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:
"intover" uses a point spacing of one (i.e., delta-h==1). You will
need to scale the result to correct for the true point delta).
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)
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)
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)
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
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]
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.
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.