Alex Leung / Mbed OS HealthTracker

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algorithm.cpp@1:bd9f39f9d91c, 2018-03-20 (annotated)

Committer:
a2824256
Date:
Tue Mar 20 02:21:49 2018 +0000
Revision:
1:bd9f39f9d91c
Parent:
0:4be500de690c 
repair main.cpp

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a2824256 0:4be500de690c 1 #include "algorithm.h"
a2824256 0:4be500de690c 2 #include "mbed.h"
a2824256 0:4be500de690c 3
a2824256 0:4be500de690c 4 void maxim_heart_rate_and_oxygen_saturation(uint32_t *pun_ir_buffer, int32_t n_ir_buffer_length, uint32_t *pun_red_buffer, int32_t *pn_spo2, int8_t *pch_spo2_valid,
a2824256 0:4be500de690c 5 int32_t *pn_heart_rate, int8_t *pch_hr_valid)
a2824256 0:4be500de690c 6 /**
a2824256 0:4be500de690c 7 * \brief Calculate the heart rate and SpO2 level
a2824256 0:4be500de690c 8 * \par Details
a2824256 0:4be500de690c 9 * By detecting peaks of PPG cycle and corresponding AC/DC of red/infra-red signal, the ratio for the SPO2 is computed.
a2824256 0:4be500de690c 10 * Since this algorithm is aiming for Arm M0/M3. formaula for SPO2 did not achieve the accuracy due to register overflow.
a2824256 0:4be500de690c 11 * Thus, accurate SPO2 is precalculated and save longo uch_spo2_table[] per each ratio.
a2824256 0:4be500de690c 12 *
a2824256 0:4be500de690c 13 * \param[in] *pun_ir_buffer - IR sensor data buffer
a2824256 0:4be500de690c 14 * \param[in] n_ir_buffer_length - IR sensor data buffer length
a2824256 0:4be500de690c 15 * \param[in] *pun_red_buffer - Red sensor data buffer
a2824256 0:4be500de690c 16 * \param[out] *pn_spo2 - Calculated SpO2 value
a2824256 0:4be500de690c 17 * \param[out] *pch_spo2_valid - 1 if the calculated SpO2 value is valid
a2824256 0:4be500de690c 18 * \param[out] *pn_heart_rate - Calculated heart rate value
a2824256 0:4be500de690c 19 * \param[out] *pch_hr_valid - 1 if the calculated heart rate value is valid
a2824256 0:4be500de690c 20 *
a2824256 0:4be500de690c 21 * \retval None
a2824256 0:4be500de690c 22 */
a2824256 0:4be500de690c 23 {
a2824256 0:4be500de690c 24 uint32_t un_ir_mean ,un_only_once ;
a2824256 0:4be500de690c 25 int32_t k ,n_i_ratio_count;
a2824256 0:4be500de690c 26 int32_t i, s, m, n_exact_ir_valley_locs_count ,n_middle_idx;
a2824256 0:4be500de690c 27 int32_t n_th1, n_npks,n_c_min;
a2824256 0:4be500de690c 28 int32_t an_ir_valley_locs[15] ;
a2824256 0:4be500de690c 29 int32_t an_exact_ir_valley_locs[15] ;
a2824256 0:4be500de690c 30 int32_t an_dx_peak_locs[15] ;
a2824256 0:4be500de690c 31 int32_t n_peak_interval_sum;
a2824256 0:4be500de690c 32
a2824256 0:4be500de690c 33 int32_t n_y_ac, n_x_ac;
a2824256 0:4be500de690c 34 int32_t n_spo2_calc;
a2824256 0:4be500de690c 35 int32_t n_y_dc_max, n_x_dc_max;
a2824256 0:4be500de690c 36 int32_t n_y_dc_max_idx, n_x_dc_max_idx;
a2824256 0:4be500de690c 37 int32_t an_ratio[5],n_ratio_average;
a2824256 0:4be500de690c 38 int32_t n_nume, n_denom ;
a2824256 0:4be500de690c 39 // remove DC of ir signal
a2824256 0:4be500de690c 40 un_ir_mean =0;
a2824256 0:4be500de690c 41 for (k=0 ; k<n_ir_buffer_length ; k++ ) un_ir_mean += pun_ir_buffer[k] ;
a2824256 0:4be500de690c 42 un_ir_mean =un_ir_mean/n_ir_buffer_length ;
