Python: Complex Number Arithmetic and Lambert Function - Printable Version +- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: HP Software Libraries (/forum-10.html) +--- Forum: HP Prime Software Library (/forum-15.html) +--- Thread: Python: Complex Number Arithmetic and Lambert Function (/thread-17247.html) Python: Complex Number Arithmetic and Lambert Function - Eddie W. Shore - 07-14-2021 02:42 PM Complex Number Arithmetic The HP Prime App "Python-Complex Arithmetic" performs the four arithmetic functions on two complex numbers. Code: ```from cmath import * print("Complex Number Arithmetic") x1=float(input("real_1: ")) # input values are not auto printed print(x1) y1=float(input("imag_y: ")) print(y1) z1=complex(x1,y1) print("z1 = "+str(z1)) x2=float(input("real_2: ")) print(x2) y2=float(input("imag_2: ")) print(y2) z2=complex(x2,y2) print("z2 = "+str(z2)) print() print("z1 + z2 = "+str(z1+z2)) print("z1 - z2 = "+str(z1-z2)) print("z1 * z2 = "+str(z1*z2)) print("z1 / z2 = "+str(z1/z2))``` Lambert W Function The HP Prime App "Python-Lambert W Function" approximates the Lambert W function. The Python script estimates w given complex number z using Newtons Method: w * e^w = z Code: ```from cmath import * print("Lambert W Function - approx") print("w * exp(w) = z, find w") zr=float(input("z_real: ")) print(zr) zj=float(input("z_imag: ")) print(zj) z=complex(zr,zj) w0=complex(1,1) w1=complex(1,1) while abs(w1)>1*10**-10:  w1=(w0*exp(w0)-z)/(exp(w0)+w0*exp(w0))  w0=w0-w1 # round low parts to zero # z.real, z.imag are read only wr=w0.real if abs(wr)<1*10**-10:  wr=0 wj=w0.imag if abs(wj)<1*10**-10:   wj=0 w0=complex(wr,wj)    print("w = "+str(w0))``` Example: Input: -1.57079362679 (about π/2) Result: approx -1.223152769062088e-06+1.57079554811127j Input: 2+3j Result: approx 1.090076534485791+0.5301397207748389j Source: Wikipedia. "Lambert W Function" Last updated June 13, 2021. https://en.wikipedia.org/wiki/Lambert_W_function Retrieved July 9, 2021 Download both apps here (zip file): https://drive.google.com/file/d/1MX5G-1MJidb2ZmoBVe57GpiUnYvY5BqD/view?usp=sharing RE: Python: Complex Number Arithmetic and Lambert Function - Albert Chan - 07-14-2021 04:17 PM Newton's method with f(w) = w*e^w - z is not stable with bad guess. https://www.hpmuseum.org/forum/thread-15792-post-138282.html#pid138282 A better setup is with f(w) = w + log(w/z), more stable and faster convergence. https://www.hpmuseum.org/forum/thread-15792-post-138355.html#pid138355 >>> from mpmath import * >>> z = 2+3j >>> w = 1+1j # guess of W(z) >>> for i in range(5): w -= (w-z*exp(-w)) / (w+1); print i+1, w ... 1 (0.925920455007468 + 0.525629062362773j) 2 (1.11168436157991 + 0.529383890736917j) 3 (1.09040865244656 + 0.530090770362652j) 4 (1.09007661082612 + 0.530139691067221j) 5 (1.09007653448579 + 0.530139720774835j) >>> w = 1+1j # guess of W(z) >>> for i in range(5): w -= (w+log(w/z))*w/(w+1); print i+1, w ... 1 (1.1220615411005 + 0.505617553600088j) 2 (1.09019950929821 + 0.530419495346751j) 3 (1.09007653522354 + 0.530139702926175j) 4 (1.09007653448579 + 0.530139720774839j) 5 (1.09007653448579 + 0.530139720774839j)