python网站开发书籍推荐,网站引导页怎么设置,企业网站排名优化方案,网站ip被屏蔽怎么办浅水方程 浅水方程可以建立起海啸和浴缸中波浪的数学模型。浅水方程建立了水或者其它不可压缩液体受扰动时传播的模型。隐含的假设是#xff0c;液体的深度和波浪的长度、扰动等相比是很小的。 在这样的记号下#xff0c;浅水方程为双曲守恒定律的一个例子。 使用拉克斯-冯特…浅水方程 浅水方程可以建立起海啸和浴缸中波浪的数学模型。浅水方程建立了水或者其它不可压缩液体受扰动时传播的模型。隐含的假设是液体的深度和波浪的长度、扰动等相比是很小的。 在这样的记号下浅水方程为双曲守恒定律的一个例子。 使用拉克斯-冯特洛夫方法计算方程的近似数值解。waterwave求解的区域为正方形区域有反射的边界条件。在初始时刻在整个区域都有h1u0v0这样解是静态的。然后在连续几个时间步长内二维高斯型峰值添加到h处用来模拟水滴滴到水面上的冲量扰动作用。 shading 设置颜色着色属性 function waterwave
% WATERWAVE 2D Shallow Water Model
%
% Lax-Wendroff finite difference method.
% Reflective boundary conditions.
% Random water drops initiate gravity waves.
% Surface plot displays height colored by momentum.
% Plot title shows t simulated time and tv a measure of total variation.
%t 模拟时间tv 总变化量
% An exact solution to the conservation law would have constant tv.
% Lax-Wendroff produces nonphysical oscillations and increasing tv.
%
% See:
% http://en.wikipedia.org/wiki/Shallow_water_equations
% http://www.amath.washington.edu/~rjl/research/tsunamis
% http://www.amath.washington.edu/~dgeorge/tsunamimodeling.html
% http://www.amath.washington.edu/~claw/applications/shallow/www% Parametersn 64; % grid size
g 9.8; % gravitational constant
dt 0.01; % hardwired timestep
dx 1.0;
dy 1.0;
nplotstep 8; %绘图间隔
ndrops 1; % 最大滴数
dropstep 200; % 液滴间隔
D droplet(1.5,21); % 模拟水滴
% Initialize graphics[surfplot,top,restart,quit] initgraphics(n); %启动图形% Outer loop, restarts.while get(quit,value) 0set(restart,value,0)H ones(n2,n2); U zeros(n2,n2); V zeros(n2,n2);Hx zeros(n1,n1); Ux zeros(n1,n1); Vx zeros(n1,n1);Hy zeros(n1,n1); Uy zeros(n1,n1); Vy zeros(n1,n1);ndrop ceil(rand*ndrops);nstep 0;% Inner loop, time steps.while get(restart,value)0 get(quit,value)0nstep nstep 1;% Random water dropsif mod(nstep,dropstep) 0 nstep ndrop*dropstepw size(D,1);i ceil(rand*(n-w))(1:w);j ceil(rand*(n-w))(1:w);H(i,j) H(i,j) (14*rand)/5*D;end% Reflective boundary conditionsH(:,1) H(:,2); U(:,1) U(:,2); V(:,1) -V(:,2);H(:,n2) H(:,n1); U(:,n2) U(:,n1); V(:,n2) -V(:,n1);H(1,:) H(2,:); U(1,:) -U(2,:); V(1,:) V(2,:);H(n2,:) H(n1,:); U(n2,:) -U(n1,:); V(n2,:) V(n1,:);% First half step% x directioni 1:n1;j 1:n;% heightHx(i,j) (H(i1,j1)H(i,j1))/2 - dt/(2*dx)*(U(i1,j1)-U(i,j1));% x momentumUx(i,j) (U(i1,j1)U(i,j1))/2 - ...dt/(2*dx)*((U(i1,j1).^2./H(i1,j1) g/2*H(i1,j1).^2) - ...(U(i,j1).^2./H(i,j1) g/2*H(i,j1).^2));% y momentumVx(i,j) (V(i1,j1)V(i,j1))/2 - ...dt/(2*dx)*((U(i1,j1).*V(i1,j1)./H(i1,j1)) - ...(U(i,j1).