312 lines
9.8 KiB
Mathematica
312 lines
9.8 KiB
Mathematica
|
function symb_pvec = sdisplay(pvec,precision)
|
||
|
|
%SDISPLAY Symbolic display of SDPVAR expression
|
||
|
|
%
|
||
|
|
% As variables in YALMIP do not have any actual names internally, the
|
||
|
|
% command is not guaranteed to recover the variable names you use in the
|
||
|
|
% work-space correctly. It tries to figure out the names of the variables
|
||
|
|
% by searching in the work-space for variables involving the same variable
|
||
|
|
% indicies, but this can fails in many instances.
|
||
|
|
%
|
||
|
|
% EXAMPLES
|
||
|
|
% sdpvar x y
|
||
|
|
% sdisplay(x^2+y^2)
|
||
|
|
% ans =
|
||
|
|
% 'x^2+y^2'
|
||
|
|
%
|
||
|
|
% Optionally, we can supply an option to round the data to N decimal digits
|
||
|
|
%
|
||
|
|
% sdisplay(pi*x1^2,4)
|
||
|
|
% ans = '3.1416*x^2'
|
||
|
|
|
||
|
|
if nargin < 2
|
||
|
|
precision = inf;
|
||
|
|
end
|
||
|
|
|
||
|
|
% Support displaying non-sdpvar input
|
||
|
|
if ~isa(pvec,'sdpvar')
|
||
|
|
for r1=1:size(pvec,1)
|
||
|
|
for r2=1:size(pvec,2)
|
||
|
|
p = pvec(r1,r2);
|
||
|
|
if isa(p,'double')
|
||
|
|
symb_pvec{r1,r2} = num2str2(p,precision);
|
||
|
|
else
|
||
|
|
symb_pvec{r1,r2} = p;
|
||
|
|
end
|
||
|
|
end
|
||
|
|
end
|
||
|
|
if prod(size(symb_pvec))==1 & nargout==0
|
||
|
|
display(symb_pvec{1,1});
|
||
|
|
clear symb_pvec
|
||
|
|
end
|
||
|
|
return;
|
||
|
|
end
|
||
|
|
|
||
|
|
% First, some boooring stuff. we need to
|
||
|
|
% figure out the symbolic names and connect
|
||
|
|
% these names to YALMIPs variable indicies
|
||
|
|
W = evalin('caller','whos');
|
||
|
|
|
||
|
|
% First, sort the variables available in the work-space based
|
||
|
|
% on the creation. Early creation means it is more likely the
|
||
|
|
% relevant variable to display
|
||
|
|
createTime = [];
|
||
|
|
for i = 1:size(W,1)
|
||
|
|
if strcmp(W(i).class,'sdpvar') || strcmp(W(i).class,'ncvar')
|
||
|
|
keep(i) = 1;
|
||
|
|
z = evalin('caller',['struct(' W(i).name ').extra.createTime;']);
|
||
|
|
createTime = [createTime z];
|
||
|
|
else
|
||
|
|
keep(i) = 0;
|
||
|
|
end
|
||
|
|
end
|
||
|
|
W = W(find(keep));
|
||
|
|
[sorted,index] = sort(createTime);
|
||
|
|
W = W(index);
|
||
|
|
|
||
|
|
global_LinearVariables = depends(pvec);
|
||
|
|
global_x = recover(global_LinearVariables);
|
||
|
|
[global_exponent_p,global_ordered_list] = exponents(pvec,global_x);
|
||
|
|
global_exponent_p = full(global_exponent_p);
|
||
|
|
global_names = cell(length(global_x),1);
|
||
|
|
|
||
|
|
for i = 1:size(W,1)
|
||
|
|
if strcmp(W(i).class,'sdpvar') || strcmp(W(i).class,'ncvar')
|
||
|
|
% Get the SDPVAR variable
|
||
|
|
thevars = evalin('caller',W(i).name);
|
||
|
|
|
||
|
|
% Distinguish 4 cases
|
||
|
|
% 1: Sclalar varible x
|
||
|
|
% 2: Vector variable x(i)
|
||
|
|
% 3: Matrix variable x(i,j)
|
||
|
|
% 4: Variable not really defined
|
||
|
|
if is(thevars,'scalar') && is(thevars,'linear') && length(getvariables(thevars))==1 & isequal(getbase(thevars),[0 1])
|
||
|
|
index_in_p = find(ismember(global_LinearVariables,getvariables(thevars)));
|
||
|
|
|
||
|
|
if ~isempty(index_in_p)
|
||
|
|
already = ~isempty(global_names{index_in_p});
|
||
|
|
if already
|
||
|
|
already = (isempty(strfind(global_names{index_in_p},'internal')) | isempty(strfind(global_names{index_in_p},'ans')));
|
||
|
|
end
|
||
|
|
else
|
||
|
|
