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For each table, insert an alpha-prefix on each column (making each row-token "|-" to sort as column zero, like prefix "Row124col00"), then sort into a new file, and then de-prefix the column entries. Again, bear in mind, the tedious hand-editing of items in each row is often faster than the potential delay of automated edits gone awry.
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.
For example, a table of 128 rows with a Boolean column requires 128 bytes a row-oriented format (one byte per Boolean) but 128 bits (16 bytes) in a column-oriented format (via a bitmap). Another example is the use of run-length encoding to encode a column.
Note how the use of A[i][j] with multi-step indexing as in C, as opposed to a neutral notation like A(i,j) as in Fortran, almost inevitably implies row-major order for syntactic reasons, so to speak, because it can be rewritten as (A[i])[j], and the A[i] row part can even be assigned to an intermediate variable that is then indexed in a separate expression.
Comma-separated values (CSV) is a text file format that uses commas to separate values, and newlines to separate records. A CSV file stores tabular data (numbers and text) in plain text, where each line of the file typically represents one data record.
Data Format Description Language (DFDL, often pronounced daff-o-dil) is a modeling language for describing general text and binary data in a standard way. It was published as an Open Grid Forum Recommendation [1] in February 2021, and in April 2024 was published as an ISO standard.
The column-wise Kronecker product of two matrices is a special case of the Khatri-Rao product as defined above, and may also be called the Khatri–Rao product. This product assumes the partitions of the matrices are their columns. In this case m 1 = m, p 1 = p, n = q and for each j: n j = q j = 1.
The same technique can be used to map two-letter country codes like "us" or "za" to country names (26 2 = 676 table entries), 5-digit ZIP codes like 13083 to city names (100 000 entries), etc. Invalid data values (such as the country code "xx" or the ZIP code 00000) may be left undefined in the table or mapped to some appropriate "null" value.