228 lines
7.0 KiB
Matlab
Executable File
228 lines
7.0 KiB
Matlab
Executable File
function new_x = monolist(x,dmax,dmin)
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% MONOLIST Generate monomials
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%
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% y = MONOLIST(x,dmax,dmin)
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%
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% Returns the monomials [1 x(1) x(1)^2 ... x(1)^dmax(1) x(2) x(1)x(2) etc...]
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%
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% >>sdpvar x y z
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% >>sdisplay(monolist([x y z],4))
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%
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% Input
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% x : Vector with SDPVAR variables
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% dmax : Integers > 0
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%
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% See also POLYNOMIAL, DEGREE
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% Flatten
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x = reshape(x,1,length(x));
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x_orig = x;
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if nargin == 3
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if length(dmin)>1 || any(dmin > dmax) || ~isequal(dmin,fix(dmin))
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error('dmin has to be an integer scalar larger than dmax');
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end
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elseif nargin == 2
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dmin = 0;
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end
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if (length(dmax)==1 | all(dmax(1)==dmax)) & islinear(x) & ~isa(x,'ncvar')
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dmax = dmax(1);
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% Powers in monomials
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powers = monpowers(length(x),dmax);
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powers = powers(find(sum(powers,2)>=dmin),:);
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% Use fast method for x^alpha
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if isequal(getbase(x),[zeros(length(x),1) eye(length(x))])
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new_x = recovermonoms(powers,x);
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return
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end
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% Monolist on dense vectors is currently extremely slow, but also
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% needed in some applications (stability analysis using SOS) For
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% performance issue, the code below is hard-coded for special cases
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% FIX : Urgent, find underlying indexing...
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% Vectorize quadratic and quadrtic case
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if dmax==2 & length(x)>1
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V=x.'*[1 x];
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ind=funkyindicies(length(x));
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new_x = [1 V(ind(:)).'].';
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return
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elseif (length(x)==4 & dmax==6)
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ind =[ 1 2 3 4 5 6 7 8,
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9 10 11 12 13 14 15 16,
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17 18 19 20 21 22 23 24,
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25 26 27 28 29 30 31 32,
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33 34 49 50 51 52 86 53,
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54 55 89 56 57 91 58 92,
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126 59 60 61 95 62 63 97,
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64 98 132 65 66 100 67 101,
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135 68 102 136 170 185 186 187,
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188 222 256 189 190 191 225 259,
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192 193 227 261 194 228 262 296,
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330 364 195 196 197 231 265 198,
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199 233 267 200 234 268 302 336,
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370 201 202 236 270 203 237 271,
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305 339 373 204 238 272 306 340,
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374 408 442 476 510 525 526 527,
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528 562 596 630 529 530 531 565,
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599 633 532 533 567 601 635 534,
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568 602 636 670 704 738 772 806,
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840 535 536 537 571 605 639 538,
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539 573 607 641 540 574 608 642,
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676 710 744 778 812 846 541 542,
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576 610 644 543 577 611 645 679,
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713 747 781 815 849 544 578 612,
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646 680 714 748 782 816 850 884,
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918 952 986 1020 1054 1088 1122 1156,
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1190 0 0 0 0 0 0 0];
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ind = ind';
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ind = ind(find(ind));
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v=monolist(x,3);
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V=v(2:end)*v.';
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new_x = [1;V(ind(:))];
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return
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elseif dmax==4 & (1<=length(x)) & length(x)<=4 %& length(x)>1
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v=monolist(x,2);
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V=v(2:end)*v.';
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% Cone to generate indicies
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%p = sdpvar(n,1);
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%v = monolist(p,2);
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%V = v(2:end)*v';V=V(:);
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%m = monolist(p,4)
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%ind = [];
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%for i = 2:length(m)
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% ind = [ind min(find(~any(V-m(i))))];
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%end
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switch length(x)
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case 1
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new_x = [1; V([1 2 4 6]')];
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return
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case 2
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new_x = [1;V([1 2 3 4 5 8 9 10 15 18 19 20 25 30]')];
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return;
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case 3
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new_x=[1;V([1 2 3 4 5 6 7 8 9 13 14 15 24 16 17 26 18 27 36 40 41 42 51 60 43 44 53 62 45 54 63 72 81 90]')];
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return
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case 4
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new_x=[1;V([ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 19 20 21 35 22 23 37 24 38 52 25 26 40 27 41 55 28 42 56 70 75 76 77 91 105 78 79 93 107 80 94 108 122 136 150 81 82 96 110 83 97 111 125 139 153 84 98 112 126 140 154 168 182 196 210]')];
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return
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otherwise
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end
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end
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% Na, we have things like (c'x)^alpha
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% precalc x^p
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for i = 1:length(x)
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temp = x(i);
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precalc{i,1} = temp;
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for j = 2:1:dmax
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temp = temp*x(i);
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precalc{i,j} = temp;
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end
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end
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new_x = [];
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for i = 1:size(powers,1) % All monomials
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temp = 1;
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for j = 1:size(powers,2) % All variables
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if powers(i,j)>0
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temp = temp*precalc{j,powers(i,j)};
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end
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end
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new_x = [new_x temp];
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end
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else
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dmax = dmax(:)*ones(1,length(x_orig));
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x = [1 x];
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% Lame loop to generate all combinations
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new_x = 1;
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for j = 1:1:max(dmax)
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temp = [];
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for i = 1:length(x)
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temp = [temp x(i)*new_x];
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end
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new_x = temp;
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new_x = fliplr(unique(new_x));
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new_degrees = degree(new_x,x(2:end));
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remv = [];
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for i = 1:length(dmax);
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if new_degrees(i)>=dmax(i)
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x = recover(setdiff(getvariables(x),getvariables(x_orig(i))));
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x = [1;x(:)];
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remv = [remv i];
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end
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end
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dmax = dmax(setdiff(1:length(dmax),remv));
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end
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end
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new_x = reshape(new_x(:),length(new_x),1);
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if dmin > 0
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for i = 1:length(new_x)
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if degree(new_x(i)) < dmin
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keep(i) = 0;
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else
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keep(i) = 1;
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end
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end
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if any(keep==0)
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new_x = new_x(find(keep));
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end
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end
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function ind = funkyindicies(n)
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M=reshape(1:n*(n+1),n,n+1);
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ind = M(:,1)';
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for i = 1:n
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ind = [ind M(i,2:i+1)];
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end
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