1. MATLAB ãšã¯: åºæ¬çãªç解ãšãã®ç¹åŸŽ
1.1 MATLABã®åºæ¬çãªç解
MATLABïŒããã©ãïŒã¯ãé«åºŠãªæ°å€èšç®ãè¡ãããã®çµ±åéçºç°å¢ã§ãããèšèªã§ããããŸããå€éšããŒã¿ã®åã蟌ã¿ããåæãã¯ãªãŒãã³ã°ãå¹³æ»åããããŠã°ã«ãŒãã³ã°ãŸã§ããŒã¿è§£æã®å šãŠãå¹ççã«è¡ãããšãå¯èœã§ãã
ãŸããMATLABã¯çµ±åéçºç°å¢ãæäŸãã匷åãªæ©èœã®äžéšã§ããã2次å ããã³3次å ã®ã°ã©ãã£ã¯ã¹æç»ãã¢ã«ãŽãªãºã éçºããã€ãã£ãããã³Webã¢ããªã±ãŒã·ã§ã³ã®äœæãããŸããŸãªèšèªãšã®é£æºãªã©ãå¯èœãšãªã£ãŠããŸãã
ããã«ãMATLABã¯ããŒããŠã§ã¢ãšã®æ¥ç¶ã䞊åèšç®ãã¢ããªã±ãŒã·ã§ã³ã®é åžãã¯ã©ãŠãã³ã³ãã¥ãŒãã£ã³ã°ãToolboxãžã®æ©èœè¿œå ãªã©ãå¯èœã«ããæ©èœãæäŸããŠããŸããããã«ãããéçºè ã¯MATLABã䜿ã£ãŠãç§åŠãå·¥åŠãçµæžãªã©å€æ§ãªåéã§ã®èšç®äœæ¥ãé«éåããå¹çåããããšãã§ããŸãã
1.2 MATLABã®åºæ¬çãªç¹åŸŽ
MATLABã®æ倧ã®ç¹åŸŽã¯ãã®åŒ·åãªæ°å€èšç®èœåã§ããè¡åæŒç®ã埮åæ¹çšåŒã®è§£æãçµ±èšåæãªã©ãç§åŠæè¡èšç®ã®ã»ãšãã©ãMATLABã§å¯èœãšãªã£ãŠããŸãããã®èœåã¯ããã£ãŒãã©ãŒãã³ã°ã®ã¢ã«ãŽãªãºã éçºãããŸããŸãªæ°å€èšç®ãã¬ããŒãã£ã³ã°ãšãã¹ããªã©ãç¹å®ã®åéã§ã®å©çšäŸã«åæ ãããŠããŸãã
ãŸãMATLABã¯Simulinkãšé£æºããããšã§ãã·ã¹ãã èšèšãã·ãã¥ã¬ãŒã·ã§ã³ããã¹ãç°å¢æ§ç¯ãå¯èœãšãªããŸããããã«ãããçµã¿èŸŒã¿ç³»ãã¯ãããšããåºç¯ãªåéã«ãããå®éšã»èšèšç°å¢ãšããŠå©çšãããŠããŸãã
ããã«ãMATLABã®å®è¡ããŒã«ãšããŠã¯ãCãC++ãPythonãªã©ãšã®çžäºéçšæ§ã確ä¿ãããŠããŸããããã«ãããMATLABãäžéšã«åã蟌ã¿ãæ¢åã®ã³ãŒãããŒã¹ãšé£æºãããããšãå¯èœãšãªã£ãŠããŸãã
1.3 MATLABã®ç°å¢æ§ç¯
MATLABã¯ãWindowsãMac OS XãLinuxã®åOSäžã§åäœããŸããç°å¢æ§ç¯ã®æé ã¯å ¬åŒãŠã§ããµã€ãã«è©³çŽ°ãèšèŒãããŠãããã¹ã ãŒãºã«å°å ¥ããããšãå¯èœã§ãããŸããå©çšè ã®çµç¹ã«å¿ããã©ã€ã»ã³ã¹ãæäŸãããŠãããäŒæ¥ããåŠçãŸã§å¹ åºãå©çšãããŠããŸãã
é»åæµéçãè³Œå ¥ããã°ãMATLABãšãã®ã¢ããªã³è£œåãããã«ããŠã³ããŒãããŠå©çšéå§ããããšãã§ããŸããã€ã³ã¹ããŒã«äœæ¥ããŠã£ã¶ãŒã圢åŒã®æ瀺ã«åŸã£ãŠé²ããã°å®¹æã«è¡ãããšãå¯èœã§ãã
ãŸããMATLABã¯ã€ã³ã¿ãŒãããæ¥ç¶ãå¿ èŠãªãªã³ã©ã€ã³ã©ã€ã»ã³ã¹ãšãã€ã³ã¿ãŒãããæ¥ç¶ãå¿ èŠãšããªããªãã©ã€ã³ã©ã€ã»ã³ã¹ãæäŸãããŠããŸãã®ã§ãå©çšç°å¢ã«å¿ããŠéžæããããšãã§ããŸãã