a2824256 0:4be500de690c 43 for (k=0 ; k<n_ir_buffer_length ; k++ ) an_x[k] = pun_ir_buffer[k] - un_ir_mean ;
a2824256 0:4be500de690c 44
a2824256 0:4be500de690c 45 // 4 pt Moving Average
a2824256 0:4be500de690c 46 for(k=0; k< BUFFER_SIZE-MA4_SIZE; k++){
a2824256 0:4be500de690c 47 n_denom= ( an_x[k]+an_x[k+1]+ an_x[k+2]+ an_x[k+3]);
a2824256 0:4be500de690c 48 an_x[k]= n_denom/(int32_t)4;
a2824256 0:4be500de690c 49 }
a2824256 0:4be500de690c 50
a2824256 0:4be500de690c 51 // get difference of smoothed IR signal
a2824256 0:4be500de690c 52
a2824256 0:4be500de690c 53 for( k=0; k<BUFFER_SIZE-MA4_SIZE-1; k++)
a2824256 0:4be500de690c 54 an_dx[k]= (an_x[k+1]- an_x[k]);
a2824256 0:4be500de690c 55
a2824256 0:4be500de690c 56 // 2-pt Moving Average to an_dx
a2824256 0:4be500de690c 57 for(k=0; k< BUFFER_SIZE-MA4_SIZE-2; k++){
a2824256 0:4be500de690c 58 an_dx[k] = ( an_dx[k]+an_dx[k+1])/2 ;
a2824256 0:4be500de690c 59 }
a2824256 0:4be500de690c 60
a2824256 0:4be500de690c 61 // hamming window
a2824256 0:4be500de690c 62 // flip wave form so that we can detect valley with peak detector
a2824256 0:4be500de690c 63 for ( i=0 ; i<BUFFER_SIZE-HAMMING_SIZE-MA4_SIZE-2 ;i++){
a2824256 0:4be500de690c 64 s= 0;
a2824256 0:4be500de690c 65 for( k=i; k<i+ HAMMING_SIZE ;k++){
a2824256 0:4be500de690c 66 s -= an_dx[k] *auw_hamm[k-i] ;
a2824256 0:4be500de690c 67 }
a2824256 0:4be500de690c 68 an_dx[i]= s/ (int32_t)1146; // divide by sum of auw_hamm
a2824256 0:4be500de690c 69 }
a2824256 0:4be500de690c 70
a2824256 0:4be500de690c 71
a2824256 0:4be500de690c 72 n_th1=0; // threshold calculation
a2824256 0:4be500de690c 73 for ( k=0 ; k<BUFFER_SIZE-HAMMING_SIZE ;k++){
a2824256 0:4be500de690c 74 n_th1 += ((an_dx[k]>0)? an_dx[k] : ((int32_t)0-an_dx[k])) ;
a2824256 0:4be500de690c 75 }
a2824256 0:4be500de690c 76 n_th1= n_th1/ ( BUFFER_SIZE-HAMMING_SIZE);
a2824256 0:4be500de690c 77 // peak location is acutally index for sharpest location of raw signal since we flipped the signal
a2824256 0:4be500de690c 78 maxim_find_peaks( an_dx_peak_locs, &n_npks, an_dx, BUFFER_SIZE-HAMMING_SIZE, n_th1, 8, 5 );//peak_height, peak_distance, max_num_peaks
a2824256 0:4be500de690c 79
a2824256 0:4be500de690c 80 n_peak_interval_sum =0;
a2824256 0:4be500de690c 81 if (n_npks>=2){
a2824256 0:4be500de690c 82 for (k=1; k<n_npks; k++)
a2824256 0:4be500de690c 83 n_peak_interval_sum += (an_dx_peak_locs[k]-an_dx_peak_locs[k -1]);
a2824256 0:4be500de690c 84 n_peak_interval_sum=n_peak_interval_sum/(n_npks-1);
a2824256 0:4be500de690c 85 *pn_heart_rate=(int32_t)(6000/n_peak_interval_sum);// beats per minutes
a2824256 0:4be500de690c 86 *pch_hr_valid = 1;
a2824256 0:4be500de690c 87 }
a2824256 0:4be500de690c 88 else {
a2824256 0:4be500de690c 89 *pn_heart_rate = -999;
a2824256 0:4be500de690c 90 *pch_hr_valid = 0;
a2824256 0:4be500de690c 91 }
a2824256 0:4be500de690c 92
a2824256 0:4be500de690c 93 for ( k=0 ; k<n_npks ;k++)
a2824256 0:4be500de690c 94 an_ir_valley_locs[k]=an_dx_peak_locs[k]+HAMMING_SIZE/2;
a2824256 0:4be500de690c 95
a2824256 0:4be500de690c 96
a2824256 0:4be500de690c 97 // raw value : RED(=y) and IR(=X)
a2824256 0:4be500de690c 98 // we need to assess DC and AC value of ir and red PPG.
