PDL::Ufunc − primitive ufunc operations for pdl

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.

use PDL::Ufunc;

**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)

prodover does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

**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.

dprodover does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

**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)

cumuprodover does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

**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.

dcumuprodover does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

**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)

sumover does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

**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.

dsumover does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

**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)

cumusumover does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

**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.

dcumusumover does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

**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)

If `"a()"` contains only bad data (and its bad flag is set), `"b()"` is set bad. Otherwise `"b()"` will have its bad flag cleared, as it will not contain any bad values.

**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)

If `"a()"` contains only bad data (and its bad flag is set), `"b()"` is set bad. Otherwise `"b()"` will have its bad flag cleared, as it will not contain any bad values.

**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)

If `"a()"` contains only bad data (and its bad flag is set), `"b()"` is set bad. Otherwise `"b()"` will have its bad flag cleared, as it will not contain any bad values.

**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)

`"a()"` contains only bad data (and its bad flag is set), `"b()"` is set bad. Otherwise `"b()"` will have its bad flag cleared, as it will not contain any bad values.

**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)

`"a()"` contains only bad data (and its bad flag is set), `"b()"` is set bad. Otherwise `"b()"` will have its bad flag cleared, as it will not contain any bad values.

**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.

intover ignores the bad-value flag of the input piddles. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

**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)

average does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

**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.

daverage does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

**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)

medover does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

**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.

oddmedover does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

**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.

`$a` = pctover($b, `$p`);

`$spectrum` = pctover `$image`−>xchg(0,1) `$p`

pctover does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

**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 "/en.wikipedia.org/wiki/Percentile" in http:.

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

$a = oddpctover($b, $p); $spectrum = oddpctover $image−>xchg(0,1) $p

oddpctover does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

**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);

This routine handles bad values (see the documentation for average). I still need to decide how to handle the case when the return value is a bad value (eg to make sure it has the same type as the input piddle OR perhaps we should die − makes sense for the conditional ops but not things like sum)

**sum**

Return the sum of all elements in a piddle

$x = sum($data);

This routine handles bad values (see the documentation for sumover). I still need to decide how to handle the case when the return value is a bad value (eg to make sure it has the same type as the input piddle OR perhaps we should die − makes sense for the conditional ops but not things like sum)

**prod**

Return the product of all elements in a piddle

$x = prod($data);

This routine handles bad values (see the documentation for prodover). I still need to decide how to handle the case when the return value is a bad value (eg to make sure it has the same type as the input piddle OR perhaps we should die − makes sense for the conditional ops but not things like sum)

**davg**

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

$x = davg($data);

This routine handles bad values (see the documentation for daverage). I still need to decide how to handle the case when the return value is a bad value (eg to make sure it has the same type as the input piddle OR perhaps we should die − makes sense for the conditional ops but not things like sum)

**dsum**

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

$x = dsum($data);

This routine handles bad values (see the documentation for dsumover). I still need to decide how to handle the case when the return value is a bad value (eg to make sure it has the same type as the input piddle OR perhaps we should die − makes sense for the conditional ops but not things like sum)

**dprod**

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

$x = dprod($data);

This routine handles bad values (see the documentation for dprodover). I still need to decide how to handle the case when the return value is a bad value (eg to make sure it has the same type as the input piddle OR perhaps we should die − makes sense for the conditional ops but not things like sum)

**zcheck**

Return the check for zero of all elements in a piddle

$x = zcheck($data);

This routine handles bad values (see the documentation for zcover). I still need to decide how to handle the case when the return value is a bad value (eg to make sure it has the same type as the input piddle OR perhaps we should die − makes sense for the conditional ops but not things like sum)

**and**

Return the logical and of all elements in a piddle

$x = and($data);

This routine handles bad values (see the documentation for andover). I still need to decide how to handle the case when the return value is a bad value (eg to make sure it has the same type as the input piddle OR perhaps we should die − makes sense for the conditional ops but not things like sum)

**band**

Return the bitwise and of all elements in a piddle

$x = band($data);

