑥𝑡𝑡𝑡𝑡𝑢𝑢𝑡𝑡 − 𝑥𝑥𝑥𝑥𝑖𝑖𝑥𝑥𝑡𝑡𝑡𝑡𝑢𝑢𝑡𝑡
𝑥𝑥𝑡𝑡𝑡𝑡𝑢𝑢𝑡𝑡 = 0.56714329최종결과
𝑥𝑥𝑥𝑥𝑡𝑡𝑒𝑒𝑒𝑒, 𝑒𝑒𝑡𝑡𝑡𝑡𝑒𝑒𝑒𝑒 획득
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MATLAB and Numerical Analysis
Radiological Imaging Sciences
Newton-Raphson
)(')(
1i
iii xf
xfxx −=+
추정된근의값
1
0)()('+−−
=ii
ii xx
xfxf
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MATLAB and Numerical Analysis
Radiological Imaging Sciences
Newton-Raphson
다음의방법들을사용하여 𝑓𝑓 𝑥𝑥 = 𝑒𝑒−𝑥𝑥 − 𝑥𝑥의근을구하고, 참백분율상대오차를하나의그래프에함께그려비교하시오. 반복횟수에따른오차의특성을살피고, 각방법들간의차이점에대해논하시오.
참값으로 0.56714329를사용.
𝑓𝑓 𝑥𝑥 = 𝑒𝑒−𝑥𝑥 − 𝑥𝑥
𝑥𝑥 = 0
𝑦𝑦 = 𝑓𝑓(𝑥𝑥)
함수및초기치설정 𝑥𝑥𝑖𝑖+1 = 𝑥𝑥𝑖𝑖 −𝑦𝑦𝑖𝑖𝑦𝑦𝑦1
iteration
𝑦𝑦𝑖𝑖+1 = 𝑓𝑓(𝑥𝑥𝑖𝑖+1)
𝑒𝑒𝑡𝑡𝑖𝑖 = 100 ×𝑥𝑥𝑡𝑡𝑡𝑡𝑢𝑢𝑡𝑡 − 𝑥𝑥𝑖𝑖+1
𝑥𝑥𝑡𝑡𝑡𝑡𝑢𝑢𝑡𝑡
𝑥𝑥𝑡𝑡𝑡𝑡𝑢𝑢𝑡𝑡 = 0.56714329최종결과
𝑥𝑥𝑡𝑡𝑒𝑒𝑒𝑒, 𝑒𝑒𝑡𝑡𝑡𝑡𝑒𝑒𝑒𝑒 획득𝑓𝑓′(𝑥𝑥) = −𝑒𝑒−𝑥𝑥 − 1
𝑦𝑦𝑦 = 𝑓𝑓𝑦(𝑥𝑥)
𝑒𝑒𝑡𝑡1 = 100 ×𝑥𝑥𝑡𝑡𝑡𝑡𝑢𝑢𝑡𝑡 − 𝑥𝑥1𝑥𝑥𝑡𝑡𝑡𝑡𝑢𝑢𝑡𝑡
𝑦𝑦𝑦𝑖𝑖+1 = 𝑓𝑓𝑦(𝑥𝑥𝑖𝑖+1)
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MATLAB and Numerical Analysis
Radiological Imaging Sciences
Newton-Raphson coding
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MATLAB and Numerical Analysis
Radiological Imaging Sciences
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MATLAB and Numerical Analysis
Radiological Imaging Sciences
Fixed-point iteration
다음의방법들을사용하여 𝑓𝑓 𝑥𝑥 = 𝑒𝑒−𝑥𝑥 − 𝑥𝑥의근을구하고, 참백분율상대오차를하나의그래프에함께그려비교하시오. 반복횟수에따른오차의특성을살피고, 각방법들간의차이점에대해논하시오.
참값으로 0.56714329를사용.
𝑓𝑓 𝑥𝑥 = 𝑒𝑒−𝑥𝑥 − 𝑥𝑥
𝑥𝑥 = 0
𝑦𝑦 = 𝑔𝑔(𝑥𝑥)
함수및초기치설정 𝑥𝑥𝑖𝑖+1 = 𝑦𝑦𝑖𝑖
iteration
𝑦𝑦𝑖𝑖+1 = 𝑔𝑔(𝑥𝑥𝑖𝑖+1)
𝑒𝑒𝑡𝑡𝑖𝑖 = 100 ×𝑥𝑥𝑡𝑡𝑡𝑡𝑢𝑢𝑡𝑡 − 𝑥𝑥𝑖𝑖+1
𝑥𝑥𝑡𝑡𝑡𝑡𝑢𝑢𝑡𝑡
𝑥𝑥𝑡𝑡𝑡𝑡𝑢𝑢𝑡𝑡 = 0.56714329최종결과
𝑥𝑥𝑡𝑡𝑒𝑒𝑒𝑒, 𝑒𝑒𝑡𝑡𝑡𝑡𝑒𝑒𝑒𝑒 획득𝑔𝑔(𝑥𝑥) = 𝑒𝑒−𝑥𝑥
𝑒𝑒𝑡𝑡1 = 100 ×𝑥𝑥𝑡𝑡𝑡𝑡𝑢𝑢𝑡𝑡 − 𝑥𝑥1𝑥𝑥𝑡𝑡𝑡𝑡𝑢𝑢𝑡𝑡
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MATLAB and Numerical Analysis
Radiological Imaging Sciences
Secant
다음의방법들을사용하여 𝑓𝑓 𝑥𝑥 = 𝑒𝑒−𝑥𝑥 − 𝑥𝑥의근을구하고, 참백분율상대오차를하나의그래프에함께그려비교하시오. 반복횟수에따른오차의특성을살피고, 각방법들간의차이점에대해논하시오.
