# [PDF] Apprendre à programmer facilement avec le langage Fortran | Cours informatique

## Texte intégral

(1)
(2)

! ! ! " # \$ %

(3)

&'( &)*+()*(,-+( .( /( .0/1,()2)01*123+3*0)*4015+&*6)2&7( .(*3)*251/230)*+& )02&230) *138&)2( 9

2012/( :13(*2() !" !(*20-+3'&2035( +( /&5&/2;5(∆.<*3')( 9

.&)*+(*3)*251/230)*&1,03)*1) (*4&/( 0-+3'&2035( .&)*+(*.0))<(*.(*(7(,4+(*(7&/2(,()21) (*4&/( +(*(745(**30)*4+&/<(*()25( /50/=(2*>? .<*3')()2.(*4&5&,;25(* 01.(*04230)*@&/1+2&23@*

( 40+6/043<&<2<</5324&5 A .( +% /0+( 14<53(15( .% )'<)3(15*.( &5*(3++(" 413* &))02<(2()53/=34&5 A 0+&6A

(4)

&'( ( (*2)< () ! .&)*+(*+&-05&2035(*.( A (*2+( 45(,3(5 +&)'&'( <80+1<.( 450'5&,,&230)A 0-B(/23@<2&32.( 5(,4+&/(5+(*+&)'&'(*2504 450/=(*.( +&,&/=3)( (2.( /0)/(8035.(*450'5&,,(*4052&-+(*. 1)( ,&/=3)( C 1)( &125(A 4&5235 .( /(22( 8(5*30) 51.3,()2&35( .1 +&)'&'(" 1)( 45(,3;5( )05,&+3*&230) (*2*0523( () ! 9 A +1*3(15* &,<+305&230)* 0)2 /0).132" 83)'22503*&)*&45;**&)&3**&)/(" C+&8(5*30) )05,&+3*<( &/21(++( .1 +&)'&'( 9 A &*<*15+(*/0)/(42*.( +&450'5&,,&230) *251/215<("

(*2,1)3.( +(**()23(+.(**251/215(*.( 450'5&,,&230) (2*&23*@&32 +( *01/3* .( 5()2&-3+32< .(* 3)8(*23**(,()2* 3)@05,&23:1(* .(* +&-05&2035(* (2 ()25(453*(*A

( (*2+( +&)'&'( 4&5(7/(++()/( .( +&450'5&,,&230) )1,<53:1(A 0)

)0, 45083()2.( D EA 4<5&230))(+.(413*45;*. 1)

:1&52.( *3;/+(" )( *06(F4&*<20))<*:13+*03225;*5<4&).1.&)*+(*.0,&3)(*.( +&5(/=(5/=( (2.( +3).1*253(A

( +&)'&'( *132+(* <80+1230)* .(* ,&2<53(+* 3)@05,&23:1(* .( 4+1* () 4+1* 413**&)2*A @3) .( 5().5( +( +&)'&'( 4+1* 4(5@05,&)2" 1) /0)*05231, ()25( /0)*251/2(15*.( ,&2<53(+(2.<8(+044(15*.( +0'3/3(+*&<2</5<<&@3) .( .<@3)351)( )018(++( )05,( 9 !#A (*4(/2&)2+&)05,( " /(22( )05,( 45(). () /0,42( .(*3)*251/230)**144+<,()2&35(**4</3@3:1(*C+&450'5&,,&230) 0-B(2A

(*21) +&)'&'( /0,43+<A ) /0.( (7</12&-+( 4(12G25( /0,40*<.( 1) 014+1*3(15*@3/=3(5* A

### ()%*)\$ (" ++

0154018035</535( 1) /0.( :1&25( <2&4(**0)2)</(**&35(*9 , %''()

(22( <2&4( 4(5,(2.( '<)<5(51) @3/=3(5*015/(A 015/(+& 0) 123+3*( 1) .(* <.32(15*.3*40)3-+(**15+( *6*2;,( .( .<8(+044(,()2A 01*1)37+%<.32(154+(3)( 4&'( *2&).&5. (*2 " ,&3**0) 123+3*&230) (*2/0,4+(7( (2+&-0))( /0))&3*&)/( .( *(*/0,,&).(*)</(**32( 1)( 123+3*&230) /015&)2(A 052=(15(1*(,()2" 3+(73*2( 4+1*3(15* <.32(15* )(22(,()2 4+1* /0)8383&17 *01* ()8350))(,()2

H<:138&+()2 .( I I *15 JA +* *0)2 *4</3@3:1(* &1 ,&2<53(+ .( .<8(+044(,()2(2)01*)( +(*/32(50)*4&*3/3A

-, (+\$'. '()

(22( <2&4( /0)*3*2( C8<53@3(5:1( +( *015/( (*2/055(/2(,()2</532/(*2C.35( :13+ 5(*4(/2( +(*5;'+(*.( *6)2&7( (2.( '5&,,&35( .1 +&)'&'(A ( 5<*1+2&2.( /(22( <2&4( (*2+&/5<&230) . 1) @3/=3(5-3)&35( 9 @3/=3(50-B(2A =&:1( @3/=3(5*015/( . 1) 450'5&,,( 4(12G25( /0,43+<*<4&5<,()2A

, %''()% .' )

(22( <2&4( /0)*3*2( C&**0/3(5201*+(*@3/=3(5*0-B(2H&44&52()&)2*032&1*6*2;,(" *032C+123+3*&2(15J@05,&)2+()*(,-+( .1450'5&,,(A )( <.3230) .( +3() /5<( 1) @3/=3(5-3)&35( 9 @3/=3(5(7</12&-+(A G,( *3+( 450'5&,,( (*2/0,40*<. 1) *(1+ @3/=3(50-B(2" /(22( <2&4( (*20-+3'&2035(A

(5)

&'( 015+&)/(51) 450'5&,,( " 3+@&12:1( +( @3/=3(5(7</12&-+( (73*2(" .0)/ :1( +(* .(17 <2&4(* 45</<.()2(* *( *03()2.<501+<(* /055(/2(,()2H*&)* (55(15*JA &*6)2&7( . (7</1230) . 1) 450'5&,,( .3@@;5( *138&)2+( *6*2;,(A

(* @3/=3(5* /5<<* C +& @3) /=&/1)( .( .(* 04<5&230)* 4052()21)( (72()*30) *2&).&5.A )( (72()*30) (*2*4</3@3<( 4&51)( 014+1*3(15*+(225(**<4&5<(*.1)0, .1@3/=3(5+13,G,( 4&51) 403)2A 138&)2+( *6*2;,( .%(74+032&230)" /(*(72()*30)* 4(18()2.3@@<5(5A

### ()

#, 1*!*. !2 +')*!*. !

)( .3@@<5()/3( )1++(,()2 +(* ,&B1*/1+(* (2 +(* ,3)1*/1+(*A )( 3)*251/230) 4(12G25( </532( 3).3@@<5(,,()2() ,3)1*/1+(*01() ,&B1*/1+(*A &)* 1) ,G,( *015/(" 1)( 8&53&-+( 4(123).3@@<5(,,()2*</535( () ,3)1*/1+(*01() ,&B1*/1+(*A (1+( K+052=0'5&4=(K.3@@<5()/3( .(178&53&-+(*A

0, !-.) !

(*-+&)/*H01(*4&/(*J*0)2.(*/&5&/2;5(*:13)( B01()2&1/1) 5L+( (2:134(18()2 G25( &B012<*H/055(/2(,()2JC80+0)2<.&)*1)( +3')( 4015() 5().5( +&+(/215( 4+1* &3*<(A

3, ( + %*) .'")

)( +3')( (*2.383*<( () 2503*/=&,4*A +(*23,4<5&23@.( 5(*4(/2(5/( @05,&2&153*:1( .( '<)<5(5.(*(55(15*.( /0,43+&230)A +**( .</0,40*()2.( +& @&M0) *138&)2(9

=&,4<23:1(22( 9 =3@@5(*()25( +(*/0+0))(* (2

=&,4*132( 9 ) /&5&/2;5( :1(+/0):1( () /0+0))( +(* 3)*251/230)*:13*13850)2*(50)23)2(545<2<(*4&5+( /0,43+&2(15/0,,( <2&)2+&*132( .(*3)*251/230)* .( +&+3')( 45</<.()2( =&,43)*251/230)*9 )*251/230)*()25( +(*/0+0))(* (2 4, (++ ) ' ! .*! *) \$ (" ++ ! (++ ) &2 \$.*! '. ! .'!'-. \$ % * %() \$( -. 2 % \$ -. 2 5 '. 6 + ') )'2 A 3() :1( 2012/0,,()2&35( *032 *1-B(/23@" 3+(*2838(,()2/0)*(3++< .( /0,,()2(5 &-0).&,,()2*(* 45045(* 450'5&,,(*A

0153)250.135( 1)( +3')( .( /0,,()2&35( H.0)/)0) /0,43+<(J" 3+@&124+&/(5+( /&5&/2;5( C+&/0+0))( A

+ @&12 )02(5 :11)( +3')( /0,4+;2(,()2 83.( 4(12 &3.(5 C +& +3*3-3+32< .1 450'5&,,(" ,&3*+( /0,43+&2(158&B1*:1C+&/0+0))( 4015*&4(5/(8035:1( /(22( +3')( (*23)123+(A 015&//50N25( +&5&43.32<.( /0,43+&230) &12&)24+&/(5+( /&5&/2;5( () 45(,3;5( /0+0))( .( 2012( +3')( 83.(A ) )( 4(5.5&53() () +3*3-3+32<A 7, / +\$. 8\$

01*.0))0)*3/31) (7(,4+( 264( .( 450'5&,,( .&)*+(:1(+2012(*+(*5;'+(* 45</<.()2(* *0)2&44+3:1<(*A +/0,,()/( 4&5 .(17 +3')(* .( /0,,()2&35(* 4(5,(22&)2.( /0))&N25( +&)1,<502&230) .(*/0+0))(*H4&..3)'J(2.0)/.( 8<53@3(5 +&/0)/05.&)/( ()25( +(*/=&,4*(2+</53215( .1/054*.1450'5&,,(A

C23456789012345678901234567890123456789012345678901234567890123456789012 C======================================================================== C Exemple de programme type : calcul d'un sinus

C======================================================================== C PROGRAM TYPE C Declarations INTEGER I, IDEUX REAL AMPLITUDE(10),T & FREQUENCE, pi C Initialisations FREQUENCE = 50. PI = 3.1416 IDEUX = 0 C Corps du programme DO I=1,10 ideux = IDEUX+2 T = FLOAT(IDEUX)

AMPLITUDE(I) = SIN (2. * PI*FREQUENCE*T) WRITE(*,100)IDEUX

ENDDO

100 FORMAT(1X,I2) END

(6)

&'( ) 450'5&,,( (*2/0)*2321<. 1) *(1+450'5&,,( 453)/34&+(2. 1) ()*(,-+( .( @0)/230)*(2\$01*01*450'5&,,(*5<4&523**151) 014+1*3(15*@3/=3(5* *015/(A =&:1( 450'5&,,( 01*01*450'5&,,( .0N2G25( 2(5,3)<4&5+3)*251/230)

A

### \$9 -

(*.37/=3@@5(*.</3,&17 (* +(225(*.( +&+4=&-(2 (*/&5&/2;5(**4</3&179 *4&/( 01-+&)/ '&+32< : 01-+( /02( ; 3,4+( /02( 6,-0+(*&532=,<23:1(* < = == &5&)2=;*(* >, 35'1+( 2 03)2 01-+( 403)2 ?

