[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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| 5 | V. Smidl |
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| 6 | |
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| 7 | Rev. 30.8.2010 |
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| 8 | |
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| 9 | 30.8.2010 Prvni verze |
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| 10 | |
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| 11 | *************************************/ |
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| 12 | #include "fixed.h" |
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| 13 | #include "stdio.h" |
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[1225] | 14 | #include <math.h> |
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| 15 | |
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| 16 | #include "matrix_vs.h" |
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| 17 | |
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[1174] | 18 | /* Matrix multiply Full matrix by upper diagonal matrix; */ |
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[1179] | 19 | void mmultAU(int *m1, int *up, int *result, unsigned int rows, unsigned int columns) { |
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| 20 | unsigned int i, j, k; |
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[1228] | 21 | long tmp_sum=0L; //in 15+qAU |
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[1179] | 22 | int *m2pom; |
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[1225] | 23 | int *m1pom=m1; |
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| 24 | int *respom=result; |
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[1174] | 25 | |
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[1179] | 26 | for (i=0; i<rows; i++) //rows of result |
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[1174] | 27 | { |
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[1179] | 28 | for (j=0; j<columns; j++) //columns of result |
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| 29 | { |
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| 30 | m2pom=up+j;//?? |
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[1174] | 31 | |
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[1179] | 32 | for (k=0; k<j; k++) //inner loop up to "j" - U(j,j)==1; |
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| 33 | { |
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[1228] | 34 | tmp_sum+=((long)(*(m1pom++))**m2pom)>>(15-qAU); |
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[1179] | 35 | m2pom+=columns; |
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| 36 | } |
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| 37 | // add the missing A(i,j) |
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[1228] | 38 | tmp_sum +=(long)(*m1pom)<<qAU; // no need to shift |
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[1225] | 39 | m1pom-=(j); // shift back to first element |
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[1174] | 40 | |
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[1179] | 41 | // saturation effect |
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[1228] | 42 | tmp_sum=tmp_sum>>15; |
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[1225] | 43 | if (tmp_sum>32767) { |
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| 44 | //tmp_sum=32767; |
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| 45 | } |
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| 46 | if (tmp_sum<-32768) { |
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| 47 | //tmp_sum=-32768; |
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| 48 | } |
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| 49 | // printf("Au - saturated\n"); |
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| 50 | |
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| 51 | *respom++=tmp_sum; |
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| 52 | |
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| 53 | tmp_sum=0; |
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| 54 | } |
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| 55 | m1pom+=(columns); |
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| 56 | } |
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| 57 | }; |
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| 58 | |
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| 59 | /* Matrix multiply Full matrix by upper diagonal matrix; */ |
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| 60 | void mmultACh(int *m1, int *up, int *result, unsigned int rows, unsigned int columns) { |
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| 61 | unsigned int i, j, k; |
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| 62 | long tmp_sum=0L; |
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| 63 | int *m2pom; |
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| 64 | int *m1pom=m1; |
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| 65 | int *respom=result; |
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| 66 | |
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| 67 | for (i=0; i<rows; i++) //rows of result |
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| 68 | { |
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| 69 | for (j=0; j<columns; j++) //columns of result |
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| 70 | { |
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| 71 | m2pom=up+j;//?? |
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| 72 | |
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| 73 | for (k=0; k<=j; k++) //inner loop up to "j" - U(j,j)==1; |
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| 74 | { |
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| 75 | tmp_sum+=(long)(*(m1pom++))**m2pom; |
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| 76 | m2pom+=columns; |
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| 77 | } |
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| 78 | m1pom-=(j+1); // shift back to first element |
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| 79 | |
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| 80 | // saturation effect |
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[1179] | 81 | tmp_sum=tmp_sum>>15; |
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[1225] | 82 | if (tmp_sum>32767) { |
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| 83 | if (i!=3) tmp_sum=32767; |
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| 84 | } |
