[2] | 1 | #include <itpp/itbase.h> |
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[7] | 2 | #include "libDC.h" |
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[2] | 3 | |
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| 4 | using namespace itpp; |
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| 5 | |
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[7] | 6 | using std::endl; |
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[2] | 7 | |
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[7] | 8 | //! Auxiliary function dydr; dyadic reduction |
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| 9 | void dydr( double * r, double *f, double *Dr, double *Df, double *R, int jl, int jh, double *kr, int m, int mx ); |
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[2] | 10 | |
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[7] | 11 | //! Auxiliary function ltuinv; inversion of a triangular matrix; |
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| 12 | //TODO can be done via: dtrtri.f from lapack |
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| 13 | mat ltuinv( const mat &L ); |
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[2] | 14 | |
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| 15 | |
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| 16 | |
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[7] | 17 | ldmat::ldmat( const mat &exL, const vec &exD ) { |
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[5] | 18 | D = exD; |
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| 19 | L = exL; |
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[12] | 20 | dim = exD.length(); |
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[2] | 21 | } |
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| 22 | |
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[7] | 23 | ldmat::ldmat() { |
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| 24 | vec D ; |
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| 25 | mat L; |
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[12] | 26 | dim = 0; |
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[2] | 27 | } |
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| 28 | |
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[7] | 29 | ldmat::ldmat( const mat V ) { |
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| 30 | //TODO check if correct!! Based on heuristic observation of lu() |
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| 31 | |
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[12] | 32 | dim = V.cols(); |
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[7] | 33 | it_assert_debug( dim == V.rows(),"ldmat::ldmat matrix V is not square!" ); |
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| 34 | |
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[12] | 35 | |
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[7] | 36 | } |
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| 37 | |
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| 38 | void ldmat::opupdt( const vec &v, double w ) { |
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| 39 | int dim = D.length(); |
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| 40 | double kr; |
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| 41 | vec r = v; |
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| 42 | //beware! it is potentionally dangerous, if ITpp change _behaviour of _data()! |
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| 43 | double *Lraw = L._data(); |
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| 44 | double *Draw = D._data(); |
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| 45 | double *rraw = r._data(); |
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| 46 | |
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| 47 | it_assert_debug( v.length() == dim, "LD::ldupdt vector v is not compatible with this ld." ); |
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| 48 | |
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| 49 | for ( int i = dim - 1; i >= 0; i-- ) { |
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| 50 | dydr( rraw, Lraw + i, &w, Draw + i, rraw + i, 0, i, &kr, 1, dim ); |
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| 51 | } |
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| 52 | } |
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| 53 | |
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[12] | 54 | std::ostream &operator<< ( std::ostream &os, ldmat &ld ) { |
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| 55 | os << "L:" << ld.L << endl; |
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| 56 | os << "D:" << ld.D << endl; |
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[7] | 57 | } |
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| 58 | |
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| 59 | mat ldmat::to_mat() { |
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| 60 | int dim = D.length(); |
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| 61 | mat V( dim, dim ); |
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| 62 | double sum; |
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| 63 | int r, c, cc; |
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| 64 | |
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| 65 | for ( r = 0;r < dim;r++ ) { //row cycle |
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| 66 | for ( c = r;c < dim;c++ ) { |
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| 67 | //column cycle, using symmetricity => c=r! |
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| 68 | sum = 0.0; |
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| 69 | for ( cc = c;cc < dim;cc++ ) { //cycle over the remaining part of the vector |
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| 70 | sum += L( cc, r ) * D( cc ) * L( cc, c ); |
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| 71 | //here L(cc,r) = L(r,cc)'; |
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| 72 | } |
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| 73 | V( r, c ) = sum; |
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| 74 | // symmetricity |
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| 75 | if ( r != c ) {V( c, r ) = sum;}; |
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| 76 | } |
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| 77 | } |
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[12] | 78 | mat V2 = L.transpose()*diag( D )*L; |
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| 79 | return V2; |
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[7] | 80 | } |
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| 81 | |
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| 82 | |
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| 83 | void ldmat::add( const ldmat &ld2, double w ) { |
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| 84 | int dim = D.length(); |
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| 85 | |
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| 86 | it_assert_debug( ld2.D.length() == dim, "LD.add() incompatible sizes of LDs;" ); |
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| 87 | |
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| 88 | //Fixme can be done more efficiently either via dydr or ldform |
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| 89 | for ( int r = 0; r < dim; r++ ) { |
