Is a flag set on the possibility of a singular matrix

Depending on the application, a good practice before operating on a matrix is to check its condition number. A very large value of condition number indicates a poorly conditioned matrix. You can find the condition number of a matrix by using the “cond” function.

The documentation for the “cond” function can be found here:

https://www.mathworks.com/help/matlab/ref/cond.html

2 个评论
显示无隐藏无

John D'Errico 2016-7-13

编辑：John D'Errico 2016-7-13

在 MATLAB Online 中打开

lastwarn can work here as shown, with one caveat. You need to reset lastwarn after checking it. Otherwise, consider this example:

clear
A1 = ones(2);
B1 = inv(A1);
Warning: Matrix is singular to working precision. 
[m,id]=lastwarn()
m =
Matrix is singular to working precision.
id =
MATLAB:singularMatrix

So, A1 was singular, and lastwarn tells us what it saw.

Now, create a new matrix, and invert it.

A2 = rand(2);
B2 = inv(A2);
[m,id]=lastwarn()
m =
Matrix is singular to working precision.
id =
MATLAB:singularMatrix

So lastwarn still retains the warning from the previous call.

The point is, if you only test the value of lastwarn, then you need to have reset lastwarn, after EVERY call to lastwarn. Part of me wants this to be the expected behavior of lastwarn, that if you ask the question a second time, it won't repeat the warning. Or perhaps it should be an option to lastwarn, an ask, THEN reset the last warning to empty automatically.

So, lets see whta happens if we reset lastwarn, then redo the computation for B2.

lastwarn('')
B2 = inv(A2);
[m,id]=lastwarn()
m =
     ''
id =
     ''

Of course, if you use cond or rank before the computation, you would have predicted that A1 was singular before even trying to compute the inverse.

Or, you might decide to use pinv instead of inv. Sometimes that is the right thing to do, depending on the problems you are trying to solve.

Steven Lord 2021-3-3

在 MATLAB Online 中打开

Another option, particularly if you're going to solve multiple systems with the same coefficient matrix, is to create a decomposition for the matrix and ask it if the matrix isIllConditioned.

M = magic(4)
M = 4×4
    16     2     3    13
     5    11    10     8
     9     7     6    12
     4    14    15     1
rank(M) % M is singular
ans = 3
D = decomposition(M);
isIllConditioned(D)
ans = logical
   1

You can also control whether or not \ and / issue warnings when called on the decomposition if the matrix is ill conditioned using its CheckCondition property.

x1 = M\[1; 0; 0; 0]
Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND =  4.625929e-18.
x1 = 4×1
   -2.6492
   -7.9475
    7.9475
    2.6492
x2 = D\[1; 0; 0; 0]
Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND =  4.625929e-18.
x2 = 4×1
   -2.6492
   -7.9475
    7.9475
    2.6492
D.CheckCondition = false;
x3 = D\[1; 0; 0; 0]
x3 = 4×1
   -2.6492
   -7.9475
    7.9475
    2.6492