This directory contains the code for the user-defined type, SEG, representing laboratory measurements as floating point intervals. RATIONALE ========= The geometry of measurements is usually more complex than that of a point in a numeric continuum. A measurement is usually a segment of that continuum with somewhat fuzzy limits. The measurements come out as intervals because of uncertainty and randomness, as well as because the value being measured may naturally be an interval indicating some condition, such as the temperature range of stability of a protein. Using just common sense, it appears more convenient to store such data as intervals, rather than pairs of numbers. In practice, it even turns out more efficient in most applications. Further along the line of common sense, the fuzziness of the limits suggests that the use of traditional numeric data types leads to a certain loss of information. Consider this: your instrument reads 6.50, and you input this reading into the database. What do you get when you fetch it? Watch: test=> select 6.50 as "pH"; pH --- 6.5 (1 row) In the world of measurements, 6.50 is not the same as 6.5. It may sometimes be critically different. The experimenters usually write down (and publish) the digits they trust. 6.50 is actually a fuzzy interval contained within a bigger and even fuzzier interval, 6.5, with their center points being (probably) the only common feature they share. We definitely do not want such different data items to appear the same. Conclusion? It is nice to have a special data type that can record the limits of an interval with arbitrarily variable precision. Variable in a sense that each data element records its own precision. Check this out: test=> select '6.25 .. 6.50'::seg as "pH"; pH ------------ 6.25 .. 6.50 (1 row) FILES ===== Makefile building instructions for the shared library README.seg the file you are now reading seg.c the implementation of this data type in c seg.sql.in SQL code needed to register this type with postgres (transformed to seg.sql by make) segdata.h the data structure used to store the segments segparse.y the grammar file for the parser (used by seg_in() in seg.c) segscan.l scanner rules (used by seg_yyparse() in segparse.y) seg-validate.pl a simple input validation script. It is probably a little stricter than the type itself: for example, it rejects '22 ' because of the trailing space. Use as a filter to discard bad values from a single column; redirect to /dev/null to see the offending input sort-segments.pl a script to sort the tables having a SEG type column INSTALLATION ============ To install the type, run make make install For this to work, make sure that: . the seg source directory is in the postgres contrib directory . the user running "make install" has postgres administrative authority . this user's environment defines the PGLIB and PGDATA variables and has postgres binaries in the PATH. This only installs the type implementation and documentation. To make the type available in any particular database, do psql -d databasename < seg.sql If you install the type in the template1 database, all subsequently created databases will inherit it. To test the new type, after "make install" do make installcheck If it fails, examine the file regression.diffs to find out the reason (the test code is a direct adaptation of the regression tests from the main source tree). SYNTAX ====== The external representation of an interval is formed using one or two floating point numbers joined by the range operator ('..' or '...'). Optional certainty indicators (<, > and ~) are ignored by the internal logics, but are retained in the data. Grammar ------- rule 1 seg -> boundary PLUMIN deviation rule 2 seg -> boundary RANGE boundary rule 3 seg -> boundary RANGE rule 4 seg -> RANGE boundary rule 5 seg -> boundary rule 6 boundary -> FLOAT rule 7 boundary -> EXTENSION FLOAT rule 8 deviation -> FLOAT Tokens ------ RANGE (\.\.)(\.)? PLUMIN \'\+\-\' integer [+-]?[0-9]+ real [+-]?[0-9]+\.[0-9]+ FLOAT ({integer}|{real})([eE]{integer})? EXTENSION [<>~] Examples of valid SEG representations: -------------------------------------- Any number (rules 5,6) -- creates a zero-length segment (a point, if you will) ~5.0 (rules 5,7) -- creates a zero-length segment AND records '~' in the data. This notation reads 'approximately 5.0', but its meaning is not recognized by the code. It is ignored until you get the value back. View it is a short-hand comment. <5.0 (rules 5,7) -- creates a point at 5.0; '<' is ignored but is preserved as a comment >5.0 (rules 5,7) -- creates a point at 5.0; '>' is ignored but is preserved as a comment 5(+-)0.3 5'+-'0.3 (rules 1,8) -- creates an interval '4.7..5.3'. As of this writing (02/09/2000), this mechanism isn't completely accurate in determining the number of significant digits for the boundaries. For example, it adds an extra digit to the lower boundary if the resulting interval includes a power of ten: template1=> select '10(+-)1'::seg as seg; seg --------- 9.0 .. 