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# Ufunc

## 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)
```

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)
```

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.

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)
```

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.

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
pdl> p qsort(\$b)
```

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
pdl> p \$b−>index( qsorti(\$b) )
```

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

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

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]
```