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EGOR AZAWAWI PWBENNETT ZMUGHAL SAPER

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Chris Marshall
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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.

 $b = prodover($a);
 $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.

 $b = dprodover($a);
 $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 element of the parameter.

 $b = cumuprodover($a);
 $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 element of the parameter.

 $b = cumuprodover($a);
 $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.

 $b = sumover($a);
 $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.

 $b = dsumover($a);
 $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.

 $b = cumusumover($a);
 $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.

 $b = cumusumover($a);
 $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.

 $b = orover($a);
 $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.

 $b = bandover($a);
 $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.

 $b = borover($a);
 $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.

 $b = zcover($a);
 $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.

 $b = andover($a);
 $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.

 $b = intover($a);
 $spectrum = intover $image->xchg(0,1)

Notes:

intover uses a point spacing of one (i.e., delta-h==1). You will need to scale the result to correct for the true point delta).

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.

 $b = average($a);
 $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.

 $b = daverage($a);
 $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.

 $b = medover($a);
 $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.

 $b = oddmedover($a);
 $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.

modeover

  Signature: (data(n); [o]out(); [t]sorted(n))

Project via mode to N-1 dimensions

This function reduces the dimensionality of a piddle by one by taking the mode along the 1st dimension.

By using xchg etc. it is possible to use any dimension.

 $b = modeover($a);
 $spectrum = modeover $image->xchg(0,1)

The mode is the single element most frequently found in a discrete data set.

It only makes sense for integer data types, since floating-point types are demoted to integer before the mode is calculated.

modeover treats BAD the same as any other value: if BAD is the most common element, the returned value is also BAD.

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 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. Values outside the allowed range are clipped to 0.0 or 1.0 respectively. The algorithm implemented here is based on the interpolation variant described at http://en.wikipedia.org/wiki/Percentile as used by Microsoft Excel and recommended by NIST.

By using xchg etc. it is possible to use any dimension.

 $b = pctover($a, $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 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. The algorithm implemented is from the textbook version described first at http://en.wikipedia.org/wiki/Percentile.

By using xchg etc. it is possible to use any dimension.

 $b = oddpctover($a, $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 nearest data value is the result.

 $x = oddpct($data, $pct);

avg

Return the average of all elements in a piddle.

See the documentation for average for more information.

 $x = avg($data);

sum

Return the sum of all elements in a piddle.

See the documentation for sumover for more information.

 $x = sum($data);

prod

Return the product of all elements in a piddle.

See the documentation for prodover for more information.

 $x = prod($data);

davg

Return the average (in double precision) of all elements in a piddle.

See the documentation for daverage for more information.

 $x = davg($data);

dsum

Return the sum (in double precision) of all elements in a piddle.

See the documentation for dsumover for more information.

 $x = dsum($data);

dprod

Return the product (in double precision) of all elements in a piddle.

See the documentation for dprodover for more information.

 $x = dprod($data);

zcheck

Return the check for zero of all elements in a piddle.

See the documentation for zcover for more information.

 $x = zcheck($data);

and

Return the logical and of all elements in a piddle.

See the documentation for andover for more information.

 $x = and($data);

band

Return the bitwise and of all elements in a piddle.

See the documentation for bandover for more information.

 $x = band($data);

or

Return the logical or of all elements in a piddle.

See the documentation for orover for more information.

 $x = or($data);

bor

Return the bitwise or of all elements in a piddle.

See the documentation for borover for more information.

 $x = bor($data);

min

Return the minimum of all elements in a piddle.

See the documentation for minimum for more information.

 $x = min($data);

max

Return the maximum of all elements in a piddle.

See the documentation for maximum for more information.

 $x = max($data);

median

Return the median of all elements in a piddle.

See the documentation for medover for more information.

 $x = median($data);

mode

Return the mode of all elements in a piddle.

See the documentation for modeover for more information.

 $x = mode($data);

oddmedian

Return the oddmedian of all elements in a piddle.

See the documentation for oddmedover for more information.

 $x = oddmedian($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 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.

 pdl> $x = pdl [1,-2,3,5,0]
 pdl> ($min, $max) = minmax($x);
 pdl> 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); indx [o]indx(n))

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

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

qsortvec

  Signature: (a(n,m); [o]b(n,m))

Sort a list of vectors lexicographically.

The 0th dimension of the source piddle is dimension in the vector; the 1st dimension is list order. Higher dimensions are threaded over.

 print qsortvec pdl([[1,2],[0,500],[2,3],[4,2],[3,4],[3,5]]);
 [
  [  0 500]
  [  1   2]
  [  2   3]
  [  3   4]
  [  3   5]
  [  4   2]
 ]
 

qsortveci

  Signature: (a(n,m); indx [o]indx(m))

Sort a list of vectors lexicographically, returning the indices of the sorted vectors rather than the sorted list itself.

As with qsortvec, the input PDL should be an NxM array containing M separate N-dimensional vectors. The return value is an integer M-PDL containing the M-indices of original array rows, in sorted order.

As with qsortvec, the zeroth element of the vectors runs slowest in the sorted list.

Additional dimensions are threaded over: each plane is sorted separately, so qsortveci may be thought of as a collapse operator of sorts (groan).

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.

 $b = minimum($a);
 $spectrum = minimum $image->xchg(0,1)

minimum_ind

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

Like minimum but returns the index rather than the value

minimum_n_ind

  Signature: (a(n); indx [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.

 $b = maximum($a);
 $spectrum = maximum $image->xchg(0,1)

maximum_ind

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

Like maximum but returns the index rather than the value

maximum_n_ind

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

Returns the index of m maximum elements

minmaximum

  Signature: (a(n); [o]cmin(); [o] cmax(); indx [o]cmin_ind(); indx [o]cmax_ind())

Find minimum and maximum and their indices for a given piddle;

 pdl> $a=pdl [[-2,3,4],[1,0,3]]
 pdl> ($min, $max, $min_ind, $max_ind)=minmaximum($a)
 pdl> 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 distribution. If this file is separated from the PDL distribution, the copyright notice should be included in the file.