a2824256 0:4be500de690c 99 for (k=0 ; k<n_ir_buffer_length ; k++ ) {
a2824256 0:4be500de690c 100 an_x[k] = pun_ir_buffer[k] ;
a2824256 0:4be500de690c 101 an_y[k] = pun_red_buffer[k] ;
a2824256 0:4be500de690c 102 }
a2824256 0:4be500de690c 103
a2824256 0:4be500de690c 104 // find precise min near an_ir_valley_locs
a2824256 0:4be500de690c 105 n_exact_ir_valley_locs_count =0;
a2824256 0:4be500de690c 106 for(k=0 ; k<n_npks ;k++){
a2824256 0:4be500de690c 107 un_only_once =1;
a2824256 0:4be500de690c 108 m=an_ir_valley_locs[k];
a2824256 0:4be500de690c 109 n_c_min= 16777216;//2^24;
a2824256 0:4be500de690c 110 if (m+5 < BUFFER_SIZE-HAMMING_SIZE && m-5 >0){
a2824256 0:4be500de690c 111 for(i= m-5;i<m+5; i++)
a2824256 0:4be500de690c 112 if (an_x[i]<n_c_min){
a2824256 0:4be500de690c 113 if (un_only_once >0){
a2824256 0:4be500de690c 114 un_only_once =0;
a2824256 0:4be500de690c 115 }
a2824256 0:4be500de690c 116 n_c_min= an_x[i] ;
a2824256 0:4be500de690c 117 an_exact_ir_valley_locs[k]=i;
a2824256 0:4be500de690c 118 }
a2824256 0:4be500de690c 119 if (un_only_once ==0)
a2824256 0:4be500de690c 120 n_exact_ir_valley_locs_count ++ ;
a2824256 0:4be500de690c 121 }
a2824256 0:4be500de690c 122 }
a2824256 0:4be500de690c 123 if (n_exact_ir_valley_locs_count <2 ){
a2824256 0:4be500de690c 124 *pn_spo2 = -999 ; // do not use SPO2 since signal ratio is out of range
a2824256 0:4be500de690c 125 *pch_spo2_valid = 0;
a2824256 0:4be500de690c 126 return;
a2824256 0:4be500de690c 127 }
a2824256 0:4be500de690c 128 // 4 pt MA
a2824256 0:4be500de690c 129 for(k=0; k< BUFFER_SIZE-MA4_SIZE; k++){
a2824256 0:4be500de690c 130 an_x[k]=( an_x[k]+an_x[k+1]+ an_x[k+2]+ an_x[k+3])/(int32_t)4;
a2824256 0:4be500de690c 131 an_y[k]=( an_y[k]+an_y[k+1]+ an_y[k+2]+ an_y[k+3])/(int32_t)4;
a2824256 0:4be500de690c 132 }
a2824256 0:4be500de690c 133
a2824256 0:4be500de690c 134 //using an_exact_ir_valley_locs , find ir-red DC andir-red AC for SPO2 calibration ratio
a2824256 0:4be500de690c 135 //finding AC/DC maximum of raw ir * red between two valley locations
a2824256 0:4be500de690c 136 n_ratio_average =0;
a2824256 0:4be500de690c 137 n_i_ratio_count =0;
a2824256 0:4be500de690c 138
a2824256 0:4be500de690c 139 for(k=0; k< 5; k++) an_ratio[k]=0;
a2824256 0:4be500de690c 140 for (k=0; k< n_exact_ir_valley_locs_count; k++){
a2824256 0:4be500de690c 141 if (an_exact_ir_valley_locs[k] > BUFFER_SIZE ){
a2824256 0:4be500de690c 142 *pn_spo2 = -999 ; // do not use SPO2 since valley loc is out of range
a2824256 0:4be500de690c 143 *pch_spo2_valid = 0;
a2824256 0:4be500de690c 144 return;
a2824256 0:4be500de690c 145 }
a2824256 0:4be500de690c 146 }
a2824256 0:4be500de690c 147 // find max between two valley locations
a2824256 0:4be500de690c 148 // and use ratio betwen AC compoent of Ir & Red and DC compoent of Ir & Red for SPO2
a2824256 0:4be500de690c 149
a2824256 0:4be500de690c 150 for (k=0; k< n_exact_ir_valley_locs_count-1; k++){
a2824256 0:4be500de690c 151 n_y_dc_max= -16777216 ;