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| 90 | // Add columns of ld2.L' (i.e. rows of ld2.L) as dyads weighted by ld2.D |
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| 91 | this->opupdt( ld2.L.get_row( r ), w*ld2.D( r ) ); |
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| 92 | } |
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| 93 | } |
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| 94 | |
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| 95 | void ldmat::clear(){L.clear(); for ( int i=0;i<L.cols();i++ ){L( i,i )=1;}; D.clear();} |
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| 96 | |
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| 97 | void ldmat::inv( ldmat &Inv ) { |
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| 98 | int dim = D.length(); |
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| 99 | Inv.clear(); //Inv = zero in LD |
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| 100 | mat U = ltuinv( L ); |
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| 101 | |
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| 102 | //Fixme can be done more efficiently either via dydr or ldform |
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| 103 | for ( int r = 0; r < dim; r++ ) { |
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| 104 | // Add columns of U as dyads weighted by 1/D |
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| 105 | Inv.opupdt( U.get_col( r ), 1.0 / D( r ) ); |
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| 106 | } |
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| 107 | } |
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| 108 | |
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[8] | 109 | void ldmat::mult_sym( const mat &C, bool trans ) { |
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[7] | 110 | |
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| 111 | //TODO better |
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| 112 | |
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[8] | 113 | it_assert_debug( C.cols()==L.cols(), "ldmat::mult_sym wrong input argument" ); |
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[7] | 114 | mat Ct=C; |
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| 115 | |
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| 116 | if ( trans==false ) { // return C*this*C' |
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| 117 | Ct *= this->to_mat(); |
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| 118 | Ct *= C.transpose(); |
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| 119 | } else { // return C'*this*C |
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| 120 | Ct = C.transpose(); |
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| 121 | Ct *= this->to_mat(); |
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| 122 | Ct *= C; |
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| 123 | } |
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| 124 | |
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| 125 | ldmat Lnew=ldmat( Ct ); |
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| 126 | L = Lnew.L; |
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| 127 | D = Lnew.D; |
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| 128 | } |
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| 129 | |
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[8] | 130 | void ldmat::mult_sym( const mat &C, ldmat &U, bool trans ) { |
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| 131 | |
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| 132 | //TODO better |
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| 133 | |
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| 134 | //TODO input test |
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| 135 | |
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| 136 | mat Ct=C; |
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| 137 | |
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| 138 | if ( trans==false ) { // return C*this*C' |
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| 139 | Ct *= U.to_mat(); |
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| 140 | Ct *= C.transpose(); |
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| 141 | } else { // return C'*this*C |
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| 142 | Ct = C.transpose(); |
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| 143 | Ct *= U.to_mat(); |
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| 144 | Ct *= C; |
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| 145 | } |
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| 146 | |
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| 147 | ldmat Lnew=ldmat( Ct ); |
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| 148 | L = Lnew.L; |
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| 149 | D = Lnew.D; |
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| 150 | } |
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| 151 | |
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[7] | 152 | double ldmat::logdet() { |
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| 153 | double ldet = 0.0; |
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| 154 | int i; |
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| 155 | // sum logarithms of diagobal elements |
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| 156 | for ( i=0; i<D.length(); i++ ){ldet+=log( D( i ) );}; |
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| 157 | } |
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| 158 | |
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| 159 | double ldmat::qform( vec &v ) { |
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| 160 | double x = 0.0, sum; |
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| 161 | int i,j; |
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| 162 | |
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| 163 | for ( i=0; i<D.length(); i++ ) { //rows of L |
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| 164 | sum = 0.0; |
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| 165 | for ( j=0; j<=i; j++ ){sum+=L( i,j )*v( j );} |
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| 166 | x +=D( i )*sum*sum; |
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| 167 | }; |
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| 168 | return x; |
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| 169 | } |
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| 170 | |
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[12] | 171 | ldmat& ldmat::operator *= ( double x ) { |
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| 172 | int i; |
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| 173 | for ( i=0;i<D.length();i++ ){D( i )*=x;}; |
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[7] | 174 | } |
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| 175 | |
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[12] | 176 | vec ldmat::sqrt_mult( vec &x ) { |
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| 177 | int i,j; |
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| 178 | vec res( dim ); |
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| 179 | double sum; |
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| 180 | for ( i=0;i<dim;i++ ) {//for each element of result |
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| 181 | res( i ) = 0.0; |
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| 182 | for ( j=i;j<dim;j++ ) {//sum D(j)*L(:,i).*x |