already = 0;
|
||
|
|
end
|
||
|
|
|
||
|
|
if ~isempty(index_in_p) & ~already
|
||
|
|
% Case 1
|
||
|
|
global_names{index_in_p}=W(i).name;
|
||
|
|
end
|
||
|
|
elseif is(thevars,'lpcone')
|
||
|
|
|
||
|
|
if size(thevars,1)==size(thevars,2)
|
||
|
|
% Case 2
|
||
|
|
vars = getvariables(thevars);
|
||
|
|
indicies = find(ismember(vars,global_LinearVariables));
|
||
|
|
for ii = indicies
|
||
|
|
index_in_p = find(ismember(global_LinearVariables,vars(ii)));
|
||
|
|
|
||
|
|
if ~isempty(index_in_p)
|
||
|
|
already = ~isempty(global_names{index_in_p});
|
||
|
|
if already
|
||
|
|
already = (isempty(strfind(global_names{index_in_p},'internal')) | isempty(strfind(global_names{index_in_p},'ans')));
|
||
|
|
end
|
||
|
|
else
|
||
|
|
already = 0;
|
||
|
|
end
|
||
|
|
|
||
|
|
if ~isempty(index_in_p) & ~already
|
||
|
|
B = reshape(getbasematrix(thevars,vars(ii)),size(thevars,1),size(thevars,2));
|
||
|
|
[ix,jx,kx] = find(B);
|
||
|
|
ix=ix(1);
|
||
|
|
jx=jx(1);
|
||
|
|
global_names{index_in_p}=[W(i).name '(' num2str(ix) ',' num2str(jx) ')'];
|
||
|
|
end
|
||
|
|
end
|
||
|
|
|
||
|
|
else
|
||
|
|
% Case 3
|
||
|
|
vars = getvariables(thevars);
|
||
|
|
indicies = find(ismember(vars,global_LinearVariables));
|
||
|
|
for ii = indicies
|
||
|
|
index_in_p = find(ismember(global_LinearVariables,vars(ii)));
|
||
|
|
|
||
|
|
if ~isempty(index_in_p)
|
||
|
|
already = ~isempty(global_names{index_in_p});
|
||
|
|
if already
|
||
|
|
already = (isempty(strfind(global_names{index_in_p},'internal')) | isempty(strfind(global_names{index_in_p},'ans')));
|
||
|
|
end
|
||
|
|
else
|
||
|
|
already = 0;
|
||
|
|
end
|
||
|
|
|
||
|
|
if ~isempty(index_in_p) & ~already
|
||
|
|
global_names{index_in_p}=[W(i).name '(' num2str(ii) ')'];
|
||
|
|
end
|
||
|
|
end
|
||
|
|
end
|
||
|
|
|
||
|
|
elseif is(thevars,'sdpcone')
|
||
|
|
% Case 3
|
||
|
|
vars = getvariables(thevars);
|
||
|
|
indicies = find(ismember(vars,global_LinearVariables));
|
||
|
|
for ii = indicies
|
||
|
|
index_in_p = find(ismember(global_LinearVariables,vars(ii)));
|
||
|
|
if ~isempty(index_in_p)
|
||
|
|
already = ~isempty(global_names{index_in_p});
|
||
|
|
if already
|
||
|
|
already = ~strfind(global_names{index_in_p},'internal');
|
||
|
|
end
|
||
|
|
else
|
||
|
|
already = 0;
|
||
|
|
end
|
||
|
|
|
||
|
|
if ~isempty(index_in_p) & ~already
|
||
|
|
B = reshape(getbasematrix(thevars,vars(ii)),size(thevars,1),size(thevars,2));
|
||
|
|
[ix,jx,kx] = find(B);
|
||
|
|
ix=ix(1);
|
||
|
|
jx=jx(1);
|
||
|
|
global_names{index_in_p}=[W(i).name '(' num2str(ix) ',' num2str(jx) ')'];
|
||
|
|
end
|
||
|
|
end
|
||
|
|
|
||
|
|
else
|
||
|
|
% Case 4
|
||
|
|
vars = getvariables(thevars);
|
||
|
|
indicies = find(ismember(vars,global_LinearVariables));
|
||
|
|
|
||
|
|
for i = indicies
|
||
|
|
index_in_p = find(ismember(global_LinearVariables,vars(i)));
|
||
|
|
if ~isempty(index_in_p) & isempty(global_names{index_in_p})
|
||
|
|
global_names{index_in_p}=['internal(' num2str(vars(i)) ')'];
|
||
|
|
end
|
||
|
|
end
|
||
|
|
|
||
|
|
end
|
||
|
|
end
|
||
|
|
end
|
||
|
|
|
||
|
|
for pi = 1:size(pvec,1)
|
||
|
|
for pj = 1:size(pvec,2)
|
||
|
|
p = pvec(pi,pj);
|
||
|
|
if isa(p,'double')
|
||
|
|
symb_p = num2str2(p,precision);
|
||
|
|
else
|
||
|
|
symb_p = createSymbolicExpression(p,global_LinearVariables,global_names,precision);
|
||
|
|
end
|
||
|
|
