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Finding Distance of a Point from Curve with al_nleqsolve

Plot x y f B 3 el 1 col B 3 el 2 col augment B 1 el transpose (1 el B 1 el transpose (2 el a 15 black 15 mat B 1 el transpose (1 el B 1 el transpose (2 el . 5 black 15 mat A transpose (1 el A transpose (2 el . 5 red 15 mat A transpose (1 el A transpose (2 el A 11 black 15 mat A B 1 el augment transpose 1 col A B 1 el augment transpose 2 col augment 71 sys :

λ 1 - (10 random -^eval :

λ1 1 - (10 random -^eval :

x0 h eps f a0 1 el x0 : k 2 A norme h / range x f x A - (2^A norme h k * - (2^- x F 21 mat : a0 k el a0 k 1 - el x f al_nleqsolve : a0 k el f 2 el abs eps ≤ s k el a0 k el : continue if 31 line for a s s rows el : dist A a - norme eval : i 12 range : m i el x f 2 el x i el diff : x J m : eNor a J a J norme / : 14 mat p1 a eNor 0.5 * dist * + : normal a transpose p1 transpose stack : 12 mat a dist normal 31 sys 71 line :

Example 1

A 0.45 15 random * 2 - (λ * 5 λ1 * stack eval :

x F x 1 el 2^x 2 el * x 1 el x 2 el + sin - :

x y f x 2^y * x y + sin - :

B 1 - 0 stack 0.004 102 -^f :

a B 1 el : 0.273 3.1827 - 21 mat

dist B 2 el : 2.2502

Plot

Example 2

A 0.45 10 random * 2 - (λ * 31 * stack eval :

x F 11 x 1 el + (3^+ 3 x 2 el * 1 x 1 el + (* - x 2 el (3^+ abs ln :

x y f 11 x + (3^+ 3 y * 1 x + (* - y (3^+ abs ln :

B 1 - 0 stack 0.004 102 -^f :

a B 1 el : 0.4752 1.5258 21 mat

dist B 2 el : 1.8543

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Example 3

A 0.45 10 random * 2 - (λ * 1.5 λ1 * stack eval :

x F 1 x 1 el (2^x 2 el 0.842 - (x 2 el 0.842 + (* + (2^2 x 1 el * x 2 el 0.842 - (* (2^+ / 2 - :

x y f 1 x 2^y 0.842 - (y 0.842 + (* + (2^2 x * y 0.842 - (* (2^+ / 2 - :

B 01 stack 0.005 103 -^f :

a B 1 el : 0.8242 0.4226 21 mat

dist B 2 el : 2.2802

Plot

Example 4

A 0.45 20 random * 0 - (λ * 6 λ1 * stack eval :

x F 1 - 3 / x 1 el (2^x 2 el (2^+ sqrt * exp 2 x 2 el (2^* - x 1 el (2^+ 816 π * sqrt * / * - 0.005 + :

x y f 1 - 3 / x (2^y (2^+ sqrt * exp 2 y (2^* - x (2^+ 816 π * sqrt * / * - 0.005 + :

B 3 - 3 stack 0.04 103 -^f :

a B 1 el : 6.5421 3.5842 - 21 mat

dist B 2 el : 2.6722

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