how to effectively find a starting point for fzero?

Question

Olga Zinovieva 2023-9-28

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2026684-how-to-effectively-find-a-starting-point-for-fzero

编辑： Bruno Luong 2023-9-28

在 MATLAB Online 中打开

G'day, I am trying to solve the following problem

where

,

is the exponential integral function,

, v and R are unknowns, and everything else is constant.

To solve this equation, I use MATLAB (the core function is `fzero`) and suppose that v is an array within a range

.

Here comes my code

%% Constants
Gibbs = 1.9*10^(-7);  
m = -3.00;            
C0 = 17.0;            
k = 0.89;             
D = 2.67*10^(-9);               
format long
p = pi;
%% Variables
v = [10^(-6):10^(-6):0.99*10^(-5) 10^(-5):10^(-5):0.99*10^(-5) 10^(-4):10^(-4):0.99*10^(-3) 10^(-3):10^(-3):0.99*10^(-2) 10^(-2):10^(-2):0.99*10^(-1) 10^(-1):10^(-3):1.0 1:0.1:10 10:0.1:100];
num = size(v,2);
Pe = zeros(1, num);
%% Solution
for j = 1:num
    Pe(j) = KGT(v(j),p,Gibbs,D,m,C0,k);
end
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 7710210.4801-22149.962337i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 8163837.4185-22371.46196i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 8624920.2942-22592.961583i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 9093459.1072-22814.461207i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 9569453.8575-23035.96083i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 10052904.5451-23257.4604533i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 10543811.17-23478.9600767i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 11042173.7322-23700.4597001i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 11547992.2317-23921.9593234i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 12061266.6685-24143.4589468i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 12581997.0426-24364.9585702i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 13110183.354-24586.4581935i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 13645825.6027-24807.9578169i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 14188923.7887-25029.4574402i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 14739477.912-25250.9570636i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 15297487.9726-25472.456687i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 15862953.9705-25693.9563103i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 16435875.9057-25915.4559337i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 17016253.7782-26136.9555571i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 17604087.5879-26358.4551804i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 18199377.335-26579.9548038i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 18802123.0194-26801.4544272i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 19412324.6411-27022.9540505i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 20029982.2001-27244.4536739i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 20655095.6964-27465.9532973i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 21287665.13-27687.4529206i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 21927690.5009-27908.952544i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 22575171.809-28130.4521674i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 23230109.0545-28351.9517907i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 23892502.2373-28573.4514141i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 24562351.3574-28794.9510375i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 25239656.4148-29016.4506608i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 25924417.4095-29237.9502842i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 26616634.3414-29459.4499075i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 27316307.2107-29680.9495309i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 28023436.0173-29902.4491543i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 28738020.7612-30123.9487776i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 29460061.4423-30345.448401i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 30189558.0608-30566.9480244i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 30926510.6166-30788.4476477i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 31670919.1097-31009.9472711i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 32422783.54-31231.4468945i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 33182103.9077-31452.9465178i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 33948880.2127-31674.4461412i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 34723112.4549-31895.9457646i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 35504800.6345-32117.4453879i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 36293944.7514-32338.9450113i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 37090544.8055-32560.4446347i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 37894600.797-32781.944258i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 38706112.7258-33003.4438814i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 39525080.5918-33224.9435048i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 40351504.3952-33446.4431281i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 41185384.1359-33667.9427515i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 42026719.8138-33889.4423748i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 42875511.4291-34110.9419982i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 43731758.9816-34332.4416216i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 44595462.4715-34553.9412449i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 45466621.8987-34775.4408683i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 46345237.2631-34996.9404917i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 47231308.5649-35218.440115i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 48124835.8039-35439.9397384i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 49025818.9803-35661.4393618i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 49934258.0939-35882.9389851i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 50850153.1449-36104.4386085i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 51773504.1331-36325.9382319i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 52704311.0587-36547.4378552i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 53642573.9215-36768.9374786i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 54588292.7217-36990.437102i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 55541467.4591-37211.9367253i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 56502098.1339-37433.4363487i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 57470184.7459-37654.9359721i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 58445727.2953-37876.4355954i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 59428725.7819-38097.9352188i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 60419180.2059-38319.4348421i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 61417090.5671-38540.9344655i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 62422456.8657-38762.4340889i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 63435279.1015-38983.9337122i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 64455557.2746-39205.4333356i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 65483291.3851-39426.932959i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 66518481.4328-39648.4325823i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 67561127.4179-39869.9322057i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 68611229.3402-40091.4318291i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 69668787.1998-40312.9314524i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 70733800.9968-40534.4310758i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 71806270.731-40755.9306992i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 72886196.4025-40977.4303225i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 73973578.0114-41198.9299459i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 75068415.5575-41420.4295693i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 76170709.0409-41641.9291926i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 77280458.4617-41863.428816i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 78397663.8197-42084.9284394i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 79522325.115-42306.4280627i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 80654442.3476-42527.9276861i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 81794015.5176-42749.4273094i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 82941044.6248-42970.9269328i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 84095529.6693-43192.4265562i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 85257470.6511-43413.9261795i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 86426867.5703-43635.4258029i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 87603720.4267-43856.9254263i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 88788029.2204-44078.4250496i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 89979793.9514-44299.924673i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 91179014.6197-44521.4242964i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 92385691.2254-44742.9239197i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 93599823.7683-44964.4235431i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 94821412.2485-45185.9231665i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 96050456.666-45407.4227898i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 97286957.0208-45628.9224132i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 98530913.3129-45850.4220366i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 99782325.5424-46071.9216599i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 101041193.7091-46293.42128329i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 102307517.8131-46514.92090665i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 103581297.8544-46736.42053002i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 104862533.833-46957.92015338i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 106151225.7489-47179.41977675i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 107447373.6021-47400.91940011i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 