240
edits
Interval package: Difference between revisions
m
→Input and output: Added hint for command syntax
m (→Compatibility) |
m (→Input and output: Added hint for command syntax) |
||
| Line 130: | Line 130: | ||
ans ⊂ [1, 1.0000000000000005] | 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. In simple cases it may help to construct intervals with the [https://www.gnu.org/software/octave/doc/interpreter/Commands.html#Commands command syntax]. | ||
octave:9> infsup (<span style = "color:red">0.2</span>) | octave:9> infsup (<span style = "color:red">0.2</span>) | ||
ans ⊂ [.20000000000000001, .20000000000000002] | ans ⊂ [.20000000000000001, .20000000000000002] | ||
octave:10> infsup (<span style = "color:green">"0.2"</span>) | octave:10> infsup (<span style = "color:green">"0.2"</span>) | ||
ans ⊂ [.19999999999999998, .20000000000000002] | |||
octave:11> infsup <span style = "color:green">0.2</span> | |||
ans ⊂ [.19999999999999998, .20000000000000002] | 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: | octave:12> infsup ("17.7") + 1 | ||
ans ⊂ [18.699999999999999, 18.700000000000003] | ans ⊂ [18.699999999999999, 18.700000000000003] | ||
octave: | octave:13> ans + "[0, 2]" | ||
ans ⊂ [18.699999999999999, 20.700000000000003] | ans ⊂ [18.699999999999999, 20.700000000000003] | ||
| Line 154: | Line 156: | ||
** <code>''E ''</code> is either empty or an exponent field comprising the character <code>e</code> followed by a decimal integer exponent (base 10). | ** <code>''E ''</code> is either empty or an exponent field comprising the character <code>e</code> followed by a decimal integer exponent (base 10). | ||
octave: | octave:14> infsup ("0x1.999999999999Ap-4") | ||
ans ⊂ [.1, .10000000000000001] | ans ⊂ [.1, .10000000000000001] | ||
octave: | octave:15> infsup ("1/3", "7/9") | ||
ans ⊂ [.33333333333333331, .7777777777777778] | ans ⊂ [.33333333333333331, .7777777777777778] | ||
octave: | octave:16> infsup ("121.2?") | ||
ans ⊂ [121.14999999999999, 121.25] | ans ⊂ [121.14999999999999, 121.25] | ||
octave: | octave:17> infsup ("5?32e2") | ||
ans = [-2700, +3700] | ans = [-2700, +3700] | ||
octave: | octave:18> infsup ("-42??u") | ||
ans = [-42, +Inf] | ans = [-42, +Inf] | ||
==== Interval vectors and matrices ==== | ==== Interval vectors and matrices ==== | ||
Vectors and matrices of intervals can be created by passing numerical matrices, char vectors or cell arrays to the <code>infsup</code> constructor. With cell arrays it is also possible to mix several types of boundaries. | Vectors and matrices of intervals can be created by passing numerical matrices, char vectors or cell arrays to the <code>infsup</code> constructor. With cell arrays it is also possible to mix several types of boundaries. | ||
octave: | octave:19> M = infsup (magic (3)) | ||
M = 3×3 interval matrix | M = 3×3 interval matrix | ||
| Line 174: | Line 176: | ||
[4] [9] [2] | [4] [9] [2] | ||
octave: | octave:20> infsup (magic (3), magic (3) + 1) | ||
ans = 3×3 interval matrix | ans = 3×3 interval matrix | ||
| Line 181: | Line 183: | ||
[4, 5] [9, 10] [2, 3] | [4, 5] [9, 10] [2, 3] | ||
octave: | octave:21> infsup (["0.1"; "0.2"; "0.3"; "0.4"; "0.5"]) | ||
ans ⊂ 5×1 interval vector | ans ⊂ 5×1 interval vector | ||
| Line 190: | Line 192: | ||
[.5] | [.5] | ||
octave: | octave:22> infsup ({1, eps; "4/7", "pi"}, {2, 1; "e", "0xff"}) | ||
ans ⊂ 2×2 interval matrix | ans ⊂ 2×2 interval matrix | ||
| Line 197: | Line 199: | ||
When matrices are resized using subscripted assignment, any implicit new matrix elements will carry an empty interval. | When matrices are resized using subscripted assignment, any implicit new matrix elements will carry an empty interval. | ||
octave: | octave:23> M (4, 4) = 42 | ||
M = 4×4 interval matrix | M = 4×4 interval matrix | ||
| Line 206: | Line 208: | ||
Note: Whilst most functions (<code>size</code>, <code>isvector</code>, <code>ismatrix</code>, …) work as expected on interval data types, the function <code>'''isempty'''</code> is evaluated element-wise and checks if an interval equals the empty set. | Note: Whilst most functions (<code>size</code>, <code>isvector</code>, <code>ismatrix</code>, …) work as expected on interval data types, the function <code>'''isempty'''</code> is evaluated element-wise and checks if an interval equals the empty set. | ||
octave: | octave:24> builtin ("isempty", empty ()), isempty (empty ()) | ||
ans = 0 | ans = 0 | ||
ans = 1 | ans = 1 | ||