### " ++ '

#, (! .&

+*/0)*2321()2+( 80/&-1+&35( .1 +&)'&'( (2*(58()2C.<@3)35+(*.</+&5&230)*.( 8&53&-+(*(2+(*3)*251/230)*9 " " " " "

"AAAAA

0, \$& )% !

+*/0)*2321()2+(*)0,**6,-0+3:1(*:1( /=03*32+( 450'5&,,(154015.<*3')(5+(* )0,*.( 8&53&-+(*(2.( 450/<.15(*H*01*450'5&,,(*01@0)/230)*JA +*.038()2 5(*4(/2(52503*5;'+(*9

/0)2()351)3:1(,()2.(*/&5&/2;5(*&+4=&)1,<53:1(* )( B&,&3*/0,,()/(54&51) /&5&/2;5( )1,<53:1( G25( /0,40*<*. &1,&73,1, /&5&/2;5(*A

(22( .(5)3;5( 5;'+( (*2.<@3)3( /0,,( 2(++( .&)*+&)05,( A 5" 3+*&8;5( :1( 45&23:1(,()2201*+(*/0,43+&2(15*0)2+&5'(,()2&1',()2(5/( ,&73,1,A 3+0) 8(3++( C</535( 1) 450'5&,,( 4052&-+(" 3+@&123,4<5&238(,()25(*4(/2(5/(22( 5;'+(A

3, &\$ * !

+*/0)*2321()2+&40)/21&230) .1+&)'&'(9 (*4&/(

35'1+( " &5()2=;*(* HOOOOJ +&*=(* \$OOOO\$

### * !

( *0)2+(*&/230)*:13*(7(5/()2*15+(*04<5&).(*A +**0)2.( :1&25( 264(*9 1)32&35(" &532=,<23:1(*" 5(+&230))(+*" +0'3:1(*A +1*3(15* 04<5&2(15* .( )&215( .3@@<5()2( 4(18()2G25( 123+3*<*.&)*1)( ,G,( (745(**30)A +@&12.0)//0))&N25( +&4530532<.( /=&/1)A (+13.( 4+1*@&3-+( 4530532<(*2(@@(/21<() 45(,3(5A

(4().&)2" *3+0) )( 5(23()24&*+(*4530532<*.( /=&:1( 04<5&2(15" 3+(*2201B015* 40**3-+( .( 4+&/(5 /=&:1( 04<5&230) <+<,()2&35( ()25( 4&5()2=;*(*A </53215( '&')( -(&1/014() +3*3-3+32<A

#, \$& * *)' ' ? . 55 '()

(*2+04<5&2(15. &@@(/2&230) . 1)( 8&53&-+( :13(*2+( *3')( <'&+HPJA +*&44+3:1( .( +&.5032( 8(5*+&'&1/=(A &)*+(7(,4+( *138&)20) &@@(/2( +&8&+(15 C+& 8&53&-+( 9 P

(7)

&'( 740)()23&230) == H 530532< J 1+234+3/&230) = H 530532< J 383*30) H 530532< J ..3230) < H 530532< J 01*25&/230) H 530532< J 3, \$& * ! . '()) .!

+**0)2201*.( 4530532< A +**0)21)( *132( .( .(17 /&5&/2;5(**2&).&5. 4+&/<* ()25( .(17403)2**&)*(*4&/( 9

0Q(5 =() AAA 253/2(,()24+1*4(232:1( AAA 5(&2(5 =()AAA 253/2(,()24+1* '5&). :1(AAA 0Q(505 :1&+AAA +1*4(23201<'&+:1(AAA

5(&2(505 :1&+AAA +1*'5&). 01<'&+:1(AAA

A R1&+AAA '&+CAAA

0) :1&+AAA 0) <'&+CAAA

4, \$& * !.("'@* ! A A <'&230) +0'3:1( H 530532< J A A 2+0'3:1( H 530532< J A A 1+0'3:1( H 530532< J

### # 8\$ !% %())& !

5(/0))&N2/3):264(*.( .0))<(*9 #, ) ' ) ()23(5(*21) *3')( HS01 J*1383. 1)( /=&N)( .( .3'32*.</3,&17 (7(,4+(*9 " S !# " 0, & . ) 5<(+4(12&8035.(17@05,(*. </53215( 9

+& @05,( .( -&*( 9 1) *3')( *1383. 1)( /=&N)( .( .3'32* .</3,&17 /0)2()&)21) 403)2*<4&5&)2+&4&523( ()23;5( .( +&4&523( .</3,&+( A

(7(,4+(*9 A " A " S A ! " A##

+&@05,( (740)()23(++( 9 /(*2+&@05,( .( -&*( *1383( .( +&+(225( 413* . 1) *3')( (2. 1)( *132( .( .</3,&17(7453,&)2+(740*&)2.</3,&+A

(7(,4+(*9 A # " #A # " S A ! " A

3, (+\$. /

012/0,4+(7( *( 5(45<*()2( *01* +& @05,( . 1) /014+( .( 5<(+* 5(45<*()2&)2 5(*4(/238(,()2+(*4&523(*5<(++( (23,&'3)&35(A &*6)2&7( (*2()25( 4&5()2=;*(* *<4&5<*4&51)( 835'1+(A =&/1) 4(12G25( </532*138&)21)( .(*.(17 @05,(*.( 5<(+*A

(7(,4+(*9 HA" A J" H#A" AJ" HA " A J

4, 9 B) % !

)( /=&N)( .( /&5&/2;5(*(*2.<+3,32<( 4&5.(**3,4+(*/L2(*H&40*2504=(*J

(8)

&'( + (73*2( 1) 04<5&2(15 4&523/1+3(5 /0)/(5)&)2 +(* /=&N)(* .( /&5&/2;5(*A (2 04<5&2(155<&+3*( +&@0)/230) .( /0)/&2<)&230) .( .(17/=&N)(*A &*6)2&7( .( /(2 04<5&2(15(*29 \$\$ H.01-+( *+&*=J

(7(,4+( .( /0)/&2<)&230) 9 P \$\$

( 5<*1+2&20-2()1*(5& P

7, ("'@*

(1+(,()2 .(17 8&+(15* *0)240**3-+(*A 0*3230))<(* ()25( .(17 403)2* *&)* (*4&/(" /(*8&+(15**0)29

A A 85&3

A A @&17

### ()!% %())& !

) " +( 264( . 1)( .0))<( (*2.<@3)3(74+3/32(,()24&51)( 3)*251/230) .( .</+&5&230)A & .</+&5&230) 4(12*( @&35( () *3,4+( H4&5.<@&12J01 .01-+( 45</3*30) 4015+(*()23(5*" +(*5<(+*(2+(*/0,4+(7(*A &45</3*30) .0))( +&2&3++( ,<,035( H() 0/2(2*J:1( 45(). +&8&53&-+(A ( 2&-+(&1/3.(**01*.0))()2+&+3*2( .(*3)*251/230)*.( .</+&5&230) .1 4015/=&:1( 264( .( .0))<(*A

8\$ % %())& ! )! * '()!%

%& . '() '+\$. \$ & '!'() (*-. \$ & '!'()

)23(5 T T <(+ T T 0,4+(7( T T =&N)( .( /&5&/2;5(* T+() +() (*2+( )-5( .( /&5&/2;5(*.( +& /=&N)( 0'3:1( (7(,4+( 9 " T " " T

)( .(*4&523/1+&532<*.1 " (*2:13+(73*2( .(*.</+&5&230)*.( .0))<(* 3,4+3/32(**138&)2+( )0, .(*8&53&-+(*A 3)*3" *3&1/1)( *4</3@3/&230) /0)25&35( ) (*25()/0)25<( " +(*.</+&5&230)*3,4+3/32(**0)29

2012( 8&53&-+( /0,,()M&)24&5 " U" V" " " (*2.( 264( 2012( 8&53&-+( /0,,()M&)24&51)( &125( +(225( (*2.( 264(

015<832(5+(*450-+;,(*.( .</+&5&230)" )01*/0)*(3++0)*.( )0,,(5+(*()23(5* () /0,,()M&)24&5+(*+(225(* "U"V" " 01 A

(4().&)2" 3+(*240**3-+( .( ,0.3@3(5 /(22( 5;'+(W4015 /( @&35(" 0) 123+3*( +3)*251/230) 4+&/<( 0-+3'&2035(,()2() 2G2( .( 450'5&,,( 01 *01* 450'5&,,(A

6)2&7( 9 ∆ 264(∆ >/ > / ?", (2 9 /&5&/2;5(*&+4=&-<23:1(*

*3')3@3( +()*(,-+( .(*/&5&/2;5(*&+4=&-<23:1(*/0,453*()25( / (2/

(7(,4+( 9 H J

H&=", 6J HFJ X

(*2503*+3')(**3')3@3()2:1( +(*8&53&-+(*.0)2+( )0, /0,,()/( 4&5+(*+(225(* " U" V 01 *0)2.( 264( ()23(5W/(++(*/0,,()M&)24&5X" *&1@+&8&53&-+(

