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yuroyoro
July 13, 2016
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関数の話
Supershipの社内勉強会で使ったやつ
yuroyoro
July 13, 2016
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Transcript
ؔͷ !ZVSPZPSP
ؔͱ
Z G Y ೖྗYʹରͯ͠ɺग़ྗZͷΛܾఆ͢Δنଇ
" # $ % *OU 4USJOH
ࣸ૾ͭͷू߹ͷରԠؔ
JOU TUS JOH ू߹ܕͱߟ͑ΔͱɺܕͱܕͷରԠنଇ
͕ؔ ϑΝʔετΫϥε
MFUGaY TIPX Y มʹʮؔʯΛೖ ଋറ Ͱ͖Δ )BTLFMM
G Y \YUP@T ^ มʹʮؔʯΛೖ ଋറ Ͱ͖Δ 3VCZ
DPOTUG Y \SFUVSOYUP4USJOH ^ มʹʮؔʯΛೖ ଋറ Ͱ͖Δ +BWB4DSJQU
ؔద༻
ධՁʮؔʯʹҾΛ༩͑ͯ݁ՌΛಘΔ͜ͱ SFUVSOYUP4USJOH GJOUTUSJOH SFUVSO ʠʡ ҾY
G H I 2Ͳͷ͔ؔΒʮධՁʯ͢Δ
G H I ਖ਼֨ධՁଆ͔Βɻී௨ͷݴޠ $+43VCZ+BWBʜ
G H I ඇਖ਼֨ධՁ֎ଆ͔ΒɻԆධՁ )BTLFMM*0ʜ
ߴ֊ؔ
MFUH *OU4USJOH TUSJOH HBʠIFMMPʠ B ʮؔʯΛड͚औΔؔ )BTLFMM
H GO \ʠIFMMPʠ GO ^ ʮؔʯΛड͚औΔؔ 3VCZ
DPOTUH GO \SFUVSOʠIFMMPʠ GO ^ ʮؔʯΛड͚औΔؔ +BWB4DSJQU
ʮؔHʯͷҾGOʹʮؔGʯΛ༩͑Δ SFUVSOYUP4USJOH SFUVSOʠIFMMPʠ GO GJOUTUSJOH H JOUTUSJOH TUSJOH lIFMMPz
SFUVSO ҾGO
ड͚औͬͨʮؔʯGOΛͬͯTUSJOHΛฦ͢ H JOUTUSJOH TUSJOH SFUVSOʠIFMMPʠ SFUVSOYUP4USJOH GOJOUTUSJOH lIFMMPz SFUVSO
ҾY SFUVSOYUP4USJOH GOJOUTUSJOH
Ϋϩʔδϟ
MFUB MFUIaYY B पғͷʮڥʯΛऔΓࠐΜͩʮؔʯ )BTLFMM
B I Y \Y B^ पғͷʮڥʯΛऔΓࠐΜͩʮؔʯ 3VCZ
DPOTUB DPOTUI Y \SFUVSOY B^ पғͷʮڥʯΛऔΓࠐΜͩʮؔʯ +BWB4DSJQU
ʮؔIʯʮBʯͱ͍͏ڥΛ͍֮͑ͯΔ SFUVSOY IJOUJOU B B ڥΛऔΓࠐΉ
