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Interval package: Difference between revisions
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Updated interval output with less decimal digits and zero before the decimal point
m (→Error handling: Added information for fixing the warning reasons) |
m (Updated interval output with less decimal digits and zero before the decimal point) |
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<span style="opacity:.5">octave:1> </span>x = infsup ("0.1"); | <span style="opacity:.5">octave:1> </span>x = infsup ("0.1"); | ||
<span style="opacity:.5">octave:2> </span>19 * x - 2 + x | <span style="opacity:.5">octave:2> </span>19 * x - 2 + x | ||
ans ⊂ [-3. | ans ⊂ [-3.191891195797326e-16, +1.3877787807814457e-16] | ||
|} | |} | ||
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infsupdec (1, 2) # [1, 2]_com | infsupdec (1, 2) # [1, 2]_com | ||
infsupdec ("3", "4") # [3, 4]_com | infsupdec ("3", "4") # [3, 4]_com | ||
infsupdec ("1.1") # [1.0999999999999998, 1. | infsupdec ("1.1") # [1.0999999999999998, 1.100000000000001]_com | ||
infsupdec ("5.8e-17") | infsupdec ("5.8e-17") | ||
# [5.799999999999999e-17, 5.800000000000001e-17]_com | # [5.799999999999999e-17, 5.800000000000001e-17]_com | ||
midrad (12, 3) # [9, 15]_com | midrad (12, 3) # [9, 15]_com | ||
midrad ("4.2", "1e-7") # [4.199999899999999, 4. | midrad ("4.2", "1e-7") # [4.199999899999999, 4.200000100000001]_com | ||
hull (3, 42, "19.3", "-2.3") # [-2. | hull (3, 42, "19.3", "-2.3") # [-2.300000000000001, +42]_co | ||
hull ("pi", "e") # [2.718281828459045, 3.1415926535897936]_trv | hull ("pi", "e") # [2.718281828459045, 3.1415926535897936]_trv | ||
</syntaxhighlight> | </syntaxhighlight> | ||
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{{Code|Beware of the conversion pitfall|<syntaxhighlight lang="octave"> | {{Code|Beware of the conversion pitfall|<syntaxhighlight lang="octave"> | ||
## The numeric constant “0. | ## The numeric constant “0.3” is an approximation of the | ||
## decimal number 0. | ## decimal number 0.3. An interval around this approximation | ||
## will not contain the decimal number 0. | ## will not contain the decimal number 0.3. | ||
infsupdec (0. | infsupdec (0.3) # [0.29999999999999998, 0.29999999999999999]_com | ||
## However, passing the decimal number 0. | ## However, passing the decimal number 0.3 as a string | ||
## to the interval constructor will create an interval which | ## to the interval constructor will create an interval which | ||
## actually encloses the decimal number. | ## actually encloses the decimal number. | ||
infsupdec ("0. | infsupdec ("0.3") # [0.29999999999999998, 0.3000000000000001]_com | ||
</syntaxhighlight> | </syntaxhighlight> | ||
}} | }} | ||
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# [4, 5] [9, 10] [2, 3] | # [4, 5] [9, 10] [2, 3] | ||
infsupdec (["0.1"; "0.2"; "0.3"; "0.4"; "0.5"]) | infsupdec (["0.1"; "0.2"; "0.3"; "0.4"; "0.5"]) | ||
# [.09999999999999999, . | # [0.09999999999999999, 0.1000000000000001]_com | ||
# [.19999999999999998, . | # [0.19999999999999998, 0.2000000000000001]_com | ||
# [.29999999999999998, . | # [0.29999999999999998, 0.3000000000000001]_com | ||
# [.39999999999999996, . | # [0.39999999999999996, 0.4000000000000001]_com | ||
# [.5]_com | # [0.5]_com | ||
infsup ({1, eps; "4/7", "pi"}, {2, 1; "e", "0xff"}) | infsup ({1, eps; "4/7", "pi"}, {2, 1; "e", "0xff"}) | ||
# | # [1, 2] [2.220446049250313e-16, 1] | ||
# [.5714285714285713, 2.7182818284590456] | # [0.5714285714285713, 2.7182818284590456] [3.141592653589793, 255] | ||
</syntaxhighlight> | </syntaxhighlight> | ||
}} | }} | ||
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{{Code|Examples of using interval arithmetic functions|<syntaxhighlight lang="octave"> | {{Code|Examples of using interval arithmetic functions|<syntaxhighlight lang="octave"> | ||
sin (infsupdec (0.5)) # [. | sin (infsupdec (0.5)) # [.4794255386042029, .4794255386042031]_com | ||