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| 183 | res( i ) += sqrt( D( j ) )*L( j,i )*x( j ); |
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| 184 | } |
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| 185 | } |
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| 186 | vec res2 = L.transpose()*diag( sqrt( D ) )*x; |
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| 187 | return res2; |
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| 188 | } |
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[7] | 189 | |
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[12] | 190 | void ldmat::ldform( mat &A,vec &D0 ) { |
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| 191 | int m = A.rows(); |
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| 192 | int n = A.cols(); |
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| 193 | int mn = (m<n) ? m :n ; |
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| 194 | |
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| 195 | it_assert_debug( A.cols()==dim,"ldmat::ldform A is not compatible" ); |
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| 196 | it_assert_debug( D.length()==A.rows(),"ldmat::ldform Vector D must have the length as row count of A" ); |
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| 197 | |
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| 198 | L=concat_vertical( zeros( n,n ), diag( sqrt( D0 ) )*A ); |
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| 199 | D=zeros( n+m ); |
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| 200 | |
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| 201 | //unnecessary big L and D will be made smaller at the end of file |
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| 202 | |
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| 203 | vec w=zeros( n ); |
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| 204 | vec v; |
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| 205 | double sum, beta, pom; |
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| 206 | |
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| 207 | int cc=0; |
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| 208 | int i=n; // +1 in .m |
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| 209 | int ii,j,jj; |
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| 210 | while (( i> ( n-mn+1-cc ) )&&( i>1 ) ) { |
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| 211 | i--; |
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| 212 | sum = 0.0; |
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| 213 | v.set_size( m+i-( n-cc ) ); //prepare v |
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| 214 | for ( ii=n-cc;ii<m+i;i++ ) { |
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| 215 | sum+= L( ii,i )*L( ii,i ); |
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| 216 | v( ii )=L( ii,i ); //assign v |
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| 217 | } |
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| 218 | if ( L( m+i,i )==0 ) { |
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| 219 | beta = sqrt( sum ); |
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| 220 | } else { |
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| 221 | beta = L( m+i,i )+sign( L( m+i,i ) )*sqrt( sum ) ; |
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| 222 | } |
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| 223 | if ( std::fabs( beta )<eps ) { |
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| 224 | cc++; |
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| 225 | L.set_row( n+1-cc, L.get_row( m+i ) ); |
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| 226 | L.set_row( m+i,0 ); |
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| 227 | D( m+i )=0; L( m+i,i )=1; |
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| 228 | L.set_submatrix( n+1-cc,m+i,i,i,0 ); |
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| 229 | continue; |
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| 230 | } |
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| 231 | |
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| 232 | sum-=v( v.length()-1 )*v( v.length()-1 ); // |
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| 233 | sum/=beta*beta; |
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| 234 | sum++; |
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| 235 | |
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| 236 | v/=beta; |
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| 237 | v( v.length()-1 )=1; |
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| 238 | |
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| 239 | pom=-2/sum; |
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| 240 | for ( j=i;i>=0;i-- ) { |
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| 241 | w( j )=0.0; |
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| 242 | for ( ii=n-cc;ii<m+i;ii++ ) { |
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| 243 | w( j )+= v( ii )*L( ii,j ); |
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| 244 | } |
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| 245 | w( j )*=pom; |
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| 246 | } |
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| 247 | |
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| 248 | for ( ii=n-cc;ii<m+i;ii++ ) { |
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| 249 | for ( jj=0;jj<i-1;jj++ ) { |
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| 250 | L( ii,jj )+= v( ii )*w( jj ); |
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| 251 | } |
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| 252 | } |
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| 253 | for ( ii=n-cc;ii<m+i;ii++ ) { |
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| 254 | L( ii,i )= 0; |
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| 255 | } |
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| 256 | L( m+i,i )+=w( i ); |
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| 257 | |
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| 258 | D( m+i )=L( m+i,i )*L( m+i,i ); |
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| 259 | for ( ii=0;ii<i;ii++ ) { |
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| 260 | L( m+i,ii )/=L( m+i,i ); |
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| 261 | } |
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| 262 | } |
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| 263 | if ( i>0 ) { |
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| 264 | for ( ii=0;ii<i-1;ii++ ) { |
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| 265 | jj = D.length()-1-n+ii; |
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| 266 | L.set_row(jj,0); |
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| 267 | L(jj,jj)=1; |
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| 268 | } |
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| 269 | } |
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| 270 | |
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| 271 | //cut-out L and D; |
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| 272 | L.del_rows(0,m-1); |
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| 273 | D.del(0,m-1); |
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| 274 | } |
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| 275 | |