1.4 MATLABã®ãµããŒãäœå¶
MATLABã¯ç¢ºããªãµããŒãäœå¶ãæŽã£ãŠããŸããå ¬åŒãŠã§ããµã€ãã§ã¯å€æ°ã®ãã¥ãŒããªã¢ã«ãããã¥ã¡ã³ããæäŸãããŠãããå©çšè ã¯ããã掻çšããããšã§MATLABãå¹çããåŠã¶ããšãå¯èœã§ãã
ãŸããéçºå ã®MathWorks瀟ã¯ããŠã§ãããŒã¹ã®ãµããŒããæäŸããŠããŸãããã©ãŒã©ã ã«ãããŠãŒã¶ãŒã³ãã¥ããã£ã®æŽ»çšããå°é家ã«ããçŽæ¥ã®ã¢ããã€ã¹ãåŸãããšãå¯èœã§ã詳现ãªæå°ãå¿ èŠãšãããŠãŒã¶ãŒã«ãšã£ãŠã¯éåžžã«åœ¹ç«ã¡ãŸãã
ããã«ãMATLABã¯é«ãæè»æ§ããã£ãŠãŠãŒã¶ãŒã®ããŒãºã«å¿ããããšãã§ãããœãããŠã§ã¢ã§ãããã®ããããœãããŠã§ã¢ã®æ¹åãæ°ããæ©èœè¿œå ã®èŠæã«å¯ŸããŠãããµããŒãäœå¶ãéããŠè¿ éã«å¯Ÿå¿ããŠããŸãã
2. MATLABã§ã§ããäº: æ©èœäžèŠ§ãšãã®èª¬æ
ãŠãŒã¶ãŒã«ãšã£ãŠæãéèŠãªèŠçŽ ã®äžã€ãããã®ããŒã«ã®æ©èœæ§ã§ããMATLABã¯å¹ åºãæ©èœãæäŸããããããæ°å€èšç®ã®æŠãæã£ãŠããŸãã以äžã«ãMATLABã®äž»ãªæ©èœãšãã®èª¬æãåæããŸãã
ãã®åŒ·åãªæ©èœã®äžéšãå©çšããããšã§ãå€ãã®å°éåéã®å°é家ãåæ§ã«ãMATLABã®å©ç¹ãå®æã§ããã§ãããã
ããã§ã¯ãMATLABã®æ©èœã®äžéšãããã¯ã¢ããããããããäœãã§ããã®ããã©ã®ããã«äœ¿çšããã®ããå ·äœçã«è§£èª¬ããŸãã
2.1 ããŒã¿è§£æãšãã®ææ³
MATLABã¯ãããŒã¿è§£æã®åŒ·åãªããŒã«ãæäŸããŠããŸãããã®å€æ§ãªæ©èœã«ãããå©çšè ã¯å€éšããŒã¿ãç°¡åã«åã蟌ãããšãã§ãããããŠãã®ããŒã¿ãåæãã¯ãªãŒãã³ã°ãå¹³æ»åãããã«ã¯ã°ã«ãŒãåããããšãå¯èœã§ãã
ãã®è±å¯ãªæ©èœã¯ãããŒã¿ãããæ·±ãç解ããããããããŠããã«åºã¥ããæŽå¯ãåŸãããã«äžå¯æ¬ ã§ãããŸããè€éãªåæããã»ã¹ãéæåããããŒã¿ãèŠèŠçã«è¡šçŸãã匷åãªã°ã©ãã£ãã¯è¡šç€ºããŒã«ãå©çšã§ããŸãã
ããã«ãããããŒã¿è§£æãäžå±€å®¹æã«ãªããå€ãã®ãããžã§ã¯ãã§æéãç¯çŽã§ããŸãã
2.2 ã¢ã«ãŽãªãºã éçºãšãã®ææ³
ã¢ã«ãŽãªãºã éçºãMATLABã®äž»èŠãªæ©èœã®äžã€ã§ãããã«ãã£ãŠãŠãŒã¶ãŒã¯ã¹ã¯ãªããã£ã³ã°çšãã¡ã€ã«ãé¢æ°ãã¯ã©ã¹ãäœæããããšãå¯èœã«ãªããŸãã
ãããã®ããŒã«ã䜿çšããŠããŠãŒã¶ãŒã¯èªå·±å®çµããã³ãŒããéçºã§ããããã«ããæéãšåŽåãç¯çŽããããšãã§ããŸãããŸããMATLABã®åªããUIèšèšããŒã«ã掻çšããããšã§ãå©çšè ã¯ç¬èªã®ãŠãŒã¶ãŒäœéšãæäŸããèªå·±å®çµåã®ã¢ããªã±ãŒã·ã§ã³ãéçºããããšãå¯èœã§ãã