:13(*21) 5<(+" *0)2.( 264( /0,4+(7(W+(*&125(**0)2.( 264( 5<(+A

0,,( +(7(,4+( /3.(**1*+( ,0)25(" +3)*251/230) ) (,4G/=( 4&*.( .</+&5(5() /+&351)( 8&53&-+(A

(9)

&'( ! (52&3)(*8(5*30)*.( 4(5,(22()2+1*&'( .( +3)*251/230)

:13&))1+( 2012(*+(*.<@3)3230)*4&5.<@&12A 012(*+(*8&53&-+(*.038()2" .&)*/( /&*" G25( .</+&5<(*(74+3/32(,()2A (22( .(5)3;5( 3)*251/230) ) <2&)24&* .&)*+& )05,( " 3+@&12*( ,<@3(5.( *0) 1*&'( *3+0) .<*35( 1) 450'5&,,( 4052&-+(A

### ' !

)( 8&53&-+( 2&-+(&101,&253/( (*2&**0/3<( C1) (*4&/( /0)23'Y( .( +&,<,035( :13/0)23()2+(*8&+(15*.(*<+<,()2*.12&-+(&1A &01+(*.3,()*30)*. 1) 2&-+(&1 .038()2@3'15(5+05*.( +&.</+&5&230) .( +&8&53&-+( 2&-+(&1 *01*+&@05,( . 1)( /0)*2&)2( )0) *3')<( ()25( 4&5()2=;*(*A ) 2&-+(&1 40**;.( &1 ,&73,1, .3,()*30)*A &//<*C1) <+<,()2*( @&324&5+3)2(5,<.3&35( . 3).3/(*&**0/3<*&1 )0, .( +&8&53&-+( 2&-+(&1A \$ +' C . * %* -. * ! 6.')%' #(2+& .(5)3;5( (*2C+3).3/( /055(*40).&)2C*&2&3++(A

+(73*2( .(17@05,(*.( .</+&5&230) .( 2&-+(&179

#, )! * '()

3)*251/230) 4(5,(2.( .<@3)35+&2&3++( . 1) 2&-+(&1.0)2+( 264( &<2< .</+&5<45</<.(,,()2.( @&M0) (74+3/32( 013,4+3/32(A

6)2&7( 9 ∆ )0,8&53&-+( >2&3++( >"2&3++( AAA"2&3++( ?,

0, &5')''()% . %'+ )!'().( !% . %& . '()

+(*2<'&+(,()240**3-+( .( .<@3)35+&2&3++( . 1) 2&-+(&101. 1)( ,&253/(" +05*:1( +&.</+&5&230) .( +&8&53&-+( (*204<5<(A (/3*(7453,( 4&51)( /0)*2&)2( ()23;5( )0) *3')<( :1( +0) 4+&/( ()25( 4&5()2=;*(*.35(/2(,()2C+&*132( .1 )0, .( +& 8&53&-+( /0)/(5)<(A

(7(,4+( 9

H##J" H##" J H#J" H##" #" J

&)*/(2(7(,4+(" (*21) 2&-+(&1 . ()23(5*.( .3,()*30) ,&73,&+( ##" (*21)( ,&253/( .( .3,()*30)* ##7 " (*21) 2&-+(&1 .( 5<(+* .( .3,()*30) ,&7 #" (2 (*21)( ,&253/( .( /0,4+(7(*.( .3,()*30)* ##7 #7 A

### !

)( /=&N)( /0,40*<( . &1,&73,1, /&5&/2;5(**( .</+&5( .( +&@&M0) *138&)2( 9

T+()

01 T+()

3 ) (*24&**4</3@3<( (*2.</+&5<( /0,,( 1) *(1+/&5&/2;5(A (7(,4+( 9

T # " H#J

T " T #

&)*/(2(7(,4+(" (*21)( 8&53&-+( /&5&/2;5( 1)3:1(" " (2 *0)2.(*/=&N)(*.( 5(*4(/238(,()2 #" (2 #/&5&/2;5(*" (*21) 2&-+(&1.(

#/=&N)(*.( #/&5&/2;5(*/=&/1)(A

020)*:1( +0) 4(12&//<.(5C) 3,4052( :1(++( *01*/=&N)( . 1)( /=&N)( /0,4+;2( () 45</3*&)2+&40*3230) .&)*+&/=&N)( .(*45(,3(5(2.(5)3(5/&5&/2;5(*.( +&*01* /=&N)( 9

H9 J.<*3')( +& *01*/=&N)( .( .1 3;,( &1 3;,( /&5&/2;5( 3)/+1*A

### !

#, ()! ) !

)( 014+1*3(15*/0)*2&)2(*123+3*<(*.&)*1) 450'5&,,( 011) *01*450'5&,,( .038()2 G25( .<@3)3(* &8&)2 01 &45<* *138&)2 +%1*&'( +(* .</+&5&230)* 4&5

+3)*251/230) 9

(10)

&'( #

(7(,4+( 9 T

T

H P A ! " P A ! ! ! #J

0, )''.'! '()% C '-. !

012( 3)323&+3*&230) .( 8&53&-+( .032 G25( 45</<.<( .( *& .</+&5&230)" *032 3,4+3/32(,()2*032(74+3/32(,()2A ++( 4(12*( @&35( 4&51)( &@@(/2&230) H*3')( <'&+J" .&)*+( /054*.1 450'5&,,( ,&3*4(12<'&+(,()2G25( (@@(/21<( .&)*+&4&523( .</+&5&230) 9

6)2&7( 9 ∆ )0,O8&53&-+( 8&+(15O3)323&+(

(7(,4+( 9 )-403)2

5&60)" 2(,4*HJ 2(,4*\$ A " #A " A\$ 5&60)")-403)2\$ #A" ##\$

&)*/(2(7(,4+(" +&8&53&-+( (*23)323&+3*<( C #A (2+( )0,-5( .( 403)2* ! "C ##A ( 2&-+(&1"#!\$.( .3,()*30) (*23)323&+3*</0,,( *1329

2(,4*HJP A 2(,4*HJP #A 2(,4*HJP A

### !

) " 2012(*+(*8&53&-+(*.</+&5<(*.&)*1)( 1)32<.( 450'5&,,( *0)2 .(*C '-. !.( . !C/(22( 1)32<A (*C '-. !".(- . !*0)24+&/<(*.&)*1)( F0)( ,<,035( &//(**3-+( 4&5/=&:1( 1)32< :13+123+3*( () 4+&M&)2+3)*251/230)

&45<*+( -+0/.( .</+&5&230)A

6)2&7( 9 ∆ )0,O-+0/8&5>"8&5"AAA?

( .<@3)321)( F0)( ,<,035( 123+3*<( 4&5&++;+(,()24&54+1*3(15*1)32<* .( 450'5&,,(A 015/(+& 3+.032G25( 5<4<2< .&)* /=&:1( *01*450'5&,,( 01 @0)/230) :13 123+3*( +(* 8&53&-+(* .<@3)3(* /0,,( &44&52()&)2 C /(22( F0)( ,<,035(A +4(126&80354+1*3(15* .&)*1) 450'5&,,(A

exemple : C Programme principal REAL X(100) CHARACTER*20 CAR INTEGER MAT(100,100) COMMON/TOTO/X,MAT,CAR . . Appel à sous-programme . . END C Sous-programme REAL ALPHA(100) CHARACTER*20 CAR INTEGER RES(100,100) COMMON/TOTO/ALPHA,RES,CAR . . . RETURN END &)*/(2(7(,4+(" +( .( )0, (*25<4<2<.&)*/=&:1( 1)32<.( 450'5&,,( 123+3*&)2+(*8&53&-+(*:13+( /0)23())()2A +@&125(,&5:1(5:1( +(* )0,*.( 8&53&-+(*.1 )( *0)24&*+(*,G,(*.&)*+( 450'5&,,( 453)/34&+ (2.&)* +( *01*450'5&,,(A +(*23,4<5&23@ /(4().&)2:1( +05.5( . </53215( .( +&+3*2( .(*8&53&-+(**032.( .</+&5&230) (2.( .3,()*30) 3.()23:1(*A

3)*3+( /0)2()1 .( +& 8&53&-+( .1 450'5&,,( 453)/34&+(*2/(+13.( +& 8&53&-+( .&)*+( *01*450'5&,,(A ( ,G,( +( /0)2()1.( /055(*40). &1 /0)2()1.( %& A

(11)

&'(

### !% () F.

( 5L+( . 1)( -01/+( (*23.()23:1( C/(+13.( () 01() A ++( *(52C'<5(5.(*/&+/1+*5<4<2323@*A &*6)2&7( 4(12G25( .( .(17@05,(*9

∆ (2: ∆ 3/42 : 3.(-1223@3)>"34&*? ∆ 3/42: 3.(-12"3@3)>"34&*? )*251/230)* 01 )*251/230)* (2: !"9 /0,42(15.( -01/+( ' ("9 45(,3;5( 8&+(15:1( 45().5& !" ) 9 .(5)3;5( 8&+(15:1( 45().5& !"

