[1174] | 1 | /************************************ |
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| 2 | Extended Kalman Filter |
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| 3 | Matrix operations |
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| 4 | |
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[1240] | 5 | V. Smidl, Z. Peroutka |
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[1174] | 6 | |
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[1240] | 7 | Rev. 28.10.2010 (ZP) |
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[1174] | 8 | |
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[1240] | 9 | 26.10.2010 Prvni verze (VS) |
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[1174] | 10 | |
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[1240] | 11 | 26.10.2010 Upravena chyba v Thorton_fast - spatne shiftovani o vypoctu SIGMA. |
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| 12 | 27.10.2010 Pokus o odstraneni problemu v Thorton_fast - potize dela omezovani (orezavani) varianci. |
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| 13 | 28.10.2010 Drobne upravy v kodu. |
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| 14 | |
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[1174] | 15 | *************************************/ |
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[1225] | 16 | |
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| 17 | #include "matrix_vs.h" |
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| 18 | |
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[1174] | 19 | /* Matrix multiply Full matrix by upper diagonal matrix; */ |
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[1240] | 20 | void mmultAU(int16 *m1, int16 *up, int16 *result, unsigned int16 rows, unsigned int16 columns) { |
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| 21 | unsigned int16 i, j, k; |
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| 22 | int32 tmp_sum=0L; //in 15+qAU |
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| 23 | int16 *m2pom; |
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| 24 | int16 *m1pom=m1; |
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| 25 | int16 *respom=result; |
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[1174] | 26 | |
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[1179] | 27 | for (i=0; i<rows; i++) //rows of result |
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[1174] | 28 | { |
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[1179] | 29 | for (j=0; j<columns; j++) //columns of result |
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[1240] | 30 | { |
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[1179] | 31 | m2pom=up+j;//?? |
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[1174] | 32 | |
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[1179] | 33 | for (k=0; k<j; k++) //inner loop up to "j" - U(j,j)==1; |
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| 34 | { |
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[1240] | 35 | tmp_sum+=((int32)(*(m1pom++))**m2pom)>>(15-qAU); |
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[1179] | 36 | m2pom+=columns; |
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| 37 | } |
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| 38 | // add the missing A(i,j) |
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[1240] | 39 | tmp_sum +=(int32)(*m1pom)<<qAU; // no need to shift |
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[1225] | 40 | m1pom-=(j); // shift back to first element |
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[1174] | 41 | |
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[1235] | 42 | *respom++=tmp_sum>>15; |
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[1225] | 43 | |
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| 44 | tmp_sum=0; |
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| 45 | } |
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| 46 | m1pom+=(columns); |
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| 47 | } |
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| 48 | }; |
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| 49 | |
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| 50 | |
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[1240] | 51 | void bierman_fast(int16 *difz, int16 *xp, int16 *U, int16 *D, int16 *R, unsigned int16 dimy, unsigned int16 dimx ) |
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| 52 | { |
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| 53 | int16 alpha; |
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| 54 | int16 beta,lambda; |
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| 55 | int16 b[5]; // ok even for 4-dim state |
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| 56 | int16 *a; // in [0,1] -> q15 |
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| 57 | unsigned int16 iy,j,i; |
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[1225] | 58 | |
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[1240] | 59 | int16 *b_j,*b_i; |
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| 60 | int16 *a_j; |
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| 61 | int16 *D_j; |
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| 62 | int16 *U_ij; |
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| 63 | int16 *x_i; |
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[1225] | 64 | |
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[1240] | 65 | int32 z_pom; |
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| 66 | int16 z_pom_int16; |
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[1174] | 67 | |
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[1179] | 68 | a = U; // iyth row of U |
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| 69 | for (iy=0; iy<dimy; iy++, a+=dimx) { |
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| 70 | // a is a row |
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| 71 | for (j=0,a_j=a,b_j=b,D_j=D; j<dimx; j++,b_j++,D_j++,a_j++) |
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[1240] | 72 | *b_j=((int32)(*D_j)*(*a_j))>>15; |
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[1179] | 73 | |
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[1240] | 74 | alpha = R[iy]; //\alpha = R+vDv = R+a*b |
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[1179] | 75 | // R in q15, a in q15, b=q15 |