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| 85 | if (tmp_sum<-32768) { |
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| 86 | tmp_sum=-32768; |
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| 87 | } |
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| 88 | // printf("Au - saturated\n"); |
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[1174] | 89 | |
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[1225] | 90 | *respom++=tmp_sum; |
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[1174] | 91 | |
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[1179] | 92 | tmp_sum=0; |
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| 93 | } |
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[1225] | 94 | m1pom+=(columns); |
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[1174] | 95 | } |
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| 96 | }; |
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| 97 | |
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[1182] | 98 | bool DBG=true; |
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| 99 | |
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| 100 | void show(const char name[10], int *I, int n) { |
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[1225] | 101 | if (!DBG) return; |
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| 102 | |
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| 103 | printf("%s: ",name); |
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[1182] | 104 | for (int i=0;i<n;i++) { |
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[1225] | 105 | printf("%d ",*(I+i)); |
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| 106 | } |
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[1179] | 107 | printf("\n"); |
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[1174] | 108 | } |
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[1179] | 109 | |
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[1174] | 110 | // Thorton procedure - Kalman predictive variance in UD |
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[1179] | 111 | void thorton(int *U, int *D, int *PSIU, int *Q, int *G, int *Dold, unsigned int rows) { |
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| 112 | unsigned int i,j,k; |
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| 113 | // copy D to Dold |
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| 114 | int *Dold_pom=Dold; |
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| 115 | for (i=0;i<rows;i++) { |
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| 116 | *Dold_pom++=*D++; |
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| 117 | } |
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| 118 | D-=rows; // back to first D |
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| 119 | |
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| 120 | // initialize G = eye() |
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| 121 | int *G_pom = G; |
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| 122 | *G_pom++=1<<14; |
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| 123 | for (i=0;i<rows-1;i++) { |
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| 124 | // clean elem before diag |
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| 125 | for (j=0; j<rows; j++) { |
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| 126 | *G_pom++=0.0; |
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| 127 | } |
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| 128 | *G_pom++=1<<14; |
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| 129 | } |
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| 130 | // eye created |
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| 131 | |
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[1182] | 132 | long sigma; // in q30!!!!!! |
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| 133 | for (i=rows-1; true;i--) { // check i==0 at the END! |
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[1179] | 134 | sigma = 0; |
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[1225] | 135 | |
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[1179] | 136 | for (j=0;j<rows; j++) { |
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[1225] | 137 | //long s1=(((long)PSIU[i+j*rows]*PSIU[i+j*rows])>>15)*(Dold[i]); |
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[1228] | 138 | long s2=((((long)PSIU[i*rows+j]*PSIU[i*rows+j]))>>(2*qAU-15))*Dold[j]; |
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[1182] | 139 | // printf("%d - %d\n",s1,s2); |
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[1225] | 140 | sigma += s2; |
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| 141 | } |
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| 142 | sigma += Q[i*rows+i]<<15; |
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[1179] | 143 | for (j=i+1;j<rows; j++) { |
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| 144 | sigma += (((long)G[i*rows+j]*G[i*rows+j])>>13)*Q[j*rows+j]; |
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[1182] | 145 | // sigma += (((long)G[i+j*rows]*G[i+j*rows])>>13)*Q[j+j*rows]; |
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[1225] | 146 | } |
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| 147 | |
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[1228] | 148 | // if (sigma>16384<<15) sigma = 16384<<15; |
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[1179] | 149 | *(D+i)=sigma>>15; |
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| 150 | if (D[i]==0) D[i]=1; |
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[1182] | 151 | //show("D",D,5); |
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[1174] | 152 | |
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[1179] | 153 | for (j=0;j<i;j++) { |
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[1174] | 154 | // printf("\n%d,%d\n",i,j); |
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[1179] | 155 | sigma =0; |
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| 156 | for (k=0;k<rows;k++) { |
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[1228] | 157 | sigma += (((long(PSIU[i*rows+k])*PSIU[j*rows+k]))>>(2*qAU-15))*Dold[k]; |
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[1225] | 158 | } |
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| 159 | for (k=0;k<rows;k++) { |
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[1179] | 160 | sigma += ((((long)G[i*rows+k])*G[j*rows+k])>>13)*Q[k*rows+k]; |
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| 161 | } |
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[1225] | 162 | long z=sigma/D[i]; // shift by 15 |
