Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

I have been getting the error "Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN."

In the '.xlsx' sheet i have bunch of numbers that have been taken from a cfd software. Can anyone help me with this one why I am getting this error? (I think the error might be due to the excel file only but am not sure since the file contain just a list of numbers)

Here is the complete code:

Main code:

clear all
clc
global K M C u;
Ne=6;
l=1; %length
t=0.02; %thickness
b=0.02; %width
modulus=2e11; %(E)
area=b*t;
imoment=(b*((t)^3))/12;
Le=l/Ne; %length of element
Rho=7850; %density
%Element stiffness matrix
K1=(modulus*imoment/(Le^3))*[12,6*Le,-12,6*Le; ...
          6*Le,4*Le*Le,-6*Le,2*Le*Le; ...
          -12,-6*Le,12,-6*Le; ...
          6*Le,2*Le*Le,-6*Le,4*Le*Le];
Kglobal=zeros(2*(Ne+1),2*(Ne+1));
M1=[156 22*Le 54 -13*Le;...
         22*Le 4*Le*Le 13*Le -3*Le*Le;...
         54 13*Le 156 -22*Le;...
         -13*Le -3*Le*Le -22*Le 4*Le*Le]*(Rho*Le*b*t)/420;
Mglobal=zeros(2*(Ne+1),2*(Ne+1));
for ii=1:Ne
    Kglobal(2*ii-1:2*(ii+1),2*ii-1:2*(ii+1))=Kglobal(2*ii-1:2*(ii+1),2*ii-1:2*(ii+1))+K1;
    Mglobal(2*ii-1:2*(ii+1),2*ii-1:2*(ii+1))=Mglobal(2*ii-1:2*(ii+1),2*ii-1:2*(ii+1))+M1;
end
K=Kglobal;
K(1:2,:)=[];
K(:,1:2)=[];
M=Mglobal;
M(1:2,:)=[];
M(:,1:2)=[];
C=0.05*Kglobal;
C(1:2,:)=[];
C(:,1:2)=[];
K
M
C
u=(2*Ne)+1;
dt=0.001;
T=300;
%Displacement initials
y0=zeros(2*(2*(Ne+1))-4,1);
y0(end-1,1)=0.5;
 
%ODE function
t_array = xlsread('l&d.xlsx','Q1:Q300'); % This is t array from xls file
f_array = xlsread('l&d.xlsx','O1:O300'); % This is F array from xls file
[tsol ysol]=ode15s(@(t, y) beam_function(t, y, t_array, f_array),[1:dt:T],y0);
plot(tsol,ysol(:,Ne))

Function code:

function [dy]=beam_function(t,y, t_array, f_array)
F = interp1(t_array,f_array,t);
dy=[y(1:u-1);
    inv(M)*(F-K*y(u:end)-C*y(1:u-1))]

Answer 1

[Walter Roberson]

Inside your function the following variables are not defined: C, K, M, u

Global variables are only accessible inside functions that declare them as global (or inside nested functions of a function that declared them global.)

Avoid using global.

http://www.mathworks.com/help/matlab/math/parameterizing-functions.html

Note: there is no point in taking inv(M) inside the function, as you do not change M inside the function. Either use M\(F-K*y(u:end)-C*y(1:u-1)) or else calculate inv(M) outside and pass in the inverse.

Note: using interp1() with no interpolation method specified results in linear interpolation. However, linear interpolation of a variable results in the derivative of F being discontinuous, which is something that will cause problems with the ode*() routines, as the ode*() routines rely upon the second derivative of all statements to be continuous. If you must interpolate, then use 'spline' method.

[Bhanu Pratap Akherya]

Now, I used the spline method for interpolation but the error shown now is "Not enough input arguments."

I don't know what that means can you explain that please?

