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Interval package: Difference between revisions
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| style = "vertical-align: top" | | | style = "vertical-align: top" | | ||
octave:1> 19 * 0.1 - 2 + 0.1 | <span style="opacity:.5">octave:1> </span>19 * 0.1 - 2 + 0.1 | ||
ans = 1.3878e-16 | ans = 1.3878e-16 | ||
| style = "vertical-align: top" | | | style = "vertical-align: top" | | ||
octave:1> x = infsup ("0.1"); | <span style="opacity:.5">octave:1> </span>x = infsup ("0.1"); | ||
octave:2> 19 * x - 2 + x | <span style="opacity:.5">octave:2> </span>19 * x - 2 + x | ||
ans ⊂ [-3.1918911957973251e-16, +1.3877787807814457e-16] | ans ⊂ [-3.1918911957973251e-16, +1.3877787807814457e-16] | ||
|} | |} | ||
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== Installation == | == Installation == | ||
The interval package is available at Octave Forge [http://octave.sourceforge.net/interval/] and can be installed from within GNU Octave (version ≥ 3.8.2). During installation parts of the package are compiled for the target system, which requires the GNU MPFR development libraries (version ≥ 3.1.0) to be installed. | The interval package is available at Octave Forge [http://octave.sourceforge.net/interval/] and can be installed from within GNU Octave (version ≥ 3.8.2). During installation parts of the package are compiled for the target system, which requires the GNU MPFR development libraries (version ≥ 3.1.0) to be installed. | ||
octave:1> pkg install -forge interval | <span style="opacity:.5">octave:1> </span>pkg install -forge interval | ||
octave:2> pkg load interval | <span style="opacity:.5">octave:2> </span>pkg load interval | ||
The ''development version'' may be obtained from its mercurial repository. For convenience a Makefile target allows running the package from source. | The ''development version'' may be obtained from its mercurial repository. For convenience a Makefile target allows running the package from source. | ||
hg clone http://hg.code.sf.net/p/octave/interval octave-interval | |||
cd octave-interval; make run | |||
== Quick start introduction == | == Quick start introduction == | ||
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| style = "vertical-align: top" | | | style = "vertical-align: top" | | ||
octave:1> A = [1, 0; 2, 0]; | <span style="opacity:.5">octave:1> </span>A = [1, 0; 2, 0]; | ||
octave:2> A \ [3; 0] # no solution | <span style="opacity:.5">octave:2> </span>A \ [3; 0] # no solution | ||
warning: matrix singular to machine precision, rcond = 0 | warning: matrix singular to machine precision, rcond = 0 | ||
ans = | ans = | ||
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0.00000 | 0.00000 | ||
octave:3> A \ [4; 8] # many solutions | <span style="opacity:.5">octave:3> </span>A \ [4; 8] # many solutions | ||
ans = | ans = | ||
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0 | 0 | ||
| style = "vertical-align: top" | | | style = "vertical-align: top" | | ||
octave:4> A = infsup (A); | <span style="opacity:.5">octave:4> </span>A = infsup (A); | ||
octave:5> A \ [3; 0] # no solution | <span style="opacity:.5">octave:5> </span>A \ [3; 0] # no solution | ||
ans = 2×1 interval vector | ans = 2×1 interval vector | ||
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[Empty] | [Empty] | ||
octave:6> A \ [4; 8] # many solutions | <span style="opacity:.5">octave:6> </span>A \ [4; 8] # many solutions | ||
ans = 2×1 interval vector | ans = 2×1 interval vector | ||
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Due to the nature of set-based interval arithmetic, one should never observe errors (in the sense of raised GNU Octave error messages) during computation. If you do, there either is a bug in the code or there are unsupported data types. Arithmetic operations which are not defined for (parts of) their input, simply ignore anything that is outside of their domain. | Due to the nature of set-based interval arithmetic, one should never observe errors (in the sense of raised GNU Octave error messages) during computation. If you do, there either is a bug in the code or there are unsupported data types. Arithmetic operations which are not defined for (parts of) their input, simply ignore anything that is outside of their domain. | ||
octave:1> infsup (2, 3) / 0 | <span style="opacity:.5">octave:1> </span>infsup (2, 3) / 0 | ||
ans = [Empty] | ans = [Empty] | ||
octave:2> infsup (0) ^ infsup (0) | <span style="opacity:.5">octave:2> </span>infsup (0) ^ infsup (0) | ||
ans = [Empty] | ans = [Empty] | ||
However, the interval constructors can produce errors depending on the input. The <code>infsup</code> constructor will fail if the interval boundaries are invalid. Contrariwise, the <code>infsupdec</code> constructor will only issue a warning and return a [NaI], which will propagate and survive through computations. | However, the interval constructors can produce errors depending on the input. The <code>infsup</code> constructor will fail if the interval boundaries are invalid. Contrariwise, the <code>infsupdec</code> constructor will only issue a warning and return a [NaI], which will propagate and survive through computations. | ||
octave:3> infsup (3, 2) + 1 | <span style="opacity:.5">octave:3> </span>infsup (3, 2) + 1 | ||
error: illegal interval boundaries: infimum greater than supremum | error: illegal interval boundaries: infimum greater than supremum | ||
''… (call stack) …'' | ''… (call stack) …'' | ||
octave:3> infsupdec (3, 2) + 1 | <span style="opacity:.5">octave:3> </span>infsupdec (3, 2) + 1 | ||
warning: illegal interval boundaries: infimum greater than supremum | warning: illegal interval boundaries: infimum greater than supremum | ||
ans = [NaI] | ans = [NaI] | ||
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* Basic operations can be found in both packages, but the availability of special functions depends | * Basic operations can be found in both packages, but the availability of special functions depends | ||
In GNU Octave the interval package can also be run | {{Code|In GNU Octave the interval package can also be run alongside INTLAB.|<syntaxhighlight lang="octave"> | ||
# INTLAB intervals | # INTLAB intervals | ||
A1 = infsup (2, 3); | A1 = infsup (2, 3); | ||
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# Computation without INTLAB | # Computation without INTLAB | ||
A2 + B2 * C2 | A2 + B2 * C2 | ||
</syntaxhighlight> | |||
}} | |||
== Related work == | == Related work == | ||