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Scilab Help >> Elementary Functions > Floating point > clean

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

See also

  • %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
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Last updated:
Thu Feb 14 14:57:12 CET 2019