Ufunc(c) User Contributed Perl Documentation Ufunc(c) NAME PDL::Ufunc - primitive ufunc operations for pdl DESCRIPTION This module provides some primitive and useful functions defined using PDL::PP based on functionality of what are sometimes called ufuncs (for example NumPY and Mathematica talk about these). It collects all the functions gener- ally used to "reduce" or "accumulate" along a dimension. These all do their job across the first dimension but by using the slicing functions you can do it on any dimen- sion. The PDL::Reduce module provides an alternative interface to many of the functions in this module. SYNOPSIS use PDL::Ufunc; FUNCTIONS prodover Signature: (a(a); int+ [o]b()) Project via product to N-1 dimensions This function reduces the dimensionality of a piddle by one by taking the product along the 1st dimension. By using xchg etc. it is possible to use any dimension. $a = prodover($b); $spectrum = prodover $image->xchg(0,1) dprodover Signature: (a(a); double [o]b()) Project via product to N-1 dimensions This function reduces the dimensionality of a piddle by one by taking the product along the 1st dimension. By using xchg etc. it is possible to use any dimension. $a = dprodover($b); $spectrum = dprodover $image->xchg(0,1) Unlike prodover, the calculations are performed in double precision. cumuprodover Signature: (a(a); int+ [o]b(b)) Cumulative product This function calculates the cumulative product along the 1st dimension. By using xchg etc. it is possible to use any dimension. The sum is started so that the first element in the cumu- lative product is the first element of the parameter. $a = cumuprodover($b); $spectrum = cumuprodover $image->xchg(0,1) dcumuprodover Signature: (a(a); double [o]b(b)) Cumulative product This function calculates the cumulative product along the 1st dimension. By using xchg etc. it is possible to use any dimension. The sum is started so that the first element in the cumu- lative product is the first element of the parameter. $a = cumuprodover($b); $spectrum = cumuprodover $image->xchg(0,1) Unlike cumuprodover, the calculations are performed in double precision. sumover Signature: (a(a); int+ [o]b()) Project via sum to N-1 dimensions This function reduces the dimensionality of a piddle by one by taking the sum along the 1st dimension. By using xchg etc. it is possible to use any dimension. $a = sumover($b); $spectrum = sumover $image->xchg(0,1) dsumover Signature: (a(a); double [o]b()) Project via sum to N-1 dimensions This function reduces the dimensionality of a piddle by one by taking the sum along the 1st dimension. By using xchg etc. it is possible to use any dimension. $a = dsumover($b); $spectrum = dsumover $image->xchg(0,1) Unlike sumover, the calculations are performed in double precision. cumusumover Signature: (a(a); int+ [o]b(b)) Cumulative sum This function calculates the cumulative sum along the 1st dimension. By using xchg etc. it is possible to use any dimension. The sum is started so that the first element in the cumu- lative sum is the first element of the parameter. $a = cumusumover($b); $spectrum = cumusumover $image->xchg(0,1) dcumusumover Signature: (a(a); double [o]b(b)) Cumulative sum This function calculates the cumulative sum along the 1st dimension. By using xchg etc. it is possible to use any dimension. The sum is started so that the first element in the cumu- lative sum is the first element of the parameter. $a = cumusumover($b); $spectrum = cumusumover $image->xchg(0,1) Unlike cumusumover, the calculations are performed in dou- ble precision. andover Signature: (a(a); int+ [o]b()) Project via and to N-1 dimensions This function reduces the dimensionality of a piddle by one by taking the and along the 1st dimension. By using xchg etc. it is possible to use any dimension. $a = andover($b); $spectrum = andover $image->xchg(0,1) zcover Signature: (a(a); int+ [o]b()) Project via == 0 to N-1 dimensions This function reduces the dimensionality of a piddle by one by taking the == 0 along the 1st dimension. By using xchg etc. it is possible to use any dimension. $a = zcover($b); $spectrum = zcover $image->xchg(0,1) orover Signature: (a(a); int+ [o]b()) Project