ã€ãã£ãªã ãäžè²«ããŠäœ¿çšããããšã«ãããMATLABãŠãŒã¶ãŒã¯ã³ãŒãã®å¯èªæ§ãšã¡ã³ããã³ã¹æ§ãåäžãããçµæçã«ãããžã§ã¯ãå šäœã®å¹çãåäžãããããšãã§ããŸãã
2.3 ã°ã©ãã£ãã¯ã¹æ©èœãšãã®å©çšæ¹æ³
MATLABã¯ã匷åãªã°ã©ãã£ãã¯ã¹ããŒã«ãšããŠãç¥ãããŠããŸããããã«ããã2次å ããã³3次å ããããã®äœæãšæé©åãå¯èœã«ãªããŸãã
ãã®æ©èœã¯ãè€éãªããŒã¿æ§é ãèŠèŠçã«è¡šçŸããäžã§éåžžã«éèŠã§ãããæ·±ãæŽå¯ãå¯èœã«ããŸãããŸããããã掻çšããããšã§ãããŒã¿ã®ãã¿ãŒã³ãçžé¢é¢ä¿ãå€ãå€ãããæ確ã«ç解ããããå ·äœçãªææ決å®ã«ã€ãªããããšãå¯èœã§ãã
æçµçãªåºåã¯ãããã§ãã·ã§ãã«ã§çŸããã°ã©ãã£ãã¯ãåŸããããã®çµæããã¬ãŒã³ããŒã·ã§ã³ãã¬ããŒãã£ã³ã°ã§ä»äººãå§åããããšãã§ããŸãã
2.4 ä»èšèªãšã®é£æºææ³
MATLABã®ããäžã€ã®åŒ·åãªç¹åŸŽãä»ã®èšèªãšã®é£æºã§ããPythonãJavaãCèšèªãC++ã.NETãªã©ãšã®é£æºãå¯èœã§ãã
ãã®ãããªä»èšèªãšã®é£æºã«ãããããªãã®MATLABãããžã§ã¯ãã¯ãããã®ããã°ã©ãã³ã°èšèªã§äœæãããã³ãŒããããŒã«ãšã®äºææ§ãæã€ããšãã§ããŸãã
ãããã£ãŠãæ¢åã®ãªãœãŒã¹ã掻çšããªããæ°ããªãããžã§ã¯ãã«åãçµãããšãå¯èœã«ãªããéåžžã¯æéãšãªãœãŒã¹ã®å€§éã®æ¶è²»ãå¿ èŠãšããæ°ããéçºãçç¥ããããšãã§ããŸãã
3. MATLABãšã¢ããªéçº: AndroidãšiOSã®äž¡æ¹ã®ãã©ãããã©ãŒã
3.1 MATLABãšã¢ããªéçºã®åºæ¬ç解
ãã®å šèœã®éçºããŒãããŒãMATLABã¯ãã¢ããªéçºã«ããå§ãããŸããã§ããã®çç±ã®äžã€ãããžã¥ã¢ã«ãã¶ã€ã³æ©èœãåãããApp Designerãã®ååšã§ãããã®ããŒã«ã«ãããGUIïŒã°ã©ãã£ã«ã«ãŠãŒã¶ãŒã€ã³ã¿ãã§ãŒã¹ïŒã®ã¢ããªã±ãŒã·ã§ã³ãå¹ççã«èšèšã§ããŸãã
ããŠãMATLABã¯ãã¢ããªéçºã«ãããŠããã°ã©ãã³ã°ãšãã¶ã€ã³äœæ¥ãã·ãŒã ã¬ã¹ã«é£æºãããããšãå¯èœã§ããããã«ãããèšèšè ãéçºè ãå€æ©èœãªãã€ãã£ãã¢ããªã±ãŒã·ã§ã³ãäžããç¬èªã«èšèšã§ããŸãã
æåŸã«ããã®ãApp Designerãã¯iOSããã³Androidãã€ãã£ãã¢ããªã®äœæã®äž¡æ¹ã«å¯Ÿå¿ããŠããŸãããã®ãããéçºè ã¯äž¡ãã©ãããã©ãŒã ã§åäœããã¢ãã€ã«ã¢ããªã®éçºãå¯èœã«ãªããŸãã
3.2 MATLABã§ã®iOSã¢ããªéçº
次ã«ãå ·äœçã«MATLABã§iOSã¢ããªãéçºããæ¹æ³ã玹ä»ããŸããåºæ¬çã«ã¯ããApp Designerãã䜿çšããŠMATLABã§iOSã¢ããªãèšèšãããããiOSããã€ã¹åãã«ã³ã³ãã€ã«ããŸãã
MATLABã¯iOSãã©ãããã©ãŒã åãã«èšèšãããã¢ããªã±ãŒã·ã§ã³ã®éçºãšãããã€ãäžæã«åŒãåããããšãå¯èœã§ããããã«ãããæŽçæŽé ãããéçºãããŒã§ã¢ããªéçºããã»ã¹ãé²ããããšãå¯èœã«ãªããŸãã
