图形界面函数计算器

gooobooo · 发表于 2018-9-17 09:13:29

function funtool(keyword,varargin)
%图形界面函数计算器，能进行函数各类初等运算、积分、微分、作图。
%FUNTOOL A function calculator.
% FUNTOOL is an interactive graphing calculator that manipulates
% functions of a single variable. At any time, there are two functions
% displayed, f(x) and g(x). The result of most operations replaces f(x).
%
% The controls labeled 'f = ' and 'g = ' are editable text that may
% be changed at any time to install a new function. The control
% labeled 'x = ' may be changed to specify a new domain. The control
% labeled 'a = ' may be changed to specify a new value of a parameter.
%
% The top row of control buttons are unary function operators that
% involve only f(x). These operators are:
% df/dx - Symbolically differentiate f(x).
% int f - Symbolically integrate f(x).
% simple f - Simplify the symbolic expression, if possible.
% num f - Extract the numerator of a rational expression.
% den f - Extract the denominator of a rational expression.
% 1/f - Replace f(x) by 1/f(x).
% finv - Replace f(x) by its inverse function.
%
% The operators int(f) and finv may fail if the corresponding symbolic
% expressions do not exist in closed form.
%
% The second row of buttons translate and scale f(x) by the parameter 'a'.
% The operations are:
% f + a - Replace f(x) by f(x) + a.
% f - a - Replace f(x) by f(x) - a.
% f * a - Replace f(x) by f(x) * a.
% f / a - Replace f(x) by f(x) / a.
% f ^ a - Replace f(x) by f(x) ^ a.
% f(x+a) - Replace f(x) by f(x + a).
% f(x*a) - Replace f(x) by f(x * a).
%
% The third row of buttons are binary function operators that
% operate on both f(x) and g(x). The operations are:
% f + g - Replace f(x) by f(x) + g(x).
% f - g - Replace f(x) by f(x) - g(x).
% f * g - Replace f(x) by f(x) * g(x).
% f / g - Replace f(x) by f(x) / g(x).
% f(g) - Replace f(x) by f(g(x)).
% g = f - Replace g(x) by f(x).
% swap - Interchange f(x) and g(x).
%
% The first three buttons in the fourth row manage a list of functions.
% The Insert button places the current active function in the list.
% The Cycle button rotates the function list.
% The Delete button removes the active function from the list.
% The list of functions is named fxlist. A default fxlist containing
% several interesting functions is provided.
%
% The Reset button sets f, g, x, a and fxlist to their initial values.
% The Help button prints this help text.
%
% The Demo button poses the following challenge: Can you generate the
% function sin(x) without touching the keyboard, using just the mouse?
% The demo does it with a reset and then nine clicks. If you can do
% it with fewer clicks, please send e-mail to moler@mathworks.com.
%
% The Close button closes all three windows.
%
% See also EZPLOT.
% $Revision: 1.11 $ $Date: 1997/11/29 01:06:25 $
%Implementation Notes:
% f,g, and a are syms.
% x is a string. fxlist is a string matrix.
%
% The values of f, g, a, and x are stored in the UserData of the text
% objects "f", "g", "a", and "x", respectively. These text objects are
% tagged "fobj", "gobj", "aobj", and "xstr", respectively.
% fxlist is stored in the UserData of the control panel figure, which is
% tagged as "figp".
% The edit text boxes for f, g, x, and a are tagged "Sf", "Sg", "Sx", and
% "Sa", respectively.
% The initial values of f, g, x, a, and fxlist are stored in a structure
% called init that has fields .f, .g, .x, .a and .l. The structure is
% stored in the UserData of the Reset button.
%%%%%%%%%%%%%%%%%%%%%%%%%% Initialization section.
if nargin == 0
init.f = 'x';
init.g = '1';
init.x = '[-2*pi, 2*pi]';
init.a = '1/2';
init.l = str2mat( ...
'1/(5+4*cos(x)); [-2*pi, 2*pi]', ...
'cos(x^3)/(1+x^2); [-2*pi, 2*pi]', ...
