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Interval package

1,105 bytes added, 15:31, 31 October 2014
octave:1> infsup (1, 3) <= infsup (2, 4)
ans = 1
 
=== Matrix operations ===
Above mentioned operations can usually also be applied to interval vectors and matrices. Many operations use [http://www.gnu.org/software/octave/doc/interpreter/Vectorization-and-Faster-Code-Execution.html#Vectorization-and-Faster-Code-Execution vectorization techniques].
 
The implemented interval matrix operations comprise: exact dot product, exact matrix multiplication, exact vector sums, (not-exact) matrix inversion, matrix powers and solving linear systems. As a result of missing hardware / low-level library support, these operations are quite slow compared to familiar operations in floating-point arithmetic.
octave:1> A = infsup ([1, 2, 3; 4, 0, 0; 0, 0, 0], [1, 2, 3; 4, 0, 6; 0, 0, 1])
A = 3×3 interval matrix
[1] [2] [3]
[4] [0] [0, 6]
[0] [0] [0, 1]
octave:2> B = inv (A)
B = 3×3 interval matrix
[0] [.25] [-Inf, 0]
[.5] [-.125] [-Inf, -.75]
[0] [0] [1, Inf]
octave:3> A * B
ans = 3×3 interval matrix
[1] [0] [Entire]
[0] [1] [Entire]
[0] [0] [0, Inf]
=== Error handling ===
240

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