ʮؔʯ͕ʮঢ়ଶʯΛ͍࣋ͬͯΔͱݴ͑Δ SFUVSOY IJOUJOU B SFUVSO
Ϋϩʔδϟͱ ߴ֊ؔ
MFUJ*OU *OU4USJOH JYaZTIPX Y Z ҾΛऔΓࠐΜͩʮΫϩʔδϟʯΛ࡞ͬͯฦ͢ʮؔʯ )BTLFMM Ϋϩʔδϟ
J Y \ Z \ Y Z UP@T^ ^
ҾΛऔΓࠐΜͩʮΫϩʔδϟʯΛ࡞ͬͯฦ͢ʮؔʯ 3VCZ Ϋϩʔδϟ
DPOTUJ Y \ SFUVSO Z \ SFUVSO Y Z UP4USJOH
^ ^ ҾΛऔΓࠐΜͩʮΫϩʔδϟʯΛ࡞ͬͯฦ͢ʮؔʯ +BWB4DSJQU Ϋϩʔδϟ
ड͚औͬͨҾΛऔΓࠐΜͩʮΫϩʔδϟʯΛฦ͢ JJOUJOUTUSJOH SFUVSO JOUTUSJOH SFUVSO Y ڥΛऔΓࠐΉ SFUVSO Z UP4USJOH
Y Y SFUVSO Z UP4USJOH ҾY JOUTUSJOH
ؔ߹
GɾH Y G H Y ̎ͭͷؔG HΛॱ൪ʹద༻͢Δ߹ؔGɾHΛੜ͢Δ͜ͱ
MFUGaYY MFUHaYTIPXY MFUHGaYHGY ؔHGҾYΛGʹద༻ͨ݁͠ՌΛHʹద༻ͯ͠ฦ͢ )BTLFMM
G Y \Y ^ H Y \YUP@T^ HG Y \H
G Y ^ ؔHGҾYΛGʹద༻ͨ݁͠ՌΛHʹద༻ͯ͠ฦ͢ 3VCZ
DPOTUG Y \SFUVSOY ^ DPOTUH Y \SFUVSOYUP4USJOH ^ DPOTUHG Y
\SFUVSOH G Y ^ ؔHGҾYΛGʹద༻ͨ݁͠ՌΛHʹద༻ͯ͠ฦ͢ +BWB4DSJQU
߹ؔHGؔGͱHΛͭʮΫϩʔδϟʯ SFUVSO HGJOUTUSJOH SFUVSOY GJOUJOU SFUVSOYUP4USJOH HJOUTUSJOH SFUVSOY
GJOUJOU SFUVSOYUP4USJOH HJOUTUSJOH
߹ؔHGؔGͱHΛͭʮΫϩʔδϟʯ SFUVSO HGJOUTUSJOH SFUVSOY GJOUJOU SFUVSOYUP4USJOH HJOUTUSJOH SFUVSO
ʠʡ
ؔ߹͢Δؔ
DPNQPTF G H GɾH ̎ͭͷؔG HΛҾʹ߹ؔHGΛฦ͢ʮؔʯ
CD BC BD MFUHGHG )BTLFMMʹΈࠐΈͰ ͕ؔ͋Δ
)BTLFMM
EFGDPNQPTF H G Y \H G Y ^
FOE 3VCZͰҾH G͔ΒMBNCEBΛੜͯ͠ฦ͢ 3VCZ
DMBTT1SPD EFGDPNQPTF G Y \TFMG G Y ^
FOE BMJBT@NFUIPE DPNQPTF FOE 1SPDΫϥεͷΠϯελϯεϝιουʹ͢Δͷ͕ࣗવ 3VCZ
G Y \Y ^ H Y \YUP@T^ HDPNQPTF G