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[1179] | 163 | if (z>32767) z=32767; |
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| 164 | if (z<-32768) z=-32768; |
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[1174] | 165 | |
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[1179] | 166 | U[j*rows+i] = (int)z; |
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| 167 | |
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| 168 | |
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| 169 | for (k=0;k<rows;k++) { |
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[1225] | 170 | PSIU[j*rows+k] -= ((long)U[j*rows+i]*PSIU[i*rows+k])>>15; //qAU*q15/q15=qAU |
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[1179] | 171 | } |
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[1225] | 172 | |
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[1179] | 173 | for (k=0;k<rows;k++) { |
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| 174 | G[j*rows+k] -= ((long)U[j*rows+i]*G[i*rows+k])>>15; |
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| 175 | } |
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[1225] | 176 | |
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[1179] | 177 | } |
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[1182] | 178 | //show("U",U,25); |
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[1225] | 179 | //show("G",G,25); |
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| 180 | if (i==0) return; |
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[1179] | 181 | } |
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[1174] | 182 | } |
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| 183 | |
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[1179] | 184 | void bierman_fast(int *difz, int *xp, int *U, int *D, int *R, unsigned int dimy, unsigned int dimx ) { |
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| 185 | int alpha; |
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| 186 | int beta,lambda; |
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| 187 | int b[5]; // ok even for 4-dim state |
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| 188 | int *a; // in [0,1] -> q15 |
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| 189 | unsigned int iy,j,i; |
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| 190 | |
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| 191 | int *b_j,*b_i; |
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| 192 | int *a_j; |
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| 193 | int *D_j; |
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| 194 | int *U_ij; |
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| 195 | int *x_i; |
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| 196 | a = U; // iyth row of U |
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| 197 | for (iy=0; iy<dimy; iy++, a+=dimx) { |
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| 198 | // a is a row |
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| 199 | 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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| 200 | *b_j=((long)(*D_j)*(*a_j))>>15; |
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| 201 | |
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| 202 | alpha = (long)R[iy]; //\alpha = R+vDv = R+a*b |
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| 203 | // R in q15, a in q15, b=q15 |
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| 204 | // gamma = (1<<15)/alpha; //(in q15) |
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| 205 | //min alpha = R[iy] = 164 |
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| 206 | //max gamma = 0.0061 => gamma_ref = q7 |
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| 207 | 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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| 208 | beta = alpha; |
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| 209 | lambda = -((long)(*a_j)<<15)/beta; |
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[1195] | 210 | alpha += ((long)(*a_j)*(*b_j))>>15; |
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| 211 | D[j] = ((((long)beta<<15)/alpha)*(*D_j))>>15; //gamma is long |
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[1179] | 212 | if (*D_j==0) *D_j=1; |
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| 213 | |
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| 214 | for (i=0,b_i=b,U_ij=U+j; i<j; i++, b_i++,U_ij+=dimx) { |
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| 215 | beta = *U_ij; |
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[1195] | 216 | *U_ij += ((long)lambda*(*b_i))>>15; |
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[1179] | 217 | *b_i += ((long)beta*(*b_j))>>15; |
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| 218 | } |
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| 219 | } |
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| 220 | int dzs = (((long)difz[iy])<<15)/alpha; // apply scaling to innovations |
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| 221 | // no shift due to gamma |
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| 222 | for (i=0,x_i=xp,b_i=b; i<dimx; i++,x_i++,b_i++) { |
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| 223 | *x_i += ((long)dzs*(*b_i))>>15; // multiply by unscaled Kalman gain |
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| 224 | } |
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| 225 | |
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| 226 | //cout << "Ub: " << U << endl; |
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| 227 | //cout << "Db: " << D << endl <<endl; |
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| 228 | |
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| 229 | } |
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| 230 | |
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| 231 | } |
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| 232 | |
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| 233 | // Thorton procedure - Kalman predictive variance in UD |
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| 234 | void thorton_fast(int *U, int *D, int *PSIU, int *Q, int *G, int *Dold, unsigned int rows) { |
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| 235 | unsigned int i,j,k; |
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| 236 | // copy D to Dold |
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| 237 | int *Dold_i,*Dold_k; |
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| 238 | int *D_i; |
