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Interval package: Difference between revisions
Updated interval output
(Updated interval output) |
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octave:1> x = infsup ("0.1"); | octave:1> x = infsup ("0.1"); | ||
octave:2> 19 * x - 2 + x | octave:2> 19 * x - 2 + x | ||
ans | ans ⊆ [-3.1918911957973251e-16, +1.3877787807814457e-16] | ||
|} | |} | ||
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ans = [3, 4] | ans = [3, 4] | ||
octave:4> infsup ("1.1") | octave:4> infsup ("1.1") | ||
ans | ans ⊆ [1.0999999999999998, 1.1000000000000001] | ||
octave:5> infsup ("[5, 6.5]") | octave:5> infsup ("[5, 6.5]") | ||
ans = [5, 6.5] | ans = [5, 6.5] | ||
octave:6> infsup ("[5.8e-17]") | octave:6> infsup ("[5.8e-17]") | ||
ans | ans ⊆ [5.799999999999999e-17, 5.800000000000001e-17] | ||
It is possible to access the exact numeric interval boundaries with the functions <code>inf</code> and <code>sup</code>. The default text representation of intervals can be created with <code>intervaltotext</code>. The default text representation is not guaranteed to be exact (see function <code>intervaltoexact</code>), because this would massively spam console output. For example, the exact text representation of <code>realmin</code> would be over 700 decimal places long! However, the default text representation is correct as it guarantees to contain the actual boundaries and is accurate enough to separate different boundaries. | It is possible to access the exact numeric interval boundaries with the functions <code>inf</code> and <code>sup</code>. The default text representation of intervals can be created with <code>intervaltotext</code>. The default text representation is not guaranteed to be exact (see function <code>intervaltoexact</code>), because this would massively spam console output. For example, the exact text representation of <code>realmin</code> would be over 700 decimal places long! However, the default text representation is correct as it guarantees to contain the actual boundaries and is accurate enough to separate different boundaries. | ||
octave:7> infsup (1, 1 + eps) | octave:7> infsup (1, 1 + eps) | ||
ans | ans ⊆ [1, 1.0000000000000003] | ||
octave:8> infsup (1, 1 + 2 * eps) | octave:8> infsup (1, 1 + 2 * eps) | ||
ans | ans ⊆ [1, 1.0000000000000005] | ||
Warning: Decimal fractions as well as numbers of high magnitude (> 2<sup>53</sup>) should always be passed as a string to the constructor. Otherwise it is possible, that GNU Octave introduces conversion errors when the numeric literal is converted into floating-point format '''before''' it is passed to the constructor. | Warning: Decimal fractions as well as numbers of high magnitude (> 2<sup>53</sup>) should always be passed as a string to the constructor. Otherwise it is possible, that GNU Octave introduces conversion errors when the numeric literal is converted into floating-point format '''before''' it is passed to the constructor. | ||
octave:9> infsup (<span style = "color:red">0.2</span>) | octave:9> infsup (<span style = "color:red">0.2</span>) | ||
ans | ans ⊆ [.20000000000000001, .20000000000000002] | ||
octave:10> infsup (<span style = "color:green">"0.2"</span>) | octave:10> infsup (<span style = "color:green">"0.2"</span>) | ||
ans | ans ⊆ [.19999999999999998, .20000000000000002] | ||
For convenience it is possible to implicitly call the interval constructor during all interval operations if at least one input already is an interval object. | For convenience it is possible to implicitly call the interval constructor during all interval operations if at least one input already is an interval object. | ||
octave:11> infsup ("17.7") + 1 | octave:11> infsup ("17.7") + 1 | ||
ans | ans ⊆ [18.699999999999999, 18.700000000000003] | ||
octave:12> ans + "[0, 2]" | octave:12> ans + "[0, 2]" | ||
ans | ans ⊆ [18.699999999999999, 20.700000000000003] | ||
=== Decorations === | === Decorations === | ||
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octave:1> sin (infsup (0.5)) | octave:1> sin (infsup (0.5)) | ||
ans | ans ⊆ [.47942553860420294, .47942553860420307] | ||
octave:2> pow (infsup (2), infsup (3, 4)) | octave:2> pow (infsup (2), infsup (3, 4)) | ||
ans = [8, 16] | ans = [8, 16] | ||
octave:3> atan2 (infsup (1), infsup (1)) | octave:3> atan2 (infsup (1), infsup (1)) | ||
ans | ans ⊆ [.7853981633974482, .7853981633974484] | ||
=== Reverse arithmetic operations === | === Reverse arithmetic operations === | ||
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In the following example, we compute the constraints for base and exponent of the power function <code>pow</code> as shown in the figure. | In the following example, we compute the constraints for base and exponent of the power function <code>pow</code> as shown in the figure. | ||
octave:1> x = powrev1 (infsup ("[1.1, 1.45]"), infsup (2, 3)) | octave:1> x = powrev1 (infsup ("[1.1, 1.45]"), infsup (2, 3)) | ||
x | x ⊆ [1.6128979635153644, 2.7148547265657923] | ||
octave:2> y = powrev2 (infsup ("[2.14, 2.5]"), infsup (2, 3)) | octave:2> y = powrev2 (infsup ("[2.14, 2.5]"), infsup (2, 3)) | ||
y | y ⊆ [.7564707973660299, 1.4440113978403289] | ||
=== Numerical operations === | === Numerical operations === | ||