data 216

25be1940-a872-4dc7-b85e-e82ca925a7f8 146 15 12 decimal

&[DATE] &[TIME] - &[FILENAME]

3 appVersion 0.98.6179 ≡ range_215 14 min ≡ 21 mat

Iterate the GivenFind solve bloc

Predefine the solver invariants a b GivenFind a b FindRoot :

A 1011 : V 1500 : 12 mat

range 61 :

Observe:

The solutions appear in the order of "init".

The negative 'Lc' has probably no meaning,

however: does not invalidate the solver.

The meaning of the system is unknown

from the Mathsoft originator MCD 8 Pro ?

]]>

i 1 range range idx i el i : d i el 2.9 i 10 / + : 21 line for

Acelerate demo: reduce range range [216] solvable range

Solutions [L, Lc] over variable 'd' wrt  'j'
Very robust, the solver supports long range. j system π d j el * L / Lc L - 2 / (2^d j el 2 / (2^+ sqrt * A L / - π d j el 2 / * - ≡ 23 / π L / * d j el 2 / (2^* Lc L - 2 / (* V L / - π d j el 2 / (2^* - ≡ 21 mat :

init L 2 ≡ Lc 1 ≡ 21 mat :

t0 1 time :

Generalise an iterative collection of  solutions [L, Lc] j Iterate L Lc Find j system init GivenFind : d sol L Lc Find vectorize : 21 line :

Collect the solver j 1 range range : Solved j Iterate vectorize : 21 line

1 time t0 - min 4

Explode/collect the solved system Plot n 1 range range L n el Solved n el 1 el eval : Lc n el Solved n el 2 el eval : 21 line for index [1] Unests solutions d L Lc augment 11 mat 1 el 31 line :

Collect the plot solutions Plot Plot : L Plot 1 col Plot 2 col augment : Lc Plot 1 col Plot 3 col augment : 31 line

solve @ user [j]
disable "Solved" j 31 : User j Iterate : 21 sys

d j el User transpose 12 mat 6 58.57 22.67 12 mat 12 mat

header j d L Lc 14 mat : data header idx Plot augment stack : 21 sys

_L d j el User 11 el + 20 black 15 mat :_Lc d j el User 21 el + 20 black 15 mat : 21 line

data j d L Lc 13 110.07 110.26 2 3.1 108 103.91 3 3.2 105.8 98.93 4 3.3 103.61 94.29 5 3.4 101.45 89.87 6 3.5 99.32 85.64 7 3.6 97.22 81.6 8 3.7 95.16 77.72 9 3.8 93.14 74.01 10 3.9 91.15 70.45 114 89.2 67.04 124 mat