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| 76 | // gamma = (1<<15)/alpha; //(in q15) |
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| 77 | //min alpha = R[iy] = 164 |
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| 78 | //max gamma = 0.0061 => gamma_ref = q7 |
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| 79 | for (j=0,a_j=a,b_j=b,D_j=D; j<dimx; j++,a_j++,b_j++,D_j++) { |
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[1240] | 80 | /* beta=alpha; |
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| 81 | lambda = -((int32)(*a_j)<<15)/beta; |
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| 82 | alpha += ((int32)(*a_j)*(*b_j))>>15; |
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| 83 | D[j] = ((int32)beta**D_j)/alpha;*/ |
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| 84 | /*xx*/ |
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| 85 | lambda=alpha; |
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| 86 | alpha += ((int32)(*a_j)*(*b_j))>>15; |
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| 87 | D[j] = ((int32)lambda**D_j)/alpha; |
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| 88 | z_pom_int16 = -((int32)(*a_j)<<15)/lambda; |
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| 89 | /*xx*/ |
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| 90 | |
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[1179] | 91 | if (*D_j==0) *D_j=1; |
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| 92 | |
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| 93 | for (i=0,b_i=b,U_ij=U+j; i<j; i++, b_i++,U_ij+=dimx) { |
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| 94 | beta = *U_ij; |
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[1240] | 95 | // *U_ij += ((int32)lambda*(*b_i))>>15; // puvodni reseni |
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| 96 | *U_ij -= ((int32)(*a_j)*(*b_i))/lambda; // pozadovane optimalni reseni |
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| 97 | // *U_ij -= ((int32)((int16)((int32)(*a_j)<<15)/lambda)**b_i)>>15; // tohle funguje - problem je s tim pretypovanim na (int16) |
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| 98 | // *U_ij -= (int16)((int32)(*a_j)*(*b_i))/lambda; |
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| 99 | // z_pom = (((int32)(*a_j)*(*b_i))/lambda); |
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| 100 | /* z_pom = (int32)(*U_ij)-(int16)((int32)(*a_j)*(*b_i))/lambda; |
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| 101 | if (z_pom > 32767) z_pom = 32767; |
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| 102 | if (z_pom < - 32768) z_pom = -32768; |
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| 103 | *U_ij = z_pom; /**/ |
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| 104 | // *U_ij += ((int32)z_pom_int16*(*b_i))>>15; // puvodni reseni - jen jina konstanta |
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| 105 | *b_i += ((int32)beta*(*b_j))>>15; |
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[1179] | 106 | } |
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| 107 | } |
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| 108 | // no shift due to gamma |
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| 109 | for (i=0,x_i=xp,b_i=b; i<dimx; i++,x_i++,b_i++) { |
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[1240] | 110 | *x_i += ((int32)difz[iy]*(*b_i))/alpha; // multiply by unscaled Kalman gain |
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[1179] | 111 | } |
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| 112 | } |
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| 113 | } |
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| 114 | |
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[1240] | 115 | |
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[1179] | 116 | // Thorton procedure - Kalman predictive variance in UD |
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[1240] | 117 | void thorton_fast(int16 *U, int16 *D, int16 *PSIU, int16 *Q, int16 *G, int16 *Dold, unsigned int16 rows) { |
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| 118 | unsigned int16 i,j,k; |
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[1179] | 119 | // copy D to Dold |
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[1240] | 120 | int16 *Dold_i,*Dold_k; |
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| 121 | int16 *D_i; |
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| 122 | int16 *PSIU_ij,*PSIU_ik,*PSIU_jk; |
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| 123 | int16 *Q_jj,*Q_ii,*Q_kk; |
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| 124 | int16 *U_ji; |
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| 125 | int16 *G_ik,*G_jk; |
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| 126 | int16 irows,jrows; |
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| 127 | int32 sigma; // in qAU+15!! |
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| 128 | int32 z; |
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[1179] | 129 | |
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| 130 | for (i=0,Dold_i=Dold,D_i=D;i<rows;i++,Dold_i++,D_i++) { |
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| 131 | *Dold_i=*D_i; |
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| 132 | } |
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| 133 | |
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| 134 | // initialize G = eye() |
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| 135 | G_ik= G; |
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[1235] | 136 | *G_ik++=32767; |
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[1179] | 137 | for (i=0;i<rows-1;i++) { |
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| 138 | // clean elem before diag |
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| 139 | for (k=0; k<rows; k++) { |
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| 140 | *G_ik++=0; |
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| 141 | } |
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[1235] | 142 | *G_ik++=32767; |
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[1179] | 143 | } |
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| 144 | // eye created |
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| 145 | |
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| 146 | for (i=rows-1, Dold_i=Dold+i, D_i=D+i; |
