- NAME
- DESCRIPTION
- SYNOPSIS
- FUNCTIONS

- prodover
- dprodover
- cumuprodover
- dcumuprodover
- sumover
- dsumover
- cumusumover
- dcumusumover
- andover
- zcover
- orover
- borover
- bandover
- intover
- average
- daverage
- medover
- oddmedover
- pctover
- oddpctover
- pct
- oddpct
- avg
- sum
- prod
- davg
- dsum
- dprod
- zcheck
- and
- band
- or
- bor
- min
- max
- median
- oddmedian
- any
- all
- minmax
- qsort
- qsorti
- minimum
- minimum_ind
- minimum_n_ind
- maximum
- maximum_ind
- maximum_n_ind
- minmaximum

- AUTHOR

# 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.

## 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)

## 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)

## 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)

## 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)

## 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)

## 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

## 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.