! \$9 4&* . 3)/5<,()2&230) ()25( ' ("(2 ) A 3 ! \$ ) (*24&* *4</3@3<+&8&+(15.( +3)/5<,()24&5.<@&12(*2

"*9 <23:1(22( 403)2&)2*151)( 3)*251/230) :13@(5,( +&-01/+(A (* 4&5&,;25(* "!" ' ("" ) (2 ! \$ .038()2G25(

.</+&5<*/0,,( A &5=&-321.(" +(*)0,*.(*8&53&-+(*.( /0,42(15.( -01/+( !"/0,,()/()24&5 " U01VA

&8&+(15.( ! \$4(12G25( )<'&238(A &-01/+( (@@(/21( &+05*1)( .</5<,()2&230) .1/0,42(15.( -01/+( (23+@&12:1( ' ("*032*14<53(15C ) A

+)( @&12B&,&3*,0.3@3(5+( /0,42(15.( -01/+( !"C+3)2<53(15.( +&-01/+(H-+0/ \$"( " \$JA (1+( +3)*251/230) .032';5(5/( /0,42(15A

3' ("(*2<'&+C ) " +( -+0/ \$"( " \$(*2(7</12<1)( *(1+( @03*A

&)*+( /&*0Z ! \$(*240*323@" *3 ' ("(*2*14<53(15C ) " +( -+0/ \$"( " \$ ) (*24&*(7</12<A ( /&* ! \$ )<'&23@*(7453,( .( @&M0) .1&+(A

exemple : INTEGER ICPT,DEB,FIN

REAL PRODAB(10,10), A(10,10) ,B(10,10) REAL Y(100),OMEGA,T

PARAMETER (OMEGA=314.16) C

C Calcul d'un produit matriciel PRODAB= A*B C

DO I=1,10

DO J =1,10

PRODAB(I,J) = 0. DO K = 1,10

PRODAB(I,J) = PRODAB(I,J) + A(I,k)*B(K,J) ENDDO

ENDDO ENDDO

C

C Calcul d'un sinus C T = 0. DEB = 100 FIN = 1 DO 10 ICPT=DEB,FIN, -2 Y(ICPT) = SIN(OMEGA*T) T = T+1. 10 CONTINUE END

3+) 6 & 4&*1) )0,-5( ()23(5.( 4&*. 3)/5<,()2&230) ()25( ' ("(2 ) " +& .(5)3;5( 8&+(15.1/0,42(15.( -01/+( !".&)*+&-01/+( (*2+&.(5)3;5( 8&+(15 3)@<53(15( C ) A +&*0523( .( +&-01/+(" +&8&+(15.( !"(*2+&45(,3;5( 8&+(15 3,,<.3&2(,()2*14<53(15( C ) A ( .(5)3(5/&*(*23++1*25<4&5+(7(,4+( *138&)29

P " #" 9

9

&)*+&-01/+(" +&45(,3;5( 8&+(15.( (*2 (2*&.(5)3;5( 8&+(15(*2 !A 45<*+&-01/+(" +&8&+(15.( (*2.( A

)( -01/+( I 4(5,(2.( 5<&+3*(51) ()*(,-+( . 3)*251/230)*2&)2:11)( /(52&3)( /0).3230) (*285&3(A 0,,( 45</<.(,,()2" 3+(73*2( .(17 *6)2&7(* 40**3-+(*9

(12)

&'( ∆ (2: ∆ G >/0).3230), G ∆ >/0).3230), )*251/230)* 01 )*251/230)* (2: "*9 <23:1(22( 403)2&)2*151)( 3)*251/230) :13@(5,( +&-01/+( ' " 9 (745(**30) +0'3:1(

3 ' " (*2@&1**( &8&)2.( 5()25(5.&)*+&-01/+(" +( -+0/ \$"( " \$)( *(5& 4&*(7</12<A

exemple : LOGICAL LTEST

INTEGER I1,I2,A(100),B(100) REAL T,TFIN,OMEGA,ALPHA(100) PARAMETER (TFIN=10.,OMEGA = 314.) C

C Calcul d'un sinus C T = 0. I1 = 1 DOWHILE(T.LT.TFIN) ALPHA(I1) = SIN(OMEGA*T) T = T+0.5 I1 = I1+1 ENDDO C

C .Permutation de deux tableaux C I1 = 1 I2 = 100 LTEST = .TRUE. DO 20 WHILE(LTEST) A(I1) = B(I2) I1 = I1 + 1 I2 = I2 - 1 IF(I1.GT.100.)LTEST=.FALSE. 20 CONTINUE END

### ()

012/0,,( () 01 () " +(*/0)25L+(*/0).3230))(+**0)25<&+3*<*4&5 +3)*251/230) A +(73*2( 4+1*3(15**6)2&7(*.( /0)25L+(*/0).3230))(+*9 >/0).3230), )*251/230)O*3,4+( ' " 9 (745(**30) +0'3:1(

&)*/( /&*" 1)( *(1+( 3)*251/230) (*2(@@(/21<( *3 ' " (*285&3A >/0).3230),

)*251/230)*

&)*/( /&*" *3 ' " (*285&3&+05*+()*(,-+( .1-+0/ \$"( " \$(*2(@@(/21<A >/0).3230)J

)*251/230)*O# )*251/230)*O

&)*/( /&*" *3 ' " (*285&3&+05*+()*(,-+( .1 -+0/ \$"( " \$+, (*2 (@@(/21<*3)0) /(*2+( -+0/ \$"( " + :13(*2(7</12<A >/0).3230)O#, )*251/230)*O# >/0).3230)O , )*251/230)*O >/0).3230)O , )*251/230)*O A A A > )*251/230)*O ?

&)*/( /&*" *3 ' " +,(*285&3&+05**(1++( -+0/ \$"( " \$+,(*2(7</12<" *3)0) *3 ' " + (*285&3&+05**(1++( -+0/ \$"( " \$+ (*2(7</12<" (2&3)*3 .( *132(AAAA 3&1/1)( /0).3230) ) (*28<53@3<( &+05**(1+.( -+0/ \$"( " \$+ (*2 (7</12<A &.(5)3;5( 3)*251/230) (*2@&/1+2&238( .&)*/(22( *6)2&7(A

(13)

&'(

exemple : LOGICAL LTEST

REAL X,Y,Z,PI PARAMETER (PI=3.1416) . . X = -1. IF(LTEST) X= 0. . . IF(X.LT.0.)THEN Y = PI/2. X = +1. ENDIF . . IF(X.EQ.0.)THEN Y = PI ELSE Y = 0. ENDIF . . IF(X.LT.0.)THEN Y = PI/4. ELSEIF(X.GT.0.)THEN Y = PI/2. ELSE Y = PI ENDIF

(2(7(,4+( *&)**3')3@3/&230) ,0)25( 2012(*+(**6)2&7(*40**3-+(*.( +3)*251/230) A

### \$ .

) 450'5&,,( /0,,()/( 201B015*4&5+( 450'5&,,( 453)/34&+A ( )0, H@&/1+2&23@ ,&3* /0)*(3++<J .1 450'5&,,( (*2 .0))< &45<* +3)*251/230)

A +*( 2(5,3)( 201B015*4&5+3)*251/230) A #, )! * '() 6)2&7( 9 ∆ )0,4 #! 9 )0, .1450'5&,,( () 5(*4(/2&)2+(*,G,(*5;'+(*:1( 4015 +(*)0,*.( 8&53&-+(* (22( 3)*251/230) 4(5,(2.( )0,,(5+( 450'5&,,( 453)/34&+A 0, )! * '() (22( 3)*251/230) 4(5,(2. 3)@05,(5 +( /0,43+&2(15 *15 +& @3) . 1)( 1)32< .( 450'5&,,(A ( :13*1321)( 3)*251/230) /0)/(5)(" *3+6&+3(1" 1)( &125( 1)32< .( 450'5&,,( :13(*2@05/<,()21) *01*450'5&,,( 011)( @0)/230)A

3, )! * '()

3)*251/230) 3).3:1( +&55G2. (7</1230) .1450'5&,,(A ++( 4(12G25( 4+&/<( ) 3,4052( 0Z.&)*+( 450'5&,,(" *138&)2+&+0'3:1( .1450-+;,(A

(14)

&'( )0,44

H+0/&+(*&1450'5&,,( 453)/34&+J H+0/&+(*&1450'5&,,( 453)/34&+J

U(1. 3)*251/230)*.1 50'5&,,( 453)/34&+

### (*!\$ (" ++ !

) *01*450'5&,,( (*21)( 1)32< .( 450'5&,,( /0,,()M&)24&5+3)*251/230) (2 *( 2(5,3)&)2 201B015* 4&5 +3)*251/230) 3).3:1&)2 &1 /0,43+&2(151)( @3) . 1)32<A 1**3" 1)( *(1+( 3)*251/230) .032@3'15(5.&)*1) *01*450'5&,,(A

#, )! * '() E

6)2&7( 9 E ∆ )0,*4>>&5' >2&5' "AAA?,?

#\$! 9 )0, :1( +0) .<*35( .0))(5&1*01*450'5&,,(A +.032 5(*4(/2(5+(*,G,(*5;'+(*:1( +(*)0,*.( 8&53&-+( - 9 &5'1,()2*014&5&,;25(*4&**<*.&)*+( *01*450'5&,,(

:13*0)2.(* )0,* .( 8&53&-+( *3,4+( 01 2&-+(&1 :13 .038()25(*4(/2(5+(*5;'+(*45</<.(,,()2.<@3)3(* (*&5'1,()2*4(18()2B01(52503*5L+(*9

&5'1,()2. ()25<( 9 4&5&,;25( 4&**<:13)( *0)24&*,0.3@3<.&)*+( *01*450'5&,,(

&5'1,()2.( *0523( 9 4&5&,;25( 3)323&+3*< (2 /&+/1+< H01 ,0.3@3<J C +3)2<53(15.1*01*450'5&,,(

&5'1,()2. ()25<(\$*0523( 9 4&5&,;25( 4&**< (2 ,0.3@3< .&)* +( *01* 450'5&,,(

9 +(*.</+&5&230)*(2.3,()*30) .(*&5'1,()2*C+3)2<53(15.1*01* 450'5&,,( .038()2G25( 3.()23:1(*.&)*+%1)32<. &44(+A

0, )! * '()

(22( 3)*251/230) .032&44&5&N25( &1,03)*1)( @03*.&)*2012*01*450'5&,,( 01 @0)/230)A 0) 5L+( (*2.( 5(*2321(5+( /0)25L+( C+&1)32<.( 450'5&,,( &44(+&)2( H450'5&,,( 453)/34&+" *01*450'5&,,( 01@0)/230)JA

3, \$\$ .% !(*!\$ (" ++ ? ')! * '()

&44(+C 1) *01*450'5&,,( *( @&32C +3)2<53(15)( ) 3,4052( :1(++( 1)32< .( 450'5&,,(A

6)2&7( 9 ∆ )0,*4>>&5' >"&5' "AAA?,? #\$! 9 )0, .1*01*450'5&,,( &44(+<

- 9 &5'1,()2*014&5&,;25(*4&**<*.&)*+( *01*450'5&,,( :13*0)2.(*)0,*.( 8&53&-+( H*3,4+( 01 2&-+(&1J" .(* /0)*2&)2(*01.(*(745(**30)*&532=,<23:1(*A

) *01*450'5&,,( 4(12<83.(,,()2() &44(+(51) &125(" ,&3*)( 4(12B&,&3* *&44(+(5+13,G,(A &)0230) .( 5</15*3832<)%(73*2( 4&*() A 05* .( *0) (7</1230)" +3)*251/230) &4015(@@(2.( .0))(5+( /0)25L+( &1*01* 450'5&,,(A

(15)

&'( E )0,*4>&5'2 AAA, H+0/&+(*&1*01*450'5&,,(J H+0/&+(*&1*01*450'5&,,(J U(1. 3)*251/230)*.1 01*450'5&,,( &8(/<8()21(++(,()2.(*3)*251/230)* 7, / +\$.

