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Ufunc(3)		       User Contributed Perl Documentation			 Ufunc(3)

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 generally 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 dimension.

       The PDL::Reduce module provides an alternative interface to many of the functions in this
       module.

SYNOPSIS
	use PDL::Ufunc;

FUNCTIONS
       prodover

	 Signature: (a(n); 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(n); 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(n); int+ [o]b(n))

       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 cumulative product is the first ele-
       ment of the parameter.

	$a = cumuprodover($b);

	$spectrum = cumuprodover $image->xchg(0,1)

       dcumuprodover

	 Signature: (a(n); double [o]b(n))

       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 cumulative product is the first ele-
       ment of the parameter.

	$a = cumuprodover($b);

	$spectrum = cumuprodover $image->xchg(0,1)

       Unlike cumuprodover, the calculations are performed in double precision.

       sumover

	 Signature: (a(n); 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(n); 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(n); int+ [o]b(n))

       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 cumulative sum is the first element of
       the parameter.

	$a = cumusumover($b);

	$spectrum = cumusumover $image->xchg(0,1)

       dcumusumover

	 Signature: (a(n); double [o]b(n))

       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 cumulative sum is the first element of
       the parameter.

	$a = cumusumover($b);

	$spectrum = cumusumover $image->xchg(0,1)

       Unlike cumusumover, the calculations are performed in double precision.

       orover

	 Signature: (a(n); 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)

       bandover

	 Signature: (a(n); 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)

       borover

	 Signature: (a(n); 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)

       zcover

	 Signature: (a(n); 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)

       andover

	 Signature: (a(n); 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)

       intover

	 Signature: (a(n); 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(h), but is the natural (and correct) choice for binned data, of
       course.

       average

	 Signature: (a(n); 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(n); 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(n); [o]b(); [t]tmp(n))

       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(n); [o]b(); [t]tmp(n))

       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(n); p(); [o]b(); [t]tmp(n))

       Project via percentile to N-1 dimensions

       This function reduces the dimensionality of a piddle by one by finding the specified per-
       centile (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(n); p(); [o]b(); [t]tmp(n))

       Project via percentile to N-1 dimensions

       This function reduces the dimensionality of a piddle by one by finding the specified per-
       centile 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 piddle. 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 piddle. The specified percentile must
       be between 0.0 and 1.0.	When the specified percentile falls between two values, the near-
       est 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 piddle.

	($mn, $mx) = minmax($pdl);

       This routine does not thread over the dimensions of $pdl; it returns the minimum and maxi-
       mum 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(n); [o]b(n))

       Quicksort a vector into ascending order.

	print qsort random(10);

       qsorti

	 Signature: (a(n); int [o]indx(n))

       Quicksort a vector and return index of elements in ascending order.

	$ix = qsorti $a;
	print $a->index($ix); # Sorted list

       minimum

	 Signature: (a(n); [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(n); int [o] c())

       Like minimum but returns the index rather than the value

       minimum_n_ind

	 Signature: (a(n); int[o]c(m))

       Returns the index of "m" minimum elements

       maximum

	 Signature: (a(n); [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(n); int [o] c())

       Like maximum but returns the index rather than the value

       maximum_n_ind

	 Signature: (a(n); int[o]c(m))

       Returns the index of "m" maximum elements

       minmaximum

	 Signature: (a(n); [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.harvard.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 dis-
       tribution. If this file is separated from the PDL distribution, the copyright notice
       should be included in the file.

perl v5.8.0				    2003-01-29					 Ufunc(3)
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