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[1237] | 147 | 1; i--, Dold_i--,D_i--) { // stop if i==0 at the END! |
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[1179] | 148 | irows=i*rows; |
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| 149 | sigma = 0; |
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[1197] | 150 | for (k=0, PSIU_ik=PSIU+irows,Dold_k=Dold; |
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[1233] | 151 | k<rows; k++, PSIU_ik++,Dold_k++) { |
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[1240] | 152 | sigma += (((int32)(*PSIU_ik)**PSIU_ik)>>(qAU))*(*Dold_k); |
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[1225] | 153 | } |
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[1240] | 154 | sigma += (int32)(*(Q+i+irows))<<qAU; |
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[1179] | 155 | for (j=i+1, G_ik=G+irows+i+1; j<rows; j++,G_ik++) { |
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[1240] | 156 | sigma += (((int32)(*G_ik)**G_ik)>>16)**(Q+j+j*rows); |
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[1237] | 157 | } |
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[1235] | 158 | |
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[1240] | 159 | if (sigma>((int32)1<<(qAU+15))) { |
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[1235] | 160 | *D_i = 32767; |
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[1237] | 161 | // *(Dold+i)-=*(Q+i+irows); |
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[1235] | 162 | } else { |
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| 163 | *D_i=sigma>>qAU; |
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| 164 | } |
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[1179] | 165 | if (*D_i==0) *D_i=1; |
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| 166 | |
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| 167 | for (j=0;j<i;j++) { |
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| 168 | jrows = j*rows; |
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| 169 | |
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| 170 | sigma =0; |
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| 171 | for (k=0, PSIU_ik=PSIU+irows, PSIU_jk=PSIU+jrows, Dold_k=Dold; |
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| 172 | k<rows; k++, PSIU_ik++, PSIU_jk++, Dold_k++) { |
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[1225] | 173 | |
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[1240] | 174 | sigma += ((((int32)(*PSIU_ik)**PSIU_jk)>>qAU)**Dold_k); |
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[1179] | 175 | } |
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[1225] | 176 | |
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[1235] | 177 | for (k=i,G_ik=G+irows+i,G_jk=G+jrows+i,Q_kk=Q+k*rows+k; |
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[1225] | 178 | k<rows;k++,G_ik++,G_jk++,Q_kk+=rows+1) { |
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[1240] | 179 | sigma += ((((int32)*G_ik)**G_jk)>>16)**Q_kk; |
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[1179] | 180 | } |
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[1225] | 181 | |
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[1237] | 182 | z=(sigma/(*D_i))<<(15-qAU); // shift to q15 |
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[1179] | 183 | if (z>32767) z=32767; |
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| 184 | if (z<-32768) z=-32768; |
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| 185 | |
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| 186 | U_ji=U+jrows+i; |
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[1240] | 187 | *U_ji = (int16)z; |
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[1179] | 188 | |
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| 189 | |
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| 190 | for (k=0,PSIU_ik=PSIU+irows,PSIU_jk=PSIU+jrows; |
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| 191 | k<rows;k++,PSIU_ik++,PSIU_jk++) { |
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[1240] | 192 | *PSIU_jk -= ((int32)*U_ji**PSIU_ik)>>15; |
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[1179] | 193 | } |
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[1225] | 194 | |
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[1179] | 195 | for (k=0,G_jk=G+jrows,G_ik=G+irows; |
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[1225] | 196 | k<rows;k++, G_jk++, G_ik++) { |
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[1240] | 197 | *G_jk -= ((int32)*U_ji**G_ik)>>15; |
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[1179] | 198 | } |
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[1225] | 199 | |
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[1179] | 200 | } |
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[1235] | 201 | if (i==0) return; |
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[1179] | 202 | } |
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| 203 | } |
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| 204 | |
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[1225] | 205 | /* square root of 0<a<1 using taylor at 0.5 in q15*/ |
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| 206 | int int_sqrt(int x) { |
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[1230] | 207 | double xd(double(x)/32768.); |
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| 208 | return round(sqrt(xd)*32768); |
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[1237] | 209 | |
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[1225] | 210 | //sqrt(x) == 1/2*2^(1/2)+1/2*2^(1/2)*(x-1/2)-1/4*2^(1/2)*(x-1/2)^2 |
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| 211 | // = k1 + k1*(x-0.5) - k2*(x-0.5)(x-0.5); |
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| 212 | #define k1 23170 //0.5*sqrt(2)*32768 |
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| 213 | #define k2 11585 //0.25*sqrt(2)*32768 |
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| 214 | |
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| 215 | int tmp; |
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| 216 | if (x>6554) { |
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| 217 | int xm05=x-16384; |
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| 218 | tmp = ((long)k1*xm05)>>15; |
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| 219 | tmp-=(((long(k2)*xm05)>>15)*xm05)>>15; |
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| 220 | tmp +=k1; |