(7(,4+( /3.(**01* (@@(/21( +( /&+/1+ .( +& 25&/( . 1)( ,&253/( .( .3,()*30)* ##7 ##(2.0))( +( 5<*1+2&2.&)* A SUBROUTINE TRACE(RES,MAT) REAL RES,MAT(100,100) C RES = 0. DO I=1,100 DO J = 1,100

IF(I.EQ.J)RES = RES +MAT(I,J) ENDDO ENDDO RETURN END

### ()!

)( @0)/230) (*2&)&+0'1( C 1) *01*450'5&,,(A ) .3*23)'1( .(17 264(*.( @0)/230)*A (++(*:13/055(*40).()2C.(*@05,1+(*,&2=<,&23:1(*/015&)2(*2(++(* :1( *3)1*" 5&/3)( /&5<(" +0' )<4(53()"AAA ++(**0)23)/+1*(*.&)*+( +&)'&'( +13 ,G,( (24502( .(* )0,* )05,&+3*<W/(*2C .35( :1( :1(+:1( *032+( *6*2;,( . (74+032&230) *15+(:1(+0) *( 25018(" +&,G,( @0)/230) ,&2=<,&23:1( &+( ,G,( )0,A ++(**0)22012(*4+&/<(*.&)*1)( -3-+302=;:1( .( 450'5&,,(A (*@0)/230)* *0)2.32(*K3)253)*;:1(*KA

( 450'5&,,(15 4(12(*23,(5 :1( /(22( -3-+302=;:1( (*23)*1@@3*&)2( (2:13+ &3,(5&32 &8035 +& ,G,( *014+(**( . 123+3*&230) 4015 .(* @0)/230)* 4+1* 4(5*0))(++(*A (*@0)/230)**0)2.32(*K123+3*&2(15*KA

! " # #

#, )! * '()

6)2&7( 9 >.</+&5&230)? ∆ )0,@)/>&5' >2&5' "AAA?,

#) 9 )0, :1( +0) .<*35( .0))(5 C +& @0)/230)A + .032 5(*4(/2(5+(*,G,(*5;'+(*:1( +(*)0,*.( 8&53&-+( (2 .032 G25( <8()21(++(,()2 45</<.< .( *& .</+&5&230) (74+3/32( .( 264(

- 9 &5'1,()2*014&5&,;25(*4&**<*.&)*+( *01*450'5&,,( :13 *0)2 .(* )0,* .( 8&53&-+( 2(+* :1( .<@3)3* 45</<.(,,()2

&55&44052C+3)*251/230) " (++( 45<*()2( .(17.3@@<5()/(*9 3+.0326&8035&1,03)*1) &5'1,()2.( 4&**&'( () ()25<(

+( )0, .( +&@0)/230) .<*3')&)2<'&+(,()2+( 5<*1+2&2" 3+(*2)</(**&35( .( +13&2253-1(51) 264(A (22( .</+&5&230) *( @&32*032.( @&M0) 3,4+3/32( H() @0)/230) .( +& 45(,3;5( +(225( .1 )0,J*032.( @&M0) (74+3/32( /0,,( 3).3:1<.&)*+&*6)2&7( /3.(**1*A

0, )! * '()

&*6)2&7( (2*0) 123+3*&230) *0)2+(*,G,(*:1( .&)*+( /&*.(**01*450'5&,,(*A 3, \$\$ .6*) 5() '()

&44(+ . 1)( @0)/230) *( @&32 () .<*3')&)2 *0) )0, .&)* ) 3,4052( :1(++( (745(**30) &532=,<23:1(A

(16)

&'( (*2+&8&53&-+( :1345().5&+&8&+(15.( +&@0)/230) &8(/+(*4&5&,;25(*4&**<*A 3+&@0)/230) #) 40**;.( 1) 264( .( .</+&5&230) &125( :1( /(+13.</01+&)2.(* 5;'+(*3,4+3/32(*" 3+(*2&-*0+1,()2)</(**&35( .( ,()230))(5/(+13/3.&)*+(* .</+&5&230)*.( 264( .( 2012( 1)32<.( 450'5&,,( &44(+&)2(A

4, * * "&)& .

)0,@/H&5'" AAAJ

H+0/&+(*C+&@0)/230)J H+0/&+(*C+&@0)/230)J

U(1. 3)*251/230)*.( +&@0)/230) /&+/1+&)2+&8&+(15.( #) &8(/<8()21(++(,()2.(*3)*251/230)*

7, / +\$.

(7(,4+( /3.(**01*(@@(/21( +( /&+/1+ [H@&/2053(+.( J INTEGER FUNCTION FACTORIEL(N)

INTEGER N C FACTORIEL = 1 DO I=1,N FACTORIEL = FACTORIEL * I ENDDO RETURN END ! " \$% (*)0,*.(*@0)/230)*3)253)*;:1(**0)2.(*)0,**6,-0+3:1(*(2() '<)<5&+9 +( )0, . 1)( @0)/230) ()23;5( /0,,()/( 4&51) +( )0, . 1)( @0)/230) .01-+( 45</3*30) /0,,()/( 4&51) +( )0, . 1)( @0)/230) /0,4+(7( /0,,()/( 4&51) +( )0, . 1)( @0)/230) /0,4+(7( .01-+( 45</3*30) /0,,()/( 4&5

(15 123+3*&230) (*2 3.()23:1( C /(++( .(* @0)/230)* K123+3*&2(15K .</532( &1 4&5&'5&4=( 45</<.()2A 01* .0))0)* /3.(**01* 1)( +3*2( )0) (7=&1*238( .(* @0)/230)*+(*4+1*1*1(++(*A 015/=&/1)(" )01**4</3@30)**0) )0, (2*0) 264( (2 /(+13.( *0) 01*(*4&5&,;25(*A (+ + 9&+ '@* (+ % \$\$ . - \$ 8\$ % ! \$ + ! 8\$ % . 5() '() &/3)( /&55<( R 3)1* 0*3)1* 0' <4;53() 0'.</3,&+ # &)'()2( &+(15&-*0+1( 0)8(5*30)* .( 264(

(17)

&'( 5&)*@<5(5 .(* 3)@05,&230)* . 1) 4<534=<53:1( H</5&)" /0)*0+(" 3,453,&)2(" @3/=3(5"AAAJ8(5*+&,&/=3)( 013)8(5*(,()2(*21)( &/230) . ()25<(\$*0523(A

### ()

#, )'&.("'@*

) 20124<534=<53:1( (*25(4<5<4&51) ()23(5W0) 4&5+( &+05*. 1)32< +0'3:1(A

(*)1,<50*. 1)32<+0'3:1( /+&83(5(2</5&) .<4().()2.1*6*2;,( *15+(:1(+0) .<8(+044(A <)<5&+(,()2" +1)32<+0'3:1( 5(45<*()2&)2+( /+&83(5(*2 " (2/(++( .( +</5&) (*2 4&5.<@&12A

&3*" *3+0) )( 8(124&*5(2()35/(*)1,<50*" 0) 4(124+&/(5+( /&5&/2;5( ." HTJ 40151)( 04<5&230) . ()25<(\$*0523( *15/(*.(171)32<*+0'3:1(*A 3)*3" 1) 05.5( .( +(/215( &1/+&83(5&15&+&*6)2&7( 9

HT"(2:J

( ,G,( 1) 05.5( . </53215( C+</5&) *(5&.( +&@05,( 9 G HT"(2:J"U"V

0Z "*5(45<*()2( 1)( <23:1(22( 5(+&238( &1@05,&2:1( )01*8(550)*4+1*2&5.A 01*123+3*(50)*+(*)1,<50*. 1)32< 4015+( /+&83(5(2 4015+</5&) .&)*+& *132( .1.0/1,()2A

0152012&125( 264( .( 4<534=<53:1(" +123+3*&2(15&+&40**3-3+32<.( /=03*35+13 ,G,( +( )1,<50. 1)32<+0'3:1( :13+*01=&32( +13&2253-1(5A

0, ) "'! + ) 2 5( +

(*()25<(*\$*0523(*)( *0)2B&,&3*5<&+3*<(*0/2(24&50/2(2" ,&3*4&5-+0/*. 0/2(2* :1( +0) )0,,( ()5('3*25(,()2A 012()5('3*25(,()2*( 2(5,3)( 201B015*4&5+(* .(17 /&5&/2;5(* \ ] H &553&'( (215) 9 5(2015.1 /15*(15() .<-12.( +3')(J(2\ ] H 3)( ((. 9 4&**&'( C+&+3')(JA

( /0)2()1. 1) ()5('3*25(,()2(*2.<@3)34&51) @05,&2. </53215( 01.( +(/215(A

### ()!% ) & !( '

0155<&+3*(51)( 04<5&230) . ()25<(\$*0523(" 3+@&12*4</3@3(59 +&+3*2( .(*8&53&-+(*/0)/(5)<(*4&5+04<5&230) +1)32<+0'3:1( /055(*40).&)2&14<534=<53:1( /=03*3

+&+0/&+3*&230) .(*3)@05,&230)*.&)*+()5('3*25(,()2/0)/(5)<(2 +& @&M0) .( +(* .</0.(5/( :13(*2+( 5L+( .( +3)*251/230) )0) (7</12&-+( A

&*6)2&7( '<)<5&+( (*29

01 G

H+1"(2:J +3*28

(2: H+3*2*J

(9 )1,<50 . 1)32< +0'3:1( 5(4<5&)2+( 4<534=<53:1(A ( 4(12 G25( 1)( /0)*2&)2( 011)( 8&53&-+(

"*9 <23:1(22( 4(5,(22&)2.( @&35( +( +3() ()25( +3)*251/230) .( +(/215( 01. </53215( (2+( @05,&2&**0/3<