ãŸããiOSã¯Apple瀟ã®åŒ·åãªããŒããŠã§ã¢ãªãœãŒã¹ãšåŒ·åºãªã»ãã¥ãªãã£ãåãããã©ãããã©ãŒã ã§ãããããMATLABã掻çšããiOSã¢ããªã®éçºã¯éåžžã«æçšã§å¹æçãªæŠç¥ãšãªããŸãã
3.3 MATLABã§ã®Androidã¢ããªéçº
MATLABã䜿ã£ãAndroidã¢ããªã®éçºãéåžžã«å®è·µçãªæé ã§ãããApp Designerãã®æŽ»çšã«ãããããã«Androidãã€ãã£ãã¢ããªã®èšèšãå§ãããããAndroidããã€ã¹åãã«ã³ã³ãã€ã«ããããšãå¯èœã§ãã
ãŸããMATLABã¯Androidãã©ãããã©ãŒã äžã®ã¢ããªã±ãŒã·ã§ã³ã®éçºãäžæã«åŒãåããçµç¹åã«ããå¹ççãªéçºãããŒãæäŸããŸãã
å ããŠãMATLABã§äœæãããã¢ããªã¯ãAndroidãæäŸããè±å¯ãªããã€ã¹çŸ€ãšåºç¯ãªãŠãŒã¶ãŒããŒã¹ãã¿ãŒã²ããã«ããããšãã§ããããã«ããé«ãã¢ã¯ã»ã·ããªãã£ãšæ¡æ£åãåŸãããšãã§ããŸãã
3.4 MATLABãšã¯ãã¹ãã©ãããã©ãŒã éçº
ã¯ãã¹ãã©ãããã©ãŒã ã®ã¢ããªã±ãŒã·ã§ã³éçºã®éãMATLABã¯éåžžã«æçšãªãã©ãããã©ãŒã ãšãªããŸããäžã€ã®ã³ãŒãããŒã¹ã§iOSããã³Androidåãã®ã¢ããªãéçºããããšãå¯èœãšãªããããéçºè ã¯ãæéãšãªãœãŒã¹ãå€§å¹ ã«ç¯çŽã§ããŸãã
é²ãã ç¹æ§ãšè±å¯ãªæ©èœãåããMATLABã¯ãç°ãªããã©ãããã©ãŒã ã«å¯Ÿå¿ããã¢ããªã±ãŒã·ã§ã³ã®éçºãç°¡åã«ããŸããããã«ãããMATLABã¯ã¢ããªéçºè ãå¿ é ãšããäžéšã®æé©ãªããŒã«ãšèšããŸãã
ãã®çµæãšããŠãMATLABã䜿ãäžã€ã®ã¢ããªéçºç°å¢ã§ãiOSãšAndroidã®äž¡ãã©ãããã©ãŒã åãã®ã¢ããªã±ãŒã·ã§ã³ã»ãœãªã¥ãŒã·ã§ã³ãçæéã§éçºããåºç¯ãªãŠãŒã¶ãŒããŒã¹ã«å¯Ÿå¿ããããšãå¯èœãšãªããŸãã
4. MATLABã䜿çšããå ·äœçãªããŒã¿è§£æ
MATLABã¯ããŒã¿è§£æã®ããã®åŒ·åãªããŒã«ã§ãããæ°åŠã®èæ¯ãæã€ãŠãŒã¶ãŒã«ã¯éåžžã«æçã§ããå¹ åºãåéã§äœ¿çšããããã®æ¹æ³è«ã¯èšç®ãçµ±èšãã°ã©ãäœæãã¢ã«ãŽãªãºã ã®éçºãã¢ãã«æ§ç¯ãªã©ãçµ±åããŸãã
ãã®ã»ã¯ã·ã§ã³ã§ã¯ãMATLABã®ããŒã¿è§£æææ³ã®åºæ¬çãªç解ããããã䜿ãããææ³ãå ·äœçãªäŸããããŠã¢ããã³ã¹ãããŒã¿è§£æææ³ãŸã§ãæ¢ããŸãã
ãã®ãããæ¢ã«MATLABã«äžå®ã®ç解ãæã€äžçŽè ããååŠè ã圹ç«ã€æ å ±ãèŠã€ããããšãã§ããŸãã
4.1 MATLABã®ããŒã¿è§£æææ³ã®ç解
MATLABã«ã¯å€ãã®çµã¿èŸŒã¿é¢æ°ããããèšç®ãçµ±èšãã°ã©ãäœæãªã©ãããŒã¿è§£æã«å¿ èŠãªããŸããŸãªææ³ãæäŸããŸãããŸãã足ããªãæ©èœã¯ToolboxïŒè¿œå æ©èœïŒã䜿çšããŠã«ã¹ã¿ãã€ãºããããšãã§ããŸãã