'x^4*(1-x)^4/(1+x^2); [0, 1]', ...
'x^7-7*x^6+21*x^5-35*x^4+35*x^3-21*x^2+7*x-1; [0.985, 1.015]', ...
'log(abs(sqrt(x))); [0, 2]', ...
'tan(sin(x))-sin(tan(x)); [-pi, pi]');
f = sym(init.f);
g = sym(init.g);
a = sym(init.a);
x = init.x;
fxlist = init.l;
% Macros
blanks = ' ';
p = .12*(1:7) - .02;
q = .60 - .14*(1:4);
r = [.10 .10];
% Position the two figures and the control panel.
figf = figure('units','normalized','pos',[.01 .50 .48 .48],...
'menu','none','tag','figf');
figg = figure('units','normalized','pos',[.50 .50 .48 .48],...
'menu','none', 'tag','figg');
figp = figure('units','normalized','pos',[.25 .05 .50 .40],'menu','none', ...
'tag','figp',...
'Color',get(0,'DefaultUIControlBackgroundColor'), ...
'DefaultUIControlUnit','norm','UserData',fxlist);
% Plot f(x) and g(x).
figure(figf)
ezplot(f,x,figf)
figure(figg)
ezplot(g,x,figg)
% Control panel
figure(figp)
uicontrol('style','frame','pos',[0.01 0.60 0.98 0.38]);
uicontrol('style','frame','pos',[0.01 0.01 0.98 0.58]);
uicontrol('style','text','string','f = ','pos',[0.04 0.86 0.09 0.10],...
'tag','fobj','UserData',f);
uicontrol('style','text','string','g = ','pos',[0.04 0.74 0.09 0.10],...
'tag','gobj','UserData',g);
uicontrol('style','text','string','x = ','pos',[0.04 0.62 0.09 0.10],...
'tag','xstr','UserData',x);
uicontrol('style','text','string','a = ','pos',[0.54 0.62 0.09 0.10],...
'tag','aobj','UserData',a);
uicontrol('pos',[.12 .86 .82 .10],'style','edit','horiz','left', ...
'backgroundcolor','white', ...
'string', [blanks char(f)],'tag','Sf', ...
'CallBack','funtool Sfcallback');
uicontrol('pos',[.12 .74 .82 .10],'style','edit','horiz','left', ...
'backgroundcolor','white', ...
'string', [blanks char(g)], 'tag','Sg',...
'CallBack','funtool Sgcallback');
uicontrol('pos',[.12 .62 .32 .10],'style','edit','horiz','left', ...
'backgroundcolor','white','string',[blanks x], 'tag','Sx',...
'CallBack','funtool Sxcallback');
uicontrol('pos',[.62 .62 .32 .10],'style','edit','horiz','left', ...
'backgroundcolor','white', 'tag','Sa',...
'string',[blanks char(a)],'CallBack','funtool Sacallback');
% Top row of unary operators.
uicontrol('pos',[p(1) q(1) r],'string','df/dx', ...
'CallBack','funtool(''row1'',''diff'')');
uicontrol('pos',[p(2) q(1) r],'string','int f', ...
'CallBack','funtool(''row1'',''int'')');
uicontrol('pos',[p(3) q(1) r],'string','simple f', ...
'CallBack','funtool(''row1'',''simple'')');
uicontrol('pos',[p(4) q(1) r],'string','num f', ...
'CallBack','funtool(''row1'',''num'')');
uicontrol('pos',[p(5) q(1) r],'string','den f', ...
'CallBack','funtool(''row1'',''den'')');
uicontrol('pos',[p(6) q(1) r],'string','1/f', ...
'CallBack','funtool(''row1'',''1/f'')');
uicontrol('pos',[p(7) q(1) r],'string','finv', ...
'CallBack','funtool(''row1'',''finverse'')');
% Second row of unary operators.
uicontrol('pos',[p(1) q(2) r],'string','f+a', ...
'CallBack','funtool(''row2'',''f+a'')');
uicontrol('pos',[p(2) q(2) r],'string','f-a', ...