*V(i,j1)./H(i,j1)));% y directioni 1:n;j 1:n1;% heightHy(i,j) (H(i1,j1)H(i1,j))/2 - dt/(2*dy)*(V(i1,j1)-V(i1,j));% x momentumUy(i,j) (U(i1,j1)U(i1,j))/2 - ...dt/(2*dy)*((V(i1,j1).*U(i1,j1)./H(i1,j1)) - ...(V(i1,j).*U(i1,j)./H(i1,j)));% y momentumVy(i,j) (V(i1,j1)V(i1,j))/2 - ...dt/(2*dy)*((V(i1,j1).^2./H(i1,j1) g/2*H(i1,j1).^2) - ...(V(i1,j).^2./H(i1,j) g/2*H(i1,j).^2));% Second half stepi 2:n1;j 2:n1;% heightH(i,j) H(i,j) - (dt/dx)*(Ux(i,j-1)-Ux(i-1,j-1)) - ...(dt/dy)*(Vy(i-1,j)-Vy(i-1,j-1));% x momentumU(i,j) U(i,j) - (dt/dx)*((Ux(i,j-1).^2./Hx(i,j-1) g/2*Hx(i,j-1).^2) - ...(Ux(i-1,j-1).^2./Hx(i-1,j-1) g/2*Hx(i-1,j-1).^2)) ...- (dt/dy)*((Vy(i-1,j).*Uy(i-1,j)./Hy(i-1,j)) - ...(Vy(i-1,j-1).*Uy(i-1,j-1)./Hy(i-1,j-1)));% y momentumV(i,j) V(i,j) - (dt/dx)*((Ux(i,j-1).*Vx(i,j-1)./Hx(i,j-1)) - ...(Ux(i-1,j-1).*Vx(i-1,j-1)./Hx(i-1,j-1))) ...- (dt/dy)*((Vy(i-1,j).^2./Hy(i-1,j) g/2*Hy(i-1,j).^2) - ...(Vy(i-1,j-1).^2./Hy(i-1,j-1) g/2*Hy(i-1,j-1).^2));% Update plotif mod(nstep,nplotstep) 0C abs(U(i,j)) abs(V(i,j)); % Color shows momemtumt nstep*dt;tv norm(C,fro);set(surfplot,zdata,H(i,j),cdata,C);set(top,string,sprintf(t %6.2f, tv %6.2f,t,tv))drawnowendif all(all(isnan(H))), break, end % Unstable, restartend
end
close(gcf)% ------------------------------------function D droplet(height,width)
% DROPLET 2D Gaussian
% D droplet(height,width)[x,y] ndgrid(-1:(2/(width-1)):1);D height*exp(-5*(x.^2y.^2));% ------------------------------------function [surfplot,top,restart,quit] initgraphics(n);
% INITGRAPHICS Initialize graphics for waterwave.
% [surfplot,top,restart,quit] initgraphics(n)
% returns handles to a surface plot, its title, and two uicontrol toggles.clfshgset(gcf,numbertitle,off,name,Shallow_water)x (0:n-1)/(n-1);surfplot surf(x,x,ones(n,n),zeros(n,n));grid offaxis([0 1 0 1 -1 3])caxis([-1 1])shading facetedc (1:64)/64;cyan [0*c c c];colormap(cyan)top title(xxx);restart uicontrol(position,[20 20 80 20],style,toggle,string,restart);quit uicontrol(position,[120 20 80 20],style,toggle,string,close);摩尔斯电码 摩尔斯电码演示了二元树binary tree和单元数组cell array。电码由短的点dot或‘.’或者长的停顿dash或‘-’分隔。 ...---...表示SOS‘...--...’表示SMS。 摩尔斯树 采用二元树来定义摩尔斯电码。从根节点开始向左移动一个链接表示一个“点”向右表示一个“划”。如可以用“.-”来表示字母A。 function M morse_tree
% MORSE_TREE
% M morse_tree is a cell array of cell arrays, the binary
% tree for the Morse code of the 26 Latin characters.
%
% M morse_tree_extended is a larger cell array of cell arrays,
% the binary tree for the Morse code of the 26 Latin characters
% plus digits, punctuation marks, and several non-Latin characters.
