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 element 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 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(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 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(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.

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 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 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.

 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

  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]
 ]

  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 distribution. If this file is separated from the PDL distribution, the copyright notice should be included in the file.