gusucode.com > symbolic工具箱matlab源码程序 > symbolic/@symfun/symfun.m
classdef (InferiorClasses={?sym}) symfun < sym
%SYMFUN Symbolic function
% F = SYMFUN(FORMULA,INPUTS) returns a symbolic function
% with inputs INPUTS and body FORMULA. INPUTS must be a
% sym array of symbolic variables and FORMULA is a
% sym object expression.
%
% Symbolic functions can represent both abstract functions
% as well as functions with a definition. To represent
% an abstract function use a formula like 'f(x)'.
%
% The SYMS function and subscripted assignment provide a
% convenient syntax for defining symbolic functions.
%
% Examples:
% syms f x y
% f = symfun(x+y, [x y])
% f(1,2) % returns 3
%
% syms z(s,t)
% z(s,t) = s+t;
% f(s,t) - z(s,t) % returns 0
%
% See also SYMS, SYM/ARGNAMES, SYM/FORMULA, DSOLVE
% Copyright 2011-2015 The MathWorks, Inc.
properties (Access=private)
vars;
end
methods(Hidden,Static)
function [name, vars] = parseString(x)
% given a string f(arg1, arg2, .., argn)
% returns f as a string,
% and [arg1, ..., argn] as cell array of sym
pos = find(x=='(',1)-1;
if isempty(pos)
% no function call.
% The user must write sym('x') instead of 'x'
error(message('symbolic:symfun:SymExpected'));
end
name = x(1:pos);
closingPos = find(x==')', 1);
varnamelist = x(pos+2:closingPos-1);
reVarname = '[A-Za-z]\w*';
if ~isvarname(name) || sym.isMathematicalConstant(name)|| ...
isempty(closingPos) || closingPos < length(x) || ...
any(ismember('[{', x)) || ...
isempty(regexp(varnamelist,['^\s*' reVarname '\s*(,\s*' reVarname '\s*)*$'],'once'))
error(message('symbolic:sym:errmsg1'));
end
varnames = regexp(varnamelist, reVarname, 'match');
vars = cellfun(@sym,varnames,'UniformOutput',false);
end
end
methods
function y = symfun(x,inputs)
if isnumeric(x)
x = sym(x);
elseif ischar(x)
% string input must be of the form f(arg1, ..., argN)
[name, vars] = symfun.parseString(x);
x = feval(symengine, 'fp::apply', sym(name), vars{:});
elseif ~isa(x,'sym')
error(message('symbolic:symfun:SymExpected'));
end
y = y@sym(formula(x));
% check variables are simple names
y.vars = validateArgNames(inputs);
end
function y = argnames(x)
%ARGNAMES Symbolic function input variables
% ARGNAMES(F) returns a sym array [X1, X2, ... ] of symbolic
% variables for F(X1, X2, ...).
%
% Example
% syms f(x,y)
% argnames(f) % returns [x, y]
%
% See also SYMFUN/FORMULA
y = x.vars;
end
function y = formula(x)
%FORMULA Symbolic function formula body
% FORMULA(F) returns the definition of symbolic
% function F as a sym object expression.
%
% Examples:
% syms f(x,y)
% f(x,y) = x+y;
% formula(f) % returns x+y
%
% syms y(x)
% formula(y) % returns y(x)
%
% See also SYMFUN/ARGNAMES
y = sym(mupadmex(x.s,11));
end
function c = isequal(a,b,varargin)
%ISEQUAL Symbolic function isequal test.
% ISEQUAL(A,B) returns true iff A and B are identical.
if ~isa(a,'symfun') || ~isa(b,'symfun') || ~isequal(a.vars, b.vars)
c = false;
else
mupc = mupadmex('symobj::isequal', a.s, b.s, 0);
c = strcmp(mupc,'TRUE');
if c && nargin > 2
c = isequal(b,varargin{:});
end
end
end
function c = isequaln(a,b,varargin)
%ISEQUALN Symbolic function isequal test.