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| 239 | int *PSIU_ij,*PSIU_ik,*PSIU_jk; |
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| 240 | int *Q_jj,*Q_ii,*Q_kk; |
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| 241 | int *U_ji; |
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| 242 | int *G_ik,*G_jk; |
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| 243 | int irows,jrows; |
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[1197] | 244 | long sigma; // in q30!! |
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[1179] | 245 | |
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| 246 | for (i=0,Dold_i=Dold,D_i=D;i<rows;i++,Dold_i++,D_i++) { |
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| 247 | *Dold_i=*D_i; |
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| 248 | } |
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| 249 | |
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| 250 | // initialize G = eye() |
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| 251 | G_ik= G; |
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| 252 | *G_ik++=1<<14; |
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| 253 | for (i=0;i<rows-1;i++) { |
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| 254 | // clean elem before diag |
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| 255 | for (k=0; k<rows; k++) { |
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| 256 | *G_ik++=0; |
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| 257 | } |
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| 258 | *G_ik++=1<<14; |
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| 259 | } |
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| 260 | // eye created |
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| 261 | |
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| 262 | for (i=rows-1, Dold_i=Dold+i, D_i=D+i; |
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| 263 | true; i--, Dold_i--,D_i--) { // stop if i==0 at the END! |
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| 264 | irows=i*rows; |
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| 265 | sigma = 0; |
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[1197] | 266 | for (k=0, PSIU_ik=PSIU+irows,Dold_k=Dold; |
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[1225] | 267 | k<rows; k++, PSIU_ik++,Dold_k++) {//Dold_i= |
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[1228] | 268 | sigma += (((long)(*PSIU_ik)**PSIU_ik)>>15)*(*Dold_k); |
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[1225] | 269 | } |
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| 270 | sigma += *(Q+i+irows)<<15; |
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[1179] | 271 | for (j=i+1, G_ik=G+irows+i+1; j<rows; j++,G_ik++) { |
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| 272 | sigma += (((long)(*G_ik)**G_ik)>>13)**(Q+j+j*rows); |
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[1225] | 273 | |
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[1179] | 274 | } |
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[1225] | 275 | |
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[1179] | 276 | *D_i=sigma>>15; |
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| 277 | if (*D_i==0) *D_i=1; |
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| 278 | |
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| 279 | |
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| 280 | for (j=0;j<i;j++) { |
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| 281 | jrows = j*rows; |
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| 282 | |
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| 283 | sigma =0; |
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| 284 | for (k=0, PSIU_ik=PSIU+irows, PSIU_jk=PSIU+jrows, Dold_k=Dold; |
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| 285 | k<rows; k++, PSIU_ik++, PSIU_jk++, Dold_k++) { |
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[1225] | 286 | |
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[1228] | 287 | sigma += ((((long)*PSIU_ik)**PSIU_jk)>>15)**Dold_k; |
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[1179] | 288 | } |
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[1225] | 289 | |
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[1179] | 290 | for (k=i,G_ik=G+irows+i,G_jk=G+jrows+i,Q_kk=Q+k*rows+k; |
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[1225] | 291 | k<rows;k++,G_ik++,G_jk++,Q_kk+=rows+1) { |
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[1179] | 292 | sigma += ((((long)*G_ik)**G_jk)>>13)**Q_kk; |
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| 293 | } |
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[1225] | 294 | |
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| 295 | long z=sigma/(*D_i); // shift by 15 |
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[1179] | 296 | if (z>32767) z=32767; |
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| 297 | if (z<-32768) z=-32768; |
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| 298 | |
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| 299 | U_ji=U+jrows+i; |
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| 300 | *U_ji = (int)z; |
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| 301 | |
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| 302 | |
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| 303 | for (k=0,PSIU_ik=PSIU+irows,PSIU_jk=PSIU+jrows; |
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| 304 | k<rows;k++,PSIU_ik++,PSIU_jk++) { |
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| 305 | *PSIU_jk -= ((long)*U_ji**PSIU_ik)>>15; |
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| 306 | } |
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[1225] | 307 | |
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[1179] | 308 | for (k=0,G_jk=G+jrows,G_ik=G+irows; |
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[1225] | 309 | k<rows;k++, G_jk++, G_ik++) { |
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[1179] | 310 | *G_jk -= ((long)*U_ji**G_ik)>>15; |
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| 311 | } |
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[1225] | 312 | |
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[1179] | 313 | } |
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| 314 | if (i==0) return; |
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| 315 | } |
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| 316 | } |
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| 317 | |