\$" 9 +3*2( .(*8&53&-+(*H*3,4+(*" 3).3/<(*01 2&-+(&17J:1( +0) .<*35( +35( 01</535(A ( )0, . 1) 2&-+(&1(*2<:138&+()2C+& +3*2( .( 201**(*<+<,()2*

\$"\$9 +3*2( .(**4</3@3/&230)*<+<,()2&35(*&**0/3<(*&17<+<,()2* .( \$"A 01*8(550)*4&5+&*132( /0,,()2*0)2.<@3)3(* /(**4</3@3/&230)*A

#, )! * '()

012( 3)*251/230) ) (*28&+&-+( :1( .&)*1)( *(1+( 1)32<.( 450'5&,,(A ++( .0320-+3'&2035(,()2G25( 45</<.<( 4&51)( <23:1(22(A ++( 4(12G25( 4+&/<( C ) 3,4052( :1(+().5032.( +1)32< .( 450'5&,,( 401581 :1( /( *032&45<* +(* .</+&5&230)*(2&8&)2+3)*251/230) A )( ,G,( 3)*251/230) 4(12G25( 123+3*<( 4&54+1*3(15*05.5(* 01I A

012(* +(* *4</3@3/&230)* C +%3)2<53(15. 1)( 3)*251/230) .038()2G25( *<4&5<(*4&5.(*835'1+(*A

(18)

&'( 0, )! * '()

;*+(7</1230) .( +05.5( *15+1)32<+0'3:1( /055(*40).&)2&1 /+&83(5+( 450'5&,,( &22().5&:1( +123+3*&2(15&328&+3.<*0) /=0374&5&4413*15+&201/=( ^ _ :13'<);5( 1) \ ] (2\ ]A

3+05.5( (*2(@@(/21<*151)( 1)32<+0'3:1( .( 264( @3/=3(5+()5('3*25(,()2 *(5&+1-+0/4&5-+0/*138&)2+( @05,&2*4</3@3<" B1*:1C/( :1( +(*/&5&/2;5(*\ ] (2\ ] *03()2&22(3)2*A

(7(,4+( 9 H" ##J "

## HAAAA"AAAJ

/(/3*3')3@3( 9 +35( +(*8&53&-+(* (2 *15+1)32<+0'3:1( H+( /+&83(54&5 .<@&12J" *138&)2+(**4</3@3/&230)*@015)3(*.&)*+3)*251/230) . <23:1(22( ##:13)( 4(12G25( 1)( &125( 3)*251/230) :11) A

3, )! * '()G

15+1)32< +0'3:1( </5&)" +05.5( I (@@(/21( +</53215( .( +()5('3*25(,()2 .(,&).<(24&**( C+&+3')(A </5&) 3)2(545;2( +(*.(17/&5&/2;5(**4</3&17\ ] (2\ ]A

+() 8&.( ,G,( 40151)( 1)32<+0'3:1( .( 264( @3/=3(5A (7(,4+( 9 I H " ###J " "X

### HAAA"AAA"AAJ

/(/3*3')3@3( 9 </535( .&)*+1)32<+0'3:1( H:13.0N2G25( /055(/2(,()2 3)323&+3*<(J+(*8&53&-+(* " (2 *138&)2+(**4</3@3/&230)*@015)3(*.&)*+( @05,&2 . <23:1(22( ###A HJ 9 9 I H" #J # HAAAAAAAAAJ /(/3*3')3@3( 9 </535( *15+1)32<+0'3:1( H</5&)J+(*:1&25( <+<,()2*.1 2&-+(&1 A ( .(5)3(5(7(,4+( 4(12<'&+(,()2*</535( 9 I H" J HJ" HJ" HJ" HJ HAA"AA"AA"AAJ

+(*23,4052&)2.( )02(5 .05(* (2.<BC :1( +(* *4</3@3/&230)* .( @05,&2.(* <23:1(22(* #(2 )( *(50)24&*+(*,G,(*A

### ()!% 5( +

01* &++0)* .</535(" .&)* /( 4&5&'5&4=(" 1) /(52&3) )0,-5( .( *4</3@3/&230)* 4(5,(22&)2.( /0)*2321(5+&+3*2( \$"\$&44&5&3**&)2.&)*+3)*251/230) A

015.</535( +&*6)2&7( .( /(**4</3@3/&230)*)01*123+3*(50)*+&)02&230) *138&)2( 9 / .<*3')(5&+( )0,-5( 202&+.( /&5&/2;5(*H/&5&/2;5(*K403)2K(2K*3')(K /0,453*J123+3*<*40155(45<*()2(51)( 8&53&-+( *15+1)32<+0'3:1(A

' .<*3')(5&H4015.(*5<(+*1)3:1(,()2J+( )0,-5( .( .</3,&+(*&45<*+( 403)2

5(45<*()2(5& 1) @&/2(15.( 5<4<23230) @&/1+2&23@:13.(85& G25( 1)( /0)*2&)2( *&)**3')(A

! & ' %

( *0)2/(++(*:134(5,(22()2.( +35( 01. </535( .(*8&53&-+(*.( 264( )1,<53:1( 9 ()23(5"5<(+*3,4+( 01.01-+( 45</3*30)A

#, \$& '5' '()

++( (*2123+3*<( 4015.(*8&53&-+(*.( 264( ()23(5A 6)2&7( 9 >)? Q

(7(,4+( 9 V " "

9

(19)

&'( ! ### H " " J

3+123+3*&2(152&4( 9 ∆∆ # " +(*8&+(15*5(*4(/238(* " (2 # *(50)2 &2253-1<(*&178&53&-+(*0 " (2 A

3+5()25( 9∆∆ ∆ # " +(*8&+(15*.( V " (2 *(50)25(*4(/238(,()2 " (2 # A

0, \$& '5' '()

++( (*2123+3*<( 4015.(*8&53&-+(*.( 264( 5<(+*3,4+( 45</3*30)A 6)2&7( 9 >)? QA. +@&12.3@@<5()/3(53/3</53215( (2+(/215( 9 &J40151)( </53215( +( )0,-5( (*2</532*01*+&@05,( 9 `77777777777A77777 . \ ] Q \ ] ( *3')( S(*2*018()20,3*A (7(,4+( 9 X" " 9 P A P A XP A I H" #JX I H" J " H A " A#J # H A J

( 5<*1+2&2/0).135&C+&@@3/=&'( *138&)29 A

∆ ∆ A ∆ !A

020)*:1( +&*4</3@3/&230) . </53215( .(*8&53&-+(* (2 ) (*24&**1@@3*&)2( () )0,-5( .( /&5&/2;5(*A &)*/( /&*+</53215( (*2&550).3&1.(5)3(5.3'32. </53215( *14<53(15A

-J40151)( +(/215(9

*3+( 403)2(*245<*()2.&)*+& .0))<(" &+05*+& 8&+(15.( ' ) (*24&* 123+3*<(A 3)*3" +(*/&5&/2;5(* A +1*() A /0).135&-3() C " :13(*2/(++( :1( +0) 0-23().5&32<'&+(,()2() +3*&)2() A 01() A#A

*3+( 403)2) (*24&*45<*()2.&)*+& .0))<(" &+05*+& 8&+(15.( ' (*2 (@@(/238(,()2123+3*<(A 3)*3+(* /&5&/2;5(* +1*() A /0).1350)2C +& 8&+(15 " W 1*() A " +&8&+(150-2()1( *(5& "

(7(,4+( 9 " " 9 H" #J H" J " # H A J H A " A J

3+123+3*&2(152&4( .&)*1) 45(,3(52(,4* A 413*^ _ +&8&53&-+( &15&40158&+(15 " A 3+123+3*&2(155()25( ()*132( +&+3')( *138&)2( 9

A ∆ ∆ ##^ _

+(*8&53&-+(* (21 &150)240158&+(155(*4(/238( 9 " (2 "

. ! %() \$ &5& -. % H \$. *)\$(') % )!*) %())& % 8\$ & .

3, \$& '5' '()

++( (*2123+3*<( 4015.(*8&53&-+(*5<(++(**3,4+( 45</3*30) </532(*() )02&230) (740)()23(++(A

6)2&7( 9 >)? QA.

(20)

&'( # &J40151)( </53215( +( )0,-5( (*2</532*01*+&@05,( 9 `#A77777777777 `66 . \ ] Q \ ]

( *3')( S .( +& 4&523( .</3,&+( (*2*018()20,3*A ) 5(,&5:1( :1( / .032 @05/<,()2G25( *14<53(15C '23A ( 4508()&)2.(*/&5&/2;5(*` .( +& 4&523( .</3,&+(" #" +( 403)2" " ` .( +& 4&523( (740*&)2(2&1 ,03)* 1) /&5&/2;5( )1,<53:1( 4015+(740*&)2A 3/(22( /0).3230) ) (*24&*8<53@3<(" +( )0,-5( </532 53*:1( . G25( /0.<3)/055(/2(,()2*15+1)32<+0'3:1( (2.0)/3++3*3-+(A (7(,4+( 9 HJ 9 HJP A HJP A I H" J HJ" HJ H A " A J ( 5<*1+2&2. &@@3/=&'( *(5&&+05*9

#A S#∆ #A S# -J40151)( +(/215( +( )0,-5( (*2</532*01*+&@05,( 9 `777A77777777777 `66 . \ ] Q \ ]

123+3*&2(1540**;.( 1)( '5&).( +3-(52<40155<.3'(5+(*)0,-5(*A (**3')(*S H/(+13.( +&4&523( .</3,&+( (2/(+13.( +(740*&)2J4(18()2G25( 0,3*A

*3+( *6,-0+( (*245<*()2.&)*+( )0,-5(" 3+(*2-3() *a5453*() /0,42(A 3+( 403)2(*245<*()2.&)*+&4&523( .</3,&+(" 3+(*2/0)*3.<5<" *3)0)" 0) *1440*(

:13+6 &' .</3,&+(*A 3)*3" A S +1 () A 01 A /0).132C+&8&+(15 " W+( 403)2&6&)2<2<453*() /0,42( 3).<4().&,,()2.( +&8&+(15.( .A &5

/0)25( S +1 () !A /0).132C A *032 " W+1 () !A 0)

0-23().5&32 A *032 " A

*3+( *6,-0+( ) (*24&*45<*()2.&)*+( )0,-5(" +( @05,&2 QA. .(83()2 <:138&+()2C QA.A 3)*3 +1() A /0).132C " A

(7(,4+( 9 "

9

H" ##J "

## H A " A J

3+123+3*&2(152&4( (7&/2(,()29 A ! ^ _ +(*8&53&-+(* (2 &150)2+(*8&+(15*5(*4(/238(*9 " ! (2 "

4, \$& '5' '()

(22( *4</3@3/&230) (*2123+3*<( 4015.(*8&53&-+(*5<(++(*.01-+( 45</3*30) </532(* () )02&230) (740)()23(++(A

6)2&7( 9 >)? QA.

