Scilab Home page | Wiki | Bug tracker | Forge | Mailing list archives | ATOMS | File exchange
Please login or create an account
Change language to: English - Português - Русский - 日本語

Please note that the recommended version of Scilab is 6.0.0. This page might be outdated.
See the recommended documentation of this function

Aide de Scilab >> Outils de développement > Assert > assert_comparecomplex

assert_comparecomplex

Compare complex numbers with a tolerance.

Calling Sequence

order = assert_comparecomplex ( a , b )
order = assert_comparecomplex ( a , b , reltol )
order = assert_comparecomplex ( a , b , reltol , abstol )

Parameters

a :

a 1-by-1 matrix of doubles, the first value to be compared

b :

a 1-by-1 matrix of doubles, the second value to be compared

reltol :

a 1-by-1 matrix of doubles, the relative tolerance (default reltol=sqrt(%eps)).

abstol :

a 1-by-1 matrix of doubles, the absolute tolerance (default abstol=0).

order :

a 1-by-1 matrix of doubles, integer values, the order. Returns order=0 is a is almost equal to b, order=-1 if a < b, order=+1 if a > b.

Description

Compare first by real parts, then by imaginary parts. Takes into account numerical accuracy issues, by using a mixed relative and absolute tolerance criteria.

Any optional input argument equal to the empty matrix is replaced by its default value.

We use the following algorithm.

We compare first the real parts. In case of tie, we compare the imaginary parts.

We process the IEEE values and choose the order : -%inf < 0 < %inf < %nan. If none of the values is special, we use the condition :

cond = ( abs(a-b) <= reltol * max(abs(a),abs(b)) + abstol )

This algorithm is designed to be used into sorting algorithms. It allows to take into account for the portability issues related to the outputs of functions producing matrix of complex doubles. If this algorithm is plugged into a sorting function, it allows to consistently produce a sorted matrix, where the order can be independent of the operating system, the compiler or other forms of issues modifying the order (but not the values).

Examples

// Compare real values
assert_comparecomplex ( 1 , -1 ) // 1
assert_comparecomplex ( -1 , 1 ) // -1
assert_comparecomplex ( 1 , 1 ) // 0

// Compare complex values #1
assert_comparecomplex ( 1+2*%i , 1+3*%i ) // -1
assert_comparecomplex ( 1+3*%i , 1+2*%i ) // 1
assert_comparecomplex ( 1+2*%i , 1+2*%i ) // 0

// Compare complex values #2
assert_comparecomplex ( 1+%i , -1+%i ) // 1
assert_comparecomplex ( -1+%i , 1+%i ) // -1
assert_comparecomplex ( 1+%i , 1+%i ) // 0
[order,msg] = assert_comparecomplex ( 1+%i , 1+%i )

// Compare with tolerances : equality cases
assert_comparecomplex ( 1.2345+%i , 1.2346+%i , %eps , 1.e-3 ) // 0
assert_comparecomplex ( 1.2345+%i , 1.2346+%i , 1.e12*%eps , 0 ) // 0
assert_comparecomplex ( 1+1.2345*%i , 1+1.2347*%i , %eps , 1.e-3 ) // 0
assert_comparecomplex ( 1+1.2345*%i , 1+1.2347*%i , 1.e12*%eps , 0 ) // 0

// Compare more realistic data
x = [
-0.123452 - 0.123454 * %i
-0.123451 + 0.123453 * %i
0.123458 - 0.123459 * %i
0.123456 + 0.123457 * %i
];
// Consider less than 4 significant digits
for i = 1 : size(x,"*")-1
order = assert_comparecomplex ( x(i) , x(i+1) , 1.e-4 );
mprintf("compare(x(%d),x(%d))=%d\n",i,i+1,order)
end

// Compare data from bug #415
x = [
-1.9914145
-1.895889
-1.6923826
-1.4815461
-1.1302576
-0.5652256 - 0.0655080 * %i
-0.5652256 + 0.0655080 * %i
0.3354023 - 0.1602902 * %i
0.3354023 + 0.1602902 * %i
1.3468911
1.5040136
1.846668
1.9736772
1.9798866
];
// Consider less than 4 significant digits
for i = 1 : size(x,"*")-1
order = assert_comparecomplex ( x(i) , x(i+1) , 1.e-5 );
mprintf("compare(x(%d),x(%d))=%d\n",i,i+1,order)
end

History

VersionDescription
5.4.0 Function introduced

Bibliography

http://gitweb.scilab.org/?p=scilab.git;a=blob;f=scilab/modules/polynomials/tests/nonreg_tests/bug_415.tst;h=0c716a3bed0dfb72c831972d19dbb0814dffde2b;hb=HEAD

http://gitweb.scilab.org/?p=scilab.git;a=blob_plain;f=scilab/modules/cacsd/tests/nonreg_tests/bug_68.tst;h=920d091d089b61bf961ea9e888b4d7d469942a14;hb=4ce3d4109dd752fce5f763be71ea639e09a12630

Scilab Enterprises
Copyright (c) 2011-2017 (Scilab Enterprises)
Copyright (c) 1989-2012 (INRIA)
Copyright (c) 1989-2007 (ENPC)
with contributors
Last updated:
Thu Oct 02 13:54:44 CEST 2014