% ISEQUALN(A,B) returns true iff A and B are identical treating
% NaNs as equal.
if ~isa(a,'symfun') || ~isa(b,'symfun') || ~isequal(a.vars, b.vars)
c = false;
else
mupc = mupadmex('symobj::isequaln', a.s, b.s, 0);
c = strcmp(mupc,'TRUE');
if c && nargin > 2
c = isequaln(b,varargin{:});
end
end
end
end
methods (Hidden=true)
function Y = sym(X, ~, ~)
if nargin > 1
error(message('symbolic:symfun:NoAdditionalArguments'))
end
Y = X;
end
function delete(~)
end
function varargout = subsindex(varargin) %#ok<STOUT>
error(message('symbolic:symfun:subsindex'))
end
function B = subsref(A,S)
%SUBSREF Subscripted reference for a sym array.
% B = SUBSREF(A,S) is called for the syntax A(I). S is a structure array
% with the fields:
% type -- string containing '()' specifying the subscript type.
% Only parenthesis subscripting is allowed.
% subs -- Cell array or string containing the actual subscripts.
%
% See also SYM.
if builtin('numel',A) ~= 1, A = normalizesym(A); end
if length(S)>1
error(message('symbolic:sym:NestedIndex'));
end
if strcmp(S.type,'()')
Avars = A.vars;
inds = S.subs;
if length(inds) ~= length(Avars)
error(message('symbolic:symfun:subsref', length(Avars), length(inds)))
end
strs = cellfun(@ischar,inds);
if any(strcmp(inds(strs),':'))
error(message('symbolic:symfun:subsrefColon'))
end
B = feval(A,inds{:});
else
error(message('symbolic:symfun:Indexing'));
end
end
function C = privResolveOutput(C,A)
C = symfun(C, A.vars);
end
function C = privResolveOutputAndDelete(C,A,x)
if isa(A, 'symfun')
fargs = privsubsref(A.vars, logical(A.vars ~= x));
% if no variables are left, C remains a sym
if ~isempty(fargs)
C = symfun(C, fargs);
end
end
end
function argout = privResolveArgs(varargin)
sfun = [];
argout = varargin;
n = nargin;
for k=1:n
arg = varargin{k};
if isa(arg,'symfun')
sfun = arg;
break
end
end
fvars = sfun.vars;
for k=1:n
arg = varargin{k};
if isa(arg,'sym') && builtin('numel',arg) ~= 1
argout{k} = normalizesym(arg);
elseif ~isa(arg,'sym')
argout{k} = sym(arg);
end
if isa(arg,'symfun') && ~isequal(fvars,arg.vars)
error(message('symbolic:symfun:InputMatch'));
else
argout{k} = symfun(argout{k},fvars);
end
end
end
function varargout = end(varargin) %#ok<STOUT>
error(message('symbolic:symfun:EndNotImplemented'));
end
function c = cross(a,b,dim)
%CROSS Vector cross product of symbolic functions.
% The cross function of Core MATLAB needs to be
% overloaded for symfun objects, because it
% requires vectors of length 3. Symfuns, however,
% are scalar objects.
% Copyright 2014 The MathWorks, Inc.
narginchk(2,3);
if ~isa(a, 'sym') && ~isa(b, 'sym')
% there must be a dim argument
c = cross(a, b, double(dim));
return;
end
args = privResolveArgs(a,b);
if nargin == 2
c = cross(formula(args{1}), formula(args{2}));
else
c = cross(formula(args{1}), formula(args{2}), double(dim));
end
c = privResolveOutput(c, args{1});
end
end
end
function args = validateArgNames(args)
%validateArgNames When creating symfuns make sure the arguments are simple sym object names
% do not allow zero arguments
if ~isequal(class(args),'sym') || ~isvector(args) || isempty(args)
error(message('symbolic:symfun:VarsExpected'))
end
args = args(:).'; % maybe we don't really want to allow f([x;y])=x+y, but currently we do ...
args2 = unique(args);
if length(args2) ~= length(args)
error(message('symbolic:symfun:VarsExpected'))
end
for k=1:length(args)
arg = args(k);
if ~isvarname(char(arg)) || ...
~strcmp(mupadmex(['testtype(' charcmd(arg) ',Type::Indeterminate)'],0),'TRUE')
error(message('symbolic:symfun:VarsExpected'))
end
end
end