[Walter Roberson]

Most likely you coded

F = interp1(t_array,f_array,t,spline);

when you neeed to have coded

F = interp1(t_array,f_array,t,'spline');

[Walter Roberson]

format long g
Ne=6;
l=1; %length
t=0.02; %thickness
b=0.02; %width
modulus=2e11; %(E)
area=b*t;
imoment=(b*((t)^3))/12;
Le=l/Ne; %length of element
Rho=7850; %density
%Element stiffness matrix
K1=(modulus*imoment/(Le^3))*[12,6*Le,-12,6*Le; ...
          6*Le,4*Le*Le,-6*Le,2*Le*Le; ...
          -12,-6*Le,12,-6*Le; ...
          6*Le,2*Le*Le,-6*Le,4*Le*Le];
Kglobal=zeros(2*(Ne+1),2*(Ne+1));
M1=[156 22*Le 54 -13*Le;...
         22*Le 4*Le*Le 13*Le -3*Le*Le;...
         54 13*Le 156 -22*Le;...
         -13*Le -3*Le*Le -22*Le 4*Le*Le]*(Rho*Le*b*t)/420;
Mglobal=zeros(2*(Ne+1),2*(Ne+1));
for ii=1:Ne
    Kglobal(2*ii-1:2*(ii+1),2*ii-1:2*(ii+1))=Kglobal(2*ii-1:2*(ii+1),2*ii-1:2*(ii+1))+K1;
    Mglobal(2*ii-1:2*(ii+1),2*ii-1:2*(ii+1))=Mglobal(2*ii-1:2*(ii+1),2*ii-1:2*(ii+1))+M1;
end
K=Kglobal;
K(1:2,:)=[];
K(:,1:2)=[];
M=Mglobal;
M(1:2,:)=[];
M(:,1:2)=[];
C=0.05*Kglobal;
C(1:2,:)=[];
C(:,1:2)=[];
K

K = 12×12

13824000 0 -6912000 576000 0 0 0 0 0 0 0 0 0 128000 -576000 32000 0 0 0 0 0 0 0 0 -6912000 -576000 13824000 0 -6912000 576000 0 0 0 0 0 0 576000 32000 0 128000 -576000 32000 0 0 0 0 0 0 0 0 -6912000 -576000 13824000 0 -6912000 576000 0 0 0 0 0 0 576000 32000 0 128000 -576000 32000 0 0 0 0 0 0 0 0 -6912000 -576000 13824000 0 -6912000 576000 0 0 0 0 0 0 576000 32000 0 128000 -576000 32000 0 0 0 0 0 0 0 0 -6912000 -576000 13824000 0 -6912000 576000 0 0 0 0 0 0 576000 32000 0 128000 -576000 32000

rank(K)

ans = 
    12

M

M = 12×12

0.388761904761905 0 0.0672857142857143 -0.00269973544973545 0 0 0 0 0 0 0 0 0 0.00027689594356261 0.00269973544973545 -0.000103835978835979 0 0 0 0 0 0 0 0 0.0672857142857143 0.00269973544973545 0.388761904761905 0 0.0672857142857143 -0.00269973544973545 0 0 0 0 0 0 -0.00269973544973545 -0.000103835978835979 0 0.00027689594356261 0.00269973544973545 -0.000103835978835979 0 0 0 0 0 0 0 0 0.0672857142857143 0.00269973544973545 0.388761904761905 0 0.0672857142857143 -0.00269973544973545 0 0 0 0 0 0 -0.00269973544973545 -0.000103835978835979 0 0.00027689594356261 0.00269973544973545 -0.000103835978835979 0 0 0 0 0 0 0 0 0.0672857142857143 0.00269973544973545 0.388761904761905 0 0.0672857142857143 -0.00269973544973545 0 0 0 0 0 0 -0.00269973544973545 -0.000103835978835979 0 0.00027689594356261 0.00269973544973545 -0.000103835978835979 0 0 0 0 0 0 0 0 0.0672857142857143 0.00269973544973545 0.388761904761905 0 0.0672857142857143 -0.00269973544973545 0 0 0 0 0 0 -0.00269973544973545 -0.000103835978835979 0 0.00027689594356261 0.00269973544973545 -0.000103835978835979

rank(M)