HG 1SPDΫϥεͷΠϯελϯεϝιουʹ͢Δͷ͕ࣗવ 3VCZ
DPOTUDPNQPTF H G \ SFUVSO Y \SFUVSOH G Y ^
^ +BWB4DSJQUͰҾH G͔ΒGVODUJPOΛੜͯ͠ฦ͢ +BWB4DSJQU
'VODUJPOQSPUPUZQFDPNQPTF GVODUJPO G \ SFUVSO Y \SFUVSOUIJT G Y ^
^ 'VODUJPOʹDPNQPTFΛఆٛ͢Δํ͕ࣗવ +BWB4DSJQU
ؔ W T ΦϒδΣΫτ
Φ ϒδΣ Ϋ τ ؔ ม
ʹ ೖͰ͖ Δ ม ʹ ೖͰ͖ Δ
Φ ϒδΣ Ϋ τ ؔ ؔ
ͷҾ ʹ ͤ Δ ؔ ͷҾ ʹ ͤ Δ
Φ ϒδΣ Ϋ τ ؔ ঢ় ଶ
Λ࣋ ͭ ϝϯό ʔ ม ঢ় ଶ Λ࣋ ͭ Ϋϩʔ δ ϟ
Φ ϒδΣ Ϋ τ ؔ ؔ
Ͱੜ ͯ͠ Γ ʹ Ͱ͖Δ ؔ Ͱੜ ͯ͠ Γ ʹ Ͱ͖Δ
Φ ϒδΣ Ϋ τ ؔ Έ
߹Θ ͤΔ͜ ͱ ͕Ͱ͖ Δ EF M FH BU F D PN Q PTJ UJP O Έ ߹Θ ͤΔ͜ ͱ ͕Ͱ͖ Δ ؔ ߹
ؔ͜Θ͘ͳ͍ ͜Θ͘ͳ͍
͔͜͜Β ͕࣌ؒ༨ͬͨΒ
ؔ߹ͷ ॱং
I H G Y YΛGʹͨ݁͠ՌΛɺHʹͯ͠ಘͨ݁ՌΛɺIʹ͢
I H G Y ӈ͔Βࠨॲཧ͕ྲྀΕ͍ͯ͘
IɾHɾG Y ߹ؔIɾHɾGӈ͔Βద༻͞Ε͍ͯ͘
GH Y H G Y ߹ͷॱংΛٯʹͯ͠߹͢Δ Λߟ͑Δ GɾH Y
G H Y
Ͱ߹͢Δͱɺॲཧ͕ࠨ͔ΒӈʹྲྀΕΔ I H G Y GHI Y
JNQPSU$POUSPM$BUFHPSZ $BUFHPSZDBUDBUBCDBUCDDBUBD )BTLFMMͰ$POUSPM$BUFHPSZʹ ͕͋Δ )BTLFMM
DMBTT1SPD EFG H Y \H TFMG Y ^
FOE FOE 3VCZͰ1SPDͷԋࢉࢠ Λॻ͖͑Δ 3VCZ
'VODUJPOQSPUPUZQFBOE5IFO GVODUJPO G \ SFUVSO Y \SFUVSOG UIJT Y ^
^ 'VODUJPOʹBOE5IFOͳͲ࡞ΕͲ͏ʹ͔ +BWB4DSJQU
ؔ߹ͷॱংΛม͑Δͱ ࠨ͔ΒӈॲཧͷྲྀΕΛ දݱ͢Δ͜ͱ͕Ͱ͖Δ ຊਓͳͷͰࠨ͔ΒಡΈ͍ͨ
ؔ͜Θ͘ͳ͍ ͜Θ͘ͳ͍
ؔద༻͢Δ ؔ
ؔద༻ࠨ͔Βӈʹྲྀ͍ͨ͠ GHI Y
] ؔద༻͢Δʮؔʯ Y]GG Y
Y͕ࠨ͔ΒӈʹG H IΛ௨ͬͯྲྀΕ͍ͯ͘ Y] GHI
] B BC C B]GGB தஔԋࢉࢠ ] ӈลͷؔʹࠨลͷΛ͢ )BTLFMM
DMBTT0CKFDU EFGʛʼ G G TFMG FOE FOE 3VCZͰશ֯
ʛʼ ͰͲ͏ʹ͔ʜ 3VCZ