0) 5L+( (*23.()23:1( C+&*4</3@3/&230) QA." +( *6,-0+( (*25(,4+&/<4&54A ) 5(25018( (7&/2(,()2+(*,G,(*,</&)3*,(*:1( 4015+&*4</3@3/&230) A +@&12 )02(5:13+(*240**3-+( .( 25018(51) (740*&)2,&2<53&+3*< 4&51) .&)*1)( .0))<( +1( 4&5 1)( *4</3@3/&230) QA." *&)* :1( /(/3)( '<);5( 1)( (55(15 . (7</1230)A

! & ' ( ) %

( *0)2/(++(*:134(5,(22()2.( +35( 01. </535( .(*8&53&-+(*.( 264( /=&N)( .( /&5&/2;5(*A

#, \$& '5' '() (.. '9 6)2&7( 9 Q 2(72(

(21)

&'( 23+3*<( 1)3:1(,()2() </53215(" (++( 4(5,(2. 3)*<5(5+&*132( .(*/ /&5&/2;5(*.( "5" .&)*+1)32<+0'3:1( . </53215(A ( 2(72( *138&)2+( *6,-0+( .032/0)2()35 (7&/2(,()2/ /&5&/2;5(*A (/34(12G25( 1) 53*:1( 3,4052&)2. (55(15*A

01*45<@<50)*+&@05,1+&230) *138&)2( 9 2(72(

</532( .35(/2(,()2.&)*+3)*251/230) A (7(,4+( 9

P A

H∆ ∆ ∆ ∆ ∆ ∆ 9∆ " A J

( 5<*1+2&2. &@@3/=&'( *(5&9∆ ∆ ∆ ∆ ∆ ∆ 9∆ A 0, \$& '5' '()

6)2&7( 9 >)? Q

++( 4(5,(2.( +35( 01. </535( 1)( /=&N)( .( / /&5&/2;5(*A (7(,4+(*9

T #

P ∆ ∆ 9∆

I H" J

H #J <*1+2&2. &@@3/=&'( 9

∆ ∆ 9∆

" T 9

H" #J "

# H " J

3+123+3*&2(152&4( +&+3')( 9

∆ ^ _

(*8&53&-+(*1 (2 &150)24015 8&+(155(*4(/238( 9

(2 ∆

! ! & '

#, \$& '5' '()I

6)2&7( 9 )

++( (*2123+3*<( 4015&8&)/(5.( /&5&/2;5(*.&)*+1)32<+0'3:1( . ()25<( 01*0523(A

(7(,4+(*9 9 P P A I H" ##J" ## H " " " A J +( 5<*1+2&2. &@@3/=&'( *(5&9

∆ ∆ ∆ ∆ ∆ ∆∆ A

V" " 9

H" ##JV" " ## H " " " J 3+123+3*&2(152&4( +&+3')( 9

^ _

(*8&53&-+(*0" (2 &150)24015 8&+(155(*4(/238( 9

(2

+@&12)02(5:1( +05* . 1) 05.5( . </53215(" +( 45(,3(5/&5&/2;5( (*23)2(545<2< /0,,( 1) /&5&/2;5( .( /0)25L+( 4&5+1)32< +0'3:1(A +@&12.0)/ 4+&/(51)( *4</3@3/&230) .( 264( () .<-12.( +3*2( .( @05,&2. </53215(A

0, \$& '5' '() 6)2&7( 9 4 ++( (*2123+3*<( 4015*( 4+&/(5.35(/2(,()2C1)( 40*3230) .0))<( !A (7(,4+(*9 "V 9 P V P I H" ###J "V ### H " " J +( 5<*1+2&2. &@@3/=&'( *(5&9 ∆ ∆ ∆

V" 9

H" ##JV"

## H " " J

3+123+3*&2(152&4( +&+3')( 9

^ _

(* 8&53&-+(* 0 (2 &150)2 4015 8&+(155(*4(/238( 9

(2 3, \$& '5' '() > .!9,

(22)

&'( (22( *4</3@3/&230) 4(5,(2 .( *<4&5(5 .(17 ()5('3*25(,()2*A ++( '<);5( 1) \ ]\ ] () </53215( (2+321) \ ]\ ] () +(/215(A (7(,4+(*9 "V 9 P V P I H" ###J "V ### H " \$" J +( 5<*1+2&2. &@@3/=&'( *(5&9 ∆ ^ _ ^ _ V" 9 9 H" ##JV" ## H "\$"\$" J

123+3*&2(15 .(85& 2&4(5 .(17 ^ _ *1//(**3@*40155()25(5+& .(173;,( 8&+(15A

3, \$& '5' '()J> (.. , 6)2&7( 9 b

(22( *4</3@3/&230) 4(5,(2. &))1+(5() </53215(" +&'<)<5&230) . 1) \ ]\ ] () @3) . ()5('3*25(,()2A 125(,()2.32" (++( &15&4015(@@(2.( ,&3)2()35+( /15*(15() @3) .( +3')( </532(A ( *6,-0+( b *( 4+&/( '<)<5&+(,()2C+&@3) .( +&+3*2( \$"\$ . 1)( 3)*251/230) A

### ()!

* + , '

01*&80)*81:1( +05*:1( +0) &8&32-(*03) .( 4+1*3(15**4</3@3/&230)*3.()23:1(*" 0) 4018&32<832(5.( +(* 5<4<2(5" () 123+3*&)21) K@&/2(15.( 5<4<23230)E 4015 /(2&3)(*. ()25( (++(*A

3)*3+&*4</3@3/&230) (*2<:138&+()2( C " " ( ,G,(" 3+(*240*3-+( .( 5<4<2(51) '5014( .( *4</3@3/&230)*A

3)*3+&*4</3@3/&230) H " J (*2 <:138&+()2( C " " " " "

* - , '

01*&++0)*,()230))<3/3" +&@&M0) .( 45().5( () /0,42( .(*2&-+(&17C1)( 01 4+1*3(15*.3,()*30)*" &8(/1)( *(1+( *4</3@3/&230)A

U1*:13/3)01*&80)*,()230))<:11)( +3*2( \$" .( +3)*251/230) 01I

<2&32/0,40*<( .( 8&53&-+(**3,4+(*013).3/<(*A 01*'<)<5&+3*0)*+&)0230) .( +3*2( .( +&,&)3;5( *138&)2( 9

+3*2*P^8&53&-+(**3,4+(*" 8&53&-+(*3).3/<(*" H2&-+(&17H3J"3P."@>"4?J_ 9 3).3/( .( 4&5/015*.12&-+(&17

' 9 8&+(153)323&+( .( +3).3/( ) 9 8&+(15@3)&+( .( +3).3/(

! 9 4&*. 3)/5<,()2&230) ()25( .(178&+(15*. 3).3/( H*3+(*20,3* *&8&+(15(*2.( J

3)*3 H HVJ"VP " J (*2<:138&+()2C HJ" HJ" HJ

(2 H HUJ" HUJ"UP " " J (*2<:138&+()2C HJ" HJ" HJ" HJ" HJ" HJ (7(,4+(*9

&J H##J

H" ###J

### H A J

+@&1.5&2&4(51) ^ _ &45<*/=&:1( 8&+(153)250.132( *032 ##&1202&+A

-J H##J

H" ###J

## H# A J

&)*/( /&*" 3+@&1.5&2&4(5.378&+(15*.( 4&5+3')( &8&)2.( /0)@35,(54&51) ^ _A 3)'2+3')(**(50)2)</(**&35(*A ) 5(,&5:1( :1( +( @05,&2.( +(/215( (*25<(74+05<&120,&23:1(,()2C/=&:1( @03*:13+(*2<413*<A

(23)

&'(

/J H##J

I H" ## JH HJ" P " ##" J

## HH " A JJ

05.5(I 3).3:1( :11) <+<,()2.( *15:1&25( *(5&&@@3/=<A 0,42( 2()1.( +&5<(74+032&230) &120,&23:1(" +05.5( 3).3:1( :13+6 &15&/3): 8&+(15* *<4&5<(*4&51) -+&)/4&5+3')(

.J H " J

P "

I H" ## JH H"UJ"UP " J

## HH " A J

( 5<*1+2&20-2()1*(5&.1264( *138&)29

H" J H" J H" J H" J H" J

H" JA AAAAAA AAAAA AAAAA AAAA

9 9 9 9 9

H " J H " J H " J H " J H " J

( ,G,( 5<*1+2&2(*20-2()1&8(/1) ,G,( @05,&2" ,&3*1) 05.5(I .3@@<5()2 9

I H" ## JHH H"UJ"UP " J" P " J

(J H " J

I H" ## JH"H H"UJ"UP " J" P " J ## H " " H " A J

( 5<*1+2&20-2()1*(5&.1264( *138&)29

H" J H" J H" J H" J H" J

H" JA AAAAAA AAAAA AAAAA AAAA

9 9 9 9 9

H " J H " J H " J H " J H " J

) @3/=3(5(*21)( 1)32< +0'3:1( &1 ,G,( 2325( :1( +</5&) 01 +( /+&83(5A (* 04<5&230)* .( +(/215( 01 . </53215( *0)2.0)/ 3.()23:1(* C /(++(* .</532(* &1 4&5&'5&4=( 45</<.()2A

### !

) " 2012@3/=3(5(*2/5<<+05*.( *0) 018(5215(A ;**&/5<&230)" 3+@&12 *4</3@3(5*&*251/215( (2*0) &//<*A

, * *

) @3/=3(5 /5<< 4&5 1) 450'5&,,( 4(12 &8035 .(17 *251/215(* .3@@<5()2(*9

2(72( 01 9 2012 ()5('3*25(,()2 *(5& </532 *01*@05,( A &8&)2&'( (*2:1( +&202&+32<.1@3/=3(5*(5&+3*3-+( 4&5) 3,4052( :1(+ .3*40*323@. &@@3/=&'( .1*6*2;,( .( .<8(+044(,()29 <.32(15" +3*23)'" AAAA

-3)&35( 9 2012()5('3*25(,()2(*2/0.< () -3)&35(A +)( *(5& +3*3-+( 4&5 &1/1) 0123+. &@@3/=&'( .1*6*2;,(A &8&)2&'( .( /(22( *251/215( (*2 :1( +( @3/=3(5 *(5& @05/<,()2 4+1* 4(232 () 2&3++( :1( 4015 +& 45</<.()2(A

-, !