ããŒã¿ã®åæã¯éåžžãã¯ãªãŒãã³ã°ãæ€æ»ãå€æãã¢ããªã³ã°ã解éã®ããã»ã¹ãçµãŠè¡ãããMATLABã¯ããããã¹ãŠãå¹ççã«è¡ãããã®ããŒã«ãæäŸããŸãã
ãŠãŒã¶ãŒã¯MATLABãæäŸããäžé£ã®ããŒã«ã䜿çšããããŒã¿ãç解ããæçšãªæ å ±ãæœåºãããã®çµæãããžã¥ã¢ã«åã§ããŸãã
4.2 MATLABã§ãã䜿ãããããŒã¿è§£æææ³
MATLABã®äžå¿çãªããŒã¿è§£æææ³ã¯ãå€éšã®ããŒã¿ã®èªã¿èŸŒã¿ãããŒã¿ã®ååŠçãçµ±èšçåæãããŒã¿ã®ããžã¥ã¢ã«åã§ããçµ±èšææ³ã§ã¯ãåºæ¬çãªå¹³åãäžå€®å€ãæšæºåå·®ãããååž°åæãæ£åžå³è¡åãäž»æååæãªã©ã®ããè€éãªææ³ãŸã§ãå«ãŸããŸãã
ãŸããã°ã©ãã£ãã¯ã·ã¹ãã ã¯ãããŒã¿ã®ããžã¥ã¢ã«è¡šçŸã«ããã匷åãªããŒã«ã§ããã2DãŸãã¯3Dã®ãããããç·å³ããã¹ãã°ã©ã ãªã©ãäœæã§ããŸãã
ãããã®ææ³ã¯ãMATLABãæäŸããçµã¿èŸŒã¿ã®é¢æ°ãè Toolboxãå©çšããŠå®è£ ããããšãã§ããŸãããŸããããã©ãã®åŒ·åãªã¢ã«ãŽãªãºã éçºæ©èœã掻çšããŠãç¬èªã®ããŒã¿è§£æææ³ãéçºããããšãå¯èœã§ãã
4.3 MATLABã§è¡ãããŒã¿è§£æã®å ·äœäŸ
MATLABã¯ãéèããŒã¿åæãçç©å»åŠããŒã¿åæãç»åããŒã¿åæãªã©ãå€çš®å€æ§ãªããŒã¿è§£æã®å ·äœäŸã§æŽ»çšãããŠããŸããããšãã°ãæ ªäŸ¡ãåžå Žååã®åæãå¿é»å³ãè³æ³¢è§£æã®ãããªçç©å»åŠããŒã¿ã®è§£æãããžã¿ã«ç»åã®è§£æãšãã£ãå ·äœäŸãæããããŸãã
ãããã®ã¿ã¹ã¯ã§ã¯ãMATLABã®çµã¿èŸŒã¿é¢æ°ãšToolboxã倧ããªå©ãã«ãªããŸããéœåã«ãããããŒã¿ãé©åã«åŠçããå¿ èŠãªçµ±èšæ å ±ãèšç®ããçµæãèŠããã圢ã§æ瀺ããããšãã§ããŸãã
ãããã®å ·äœäŸãéããŠãMATLABãã©ã®ããã«åŒ·åã§æè»æ§ã®ããããŒã¿è§£æããŒã«ã§ããããç解ããããšãã§ããŸãã
4.4 MATLABã®ã¢ããã³ã¹ãããŒã¿è§£æææ³
å é²çãªããŒã¿è§£æææ³ãšããŠã¯ããã£ãŒãã©ãŒãã³ã°ãä¿¡å·åŠçãæéç³»å解æãæé©åãªã©ãMATLABã§å¯èœã§ãããããã®ææ³ã掻çšããã°ã倧éã®ããŒã¿ããæçšãªæ å ±ãæœåºããæ矩深ãç¥èŠãå°ãåºãããšãã§ããŸãã
äŸãã°ããã£ãŒãã©ãŒãã³ã°ã«ã€ããŠã¯ãMATLABã®ãã£ãŒãã©ãŒãã³ã°Toolboxãè±å¯ãªé¢æ°ãšã¢ããªãæäŸããŠããŸããããã«ããã深局åŠç¿ãããã¯ãŒã¯ã®èšèšãšãã¬ãŒãã³ã°ãäºæž¬ããã£ãŒãã£ãŒã®æœåºãªã©ãå¯èœã«ãªããŸãã
æé©åã«ã€ããŠããMATLABã®çµã¿èŸŒã¿é¢æ°ãæé©åToolboxã䜿çšããã°ãæ¬çªç°å¢ã§ã®é床ãªã³ã³ãã¥ãŒãã£ã³ã°æéãåæžã§ããé«æ§èœãªã¢ã«ãŽãªãºã ãå©çšå¯èœã§ãã
5. MATLABã§ã®ã¢ã«ãŽãªãºã éçº
