
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 N1 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 N1 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 N1 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 N1 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 N1 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 N1 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 N1 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 N1 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 N1 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 N1 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 N1 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 N1 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 N1 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 N1 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 halfway between the two middle values  thus it does not always correspond to a
data value. The lowerodd 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 N1 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 N1 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 N1 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 N1 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 20030129 Ufunc(3) 
