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| valsi |
daigno |
| type |
fu'ivla |
| creator |
krtisfranks |
| time entered |
Thu Jan 23 22:28:15 2014 |
Examples
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English
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Definition #52665
- Preferred
[edit]
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| definition |
x1 (ordered list) is a sampling of entries of matrix/tensor x2 in which exactly one entry is sampled from each row and/or column (etc.) between entries x3 (list; default: the largest 'square'/'hypercubic' sampling possible in the entire tensor starting with the first entry, see notes) inclusively following selection procedure/rule/function/order x4 (default: diagonally, see notes), where the tensor/matrix is expressed in basis/under conditions x5 |
| notes |
Entries of the list in x3 need not actually be sampled; the entries listed are merely to name the minimal and maximal indices between which the sampling may be drawn. Thus, the indices/labels specified are included in the range of sampling; id est: if the matrix entries listed belong to the ith row and jth column and the (i+n)th row and (j+m)th column respectively (for positive integers i,j,n,m), then the sampling will be conducted in all rows of number between (and including) i and i+n (yielding n+1 sampled rows) and in all columns of number between (and including) j and j+m (yielding m+1 sampled columns). The default diagonal sampling procedure for x4 is as follows: The first sampled entry has the minimum allowed (as specified in x3) indices. All latter sampled entries (by default) have indices of the immediately previous sampled entry each augmented by 1. (Which is to say that if the kth sampled entry has indices (x,y,...), in that order, then the (k+1)th sampled entry has indices (x+1,y+1,...), in that order and where each subsequent index would be the respective index of the kth sampled entry augmented by 1). The process terminates generally whenever exactly one entry is sampled from each of the rows, each of the columns, etc. of the tensor. In the default, the process terminates when at least one of the indices of a sampled entry of the tensor is as large as possible in the range specified by x3. Thus, in order to reconcile the general and the default termination conditions, the range specified by x3 must be compatible with both; id est: it must be a r-dimensional hypercube of entries, so to speak, where r is the rank of tensor x2. The default for sampling range x3 is between and including the entry in the first row and first column (etc.) and the entry in the last row and last column (etc.) for an r-dimensional hypercube tensor (meaning that each row, column, etc. of the tensor has exactly the same number of entries as the others). Generally, the default range begins with the entry of indices each minimal in the tensor (called 'the first entry') and extends to include ("draw") the maximal r-dimensional hypercube of entries in the tensor with one vertex on the first entry; in other words, if the minimum of the set of maximal indices in the tensor is g, then the sampling range is every row between the first and the gth, every column between the first and the gth, etc. Generally, the sampling range must be an r-dimensional orthotope of some positive size (that is to say: including at least one entry) no larger than the tensor itself, but with the freedom to place at most r of its vertices among the entries thereof; if the default sampling procedure x4 is being used, then the r-dimensional orthotope must be an r-dimensional hypercube. Generalizes to any tensor, but is only interesting for tensors of rank at least 1. Any mention of geometric terminology (such as mention of diagonals, orthotopes, etc.) in the definition or notes of this word should be interpreted cautiously and is not necessarily good Lojbanic practice; such terminology should not necessarily be emulated in practicing Lojbanic thought or speech. Not for use for geometric diagonals (such as between vertices); confer: digno. |
| jargon type |
mathematics, physics |
| gloss words |
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| created by |
krtisfranks |
| vote information |
2
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| time |
Sat Jan 25 10:26:05 2014 |
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