MATLABã䜿çšãããšãåçš®æ°å€èšç®ã®ããã®ã¢ã«ãŽãªãºã ãéçºããããšãå¯èœãšãªããŸããMATLABã掻çšããããšã«ãããã¢ã«ãŽãªãºã ã®ã³ãŒãã£ã³ã°ãè©Šéšãããã³ãããã°ãå¹ççã«è¡ããŸãããããã®ããšã¯æ²¢å±±ã®æéãšåŽåãç¯çŽãããšããã ãã§ãªããå質ãšä¿¡é Œæ§ã®åäžã«å¯äžããŸãã
5.1 MATLABã«ãããã¢ã«ãŽãªãºã éçºã®åºæ¬
ã¢ã«ãŽãªãºã éçºã®åºæ¬çãªããã»ã¹ã¯ãåé¡å®çŸ©ãã¢ã«ãŽãªãºã ãã¶ã€ã³ãã³ãŒãã£ã³ã°ããã¹ãããããŠãããã°ã®ç¹°ãè¿ãã§ããMATLABã§ã¯ããã®ããã»ã¹ã容æã«ããŸããéçºç°å¢ã¯ã·ã³ãã«ãã€å¹ççã«äœæ¥ãè¡ãããšãã§ããŸãããŸãã¹ã¯ãªããã£ã³ã°çšãã¡ã€ã«ãé¢æ°ãã¯ã©ã¹äœæãªã©ã容æã«å®è¡ã§ããŸãã
åºæ¬çãªã¢ã«ãŽãªãºã ãéçºããæåã®ã¹ãããã¯ãé©åãªã¢ã«ãŽãªãºã ãç¹å®ããããšã§ããããã«ã¯ãå ·äœçãªåé¡ã解ãããã«ã©ã®ãããªææ³ã䜿çšããããç解ããããšãå«ãŸããŸããMATLABã«ã¯ãã¢ã«ãŽãªãºã ãéçºããããã®åŒ·åãªãã«ãã€ã³é¢æ°ãšããŒã«ãæšæºã§æäŸãããŠããŸãã
次ã«ãMATLABã䜿çšããŠã¢ã«ãŽãªãºã ãå®è£ ããŸããMATLABã«ã¯ãMATLABã®åŒ·åãªæ°åŠé¢æ°ãå©çšããŠé«åºŠãªã¢ã«ãŽãªãºã ãéçºã§ããããã«èšèšãããå€æ°ã®åœä»€åœ¢åŒã®ããã°ã©ãã³ã°èšèªããããŸãããããã®é¢æ°ã䜿ã£ãŠãã¢ã«ãŽãªãºã ãçæéã§èšèšããè©Šéšããããšãã§ããŸãã
5.2 MATLABã§ã®åºæ¬çãªã¢ã«ãŽãªãºã äŸ
MATLABã§ã¢ã«ãŽãªãºã ãéçºããéã®åºæ¬çãªäŸãšããŠããã¯ãã«åãæé©åãæããããŸãããã¯ãã«åã¯ãè¡åæŒç®ã䜿çšããŠã«ãŒããé¿ããããã°ã©ã ã®ããã©ãŒãã³ã¹ãåäžããããã¯ããã¯ã§ããæé©åã¯ãç¹å®ã®ç®æšãéæããããã«å¿ èŠãªãªãœãŒã¹ãæå°éã«ããããã«ã¢ã«ãŽãªãºã ã調æŽããããã»ã¹ã§ãã
ããã«MATLABã¯ãçµ±èšè§£æãä¿¡å·åŠçãç»ååŠçãªã©ãå€å²ã«ãããåéã§ã¢ã«ãŽãªãºã éçºãå¯èœã§ããããšãã°çµ±èšè§£æã§ã¯ãããŒã¿ã®å¹³åå€ãæ±ããã¢ã«ãŽãªãºã ããç°åžžæ€ç¥ã®ã¢ã«ãŽãªãºã ãªã©ãéçºã§ããŸãã
ãŸããç»ååŠçã§ã¯ãç»åãåç»ã®ãã€ãºé€å»ããšããžæ€åºãç¹åŸŽæœåºãªã©ãè¡ãã¢ã«ãŽãªãºã ãéçºããããšãã§ããŸãããããã®ã¢ã«ãŽãªãºã ã®éçºã¯ãMATLABã®é«ã¬ãã«ãªããã°ã©ãã³ã°èšèªæ©èœãšè±å¯ãªããžã¥ã¢ã«åããŒã«ã掻çšããããšã§ãå¹çããå®è¡ã§ããŸãã
5.3 MATLABã®é«åºŠãªã¢ã«ãŽãªãºã éçº
Matlabã®åŒ·åºãªéçºãã¬ãŒã ã¯ãŒã¯ã«ãããé«åºŠãªã¢ã«ãŽãªãºã ã®éçºããããã容æãšãªããŸããããšãã°ããã£ãŒãã©ãŒãã³ã°ãæ©æ¢°åŠç¿ãšãã£ãåéã§ãé«åºŠãªã¢ã«ãŽãªãºã ãéçºããããšãå¯èœã§ãã
