[37] | 1 | function y = power(x,d) |
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| 2 | %POWER (overloaded) |
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| 3 | |
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| 4 | % Author Johan Löfberg |
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| 5 | % $Id: power.m,v 1.1 2006/08/10 18:00:22 joloef Exp $ |
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| 6 | |
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| 7 | |
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| 8 | % Sanity check |
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| 9 | if prod(size(x))==1 & (prod(size(d))>1) |
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| 10 | x = x.*ones(size(d)); |
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| 11 | end |
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| 12 | if prod(size(d))>1 |
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| 13 | if any(size(d)~=size(x)) |
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| 14 | error('Matrix dimensions must agree.'); |
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| 15 | end |
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| 16 | else |
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| 17 | d = ones(x.dim(1),x.dim(2))*d; |
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| 18 | end |
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| 19 | |
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| 20 | % Trivial cases |
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| 21 | if all(all(d==0)) |
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| 22 | if x.dim(1)~=x.dim(2) |
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| 23 | error('Matrix must be square.') |
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| 24 | end |
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| 25 | y = eye(x.dim(1),x.dim(2)).^0; |
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| 26 | return |
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| 27 | end |
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| 28 | if all(all(d==1)) |
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| 29 | y = x; |
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| 30 | return |
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| 31 | end |
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| 32 | |
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| 33 | % Fractional, negative or different powers are |
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| 34 | % treated less efficiently using simple code. |
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| 35 | fractional = any(any((ceil(d)-d>0))); |
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| 36 | negative = any(any(d<0)); |
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| 37 | different = ~all(all(d==d(1))); |
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| 38 | if fractional | negative | different |
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| 39 | if x.dim(1)>1 | x.dim(2)>1 |
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| 40 | [n,m] = size(x); |
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| 41 | y = []; |
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| 42 | for i = 1:n % FIX : Vectorize! |
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| 43 | temp = []; |
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| 44 | for j = 1:m |
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| 45 | temp = [temp extsubsref(x,i,j).^d(i,j)]; |
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| 46 | end |
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| 47 | y = [y;temp]; |
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| 48 | end |
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| 49 | return |
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| 50 | else |
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| 51 | base = getbase(x); |
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| 52 | if isequal(base,[0 1]) |
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| 53 | mt = yalmip('monomtable'); |
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| 54 | var = getvariables(x); |
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| 55 | previous_var = find((mt(:,var)==d) & (sum(mt~=0,2)==1)); |
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| 56 | if isempty(previous_var) |
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| 57 | mt(end+1,:) = mt(getvariables(x),:)*d; |
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| 58 | yalmip('setmonomtable',mt); |
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| 59 | y = recover(size(mt,1)); |
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| 60 | else |
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| 61 | y = recover(previous_var); |
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| 62 | end |
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| 63 | elseif (size(base,2) == 2) & base(1)==0 |
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| 64 | % Something like a*t^-d |
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| 65 | y = base(2)^d*recover(getvariables(x))^d; |
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| 66 | else |
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| 67 | error('Only unit scalars can have negative or non-integer powers.'); |
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| 68 | end |
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| 69 | end |
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| 70 | return |
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| 71 | end |
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| 72 | |
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| 73 | % Back to scalar power... |
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| 74 | d = d(1,1); |
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| 75 | if x.dim(1)>1 | x.dim(2)>1 |
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| 76 | switch d |
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| 77 | case 0 |
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| 78 | y = 1; |
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| 79 | case 1 |
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| 80 | y = x; |
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| 81 | otherwise |
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| 82 | y = x.*power(x,d-1); |
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| 83 | end |
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| 84 | else |
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| 85 | base = getbase(x); |
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| 86 | if isequal(base,[0 1]) |
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| 87 | mt = yalmip('monomtable'); |
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| 88 | var = getvariables(x); |
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| 89 | previous_var = find((mt(:,var)==d) & (sum(mt~=0,2)==1)); |
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| 90 | if isempty(previous_var) |
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| 91 | mt(end+1,:) = mt(getvariables(x),:)*d; |
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| 92 | yalmip('setmonomtable',mt); |
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| 93 | y = x; |
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| 94 | y.lmi_variables = size(mt,1); |
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| 95 | else |
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| 96 | y = x; |
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| 97 | y.lmi_variables = previous_var; |
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| 98 | end |
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| 99 | else |
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| 100 | switch d |
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| 101 | case 0 |
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| 102 | y = 1; |
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| 103 | case 1 |
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| 104 | y = x; |
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| 105 | otherwise |
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| 106 | y = x.*power(x,d-1); |
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| 107 | end |
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| 108 | end |
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| 109 | end |
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