In orthogonal sampling, the sample space is divided into equally probable subspaces.Such configuration is similar to having N rooks on a chess board without threatening each other. In Latin hypercube sampling one must first decide how many sample points to use and for each sample point remember in which row and column the sample point was taken.One does not necessarily need to know beforehand how many sample points are needed. In random sampling new sample points are generated without taking into account the previously generated sample points.In two dimensions the difference between random sampling, Latin hypercube sampling, and orthogonal sampling can be explained as follows: Another advantage is that random samples can be taken one at a time, remembering which samples were taken so far. This sampling scheme does not require more samples for more dimensions (variables) this independence is one of the main advantages of this sampling scheme. When sampling a function of N, to be equal for each variable. A Latin hypercube is the generalisation of this concept to an arbitrary number of dimensions, whereby each sample is the only one in each axis-aligned hyperplane containing it. In the context of statistical sampling, a square grid containing sample positions is a Latin square if (and only if) there is only one sample in each row and each column.
#Hypercube scheme manuals
Detailed computer codes and manuals were later published. An independently equivalent technique was proposed by Vilnis Eglājs in 1977. LHS was described by Michael McKay of Los Alamos National Laboratory in 1979. The sampling method is often used to construct computer experiments or for Monte Carlo integration. The analysis indicates that two-dimensional arrays of 512 × 512 nodes interconnected in a hypercube (18-cube) topology could be implemented.Latin hypercube sampling ( LHS) is a statistical method for generating a near-random sample of parameter values from a multidimensional distribution. A theoretical analysis of the physical limitations of the implementation method is also presented. We present a space-invariant optical implementation technique for the realization of such networks. Owing to their totally space-invariant nature, the resulting three-dimensional hypercube networks are highly amenable to optical implementations by use of simple optical hardware such as multiple-imaging components and space-invariant holographic techniques. An example network is provided that illustrates the proposed design method. It is shown that the proposed methodology greatly improves area utilization as compared with previous methods. The methodology permits the construction of larger hypercube networks from smaller networks in a systematic and incremental fashion. Note: Author names will be searched in the keywords field, also, but that may find papers where the person is mentioned, rather than papers they authored.Ī new design methodology for constructing optical space-invariant hypercube interconnection networks for connection of a two-dimensional array of inputs to a two-dimensional array of outputs is presented.Use a comma to separate multiple people: J Smith, RL Jones, Macarthur.Use these formats for best results: Smith or J Smith.For best results, use the separate Authors field to search for author names.Use quotation marks " " around specific phrases where you want the entire phrase only.Question mark (?) - Example: "gr?y" retrieves documents containing "grey" or "gray".Asterisk ( * ) - Example: "elect*" retrieves documents containing "electron," "electronic," and "electricity".Improve efficiency in your search by using wildcards.Example: (photons AND downconversion) - pump.Example: (diode OR solid-state) AND laser.Note the Boolean sign must be in upper-case. Separate search groups with parentheses and Booleans.Keep it simple - don't use too many different parameters.
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