via or to N-1 dimensions This function reduces the dimensionality of a piddle by one by taking the or along the 1st dimension. By using xchg etc. it is possible to use any dimension. $a = orover($b); $spectrum = orover $image->xchg(0,1) borover Signature: (a(a); int+ [o]b()) Project via bitwise or to N-1 dimensions This function reduces the dimensionality of a piddle by one by taking the bitwise or along the 1st dimension. By using xchg etc. it is possible to use any dimension. $a = borover($b); $spectrum = borover $image->xchg(0,1) bandover Signature: (a(a); int+ [o]b()) Project via bitwise and to N-1 dimensions This function reduces the dimensionality of a piddle by one by taking the bitwise and along the 1st dimension. By using xchg etc. it is possible to use any dimension. $a = bandover($b); $spectrum = bandover $image->xchg(0,1) intover Signature: (a(a); int+ [o]b()) Project via integral to N-1 dimensions This function reduces the dimensionality of a piddle by one by taking the integral along the 1st dimension. By using xchg etc. it is possible to use any dimension. $a = intover($b); $spectrum = intover $image->xchg(0,1) Notes: For "n > 3", these are all "O(h^4)" (like Simpson's rule), but are integrals between the end points assuming the pdl gives values just at these centres: for such `functions', sumover is correct to O(O), but is the natural (and cor- rect) choice for binned data, of course. average Signature: (a(a); int+ [o]b()) Project via average to N-1 dimensions This function reduces the dimensionality of a piddle by one by taking the average along the 1st dimension. By using xchg etc. it is possible to use any dimension. $a = average($b); $spectrum = average $image->xchg(0,1) daverage Signature: (a(a); double [o]b()) Project via average to N-1 dimensions This function reduces the dimensionality of a piddle by one by taking the average along the 1st dimension. By using xchg etc. it is possible to use any dimension. $a = daverage($b); $spectrum = daverage $image->xchg(0,1) Unlike average, the calculation is performed in double precision. medover Signature: (a(a); [o]b(); [t]tmp(p)) Project via median to N-1 dimensions This function reduces the dimensionality of a piddle by one by taking the median along the 1st dimension. By using xchg etc. it is possible to use any dimension. $a = medover($b); $spectrum = medover $image->xchg(0,1) oddmedover Signature: (a(a); [o]b(); [t]tmp(p)) Project via oddmedian to N-1 dimensions This function reduces the dimensionality of a piddle by one by taking the oddmedian along the 1st dimension. By using xchg etc. it is possible to use any dimension. $a = oddmedover($b); $spectrum = oddmedover $image->xchg(0,1) The median is sometimes not a good choice as if the array has an even number of elements it lies half-way between the two middle values - thus it does not always correspond to a data value. The lower-odd median is just the lower of these two values and so it ALWAYS sits on an actual data value which is useful in some circumstances. pctover Signature: (a(a); p(); [o]b(); [t]tmp(p)) Project via percentile to N-1 dimensions This function reduces the dimensionality of a piddle by one by finding the specified percentile (p) along the 1st dimension. The specified percentile must be between 0.0 and 1.0. When the specified percentile falls between data points, the result is interpolated. By using xchg etc. it is possible to use any dimension. $a = pctover($b, $p); $spectrum = pctover $image->xchg(0,1) $p oddpctover Signature: (a(a); p(); [o]b(); [t]tmp(p)) Project via percentile to N-1 dimensions This function reduces the dimensionality of a piddle by one by finding the specified percentile along the 1st dimension. The specified percentile must be between 0.0 and 1.0. When the specified percentile falls between two values, the nearest data value is the result. By using xchg etc. it is possible to use any dimension. $a = oddpctover($b, $p); $spectrum = oddpctover $image->xchg(0,1) $p pct Return the specified percentile of all elements in a pid- dle. The specified percentile (p) must be between 0.0 and 1.0. When the specified percentile falls between data points, the result is