ans = 
    12

C

C = 12×12

691200 0 -345600 28800 0 0 0 0 0 0 0 0 0 6400 -28800 1600 0 0 0 0 0 0 0 0 -345600 -28800 691200 0 -345600 28800 0 0 0 0 0 0 28800 1600 0 6400 -28800 1600 0 0 0 0 0 0 0 0 -345600 -28800 691200 0 -345600 28800 0 0 0 0 0 0 28800 1600 0 6400 -28800 1600 0 0 0 0 0 0 0 0 -345600 -28800 691200 0 -345600 28800 0 0 0 0 0 0 28800 1600 0 6400 -28800 1600 0 0 0 0 0 0 0 0 -345600 -28800 691200 0 -345600 28800 0 0 0 0 0 0 28800 1600 0 6400 -28800 1600

rank(C)

ans = 
    12

u=(2*Ne)+1;
dt=0.001;
T=300;
%Displacement initials
y0=zeros(2*(2*(Ne+1))-4,1);
y0(end-1,1)=0.5;
 
%ODE function
t_array = xlsread('l&d.xlsx','Q1:Q300'); % This is t array from xls file

Error using xlsread (line 136)
Unable to open file 'l&d.xlsx'.
File '/users/mss.system.M0BtCI/l&d.xlsx' not found.

f_array = xlsread('l&d.xlsx','O1:O300'); % This is F array from xls file
[tsol ysol]=ode15s(@(t, y) beam_function(t, y, t_array, f_array, C, K, M, u),[1:dt:T],y0);
plot(tsol,ysol(:,Ne))

function [dy]=beam_function(t,y, t_array, f_array)
F = interp1(t_array,f_array,t,'spline');
dy=[y(1:u-1);
    M\(F-K*y(u:end)-C*y(1:u-1))]
end

[Bhanu Pratap Akherya]

thanks for your help the issue was exactly as you told. But the original error is still showing up: "Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN." could it be due to the .xlsx file?

[Walter Roberson]

It would help if we had the file to test with.

[Bhanu Pratap Akherya]

here it is

[Walter Roberson]

I am not seeing it in R2021a.

The current code is

filename = 'https://www.mathworks.com/matlabcentral/answers/uploaded_files/718084/l&d.xlsx';

format long g
Ne=6;
l=1; %length
t=0.02; %thickness
b=0.02; %width
modulus=2e11; %(E)
area=b*t;
imoment=(b*((t)^3))/12;
Le=l/Ne; %length of element
Rho=7850; %density
%Element stiffness matrix
K1=(modulus*imoment/(Le^3))*[12,6*Le,-12,6*Le; ...
          6*Le,4*Le*Le,-6*Le,2*Le*Le; ...
          -12,-6*Le,12,-6*Le; ...
          6*Le,2*Le*Le,-6*Le,4*Le*Le];
Kglobal=zeros(2*(Ne+1),2*(Ne+1));
M1=[156 22*Le 54 -13*Le;...
         22*Le 4*Le*Le 13*Le -3*Le*Le;...
         54 13*Le 156 -22*Le;...
         -13*Le -3*Le*Le -22*Le 4*Le*Le]*(Rho*Le*b*t)/420;
Mglobal=zeros(2*(Ne+1),2*(Ne+1));
for ii=1:Ne
    Kglobal(2*ii-1:2*(ii+1),2*ii-1:2*(ii+1))=Kglobal(2*ii-1:2*(ii+1),2*ii-1:2*(ii+1))+K1;
    Mglobal(2*ii-1:2*(ii+1),2*ii-1:2*(ii+1))=Mglobal(2*ii-1:2*(ii+1),2*ii-1:2*(ii+1))+M1;
end
K=Kglobal;
K(1:2,:)=[];
K(:,1:2)=[];
M=Mglobal;
M(1:2,:)=[];
M(:,1:2)=[];
C=0.05*Kglobal;
C(1:2,:)=[];
C(:,1:2)=[];
K