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| 221 | } else { |
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| 222 | tmp = 4*x; |
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| 223 | tmp-=long(8*x)*x>>15; |
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| 224 | } |
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| 225 | return tmp; |
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| 226 | } |
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| 227 | |
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| 228 | void householder(int *Ch /*= int *PSICh*/, int *Q, unsigned int dimx) { |
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| 229 | int k,j,i; |
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[1237] | 230 | int alpha,beta; |
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| 231 | long sigma; |
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[1225] | 232 | int B[25];//beware |
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| 233 | int w[5]; |
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| 234 | int v[5]; |
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| 235 | |
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| 236 | // copy Q to B |
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[1237] | 237 | for (i=0;i<dimx*dimx;i++) |
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| 238 | { |
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[1225] | 239 | B[i]=Q[i]; |
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| 240 | } |
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| 241 | |
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[1237] | 242 | for (k=dimx-1; k>=0; k--) |
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| 243 | { |
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[1225] | 244 | sigma=0; |
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[1237] | 245 | for (j=0;j<dimx;j++) |
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| 246 | { |
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| 247 | sigma+=(long)B[k*dimx+j]*B[k*dimx+j]; |
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[1225] | 248 | } |
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[1237] | 249 | for (j=0;j<=k;j++) |
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| 250 | { |
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| 251 | sigma+=(long)Ch[k*dimx+j]*Ch[k*dimx+j]; |
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[1225] | 252 | } |
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| 253 | /* double sigf=double(sigma)/(1<<15); |
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| 254 | double alpf = sqrt(sigf);*/ |
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[1237] | 255 | // if (sigma>16384) sigma=16384; |
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| 256 | // alpha=int_sqrt(sigma); |
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| 257 | alpha = (int)(sqrt((double)sigma)+0.5); // predelat pro DSP |
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[1225] | 258 | // alpha = alpf*(1<<15); |
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| 259 | // |
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| 260 | sigma=0; |
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| 261 | for (j=0;j<dimx;j++) { |
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| 262 | w[j]=B[k*dimx+j]; |
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[1237] | 263 | sigma+=(long)w[j])*w[j]; |
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[1225] | 264 | } |
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| 265 | for (j=0; j<=k;j++) { |
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| 266 | if (j==k) { |
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| 267 | v[j]=Ch[k*dimx+j]-alpha; |
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| 268 | } else { |
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| 269 | v[j]=Ch[k*dimx+j]; |
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| 270 | } |
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[1237] | 271 | sigma+=(long)v[j]*v[j]; |
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[1225] | 272 | } |
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[1237] | 273 | |
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| 274 | alpha=sigma>>16; |
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| 275 | if (alpha==0) alpha =1; |
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| 276 | |
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[1225] | 277 | for (i=0;i<=k;i++) { |
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| 278 | sigma=0; |
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| 279 | for (j=0;j<dimx;j++) { |
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[1237] | 280 | sigma+=(long)B[i*dimx+j]*w[j]; |
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[1225] | 281 | } |
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| 282 | for (j=0;j<=k;j++) { |
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[1237] | 283 | sigma+=(long)Ch[i*dimx+j]*v[j]; |
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[1225] | 284 | } |
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[1237] | 285 | |
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| 286 | sigma = sigma >> 15; // navrat do Q15 |
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| 287 | |
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| 288 | for (j=0;j<dimx;j++) |
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| 289 | { |
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| 290 | B[i*dimx+j]-=(sigma*w[j])/alpha; |
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[1225] | 291 | }; |
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[1237] | 292 | |
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| 293 | for (j=0;j<=k;j++) |
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| 294 | { |
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| 295 | Ch[i*dimx+j]-=(sigma*v[j])/alpha; |
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[1225] | 296 | } |
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| 297 | } |
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| 298 | } |
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| 299 | |
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| 300 | } |
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| 301 | |
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| 302 | void carlson(int *difz, int *xp, int *Ch, int *R, unsigned int dimy, unsigned int dimx ) { |
