 㜞ᯏ⢻ᢙ୯⸘▚࡮นⷞൻᯏ⢻࠰ࡈ࠻/#6.#$ ߩၮᧄ⊛ߥ૶޿ᣇ
㩷⑺↰⋵┙ᄢቇ 㒸 ࿖べ᧲ർᄢቇᖱႎㇱᖱႎၮ⋚⺖ ౒ห೑↪ᡰេଥ᭎ⷐ

MATLAB ߪ‫ޔ‬㜞ᯏ⢻ߥᢙ୯⸘▚ᯏ⢻ߣᄙᓀߥนⷞൻᯏ⢻ࠍ஻߃ߚᛛⴚ⸘▚࠰ࡈ࠻࠙ࠚࠕߢߔ‫⑼ޕ‬ቇ⊛‫ޔ‬Ꮏቇ⊛ಽ㊁ߩ᭽‫ߥޘ‬ᢙ୯⸘▚ ․ߦⴕ೉Ṷ▚ ‫⸃࠲࡯࠺ޔ‬ᨆ‫⛔ߩ߼ߚߩࡦ࡚ࠪ࡯࠯ࠗ࡜ࠕࡘࠫࡆ߮ࠃ߅ޔࡦ࡚ࠪ࡯࡟ࡘࡒࠪޔ‬วⅣႺࠍឭଏߒߡ޿߹ߔ‫ޔߚ߹ޕ‬MATLAB ߪ㜞ᕈ⢻ߥᢙ୯⸘▚ᯏ⢻ࠍᜬߟ߫߆ࠅߢߥߊ‫ޔ‬ᄙᓀߥนⷞൻᯏ⢻ࠍ஻߃ߡ߅ࠅ‫⚿▚⸘ޔ‬ᨐࠍ◲නߦࠣ࡜ࡈߦ⴫␜ߔࠆߎߣ߇ߢ߈߹ߔ‫ޕ‬੹࿁ߪ‫ޔ‬MATLAB ߩၮᧄ⊛ߥ૶޿ᣇࠍ⚫੺ߒ߹ߔ‫ޕ‬ࠠ࡯ࡢ࡯࠼㧦㜞ᯏ⢻ߥᢙ୯⸘▚‫ⴕޔ‬೉Ṷ▚‫ޔ‬นⷞൻᯏ⢻‫ࡈ࡜ࠣޔ‬ಣℂ㧝 ߪߓ߼ߦMATLAB ߪ‫ޔ‬ኾ㐷ߩࡊࡠࠣ࡜ࡑ߿ࠦࡦࡇࡘ࡯࠲ߦ⹦ߒ޿ੱߛߌߢߪߥߊ‫ߩ⥸৻ޔ‬೑↪⠪ߦ߽㜞ᰴߥᯏ⢻߇◲නߦ૶߃ࠆࠃ߁ߦ૞ࠄࠇߡ޿߹ߔ‫ޔ߼ߚߩߎޕ‬ᰴߦ޽ߍࠆࠃ߁ߥ․ᓽࠍ߽ߞߡ޿߹ߔ‫ޕ‬
࡮MATLAB ߣ޿߁ฬ⒓߇̌matrix laboratory̍ߩ⇛⒓ߣ޿߁ߛߌ޽ߞߡ‫ⴕޔߦ․ޔ‬೉ߣࡌࠢ࠻࡞ߩ⸘▚ߪ‫ޔ‬ᢙቇ⊛ߥ⸥ㅀߦㄭ޿⴫⃻ߢ◲නߦṶ▚ߢ߈߹ߔ‫ޔ߼ߚߩߎޕ‬Fortran‫ޔ‬Basic‫ޔ‬C ߣ޿ߞߚ⸒⺆ߢࡊࡠࠣ࡜ࡓࠍ⸥ㅀߔࠆߩߦⷐߔࠆᤨ㑆ߣᲧߴ‫ޔ‬MATLAB ߪ㕖Ᏹߦዋߥ޿ᤨ㑆ߢᄙߊߩ໧㗴ࠍ⸃ߊߎߣ߇น⢻ߣߥࠅ߹ߔ‫ޔߦ․ޕ‬ᄢⷙᮨߥⴕ೉⸘▚ߪ‫ޔ‬MATLAB ߇ᧄ᧪ᓧᗧߣߔࠆߣߎࠈߢ޽ࠅ߹ߔ‫ޕ‬࡮ᢙ୯ታ㛎ߩ⚿ᨐࠍ 2 ᰴర߅ࠃ߮ 3 ᰴర࿑㕙ߢ◲නߦ⴫␜ߢ߈ࠆߣหᤨߦ‫࡞ࠗࠔࡈޔ‬಴ജ߿ශ೚಴ജ߇ߢ߈߹ߔ‫࡞ࠗࠔࡈޕ‬಴ജߒߚ࿑㕙ࠍᢥᦠ✬㓸ᷡᦠࡊࡠࠣ࡜ࡓ TeX ߩ౉ജߣߔࠆߎߣ߇ߢ߈߹ߔ‫ޕ‬࡮ኻ⹤ဳߩታⴕߦࠃࠅ‫ߩ࡞࠺ࡕޔ‬ᄌᢙ߿ࡄ࡜ࡔ࡯࠲ࠍ⒳‫ޘ‬ᄌᦝߒߡᢙ୯ታ㛎߇ߢ߈߹ߔ‫ޕ‬࡮૶޿ᣇߦߟ޿ߡߪ‫ޔ‬ᔅⷐߥᤨὐߢ᩺ౝᖱႎࠍ↹㕙ߦ಴ߔߎߣߦࠃߞߡ‫ޔ‬ᭂജᚻᒁᦠߦ㗬ࠄߕߦߔ߻ࠃ߁ help ࠦࡑࡦ࠼ߦࠃࠆࠝࡦ࡜ࠗࡦࡑ࠾ࡘࠕ࡞߇ቢ஻ߒߡ޿߹ߔ‫ޕ‬࡮࠷࡯࡞ࡏ࠶ࠢࠬߣ๭߫ࠇࠆ․ቯಽ㊁ߩ⸃ᴺࠍ㓸߼ߚࠫࡘ࡯࡞ࠍ⚵ߺㄟ߻ߎߣߦࠃࠅ‫ޔ‬ኈᤃߦᯏ⢻᜛ᒛࠍⴕ߁ߎߣ߇ߢ߈‫ޔ‬ኾ㐷⊛ߥ೑↪ߦ߽ᨵエߦኻᔕߢ߈߹ߔ‫ޕ‬
MATLAB ߪࠦࠕࡕࠫࡘ࡯࡞ߩ MATLAB ࠍਛᔃߣߒߡ‫ߩ࠲࡯࡟ࡘࡒࠪࡓ࡜ࠣࠕࠗ࠳ࠢ࠶ࡠࡉޔ‬Simulink‫ ߮ࠃ߅ޔ‬Toolbox ߣ๭߫ࠇࠆࠕࡊ࡝ࠤ࡯࡚ࠪࡦࡕࠫࡘ࡯࡞߆ࠄ᭴ᚑߐࠇߡ޿߹ߔ‫࡯࠲ࡦ࠮ᧄޕ‬ߢߪᰴߩ Toolbox ࠍ૶↪ߢ߈߹ߔ‫ޕ‬  