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| 318 | void bierman(int *difz, int *xp, int *U, int *D, int *R, unsigned int dimy, unsigned int dimx ) { |
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| 319 | long alpha; |
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| 320 | long gamma,beta,lambda; |
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| 321 | int b[5]; // ok even for 4-dim state |
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| 322 | int *a; // in [0,1] -> q15 |
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| 323 | unsigned int iy,j,i; |
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| 324 | |
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| 325 | for (iy=0; iy<dimy; iy++) { |
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| 326 | // a is a row |
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| 327 | a = U+iy*dimx; // iyth row of U |
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[1225] | 328 | for (j=0;j<dimx;j++) { |
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| 329 | (j<iy)? b[j]=0: (j==iy)? b[j]=D[j] : b[j]=((long)D[j]*a[j])>>15; |
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| 330 | } |
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[1179] | 331 | |
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| 332 | alpha = (long)R[iy]; //\alpha = R+vDv = R+a*b |
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| 333 | // R in q15, a in q15, b=q15 |
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| 334 | // gamma = (1<<15)/alpha; //(in q15) |
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| 335 | //min alpha = R[iy] = 164 |
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| 336 | //max gamma = 0.0061 => gamma_ref = q7 |
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| 337 | for (j=0;j<dimx;j++) { |
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| 338 | beta = alpha; |
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[1225] | 339 | lambda = -(((long)a[j])<<15)/beta; |
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| 340 | alpha += (((long)(a[j])*b[j])>>15); |
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| 341 | D[j] = (((((long)beta)<<15)/alpha)*D[j])>>15; //gamma is long |
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[1179] | 342 | if (D[j]==0) D[j]=1; |
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| 343 | |
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| 344 | // cout << "a: " << alpha << "g: " << gamma << endl; |
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| 345 | for (i=0;i<j;i++) { |
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| 346 | beta = U[i*dimx+j]; |
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| 347 | U[i*dimx+j] += (lambda*b[i])>>15; |
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| 348 | b[i] += (beta*b[j])>>15; |
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| 349 | } |
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| 350 | } |
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| 351 | int dzs = (((long)difz[iy])<<15)/alpha; // apply scaling to innovations |
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| 352 | // no shift due to gamma |
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| 353 | for (i=0; i<dimx; i++) { |
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| 354 | xp[i] += ((long)dzs*b[i])>>15; // multiply by unscaled Kalman gain |
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| 355 | } |
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| 356 | |
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| 357 | //cout << "Ub: " << U << endl; |
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| 358 | //cout << "Db: " << D << endl <<endl; |
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| 359 | |
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| 360 | } |
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| 361 | |
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| 362 | } |
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[1225] | 363 | |
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| 364 | /* square root of 0<a<1 using taylor at 0.5 in q15*/ |
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| 365 | int int_sqrt(int x) { |
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| 366 | //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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| 367 | // = k1 + k1*(x-0.5) - k2*(x-0.5)(x-0.5); |
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| 368 | #define k1 23170 //0.5*sqrt(2)*32768 |
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| 369 | #define k2 11585 //0.25*sqrt(2)*32768 |
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| 370 | |
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| 371 | int tmp; |
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| 372 | if (x>6554) { |
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| 373 | int xm05=x-16384; |
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| 374 | tmp = ((long)k1*xm05)>>15; |
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| 375 | tmp-=(((long(k2)*xm05)>>15)*xm05)>>15; |
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| 376 | tmp +=k1; |
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| 377 | } else { |
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| 378 | tmp = 4*x; |
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| 379 | tmp-=long(8*x)*x>>15; |
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| 380 | } |
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| 381 | return tmp; |
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| 382 | } |
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| 383 | |
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| 384 | void householder(int *Ch /*= int *PSICh*/, int *Q, unsigned int dimx) { |
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| 385 | int k,j,i; |
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| 386 | int sigma,alpha,beta; |
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| 387 | int B[25];//beware |
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| 388 | int w[5]; |
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| 389 | int v[5]; |
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| 390 | |
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| 391 | // copy Q to B |
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| 392 | for (i=0;i<dimx*dimx;i++) { |
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| 393 | B[i]=Q[i]; |
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| 394 | } |
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| 395 | |
