37c3f4d9-3a3c-4493-861d-4604863f6895 21 4 5 decimal

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

vx vy a b c plotG a char ≡ b size ≡ c color ≡ 13 mat n vx length : plot vx 1 el vy 1 el a b c augment : i 2 n range plot plot vx i el vy i el a b c augment stack : for plot 51 line :

X 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1111 mat :

W1 000 0.02 0.16 1.65 0.08 0.71 6.83 0.16 1.55 15.2 0.26 2.57 25.4 0.37 3.75 37.7 0.48 5.05 52 0.62 6.49 66.1 0.76 8.09 83.1 0.82 9.84 103 1.09 11.8 156113 mat :

W2 000 0.02 0.18 2.18 0.08 0.73 10.6 0.16 1.5 19.1 0.26 2.54 31.7 0.37 3.86 45.9 0.47 5.22 61.5 0.61 6.77 81.1 0.75 8.47 104 0.9 10.4 161 1.07 12.3 198113 mat :

W3 000 0.02 0.17 2.79 0.07 0.72 10.6 0.14 1.49 24.4 0.23 2.5 40.4 0.32 3.8 58.4 0.42 5.17 78.4 0.54 6.7 103 0.66 8.36 133 0.8 10.3 205 0.95 12.2 253113 mat :

c1 0.0171 - 1.2151 0.3617 - 0.2326 41 mat 0.1152 - 10.0402 2.2093 0.3557 - 41 mat 2.9591 - 137.8078 75.2572 - 93.7302 41 mat 13 mat :

c2 0.0078 - 1.0403 0.0093 0.0277 41 mat 0.0943 - 9.4438 4.3783 1.4377 - 41 mat 0.2036 106.2887 43.2709 51.761 41 mat 13 mat :

c3 0.006 - 0.9048 0.0318 0.019 41 mat 0.0964 - 9.3496 4.2785 1.3416 - 41 mat 0.4119 - 136.7433 54.659 66.3332 41 mat 13 mat :

suggested interpolation x Φ 1 x 1.5^x 3^x 6^41 mat :

recast the function x b f b x Φ * :

Ω1 x 01 0.05 range : i 1 x rows range j 13 range M i j el x i el c1 j el f : for for i 12 range j 13 range M i j el 0 : for for x M augment 41 line :

Ω2 x 01 0.05 range : i 1 x rows range j 13 range M i j el x i el c2 j el f : for for i 12 range j 13 range M i j el 0 : for for x M augment 41 line :

Ω3 x 01 0.05 range : i 1 x rows range j 13 range M i j el x i el c3 j el f : for for i 12 range j 13 range M i j el 0 : for for x M augment 41 line :

Ω1 11 mat 0000 0.05 000 0.1 0.02 0.2 1.32 0.15 0.05 0.48 4.79 0.2 0.09 0.8 8.77 0.25 0.13 1.17 13.11 0.3 0.17 1.59 17.72 0.35 0.22 2.06 22.52 0.4 0.27 2.56 27.47 0.45 0.32 3.11 32.56 0.5 0.37 3.71 37.82 0.55 0.42 4.34 43.33 0.6 0.48 5.01 49.21 0.65 0.54 5.73 55.66 0.7 0.6 6.48 62.96 0.75 0.66 7.27 71.48 0.8 0.73 8.11 81.69 0.85 0.8 8.98 94.17 0.9 0.88 9.88 109.65 0.95 0.97 10.81 129.02 1 1.07 11.78 153.32 214 mat 11 mat

Ω2 11 mat 0000 0.05 000 0.1 0.03 0.21 3.61 0.15 0.05 0.47 6.53 0.2 0.09 0.79 10.06 0.25 0.12 1.15 14.18 0.3 0.16 1.57 18.87 0.35 0.21 2.05 24.16 0.4 0.26 2.57 30.07 0.45 0.31 3.14 36.66 0.5 0.36 3.77 44 0.55 0.42 4.45 52.19 0.6 0.48 5.17 61.36 0.65 0.54 5.95 71.69 0.7 0.61 6.77 83.38 0.75 0.68 7.63 96.71 0.8 0.75 8.53 111.98 0.85 0.82 9.45 129.59 0.9 0.9 10.4 150.01 0.95 0.98 11.35 173.77 1 1.07 12.29 201.52 214 mat 11 mat

Ω3 11 mat 0000 0.05 000 0.1 0.02 0.2 3.97 0.15 0.05 0.46 7.72 0.2 0.08 0.77 12.26 0.25 0.11 1.14 17.55 0.3 0.14 1.55 23.58 0.35 0.18 2.02 30.37 0.4 0.23 2.54 37.95 0.45 0.27 3.1 46.4 0.5 0.32 3.72 55.8 0.55 0.37 4.39 66.29 0.6 0.42 5.11 78.04 0.65 0.48 5.88 91.26 0.7 0.54 6.69 106.23 0.75 0.6 7.54 123.27 0.8 0.66 8.43 142.81 0.85 0.73 9.35 165.33 0.9 0.8 10.29 191.44 0.95 0.87 11.24 221.83 1 0.95 12.19 257.32 214 mat 11 mat

vx vy char size color plotG

j 3 :

vx Ω1 1 col : vy Ω1 j 1 + col : select vx vy o 5 black plotG : 31 line

x c 1 0.1 x ≤ (x 1.25 ≤ (& cases :

x interpolated x c1 j el f (:

After duplication of the interpolation, any of the Smath [linterp, ainterp, cinterp] is valid

select x interpolated x c * 2 1 sys

X 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1111 mat :

W1 000 0.02 0.16 1.65 0.08 0.71 6.83 0.16 1.55 15.2 0.26 2.57 25.4 0.37 3.75 37.7 0.48 5.05 52 0.62 6.49 66.1 0.76 8.09 83.1 0.82 9.84 103 1.09 11.8 156113 mat :

W2 000 0.02 0.18 2.18 0.08 0.73 10.6 0.16 1.5 19.1 0.26 2.54 31.7 0.37 3.86 45.9 0.47 5.22 61.5 0.61 6.77 81.1 0.75 8.47 104 0.9 10.4 161 1.07 12.3 198113 mat :

W3 000 0.02 0.17 2.79 0.07 0.72 10.6 0.14 1.49 24.4 0.23 2.5 40.4 0.32 3.8 58.4 0.42 5.17 78.4 0.54 6.7 103 0.66 8.36 133 0.8 10.3 205 0.95 12.2 253113 mat :

j 1 :

x φ 1 x 1.5^x 3^x 6^41 mat :

Y W1 j col : 11 line

jj 1 x φ length range i 1 X length range M i jj el X i el φ jj el : for for Φ M transpose M * : d M transpose Y * : b Φ 1 -^eval d * : 41 line

b 0.0171 - 1.2151 0.3617 - 0.2326 41 mat

<= recast the scalar model x fit b x φ * :

x c 1 0.1 x ≤ (x 1 ≤ (& cases :

pts X Y o 5 black plotG :

X W1 j col augment x fit 1 * pts 3 1 sys

X Y augment 00 0.1 0.02 0.2 0.08 0.3 0.16 0.4 0.26 0.5 0.37 0.6 0.48 0.7 0.62 0.8 0.76 0.9 0.82 1 1.09 112 mat