㧖Communications System Toolbox㧦ㅢାࠪࠬ࠹ࡓߩ⸳⸘‫⸃ޔ‬ᨆ㧖Control System Toolbox㧦✢ᒻ೙ᓮࠪࠬ࠹ࡓߩ⸳⸘‫⸃ޔ‬ᨆ
㧖Curve Fitting Toolbox㧦ᢙᑼㄭૃ࠷࡯࡞
㧖DSP System Toolbox㧦ାภಣℂࠪࠬ࠹ࡓߩ⸳⸘ߣࠪࡒࡘ࡟࡯࡚ࠪࡦ㧖Fixed-Point Toolbox㧦࿕ቯዊᢙὐ࠺࡯࠲࠲ࠗࡊߣṶ▚ᯏ⢻ࠍឭଏ㧖Fuzzy Logic Toolbox㧦ࡈࠔࠫ࡯ℂ⺰ߦၮߠߊࠪࠬ࠹ࡓߩ⸳⸘‫⸃ޔ‬ᨆ㧖Image Processing Toolbox㧦↹௝ಣℂ‫⸃ޔ‬ᨆ‫ޔ‬นⷞൻ߅ࠃ߮ࠕ࡞ࠧ࡝࠭ࡓ㐿⊒ߩߚ߼ߩࠣ࡜ࡈࠖࠞ࡞ ࠷࡯࡞㧖MATLAB Coder㧦MATLAB ࠦ࡯࠼߆ࠄࠬ࠲ࡦ࠼ࠕࡠࡦߩ C ࠦ࡯࠼ߣ C++ ࠦ࡯࠼ࠍ↢ᚑ㧖MATLAB Compiler㧦MATLAB ࠕࡊ࡝ࠤ࡯࡚ࠪࡦࠍታⴕࡈࠔࠗ࡞‫↢ߡߒߣ࡝࡜ࡉࠗ࡜᦭౒ޔ‬ᚑ㧖Model Predictive Control Toolbox㧦੍᷹೙ᓮࠪࠬ࠹ࡓߩ⸳⸘‫⸃ޔ‬ᨆ㧖Neural Network Toolbox㧦࠾ࡘ࡯࡜࡞ࡀ࠶࠻ࡢ࡯ࠢℂ⺰ࠍ↪޿ߚⶄ㔀㕖✢ᒻ੐⽎ߩࡕ࠺࡝ࡦࠣ
㧖Optimization Toolbox㧦ᮡḰ⊛߅ࠃ߮ᄢⷙᮨߥᦨㆡൻߦᐢߊ૶↪ߐࠇࠆࠕ࡞ࠧ࡝࠭ࡓࠍឭଏ
㧖Partial Differential Equation Toolbox㧦஍ᓸಽᣇ⒟ᑼߩ⸃ᴺ࠷࡯࡞
㧖Robust Control Toolbox㧦ࡠࡃࠬ࠻ᕈߩ⹏ଔ‫⸃ޔ‬ᨆ㧖Signal Processing Toolbox㧦ࠕ࠽ࡠࠣ߅ࠃ߮࠺ࠫ࠲࡞ାภಣℂ (DSP) ߩࠕ࡞ࠧ࡝࠭ࡓࠍឭଏ㧖Simulink Coder㧦Simulink ࠳ࠗࠕࠣ࡜ࡓ‫ ߮ࠃ߅ޔ‬MATLAB 㑐ᢙ߆ࠄ C ࠦ࡯࠼ߣ C++ ࠦ࡯࠼ࠍ↢ᚑ
㧖Simulink Control Design㧦Simulink ߢࡕ࠺࡞ൻߐࠇߚ೙ᓮࠪࠬ࠹ࡓߩ⸳⸘ߣ⸃ᨆ㧖Simulink Design Optimization㧦Simulink ߢࡕ࠺࡞ൻߐࠇߚ೙ᓮࠪࠬ࠹ࡓߩᢙ୯ᦨㆡൻ㧖Simulink Fixed Point㧦Simulink ࡊࡠ࠳ࠢ࠻ࡈࠔࡒ࡝ߢ࿕ቯዊᢙὐᯏ⢻߇೑↪น⢻㧖Simulink Verification and Validation㧦Simulink ߢࡕ࠺࡞ൻߐࠇߚ೙ᓮࠪࠬ࠹ࡓߩ⏕⹺‫ޔ‬ᬌ⸽߅ࠃ߮࠹ࠬ࠻㧖Statistics Toolbox㧦࠺࡯࠲ߩᢛℂ‫⸃ޔ‬ᨆ‫ࠍ࡞࡯࠷ߣࡓ࠭࡝ࠧ࡞ࠕߩ߼ߚߩࠣࡦ࡝࠺ࡕ߮ࠃ߅ޔ‬ឭଏ㧖Symbolic Math Toolbox㧦ᢙᑼಣℂߣนᄌ♖ᐲṶ▚ࠍⴕ߁ߚ߼ߩ࠷࡯࡞ࠍឭଏ
㧖System Identification Toolbox㧦᷹ቯߐࠇߚ౉಴ജ࠺࡯࠲߆ࠄേ⊛ࠪࠬ࠹ࡓߩᢙቇࡕ࠺࡞ࠍ᭴▽㧖Wavelet Toolbox㧦࠙ࠚ࡯ࡉ࡟࠶࠻ᄌ឵ࠍ↪޿ߚ↹௝ಣℂ‫⸃ޔ‬ᨆ‫ޔ‬นⷞൻ࠷࡯࡞

