Some math tricks in GNU awk

 0           0.0165
10           0.0124
20           0.0093
30           0.0071
40           0.0053
50           0.0039
60           0.0029

1. Sum of the 1^st column:
   awk '{ sum += $1} ; END {print sum}' N2O5.txt
   210
   
   
2. Math inside awk :
   awk -F' ' '{print $1, $2, log($2), 1/($2)}' N2O5.txt
   Or
   awk -F' ' '{natlog=log($2); inv=1/$2; print $1, $2, natlog, inv}' N2O5.txt
   Compare the output with
   awk -F' ' '{natlog=log($2); inv=1/$2; printf "%2d %.8f %.8f %.8f\n", $1, $2, natlog, inv}' N2O5.txt

   
   
3. Example of floating-point (FP) precision consideration: the IEEE Standard for FP Arithmetic
   awk 'BEGIN { printf "%.17f\n", 99.15-20.85 }'
awk -M -v PREC="double" 'BEGIN { printf "%.17f\n", 99.15-20.85 }'
awk -M -v PREC="quad" 'BEGIN { printf "%.17f\n", 99.15-20.85 }'
awk -M -v PREC=113 'BEGIN { printf "%.17f\n", 99.15-20.85 }'

   
   
4. awk loops to calculate $y_2-y_1$, $y_3-y_2$, $y_4-y_3$ ... etc, or divisions alike.
   
   awk -F' ' '{printf " " $2}' N2O5.txt | awk -F' ' '{for (i=1;i<NF;++i) print $(i+1)"-"$i}' | bc -l
awk -F' ' '{printf " " $2}' N2O5.txt | awk -F' ' '{for (i=1;i<NF;++i) printf $(i+1)-$i"\n"}'
awk -F' ' '{printf " " $2}' N2O5.txt | awk -F' ' '{for (i=1;i<NF;++i) printf "%.8f\n", $(i+1)-$i}'
awk -F' ' '{printf " " $2}' N2O5.txt | awk -F' ' '{for (i=1;i<NF;++i) print "scale=8; "$(i+1)"/"$i}' | bc -l

   
   
5. Calculate devation and derivative using column-based recursive operations in awk :
   awk '{if (NR>1) printf "%3d\t %s\t %.8f\n", $1, $2, ($3-y); y=$3 }' ~jsyu/atom.3 |grep -B1 -
awk '{if (NR>1) printf "%.8f\n", ($2-y)/($1-x); x=$1; y=$2 }' N2O5.txt
awk '{if (NR>1) print "("$2"-y)/("$1"-x)"; x=$1; y=$2 }' N2O5.txt | bc -l
↑↑↑ The loop will NOT work outside awk!!

   
   
6. Least square fitting using awk, script driven by bash

   #!/bin/bash exec awk ' BEGIN { FS = "[ ,\t]+" } NF == 2 { x_sum += $1 y_sum += $2 xy_sum += $1*$2 x2_sum += $1*$1 num += 1 x[NR] = $1 y[NR] = $2 } END { mean_x = x_sum / num mean_y = y_sum / num mean_xy = xy_sum / num mean_x2 = x2_sum / num slope = (mean_xy - (mean_x*mean_y)) / (mean_x2 - (mean_x*mean_x)) inter = mean_y - slope * mean_x for (i = num; i > 0; i--) { ss_total += (y[i] - mean_y)**2 ss_residual += (y[i] - (slope * x[i] + inter))**2 } r2 = 1 - (ss_residual / ss_total) printf("Slope : %g\n", slope) printf("Intercept : %g\n", inter) printf("R-Squared : %g\n", r2) }'

   Save the script as linereg_awk.bash then chmod +x linereg_awk.bash and run it by:
   ./linereg_awk.bash < N2O5.txt
   Slope : -0.000187143
   Intercept : 0.0133667
   R-Squared : -0.904708
   
   
   
7. Transpose of matrix by awk :
   transpose.bash
   

   #!/bin/bash # Transpose the row and column for a matrix. # Written by Geoff Clare # Published in "sed & awk" O'Reilly, page 432, ISBN:9781565922259 (Mandarin Chinese version). exec awk ' NR == 1 { n = NF for ( i=1 ; i <= NF ; i++ ) row[i] = $i next } { if ( NF > n ) n = NF for ( i=1 ; i <= NF ; i++ ) row[i] = row[i] " " $i } END { for ( i=1 ; i <= NF ; i++ ) print row[i] }' ${1+"$@"}

   
   For an ASCII file matrix.txt containing an 8×8 matrix:
   101 102 103 104 105 106 107 108
   109 110 111 112 113 114 115 116
   117 118 119 120 121 122 123 124
   125 126 127 128 129 130 131 132
   133 134 135 136 137 138 139 140
   141 142 143 144 145 146 147 148
   149 150 151 152 153 154 155 156
   157 158 159 160 161 162 163 164
   
   The output of ./transpose.bash < matrix.txt gives:
   101 109 117 125 133 141 149 157
   102 110 118 126 134 142 150 158
   103 111 119 127 135 143 151 159
   104 112 120 128 136 144 152 160
   105 113 121 129 137 145 153 161
   106 114 122 130 138 146 154 162
   107 115 123 131 139 147 155 163
   108 116 124 132 140 148 156 164