参考一下taylor公式的源代码。也许有所帮助。
function H = taylortool(varargin)
%TAYLORTOOL A Taylor series calculator.
%
% TAYLORTOOL is an interactive Taylor series calculator that
% graphs a function f against the Nth partial sum of its
% Taylor series over [-2*pi,2*pi]. The default values for f
% and N are x*cos(x) and 7, respectively.
%
% TAYLORTOOL(f) Graphs the function f versus the Nth
% partial sum of the Taylor series for f over [-2*pi,2*pi].
% The default value for N is 7.
% Note that f must be a quoted string.
%
% Example: taylortool('sin(tan(x)) - tan(sin(x))')
%
% See also, FUNTOOL
% Copyright 1993-2002 The MathWorks, Inc.
% $Revision: 1.7 $
% P. J. Costa
% Define the set of actions.
S = {'initialize','plot','Reset','Help','Increment','Close'};
switch nargin
case 0
ud.f = sym('x*cos(x)');
action = 'initialize';
case 1
ud = get(gcbf,'Userdata');
% taylortool(f)
if isempty(intersect(varargin{1},S))
ud.f = sym(varargin{1});
action = 'initialize';
% taylortool('plot')
elseif ~isempty(intersect(varargin{1},S)) & isempty(ud)
ud.f = sym('x*cos(x)');
action = varargin{1};
% taylortool('plot') & a function is already in Feditbox.
elseif ~isempty(intersect(varargin{1},S)) & ~isempty(ud)
ud.f = sym(get(ud.Handle.Feditbox,'String'));
action = varargin{1};
else
ud.f = sym('x*cos(x)');
action = 'initialize';
end
end
switch action
case 'initialize'
ud.N = 7; % N = order of the partial sum.
ud.a = 0; % a = center or basepoint of the series.
ud.D = [-2*pi,2*pi]; % Initial domain.
ud.t = taylor(ud.f,ud.N+1,ud.a);
fig = LocalOpenFig(ud);
taylorplot(ud.f,ud.N+1,ud.a,ud.D,fig);
set(fig,'HandleVisibility','CallBack');
case 'plot'
ud = get(gcbf,'Userdata');
try
ud.f = sym(get(ud.Handle.Feditbox,'String'));
catch
Errstr = [get(ud.Handle.Feditbox,'String') ...
' is not a valid symbolic object.'];
errordlg(Errstr);
set(ud.Handle.taylortext,'String',Errstr);
return
end
% f = sym(get(ud.Handle.Feditbox,'String'));
ud.N = str2double(get(ud.Handle.Neditbox,'String'));
Errstr = '';
if isnan(ud.N) | ~(floor(ud.N) == ud.N) | (ud.N < 0)
Errstr = 'N must be a non-negative integer.';
end
if ~isempty(Errstr)
errordlg(Errstr);
set(ud.Handle.taylortext,'String',Errstr);
return
end
% N = eval(get(ud.Handle.Neditbox,'String'));
try
ud.a = eval(get(ud.Handle.Aeditbox,'String'));
Errstr = '';
catch
Errstr = 'a must use floating point (double) number.';
end
if ~isempty(Errstr)
errordlg(Errstr);
set(ud.Handle.taylortext,'String',Errstr);
return
end
% a = eval(get(ud.Handle.Aeditbox,'String'));
try
ud.D(1) = eval(get(ud.Handle.Leditbox,'String'));
ud.D(2) = eval(get(ud.Handle.Reditbox,'String'));
Errstr = '';
catch
Errstr = ['The domain endpoints must be floating point' ...
'(double) numbers.'];
end
if ud.D(1) >= ud.D(2)
Errstr = 'The left endpoint must be less than the right endpoint.';
end
if ~isempty(Errstr)
errordlg(Errstr);
set(ud.Handle.taylortext,'String',Errstr);
return
end
set(gcbf,'Userdata',ud);
try
t = taylorplot(ud.f,ud.N+1,ud.a,ud.D,gcbf);
Errstr = '';
catch
Errstr = ['The function ' char(ud.f) ' does not have ' ...