੹࿁‫ޔ‬MATLAB ߩ౉㐷ߣߒߡ‫ߩߘޔ‬ၮᧄ⊛ߥ೑↪ᴺߣ૶↪଀ࠍᐞߟ߆⚫੺ߒ߹ߔ‫ޕ‬Simulink ߣToolbox ߦߟ޿ߡߪ‫ޔ‬ᰴߩᯏળߦ⚫੺ߔࠆߎߣߦ޿ߚߒ߹ߔ‫ޕ‬㧞 MATLAB ࠍ૶߁ߚ߼ߦ2.1 ၮᧄ⊛ߥⅣႺ⸳ቯ
MATLAB ߪ‫ ߩ࡯࠲ࡦ࠮ࠬࡦࠛࠗࠨ࡯ࡃࠗࠨޔ‬gen ߣ޿߁ฬߩਗ೉ࠦࡦࡇࡘ࡯࠲ߦࠗࡦࠬ࠻࡯࡞ߐࠇߡ޿߹ߔ‫ޔߪߢߎߎޕ‬೑↪⠪ߩᣇ߇‫⥄ޔ‬ಽߩ૶↪ߒߡ޿ࠆࡢ࡯ࠢࠬ࠹࡯࡚ࠪࡦ޽ࠆ޿ߪ X ┵ᧃ߆ࠄ gen߳࡝ࡕ࡯࠻ࡠࠣࠗࡦߒߡ೑↪ߔࠆߎߣࠍᗐቯߒߡ⹤ࠍㅴ߼߹ߔ‫ౕޕ‬૕⊛ߥ଀ࠍਅߦ␜ߒ߹ߔ‫ޕ‬ssh ࠦࡑ
ࡦ࠼ߩ X11Forwarding ᯏ⢻ࠍ᦭ലߦߒߡ‫ޔ‬gen ߦធ⛯ߒ߹ߔ‫ޕ‬ 

!"#$%&'()*+,-./0% ssh –X ೑↪⠪⇟ภ@gen.isc.tohoku.ac.jp<R>ᵈ㧦㆙㓒ࡎࠬ࠻ gen ߳ធ⛯

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Last login: Mon Apr 1 09:26:11 2012 from yyy.yyy.tohoku.ac.jp 4 ᦬ 1 ᣣ 13:29:59 JST 2012[೑↪⠪⇟ภ@gen ~]$ᵈ㧦ࠦࡑࡦ࠼౉ജᓙߜᵈ㧦㧨R㧪ߪ࡝࠲࡯ࡦ(ᡷⴕ)ߩᗧ๧ߢ‫ޔ‬એਅߢ߽หߓᗧ๧ࠍ⴫ߒ߹ߔ
2.2

MATLAB ߩ⿠േߣ⚳ੌ

MATLAB ߩ⿠േߦߪ‫ޔ‬matlab ߣ޿߁ࠦࡑࡦ࠼ࠍ૶↪ߒ߹ߔ‫↹ࡘࠪ࠶࡜ࡊࠬޕ‬㕙ߩ⴫␜ߩᓟ‫ޔ‬GUI࠙ࠖࡦ࠼࠙߇⴫␜ߐࠇ߹ߔ‫ޕ‬ ࠬࡊ࡜࠶ࠪࡘ↹㕙߇⴫␜ߐࠇߥ޿႐วߪ‫ ߢᧃ┵࡞ࠞ࡯ࡠޔ‬X ⅣႺ߇૶↪ߢ߈ࠆߎߣߣ‫ޔ‬ssh ࠦࡑࡦ࠼ࠍౣ⏕⹺ߔࠆࠃ߁ߦߒߡߊߛߐ޿‫ ߪ>>ޔߢߎߎޕ‬MATLAB ߩ౉ജଦㅴ⸥ภ(ࡊࡠࡦࡊ࠻)ߢߔ‫ޔ߫߃଀ޕ‬MATLAB ࠍ⚳ੌߒߚ޿႐วߦߪ‫ޔ‬quit ޽ࠆ޿ߪ exit ࠍ౉ജߔࠇ߫⚳ੌߒ߹ߔ‫ ߥ߁ࠃߩߎޕ‬quit ߿ exitߥߤࠍ‫ޕߔ߹޿޿ߣ࠼ࡦࡑࠦޔ‬  


3 ᢙ୯⸘▚
3.1ၮᧄṶ▚ᢙ୯⸘▚ߩ႐วߪ‫ޔ‬MATLAB ਄ߢߘߩ߹߹౉ജߒߡ◲නߦṶ▚ߢ߈߹ߔ‫ޕ‬೑↪น⢻ߥṶ▚ሶߣ㑐ᢙࠍઃ㍳ߦ⸥ߒ߹ߔ‫ޕ‬એਅߢߪ‫ޔ‬ᑼ(1) (2)ࠍ೑↪ߒߡ‫▚⸘ޔ‬ᣇᴺࠍ␜ߒ߹ߔ‫ޕ‬5(3  4)2>> 5*(3+4)/2<R>
ans =17.5000>> x = 3, y = 2, z = 1.5X=
3y=2
Z=1.5000>> (x^2+y^5)/sin(z) <R>
ans =41.1030<R>( x2  y5 )    (ೋᦼ୯ xsin( z )3.2(1)

3y2 z 1.5 )        (2)ࡌࠢ࠻࡞࡮ⴕ೉ߩṶ▚ࡌࠢ࠻࡞࡮ⴕ೉ߩṶ▚߇‫ޔ‬ᢙቇ⊛ߥ⸥ㅀߦㄭ޿ᒻߢⴕ߃ࠆߩ߇‫ޔ‬MATLAB ߩᄢ߈ߥ․ᓽߩ৻ߟߢߔ‫ޕ‬ߘߎߢ‫ޔ‬એਅߢߪ‫ޔ‬ᑼ(3)ߦ␜ߔⴕ೉Ṷ▚ࠍ‫ޔ‬MATLAB ਄ߢታ⃻ߔࠆᣇᴺߦߟ޿ߡ⚫੺ߒ߹ߔ‫ޕ‬AX

