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fvar_m20.cpp
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00001 
00007 #include <fvar.hpp>
00008 #ifdef __TURBOC__
00009   #pragma hdrstop
00010   #include <iomanip.h>
00011 #endif
00012 
00013 #ifdef __ZTC__
00014   #include <iomanip.hpp>
00015 #endif
00016 
00017 #define TINY 1.0e-20;
00018 void dfinvpret(void);
00019 
00020 // int min(int a,int b);
00021 void df_xdet(void);
00022 
00033 dvariable det(const dvar_matrix& aa)
00034 {
00035   int i,imax,j,k,n;
00036   n=aa.colsize();
00037   int lb=aa.colmin();
00038   int ub=aa.colmax();
00039   ivector indx(lb,ub);
00040   if (lb!=aa.rowmin()||ub!=aa.colmax())
00041   {
00042     cerr << "Error matrix not square in det()"<<endl;
00043     ad_exit(1);
00044   }
00045   int One=1;
00046   indx.fill_seqadd(lb,One);
00047   double d;
00048   double big,dum,sum,temp;
00049   dvar_matrix_position dmp(aa,1);
00050   dmatrix bb=value(aa);
00051   dvector vv(lb,ub);
00052   dvector part_prod(lb,ub);
00053 
00054   d=1.0;
00055   for (i=lb;i<=ub;i++)
00056   {
00057     big=0.0;
00058     for (j=lb;j<=ub;j++)
00059     {
00060       temp=fabs(bb.elem(i,j));
00061       if (temp > big)
00062       {
00063         big=temp;
00064       }
00065     }
00066     if (big == 0.0)
00067     {
00068       cerr << "Error in matrix inverse -- matrix singular in inv(dmatrix)\n";
00069     }
00070     vv[i]=1.0/big;
00071   }
00072 
00073   for (j=lb;j<=ub;j++)
00074   {
00075     for (i=lb;i<j;i++)
00076     {
00077       sum=bb.elem(i,j);
00078       for (k=lb;k<i;k++)
00079       {
00080         sum = sum - bb.elem(i,k)*bb.elem(k,j);
00081       }
00082       //a[i][j]=sum;
00083       bb(i,j)=sum;
00084     }
00085     big=0.0;
00086     for (i=j;i<=ub;i++)
00087     {
00088       sum=bb.elem(i,j);
00089       for (k=lb;k<j;k++)
00090       {
00091         sum = sum - bb(i,k)*bb(k,j);
00092       }
00093       bb(i,j)=sum;
00094       dum=vv.elem(i)*fabs(sum);
00095       if ( dum >= big)
00096       {
00097         big=dum;
00098         imax=i;
00099       }
00100     }
00101     if (j != imax)
00102     {
00103       for (k=lb;k<=ub;k++)
00104       {
00105         dum=bb.elem(imax,k);
00106         bb.elem(imax,k)=bb.elem(j,k);
00107         bb.elem(j,k)=dum;
00108       }
00109       d = -1.*d;
00110       vv.elem(imax)=vv.elem(j);
00111 
00112       //if (j<ub)
00113       {
00114         int itemp=indx.elem(imax);
00115         indx.elem(imax)=indx.elem(j);
00116         indx.elem(j)=itemp;
00117       }
00118       //cout << "indx= " <<indx<<endl;
00119     }
00120 
00121     if (bb.elem(j,j) == 0.0)
00122     {
00123       bb(j,j)=TINY;
00124     }
00125 
00126     if (j != n)
00127     {
00128       dum=1.0/bb(j,j);
00129       for (i=j+1;i<=ub;i++)
00130       {
00131         bb.elem(i,j) *= dum;
00132       }
00133     }
00134   }
00135   double det=d;
00136 
00137   // SM Bug 129, issue appears to be at this line
00138   // part_prod is declared above as dvector(lb,ub)
00139   // cout<<"Bug 129 ="<<part_prod(lb)<<endl;
00140   // part_prod(1)=d*bb(1,1);  // replaced this line with:
00141   part_prod(lb) = d*bb(lb,lb);
00142   // cout<<"Ok got this far; det = "<<det<<endl;
00143   for (j=lb+1;j<=ub;j++)
00144   {
