monotonicDifferenceMatrix

Build coefficient-difference inequalities along one dimension.

Developer documentation: this item describes internal implementation details.

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Declaration

 A = monotonicDifferenceMatrix(basisSize,dim,direction)

Parameters

• basisSize tensor basis size per dimension
• dim constrained tensor dimension
• direction “increasing” or “decreasing”

Returns

• A sparse inequality matrix acting on xi(:)

Discussion

This helper constructs a sparse matrix A such that A*xi <= 0 enforces adjacent coefficient differences of one sign along the selected tensor dimension.

For the increasing case, each row encodes

\[\xi_{j_1,\ldots,j_d} - \xi_{j_1,\ldots,j_k+1,\ldots,j_d} \le 0,\]

so adjacent coefficients are nondecreasing along dimension dim. The decreasing case flips the sign pattern.