32 ·§ x1 ·§ 1¨¸¨ ¸B     ¨ 5 1.2 3.4 ¸¨ x 2 ¸¨1.5 4 5.1 ¸¨ x3 ¸©
¹© ¹§ 6 .1 ·¨ ¸
¨ 4 ¸                (3)¨ 5 .8 ¸© ¹એਅߦ␜ߔࠃ߁ߦ‫ޔ‬MATLABߪⴕ೉ߩᏀ㒰▚(\㧦ࡃ࠶ࠢࠬ࡜࠶ࠪࡘ)ࠍឭଏߒߡ޿߹ߔ‫ ޕ‬A ߇ᱜᣇⴕ೉ߥࠄ߫‫ ⸃ޔ‬X ߪ A \ B (ᣇᴺ㧞)ߢ᳞߼ߚ߽ߩߣ inv(A) B (ᣇᴺ㧝)ߢ᳞߼ߚ߽ߩߣ߶߷หߓߢߔ߇⸘▚ᣇᴺߪ⇣ߥࠅ߹ߔ‫ ޕ‬A ߇nⴕn೉ߢ㧮߇n୘ߩ೉ࡌࠢ࠻࡞߆n୘ߩ೉ⴕ೉ߥࠄ߫‫ ޔ‬XAXA \ B ߪᣇ⒟ᑼB ࠍࠟ࠙ࠬᶖ෰ߢ⸘▚ߒߚ⸃ߦߥࠅ߹ߔ‫ ޕ‬A ߩࠬࠤ࡯࡝ࡦࠣ߇ᖡ߆ߞߚࠅ‫⇣․ޔ‬ὐߦㄭ߆ߞߚࠅߔࠆߣ⼊๔ࡔ࠶࠮࡯ࠫ߇⴫␜ߐࠇ߹ߔ‫ޕ‬䎃 A ߇mⴕn೉(mҁn)ߢ B ߇m୘ߩ೉ࡌࠢ࠻࡞߆m୘ߩ೉ⴕ೉ߥࠄ߫‫ ޔ‬Xᑼߩᢙ߇৻⥌ߒߥ޿ᣇ⒟ᑼ AX

A \ B ߪᧂ⍮ᢙߩᢙߣᣇ⒟B ߩᦨዊੑਸ਼⊛ߥ⸃ߦߥࠅ߹ߔ‫ޕ‬A ߩ࡜ࡦࠢkߪࡇࡏ࠶࠻ࠍⴕߞߚQRಽ⸃߆ࠄ᳞߼ࠄࠇ߹ߔ‫ ⸃ޕ‬X ߪ‫ޔ‬k୘ߩ࠯ࡠߢߥ޿ᚑಽࠍᜬߜ߹ߔ‫ޕ‬k㧨nߢ޽ࠇ߫‫ޔ‬XA \ B ߪㅢᏱ‫ޔ‬ᦨዊᱷᏅࡁ࡞ࡓ AX  B ߦࠃࠆᦨዊੑਸ਼⸃ߢ޽ࠆ pinv(A) B ߣหߓ⸃ߦߪߥࠅ߹ߖࠎ‫ޕ‬ !"#$%&'()*+,-./0
>> C=[6.1 4 5.8]<R>ᵈ㧦ࡌࠢ࠻࡞ߩ౉ജ (ᣇᴺ㧝)C=
6.10004.00005.8000   ᵈ㧦’ ߪォ⟎ߩṶ▚ሶ>> B = C’<R>
B=
6.10004.00005.8000>> B2 = [ 6.1
<R>
4
<R>
5.8]
<R>         ᵈ㧦ࡌࠢ࠻࡞ߩ౉ജ (ᣇᴺ㧞)
B2 =6.10004.00005.8000>> A = [1 3 2; 5 1.2 3.4; 1.5 4 5.1]        ᵈ㧦ⴕ೉ߩ౉ജ (ᣇᴺ㧝)A=
1.00003.00002.00005.00001.20003.40001.50004.00005.1000>> A1 = [1 3 2; 5 1.2 3.4; 1.5 4 5.1]        ᵈ㧦ⴕ೉ߩ౉ജ (ᣇᴺ㧝)ᵈ㧦ᢥߩ⚳ࠊࠅߦ㧧ࠍ౉ࠇࠆߣߘߩ୯ߪ↹㕙ߦ⃻ࠇߥ޿>> A2 = [1 3 2<R>
5 1.2 3.4<R>
1.5 4 5.1]
<R>            ᵈ㧦ⴕ೉ߩ౉ജ (ᣇᴺ㧞)A2 =1.0000 3.0000 2.0000
5.0000 1.2000 3.4000
1.5000 4.0000 5.1000>> eig( A )<R>            ᵈ㧦ⴕ೉ A ߩ࿕᦭୯ans =9.0284-2.9432
1.2148>> X = inv(A)*B <R>ᵈ㧦ࡌࠢ࠻࡞ X ߩ⸃(ᣇᴺ㧝)
X =                 (ߎߩᣇᴺߪ‫ޔ‬ㅢᏱ⦟޿ᣇᴺߢߪ޽ࠅ߹ߖࠎߩߢ‫ߏޔ‬ᵈᗧ㧍)
0.91662.4089-1.0217>> X = A \ B<R>            ᵈ㧦ࡌࠢ࠻࡞ X ߩ⸃ (ᣇᴺ㧞)X=
0.91662.4089-1.0217>> max(X)<R>            ᵈ㧦ࡌࠢ࠻࡞ X ߩⷐ⚛ߩᦨᄢ୯ans =2.4089>> mean(X)<R>            ᵈ㧦ࡌࠢ࠻࡞ X ߩⷐ⚛ߩᐔဋ୯ans =0.7679>> n=length(X) <R>            ᵈ㧦ࡌࠢ࠻࡞ X ߩⷐ⚛ߩ㐳ߐn=3>> x2 = X(2)<R>            ᵈ㧦ࡌࠢ࠻࡞ X ߩ㧞⇟⋡ߩⷐ⚛
x2 =2.4089

