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1 ## Copyright (C) 1996 Auburn University. All rights reserved. |
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2 ## |
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3 ## This file is part of Octave. |
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4 ## |
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5 ## Octave is free software; you can redistribute it and/or modify it |
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6 ## under the terms of the GNU General Public License as published by the |
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7 ## Free Software Foundation; either version 2, or (at your option) any |
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8 ## later version. |
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9 ## |
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10 ## Octave is distributed in the hope that it will be useful, but WITHOUT |
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11 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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12 ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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13 ## for more details. |
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14 ## |
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15 ## You should have received a copy of the GNU General Public License |
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16 ## along with Octave; see the file COPYING. If not, write to the Free |
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17 ## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA. |
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18 |
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19 ## -*- texinfo -*- |
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20 ## @deftypefn {Function File} {[@var{retsys}, @var{nc}, @var{no}] =} sysmin (@var{sys}, @var{flg}) |
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21 ## return a minimal (or reduced order) system |
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22 ## inputs: |
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23 ## sys: system data structure |
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24 ## flg: 0 [default] return minimal system; state names lost |
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25 ## : 1 return system with physical states removed that |
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26 ## are either uncontrollable or unobservable |
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27 ## (cannot reduce further without discarding physical |
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28 ## meaning of states) |
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29 ## outputs: |
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30 ## retsys: returned system |
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31 ## nc: number of controllable states in the returned system |
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32 ## no: number of observable states in the returned system |
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33 ## cflg: is_controllable(retsys) |
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34 ## oflg: is_observable(retsys) |
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35 ## @end deftypefn |
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36 |
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37 ## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> |
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38 |
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39 function [retsys, nc, no, cflg, oflg] = sysmin (sys, flg) |
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40 |
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41 switch(nargin) |
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42 case(1), flg = 0; |
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43 case(2), jnk = flg; # dummy operation |
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44 otherwise, |
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45 usage("[retsys,nc,no] = sysmin(sys{,flg})"); |
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46 endswitch |
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47 dflg = is_digital(sys,2); |
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48 [n,nz,m,p] = sysdimensions(sys); |
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49 if(n*nz > 0) |
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50 # both continuous and discrete states |
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51 [aa,bb,cc,dd,tsam,n,nz,stnam,innam,outnam,yd] = sys2ss(sys); |
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52 crng = 1:n; |
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53 drng = n+(1:nz); |
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54 |
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55 # get minimal realization of continuous part |
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56 Ac = aa(crng,crng); |
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57 Acd = aa(crng,drng); |
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58 Adc = aa(drng,crng); |
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59 Ad = aa(drng,drng); |
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60 Bc = bb(crng,:); |
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61 Bd = bb(drng,:); |
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62 Cc = cc(:,crng); |
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63 Cd = cc(:,drng); |
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64 |
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65 cstnam = stnam(crng); |
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66 dstnam = stnam(drng); |
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67 cinnam = append(innam,stnam(drng)); |
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68 coutnam = append(outnam,stnam(drng)); |
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69 csys = ss2sys(Ac,[Bc,Acd],[Cc;Adc]); |
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70 csys = syssetsignals(csys,"st",cstnam); |
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71 csys = syssetsignals(csys,"in",cinnam); |
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72 csys = syssetsignals(csys,"out",coutnam); |
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73 |
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74 # reduce continuous system, recombine with discrete part |
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75 csys = sysmin(csys,flg); |
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76 cn = sysdimensions(csys); |
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77 |
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78 if(cn == 0) |
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79 # continuous states are removed; just reduce the discrete part |
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80 sys = sysprune(sys,1:p,1:m,drng); |
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81 retsys = sysmin(sys,flg); |
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82 else |
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83 # extract updated parameters from reduced continuous system |
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84 [caa,cbb,ccc,cdd,ctsam,cn,cnz,cstnam,cinnam,coutnam] = sys2ss(csys); |
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85 crng = 1:cn; |