참값으로 0.56714329를사용.
𝑓𝑓 𝑥𝑥 = 𝑒𝑒−𝑥𝑥 − 𝑥𝑥
𝑥𝑥1 = 1𝑦𝑦𝑦 = 𝑓𝑓(𝑥𝑥1)
함수및초기치설정 𝑥𝑥𝑖𝑖+1 = 𝑥𝑥𝑖𝑖 −𝛿𝛿 × 𝑥𝑥𝑖𝑖 × 𝑦𝑦𝑦𝑖𝑖𝑦𝑦𝑦𝑖𝑖 − 𝑦𝑦𝑦𝑖𝑖
iteration
𝑦𝑦𝑦𝑖𝑖+1 = 𝑓𝑓(𝑥𝑥𝑖𝑖+1)
𝑒𝑒𝑡𝑡𝑖𝑖 = 100 ×𝑥𝑥𝑡𝑡𝑡𝑡𝑢𝑢𝑡𝑡 − 𝑥𝑥𝑖𝑖+1
𝑥𝑥𝑡𝑡𝑡𝑡𝑢𝑢𝑡𝑡
𝑥𝑥𝑡𝑡𝑡𝑡𝑢𝑢𝑡𝑡 = 0.56714329최종결과
𝑥𝑥𝑡𝑡𝑒𝑒𝑒𝑒, 𝑒𝑒𝑡𝑡𝑡𝑡𝑒𝑒𝑒𝑒 획득
𝑒𝑒𝑡𝑡1 = 100 ×𝑥𝑥𝑡𝑡𝑡𝑡𝑢𝑢𝑡𝑡 − 𝑥𝑥1𝑥𝑥𝑡𝑡𝑡𝑡𝑢𝑢𝑡𝑡
𝑦𝑦𝑦 = 𝑓𝑓 𝑥𝑥1 + 𝛿𝛿𝑥𝑥1
𝛿𝛿 = 0.000001𝑦𝑦𝑦𝑖𝑖+1 = 𝑓𝑓 𝑥𝑥𝑖𝑖+1 + 𝛿𝛿 × 𝑥𝑥𝑖𝑖+1
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MATLAB and Numerical Analysis
Radiological Imaging Sciences
Structure & Save
Mat 파일로저장
Structure
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MATLAB and Numerical Analysis
Radiological Imaging Sciences
Graph plot
1) Load
2) Plotting
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MATLAB and Numerical Analysis
Radiological Imaging Sciences
Graph plot
3) Axis control
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MATLAB and Numerical Analysis
Radiological Imaging Sciences
Graph plot
4) Labeling
![Page 19: MATLAB and Numerical Analysisbml.pusan.ac.kr/LectureFrame/Lecture/Undergraduates... · 2018-04-04 · MATLAB and Numerical Analysis. Radiological Imaging Sciences. Graph plot. Y](https://reader034.vdocuments.net/reader034/viewer/2022042613/5f8d875956dfa045246db696/html5/thumbnails/19.jpg)
MATLAB and Numerical Analysis
Radiological Imaging Sciences
Graph plot
5) Legend
6) save
![Page 20: MATLAB and Numerical Analysisbml.pusan.ac.kr/LectureFrame/Lecture/Undergraduates... · 2018-04-04 · MATLAB and Numerical Analysis. Radiological Imaging Sciences. Graph plot. Y](https://reader034.vdocuments.net/reader034/viewer/2022042613/5f8d875956dfa045246db696/html5/thumbnails/20.jpg)
MATLAB and Numerical Analysis
Radiological Imaging Sciences
Graph plot
Y축 log-scale로 plot 그래프선굵기한그래프에여러 line plot
Line의형태및색Legend (범례)
격자x & y 축범위설정 x 축범위설정및해당값설정
x 축설명y 축설명
타이틀
저장
Mat파일불러오기
Color: k(black), b(blue), r(red), m(magenta), g(green)Line style: -, --, -., :