&//;*C1) @3/=3(5/055(*40). &1,0.( +(/215( 01. </53215( .(*()5('3*25(,()2* :13+/0)23()201/0)23().5&A (*.(17&//;*453)/34&17. 1) @3/=3(5*0)29

<:1()23(+9 4015&//<.(5C1) ()5('3*25(,()2 " 3+@&12&8035&//<.<&1 45</<.()2A &8&)2&'( (*2:1( +&'(*230) . &//;*.(*()5('3*25(,()2* (*2&120,&23:1(A

35(/29 +(*()5('3*25(,()2**0)25(4<5<*4&51) 3).3/(A 3)*30) 4(12 &//<.(5.35(/2(,()2C1) ()5('3*25(,()2.0))<A &8&)2&'( 4052( *15 +&5&43.32<. &//;*C1) ()5('3*25(,()2" ,&3*3+@&12.(8035'<5(5+(* 3).3/(*. ()5('3*25(,()2*A

(24)

&'( (22( 3)*251/230) 4(5,(2. &**0/3(51)( 1)32<+0'3:1( C1) @3/=3(5A ( 4+1*(++( 4(5,(2.( .<@3)35+( ,0.( . &//;* &1 @3/=3(5H*<:1()23(+" .35(/2J&3)*3:1( *& *251/215( H2&3++( (2 @05,&2 .(* ()5('3*25(,()2*" AAAJ (2 /(52&3)(* 3)@05,&230)* *4</3@3:1(*H(73*2()/(" (55(15. 018(5215(" 4502(/230) () </53215("AAAAJA

6)2&7( 9 >V I P8"AAAA,

(*4&5&,;25(*C 4&**(5.&)*1) 05.5( *0)2.<@3)3*4&51) ()*(,-+( .( ,02*/+<H0 6 4J.0)20) .0))( +&8&+(15 A ( 264( .( +&8&+(15 .<4(). .1 ,02/+<:13+13(*2&**0/3<(24(12G25( 1) ()23(5011)( /=&N)( .( /&5&/2;5(*A

01*)( .0))0)*3/3:11) )0,-5( ,3)3,&+A ) (@@(2" +&+3*2( .( +()*(,-+( .(* ,02*/+<*(5&322504+0)'1( C.0))(53/3A ++( *( 25018( () A K LG C 8\$ % C + @* ! )1,<50 . 1)32< +0'3:1( )23(5 )@<53(15C!! )0, .1 @3/=3(5 C 018535 =&N)( .( /&5&/2;5(* I 0)*2&)2( /=&N)( .( /&5&/2;5(* 5<&230) 0.3@3/&230)\$+(/215( . 1) @3/=3(5 R H.<@&12J 0)*2&)2( /=&N)( .( /&5&/2;5(* 0.( . &//<* <:1()23(+ 35(/2 H.<@&12J 0)*2&)2( /=&N)( .( /&5&/2;5(* 05,&22&'( .(* ()5('3*25(,()2 0)'1(15.(* ()5('3*25(,() 2* )23(5 ) 0/2(2* &-(+. (55(15 . 018(5215( 0)*2&)2( ()23;5( 23:1(22( .( *&12 *3 (55(15. 018(5215(

### ()

(22( 3)*251/230) 4(5,(2.( .3**0/3(51)( 1)32<+0'3:1( . 1) @3/=3(5A 125(,()2.32" (++( @(5,( +( @3/=3(5A ( ,G,( :1( " (++( 40**;.( 1)( *<53( .( 4&5&,;25(* :1( )01*)( +3*2(50)*4&*3/3A ( *(1+,02/+<0-+3'&2035( C.0))(5(*2 *1383 .1)1,<50. 1)32<+0'3:1( :1( +0) .<*35( @(5,(5A 6)2&7( 9 >V I P8"AAAA,

### 4 * & '* %M*)5'9'

(* 04<5&230)* .( +(/215( (2 .%</53215( .%1) @3/=3(5 *0)2 .(* 04<5&230)* .%()25<(\$*0523(A (*04<5&230)**0)25<&+3*<(*4&5+(*3)*251/230) (2I " (23+/0)83()2.( *( 5<@<5(5&1/=&4325( 45</<.()24015() /0))&N25( +%1*&'(A +@&12 ,&+'5<201245</3*(5:1( +%1)32<+0'3:1( :13(*2+( 45(,3(54&5&,;25( .( /(*.(17 3)*251/230)*.032/055(*40).5( C/(++( 123+*<( +05*.( +%018(5215( .1@3/=3(5A

### 7 / +\$.

,&'3)0)*:1( +%0) 8(13++( 5(45<*()2(5'5&4=3:1(,()24+1*3(15*4<530.(*.%1) *3)1*A 015/(+& )01*&++0)*/&+/1+(5+& 8&+(15.1 *3)1*C 3)2(58&++(*.( 2(,4*

(25)

&'( 5<'1+3(5*(2)01*&++0)*4+&/(5/(*8&+(15*.&)*1) @3/=3(5A ( @05,&2.%</53215( .1 @3/=3(5*(5& +( *138&)29 45(,3;5( 8&+(15)0,-5( .( 403)2* 202&+.1 @3/=3(5" (2 /=&:1( ()5('3*25(,()2/0)23().5&1) 45(,3(55<(+:13*(5&+%3)*2&)2.( /&+/1+" (21) *(/0). :13*(5&+&8&+(15.1*3)1*C/(23)*2&)2A ) 450'5&,,( '5&4=3:1( 40155& &3)*3+35( /( @3/=3(5*138&)2+( @05,&2.<@3)3/3.(**1*A

( 450'5&,,( 264( /055(*40).&)2C/( /&=3(5.(*/=&5'(**3,4+( &15&+%&++15( *138&)2( 9

C23456789012345678901234567890123456789012345678901234567890123456789012 C

C Calcul d'un sinus et mise en fichier du résultat. On calcule 20 points par

C période et on calcule au maximum NPMAX points C

PROGRAM CALCUL_SINUS C

C Declarations

INTEGER I,IDEUX,NPMAX

REAL FREQUENCE, AMPLITUDE,PI,PHI REAL T,TFIN,PAS

PARAMETER (PI = 3.1416, NPMAX=100))

REAL VALEUR(NPMAX),TEMPS(NPMAX) C

C Initialisations WRITE(6,10)

10 FORMAT(1X,’Frequence (en Hertz) ? ‘) READ(5,20)FREQUENCE 20 FORMAT(E14.7) WRITE(6,30) 30 FORMAT(1X,’Amplitude ? ‘) READ(5,20)AMPLITUDE WRITE(6,40)

40 FORMAT(1X,’Dephasage (en Radians) ? ‘) READ(5,20)PHI

WRITE(6,50)

50 FORMAT(1X,’Temps final (en Secondes) ? ‘) READ(5,20)TFIN C T = 0. I = 0 PAS = 1./(FREQUENCE*20.) C C Calcul du sinus

DOWHILE (T.LE.TFIN .AND. I.LE.NPMAX) I = I+1

T = T +PAS

VALEUR(I) = AMPLITUDE*SIN (2. * PI*FREQUENCE*T + PHI) TEMPS (I) = T WRITE(6,60)TEMPS(I),VALEUR(I) ENDDO NP = I 60 FORMAT(1X,E14.7,5X,E14.7) C C Enregistrement du fichier CALL ECRIRE(NPMAX,NP,TEMPS,VALEUR) END .../... C

C Sous-programme assurant l’enregistrement des résultats C dans le fichier RES.DAT

C

SUBROUTINE ECRIRE(MAX,NP,T,VALEUR) C

INTEGER NP,MAX

REAL T(MAX), VALEUR(MAX) C

C Creation et ouverture du fichier RES.DAT

OPEN(UNIT=50, FILE=‘RES.DAT’, STATUS =‘NEW’) C C Ecriture du fichier WRITE(50,10)NP 10 FORMAT(1X,I3) DO I=1,NP WRITE(50,20)T(I),VALEUR(I) ENDDO 20 FORMAT(1X,E14.7,5X,E14.7) C C Fermeture du fichier CLOSE(UNIT=50) RETURN END

13*:1%&1/1)( 04230) 4&523/1+3;5( )%(*2,()230))<( .&)*+%3)*251/230) .%018(5215( .1@3/=3(5" /( *0)2/(++(*4&5.<@&12:13*0)2453*(*() /0,42(A A (*2.0)/ 1) @3/=3(5 @05,&22<A

%&8&)2&'( .%(@@(/21(5+%()5('3*25(,()2.1 @3/=3(5.&)*1) *01*450'5&,,( (*2 :1( *3+%0) &-(*03) .( +35( /( @3/=3(5" 3+*1@@35&.%</535( 1) *01*450'5&,,( .( +(/215( :13*(5&+( 4().&)2.( /(+13.%</53215(A +*%</535&&3)*39

C

C Sous-programme assurant la lecture des résultats situés dans le fichier RES.DAT

C

(26)

&'( C

INTEGER NP,MAX

REAL T(MAX), VALEUR(MAX) C

C Ouverture du fichier RES.DAT

OPEN(UNIT=50, FILE=‘RES.DAT’, STATUS =‘OLD’) C C Lecture du fichier READ(50,10)NP 10 FORMAT(1X,I3) DO I=1,NP READ(50,20)T(I),VALEUR(I) ENDDO 20 FORMAT(1X,E14.7,5X,E14.7) C C Fermeture du fichier CLOSE(UNIT=50) RETURN END

Updating...

## Références

Updating...

Sujets connexes :