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86 Ac = caa; |
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87 Bc = cbb(:,1:m); |
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88 Acd = cbb(:,m+(1:nz)); |
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89 Cc = ccc(1:p,:); |
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90 Adc = ccc(p + (1:nz),:); |
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91 |
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92 # recombine to reduce discrete part of the system |
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93 dinnam = append(innam,cstnam); |
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94 doutnam = append(outnam,cstnam); |
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95 dsys = ss2sys(Ad,[Bd,Adc],[Cd;Acd],[],tsam); |
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96 dsys = syssetsignals(dsys,"st",dstnam); |
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97 dsys = syssetsignals(dsys,"in",dinnam); |
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98 dsys = syssetsignals(dsys,"out",doutnam); |
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99 |
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100 # reduce discrete subsystem |
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101 dsys = sysmin(dsys); |
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102 [n1,nz] = sysdimensions(dsys); |
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103 if(nz == 0) |
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104 # discrete subsystem is not needed |
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105 retsys = sysprune(csys,1:p,1:m); |
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106 else |
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107 # combine discrete, continuous subsystems |
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108 [Ad,dbb,dcc] = sys2ss(dsys); |
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109 dstnam = sysgetsignals(dsys,"st"); |
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110 Bd = dbb(:,1:m); |
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111 Adc = dbb(:,m+(1:cn)); |
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112 Cd = dcc(1:p,:); |
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113 Acd = dcc(p+(1:cn),:); |
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114 stnam = append(cstnam,dstnam); |
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115 aa = [Ac, Acd; Adc, Ad]; |
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116 bb = [Bc; Bd]; |
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117 cc = [Cc, Cd]; |
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118 retsys = ss2sys([Ac, Acd; Adc, Ad], [Bc ; Bd], [Cc, Cd], dd, tsam, ... |
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119 cn, nz, stnam, innam, outnam, find(yd == 1)); |
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120 end |
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121 endif |
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122 else |
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123 Ts = sysgettsam(sys); |
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124 switch(flg) |
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125 case(0), |
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126 ## reduce to a minimal system |
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127 [aa,bb,cc,dd] = sys2ss(sys); |
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128 [cflg,Uc] = is_controllable(aa,bb); |
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129 if(!cflg) |
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130 ## reduce to controllable states |
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131 if(!isempty(Uc)) |
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132 aa = Uc'*aa*Uc; |
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133 bb = Uc'*bb; |
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134 cc = cc*Uc; |
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135 else |
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136 aa = bb = cc = []; |
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137 endif |
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138 endif |
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139 if(!isempty(aa)) |
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140 [oflg,Uo] = is_observable(aa,cc); |
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141 if(!oflg) |
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142 if(!isempty(Uo)) |
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143 aa = Uo'*aa*Uo; |
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144 bb = Uo'*bb; |
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145 cc = cc*Uo; |
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146 else |
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147 aa = bb = cc = []; |
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148 endif |
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149 endif |
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150 endif |
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151 switch(dflg) |
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152 case(0), |
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153 nc = no = nn = columns(aa); |
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154 nz = 0; |
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155 case(1), |
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156 nc = no = nz = columns(aa); |
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157 nn = 0; |
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158 endswitch |
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159 innam = sysgetsignals(sys,"in"); |
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160 outnam= sysgetsignals(sys,"out"); |
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161 retsys = ss2sys(aa,bb,cc,dd,Ts,nn,nz,[],innam,outnam); |
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162 case(1), |
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163 ## reduced model with physical states |
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164 [cflg,Uc] = is_controllable(sys); xc = find(max(abs(Uc')) != 0); |
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165 [oflg,Uo] = is_observable(sys); xo = find(max(abs(Uo')) != 0); |
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166 xx = intersection(xc,xo); |
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167 if(isempty(xx)) xx = 0; endif # signal no states in reduced model |
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168 retsys = sysprune(sys,[],[],xx); |
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169 otherwise, |
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170 error ("invalid value of flg = %d", flg); |
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171 endswitch |
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172 if(sysdimensions(retsys,"st") > 0) |
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173 [cflg,Uc] = is_controllable(retsys); nc = columns(Uc); |
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174 [oflg,Uo] = is_observable(retsys); no = columns(Uo); |
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175 else |
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176 nc = no = 0; |
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177 endif |
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178 endif |
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179 endfunction |