a2824256 0:4be500de690c 152 n_x_dc_max= - 16777216;
a2824256 0:4be500de690c 153 if (an_exact_ir_valley_locs[k+1]-an_exact_ir_valley_locs[k] >10){
a2824256 0:4be500de690c 154 for (i=an_exact_ir_valley_locs[k]; i< an_exact_ir_valley_locs[k+1]; i++){
a2824256 0:4be500de690c 155 if (an_x[i]> n_x_dc_max) {n_x_dc_max =an_x[i];n_x_dc_max_idx =i; }
a2824256 0:4be500de690c 156 if (an_y[i]> n_y_dc_max) {n_y_dc_max =an_y[i];n_y_dc_max_idx=i;}
a2824256 0:4be500de690c 157 }
a2824256 0:4be500de690c 158 n_y_ac= (an_y[an_exact_ir_valley_locs[k+1]] - an_y[an_exact_ir_valley_locs[k] ] )*(n_y_dc_max_idx -an_exact_ir_valley_locs[k]); //red
a2824256 0:4be500de690c 159 n_y_ac= an_y[an_exact_ir_valley_locs[k]] + n_y_ac/ (an_exact_ir_valley_locs[k+1] - an_exact_ir_valley_locs[k]) ;
a2824256 0:4be500de690c 160
a2824256 0:4be500de690c 161
a2824256 0:4be500de690c 162 n_y_ac= an_y[n_y_dc_max_idx] - n_y_ac; // subracting linear DC compoenents from raw
a2824256 0:4be500de690c 163 n_x_ac= (an_x[an_exact_ir_valley_locs[k+1]] - an_x[an_exact_ir_valley_locs[k] ] )*(n_x_dc_max_idx -an_exact_ir_valley_locs[k]); // ir
a2824256 0:4be500de690c 164 n_x_ac= an_x[an_exact_ir_valley_locs[k]] + n_x_ac/ (an_exact_ir_valley_locs[k+1] - an_exact_ir_valley_locs[k]);
a2824256 0:4be500de690c 165 n_x_ac= an_x[n_y_dc_max_idx] - n_x_ac; // subracting linear DC compoenents from raw
a2824256 0:4be500de690c 166 n_nume=( n_y_ac *n_x_dc_max)>>7 ; //prepare X100 to preserve floating value
a2824256 0:4be500de690c 167 n_denom= ( n_x_ac *n_y_dc_max)>>7;
a2824256 0:4be500de690c 168 if (n_denom>0 && n_i_ratio_count <5 && n_nume != 0)
a2824256 0:4be500de690c 169 {
a2824256 0:4be500de690c 170 an_ratio[n_i_ratio_count]= (n_nume*100)/n_denom ; //formular is ( n_y_ac *n_x_dc_max) / ( n_x_ac *n_y_dc_max) ;
a2824256 0:4be500de690c 171 n_i_ratio_count++;
a2824256 0:4be500de690c 172 }
a2824256 0:4be500de690c 173 }
a2824256 0:4be500de690c 174 }
a2824256 0:4be500de690c 175
a2824256 0:4be500de690c 176 maxim_sort_ascend(an_ratio, n_i_ratio_count);
a2824256 0:4be500de690c 177 n_middle_idx= n_i_ratio_count/2;
a2824256 0:4be500de690c 178
a2824256 0:4be500de690c 179 if (n_middle_idx >1)
a2824256 0:4be500de690c 180 n_ratio_average =( an_ratio[n_middle_idx-1] +an_ratio[n_middle_idx])/2; // use median
a2824256 0:4be500de690c 181 else
a2824256 0:4be500de690c 182 n_ratio_average = an_ratio[n_middle_idx ];
a2824256 0:4be500de690c 183
a2824256 0:4be500de690c 184 if( n_ratio_average>2 && n_ratio_average <184){
a2824256 0:4be500de690c 185 n_spo2_calc= uch_spo2_table[n_ratio_average] ;
a2824256 0:4be500de690c 186 *pn_spo2 = n_spo2_calc ;
a2824256 0:4be500de690c 187 *pch_spo2_valid = 1;// float_SPO2 = -45.060*n_ratio_average* n_ratio_average/10000 + 30.354 *n_ratio_average/100 + 94.845 ; // for comparison with table
a2824256 0:4be500de690c 188 }
a2824256 0:4be500de690c 189 else{
a2824256 0:4be500de690c 190 *pn_spo2 = -999 ; // do not use SPO2 since signal ratio is out of range