L Lc 3 200 3 50 - 2 2 mat _L _Lc 5 1 sys

Search nearest in col ... export this section

data 216

data j d L Lc 13 110.07 110.26 2 3.1 108 103.91 3 3.2 105.8 98.93 4 3.3 103.61 94.29 5 3.4 101.45 89.87 6 3.5 99.32 85.64 7 3.6 97.22 81.6 8 3.7 95.16 77.72 9 3.8 93.14 74.01 10 3.9 91.15 70.45 114 89.2 67.04 12 4.1 87.3 63.77 13 4.2 85.43 60.64 14 4.3 83.61 57.64 15 4.4 81.83 54.77 16 4.5 80.08 52.03 17 4.6 78.38 49.4 18 4.7 76.72 46.89 19 4.8 75.1 44.49 20 4.9 73.52 42.19 215 71.98 39.99 22 5.1 70.47 37.88 23 5.2 69.01 35.87 24 5.3 67.58 33.95 25 5.4 66.19 32.11 26 5.5 64.83 30.36 27 5.6 63.51 28.68 28 5.7 62.22 27.07 29 5.8 60.97 25.54 30 5.9 59.75 24.07 316 58.57 22.67 32 6.1 57.41 21.33 33 6.2 56.29 20.05 34 6.3 55.19 18.83 35 6.4 54.13 17.66 36 6.5 53.09 16.54 37 6.6 52.08 15.47 38 6.7 51.1 14.45 39 6.8 50.14 13.47 40 6.9 49.21 12.53 417 48.3 11.64 42 7.1 47.42 10.79 43 7.2 46.56 9.97 44 7.3 45.72 9.19 45 7.4 44.9 8.44 46 7.5 44.11 7.73 47 7.6 43.33 7.04 48 7.7 42.58 6.39 49 7.8 41.85 5.76 50 7.9 41.13 5.17 518 40.43 4.59 52 8.1 39.75 4.05 53 8.2 39.09 3.52 54 8.3 38.44 3.02 55 8.4 37.81 2.55 56 8.5 37.2 2.09 57 8.6 36.6 1.65 58 8.7 36.01 1.23 59 8.8 36.51 0.96 60 8.9 34.89 0.45 619 34.34 0.08 62 9.1 33.81 0.27 - 63 9.2 33.29 0.6 - 64 9.3 32.79 0.92 - 65 9.4 32.29 1.23 - 66 9.5 31.81 1.52 - 67 9.6 31.34 1.8 - 68 9.7 30.88 2.07 - 69 9.8 30.43 2.33 - 70 9.9 29.99 2.57 - 7110 29.56 2.8 - 72 10.1 29.14 3.02 - 73 10.2 28.72 3.24 - 74 10.3 28.32 3.44 - 75 10.4 27.93 3.63 - 76 10.5 27.54 3.82 - 77 10.6 27.16 3.99 - 78 10.7 26.79 4.16 - 79 10.8 26.43 4.32 - 80 10.9 26.08 4.47 - 8111 25.73 4.61 - 82 11.1 25.39 4.75 - 83 11.2 25.06 4.88 - 84 11.3 24.73 5 - 85 11.4 24.41 5.12 - 86 11.5 24.1 5.23 - 87 11.6 23.79 5.33 - 88 11.7 23.48 5.43 - 89 11.8 23.19 5.53 - 90 11.9 22.9 5.61 - 9112 22.61 5.7 - 92 12.1 22.33 5.78 - 93 12.2 22.06 5.85 - 94 12.3 21.79 5.92 - 95 12.4 21.52 5.98 - 96 12.5 21.26 6.04 - 97 12.6 21 6.1 - 98 12.7 20.75 6.15 - 99 12.8 20.5 6.2 - 100 12.9 20.26 6.24 - 10113 20.02 6.28 - 102 13.1 19.79 6.32 - 103 13.2 19.55 6.35 - 104 13.3 19.33 6.38 - 105 13.4 19.1 6.4 - 106 13.5 18.88 6.43 - 107 13.6 18.66 6.45 - 108 13.7 18.45 6.46 - 109 13.8 18.24 6.48 - 110 13.9 18.03 6.49 - 11114 17.83 6.5 - 112 14.1 17.63 6.5 - 113 14.2 17.43 6.5 - 114 14.3 17.23 6.5 - 115 14.4 17.04 6.5 - 116 14.5 16.85 6.5 - 117 14.6 16.66 6.49 - 118 14.7 16.47 6.48 - 119 14.8 16.29 6.47 - 120 14.9 16.11 6.45 - 12115 15.93 6.44 - 122 15.1 15.75 6.42 - 123 15.2 15.58 6.4 - 124 15.3 15.41 6.38 - 125 15.4 15.24 6.35 - 126 15.5 15.07 6.32 - 127 15.6 14.91 6.3 - 128 15.7 14.74 6.26 - 129 15.8 14.58 6.23 - 130 15.9 14.42 6.2 - 13116 14.26 6.16 - 132 16.1 14.1 6.12 - 133 16.2 13.95 6.08 - 134 16.3 13.79 6.04 - 135 16.4 13.64 6 - 136 16.5 13.49 5.95 - 137 16.6 13.34 5.9 - 138 16.7 13.19 5.86 - 139 16.8 13.05 5.8 - 140 16.9 12.9 5.75 - 14117 12.76 5.7 - 142 17.1 12.61 5.64 - 143 17.2 12.47 5.59 - 144 17.3 12.33 5.53 - 145 17.4 12.19 5.47 - 146 17.5 12.05 5.4 - 147 17.6 11.91 5.34 - 148 17.7 11.78 5.27 - 149 17.8 11.64 5.21 - 150 17.9 11.51 5.14 - 15118 11.37 5.07 - 152 18.1 11.24 5 - 153 18.2 11.11 4.92 - 154 18.3 10.97 4.85 - 155 18.4 10.84 4.77 - 156 18.5 10.71 4.69 - 157 18.6 10.58 4.61 - 158 18.7 10.45 4.53 - 159 18.8 10.32 4.44 - 160 18.9 10.2 4.36 - 16119 10.07 4.27 - 162 19.1 9.94 4.18 - 163 19.2 9.81 4.09 - 164 19.3 9.69 4 - 165 19.4 9.56 3.9 - 166 19.5 9.43 3.8 - 167 19.6 9.31 3.71 - 168 19.7 9.18 3.6 - 169 19.8 9.06 3.5 - 170 19.9 8.93 3.4 - 17120 8.81 3.29 - 172 20.1 8.68 3.18 - 173 20.2 8.56 3.07 - 174 20.3 8.43 2.96 - 175 20.4 8.3 2.84 - 176 20.5 8.18 2.72 - 177 20.6 8.05 2.6 - 178 20.7 7.92 2.48 - 179 20.8 7.8 2.35 - 180 20.9 7.67 2.22 - 18121 7.54 2.09 - 182 21.1 7.41 1.96 - 183 21.2 7.29 1.82 - 184 21.3 7.16 1.68 - 185 21.4 7.03 1.54 - 186 21.5 6.89 1.39 - 187 21.6 6.76 1.24 - 188 21.7 6.63 1.09 - 189 21.8 6.49 0.93 - 190 21.9 6.36 0.77 - 19122 6.22 0.6 - 192 22.1 6.08 0.43 - 193 22.2 5.94 0.26 - 194 22.3 5.8 0.08 - 195 22.4 5.66 0.11 196 22.5 5.51 0.3 197 22.6 5.36 0.5 198 22.7 5.21 0.7 199 22.8 5.06 0.91 200 22.9 4.9 1.13 20123 4.74 1.36 202 23.1 4.57 1.59 203 23.2 4.4 1.84 204 23.3 4.23 2.1 205 23.4 4.05 2.37 206 23.5 3.86 2.66 207 23.6 3.66 2.96 208 23.7 3.46 3.29 209 23.8 3.24 3.64 210 23.9 3.01 4.01 21124 2.76 4.43 212 24.1 2.49 4.89 213 24.2 2.18 5.42 214 24.3 1.82 6.07 215 24.4 1.35 6.93 216 24.5 0.25 9.06 2174 mat :

