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# clean

cleans matrices (round to zero small entries)

### Syntax

```B = clean(A)
B = clean(A, epsa)
B = clean(A, epsa, epsr)```

### Arguments

A

scalar, vector, matrix or hypermatrix of decimal numbers or of complex numbers, in dense or sparse encoding, or of polynomials or rationals with real or complex coefficients.

epsa, epsr

positive real numbers: Cleaning tolerances. Both default values are 10-10.

### Description

This function sets to 0 all the elements of `A` with absolute value < `epsa` or relative value < `epsr` (relative w.r.t. to max(abs(A)), ignoring %inf and %nan values of `A`).

For an array of polynomials or of rationals, clean() applies in the same way to the whole set of their coefficients.

### Examples

```m = grand(3,5,"uin",1,9) .* 10.^grand(3,5,"uin",-16,1)
clean(m)
clean(m, 1e-7)```
```--> m = grand(3,5,"uin",1,9) .* 10.^grand(3,5,"uin",-16,1)
m  =
5.000D-08   5.          0.8         7.000D-08   4.000D-11
0.00007     7.          4.000D-09   6.000D-13   2.000D-16
2.000D-08   1.000D-14   1.          8.          0.7

--> clean(m)
ans  =
5.000D-08   5.   0.8         7.000D-08   0.
0.00007     7.   4.000D-09   0.          0.
2.000D-08   0.   1.          8.          0.7

--> clean(m, 1e-7)
ans  =
0.        5.   0.8   0.   0.
0.00007   7.   0.    0.   0.
0.        0.   1.    8.   0.7
```

For rationals:

```x = poly(0,'x');
w = [3+2*x, 2+x; 3+x, 2-x]/5
r = w * inv(w)
clean(r)```
```--> w = [3+2*x, 2+x; 3+x, 2-x]/5
w  =
0.6 +0.4x   0.4 +0.2x
0.6 +0.2x   0.4 -0.2x

--> r = w * inv(w)
r  =
2
-3.140D-16 + x                        -1.110D-15 + 3.331D-16x
---------------                       ------------------------
2
x                                   1.3333333x + x
2                             2
1.110D-15 - 2.220D-16x - 5.551D-17x   -1.110D-15 + 1.3333333x + x
------------------------------------  ----------------------------
2                                 2
1.3333333x + x                    1.3333333x + x

--> clean(r)
ans  =
1   0
--  --
1   1

0   1
--  --
1   1
```

• %eps — epsilon (floating-point relative accuracy)
• cond — condition number of a matrix
• nearfloat — get previous or next floating-point number
• number_properties — determine floating-point parameters