'CallBack','funtool(''row2'',''f-a'')');
uicontrol('pos',[p(3) q(2) r],'string','f*a', ...
'CallBack','funtool(''row2'',''f*a'')');
uicontrol('pos',[p(4) q(2) r],'string','f/a', ...
'CallBack','funtool(''row2'',''f/a'')');
uicontrol('pos',[p(5) q(2) r],'string','f^a', ...
'CallBack','funtool(''row2'',''f^a'')');
uicontrol('pos',[p(6) q(2) r],'string','f(x+a)', ...
'CallBack','funtool(''row2'',''f(x+a)'')');
uicontrol('pos',[p(7) q(2) r],'string','f(x*a)', ...
'CallBack','funtool(''row2'',''f(x*a)'')');
% Third row, binary operators.
uicontrol('pos',[p(1) q(3) r],'string','f + g', ...
'CallBack','funtool(''row3'',''f+g'')');
uicontrol('pos',[p(2) q(3) r],'string','f - g', ...
'CallBack','funtool(''row3'',''f-g'')');
uicontrol('pos',[p(3) q(3) r],'string','f * g', ...
'CallBack','funtool(''row3'',''f*g'')');
uicontrol('pos',[p(4) q(3) r],'string','f / g', ...
'CallBack','funtool(''row3'',''f/g'')');
uicontrol('pos',[p(5) q(3) r],'string','f(g)', ...
'CallBack','funtool(''row3'',''f(g)'')');
uicontrol('pos',[p(6) q(3) r],'string','g = f', ...
'CallBack','funtool(''row3'',''g=f'')');
uicontrol('pos',[p(7) q(3) r],'string','swap', ...
'CallBack','funtool(''row3'',''swap'')');
% Fourth row, auxilliary controls.
uicontrol('pos',[p(1) q(4) r],'string','Insert','CallBack','funtool Insert');
uicontrol('pos',[p(2) q(4) r],'string','Cycle','CallBack','funtool Cycle');
uicontrol('pos',[p(3) q(4) r],'string','Delete','CallBack','funtool Delete');
uicontrol('pos',[p(4) q(4) r],'string','Reset','Tag','reset', ...
'UserData', init, 'CallBack', 'funtool Reset');
uicontrol('pos',[p(5) q(4) r],'string','Help', ...
'CallBack','helpwin funtool');
uicontrol('pos',[p(6) q(4) r],'string','Demo', ...
'CallBack','funtool Demo');
uicontrol('pos',[p(7) q(4) r],'string','Close', ...
'CallBack','funtool close');
%%%%%%%%%%%%%%%%%%%%%%%%%% end of Initialization section
else
switch keyword
%%%%%%%%%%%%%%%%%%%%%%%%%% Callback for top row of unary operators.
case 'row1'
figp = findobj(0,'tag','figp');
fhndl = findobj(figp,'tag','fobj');
f = get(fhndl,'UserData');
x = get(findobj(figp,'tag','xstr'),'UserData');
figf = findobj(0,'tag','figf');
switch varargin{1}
case 'diff'
f = diff(f);
case 'int'
f = int(f);
case 'simple'
f = simple(f);
case 'num'
[f,ans] = numden(f);
case 'den'
[ans,f] = numden(f);
case '1/f'
f = 1/f;
case 'finverse'
f = finverse(f);
end
set(fhndl,'UserData',f);
ezplot(f,x,figf)
blanks = ' ';
set(findobj(figp,'tag','Sf'),'string',[blanks char(f)]);
%%%%%%%%%%%%%%%%%%%%%%%%%% Callback for second row of unary operators.
case 'row2'
figp = findobj(0,'tag','figp');
fhndl = findobj(figp,'tag','fobj');
f = get(fhndl,'UserData');
x = get(findobj(figp,'tag','xstr'),'UserData');
a = get(findobj(figp,'tag','aobj'),'UserData');
figf = findobj(0,'tag','figf');
switch varargin{1}
case 'f+a'
f = f+a;
case 'f-a'
f = f-a;
case 'f*a'
f = f*a;
case 'f/a'
f = f/a;
case 'f^a'
f = f^a;
case 'f(x+a)'
f = subs(f,sym('x'),sym('x')+a);
case 'f(x*a)', ...
