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升级   91% TA的每日心情 | 难过 2012-8-27 18:22 |
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签到天数: 1 天 [LV.1]初来乍到
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Forcal优化库FcOpt中新增函数fcopt::solve,试图求解方程的全部解。正在测试修改,请大家多提意见。
) G$ w) u0 `( q6 F8 p参考:http://www.forcal.net/sysm/forcal9/fchtm/fcopt.htm
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5 U$ F2 U/ [$ ]+ B _- S, ~" P$ `例子1:解方程组:8 r% U. o C" R) W+ F
- (x-y)^2-3*(x-y) = 104 r2 T; t- z- F7 }4 d
- x^2+2*x*y+y^2 = 9
复制代码
1 O4 V% J& @' h4 G代码:$ z8 o: p" X9 i9 ?4 f
- f(x,y,y1,y2)=
& E7 C6 o5 ~* i& E0 W& r G0 ` - {
& i/ s3 O6 ]$ |* N5 Q - y1=(x-y)^2-3*(x-y)-10,8 y) a4 s3 D' |/ `
- y2=x^2+2*x*y+y^2-9; ?& X8 p% a& Q- U1 p. U- F
- };- |9 d& i8 b# c3 b- v1 C, C
- fcopt::solve[HFor("f")];
复制代码
! ]0 _1 u ]5 a7 p: F6 N结果:
3 z! u; S! h/ l0 T5 o4 j0.5 2.5 0.
/ z3 D" F8 G8 r) _-2.5 -0.5 0.( L$ {/ [# K: M
1.000000000225044 -4.00000000022569 2.231017652693784e-009' k8 k0 C( r" x6 S6 A* P
4.000000000395746 -1.00000000039106 3.894538219597456e-009" A: ]( g: _! t$ @. n# A8 g
4.
* b8 T5 \, _6 U+ q7 A5 c! ~& X+ N8 W( d) g( i. d: H( I$ M9 |
例子2:解方程组:
7 r* y& E" ?3 J- b& C- 2*x1-x2^2-exp(-x1) = 0) r4 I8 O) x- p y
- -(x1^3)+x1*x2-exp(-x2) = 0
复制代码 3 d) N; p) \4 T
代码:
) u; a6 M2 I6 s9 l U( Q* F- f(x1,x2,y1,y2)=6 e. C* g2 m+ Y& k9 f* Q0 M5 F/ L7 `
- {
4 G( @- G; i3 r\" R8 w# ^! ~ - y1=2*x1-x2^2-exp(-x1),
5 ]( e; f7 W/ n U* d7 q, u0 {0 E' T - y2=-(x1^3)+x1*x2-exp(-x2)0 x/ |) A5 j4 X8 a* A4 u
- };
2 f0 @( i4 a0 Z# v& Y - fcopt::solve[HFor("f")];
复制代码
{& ~9 f& y8 E/ Q& U; k/ q$ {/ H3 ~结果:2 L, f/ ]9 J8 r. U# r' V
0.7914550065632104 1.062885264188035 0.
4 j2 b# s7 S& ` \8 M0.9977869653328695 1.275491849454102 3.925231146709438e-0171 B7 i5 p0 O" Q6 C) R! G
2.. K, q' b @3 L' ]% }
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例子3:解方程组:t取-7~7
% r9 M. o4 D! {" M2 n- -b*sin(a+6*t)+n-40.4945=0
2 X- i! }6 i0 k6 g; L# ^ - -b*sin(a+7*t)+n-40.5696=0
' f2 F( f1 Y4 i0 F: t. S: U) c - -b*sin(a+8*t)+n-41.0443=02 K4 V8 ^\" S& l% r: S9 n/ v
- -b*sin(a+9*t)+n-41.4190=0
复制代码
" M3 M! l# z5 P- P代码:: V# v5 z# E3 t
 - !using["fcopt"];
- & ?9 A) W; e; D o3 V& |
- f(a,b,n,t,y1,y2,y3,y4)=9 A$ V8 p. I% H
- {
- : o1 z3 {% g$ k; u3 [+ `7 e
- y1=-b*sin(a+6*t)+n-40.4945,
- . c0 j* {0 r; S) u
- y2=-b*sin(a+7*t)+n-40.5696,
- ' Y3 s1 C8 T9 b4 M
- y3=-b*sin(a+8*t)+n-41.0443,
- 2 u6 s7 W+ M, ], r% X1 [
- y4=-b*sin(a+9*t)+n-41.41904 B* r+ ~+ D9 q ?7 S# W/ h& }
- };
- ( E- k$ R' G5 w& X! w* }
- solve[HFor("f"), optrange,-1e50,1e50,-1e50,1e50,-1e50,1e50,-7,7];
2 \0 `8 S3 u) E一种可能的结果(该方程组有无穷解):0 x3 h3 S4 s p, N$ ]6 v
-2.140093203561007 -0.4915300827061839 40.94928398718974 1.077226214994063 3.552713678800501e-015
0 A# J) y% ~2 A) ~+ l1 }( G- o-11.56487116433041 0.491530082706186 40.94928398718974 1.077226214994066 5.024295867788081e-015
& @, ^3 U# D5 i7 o* e7 O8 K# ?-8.423278510740103 -0.4915300827061995 40.94928398718977 1.077226214993991 8.702335715267317e-015" @: R6 d" }" C8 d n& U
2555.116326818533 -0.4915300827062283 40.94928398718988 1.07722621499373 4.819135301037582e-014
8 [8 O: C1 T |1 U- i1.001499450023601 0.4915300827059401 40.94928398718962 -5.205959092184797 1.64387405750109e-013
+ w3 A2 l( j8 d; v1 ~' l2 F-17.84805647151125 0.4915300827056817 40.9492839871897 1.077226214994272 3.642354617502926e-013( O3 J& k* s4 E; J! [5 v
3146.874339449554 -0.4915300825865869 40.94928398712157 -1.077226215397079 1.198690006101687e-010
0 P7 D7 H, ^: ]. V4.14309210834897 -0.4915300817987574 40.94928398665894 -5.205959092793353 8.618584276014861e-010
1 \- v, n5 Q! ^7 u, ?, t* M5628.732535974947 -0.491530080064976 40.9492839770687 -1.077226245248003 7.394104227928194e-0095 T7 z- i W. U9 s2 x: _ H- h
1934.219575147075 -0.4915300766540718 40.94928398081019 -1.077226212465366 8.617217026839414e-0097 U$ s: ?5 O6 w8 }& z
10.
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