3.3 ⶄ⚛ᢙ

 MATLABߢߪ‫⚛ⶄޔ‬ᢙࠍߔߴߡߩṶ▚߿㑐ᢙߦ߅޿ߡ૶↪ߔࠆߎߣ߇ߢ߈߹ߔ‫⯯ޕ‬ᢙ⴫⃻ߣߒߡߪ‫ޔ‬i ߣ j ߩߤߜࠄ߽⸵ኈߐࠇ߹ߔ‫৻ޕ‬ᣇ‫ޔ‬i ߿ j ࠍታᄌᢙߣߒߡ೑↪ߔࠆߎߣ߽น⢻ߢߔ‫ߢࠄߜߤޕ‬೑↪ߒߡ޿ࠆߩ߆ߪ‫⃻⴫ޔ‬ᣇᴺ߿ߘࠇ߹ߢߩᵹࠇߥߤ߆ࠄMATLAB߇⥄േ⊛ߦ⸃㉼ߒ߹ߔߩߢ‫ࠍࠄࠇߘޔ‬ᷙหߒߥ޿ࠃ߁ߦᵈᗧߔࠆᔅⷐ߇޽ࠅ߹ߔ‫ޕ‬એਅߢߪ‫ޔ‬MATLAB਄ߢⶄ⚛ᢙṶ▚ߩ଀ࠍᑼ(4)(5)ࠍ↪޿ߡ␜ߒ߹ߔ‫ޕ‬A

Z1 3  4i
§1 2·
§5¨¨
¸¸  i ¨¨
©3 4¹
©76·
¸8 ¸¹BZ 2 1  7i
§ 3  2· § 7  3·¨¨¸¸  i¨¨¸¸

481
2
©
¹ ©
¹>> z1 = 3+4*i
z1 =3.0000 + 4.0000i>> z2 = 1-7*j
z2 =1.0000 – 7.0000i>> z1+z2
ans =4.0000 – 3.0000i>> z1*z2
ans =31.0000 – 17.0000i>> z1 / z2
ans =-0.5000 + 0.5000i>> A = [ 1 2 ; 3 4 ] + i*[ 5 6 ; 7 8]ᵈ㧦ⶄ⚛ᢙⴕ೉ߩ౉ജ(ᣇᴺ㧝)A=
1.0000 + 5.0000i 2.0000 + 6.0000i
3.0000 + 7.0000i 4.0000 + 8.0000i>> B = [ 3+7i -2-3i ; -4+1j 8-2j ]    ᵈ㧦ⶄ⚛ᢙⴕ೉ߩ౉ജ(ᣇᴺ㧝)B=
3.0000 + 7.0000i -2.0000 – 3.0000i-4.0000 + 1.0000i 8.0000 – 2.0000i>> eig ( A*B )               ᵈ㧦ⶄ⚛ᢙⴕ೉ A*B ߩ࿕᦭୯ans =-0.7101 – 4.5909i     
17.7101 +37.5909i>>real(eig(A*B))ᵈ㧦࿕᦭୯ߩታᢙㇱans =-0.7101
17.7101          >> imag( eig(A*B) )ᵈ㧦࿕᦭୯ߩ⯯ᢙㇱ
ans =        -4.5909               
37.5909>> abs( eig(A*B) )ᵈ㧦࿕᦭୯ߩ⛘ኻ୯
ans =                 
4.645541.5539(4)(5)

 

!"#$%&'()*+,-./01ࡈࠔࠗ࡞ߣ࠺࡯࠲ߩ౉಴ജ

4MATLABߢߪ‫ޔ‬saveߣloadߣ޿߁ࠦࡑࡦ࠼ߦࠃߞߡ‫ޔ‬MATLABߢ૶↪ߒߡ޿ߚߣ߈ߩᄌᢙࠍ࠺ࠖࠬࠢ਄ߦᦠ߈ㄟࠎߛࠅ‫ߺ⺒ޔ‬ㄟࠎߛࠅߔࠆߎߣ߇ߢ߈߹ߔ‫ޕ‬એਅߢߪ‫ޔ‬loadࠦࡑࡦ࠼ߦࠃࠅࡈࠔࠗ࡞߆ࠄ
MATLAB਄߳ASCII࠺࡯࠲ࠍ⺒ߺㄟ߻ᣇᴺࠍ⺑᣿ߒ߹ߔ‫ߪ࡞ࠗࠔࡈ࠲࡯࠺ޔ߹޿ޕ‬sam1.dat, sam2.dat,sam3.datߣߒ߹ߔ‫ޕ‬1) sam1.datߣ޿߁ࡈࠔࠗ࡞ߩౝኈ(ᰴߩ࠺࡯࠲߇৻ⴕߦᦠ߆ࠇߡ޿ࠆߎߣߦᵈᗧ)㧦
0.0 0.3 0.95

-0.4 0.4 0.2-0.3

0.0 0.3 0.0 -0.2

0.1 0.00.0

0.00.02) sam2.datߣ޿߁ࡈࠔࠗ࡞ߩౝኈ(ᰴߩ࠺࡯࠲߇7ⴕߦᦠ߆ࠇߡ޿ࠆߎߣߦᵈᗧ)㧦
0395-42-33) sam3.datߣ޿߁ࡈࠔࠗ࡞ߩౝኈ(5ⴕ3೉ߩ࠺࡯࠲ߢߔ)㧦
1.1
2.13.1
4.1
5.1

1.2
2.2
3.2
4.2
5.2

1.3
2.3
3.3
4.2
5.3

એ਄3ߟߩ࠺࡯࠲ࡈࠔࠗ࡞ߦߟ޿ߡ‫ޔ‬MATLAB਄߳ࠦࡑࡦ࠼loadߦࠃࠅASCII࠺࡯࠲ࠍ⺒ߺㄟࠎߛ⚿ᨐࠍᰴ㗁ߦ␜ߒ߹ߔ‫ޕ‬߹ߚ‫ޔ‬MATLABߢ߽C⸒⺆ߩࠃ߁ߦ‫ޔ‬freadߣfscanfࠦࡑࡦ࠼ߦࠃࠅ‫߿࠲࡯࠺࡝࠽ࠗࡃࠄ߆࡞ࠗࠔࡈޔ‬ᦠᑼઃ߈࠺࡯࠲ࠍ⺒ߺㄟ߻ߎߣ߇ߢ߈߹ߔ‫ޕ‬ㅒߦ‫ᦠ߿࠲࡯࠺࡝࠽ࠗࡃ߳࡞ࠗࠔࡈޔ‬ᑼઃ߈࠺࡯࠲ࠍᦠ߈
ㄟ߻႐วߦߪ‫ޔ‬fwriteߣfscanfࠦࡑࡦ࠼ࠍ↪޿߹ߔ‫↪૶޿ߒ⹦ޕ‬ᴺߦߟ޿ߡߪ‫ࠍ࡞ࠕࡘ࠾ࡑޔ‬ෳᾖߒߡߊߛߐ޿‫ޕ‬>> load sam1.dat>> sam1
sam1 =
Columns 1 through 70 0.3000
0.9500Columns 8 through 14
0 0.3000
0
Columns 15 through 1600>>load sam2.dat>>sam2sam2 =03
95-4
2-30>> load sam3.dat>> sam3
sam3 =
1.10001.20001.30002.10002.20002.30003.10003.20003.30004.10004.20004.30005.10005.20005.3000 
-0.4000