f = subs(f,sym('x'),sym('x')*a);
end
set(fhndl,'UserData',f);
ezplot(f,x,figf)
blanks = ' ';
set(findobj(figp,'tag','Sf'),'string',[blanks char(f)]);
%%%%%%%%%%%%%%%%%%%%%%%%%% Callback for third row, binary operators.
case 'row3'
blanks = ' ';
% Get variables.
figp = findobj(0,'tag','figp');
fhndl = findobj(figp,'tag','fobj');
ghndl = findobj(figp,'tag','gobj');
f = get(fhndl,'UserData');
g = get(ghndl,'UserData');
x = get(findobj(figp,'tag','xstr'),'UserData');
a = get(findobj(figp,'tag','aobj'),'UserData');
figf = findobj(0,'tag','figf');
figg = findobj(0,'tag','figg');
if strcmp(varargin{1}, 'g=f')
g = f;
set(ghndl,'UserData',g);
ezplot(g,x,figg)
set(findobj(figp,'tag','Sg'),'string',[blanks char(g)]);
elseif strcmp(varargin{1}, 'swap')
h = f; f = g; g = h;
set(fhndl,'UserData',f);
ezplot(f,x,figf)
set(findobj(figp,'tag','Sf'),'string',[blanks char(f)]);
set(ghndl,'UserData',g);
ezplot(g,x,figg)
set(findobj(figp,'tag','Sg'),'string',[blanks char(g)]);
else
switch varargin{1}
case 'f+g'
f = f+g;
case 'f-g'
f = f-g;
case 'f*g'
f = f*g;
case 'f/g'
f = f/g;
case 'f(g)'
f = compose(f,g);
end
set(fhndl,'UserData',f);
ezplot(f,x,figf)
set(findobj(figp,'tag','Sf'),'string',[blanks char(f)]);
end
%%%%%%%%%%%%%%%%%%%%%%%%%% Callback for F's edit text box.
case 'Sfcallback'
figp = findobj(0,'tag','figp');
f = sym(get(gco,'string'));
fhndl = findobj(figp,'tag','fobj');
set(fhndl,'UserData',f);
x = get(findobj(figp,'tag','xstr'),'UserData');
figf = findobj(0,'tag','figf');
ezplot(f,x,figf)
%%%%%%%%%%%%%%%%%%%%%%%%%% Callback for G's edit text box.
case 'Sgcallback'
figp = findobj(0,'tag','figp');
g = sym(get(gco,'string'));
ghndl = findobj(figp,'tag','gobj');
set(ghndl,'UserData',g);
x = get(findobj(figp,'tag','xstr'),'UserData');
figg = findobj(0,'tag','figg');
ezplot(g,x,figg)
%%%%%%%%%%%%%%%%%%%%%%%%%% Callback for A's edit text box.
case 'Sacallback'
a = sym(get(gco,'String'));
set(findobj(gcf,'tag','aobj'),'UserData',a);
%%%%%%%%%%%%%%%%%%%%%%%%%% Callback for X's edit text box.
case 'Sxcallback'
figp = findobj(0,'tag','figp');
x = get(gco,'String');
% add brackets if needed
if isempty(x=='['),
x = ['[' x ']'];
blanks = ' ';
set(gco,'string',[blanks x]),
end;
set(findobj(figp,'tag','xstr'),'UserData',x);
fhndl = findobj(figp,'tag','fobj');
ghndl = findobj(figp,'tag','gobj');
f = get(fhndl,'UserData');
g = get(ghndl,'UserData');
a = get(findobj(figp,'tag','aobj'),'UserData');
figf = findobj(0,'tag','figf');
figg = findobj(0,'tag','figg');
ezplot(f,x,figf)
ezplot(g,x,figg)
%%%%%%%%%%%%%%%%%%%%%%%%%% Callback for Insert button.
