1 | function y = mpower(x,d) |
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2 | %MPOWER (overloaded) |
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3 | |
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4 | % Author Johan Löfberg |
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5 | % $Id: mpower.m,v 1.18 2006/09/21 14:31:06 joloef Exp $ |
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6 | |
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7 | %Sanity check |
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8 | if prod(size(d))>1 |
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9 | error('The power must be scalar.'); |
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10 | end |
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11 | if x.dim(1)~=x.dim(2) |
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12 | error('Matrix must be square.') |
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13 | end |
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14 | |
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15 | % Trivial cases |
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16 | if d==0 |
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17 | y = eye(x.dim(1),x.dim(2))^0; |
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18 | return |
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19 | end |
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20 | if d==1 |
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21 | y = x; |
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22 | return |
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23 | end |
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24 | |
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25 | % Fractional and negative powers |
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26 | if (ceil(d)-d>0) | (d<0) |
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27 | if x.dim(1)>1 | x.dim(2)>1 |
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28 | error('Only scalars can have negative or non-integer powers'); |
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29 | else |
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30 | base = getbase(x); |
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31 | if isequal(base,sparse([0 1])) % Simple unit scalar |
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32 | [mt,variabletype] = yalmip('monomtable'); |
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33 | var = getvariables(x); |
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34 | hash = randn(size(mt,2),1); |
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35 | hashM = mt*hash; |
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36 | hashV = (mt(var,:)*d)*hash; |
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37 | previous_var = find(abs(hashM - hashV) < 1e-20); |
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38 | if isempty(previous_var) |
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39 | newmt = mt(getvariables(x),:)*d; |
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40 | mt(end+1,:) = newmt; |
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41 | yalmip('setmonomtable',mt,[variabletype newvariabletypegen(newmt)]); |
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42 | y = recover(size(mt,1)); |
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43 | else |
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44 | y = recover(previous_var); |
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45 | end |
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46 | elseif (size(base,2) == 2) & base(1)==0 |
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47 | % Something like a*t^-d |
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48 | y = base(2)^d*recover(getvariables(x))^d; |
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49 | else |
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50 | % Bummer, something more complex, add an internal equality constraint |
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51 | y = (yalmip('addextendedvariable','mpower',x))^d; |
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52 | end |
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53 | end |
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54 | return |
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55 | end |
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56 | |
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57 | % Integer power of matrix |
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58 | if x.dim(1)>1 | x.dim(2)>1 |
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59 | switch d |
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60 | case 0 |
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61 | y = 1; |
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62 | case 1 |
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63 | y = x; |
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64 | otherwise |
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65 | y = x*mpower(x,d-1); |
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66 | end |
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67 | else %Integer power of scalar |
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68 | |
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69 | base = x.basis; |
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70 | if isequal(base,[0 1]) % Unit scalar can be done fast |
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71 | [mt,variabletype] = yalmip('monomtable'); |
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72 | %var = getvariables(x); |
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73 | var = x.lmi_variables; |
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74 | possible = find(mt(:,var)); |
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75 | if length(possible)==1 |
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76 | % Even faster, we don't need to search, cannot have been |
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77 | % definded earlier, since only the linear terms is in monom |
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78 | % table |
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79 | newmt = mt(var,:)*d; |
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80 | mt = [mt;newmt]; |
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81 | yalmip('setmonomtable',mt,[variabletype newvariabletypegen(newmt)]); |
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82 | y = x; |
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83 | y.lmi_variables = size(mt,1); |
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84 | else |
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85 | hash = randn(size(mt,2),1); |
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86 | mt_hash = mt*hash; |
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87 | mt_hash = mt_hash(possible); |
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88 | previous_var = findhash(mt_hash , (d*mt(var,:))*hash); |
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89 | if isempty(previous_var) |
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90 | newmt = mt(var,:)*d; |
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91 | % mt(end+1,:) = newmt; |
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92 | mt = [mt;newmt]; |
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93 | yalmip('setmonomtable',mt,[variabletype newvariabletypegen(newmt)]); |
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94 | y = x; |
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95 | y.lmi_variables = size(mt,1); |
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96 | else |
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97 | previous_var = possible(previous_var); |
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98 | y = x; |
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99 | y.lmi_variables = previous_var; |
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100 | end |
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101 | end |
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102 | else % General scalar |
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103 | switch d |
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104 | case 0 |
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105 | y = 1; |
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106 | case 1 |
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107 | y = x; |
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108 | otherwise |
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109 | y = x*mpower(x,d-1); |
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110 | end |
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111 | end |
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112 | end |
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113 | |
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114 | function newvariabletype = newvariabletypegen(newmt) |
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115 | newvariabletype = spalloc(size(newmt,1),1,0)'; |
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116 | nonlinear = ~(sum(newmt,2)==1 & sum(newmt~=0,2)==1); |
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117 | if ~isempty(nonlinear) |
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118 | newvariabletype(nonlinear) = 3; |
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119 | quadratic = sum(newmt,2)==2; |
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120 | newvariabletype(quadratic) = 2; |
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121 | bilinear = max(newmt,[],2)<=1; |
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122 | newvariabletype(bilinear & quadratic) = 1; |
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123 | sigmonial = any(0>newmt,2) | any(newmt-fix(newmt),2); |
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124 | newvariabletype(sigmonial) = 4; |
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125 | end |
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126 | |
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127 | |
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