K = 12×12

13824000 0 -6912000 576000 0 0 0 0 0 0 0 0 0 128000 -576000 32000 0 0 0 0 0 0 0 0 -6912000 -576000 13824000 0 -6912000 576000 0 0 0 0 0 0 576000 32000 0 128000 -576000 32000 0 0 0 0 0 0 0 0 -6912000 -576000 13824000 0 -6912000 576000 0 0 0 0 0 0 576000 32000 0 128000 -576000 32000 0 0 0 0 0 0 0 0 -6912000 -576000 13824000 0 -6912000 576000 0 0 0 0 0 0 576000 32000 0 128000 -576000 32000 0 0 0 0 0 0 0 0 -6912000 -576000 13824000 0 -6912000 576000 0 0 0 0 0 0 576000 32000 0 128000 -576000 32000

rank(K)

ans = 
    12

M

M = 12×12

0.388761904761905 0 0.0672857142857143 -0.00269973544973545 0 0 0 0 0 0 0 0 0 0.00027689594356261 0.00269973544973545 -0.000103835978835979 0 0 0 0 0 0 0 0 0.0672857142857143 0.00269973544973545 0.388761904761905 0 0.0672857142857143 -0.00269973544973545 0 0 0 0 0 0 -0.00269973544973545 -0.000103835978835979 0 0.00027689594356261 0.00269973544973545 -0.000103835978835979 0 0 0 0 0 0 0 0 0.0672857142857143 0.00269973544973545 0.388761904761905 0 0.0672857142857143 -0.00269973544973545 0 0 0 0 0 0 -0.00269973544973545 -0.000103835978835979 0 0.00027689594356261 0.00269973544973545 -0.000103835978835979 0 0 0 0 0 0 0 0 0.0672857142857143 0.00269973544973545 0.388761904761905 0 0.0672857142857143 -0.00269973544973545 0 0 0 0 0 0 -0.00269973544973545 -0.000103835978835979 0 0.00027689594356261 0.00269973544973545 -0.000103835978835979 0 0 0 0 0 0 0 0 0.0672857142857143 0.00269973544973545 0.388761904761905 0 0.0672857142857143 -0.00269973544973545 0 0 0 0 0 0 -0.00269973544973545 -0.000103835978835979 0 0.00027689594356261 0.00269973544973545 -0.000103835978835979

rank(M)

ans = 
    12

C

C = 12×12

691200 0 -345600 28800 0 0 0 0 0 0 0 0 0 6400 -28800 1600 0 0 0 0 0 0 0 0 -345600 -28800 691200 0 -345600 28800 0 0 0 0 0 0 28800 1600 0 6400 -28800 1600 0 0 0 0 0 0 0 0 -345600 -28800 691200 0 -345600 28800 0 0 0 0 0 0 28800 1600 0 6400 -28800 1600 0 0 0 0 0 0 0 0 -345600 -28800 691200 0 -345600 28800 0 0 0 0 0 0 28800 1600 0 6400 -28800 1600 0 0 0 0 0 0 0 0 -345600 -28800 691200 0 -345600 28800 0 0 0 0 0 0 28800 1600 0 6400 -28800 1600

rank(C)

ans = 
    12

u=(2*Ne)+1;
dt=0.001;
T=300;
%Displacement initials
y0=zeros(2*(2*(Ne+1))-4,1);
y0(end-1,1)=0.5;
 
%ODE function
t_array = readmatrix(filename, 'range', 'Q1:Q300'); % This is t array from xls file
f_array = readmatrix(filename, 'range', 'O1:O300'); % This is F array from xls file
[tsol, ysol]=ode15s(@(t, y) beam_function(t, y, t_array, f_array, C, K, M, u),[1:dt:T],y0);
plot(tsol,ysol(:,Ne))

function [dy]=beam_function(t,y, t_array, f_array, C, K, M, u)
F = interp1(t_array,f_array,t,'spline');
dy=[y(1:u-1);
    M\(F-K*y(u:end)-C*y(1:u-1))];
end

[Bhanu Pratap Akherya]

did you get the result on 2021a? can please share what were the results?

[Walter Roberson]

Now posted above.

You get a huge value, but no error.

[Bhanu Pratap Akherya]

okay, thanks for your help.