'a Taylor series expansion about ' mat2str(ud.a) '.'];
end
if ~isempty(Errstr)
errordlg(Errstr);
set(ud.Handle.taylortext,'String',Errstr);
return
end
set(ud.Handle.taylortext,'String',texlabel(slen(char(t)),70));
case 'Increment'
ud = get(gcbf,'Userdata');
tag = get(gcbo,'Tag');
N = str2num(get(ud.Handle.Neditbox,'String'));
switch tag
case 'Nup'
N = N + 1;
case 'Ndown'
N = N - 1;
otherwise
N = N;
end
set(ud.Handle.Neditbox,'String',num2str(N) );
taylortool('plot')
case 'Help'
MyHelp;
case 'Reset'
ud = get(gcbf,'Userdata');
% Keep the current function . . .
set(ud.Handle.Feditbox,'String',char(ud.f));
% . . . but reset a, N, D, and t to their initial states.
ud.N = 7; % N = order of the partial sum.
ud.a = 0; % a = center or basepoint of the series.
ud.D = [-2*pi,2*pi]; % Initial domain.
ud.t = taylor(ud.f,ud.N+1,ud.a); % Taylor series.
set(ud.Handle.Aeditbox,'String',num2str(ud.a) );
set(ud.Handle.Neditbox,'String',num2str(ud.N) );
set(ud.Handle.Leditbox,'String',char(sym(ud.D(1))) );
set(ud.Handle.Reditbox,'String',char(sym(ud.D(2))) );
set(ud.Handle.taylortext,'String',texlabel(ud.t))
taylorplot(ud.f,ud.N+1,ud.a,ud.D,gcbf);
set(gcbf,'HandleVisibility','CallBack');
set(gcbf,'Userdata',ud);
case 'Close'
close;
end
if nargout > 0, H = fig; end
%---------------------------%
function H = LocalOpenFig(ud)
%LOCALOPENFIG Opens the GUI for the Taylor Series Tool.
% LOCALOPENFIG(ud.f,ud.N,ud.a,ud.D,ud.t) sets the function f = f(x), the
% number of terms in the Talyor partial sum N, the center
% or base point a, and the Taylor series t. The Domain over
% which the approximation will be plotted D.
%
% Example: LocalOpenFig('x*cos(x)',12,0,[-2*pi,2*pi],'x-1/2*x^3')
StdUnit = 'point';
StdColor = get(0,'DefaultUIcontrolBackgroundColor');
PointsPerPixel = 72/get(0,'ScreenPixelsPerInch');
h0 = figure('Color',[13/15 13/15 13/15], ...
'Units','points','name','Taylor Tool', ...
'number','off','IntegerHandle','off', ...
'Position',[150 100 520 420]*PointsPerPixel, ...
'Tag','Taylor Tool');
h1 = axes('Parent',h0, ...
'Units','points', ...
'CameraUpVector',[0 1 0], ...
'CameraUpVectorMode','manual', ...
'Color',[1 1 1], ...
'Position',[40 203 453 167]*PointsPerPixel, ...
'Tag','FigAxis', ...
'XColor',[0 0 0], ...
'YColor',[0 0 0], ...
'ZColor',[0 0 0]);
h1 = axes('Parent',h0, ...
'Units','points', ...
'Position',[28 125 464 54]*PointsPerPixel, ...
'HandleVisibility','off', ...
'box','on', ...
'xlim',[0,1],'ylim',[0,1], ...
'xtick',[],'ytick',[], ...
'color',[0.8,0.8,0.8], ...
'Tag','Tayframe');
h2 = text(0.01,0.5,'T_N(x) =','Parent',h1, ...
'Interpreter','tex', ...
'Tag','FrameText');
ud.Handle.taylortext = ...
text(0.1125,0.545,texlabel(slen(char(ud.t)),70),'Parent',h1, ...
'Interpreter','tex', ...
'Tag','taylortext');
h1 = uicontrol('Parent',h0, ...
'Units','points', ...
'HorizontalAlignment','left', ...
'Position',[28 94 32 20]*PointsPerPixel, ...
'BackGroundColor',[13/15 13/15 13/15], ...
'String','f(x) = ', ...