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| 303 | int alpha,beta,gamma; |
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| 304 | int delta, eta,epsilon,zeta,sigma,tau; |
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| 305 | int i,j,iy; |
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| 306 | int w[5]; |
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| 307 | |
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[1237] | 308 | for (iy=0; iy<dimy; iy++) |
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| 309 | { |
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[1225] | 310 | alpha=R[iy]; |
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| 311 | delta = difz[iy]; |
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| 312 | |
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[1237] | 313 | for (j=0;j<dimx;j++) |
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| 314 | { |
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[1225] | 315 | sigma=Ch[iy*dimx+j]; |
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| 316 | beta=alpha; |
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[1237] | 317 | alpha+=((long)sigma*sigma)>>15; |
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[1225] | 318 | // double ab=(double)alpha*beta/32768./32768.; |
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| 319 | // double s_ab=sqrt(ab); |
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[1239] | 320 | gamma=(int)(sqrt((double)((long)alpha*beta))+0.5); // predelat v DSP |
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[1225] | 321 | //gamma = round(s_ab*(1<<15)); |
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[1237] | 322 | // eta=((long)beta<<15) / gamma; |
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[1225] | 323 | //zeta=(long(sigma)<<15)/ gamma; |
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| 324 | w[j]=0; |
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| 325 | for (i=0;i<=j;i++) { |
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| 326 | tau=Ch[i*dimx+j]; |
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[1237] | 327 | Ch[i*dimx+j]=((long)beta*Ch[i*dimx+j] -(long)sigma*w[i])/gamma; |
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| 328 | w[i]+=((long)tau*sigma)>>15; |
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[1225] | 329 | } |
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| 330 | } |
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| 331 | |
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| 332 | //epsilon=(long(difz)<<15) / (alpha); // q15*q13/q13 = q15 |
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| 333 | for (i=0;i<dimx;i++) { |
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[1237] | 334 | xp[i]+=((long)w[i]*delta)/alpha; |
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[1225] | 335 | } |
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| 336 | } |
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| 337 | } |
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[1230] | 338 | |
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| 339 | /* perform Householder update of Ch matrix using PSI*Ch , Q, */ |
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| 340 | extern void givens(int *Ch /*= int *PSICh*/, int *Q, unsigned int dimx){ |
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| 341 | int i,j,k; |
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| 342 | int rho,s,c,tau; |
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[1237] | 343 | |
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[1230] | 344 | int A[25];//beware |
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| 345 | // copy Q to A |
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| 346 | for (i=0;i<dimx*dimx;i++) { |
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| 347 | A[i]=Q[i]; |
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| 348 | } |
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[1237] | 349 | |
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| 350 | |
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[1230] | 351 | for (i=dimx-1; i>=0; i--){ |
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| 352 | for (j=0; j<dimx; j++) { |
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| 353 | rho=int_sqrt(((long)Ch[i*dimx+i]*Ch[i*dimx+i]+long(A[i*dimx+j])*A[i*dimx+j])>>15); |
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| 354 | if (rho==0) break; |
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| 355 | s=(long(A[i*dimx+j])<<15)/rho; |
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| 356 | c=(long(Ch[i*dimx+i])<<15)/rho; |
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| 357 | for (k=0;k<=i; k++){ |
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| 358 | tau=(long(c)*A[k*dimx+j]-long(s)*Ch[k*dimx+i])>>15; |
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| 359 | Ch[k*dimx +i]=(long(s)*A[k*dimx+j]+long(c)*Ch[k*dimx+i])>>15; |
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| 360 | A[k*dimx +j]=tau; |
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| 361 | } |
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| 362 | } |
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| 363 | } |
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| 364 | for (j=0; j<i; j++){ |
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| 365 | rho=int_sqrt((long(Ch[i*dimx+i])*Ch[i*dimx+i]+long(Ch[i*dimx+j])*Ch[i*dimx+j])>>15); |
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| 366 | if (rho==0) break; |
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| 367 | s=(long(Ch[i*dimx+j])<<15)/rho; |
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| 368 | c=(long(Ch[i*dimx+i])<<15)/rho; |
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| 369 | for (k=0; k<=i; k++){ |
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| 370 | tau=(long(c)*Ch[k*dimx+j]-long(s)*Ch[k*dimx+i])>>15; |
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| 371 | Ch[k*dimx+i]=(long(s)*Ch[k*dimx+j]+long(c)*Ch[k*dimx+i])>>15; |
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| 372 | Ch[k*dimx+j]=tau; |
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| 373 | } |
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| 374 | } |
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| 375 | } |
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