11 -- should be: 9 .. 11 Also, the (+-) notation is not preserved: 'a(+-)b' will always be returned as '(a-b) .. (a+b)'. The purpose of this notation is to allow input from certain data sources without conversion. 50 .. (rule 3) -- everything that is greater than or equal to 50 .. 0 (rule 4) -- everything that is less than or equal to 0 1.5e-2 .. 2E-2 (rule 2) -- creates an interval (0.015 .. 0.02) 1 ... 2 The same as 1...2, or 1 .. 2, or 1..2 (space is ignored). Because of the widespread use of '...' in the data sources, I decided to stick to is as a range operator. This, and also the fact that the white space around the range operator is ignored, creates a parsing conflict with numeric constants starting with a decimal point. Examples of invalid SEG input: ------------------------------ .1e7 should be: 0.1e7 .1 .. .2 should be: 0.1 .. 0.2 2.4 E4 should be: 2.4E4 The following, although it is not a syntax error, is disallowed to improve the sanity of the data: 5 .. 2 should be: 2 .. 5 PRECISION ========= The segments are stored internally as pairs of 32-bit floating point numbers. It means that the numbers with more than 7 significant digits will be truncated. The numbers with less than or exactly 7 significant digits retain their original precision. That is, if your query returns 0.00, you will be sure that the trailing zeroes are not the artifacts of formatting: they reflect the precision of the original data. The number of leading zeroes does not affect precision: the value 0.0067 is considered to have just 2 significant digits. USAGE ===== The access method for SEG is a GiST (gist_seg_ops), which is a generalization of R-tree. GiSTs allow the postgres implementation of R-tree, originally encoded to support 2-D geometric types such as boxes and polygons, to be used with any data type whose data domain can be partitioned using the concepts of containment, intersection and equality. In other words, everything that can intersect or contain its own kind can be indexed with a GiST. That includes, among other things, all geometric data types, regardless of their dimensionality (see also contrib/cube). The operators supported by the GiST access method include: [a, b] << [c, d] Is left of The left operand, [a, b], occurs entirely to the left of the right operand, [c, d], on the axis (-inf, inf). It means, [a, b] << [c, d] is true if b < c and false otherwise [a, b] >> [c, d] Is right of [a, b] is occurs entirely to the right of [c, d]. [a, b] >> [c, d] is true if b > c and false otherwise [a, b] &< [c, d] Over left The segment [a, b] overlaps the segment [c, d] in such a way that a <= c <= b and b <= d [a, b] &> [c, d] Over right The segment [a, b] overlaps the segment [c, d] in such a way that a > c and b <= c <= d [a, b] = [c, d] Same as The segments [a, b] and [c, d] are identical, that is, a == b and c == d [a, b] @ [c, d] Contains The segment [a, b] contains the segment [c, d], that is, a <= c and b >= d [a, b] @ [c, d] Contained in The segment [a, b] is contained in [c, d], that is, a >= c and b <= d Although the mnemonics of the following operators is questionable, I preserved them to maintain visual consistency with other geometric data types defined in Postgres. Other operators: [a, b] < [c, d] Less than [a, b] > [c, d] Greater than These operators do not make a lot of sense for any practical purpose but sorting. These operators first compare (a) to (c), and if these are equal, compare (b) to (d). That accounts for reasonably good sorting in most cases, which is useful if you want to use ORDER BY with this type There are a few other potentially useful functions defined in seg.c that vanished from the schema because I stopped using them. Some of these were meant to support type casting. Let me know if I was wrong: I will then add them back to the schema. I would also appreciate other ideas that would enhance the type and make it more useful. For examples of usage, see sql/seg.sql NOTE: The performance of an R-tree index can largely depend on the order of input values. It may be very helpful to sort the input table on the SEG column (see the script sort-segments.pl for an example) CREDITS ======= My thanks are primarily to Prof. Joe Hellerstein (http://db.cs.berkeley.edu/~jmh/) for elucidating the gist of the GiST (http://gist.cs.berkeley.edu/). I am also grateful to all postgres developers, present and past, for enabling myself to create my own world and live undisturbed in it. And I would like to acknowledge my gratitude to Argonne Lab and to the U.S. Department of Energy for the years of faithful support of my database research. ------------------------------------------------------------------------ Gene Selkov, Jr. Computational Scientist Mathematics and Computer Science Division Argonne National Laboratory 9700 S Cass Ave. Building 221 Argonne, IL 60439-4844 selkovjr@mcs.anl.gov