CODEWITHSUNDEEP
cfloating-accuracy
WhiteWolf
WhiteWolf

Reputation: 25

What is the recommended minimal epsilon for double?

I'm trying to create a Gauss Eliminator in C. For this, from time to time, I need to check whether a matrix is numerically singular: if a certain number (double) is very very very small.

My problem is, that if I try to do this:

if(0 == matrix->items[from]){
        fprintf(stderr,"Matrix is still singular after attempting pivot. Exitig.\n");
}

This will never yield true. Because of the inaccuracy of double, it will never be exactly 0. However, when trying to run the program, cases like this fill up the numbers with inf or NaN, depending on whether multiplying or dividing with it and its combinations.

In order to filter these, I would need something like this:

#define EPSILON very_small
// rest of the code
if(matrix->items[from] < EPSILON){
     ...singular
}

What is the recommended value for this EPSILON? Is it the absolute accuracy of double, or maybe a bit larger value?

By the way, which would be better, defining it as a macro as above, or using it like:

const double EPSILON = ...;

Sorry if I'm not being clear enough, English is not my native language.

Thanks for your replies.

Upvotes: 0

Views: 266

Answers (1)

chux
chux

Reputation: 154602

I need to check whether a matrix is numerically singular

Usually this is detected by preventing double overflow.

// Check if 1.0/determinant will overflow.
if (fabs(determinant) <= 1.0/(0.99*DBL_MAX)) {
  Handle_Singular_Case()
} else {
  one_over_det = 1.0/determinant;
}

Using DBL_EPSILON (example: 2e-16) is usually the wrong solution. double math needs relative comparisons to insure good calculations far way from 1.0 magnitude.

// Rarely the right thing to do.
#define EPSILON DBL_EPSILON
if(fabs(matrix->items[from]) < EPSILON){

Yet this is very context sensitive @Weather Vane.

Yet OP's real problem is certainly here: "when trying to run the program, cases like this fill up the numbers with inf or NaN, depending on whether multiplying or dividing with it and its combinations.". Various techniques can be used to avoid this issue like doing elimination with partial pivoting.

To address that issue, best to post code and sample data.

Upvotes: 2

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