'Style','text', ...
'fontsize',12,...
'Tag','Function');
ud.Handle.Feditbox = ...
uicontrol('Parent',h0, ...
'Units','points', ...
'BackgroundColor',[1 1 1], ...
'Callback','taylortool(''plot'');', ...
'HorizontalAlignment','left', ...
'Position',[69 91 423 24]*PointsPerPixel, ...
'String',char(ud.f), ...
'Style','edit', ...
'fontsize',12,...
'Tag','Feditbox');
h1 = uicontrol('Parent',h0, ...
'Units','points', ...
'HorizontalAlignment','left', ...
'Position',[161 59 25 20]*PointsPerPixel, ...
'BackGroundColor',[13/15 13/15 13/15], ...
'String','a = ', ...
'Style','text', ...
'fontsize',12,...
'Tag','Basepoint');
ud.Handle.Aeditbox = ...
uicontrol('Parent',h0, ...
'Units','points', ...
'BackgroundColor',[1 1 1], ...
'Callback','taylortool(''plot'');', ...
'HorizontalAlignment','left', ...
'Position',[188 57 70 24]*PointsPerPixel, ...
'String',ud.a, ...
'fontsize',12, ...
'Style','edit', ...
'Tag','Aeditbox');
h1 = uicontrol('Parent',h0, ...
'Units','points', ...
'HorizontalAlignment','left', ...
'Position',[28 40 25 20]*PointsPerPixel, ...
'BackGroundColor',[13/15 13/15 13/15], ...
'String','N = ', ...
'Style','text', ...
'fontsize',12, ...
'Tag','Number');
ud.Handle.Neditbox = ...
uicontrol('Parent',h0, ...
'Units','points', ...
'BackgroundColor',[1 1 1], ...
'Callback','taylortool(''plot'');', ...
'HorizontalAlignment','left', ...
'Position',[54 38 44 23]*PointsPerPixel, ...
'String',ud.N, ...
'Style','edit', ...
'fontsize',12, ...
'Tag','Neditbox');
ud.Handle.Leditbox = ...
uicontrol('Parent',h0, ...
'Units','points', ...
'BackgroundColor',[1 1 1], ...
'Callback','taylortool(''plot'');', ...
'HorizontalAlignment','left', ...
'Position',[309 57 70 24]*PointsPerPixel, ...
'String',char(sym(ud.D(1))), ...
'Style','edit', ...
'fontsize',12, ...
'Tag','Leditbox');
ud.Handle.Reditbox = ...
uicontrol('Parent',h0, ...
'Units','points', ...
'BackgroundColor',[1 1 1], ...
'Callback','taylortool(''plot'');', ...
'HorizontalAlignment','left', ...
'Position',[422 55.5 70 24]*PointsPerPixel, ...
'String',char(sym(ud.D(2))), ...
'Style','edit', ...
'fontsize',12, ...
'Tag','Reditbox');
h1 = uicontrol('Parent',h0, ...
'Units','points', ...
'Position',[385 59 32 20]*PointsPerPixel, ...
'BackGroundColor',[13/15 13/15 13/15], ...
'String',' < x < ', ...
'Style','text', ...
'fontsize',12, ...
'Tag','Domain');
h1 = uicontrol('Parent',h0, ...
'Units','points', ...
'Position',[315 19 60 25]*PointsPerPixel, ...
'Callback','taylortool(''Reset'');', ...
'String','Reset', ...
'Tag','Reset');
h1 = uicontrol('Parent',h0, ...
'Units','points', ...
'Position',[432 19 60 25]*PointsPerPixel, ...
'Callback','taylortool(''Close'');', ...
'String','Close', ...
'Tag','Close');
h1 = uicontrol('Parent',h0, ...
'Units','points', ...
'Position',[192 19 60 25]*PointsPerPixel, ...
'Callback','taylortool(''Help'');', ...
'String','Help', ...
'Tag','Help');
h1 = uicontrol('Parent',h0, ...
'Units','points', ...
'Position',[106 51 16 15]*PointsPerPixel, ...
'Callback','taylortool(''Increment'');', ...
'String','�,'Fontname','Courier', ...