pow (infsupdec (2), infsupdec (3, 4)) # [8, 16]_com | pow (infsupdec (2), infsupdec (3, 4)) # [8, 16]_com | ||
atan2 (infsupdec (1), infsupdec (1)) | atan2 (infsupdec (1), infsupdec (1)) | ||
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# [0] [0] [1] | # [0] [0] [1] | ||
B = inv (A) | B = inv (A) | ||
# | # [0] [0.25] [-1.5, 0] | ||
# [.5] [-.125] [-1.5, -.75] | # [0.5] [-0.125] [-1.5, -0.75] | ||
# | # [0] [0] [1] | ||
A * B | A * B | ||
# [1] [0] [-1.5, +1.5] | # [1] [0] [-1.5, +1.5] | ||
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# [4] [9] [2] | # [4] [9] [2] | ||
c = A \ [3; 4; 5] | c = A \ [3; 4; 5] | ||
# [. | # [0.18333333333333315, 0.18333333333333358] | ||
# [. | # [0.43333333333333318, 0.43333333333333346] | ||
# [. | # [0.18333333333333307, 0.18333333333333355] | ||
A * c | A * c | ||
# [2. | # [2.9999999999999964, 3.0000000000000036] | ||
# [3. | # [3.9999999999999964, 4.000000000000004] | ||
# [4. | # [4.999999999999997, 5.000000000000003] | ||
</syntaxhighlight> | </syntaxhighlight> | ||
}} | }} | ||
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{{Code|Examples of using the decoration system|<syntaxhighlight lang="octave"> | {{Code|Examples of using the decoration system|<syntaxhighlight lang="octave"> | ||
x = infsupdec (3, 4) # [3, 4]_com | x = infsupdec (3, 4) # [3, 4]_com | ||
y = x - 3.5 # [-.5, +.5]_com | y = x - 3.5 # [-0.5, +0.5]_com | ||
## The square root function ignores any negative part of the input, | ## The square root function ignores any negative part of the input, | ||
## but the decoration indicates whether this has or has not happened. | ## but the decoration indicates whether this has or has not happened. | ||
sqrt (x) # [1. | sqrt (x) # [1.732050807568877, 2]_com | ||
sqrt (y) # [0, .7071067811865476]_trv | sqrt (y) # [0, 0.7071067811865476]_trv | ||
</syntaxhighlight> | </syntaxhighlight> | ||
}} | }} | ||
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{{Code|Examples of different formats during interval construction|<syntaxhighlight lang="octave"> | {{Code|Examples of different formats during interval construction|<syntaxhighlight lang="octave"> | ||
infsup ("0x1.999999999999Ap-4") # hex-form | infsup ("0x1.999999999999Ap-4") # hex-form | ||
# [.1, . | # [0.1, 0.1000000000000001] | ||
infsup ("1/3", "7/9") # rational form | infsup ("1/3", "7/9") # rational form | ||
# [. | # [0.3333333333333333, 0.7777777777777778] | ||
infsup ("121.2?") # uncertain form | infsup ("121.2?") # uncertain form | ||
# [121.14999999999999, 121.25] | # [121.14999999999999, 121.25] | ||
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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. | ||
<span style="opacity:.5">octave:1> </span>x = powrev1 (infsup ("[1.1, 1.45]"), infsup (2, 3)) | <span style="opacity:.5">octave:1> </span>x = powrev1 (infsup ("[1.1, 1.45]"), infsup (2, 3)) | ||
x ⊂ [1.6128979635153646, 2. | x ⊂ [1.6128979635153646, 2.714854726565793] | ||
<span style="opacity:.5">octave:2> </span>y = powrev2 (infsup ("[2.14, 2.5]"), infsup (2, 3)) | <span style="opacity:.5">octave:2> </span>y = powrev2 (infsup ("[2.14, 2.5]"), infsup (2, 3)) | ||
y ⊂ [.7564707973660299, 1. | y ⊂ [0.7564707973660299, 1.4440113978403289] | ||
=== Tips & Tricks === | === Tips & Tricks === | ||
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<span style="opacity:.5">octave:1> </span>infsupdec ("17.7") + 1 | <span style="opacity:.5">octave:1> </span>infsupdec ("17.7") + 1 | ||
ans ⊂ [18.699999999999999, 18. | ans ⊂ [18.699999999999999, 18.70000000000001]_com | ||
<span style="opacity:.5">octave:2> </span>ans + "[0, 2]" | <span style="opacity:.5">octave:2> </span>ans + "[0, 2]" | ||
ans ⊂ [18.699999999999999, 20. | ans ⊂ [18.699999999999999, 20.70000000000001]_com | ||
Interval functions with only one argument can be called by using property syntax, e. g. <code>x.inf</code>, <code>x.sup</code> or even <code>x.sqr</code>. | Interval functions with only one argument can be called by using property syntax, e. g. <code>x.inf</code>, <code>x.sup</code> or even <code>x.sqr</code>. | ||