# How to solve error message in fsolve stating: "The vector of function values is near zero, as measured by the selected value of the function tolerance. However, the last step was ineffective"

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Yonas Gezahegn on 14 Nov 2018
Edited: Yonas Gezahegn on 1 Apr 2020
Dear all, I am trying to solve transcendental equations of TM mode using fsolve, but I constantly get error message stating:
"The vector of function values is near zero, as measured by the selected value of the function tolerance. However, the last step was ineffective."
Thxs!
% Given:
close all; clear all;
mu_o = 4*pi*10^(-7); mu_r = 1;
esp_o = (10^(-9))/(36*pi); esp_r = 2.56;
esp_d = esp_o*esp_r;
mu_d = mu_o*mu_r;
h = 0.3175; % [cm]
f_c1 = 18.913e9; % from example 8-11 pp 17.
f = 0:f_c1/1000:2*f_c1;
b_z = 0; %Initialization
for f_index = 1:1:length(f)
w = (2*pi*f(f_index));
b_z = 793; % Initial point guessing
options = optimset('Display','iter','MaxFunEvals',1e20,'TolFun',1e-10,'TolX',1e-10);
b_z_sol = fsolve(@myfun, b_z, options);
end
b_yd_sol = (sqrt(w.^2*mu_d*esp_d - b_z_sol.^2))/100; % [rad/cm] equ. 8-160c
a_sol = (sqrt(b_z_sol.^2 - (w.^2*mu_o*esp_o)))/100; % [rad/cm] equ. 8-160d
b_o = w*sqrt(mu_o*esp_o);
b_d = w*sqrt(mu_d*esp_d);
% Figure-a
subplot(2,1,1);
plot(f(f_index)/f_c1,real(b_z_sol));
hold on;
plot(f(f_index)/f_c1, real(b_yd_sol), ':');
plot(f(f_index)/f_c1, real(a_sol), '--');
hold off;
axis([0 f(f_index)/f_c1 0 9]);
xlabel('Normalized frequency (f/f_C_1)');
title('Attenuation and Phase Constants of TM^{Z}_m');
subplot(2,1,2);
% Figure-b
plot(b_o, w);
hold on;
plot(b_d, w);
plot(real(b_z_sol), w);
axis([0 13e2 0 2e11]);
xlabel('\beta_o \beta_z \beta_d');
ylabel('\omega(\beta_o \beta_z \beta_d)');
title('Dispersion Curve');
hold off;
% myfum.m file code:
function F = myfun(b_z)
global w;
mu_o = 4*pi*10^(-7);
mu_r = 1;
esp_o = (10^(-9))/(36*pi);
esp_r = 2.56;
esp_d = esp_o*esp_r;
mu_d = mu_o*mu_r;
h = 0.3175; % [cm]
f_c1 = 18.913e9; % from example 8-11 pp 417
f = 0:18.913e6:2*f_c1;
for f_index = 1:1:length(f)
end
w = (2*pi*f(f_index));
% Iteration equations for the three unknowns
b_yd = (sqrt(w.^2*mu_d*esp_d - b_z.^2))/100; % [rad/cm] equ. 8-160c
a = (sqrt(b_z.^2 - (w.^2*mu_o*esp_o)))/100; % [rad/cm] equ. 8-160d
F = (a*(esp_d/esp_o)) - (b_yd*h*tan(b_yd*h)); % equ 8-160b
end
##### 2 CommentsShowHide 1 older comment
Kai Wang on 31 Mar 2020
Hi, I think what you have plotted is a single point. You should let b_o, b_d and w to be a colume vector.

Alan Weiss on 15 Nov 2018
Without running your code, I can tell you that the exit message you give is NOT an error message. Read its first part:
"The vector of function values is near zero, as measured by the selected value of the function tolerance."
This means that fsolve found a solution. So I think that you should't worry about the second part of the message, which is about algorithm internals.
Alan Weiss
MATLAB mathematical toolbox documentation
##### 2 CommentsShowHide 1 older comment
Alan Weiss on 16 Nov 2018
I don't understand what you want to plot. I suggest that you start a new question with some details.
Alan Weiss
MATLAB mathematical toolbox documentation