0.40000.2000-0.3000-0.2000

0.1000005 ࠬࠢ࡝ࡊ࠻ࡈࠔࠗ࡞
MATLAB਄ߢ‫ޔ‬೙ᓮࠦࡑࡦ࠼ࠍ৻ⴕ৻ⴕ౉ജߔࠆߩߪ‫ࠅߥ߆ޔ‬㕙ୟߥ૞ᬺߢߔ‫ࠢࠬ࡞ࠚࠪޔߢߎߘޕ‬࡝ࡊ࠻߿ࡃ࠶࠴ࡈࠔࠗ࡞ߩࠃ߁ߦ‫߼੍ޔ‬ታⴕߒߚ޿ࠦࡑࡦ࠼⟲ࠍ߹ߣ߼ߡࡈࠔࠗ࡞ߦᦠ޿ߡ߅߈‫ߣ߹ޔ‬߼ߡታⴕߐߖࠆߎߣ߇น⢻ߢߔ‫ޕ‬ⅣႺᄌᢙMATLABPATHߢᜰቯߐࠇߚ࠺ࠖ࡟ࠢ࠻࡝ߦ‫ ޔ‬.m ߣ޿߁᜛ᒛሶࠍᜬߟࡈࠔࠗ࡞ࠍ૞ᚑߔࠆߣ‫ߪ࡞ࠗࠔࡈߩߘޔ‬MATLABߩࠬࠢ࡝ࡊ࠻ࡈࠔࠗ࡞ߣߺߥߐࠇ߹ߔ‫ޕ‬
sample.m ߣ޿߁ࡈࠔࠗ࡞ߩౝኈ߇એਅߩࠃ߁ߢ޽ࠆߣߒ߹ߔ‫ޕ‬load sam1.dat
sam1load sam2.datsam2
load sam3.dat
sam3
MATLAB਄ߢߪ̌㧪㧪sample 㧨R㧪̍ߣ౉ജߔࠆߣ‫ޔ‬೨▵ߦ␜ߒߚ߽ߩߣหߓ⚿ᨐߦߥࠅ߹ߔ‫ޕ‬ 

!"#$%&'()*+,-./0㧢 ࠣ࡜ࡈࠖ࠶ࠢࠬ⴫␜ᯏ⢻6.1 ◲නߥࠣ࡜ࡈࠖ࠶ࠢࠬߩ⴫␜
 MATLAB ߪ‫ޔ‬ᢙ୯⸘▚ߩઁߦ߽‫ߩ࠲࡯࠺ޔ‬นⷞൻߦ㑐ߒߡఝࠇߚᯏ⢻ࠍᜬߞߡ޿߹ߔ‫ޕ‬ᐳᮡ♽ߥߤࠍᜰቯߒߥ޿႐วߪ‫⥄ޔ‬േ⊛ߦ⷗ᤃ޿▸࿐ߢ⴫␜ߒߡߊࠇ߹ߔ‫␜⴫ޔࠎࠈߜ߽ޕ‬ᣇᴺࠍ୘ੱߩᅢߺߦࠃࠅ⚦߆ߊᜰቯߔࠆߎߣ߽น⢻ߢߔ‫ޕ‬ એਅߢߪ‫ޔ‬Უ㖸 /a/ ߩ࠺࡯࠲㧔ࠨࡦࡊ࡝ࡦࠣ๟ᵄᢙ 16kHz㧘60ms㧕ࠍ speech.dat ߣ޿߁࠺࡯࠲ࡈࠔࠗ࡞ࠍ૶ߞߡ‫ᤨޔ‬㑆ᵄᒻߣߘߩ๟ᵄᢙ․ᕈ㧔ࠬࡍࠢ࠻࡞㧕ࠍឬߊ଀ࠍ␜ߒ߹ߔ‫ޕ‬>> load speech.dat>> plot(speech)>> close>> freq = 20*log10(abs(fft(speech)))>> plot( freq(1:length(speech)/2))
 plot㧘close㧘log10㧘abs㧘fft㧘length ߥߤࠦࡑࡦ࠼ߩᯏ⢻ߦߟ޿ߡߪ‫ޔ‬ෳ⠨ᦠ޽ࠆ޿ߪࠝࡦ࡜ࠗࡦࡑ
࠾ࡘࠕ࡞ࠍෳᾖߒߡߊߛߐ޿‫ޕ‬࿑㧝㧦Უ㖸/a/ߩ㖸ჿ࠺࡯࠲ߩᤨ㑆ᵄᒻ     ࿑㧞㧦Უ㖸/a/ߩ㖸ჿ࠺࡯࠲ߩ๟ᵄᢙ․ᕈ
 ᰴߩ଀ߪ‫ޔ‬࿑㧞ߦ␜ߒߚࠃ߁ߥ๟ᵄᢙ․ᕈࠍ‫ޔ‬࿑㧟ߦ␜ߒߚࠃ߁ߦ AR ࡕ࠺࡞ߦࠃࠅ‫ߩߘޔ‬๟ᵄᢙ․ᕈߩ൮⛊✢ࠍ⸘▚ߒߡ⴫␜ߐߖߚ߽ߩߢߔ‫ޕ‬㧔ߥ߅‫ ࠼ࡦࡑࠦޔ‬lpc ߣ freqz ߪ System Identification
Toolbox ߩᯏ⢻ߢߔ㧕‫઀ߥ߁ࠃߩߎޕ‬੐߽ᄢᄌ◲නߦߢ߈ߡߒ߹߁ߎߣ߇߅ಽ߆ࠅ޿ߚߛߌࠆߢߒࠂ߁‫ޕ‬                                                                                                             load speech.dat                           a = lpc( speech, 12 );                           freqz( 1, a );  ࿑㧟㧦࿑㧞ߦ␜ߒߚ๟ᵄᢙ․ᕈߩ൮⛊✢6.2 ࠞ࡜࡯ࠣ࡜ࡈࠖ࠶ࠢࠬ
 MATLAB ߢߪ‫߽␜⴫ߩࠬࠢ࠶ࠖࡈ࡜ࠣ࡯࡜ࠞޔ‬ኈᤃߦⴕ߃߹ߔ‫ޕ‬plot(x,y,’linetype’)ߪ‫ ࡞࠻ࠢࡌޔ‬x
ࠍ x ゲ‫ ࡞࠻ࠢࡌޔ‬y ࠍ y ゲߣߒߚᦛ✢ࠍ’linetype’ߢᜰቯߐࠇߚ࠲ࠗࡊߩ✢⒳ߢࡊࡠ࠶࠻ߒ߹ߔ‫ޕ‬X ࠍ⋭  
⇛႐วߦߪ‫ޔ‬y ߩࠗࡦ࠺࠶ࠢࠬ߇ x ゲߦኻᔕߔࠆߎߣߦߥࠅ߹ߔ‫’ޕ‬linetype’ߪ‫⦡ߣࡊࠗ࠲ߩ✢ޔ‬㧔⴫㧝㧕ࠍᜰቯߒ߹ߔ‫’ޕ‬linetype’ࠍ⋭⇛ߒߚ႐ว‫⥄ޔ‬േ⊛ߦ㕍⦡ߩታ✢ࠍ૶↪ߒ߹ߔ‫ޕ‬หߓ࿑㕙਄ߢ⇣ߥࠆ࡜ࠗࡦ࠲ࠗࡊߣหߓ⦡ࠍᜰቯߔࠆߎߣ߽ߢ߈߹ߔ‫ޕ‬࿑㧠ߦߘߩ଀ࠍ␜ߒ߹ߔ‫ޕ‬⴫㧝㧦࡜ࠗࡦߩ࠲ࠗࡊߣ⦡