0CKFDUQSPUPUZQFSFWBQQMZ GVODUJPO G \SFUVSOG UIJT ^ 0CKFDUQSPUPUZQFԚછ +BWB4DSJQU
ؔద༻͢ΔؔͰ Ҿ͕ࠨ͔ΒӈྲྀΕΔ༷Λ දݱ͢Δ͜ͱ͕Ͱ͖Δ ຊਓͳͷͰࠨ͔ΒಡΈ͍ͨ
6OJYͷQJQF &MJYJSͷ]ͳͲ Ͱ͋Μ·Γ͜͏͍͏ॻ͖ํ͠ͳ͍͚Ͳʜ
ؔ͜Θ͘ͳ͍ ͜Θ͘ͳ͍
ؔ߹ͷ จ຺
EFGDPNQPTF G Y \TFMG G Y ^ FOE
ؔ߹ͷ࣮Ͱʜ 3VCZ
EFG G Y \TFMG G Y
^ FOE G Y ͷ݁ՌΛഒʹͯ͠ΈΔ 3VCZ
G Y \Y ^ H Y \Y ^ I Y
\YUP@T^ IHG ʠʡ ߹͞ΕͨؔͷؒͰҾ͕ഒʹ 3VCZ
߹͞ΕͨؔͷؒͰҾ͕ഒʹ Y GJOUJOU Y HJOUJOU YUP@T IJOUTUSJOH
ʠʡ
EFG G Y \ SFTG Y SFTOJM
OJMTFMG SFT ^ FOE G Y ͕OJMͳΒɺ߹͞ΕͨؔΛݺͣʹऴྃ͢Δ 3VCZ
G Y \<OJM Y >TBNQMF^ H Y \<OJM Y >TBNQMF^
I Y \YUP@T^ IHG OJMPSʠʡ G HͷͲͪΒ͔͕OJMΛฦ͢ͱશମͷ݁Ռ͕OJMʹͳΔ 3VCZ
߹͞ΕͨؔͷؒͰOJMνΣοΫ <OJM Y >TBNQMF GJOUJOU <OJM Y >TBNQMF HJOUJOU YUP@T
IJOUTUSJOH OJM OJM ʠʡ ऴྃ ऴྃ
ʮ݁Ռ͕ഒʹͳΔʯจ຺ ʮOJMͩͱதࢭ͢Δʯจ຺ ؔ߹ʹ༷ʑͳʮจ຺ʯΛ༩͑Δ͜ͱ͕Ͱ͖Δ
ʮঢ়ଶ͕มԽ͢Δʯจ຺ ʮೖग़ྗ͕ൃੜ͢Δʯจ຺ ʮඇಉظͰܭࢉ͢Δʯจ຺ ଞʹ͍Ζ͍Ζͳʮจ຺ʯ͕͋Δ
ؔ߹ΛநԽ͢Δͱ ੜ͞ΕΔؔʹ༷ʑͳ ੑ࣭Λ༩͑Δ͜ͱ͕Ͱ͖Δ ͔ͯ͠͠Ϟφʜʜ ҧ͍·͢
ؔ͜Θ͘ͳ͍ ͜Θ͘ͳ͍
ྫ ؔ߹Ͱ 'J[[#V[[
DMBTT1SPD EFGPS G Y \ SFTTFMG Y
SFTOJM G Y SFT ^ FOE FOE ࣗʹYΛద༻ͨ݁͠Ռ͕OJMͳΒɺ߹͞ΕͨؔΛݺͿ 3VCZ
GJ[[ Y \Y GJ[[OJM^ CV[[ Y \Y CV[[OJM^ GJ[[CV[[ Y
\ YY GJ[[CV[[OJM^ JE Y \YUP@T^ GJ[[ CV[[ GJ[[CV[[ͱࣈΛग़ྗ͢ΔؔΛ༻ҙ 3VCZ
NBQ GJ[[CV[[PSGJ[[PSCV[[PSJE ֤ؔΛPSͰ߹ͯ͠NBQ͢ΕGJ[[CV[[Ͱ͖Δ 3VCZ
ͦͷଞͷ τϐοΫ
wŋࢀরಁա wŋΧϦʔԽ wŋ෦ద༻ wŋ࠶ؼ wŋΈࠐΈؔ wŋσʔλߏ ϞϊΠυͱ͔ ͜ͷ͋ͨΓͷػձ͕͋ͬͨΒ
ؔ͜Θ͘ͳ͍ ͜Θ͘ͳ͍