symb_pvec{pi,pj} = symb_p;
|
||
|
|
end
|
||
|
|
end
|
||
|
|
|
||
|
|
if prod(size(symb_pvec))==1 & nargout==0
|
||
|
|
display(symb_pvec{1,1});
|
||
|
|
clear symb_pvec
|
||
|
|
end
|
||
|
|
|
||
|
|
function symb_p = createSymbolicExpression(p,global_LinearVariables,global_names,precision)
|
||
|
|
LinearVariables = depends(p);
|
||
|
|
x = recover(LinearVariables);
|
||
|
|
[exponent_p,ordered_list] = exponents(p,x);
|
||
|
|
exponent_p = full(exponent_p);
|
||
|
|
[~,map] = ismember(LinearVariables,global_LinearVariables);
|
||
|
|
names = {global_names{map}};
|
||
|
|
|
||
|
|
% Remove 0 constant
|
||
|
|
symb_p = '';
|
||
|
|
if size(ordered_list,1)>0
|
||
|
|
nummonoms = size(ordered_list,1);
|
||
|
|
if full(getbasematrix(p,0)) ~= 0
|
||
|
|
symb_p = num2str2(full(getbasematrix(p,0)),precision);
|
||
|
|
end
|
||
|
|
elseif all(exponent_p(1,:)==0)
|
||
|
|
symb_p = num2str2(full(getbasematrix(p,0)),precision);
|
||
|
|
exponent_p = exponent_p(2:end,:);
|
||
|
|
nummonoms = size(exponent_p,1);
|
||
|
|
else
|
||
|
|
nummonoms = size(exponent_p,1);
|
||
|
|
end
|
||
|
|
|
||
|
|
% Loop through all monomial terms
|
||
|
|
for i = 1:nummonoms
|
||
|
|
coeff = full(getbasematrixwithoutcheck(p,i));
|
||
|
|
switch coeff
|
||
|
|
case 1
|
||
|
|
coeff='+';
|
||
|
|
case -1
|
||
|
|
coeff = '-';
|
||
|
|
otherwise
|
||
|
|
if isreal(coeff)
|
||
|
|
if coeff >0
|
||
|
|
coeff = ['+' num2str2(coeff,precision)];
|
||
|
|
else
|
||
|
|
coeff=[num2str2(coeff,precision)];
|
||
|
|
end
|
||
|
|
else
|
||
|
|
coeff = ['+' '(' num2str2(coeff,precision) ')' ];
|
||
|
|
end
|
||
|
|
end
|
||
|
|
if isempty(ordered_list)
|
||
|
|
symb_p = [symb_p coeff symbmonom(names,exponent_p(i,:))];
|
||
|
|
else
|
||
|
|
symb_p = [symb_p coeff symbmonom_noncommuting(names,ordered_list(i,:))];
|
||
|
|
end
|
||
|
|
end
|
||
|
|
% Clean up some left overs, lazy coding...
|
||
|
|
symb_p = strrep(symb_p,'+*','+');
|
||
|
|
symb_p = strrep(symb_p,'-*','-');
|
||
|
|
if symb_p(1)=='+'
|
||
|
|
symb_p = symb_p(2:end);
|
||
|
|
end
|
||
|
|
if symb_p(1)=='*'
|
||
|
|
symb_p = symb_p(2:end);
|
||
|
|
end
|
||
|
|
|
||
|
|
|
||
|
|
function s = symbmonom(names,monom)
|
||
|
|
s = '';
|
||
|
|
for j = 1:length(monom)
|
||
|
|
if abs( monom(j))>0
|
||
|
|
if isempty(names{j})
|
||
|
|
names{j} = ['internal(' num2str(j) ')'];
|
||
|
|
end
|
||
|
|
s = [s '*' names{j}];
|
||
|
|
if monom(j)~=1
|
||
|
|
s = [s '^' num2str(monom(j))];
|
||
|
|
end
|
||
|
|
end
|
||
|
|
end
|
||
|
|
|
||
|
|
function s = symbmonom_noncommuting(names,monom)
|
||
|
|
s = '';
|
||
|
|
j = 1;
|
||
|
|
while j <= length(monom)
|
||
|
|
if abs( monom(j))>0
|
||
|
|
if isempty(names{monom(j)})
|
||
|
|
names{monom(j)} = ['internal(' num2str(j) ')'];
|
||
|
|
end
|
||
|
|
s = [s '*' names{monom(j)}];
|
||
|
|
power = 1;
|
||
|
|
k = j;
|
||
|
|
while j<length(monom) & monom(j) == monom(j+1)
|
||
|
|
power = power + 1;
|
||
|
|
j = j + 1;
|
||
|
|
%if j == (length(monom)-1)
|
||
|
|
% j = 5;
|
||
|
|
%end
|
||
|
|
end
|
||
|
|
if power~=1
|
||
|
|
s = [s '^' num2str(power)];
|
||
|
|
end
|
||
|
|
end
|
||
|
|
j = j + 1;
|
||
|
|
end
|
||
|
|
|
||
|
|
function s = num2str2(x,precision)
|
||
|
|
if isinf(precision)
|
||
|
|
s = sprintf('%.12g',x);
|
||
|
|
else
|
||
|
|
s = sprintf('%.12g',round(x*10^precision)/10^precision);
|
||
|
|
end
|
||
|
|
s(s==10)=[];
|
||
|
|
s(s==32)=[];
|
||
|
|
|
||
|
|
|