%
% _____ root _____
% / \
% _ E _ _ T _
% / \ / \
% I A N M
% / \ / \ / \ / \
% S U R W D K G O
% / \ / / / \ / \ / \ / \
% H V F L P J B X C Y Z Q
%global extend
if extend1M morse_tree_extended;return
end% Level 4
h {H {} {}};
v {V {} {}};
f {F {} {}};
l {L {} {}};
p {P {} {}};
j {J {} {}};
b {B {} {}};
x {X {} {}};
c {C {} {}};
y {Y {} {}};
z {Z {} {}};
q {Q {} {}};% Level 3
s {S h v};
u {U f {}};
r {R l {}};
w {W p j};
d {D b x};
k {K c y};
g {G z q};
o {O {} {}};% Level 2
i {I s u};
a {A r w};
n {N d k};
m {M g o};% Level 1
e {E i a};
t {T n m};% Level 0
M { e t}; 树的搜索 反复选择树上的不同分支对应着遍历这个树的不同顺序。在众多可能的排序中有两种有着标准的名字深度优先搜索方法depth-first search和广度优先搜索breadth-first search。 深度优先的方法使用的是成为栈stack的数据结构。栈S为单元数组只要栈是非空的while循环就一直进行下去。 S {morse_tree};while ~isempty(S)N S{1};S S(2:end);if ~isempty(N)fprintf( %s,N{1})S {N{2} N{3} S{:}};endendfprintf(\n) 广度优先搜索算法用了称为队列queue的数据结构。 %% Breadth first, with a queue.Q {morse_tree};while ~isempty(Q)N Q{1};Q Q(2:end);if ~isempty(N)fprintf( %s,N{1})Q {Q{:} N{2} N{3}};endendfprintf(\n) 队列采用了先进先出FIFO的策略而堆栈采用了后进先出LIFO的策略。 function morse_gui(arg)
% MORSE_GUI Interactive demonstration of Morse code and binary trees.if nargin 0init_guielseif isequal(arg,_depth)depthelseif isequal(arg,_breadth) breadthelsetranslateend% ------------------------------------function depth% Depth first traversal of Morse code binary tree% Stack, LIFO, last in first out.% Insert new items at the top of the stack.S {morse_tree};X 0;Y 0;while ~isempty(S)N S{1};S S(2:end);x X(1);X X(2:end);y Y(1);Y Y(2:end);if ~isempty(N)node(N{1},x,y)S {N{2} N{3} S{:}};X [2*x-(x0); 2*x(x0); X];Y [y1; y1; Y];endendend % depth% ------------------------------------function breadth% Breadth first traversal of Morse code binary tree.% Queue, FIFO, first in first out.% Insert new items at the end of the queue.Q {morse_tree};X 0;Y 0;while ~isempty(Q)N Q{1};Q Q(2:end);x X(1);X X(2:end);y Y(1);Y Y(2:end);if ~isempty(N)node(N{1},x,y);Q {Q{:} N{2} N{3}};X [X; 2*x-(x0); 2*x(x0)];Y [Y; y1; y1];endendend % breadth% ------------------------------------function translate% Translate to and from Morse code.e findobj(style,edit);s findobj(string,sound);t get(e,string);if all(t. | t- | t | t*)t decode(t);set(e,string,t);elsecode encode(t);set(e,string,code);if get(s,value) 1morse_sound(code)endendif length(t)3 isequal(t(1:3),SOS)screamendend% ------------------------------------function code encode(text)% ENCODE Translate text to dots and dashes.% encode(text)code ;text upper(text);for k 1:length(text);ch text(k);% A blank in the text is worth three in the code.if ch code [code ];elsecode [code encode_ch(ch) ];endendend % encode% ------------------------------------function dd encode_ch(ch)% ENCODE_CH Translate one character to dots and dashes.S {morse_tree};D {};while ~isempty(S)N S{1};dd D{1};S S(2:end);D D(2:end);if ~isempty(N)if N{1} ch;returnelseS {N{2} N{3} S{:}};D {[dd .] [dd -] D{:}};endendenddd *;end % encode_ch% ------------------------------------function text decode(code)% DECODE Translate strings of dots and dashes to text.% decode(string of dots, dashes and spaces)text [];code [code ];while ~isempty(code);k find(code ,1);ch decode_dd(code(1:k));text [text ch];code(1:k) [];% Many blanks in the code is worth one in the text.if ~isempty(code) code(1) text [text ];while ~isempty(code) code(1) code(1) [];endendendend % decode% ------------------------------------function ch decode_dd(dd)% DECODE_DD Translate one characters worth of dots% and dashes to a single character of text.M morse_tree;for k 1:length(dd)if dd(k) .M M{2};elseif dd(k) -M M{3};endif isempty(M)ch *;returnendendch M{1};end % decode_dd% ------------------------------------function init_gui% Initialize Morse code gui.global extendextend 0;clf resetaxes(pos,[0 0 1 1])axis(16*[-1 1 0 2])axis square offset(gcf,color,white)set(gca,ydir,rev)uicontrol(style,push,string,depth, ...units,normal,pos,[0.16 0.20 0.12 