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函数的数值导数和切平面
7 @0 d; e, R( }, s, ]$ H% o1 法线
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+ L& t4 \; m8 d6 b4 B$ O1 u7 @【例 1】曲面法线演示。
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' j: d; e" U, q, R1 Z. z" Yy=-1:0.1:1;x=2*cos(asin(y));
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' @/ F4 A2 X( h, Y[X,Y,Z]=cylinder(x,20);
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suRFnorm(X(:,11:21),Y(:,11:21),Z(:,11:21));2 ?4 O# E# s$ Y2 e+ ~7 N
7 E% n" A+ i2 H, B- Oview([120,18]) & D0 j+ q B) p
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梯度 L% V1 N: W; ]7 n* e) `7 b
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* K2 a% M, _/ l0 a3 eclear;clf;q=2e-6;k=9e9;a=1.5;b=-1.5;x=-6:0.6:6;y=x;' y, ]* A+ Z' z
$ \2 ]8 a1 }/ ?) {+ M[X,Y]=meshgrid(x,y);
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" u( ^4 I a' n$ I! e; drp=sqrt((X-a).^2+(Y-b).^2);rm=sqrt((X+a).^2+(Y+b).^2);
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* r1 g, i1 I* |0 d8 WV=q*k*(1./rp-1./rm);8 n9 f; M* F/ s5 t, s
2 @7 L( m) p. y2 v* E2 S# c% Z[Ex,Ey]=gradient(-V);& O3 s. y0 O' {- ~, m4 z9 \4 w
# m* e+ m8 r3 q, V# }AE=sqrt(Ex.^2+Ey.^2);Ex=Ex./AE;Ey=Ey./AE;
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. N% ~& M+ f1 ?7 ucv=linspace(min(min(V)),max(max(V)),49);
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contourf(X,Y,V,cv,'k-')* ~ @9 }% b" d \
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%axis('square')
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- D9 r8 [9 i$ W/ [# ftitle('fontname {隶书}fontsize{22}偶极子的场'),hold on
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quiver(X,Y,Ex,Ey,0.7)8 \0 i% M1 k5 N* |0 V/ t% O! g
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plot(-a,-b,'wo',-a,-b,'w-')
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, J. J$ ~0 N* ?5 o/ y9 Mxlabel('x');ylabel('y'),hold off
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" @; l4 z. e" h& l2 多元函数的零点
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(1)% l! C8 F* d- y) \) ^4 r j0 G% h: x
: g1 B0 e0 ^0 k3 D- D+ jx=-2:0.5:2;y=x;[X,Y]=meshgrid(x,y);) L0 _/ v; A8 y( D/ I. h
( k- y( c7 `1 DF1=sin(X-Y);F2=cos(X+Y);6 M8 t+ Q0 a! \! q/ e- B& u
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v=[-0.2, 0, 0.2];
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% w, f! I4 v# u3 U7 ycontour(X,Y,F1,v)/ d# L/ ?, X* k/ L" B9 g
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hold on,contour(X,Y,F2,v),hold off
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[x0,y0]=ginput(2); 2 n e# K* ^9 y. @
( H; |8 N& |, q. |! rdisp([x0,y0]) : |/ m. B' l9 ?; ~: A0 N0 J- b
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-0.7926 -0.7843
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) k- _+ t% G* l- G. n 0.7926 0.7843
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(3)
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fun='[sin(x(1)-x(2)),cos(x(1)+x(2))]'; %<12>
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[xy,f,exit]=fsolve(fun,[x0(2),y0(2)]) %<13>
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6 M9 v6 G+ L/ r8 _+ W; X9 LOptimization terminated successfully:, u* ], ?2 h8 p/ ^7 s
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First-order optimality less than OPTIONS.TolFun, and no negative/zero curvature detected
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# G$ I$ v) @* \! l4 Oxy =% W. R7 W7 e5 O* i) m2 U! ~
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f =
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-0.0984 0.2011
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exit =
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* N+ g- I+ p% u4 R 〖说明〗4 \3 t, |7 l S q5 m6 i b
* A' C! I" u+ \3 P4 a[fun.m]
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function ff=fun(x)
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ff(1)=sin(x(1)-x(2));# ~8 p1 {5 c/ s) M6 ~' a. z
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ff(2)=cos(x(1)+x(2));
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