Stem(data)

Stem plot for QuickPlot  ... given paired data data Stem stem 0 : stemX 1 data rows range : i 1 stemX rows range stem i el data i 1 el data i 2 el data i 1 el 022 mat : for i 1 stem rows 1 - (range stem i el stem i el stem i 1 + (1 el 1 el 012 mat stack : for V stem 1 el : j 2 stem rows 1 - (range V V stem j el stack : for V V data data rows row stack : 81 line :

project data 2 data rows range 14 range el : L project 2 col project 3 col augment : Lc project 2 col project 4 col augment : 31 sys

S data 61194 range 14 range el : neg S 2 col S 4 col augment : 21 sys

data data rows row 216 24.5 0.25 9.06 14 mat

Lc L 3 200 3 50 - 2 2 mat 9 0 + 150 black 1 5 mat neg Stem 22.3 0 + 50 black 1 5 mat 6 1 sys

data data 210 range 14 range el :

Scan down for nearest lower V threshold FindIdx j 1 : V j el abs threshold ≥ j j 1 + : while j 1 - V j el 21 mat 31 line :

data 13 110.07 110.26 2 3.1 108 103.91 3 3.2 105.8 98.93 4 3.3 103.61 94.29 5 3.4 101.45 89.87 6 3.5 99.32 85.64 7 3.6 97.22 81.6 8 3.7 95.16 77.72 9 3.8 93.14 74.01 94 mat

V data 3 col :

idx V 100 FindIdx : 5 99.32 21 mat

data idx 1 el row 5 3.4 101.45 89.87 14 mat

Circle/line intersection

D 4 : (Circle ≡

L 0.5 : (Line ≡

Φ vector equalities Φ D x 2^y 2^+ ≡ L x y + ≡ 21 mat :

init x 1 ≡ y 0.5 ≡ 21 mat :

Collect solutions at kernel level x y sol Φ init FindRoot :

Assign the solutions sol x y sol vectorize : 1.643038 1.143038 - 21 mat

x y 21 mat x y sol vectorize : 1.643038 1.143038 - 21 mat

D x 2 ^ - sqrt ± L x - sol 1 el sol 2 el . 14 black sol 2 el sol 1 el . 14 black 2 5 mat 3 1 sys

D x 2^- sqrt ± L x - sol 1 el sol 2 el . 14 black sol 2 el sol 1 el . 14 black 25 mat 31 sys

x y Clear 1

D 4 : (Circle ≡

L 0 : (Line ≡

Φ vector equalities Φ D x 2^y 2^+ ≡ L x y + ≡ 21 mat :

init x 1 ≡ y 0.5 ≡ 21 mat :

Collect solutions at kernel level x y sol Φ init FindRoot :

Assign the solutions sol x y sol vectorize : 1.416072 1.416072 - 21 mat

x y 21 mat x y sol vectorize : 1.416072 1.416072 - 21 mat

D x 2 ^ - sqrt ± L x - sol 1 el sol 2 el . 14 black sol 2 el sol 1 el . 14 black 2 5 mat 3 1 sys

D x 2^- sqrt ± L x - sol 1 el sol 2 el . 14 black sol 2 el sol 1 el . 14 black 25 mat 31 sys

jmGiraud: 2015/12/31