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[7] | 276 | //////// Auxiliary Functions |
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| 277 | |
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| 278 | mat ltuinv( const mat &L ) { |
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| 279 | int dim = L.cols(); |
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| 280 | mat Il = eye( dim ); |
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| 281 | int i, j, k, m; |
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| 282 | double s; |
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| 283 | |
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| 284 | //Fixme blind transcription of ltuinv.m |
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| 285 | for ( k = 1; k < ( dim );k++ ) { |
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| 286 | for ( i = 0; i < ( dim - k );i++ ) { |
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| 287 | j = i + k; //change in .m 1+1=2, here 0+0+1=1 |
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| 288 | s = L( j, i ); |
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| 289 | for ( m = i + 1; m < ( j - 1 ); m++ ) { |
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| 290 | s += L( m, i ) * Il( j, m ); |
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| 291 | } |
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| 292 | Il( j, i ) = -s; |
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| 293 | } |
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| 294 | } |
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| 295 | |
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| 296 | return Il; |
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| 297 | } |
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| 298 | |
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| 299 | void dydr( double * r, double *f, double *Dr, double *Df, double *R, int jl, int jh, double *kr, int m, int mx ) |
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| 300 | /******************************************************************** |
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| 301 | |
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| 302 | dydr = dyadic reduction, performs transformation of sum of |
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| 303 | 2 dyads r*Dr*r'+ f*Df*f' so that the element of r pointed |
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| 304 | by R is zeroed. This version allows Dr to be NEGATIVE. Hence the name negdydr or dydr_withneg. |
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| 305 | |
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| 306 | Parameters : |
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| 307 | r ... pointer to reduced dyad |
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| 308 | f ... pointer to reducing dyad |
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| 309 | Dr .. pointer to the weight of reduced dyad |
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| 310 | Df .. pointer to the weight of reducing dyad |
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| 311 | R ... pointer to the element of r, which is to be reduced to |
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| 312 | zero; the corresponding element of f is assumed to be 1. |
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| 313 | jl .. lower index of the range within which the dyads are |
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| 314 | modified |
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| 315 | ju .. upper index of the range within which the dyads are |
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| 316 | modified |
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| 317 | kr .. pointer to the coefficient used in the transformation of r |
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| 318 | rnew = r + kr*f |
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| 319 | m .. number of rows of modified matrix (part of which is r) |
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| 320 | Remark : Constant mzero means machine zero and should be modified |
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| 321 | according to the precision of particular machine |
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| 322 | |
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| 323 | V. Peterka 17-7-89 |
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| 324 | |
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| 325 | Added: |
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| 326 | mx .. number of rows of modified matrix (part of which is f) -PN |
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| 327 | |
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| 328 | ********************************************************************/ |
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[5] | 329 | { |
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[7] | 330 | int j, jm; |
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| 331 | double kD, r0; |
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| 332 | double mzero = 2.2e-16; |
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| 333 | double threshold = 1e-4; |
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| 334 | |
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| 335 | if ( fabs( *Dr ) < mzero ) *Dr = 0; |
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| 336 | r0 = *R; |
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| 337 | *R = 0.0; |
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| 338 | kD = *Df; |
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| 339 | *kr = r0 * *Dr; |
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| 340 | *Df = kD + r0 * ( *kr ); |
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| 341 | if ( *Df > mzero ) { |
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| 342 | kD /= *Df; |
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| 343 | *kr /= *Df; |
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| 344 | } else { |
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| 345 | kD = 1.0; |
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| 346 | *kr = 0.0; |
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[8] | 347 | if ( *Df < -threshold ) { |
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[12] | 348 | it_warning( "Problem in dydr: subraction of dyad results in negative definitness. Likely mistake in calling function." ); |
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| 349 | } |
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[7] | 350 | *Df = 0.0; |
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| 351 | } |
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| 352 | *Dr *= kD; |
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| 353 | jm = mx * jl; |
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| 354 | for ( j = m * jl; j < m*jh; j += m ) { |
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| 355 | r[j] -= r0 * f[jm]; |
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| 356 | f[jm] += *kr * r[j]; |
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| 357 | jm += mx; |
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| 358 | } |
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[2] | 359 | } |
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[7] | 360 | |
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