108750977.3926-47622.41902348i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 110062037.1204-47843.91864684i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 111380552.7855-48065.41827021i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 112706524.3879-48286.91789357i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 114039951.9277-48508.41751694i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 115380835.4047-48729.9171403i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 116729174.819-48951.41676367i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 118084970.1706-49172.91638703i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 119448221.4595-49394.4160104i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 120818928.6857-49615.91563376i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 122197091.8492-49837.41525713i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 123582710.95-50058.91488049i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 124975785.9881-50280.41450386i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 126376316.9635-50501.91412722i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 127784303.8761-50723.41375059i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 129199746.7261-50944.91337395i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 130622645.5134-51166.41299732i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 132053000.238-51387.91262068i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 133490810.8999-51609.41224405i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 134936077.4991-51830.91186741i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 136388800.0356-52052.41149078i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 137848978.5094-52273.91111414i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 139316612.9205-52495.41073751i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 140791703.2689-52716.91036087i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 142274249.5545-52938.40998424i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 143764251.7775-53159.9096076i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 145261709.9378-53381.40923097i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 146766624.0354-53602.90885433i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 148278994.0703-53824.4084777i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 149798820.0425-54045.90810106i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 151326101.952-54267.40772443i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 152860839.7987-54488.90734779i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 154403033.5828-54710.40697116i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 155952683.3042-54931.90659452i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 157509788.9629-55153.40621789i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 159074350.5588-55374.90584125i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 160646368.0921-55596.40546462i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 162225841.5627-55817.90508798i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 163812770.9706-56039.40471135i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 165407156.3157-56260.90433471i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 167008997.5982-56482.40395808i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 168618294.818-56703.90358144i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 170235047.9751-56925.40320481i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 171859257.0694-57146.90282817i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 173490922.1011-57368.40245154i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 175130043.0701-57589.9020749i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 176776619.9763-57811.40169827i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 178430652.8199-58032.90132163i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 180092141.6008-58254.400945i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 181761086.3189-58475.90056836i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 183437486.9744-58697.40019173i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 185121343.5672-58918.89981509i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 186812656.0972-59140.39943846i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 188511424.5646-59361.89906182i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 190217648.9692-59583.39868519i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 191931329.3112-59804.89830855i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 193652465.5905-60026.39793192i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 195381057.807-60247.89755528i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 197117105.9609-60469.39717865i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 198860610.052-60690.89680201i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 200611570.0805-60912.39642538i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 202369986.0462-61133.89604874i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 204135857.9493-61355.39567211i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 205909185.7896-61576.89529547i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 207689969.5673-61798.39491884i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 209478209.2822-62019.8945422i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 211273904.9345-62241.39416557i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 213077056.524-62462.89378893i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 214887664.0509-62684.3934123i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 216705727.515-62905.89303566i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 218531246.9165-63127.39265903i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 220364222.2552-63348.89228239i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 222204653.5313-63570.39190576i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 224052540.7446-63791.89152912i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 225907883.8953-64013.39115249i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 227770682.9832-64234.89077585i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 229640938.0085-64456.39039922i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 231518648.971-64677.89002258i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 233403815.8708-64899.38964595i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 235296438.708-65120.88926931i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 237196517.4824-65342.38889268i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 239104052.1941-65563.88851604i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 241019042.8432-65785.38813941i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 242941489.4295-66006.88776277i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 244871391.9531-66228.38738614i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 246808750.4141-66449.8870095i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 248753564.8123-66671.38663287i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 250705835.1478-66892.88625623i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 252665561.4207-67114.3858796i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 254632743.6308-67335.88550296i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 256607381.7782-67557.38512633i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 258589475.863-67778.88474969i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 260579025.885-68000.38437306i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 262576031.8443-68221.88399642i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 264580493.7409-68443.38361979i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 266592411.5749-68664.88324315i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 268611785.3461-68886.38286652i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 270638615.0546-69107.88248988i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 272672900.7004-69329.38211325i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 274714642.2836-69550.88173661i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 276763839.804-69772.38135998i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 278820493.2617-69993.88098334i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 280884602.6567-70215.38060671i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 282956167.989-70436.88023007i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 285035189.2587-70658.37985344i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 287121666.4656-70879.8794768i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 289215599.6098-71101.37910017i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 291316988.6913-71322.87872353i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 293425833.7101-71544.3783469i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 295542134.6662-71765.87797026i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 297665891.5596-71987.37759363i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 299797104.3903-72208.87721699i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 301935773.1584-72430.37684036i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 304081897.8637-72651.87646372i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 306235478.5063-72873.37608709i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 308396515.0862-73094.87571045i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 310565007.6034-73316.37533382i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 312740956.0579-73537.87495718i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 314924360.4497-73759.37458055i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 317115220.7788-73980.87420391i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at -8.4 is 319313537.0452-74202.37382728i.)
Check function or try again with a different starting value.
Exiting fzero: aborting search for an interval containing a sign change
    because complex function va...
function F1 = KGT(v,p,Gibbs,D,m,C0,k)
    func = @(Pe) v*v*(p^2*Gibbs/(Pe^2*D^2)) + v*((m*C0*(1-k)*ksi(k,p,Pe))/(D*(1-(1-k)*Iv(Pe)))); %standard KGT
    
