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For t ≤ k, an orthogonal array of type (N, k, v, t) – an OA(N, k, v, t) for short – is an N × k array whose entries are chosen from a set X with v points (a v-set) such that in every subset of t columns of the array, every t-tuple of points of X is repeated the same number of times. The number of repeats is usually denoted λ.
Orthogonal matrix: A matrix whose inverse is equal to its transpose, A −1 = A T. They form the orthogonal group. Orthonormal matrix: A matrix whose columns are orthonormal vectors. Partially Isometric matrix: A matrix that is an isometry on the orthogonal complement of its kernel. Equivalently, a matrix that satisfies AA * A = A.
Orthogonal array testing is a systematic and statistically-driven black-box testing technique employed in the field of software testing. [ 1 ] [ 2 ] This method is particularly valuable in scenarios where the number of inputs to a system is substantial enough to make exhaustive testing impractical.
English: An orthogonal array OA(N, k, s, t) is an N × k matrix with s kinds of elements as components such that each t-tuple of the elements are contained same times as a row in any N × t subarray constructed by taking t columns. In this image, for OA(18, 7, 3, 2) on the right side, you can see that every 18 × 2 subarray on the left side ...
An orthogonal array, OA(k,n), of strength two and index one is an n 2 × k array A (k ≥ 2 and n ≥ 1, integers) with entries from a set of size n such that within any two columns of A (strength), every ordered pair of symbols appears in exactly one row of A (index). [33] An OA(s + 2, n) is equivalent to s MOLS(n). [33]
If each entry of an n × n Latin square is written as a triple (r,c,s), where r is the row, c is the column, and s is the symbol, we obtain a set of n 2 triples called the orthogonal array representation of the square. For example, the orthogonal array representation of the Latin square
In two dimensions the difference between random sampling, Latin hypercube sampling, and orthogonal sampling can be explained as follows: In random sampling new sample points are generated without taking into account the previously generated sample points. One does not necessarily need to know beforehand how many sample points are needed.
An alternate representation of a Latin square is given by an orthogonal array. For a Latin square of order n this is an n 2 × 3 matrix with columns labeled r, c and s and whose rows correspond to a single position of the Latin square, namely, the row of the position, the column of the position and the symbol in the position. Thus for the order ...