case 'Insert'
f = get(findobj(gcf,'tag','fobj'),'UserData');
x = get(findobj(gcf,'tag','xstr'),'UserData');
fxlist = get(gcf,'UserData');
fxlist = str2mat(fxlist,[char(f) '; ' x]);
set(gcf,'UserData',fxlist);
%%%%%%%%%%%%%%%%%%%%%%%%%% Callback for Cycle button.
case 'Cycle'
% Get variables.
figp = gcf;
figf = findobj(0,'tag','figf');
fxlist = get(figp,'UserData');
fx = fxlist(1,:);
fx(find(fx==' ')) = [];
k = find(fx == ';');
fstr = fx(1:k-1); f = sym(fstr);
set(findobj(figp,'tag','fobj'),'UserData',f);
x = fx(k+1:length(fx));
set(findobj(figp,'tag','xstr'),'UserData',x);
blanks = ' ';
set(findobj(figp,'tag','Sx'),'string',[blanks x]);
set(findobj(figp,'tag','Sf'),'string',[blanks fstr]);
ezplot(f,x,figf);
k = [2:size(fxlist,1),1];
fxlist = fxlist(k,:);
set(figp,'UserData',fxlist);
%%%%%%%%%%%%%%%%%%%%%%%%%% Callback for Delete button.
case 'Delete'
% Get variables.
figp = gcf;
f = get(findobj(figp,'tag','fobj'),'UserData');
x = get(findobj(figp,'tag','xstr'),'UserData');
fxlist = get(figp,'UserData');
fx = [char(f) ';' x];
fx(find(fx==' ')) = [];
for k = 1:size(fxlist,1),
element = fxlist(k,:);
element(find(element==' ')) = [];
if strcmp(fx,element)
fxlist(k,:) = [];
break
end
end;
if isempty(fxlist), fxlist = '0-0; [0,1]'; end
set(figp,'UserData',fxlist);
%%%%%%%%%%%%%%%%%%%%%%%%%% Callback for Reset button.
case 'Reset'
blanks = ' ';
% Get variables.
figp = gcf;
figf = findobj(0,'tag','figf');
figg = findobj(0,'tag','figg');
init = get(findobj(figp,'tag','reset'),'UserData');
set(findobj(figp,'tag','fobj'),'UserData',sym(init.f));
set(findobj(figp,'tag','Sf'),'String',[blanks init.f]);
ezplot(sym(init.f),init.x,figf);
set(findobj(figp,'tag','gobj'),'UserData',sym(init.g));
set(findobj(figp,'tag','Sg'),'String',[blanks init.g]);
ezplot(sym(init.g),init.x,figg);
set(findobj(figp,'tag','xstr'),'UserData',init.x);
set(findobj(figp,'tag','Sx'),'string',[blanks init.x]);
set(findobj(figp,'tag','aobj'),'UserData',sym(init.a));
set(findobj(figp,'tag','Sa'),'string',[blanks init.a]);
set(figp,'UserData',init.l);
% Reset all buttons to default bkgd color.
set(findobj(figp,'Style','pushbutton'),'BackgroundColor','default');
%%%%%%%%%%%%%%%%%%%%%%%%%% Callback for Close button.
case 'close'
close(findobj(0,'tag','figf'));
close(findobj(0,'tag','figg'));
close(findobj(0,'tag','figp'));
%%%%%%%%%%%%%%%%%%%%%%%%%% Callback for Demo button.
case 'Demo'
% "B" is the vector of button handles in the control panel.
% "prog" is a "program" consisting of button codes.
prog = {'Reset','f/a','int f','f + g','1/f', ...
'int f','finv','int f','df/dx','num f'};
B = findobj(gcf,'Style','pushbutton');
for k = 1: length(prog)
currB = findobj(B,'String',prog{k});
set(currB,'BackgroundColor','white');
eval(get(currB,'Callback'));
pause(1)
set(currB,'BackgroundColor','default');
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
end % switch statement for callbacks
end % end of FUNTOOL

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