interpolated. $x = pct($data, $pct); oddpct Return the specified percentile of all elements in a pid- dle. The specified percentile must be between 0.0 and 1.0. When the specified percentile falls between two values, the nearest data value is the result. $x = oddpct($data, $pct); avg Return the average of all elements in a piddle $x = avg($data); sum Return the sum of all elements in a piddle $x = sum($data); prod Return the product of all elements in a piddle $x = prod($data); davg Return the average (in double precision) of all elements in a piddle $x = davg($data); dsum Return the sum (in double precision) of all elements in a piddle $x = dsum($data); dprod Return the product (in double precision) of all elements in a piddle $x = dprod($data); zcheck Return the check for zero of all elements in a piddle $x = zcheck($data); and Return the logical and of all elements in a piddle $x = and($data); band Return the bitwise and of all elements in a piddle $x = band($data); or Return the logical or of all elements in a piddle $x = or($data); bor Return the bitwise or of all elements in a piddle $x = bor($data); min Return the minimum of all elements in a piddle $x = min($data); max Return the maximum of all elements in a piddle $x = max($data); median Return the median of all elements in a piddle $x = median($data); oddmedian Return the oddmedian of all elements in a piddle $x = oddmedian($data); any Return true if any element in piddle set Useful in conditional expressions: if (any $a>15) { print "some values are greater than 15\n" } all Return true if all elements in piddle set Useful in conditional expressions: if (all $a>15) { print "all values are greater than 15\n" } minmax Returns an array with minimum and maximum values of a pid- dle. ($mn, $mx) = minmax($pdl); This routine does not thread over the dimensions of $pdl; it returns the minimum and maximum values of the whole array. See minmaximum if this is not what is required. The two values are returned as Perl scalars similar to min/max. perldl> $x = pdl [1,-2,3,5,0] perldl> ($min, $max) = minmax($x); perldl> p "$min $max\n"; -2 5 qsort Signature: (a(a); [o]b(b)) Quicksort a vector into ascending order. print qsort random(m); qsorti Signature: (a(a); int [o]indx(x)) Quicksort a vector and return index of elements in ascend- ing order. $ix = qsorti $a; print $a->index($ix); # Sorted list minimum Signature: (a(a); [o]c()) Project via minimum to N-1 dimensions This function reduces the dimensionality of a piddle by one by taking the minimum along the 1st dimension. By using xchg etc. it is possible to use any dimension. $a = minimum($b); $spectrum = minimum $image->xchg(0,1) minimum_ind Signature: (a(a); int [o] c()) Like minimum but returns the index rather than the value minimum_n_ind Signature: (a(a); int[o]c(c)) Returns the index of "m" minimum elements maximum Signature: (a(a); [o]c()) Project via maximum to N-1 dimensions This function reduces the dimensionality of a piddle by one by taking the maximum along the 1st dimension. By using xchg etc. it is possible to use any dimension. $a = maximum($b); $spectrum = maximum $image->xchg(0,1) maximum_ind Signature: (a(a); int [o] c()) Like maximum but returns the index rather than the value maximum_n_ind Signature: (a(a); int[o]c(c)) Returns the index of "m" maximum elements minmaximum Signature: (a(a); [o]cmin(); [o] cmax(); int [o]cmin_ind(); int [o]cmax_ind()) Find minimum and maximum and their indices for a given piddle; perldl> $a=pdl [[-2,3,4],[1,0,3]] perldl> ($min, $max, $min_ind, $max_ind)=minmaximum($a) perldl> p $min, $max, $min_ind, $max_ind [-2 0] [4 3] [0 1] [2 2] See also minmax, which clumps the piddle together. AUTHOR Copyright (C) Tuomas J. Lukka 1997 (lukka@husc.har- vard.edu). Contributions by Christian Soeller (c.soeller@auckland.ac.nz) and Karl Glazebrook (kgb@aaoepp.aao.gov.au). All rights reserved. There is no warranty. You are allowed to redistribute this software / documentation under certain conditions. For details, see the file COPYING in the PDL distribution. If this file is separated from the PDL distribution, the copyright notice should be included in the file. perl v5.6.1 2002-04-08 Ufunc(c)