6.3ࠪࡦࡏ࡞࡜ࠗࡦ࠲ࠗࡊࠪࡦࡏ࡞࡜ࠗࡦ࠲ࠗࡊࠪࡦࡏ࡞

⦡

-ታ✢.

ὐb㕍

:ὐ✢o౞g✛-.

㎮✢xxශr⿒--⎕✢+ࡊ࡜ࠬ⸥ภcࠪࠕࡦ(none)✢ߥߒ*ᤊශmࡑ࠯ࡦ࠲sᱜᣇᒻy㤛d࠳ࠗࠕࡕࡦ࠼w⊕v

ਃⷺᒻ㧔਄ะ߈㧕k㤥^ਃⷺᒻ㧔ਅะ߈㧕<ਃⷺᒻ㧔Ꮐะ߈㧕>ਃⷺᒻ㧔ฝะ߈㧕p੖ⷺᒻh౐ⷺᒻࠣ࡜ࡈࠖ࠶ࠢࠬߩ಴ജ ૞ᚑߒߚ࿑㕙ࠍ಴ജߔࠆߦߪ‫ޔ‬print ߣ޿߁ࠦࡑࡦ࠼ࠍ૶↪ߒ߹ߔ‫ ޕ‬೑↪⠪߇⥄ಽߩߣߎࠈߦ޽ࠆࡊ࡝ࡦ࠲߆ࠄ಴ജߔࠆ႐วߦߪ‫ޔ‬એਅߦ␜ߔࠝࡊ࡚ࠪࡦࠍ೑↪ߒߡ‫৻ޔ‬ᐲࡐࠬ࠻ࠬࠢ࡝ࡊ࠻ࡈࠔࠗ࡞ߥߤ߳಴ജߒ‫⥄ࠍ࡞ࠗࠔࡈߩߘޔ‬ಽߩߣߎࠈߦ sftp ߢㅍࠆߎߣߦߥࠅ߹ߔ‫ޕ‬
print [ -option ] filename
option:dps:⊕㤥 ps ࡈࠔࠗ࡞    dpsc: ࠞ࡜࡯ ps ࡈࠔࠗ࡞          deps: ⊕㤥 eps ࡈࠔࠗ࡞   depsc: ࠞ࡜࡯ eps ࡈࠔࠗ࡞ߎࠇએᄖߩ࠺ࡃ߽ࠗࠬᜰቯน⢻ߢߔߩߢ‫ࠍ࡞ࠕࡘ࠾ࡑޔ‬ෳᾖߒߡߊߛߐ޿‫ޕ‬
6.4 3 ᰴరࠣ࡜ࡈࠖ࠶ࠢࠬ ߎߩ⺑ߪ‫ޔ‬MATLAB ߦ⚵ߺㄟ߹ࠇߡ޿ࠆ peaks ߣ޿߁․ᱶߥᄙፄဳ㑐ᢙࠍ↪޿ߡ‫ޔ‬3 ᰴరࠣ࡜ࡈࠖ࠶ࠢࠬߩ૞ᚑࠍ⺑᣿ߒ߹ߔ‫ޕ‬Peaks 㑐ᢙߪ‫ޔ‬x ߣ y ߩ㑐ᢙߢ‫ޔ‬ᰴߩᒻࠍߒߡ޿߹ߔ‫ޕ‬ f ( x, y )222222x13(1  x) 2 e  x ( y 1)  10(  x 3  y 5 )e  x  y  e ( x 1)  y    
53(6)MATLAB ߢ peaks(n)ࠍታⴕߔࠆߣ‫ ޔ‬n u n ߩᱜᣇⴕ೉߇ᓧࠄࠇ߹ߔ‫ޕ‬ᒁᢙߩ n ࠍ⋭ߊߣ‫ޔ‬ᮡḰ୯ 49 ߇ណ↪ߐࠇ߹ߔ‫ޕ‬ 