'Tag','Nup');
h1 = uicontrol('Parent',h0, ...
'Units','points', ...
'Position',[106 31 16 15]*PointsPerPixel, ...
'Callback','taylortool(''Increment'');', ...
'String','�,'Fontname','Courier', ...
'Tag','Ndown');
Hui = findobj(gcf,'type','uicontrol');
Hax = findall(gcf,'type','axes');
set(Hui,'Units','normalized');
set(Hax,'Units','normalized');
set(h0,'UserData',ud);
if nargout > 0, H = h0; end
%----------------------------------%
function MyHelp
%MYHELP is the Window Help information for TAYLORTOOL.
Helpstr = {'TAYLORTOOL is a pedagogical utility designed to';
'help you understand how Taylor series are used to';
'approximate functions of a single variable. The';
'notation T (x) denotes the Nth partial sum of the';
' N ;'
'Taylor series for the function f(x) centered about'
'the point x = a. ';
' ';
'TAYLORTOOL(f) illustrates the relationship between the';
'function f(x), the number of terms N in the partial sum';
'T (x), and the point (x = a) about which the series is'
' N ';
'centered. Both f(x) and T (x) are plotted over a';
' N ';
'prescribed interval for x. ';
' ';
'The default values are f(x) = x*cos(x), a = 0; N = 7,';
'and -2*pi < x < 2*pi ';
' ';
'To change any value of f(x), N, a, or the limits';
'over which f(x) is plotted, change the entry in';
'the appropriate box and press the
'or
'of N by 1 by performing a mouse click on the �or �button,';
'respectively. ';};
helpwin(Helpstr,'taylortool');
%-------------------------
function c = plmin(s)
%PLMIN PLMIN(s) is true for + or - not inside parentheses.
p = cumsum((s == '(') - (s == ')'));
c = (s == '+' | s == '-') & (p == 0);
%----------------------------------%
function S = slen(S)
% SLEN Reduces the length of a Taylor series by removing
% terms until the string is less than 70 characters long.
%
% Example:
% S = ['1+x+1/2*x^2-1/8*x^4-1/15*x^5-1/240*x^6+1/90*x^7+' ...
% '31/5760*x^8+1/5670*x^9-2951/3628800*x^10-1/3150*x^11'];
% slen(S) returns
% 1+x+1/2*x^2-1/8*x^4-1/15*x^5-1/240*x^6+1/90*x^7+...-1/3150*x^11
B = plmin(S); % Determine where S has + or -.
B1 = find(B == 1);
S1 = S;
for j = 1:length(B1)-1
if length(S) < 70
return;
else
S = [S(1:B1(end-j)) '...' S1(B1(end):end)];
end
end
%----------------------------------%
function t = taylorplot(f,N,a,D,fig)
% TAYLORPLOT is the callback function that produces
% the plot for the Taylor GUI.
%
% TAYLORPLOT(f,N,a,D) plots a comparison of the
% function f(x) to the partial sum of order N of the Taylor series
% for f(x) about the basepoint a over the interval D = [xo,x1],
% in the figure window FIG. Here the partial sum of order N is,
% n
% d f n
% T_N(x) = sum( ---- (a) * (x - a) , n = 0 .. N )
% n
% dx
%
% Define a symbolic variable.
x = findsym(sym(f),1);
% Let N be the number of terms and a be the basepoint
% of the Taylor Approximant to f(x).
% Compute the first N terms of the Taylor series for f(x)
% about the basepoint a.
t = taylor(f,x,N,a);
% The functions f and t will be ploted over the interval
% [xo,x1];
ezplot(f,D,fig);
a = axis;
a(3:4) = 2*a(3:4);
hold on;
ezplot(t,D,fig);
axis(a);
xlabel(''); title('Taylor Series Approximation');
% Find the curves being plotted . . .
hT = findobj(gcf,'type','line');
% . . . and color them.
set(hT(1),'color','r','LineStyle',':','Linewidth',2.5); % red
set(hT(2),'color','b'); % blue
% Place a "map legend" in the upper right hand corner of the plot
% legend('Function','Taylor',1);
hold off;
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