a2824256 0:4be500de690c 191 *pch_spo2_valid = 0;
a2824256 0:4be500de690c 192 }
a2824256 0:4be500de690c 193 }
a2824256 0:4be500de690c 194
a2824256 0:4be500de690c 195
a2824256 0:4be500de690c 196 void maxim_find_peaks(int32_t *pn_locs, int32_t *pn_npks, int32_t *pn_x, int32_t n_size, int32_t n_min_height, int32_t n_min_distance, int32_t n_max_num)
a2824256 0:4be500de690c 197 /**
a2824256 0:4be500de690c 198 * \brief Find peaks
a2824256 0:4be500de690c 199 * \par Details
a2824256 0:4be500de690c 200 * Find at most MAX_NUM peaks above MIN_HEIGHT separated by at least MIN_DISTANCE
a2824256 0:4be500de690c 201 *
a2824256 0:4be500de690c 202 * \retval None
a2824256 0:4be500de690c 203 */
a2824256 0:4be500de690c 204 {
a2824256 0:4be500de690c 205 maxim_peaks_above_min_height( pn_locs, pn_npks, pn_x, n_size, n_min_height );
a2824256 0:4be500de690c 206 maxim_remove_close_peaks( pn_locs, pn_npks, pn_x, n_min_distance );
a2824256 0:4be500de690c 207 *pn_npks = min( *pn_npks, n_max_num );
a2824256 0:4be500de690c 208 }
a2824256 0:4be500de690c 209
a2824256 0:4be500de690c 210 void maxim_peaks_above_min_height(int32_t *pn_locs, int32_t *pn_npks, int32_t *pn_x, int32_t n_size, int32_t n_min_height)
a2824256 0:4be500de690c 211 /**
a2824256 0:4be500de690c 212 * \brief Find peaks above n_min_height
a2824256 0:4be500de690c 213 * \par Details
a2824256 0:4be500de690c 214 * Find all peaks above MIN_HEIGHT
a2824256 0:4be500de690c 215 *
a2824256 0:4be500de690c 216 * \retval None
a2824256 0:4be500de690c 217 */
a2824256 0:4be500de690c 218 {
a2824256 0:4be500de690c 219 int32_t i = 1, n_width;
a2824256 0:4be500de690c 220 *pn_npks = 0;
a2824256 0:4be500de690c 221
a2824256 0:4be500de690c 222 while (i < n_size-1){
a2824256 0:4be500de690c 223 if (pn_x[i] > n_min_height && pn_x[i] > pn_x[i-1]){ // find left edge of potential peaks
a2824256 0:4be500de690c 224 n_width = 1;
a2824256 0:4be500de690c 225 while (i+n_width < n_size && pn_x[i] == pn_x[i+n_width]) // find flat peaks
a2824256 0:4be500de690c 226 n_width++;
a2824256 0:4be500de690c 227 if (pn_x[i] > pn_x[i+n_width] && (*pn_npks) < 15 ){ // find right edge of peaks
a2824256 0:4be500de690c 228 pn_locs[(*pn_npks)++] = i;
a2824256 0:4be500de690c 229 // for flat peaks, peak location is left edge
a2824256 0:4be500de690c 230 i += n_width+1;
a2824256 0:4be500de690c 231 }
a2824256 0:4be500de690c 232 else
a2824256 0:4be500de690c 233 i += n_width;
a2824256 0:4be500de690c 234 }
a2824256 0:4be500de690c 235 else
a2824256 0:4be500de690c 236 i++;
a2824256 0:4be500de690c 237 }
a2824256 0:4be500de690c 238 }
a2824256 0:4be500de690c 239
a2824256 0:4be500de690c 240
a2824256 0:4be500de690c 241 void maxim_remove_close_peaks(int32_t *pn_locs, int32_t *pn_npks, int32_t *pn_x, int32_t n_min_distance)
a2824256 0:4be500de690c 242 /**
a2824256 0:4be500de690c 243 * \brief Remove peaks
a2824256 0:4be500de690c 244 * \par Details
a2824256 0:4be500de690c 245 * Remove peaks separated by less than MIN_DISTANCE