    if v<10^(-5)
        Pe0 = 5*10^(-2); % starting point
    elseif (v>=10^(-5)) && (v<=0.5*10^(-4))
        Pe0 = 10^(-1);
    elseif (v>0.5*10^(-4)) && (v<=10^(-4))
        Pe0 = 2*10^(-1);
    elseif (v>10^(-4)) && (v<=10^(-3))
        Pe0 = 5*10^(-1);
    elseif (v>10^(-3)) && (v<=10^(-2))
        Pe0 = 1;       
    elseif (v>10^(-2)) && (v<=8*10^(-2))
        Pe0 = 6;
    elseif (v>8*10^(-2)) && (v<=9*10^(-2))
        Pe0 = 15;
    else
        Pe0 = 30; % this value yields NaN
    end
    
    F1 = fzero(func,Pe0);
end
function ksic = ksi(k,p,Pe)
    ksic = 1-2*k/(sqrt(1+(2*p/Pe)^2)-1+2*k);
end
function Ivantsov = Iv(Pe)
     Ivantsov = Pe*exp(Pe)*expint(Pe);
end 

I am trying to understand how to organise this in a more efficient way rather than finding an initial guess manually. Tried to use

        while isnan(func)
            Pe0 = Pe0+1;
        end

but it does not work.

Thanks.

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Answer 1

Bruno Luong 2023-9-28

0
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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2026684-how-to-effectively-find-a-starting-point-for-fzero#answer_1320674

编辑：Bruno Luong 2023-9-28

在 MATLAB Online 中打开

The problem is not finding the right starting point, the problem is that your function func implementation returns NaN for large v (above 0.1) and large Pe and func(Pe) never cross 0 below the value where NaN is retuned.

Try to replace with function that find Pe0 but fails for large v (nothing can be done to fix your cirrent implementation)

function F1 = KGT(v,p,Gibbs,D,m,C0,k)
    func = @(Pe) v*v*(p^2*Gibbs/(Pe^2*D^2)) + v*((m*C0*(1-k)*ksi(k,p,Pe))/(D*(1-(1-k)*Iv(Pe)))); %standard KGT
    Pe = logspace(-3,4,200);
    fPe = arrayfun(func, Pe);
    ix = find(fPe(1:end-1).*fPe(2:end)<0, 1);
    Pe0 = Pe(ix),
    if isempty(Pe0)
        disp(fPe)
        loglog(Pe,fPe)
        error('cannot find starting point');
    end
    
    F1 = fzero(func,Pe0);
end