ãŸããæç³»ååæãæé©ååé¡ãéåã³ã³ãã¥ãŒãã£ã³ã°ãšãã£ãé«åºŠãªèšç®ãMATLABã®åŒ·åãªæ°å€èšç®èœåã«ããå¯èœãšãªããŸãããã®ããã«ãMATLABã¯ã¢ã«ãŽãªãºã éçºã®ããã®é«åºŠãªããŒã«ãæäŸããŠããŸãã
ãããã®é«åºŠãªã¢ã«ãŽãªãºã ãéçºããå ŽåãMATLABã§ã¯ããã°ã©ãã³ã°ã¹ãã«ã ãã§ãªããé¢é£åéã®å°éç¥èãå¿ èŠãšãªããŸãããããã£ãŠãé«åºŠãªã¢ã«ãŽãªãºã ã®éçºã«ã¯ãé©åãªèæ¯ãçµéšãæã€éçºè ãå¿ èŠãšãªããŸãã
5.4 MATLABã§ã®ã¢ã«ãŽãªãºã éçºåé¡è§£æ±ºæ¹æ³
ã¢ã«ãŽãªãºã éçºã«ã¯ããŸããŸãªåé¡ãä»éããŸãããMATLABã§ã¯ãããã®åé¡ãå¹æçã«è§£æ±ºã§ããŸããMATLABã¯éçºäžã®åé¡ãå¹ççã«ç¹å®ããä¿®æ£ããããã®åŒ·åãªãããã°ããŒã«ãæäŸããŠããŸãã
ããšãã°ãMATLABã䜿çšããã°ãã³ãŒãã®è¡ããšã«ãã¬ãŒã¯ãã€ã³ããèšå®ããŠãããã°ãè¡ãããšãå¯èœã§ããããã«ãããåé¡ç¹ãç¹å®ãããããªããŸãããŸããMATLABã®ãšã©ãŒã¡ãã»ãŒãžã¯éåžžã«è©³çŽ°ã§ããšã©ãŒã®åå ãæ£ç¢ºã«ç¹å®ããå©ãã«ãªããŸãã
ããã«ãMATLABã§ã¯ãäžåºŠã«å€§éã®ããŒã¿ãåŠçããã¢ã«ãŽãªãºã éçºã«ãããŠããé«éãªåäœãä¿èšŒããŸãã倧èŠæš¡ãªããŒã¿ãæ±ãéã«ããMATLABã®åŒ·åãªãã¯ãã«èšç®ãšäžŠåèšç®æ©èœãå©çšããã°ãèšç®ã³ã¹ããæãã€ã€ãé«ããã©ãŒãã³ã¹ãç¶æããããšãå¯èœã§ãã
6. MATLABã§ã®3Dã°ã©ãã£ãã¯ã¹è¡šçŸ
æ°å€è§£æããã³ããã°ã©ãã³ã°èšèªããŒã«ã®å€§å®¶ãMATLABã¯ã3Dã°ã©ãã£ãã¯ã®çæã«ãåªããæ©èœãåããŠããŸããããŒã¿ããžã¥ã¢ã©ã€ãºã®äžç°ãšããŠããŸãç 究çºè¡šãè€éãªããŒã¿ã®èª¬æã«ãããŠæçšãªããŒã«ãšèšããã§ãããã
MATLABã§ã¯ã3D空éã«ãããããŒã¿ã®è¡šçŸãè¡ããèŠèŠçã«ããŒã¿ã解éããããããããã®å€ãã®ããããé¢æ°ãæäŸãããŠããŸããå°åœ¢ããŒã¿ãè€éãªæ°åŠåŒã®å¯èŠåãããã«ã¯ãããã£ã³ã°ã¢ãã«ãã·ãã¥ã¬ãŒã·ã§ã³çµæã®è¡šçŸãªã©ãæ§ã ãªåéã§æŽ»çšãããŠããŸãã
ãã®ç¯ã§ã¯ãMATLABã§ã®3Dã°ã©ãã£ãã¯ã¹ã®åºæ¬ãšçææ¹æ³ãç·šéæ³ããããŠå ·äœçãªæŽ»çšäºäŸã«ã€ããŠè©³ãã説æããŠãããŸãã
6.1 MATLABã§ã®3Dã°ã©ãã£ãã¯ã¹ã®åºæ¬
ãŸãã¯ããã«ãMATLABã§ã®3Dã°ã©ãã£ãã¯ã¹ã®åºæ¬ã«ã€ããŠè§£èª¬ããŸããMATLABã§ã¯ã3Dãããããå«ãå¹ åºãã°ã©ãã£ãã¯ã¹é¢æ°ãçšæãããŠãããããããçµã¿åãããããšã§è±ããªèŠèŠè¡šçŸãäœãåºãããšãã§ããŸãã