a2824256 0:4be500de690c 246 *
a2824256 0:4be500de690c 247 * \retval None
a2824256 0:4be500de690c 248 */
a2824256 0:4be500de690c 249 {
a2824256 0:4be500de690c 250
a2824256 0:4be500de690c 251 int32_t i, j, n_old_npks, n_dist;
a2824256 0:4be500de690c 252
a2824256 0:4be500de690c 253 /* Order peaks from large to small */
a2824256 0:4be500de690c 254 maxim_sort_indices_descend( pn_x, pn_locs, *pn_npks );
a2824256 0:4be500de690c 255
a2824256 0:4be500de690c 256 for ( i = -1; i < *pn_npks; i++ ){
a2824256 0:4be500de690c 257 n_old_npks = *pn_npks;
a2824256 0:4be500de690c 258 *pn_npks = i+1;
a2824256 0:4be500de690c 259 for ( j = i+1; j < n_old_npks; j++ ){
a2824256 0:4be500de690c 260 n_dist = pn_locs[j] - ( i == -1 ? -1 : pn_locs[i] ); // lag-zero peak of autocorr is at index -1
a2824256 0:4be500de690c 261 if ( n_dist > n_min_distance || n_dist < -n_min_distance )
a2824256 0:4be500de690c 262 pn_locs[(*pn_npks)++] = pn_locs[j];
a2824256 0:4be500de690c 263 }
a2824256 0:4be500de690c 264 }
a2824256 0:4be500de690c 265
a2824256 0:4be500de690c 266 // Resort indices longo ascending order
a2824256 0:4be500de690c 267 maxim_sort_ascend( pn_locs, *pn_npks );
a2824256 0:4be500de690c 268 }
a2824256 0:4be500de690c 269
a2824256 0:4be500de690c 270 void maxim_sort_ascend(int32_t *pn_x,int32_t n_size)
a2824256 0:4be500de690c 271 /**
a2824256 0:4be500de690c 272 * \brief Sort array
a2824256 0:4be500de690c 273 * \par Details
a2824256 0:4be500de690c 274 * Sort array in ascending order (insertion sort algorithm)
a2824256 0:4be500de690c 275 *
a2824256 0:4be500de690c 276 * \retval None
a2824256 0:4be500de690c 277 */
a2824256 0:4be500de690c 278 {
a2824256 0:4be500de690c 279 int32_t i, j, n_temp;
a2824256 0:4be500de690c 280 for (i = 1; i < n_size; i++) {
a2824256 0:4be500de690c 281 n_temp = pn_x[i];
a2824256 0:4be500de690c 282 for (j = i; j > 0 && n_temp < pn_x[j-1]; j--)
a2824256 0:4be500de690c 283 pn_x[j] = pn_x[j-1];
a2824256 0:4be500de690c 284 pn_x[j] = n_temp;
a2824256 0:4be500de690c 285 }
a2824256 0:4be500de690c 286 }
a2824256 0:4be500de690c 287
a2824256 0:4be500de690c 288 void maxim_sort_indices_descend(int32_t *pn_x, int32_t *pn_indx, int32_t n_size)
a2824256 0:4be500de690c 289 /**
a2824256 0:4be500de690c 290 * \brief Sort indices
a2824256 0:4be500de690c 291 * \par Details
a2824256 0:4be500de690c 292 * Sort indices according to descending order (insertion sort algorithm)
a2824256 0:4be500de690c 293 *
a2824256 0:4be500de690c 294 * \retval None
a2824256 0:4be500de690c 295 */
a2824256 0:4be500de690c 296 {
a2824256 0:4be500de690c 297 int32_t i, j, n_temp;
a2824256 0:4be500de690c 298 for (i = 1; i < n_size; i++) {
a2824256 0:4be500de690c 299 n_temp = pn_indx[i];
a2824256 0:4be500de690c 300 for (j = i; j > 0 && pn_x[n_temp] > pn_x[pn_indx[j-1]]; j--)
a2824256 0:4be500de690c 301 pn_indx[j] = pn_indx[j-1];
a2824256 0:4be500de690c 302 pn_indx[j] = n_temp;
a2824256 0:4be500de690c 303 }
a2824256 0:4be500de690c 304 }