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| 396 | for (k=dimx-1; k>=0; k--) { |
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| 397 | sigma=0; |
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| 398 | for (j=0;j<dimx;j++) { |
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| 399 | sigma+=(long(B[k*dimx+j])*B[k*dimx+j])>>15; |
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| 400 | } |
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| 401 | for (j=0;j<=k;j++) { |
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| 402 | sigma+=(long(Ch[k*dimx+j])*Ch[k*dimx+j])>>15; |
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| 403 | } |
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| 404 | /* double sigf=double(sigma)/(1<<15); |
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| 405 | double alpf = sqrt(sigf);*/ |
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| 406 | alpha=int_sqrt(sigma); |
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| 407 | // alpha = alpf*(1<<15); |
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| 408 | // |
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| 409 | sigma=0; |
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| 410 | for (j=0;j<dimx;j++) { |
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| 411 | w[j]=B[k*dimx+j]; |
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| 412 | sigma+=(long(w[j])*w[j])>>15; |
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| 413 | } |
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| 414 | for (j=0; j<=k;j++) { |
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| 415 | if (j==k) { |
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| 416 | v[j]=Ch[k*dimx+j]-alpha; |
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| 417 | } else { |
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| 418 | v[j]=Ch[k*dimx+j]; |
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| 419 | } |
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| 420 | sigma+=(long(v[j])*v[j])>>15; |
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| 421 | } |
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| 422 | alpha=sigma>>1; |
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| 423 | for (i=0;i<=k;i++) { |
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| 424 | sigma=0; |
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| 425 | for (j=0;j<dimx;j++) { |
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| 426 | sigma+=(long(B[i*dimx+j])*w[j])>>15; |
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| 427 | } |
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| 428 | for (j=0;j<=k;j++) { |
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| 429 | sigma+=(long(Ch[i*dimx+j])*v[j])>>15; |
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| 430 | } |
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| 431 | for (j=0;j<dimx;j++) { |
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| 432 | B[i*dimx+j]-=(long(sigma)*w[j]/alpha); |
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| 433 | }; |
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| 434 | for (j=0;j<=k;j++) { |
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| 435 | Ch[i*dimx+j]-=(long(sigma)*v[j]/alpha); |
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| 436 | } |
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| 437 | } |
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| 438 | } |
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| 439 | |
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| 440 | } |
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| 441 | |
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| 442 | void carlson(int *difz, int *xp, int *Ch, int *R, unsigned int dimy, unsigned int dimx ) { |
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| 443 | int alpha,beta,gamma; |
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| 444 | int delta, eta,epsilon,zeta,sigma,tau; |
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| 445 | int i,j,iy; |
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| 446 | int w[5]; |
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| 447 | |
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| 448 | for (iy=0; iy<dimy; iy++) { |
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| 449 | alpha=R[iy]; |
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| 450 | delta = difz[iy]; |
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| 451 | |
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| 452 | for (j=0;j<dimx;j++) { |
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| 453 | sigma=Ch[iy*dimx+j]; |
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| 454 | beta=alpha; |
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| 455 | alpha+=(long(sigma)*sigma)>>15; |
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| 456 | // double ab=(double)alpha*beta/32768./32768.; |
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| 457 | // double s_ab=sqrt(ab); |
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| 458 | gamma=int_sqrt(((long)alpha*beta)>>15); |
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| 459 | //gamma = round(s_ab*(1<<15)); |
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| 460 | eta=(long (beta)<<15) / gamma; |
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| 461 | //zeta=(long(sigma)<<15)/ gamma; |
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| 462 | w[j]=0; |
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| 463 | for (i=0;i<=j;i++) { |
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| 464 | tau=Ch[i*dimx+j]; |
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| 465 | Ch[i*dimx+j]=((long(eta)*Ch[i*dimx+j])>>15) -(long(sigma)*w[i])/gamma; |
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| 466 | w[i]+=(long(tau)*sigma)>>15; |
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| 467 | } |
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| 468 | } |
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| 469 | |
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| 470 | //epsilon=(long(difz)<<15) / (alpha); // q15*q13/q13 = q15 |
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| 471 | for (i=0;i<dimx;i++) { |
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| 472 | xp[i]+=(long(w[i])*delta)/alpha; |
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| 473 | } |
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| 474 | } |
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| 475 | } |
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