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The pandas package in Python implements this operation as "melt" function which converts a wide table to a narrow one. The process of converting a narrow table to wide table is generally referred to as "pivoting" in the context of data transformations.
The transpose (indicated by T) of any row vector is a column vector, and the transpose of any column vector is a row vector: […] = [] and [] = […]. The set of all row vectors with n entries in a given field (such as the real numbers ) forms an n -dimensional vector space ; similarly, the set of all column vectors with m entries forms an m ...
Most relational database management systems do not support nested records, so tables are in first normal form by default. In particular, SQL does not have any facilities for creating or exploiting nested tables. Normalization to first normal form would therefore be a necessary step when moving data from a hierarchical database to a relational ...
In Python NumPy arrays implement the flatten method, [note 1] while in R the desired effect can be achieved via the c() or as.vector() functions. In R , function vec() of package 'ks' allows vectorization and function vech() implemented in both packages 'ks' and 'sn' allows half-vectorization.
(This is just a consequence of the fact that the inverse of an N×M transpose is an M×N transpose, although it is also easy to show explicitly that P −1 composed with P gives the identity.) As proved by Cate & Twigg (1977), the number of fixed points (cycles of length 1) of the permutation is precisely 1 + gcd( N −1, M −1) , where gcd is ...
In computer programming, array slicing is an operation that extracts a subset of elements from an array and packages them as another array, possibly in a different dimension from the original. Common examples of array slicing are extracting a substring from a string of characters, the " ell " in "h ell o", extracting a row or column from a two ...
However, the array will store pre-computed range minimum queries not for every range [i, j], but only for ranges whose size is a power of two. There are O(log n) such queries for each start position i, so the size of the dynamic programming table B is O(n log n). The value of B[i, j] is the index of the minimum of the range A[i…i+2 j-1].
SQL was initially developed at IBM by Donald D. Chamberlin and Raymond F. Boyce after learning about the relational model from Edgar F. Codd [12] in the early 1970s. [13] This version, initially called SEQUEL (Structured English Query Language), was designed to manipulate and retrieve data stored in IBM's original quasirelational database management system, System R, which a group at IBM San ...