!"#$%&'()*+,-./01 એਅߪ‫ޔ‬Z=peaks(7)ߩ⚿ᨐߢߔ‫ⴕߩߎޕ‬೉ߩฦⷐ⚛ߪ‫ޔ‬x ߅ࠃ߮ y ࠍ㧙3 ߆ࠄ 3 ߹ߢᄌൻߐߖߚ႐วߩ୯ߦߥࠅ߹ߔ‫ޕ‬೉ᣇะ߇ x‫ⴕޔ‬ᣇะ߇ y ߩᄌൻߦኻᔕߒ߹ߔ‫ޕ‬>> z = peaks(7)z=0.0001
0.00340.00070.0468-0.0088 -0.1301-0.0365 -1.3327-0.0137 -0.4808
0.00000.07970.00000.0053-0.0299-0.59211.8559-1.65230.22892.09670.1099-0.2450-4.7596-0.72390.98103.68865.85910.2999-0.1100-2.1024-0.27292.93692.43382.20990.1107-0.0043-0.06160.49961.41220.58050.13280.00570.00000.00040.01300.03310.01250.00130.0000 ࿑ 5ޯ࿑ 6 ߦ‫ޔ‬3 ᰴరߩࠞ࡜࡯ࠣ࡜ࡈࠖ࠶ࠢࠬߩ଀ࠍ␜ߒ߹ߔ‫ޕߚ߹ޕ‬࿑ 5 ߦ␜ߔ 3 ᰴరࠣ࡜ࡈࠖ࠶
ࠢࠬߪ‫ޔ‬࿑ 7ޯ࿑ 11 ߦ␜ߔࠃ߁ߥ᭽‫ߥޘ‬ᣇᴺߦࠃߞߡ╬㜞✢⴫␜ࠍߔࠆߎߣ߽น⢻ߢߔ‫ޕ‬

c1=[0.0 1.9 1.2 1.8 3.8 5.0 4.8];
c2=[0.0 2.8 2.5 4.7 5.6 5.5 8.5];
c3=[0.0 4.6 5.5 5.3 7.6 9.5 9.1];
plot(c1)
hold onplot(c2, 'b*')plot(c3, 'r--')plot(c3, 'ro')hold offaxis([1 7 0 10])set(gca,'XTick',[1:2:7])
set(gca,'YTick',[0:2:10])
xlabel('xlabel');ylabel('ylabel');title('Sample ');grid
h=legend('CASE A','CASE B','CASE C');set(h,'Position',[0.2,0.65,0.3,0.22]);axes(h)print -depsc fig4

࿑㧠

surf(peaks(35))
print -depsc fig5  ࿑㧡  


mesh(peaks(35)+15)
holdpcolor(peaks(35))
hold off
print -depsc fig6

   ࿑㧢

surfc(peaks(30))
colormap(hot)colorbar('vert')
gridprint -depsc fig7

 
࿑㧣pcolor(peaks(30))
colormap(hot)colorbar('vert')
print -depsc fig8

 
࿑㧤


 

!"#$%&'()*+,-./0

 

pcolor(peaks(30))
colormap(hot)shading flat
hold oncontour(peaks(30),15,'g')hold offcolorbar('vert')
print -depsc fig9
 ࿑㧥b=contour(peaks(35),15);clabel(b)gridprint -depsc fig10

࿑ 10

b=contour3(peaks(35),15);clabel(b)gridprint -depsc fig11

 
࿑ 11  


6.5 ⷞὐ 㧟ᰴరࠣ࡜ࡈࠖ࠶ࠢࠬߩ⴫␜ߦ߅        ޿ߡ㊀ⷐߥ‫ⷞޔ‬ὐߩⷺᐲߩ⺞▵ߦߪ
view ߣ޿߁ࠦࡑࡦ࠼ࠍ↪޿߹ߔ‫ޕ‬view(Azimuth,Elevation)ࠦࡑࡦ࠼ߪ‫ޔ‬᳓ᐔᣇะߣု⋥ᣇะߩ࿁ォⷺࠍ࿑㧝㧞ߦ␜ߔࠃ߁ߦᜰቯߔࠆߎߣߦࠃࠅ‫ⷞޔ‬ὐߩⷺᐲࠍ⺞▵ߒ߹ߔ‫ޕ‬ ଀߃߫‫ޔ‬࿑ 13 ߪ speaks ࠦࡑࡦ࠼ߦࠃࠅᓧࠄࠇߚⴕ೉ࠍ⇣ߥࠆ㧠ߟߩⷞὐ࿑㧝㧞㧦3 ᰴరࡊࡠ࠶࠻ߩⷞὐⷺᐲߩ⸳ቯ

߆ࠄ⴫␜ߒߚ߽ߩߢߔ‫ޕ‬view(-37.5,30) view(-7,80)
view(-90,0)view(-7,-10)

Azimuth=-7.5

Azimuth=-90

Elevation=30

Azimuth=-7Elevation=80

Elevation=0

Azimuth=-7

Elevation=-10࿑㧝㧟㧦peaks 㑐ᢙߦࠃࠆ 3 ᰴరࠣ࡜ࡈࠖ࠶ࠢࠬࠍ⇣ߥࠆ 4 ߟߩⷞὐ߆ࠄ⴫␜ߒߚ଀㧣 ߹ߣ߼ ᧄⓂߢߪ‫ޔ‬㜞ᕈ⢻ߥᢙ୯⸘▚ᯏ⢻ߣᄙᓀߥนⷞൻᯏ⢻ࠍ஻߃ߚᛛⴚ⸘▚࠰ࡈ࠻ MATLAB ߩ౉㐷ߣߒߡ‫․ߩߘޔ‬ᓽ‫ޔ‬ᢙ୯⸘▚ߩᜰ␜ᣇᴺ‫ߩࠬࠢ࠶ࠖࡈ࡜ࠣޔ‬૞ᚑᣇᴺߥߤࠍ⚫੺ߒ߹ߒߚ‫੹ޕ‬࿁⚫੺ߒߚ߽ߩߪ‫ޔ‬MATLAB ߩ೑↪ᴺߩ߶ࠎߩ৻ㇱಽߦߔ߉߹ߖࠎ‫ޕ‬ᤚ㕖৻ᐲ‫ޔ‬ታ㓙ߦ⥄ಽߢ೑↪ߒߡ‫⼾ߩߘޔ‬ንߥᯏ⢻ߣ㜞޿↢↥ᕈࠍ૕㛎ߒߡ޿ߚߛ߈ߚ޿ߣᕁ޿߹ߔ‫ࡦ࠮ࠬࡦࠛࠗࠨ࡯ࡃࠗࠨ߇࡞ࠕࡘ࠾ࡑޔ߅ߥޕ‬࠲࡯㧝㓏ߩࡊࡠࠣ࡜ࡓ⋧⺣ቶߦ⸳⟎ߒߡ޽ࠅ߹ߔߩߢ‫޿૶ޔ‬ᣇ߽߽ߞߣ⹦ߒߊ⍮ࠅߚ޿ᣇߪߘߜࠄࠍߏⷩߊߛߐ޿‫ޕ‬ 

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