<p>Plot, λ</p>

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Finding Distance of a Point from Curve with al_nleqsolve

<p>Plot, λ</p>

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 :

x0 h eps f k 1 A norme h / range x f x A - (2^A norme h k * - (2^- x F 21 mat : a0 k el x0 x f al_nleqsolve eval : a0 k el f 2 el eps ≤ s k el a0 k el : break if 31 line for rows(s)-the number of steps to determine the minimum distance a s s rows el : dist A a - norme eval : eNor-unit normal vector k 12 range : m k el x f 2 el x k 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 81 line :

Example 1

A 120 random 10.09 - 6 λ * stack (* eval :

x F 2 x 1 el (2^* 4 x 1 el * x 2 el * + 4 x 2 el (3^* + 26 x 2 el * - 22 - :

x y f 2 x 2^* 4 x * y * + 4 y 3^* + 26 y * - 22 - :

B 30 - stack 0.01 101 -^f :

Plot

dist B 2 el : 3.4095

Example 2

A 0.5 10 random * 2 - 1 λ * stack eval :

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

x y f x 2^y 2^+ (2^x 3^3 x * y 2^* - (- :

B 0.1 0.1 stack 0.0025 102 -^f :

Plot

dist B 2 el : 1.7783

Example 3

A 20 random 10 - 3 λ * stack eval :

x F x 1 el 6^x 2 el 6^+ 26^- :

x y f x (6^y (6^+ 26^- :

B 20 stack 0.01 102 -^f :

Plot

dist B 2 el : 0.9999

Example 4

A 0.7 20 random * 5 - 3 λ * stack eval :

x F x 1 el 2 - (2^5 x 2 el (2^* + x 1 el (2^x 2 el (10^* + 3 x 1 el x 2 el * sin * - 9 - :

x y f x 2 - (2^5 y (2^* + x (2^y (10^* + 3 x y * sin * - 9 - :

B 11 stack 0.01 101 -^f :

Plot

dist B 2 el : 2.1804

Example 5

A 0.4 7 random * 0.7 - 0.4 stack eval :

x F x 1 el (4^x 1 el (2^x 2 el * - x 2 el (3^+ :

x y f x (4^x (2^y * - y (3^+ :

B 0.3 - 0 stack 0.01 9104 -^(* f :

Plot

dist B 2 el : 0.3463

Example 6

A 0.4 10 random * 2 - (1 λ * stack eval :

x F x 1 el 0.125 10 x 2 el * sin * + (4^x 2 el 0.125 10 x 1 el * sin * + (4^+ 0.4 4^- :

x y f x 0.125 10 y * sin * + (4^y 0.125 10 x * sin * + (4^+ 0.4 4^- :

B 0 - 0.3 - stack 0.0005 103 -^f :

Plot

dist B 2 el : 1.8591

Example 7

A 0.8 20 random * 1 - 8 λ * 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 33 stack 0.1 103 -^f :

Plot

dist B 2 el : 4.8282