00145     part_prod(j)=part_prod(j-1)*bb(j,j);
00146   }
00147   det=part_prod(ub);
00148   dvariable rdet=nograd_assign(det);
00149   save_identifier_string("PLACE7");
00150   part_prod.save_dvector_value();
00151   part_prod.save_dvector_position();
00152   indx.save_ivector_value();
00153   indx.save_ivector_position();
00154   save_identifier_string("PLACE3");
00155   aa.save_dvar_matrix_position();
00156   save_identifier_string("PLACE2b");
00157   rdet.save_prevariable_position();
00158   save_identifier_string("PLACE2a");
00159   bb.save_dmatrix_value();
00160   save_identifier_string("PLACE2");
00161   bb.save_dmatrix_position();
00162   save_identifier_string("PLACE1");
00163   save_double_value(d);
00164   save_identifier_string("PLACE0");
00165   gradient_structure::GRAD_STACK1->
00166       set_gradient_stack(df_xdet);
00167   return rdet;
00168 }
00169 
00171 void df_xdet(void)
00172 {
00173   verify_identifier_string("PLACE0");
00174   double d=restore_double_value();
00175   verify_identifier_string("PLACE1");
00176   dmatrix_position bpos=restore_dmatrix_position();
00177   verify_identifier_string("PLACE2");
00178   dmatrix b=restore_dmatrix_value(bpos);
00179   verify_identifier_string("PLACE2a");
00180   //dvar_matrix_position rdet_pos=restore_prevariable_position();
00181   double dfdet=restore_prevariable_derivative();
00182   verify_identifier_string("PLACE2b");
00183   dvar_matrix_position a_pos=restore_dvar_matrix_position();
00184   verify_identifier_string("PLACE3");
00185   ivector_position indx_pos=restore_ivector_position();
00186   ivector indx=restore_ivector_value(indx_pos);
00187   dvector_position part_prod_pos=restore_dvector_position();
00188   dvector part_prod=restore_dvector_value(part_prod_pos);
00189   verify_identifier_string("PLACE7");
00190   int lb=b.colmin();
00191   int ub=b.colmax();
00192   dmatrix dfb(lb,ub,lb,ub);
00193 
00194   dvector dfpart_prod(lb,ub);
00195 
00196   #ifndef SAFE_INITIALIZE
00197     dfb.initialize();
00198     dfpart_prod.initialize();
00199   #endif
00200 
00201 
00202   dfpart_prod(ub)=dfdet;
00203   int j;
00204   for (j=ub;j>=lb+1;j--)
00205   {
00206     // part_prod(j)=part_prod(j-1)*b(j,j);
00207     dfpart_prod(j-1)+=dfpart_prod(j)*b(j,j);
00208     dfb(j,j)+=dfpart_prod(j)*part_prod(j-1);
00209     dfpart_prod(j)=0.;
00210   }
00211   //part_prod(1)=d*b(lb,lb);
00212   dfb(lb,lb)+=dfpart_prod(lb)*d;
00213   dfpart_prod(lb)=0.;
00214 
00215   double dfsum=0.;
00216   for (j=ub;j>=lb;j--)
00217   {
00218     for (int i=ub;i>=lb;i--)
00219     {
00220       if (i<=j)
00221       {
00222         // b(i,j)=sum;
00223         dfsum+=dfb(i,j);
00224         dfb(i,j)=0.;
00225       }
00226       else
00227       {
00228         // b(i,j)=sum/b(j,j);
00229         dfsum+=dfb(i,j)/b(j,j);
00230         dfb(j,j)-=dfb(i,j)*b(i,j)/b(j,j);
00231         dfb(i,j)=0.;
00232       }
00233 
00234       for (int k=min(i-1,j-1);k>=lb;k--)
00235       {
00236         // sum-=b(i,k)*b(k,j);
00237         dfb(i,k)-=dfsum*b(k,j);
00238         dfb(k,j)-=dfsum*b(i,k);
00239       }
00240       // sum=value(a(indx(i),j);
00241       save_dmatrix_derivatives(a_pos,dfsum,indx(i),j); // like this
00242       dfsum=0.;
00243     }
00244   }
00245 }
00246 
00247 #undef TINY