åºæ¬çãª3Dããããé¢æ°ãšããŠã¯ãäŸãã°ãsurf()ãããmesh()ãããããŸããããããå©çšãããšãx,y,z軞ã®äžæ¬¡å 空éã®äžã«ãè¡šé¢ãããããã¡ãã·ã¥ãããããæç»ããããšãã§ããŸãã
ãããããã åçŽã«3Dã°ã©ãã£ãã¯ã¹ãæãã ãã§ãªããè²ä»ãã軞ã©ãã«ãã¿ã€ãã«ã®è¿œå ãšãã£ãç·šéå å·¥ãå¯èœã§ãã次ã®ç« ç¯ã§ãã®ææ³ã«ã€ããŠã觊ããŠãããŸãã
6.2 MATLABã§ã®3Dã°ã©ãã£ãã¯ã¹ã®çææ¹æ³
MATLABã§3Dã°ã©ãã£ãã¯ã¹ãçæããã«ã¯ããŸãé©åœãª3DããŒã¿ãå¿ èŠãšãªããŸããããŒã¿ãçšæãããããplot3()ãããsurf()ãããmesh()ããªã©ã®é¢æ°ã䜿çšããŠ3Dã°ã©ãã£ãã¯ã¹ãæããŸãã
äŸãã°ããmesh()ãé¢æ°ã䜿ãã°ãæ Œåç¹äžã®zå€ãè²ã§è¡šçŸãã3次å ã¡ãã·ã¥ãããããæç»ããããšãã§ããŸããããããã®é¢æ°ãã©ã®ããã«æ¯ãèããã¯ãMATLABã®å ¬åŒããã¥ã¡ã³ããŒã·ã§ã³ãåç §ãããšãã詳ããæ å ±ãåŸãããšãã§ããŸãã
ãã®ãããªåºæ¬çãªé¢æ°ã䜿ãã°ãåçŽãª3次å ã°ã©ãããè€éãª3次å ã°ã©ããŸã§ãæ§ã ãªã¿ã€ãã®ã°ã©ãã£ãã¯ã¹ãçæããããšãå¯èœãšãªããŸãã
6.3 MATLABã§ã®3Dã°ã©ãã£ãã¯ã¹ç·šéæ³
次ã«ãMATLABã§3Dã°ã©ãã£ãã¯ã¹ã®ç·šéã«ã€ããŠè§£èª¬ããŸããåºæ¬çãª3Dã°ã©ãã£ãã¯ã¹ãæããåŸã«ãè²ä»ãã軞ã©ãã«ãã¿ã€ãã«ã®è¿œå ãªã©ã®ç·šéãè¡ãããšã§ãããã«æ å ±éã®å€ãèŠèŠè¡šçŸãåŸãããšãå¯èœãšãªããŸãã
ç¹ã«ããtitle()ãããxlabel()ãããylabel()ãããzlabel()ããšãã£ãé¢æ°ã䜿çšããããšã§ãã°ã©ãã£ãã¯ã¹ã«ã¿ã€ãã«ãå軞ã®ã©ãã«ãè¿œå ã§ããŸãããŸãããcolorbar()ããå©çšãããšãã«ã©ãŒããŒã衚瀺ããããšãå¯èœã§ãã
ãŸããèŠç¹ãèŠéãå€æŽããããšãå¯èœã§ããããã«ã¯ããview()ãé¢æ°ã䜿ãã2ã€ã®è§åºŠïŒèŠç·æ¹åãšåçŽæ¹åïŒãæå®ããããšã§è¡ããŸãã
6.4 MATLABã§ã®3Dã°ã©ãã£ãã¯ã¹æŽ»çšäºäŸ
æåŸã«ãMATLABã§ã®3Dã°ã©ãã£ãã¯ã¹ã®å ·äœçãªå©çšå Žé¢ã«ã€ããŠèª¬æããŸãã3Dã°ã©ãã£ãã¯ã¹ã¯ãæ°å€ãã®åéã§æŽ»çšãããŠããŸãã
äžäŸãæãããšãå°çæ å ±åŠã§ã¯ãå°åœ¢ããŒã¿ã3次å ã§èŠèŠåããå°åœ¢ã®ç解ãå°ççãªçŸè±¡ã®åæã«äœ¿çšããŸãããŸããæ©æ¢°åŠç¿ããã¥ãŒã©ã«ãããã¯ãŒã¯ã®è§£æã«ã掻çšãããŸããç¹ã«ãé«æ¬¡å ããŒã¿ã®å¯èŠåã«3DãŸãã¯å€æ¬¡å ããããã¯æå¹ã§ãããèŠèŠçãªè§£éãå¯èœã«ãªããŸãã
ãŸãã3Dã°ã©ãã£ãã¯ã¹ã¯ãç§åŠè ããšã³ãžãã¢ãå®éšããŒã¿ãã·ãã¥ã¬ãŒã·ã§ã³çµæãèŠèŠçã«è§£éããå ±æããã®ã«ãéåžžã«äŸ¿å©ã§ããå ·äœçãªåé¡ã«å¯Ÿãã解ãã€ã³ãµã€ããåŸãããã«ããããã®ããŒã«ã¯é »ç¹ã«çšããããŸãã