PDL::Ufunc

Ufunc(3pm)            User Contributed Perl Documentation           Ufunc(3pm)



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 dimen-
       sion.

       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 dimen-
       sion.

       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 preci-
       sion.

       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 per-
       centile 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 speci-
       fied 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 speci-
       fied percentile must be between 0.0 and 1.0.  When the specified per-
       centile 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 AT husc.edu).  Contribu-
       tions by Christian Soeller (c.soeller AT auckland.nz) and Karl Glaze-
       brook (kgb AT aaoepp.au).  All rights reserved. There is no war-
       ranty. 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.



perl v5.8.8                       2007-01-14                        Ufunc(3pm)