0.06], ...callback,cla, morse_gui(_depth))uicontrol(style,push,string,breadth, ...units,normal,pos,[0.35 0.20 0.12 0.06], ...callback,cla, morse_gui(_breadth))uicontrol(style,toggle,string,sound,value,1, ...units,normal,pos,[0.54 0.20 0.12 0.06]);uicontrol(style,toggle,string,extend,value,0, ...units,normal,pos,[0.72 0.20 0.12 0.06], ...callback, [global extend, extendget(gcbo,value); ...if extend0, cla, end, axis(2^(4extend)*[-1 1 0 2])]);uicontrol(style,edit,string, ...Enter text or code to translate, ...units,normal,pos,[0.16 0.04 0.68 0.08], ...callback,cla, morse_gui(_translate))end% ------------------------------------function node(ch,x,y)% Plot, and possibly play, node of Morse code binary tree.global extendr 0.90;z r*exp(2*pi*i*(0:32)/32);delta 1/3;dkgreen [0 1/2 0];lw get(0,defaultlinelinewidth)0.5;fs get(0,defaulttextfontsize);if ~extendlw lw1;fs fs2;endp 2^(4extend-y);u (x~0)*(2*x2*(x0)-1)*p;v 4*(y1);% Circleline(ureal(z),vimag(z),color,black,linewidth,lw)% Charactertext(u-delta,v,ch,fontweight,bold,color,dkgreen,fontsize,fs);% Connect node to parentif (x~0)if y1w 0;elseif rem(x,2)(x0)w up;elsew u-p;endline([u w],[v-r vr-4],color,black,linewidth,lw)endif get(findobj(string,sound),value) 1morse_sound(encode_ch(ch))pause(0.2)endpause(0.1)end% ------------------------------------function morse_sound(code,delta,note)% MORSE_SOUND Play sound for dots and dashes.% morse_sound(code) plays code, a string of dots, dashes and spaces.% morse_sound(code,delta,note) time slice is delta and tone is note.% Default delta 1/16 second.% Default note 6, which is F above middle C. See play_note.if nargin 2delta 1/16;endif nargin 3note 6;ends findobj(string,sound);for k 1:length(code)if get(s,value) 1switch code(k)case .play_note(note,delta)case -play_note(note,3*delta)case pause(3*delta)otherwise% Skip the characterendpause(delta)endendend % morse_sound% ------------------------------------function play_note(note,T)% PLAY_NOTE Play a musical note.% play_note(note,T) Play a note for T seconds.% note is an integer specifying semitones above and below middle C.% There are 12 notes per octave.% play_note(0,1/2) plays middle C (~261.625 Hz) for 1/2 second.C4 440/2^(3/4); % Middle C, hertzFs 44100; % Sample rate, hertzt (0:1/Fs:T); % Linear time rampf C4 * 2^(note/12); % Frequency, hertzy sin(2*pi*f*t); % Sinusoidal signalk 1:1000; % Attack and releaser (k/1000);y(k) r.*y(k);y(end1-k) r.*y(end1-k);sound(y,Fs) % Playend % play_noteend % morse_gui解码和编码 解码是将 “点和划” 描述的东西变成文字编码过程正好反过来。 function text decode(code)% DECODE Translate strings of dots and dashes to text.% decode(string of dots, dashes and spaces)text [];code [code ];while ~isempty(code);k find(code ,1);ch decode_dd(code(1:k));text [text ch];code(1:k) [];% Many blanks in the code is worth one in the text.if ~isempty(code) code(1) text [text ];while ~isempty(code) code(1) code(1) [];endendendend % decode function dd encode_ch(ch)% ENCODE_CH Translate one character to dots and dashes.S {morse_tree};D {};while ~isempty(S)N S{1};dd D{1};S S(2:end);D D(2:end);if ~isempty(N)if N{1} ch;returnelseS {N{2} N{3} S{:}};D {[dd .] [dd -] D{:}};endendenddd *;end % encode_ch 摩尔斯电码表 morse_code使用了递归算法函数traverse这种递归调用的结果把C表格和含有“点”和“划”的dd字符串合并。在matlab中可以使用char函数将数字转换成字母如char65命令转换为A。
function C morse_code(C,M,dd)
% MORSE_CODE
% C morse_code
% C morse_code(morse_tree)
% C morse_code(morse_tree_extended)
% Generate tables of the ASCII and Morse codes
% for the characters defined by the binary trees.if nargin 3 % Choose binary treeif nargin 0M morse_tree;elseM C;endC cell(256,1); % The temporary code tabledd ; % dots and dashesendif ~isempty(M) % Depth first searchif ~isempty(M{1})C{double(M{1})} dd; % Use ASCII value as an indexendC morse_code(C,M{2},[dd .]); % Recursive callC morse_code(C,M{3},[dd -]); % Recursive callendif nargin 3 % Final processing, convert to char.c char(C{:});k find(c(:,1) ~ ); % Find the nonblank entries.b blanks(length(k));C [char(k) b b int2str(k) b b char(C{k})];end
