| 摘要 |
Method for generating piecewise-affine multivariate functions, wherein the online computation of the search tree is performed in order to locate the input value in the polytopes of the partition, and the subsequent generation of the corresponding affine function. It also proposes a configurable and programmable device for generating piecewise-affine multivariate functions composed of an architecture with four functional blocks namely: a control unit block (1), a tree memory block, a parameter memory block and an arithmetic unit block; and it has at least three operating modes which can be selected using different values of a bus (config): writing of the tree memory, writing of the parameter memory and evaluating the affine function. It may include a fourth operating mode, which is the test mode. |
| 主权项 |
1. Method for generating piecewise-affine multivariate functions, comprising:
an online computation of a search tree is performed in order to locate an input value in a plurality of polytopes of a partition, and a subsequent generation of a corresponding affine function; and wherein a piecewise-affine (PWA) function, fPWA: D→R, defined on a compact domain D⊂Rn, verifies that:
fPWA(x)=fjTx+gi,xεΩi,i=1, . . . , NP wherein fiεRn, giεR and Ωi are NP polytopes, which do not overlap and a joining thereof induces a polyhedral partition in a domain D;
wherein each polytope is a closed region delimited by hyperplanes (hTj x+kj=0, wherein hjεRn, kjεR); wherein throughout a plane it is possible to distinguish NE hyperplanes which delimit the polytopes, wherein each hyperplane divides the domain in two parts, and the function fPWA is affine on each polytope, Ωi; so that a problem of locating a desired point has an objective of finding an index i so that xεΩi to thus provide the affine function in that point; wherein said method comprises the steps of: forming a binary search tree from a single root, which is a first state (S[1]) which branches into two states, which are a second state (S[2]) and a third state (S[3]) which, in turn and successively, branch into two states, so that for a depth of a tree d, a number of states is 2d-1, the 2d-1 states of the deepest level being a leaves of the tree; locating a polytope from the Ωi polytopes containing an input vector by successively performing the comparisons (hTjx+kj<0); and performing the online search tree computation so that a vector x, the computation starts from the first state (S[1]) checking if hT1x+k1<0: is correct, the computation selects a branch that leads to the second state (S[2]), if this is not correct, it selects the one that leads to the third state (S[3]), progressing in states until a state associated with the desired point is achieved. |