This routine handles bad values (see the documentation for bandover). I still need to decide how to handle the case when the return value is a bad value (eg to make sure it has the same type as the input piddle OR perhaps we should die − makes sense for the conditional ops but not things like sum)

**or**

Return the logical or of all elements in a piddle

$x = or($data);

This routine handles bad values (see the documentation for orover). I still need to decide how to handle the case when the return value is a bad value (eg to make sure it has the same type as the input piddle OR perhaps we should die − makes sense for the conditional ops but not things like sum)

**bor**

Return the bitwise or of all elements in a piddle

$x = bor($data);

This routine handles bad values (see the documentation for borover). I still need to decide how to handle the case when the return value is a bad value (eg to make sure it has the same type as the input piddle OR perhaps we should die − makes sense for the conditional ops but not things like sum)

**min**

Return the minimum of all elements in a piddle

$x = min($data);

This routine handles bad values (see the documentation for minimum). I still need to decide how to handle the case when the return value is a bad value (eg to make sure it has the same type as the input piddle OR perhaps we should die − makes sense for the conditional ops but not things like sum)

**max**

Return the maximum of all elements in a piddle

$x = max($data);

This routine handles bad values (see the documentation for maximum). I still need to decide how to handle the case when the return value is a bad value (eg to make sure it has the same type as the input piddle OR perhaps we should die − makes sense for the conditional ops but not things like sum)

**median**

Return the median of all elements in a piddle

$x = median($data);

This routine handles bad values (see the documentation for medover). I still need to decide how to handle the case when the return value is a bad value (eg to make sure it has the same type as the input piddle OR perhaps we should die − makes sense for the conditional ops but not things like sum)

**oddmedian**

Return the oddmedian of all elements in a piddle

$x = oddmedian($data);

This routine handles bad values (see the documentation for oddmedover). I still need to decide how to handle the case when the return value is a bad value (eg to make sure it has the same type as the input piddle OR perhaps we should die − makes sense for the conditional ops but not things like sum)

**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" }

See or for comments on what happens when all elements in the check are bad.

**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" }

See and for comments on what happens when all elements in the check are bad.

**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);

Bad values are moved to the end of the array:

pdl> p $b [42 47 98 BAD 22 96 74 41 79 76 96 BAD 32 76 25 59 BAD 96 32 BAD] pdl> p qsort($b) [22 25 32 32 41 42 47 59 74 76 76 79 96 96 96 98 BAD BAD BAD BAD]

**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

Bad elements are moved to the end of the array:

pdl> p $b [42 47 98 BAD 22 96 74 41 79 76 96 BAD 32 76 25 59 BAD 96 32 BAD] pdl> p $b−>index( qsorti($b) ) [22 25 32 32 41 42 47 59 74 76 76 79 96 96 96 98 BAD BAD BAD BAD]

**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] ]

Vectors with bad components should be moved to the end of the array:

**qsortveci**

Signature: (a(n,m); int [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).

Vectors with bad components should be moved to the end of the array:

**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)

Output is set bad if all elements of the input are bad, otherwise the bad flag is cleared for the output piddle.

Note that `"NaNs"` are considered to be valid values; see isfinite and badmask for ways of masking NaNs.

**minimum_ind**

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

Like minimum but returns the index rather than the value

Output is set bad if all elements of the input are bad, otherwise the bad flag is cleared for the output piddle.

**minimum_n_ind**

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

Returns the index of `"m"` minimum elements

Not yet been converted to ignore bad values

**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)

Output is set bad if all elements of the input are bad, otherwise the bad flag is cleared for the output piddle.

Note that `"NaNs"` are considered to be valid values; see isfinite and badmask for ways of masking NaNs.

**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

Not yet been converted to ignore bad values

**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;

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.

If `"a()"` contains only bad data, then the output piddles will be set bad, along with their bad flag. Otherwise they will have their bad flags cleared, since they will not contain any bad values.

Copyright (C) Tuomas J. Lukka 1997 (lukka AT husc DOT harvard DOT edu). Contributions by Christian Soeller (c DOT soeller AT auckland DOT ac DOT nz) and Karl Glazebrook (kgb AT aaoepp DOT aao DOT gov DOT 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.