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())
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble cfloat cdouble cldouble)$b = prodover($a);
prodover($a, $b); # all arguments given
$b = $a->prodover; # method call
$a->prodover($b);Project via product to N-1 dimensions
This function reduces the dimensionality of an ndarray by one by taking the product along the 1st dimension.
By using xchg etc. it is possible to use any dimension.
Broadcasts over its inputs.
prodover processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
dprodover
Signature: (a(n); double [o]b())
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble)$b = dprodover($a);
dprodover($a, $b); # all arguments given
$b = $a->dprodover; # method call
$a->dprodover($b);Project via product to N-1 dimensions
This function reduces the dimensionality of an ndarray by one by taking the product along the 1st dimension.
By using xchg etc. it is possible to use any dimension.
Unlike "prodover", the calculations are performed in double precision.
Broadcasts over its inputs.
dprodover processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
cumuprodover
Signature: (a(n); int+ [o]b(n))
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble cfloat cdouble cldouble)$b = cumuprodover($a);
cumuprodover($a, $b); # all arguments given
$b = $a->cumuprodover; # method call
$a->cumuprodover($b);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.
Broadcasts over its inputs.
cumuprodover processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
dcumuprodover
Signature: (a(n); double [o]b(n))
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble)$b = dcumuprodover($a);
dcumuprodover($a, $b); # all arguments given
$b = $a->dcumuprodover; # method call
$a->dcumuprodover($b);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.
Unlike "cumuprodover", the calculations are performed in double precision.
Broadcasts over its inputs.
dcumuprodover processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
sumover
Signature: (a(n); int+ [o]b())
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble cfloat cdouble cldouble)$b = sumover($a);
sumover($a, $b); # all arguments given
$b = $a->sumover; # method call
$a->sumover($b);Project via sum to N-1 dimensions
This function reduces the dimensionality of an ndarray by one by taking the sum along the 1st dimension.
By using xchg etc. it is possible to use any dimension.
Broadcasts over its inputs.
sumover processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
dsumover
Signature: (a(n); double [o]b())
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble)$b = dsumover($a);
dsumover($a, $b); # all arguments given
$b = $a->dsumover; # method call
$a->dsumover($b);Project via sum to N-1 dimensions
This function reduces the dimensionality of an ndarray by one by taking the sum along the 1st dimension.
By using xchg etc. it is possible to use any dimension.
Unlike "sumover", the calculations are performed in double precision.
Broadcasts over its inputs.
dsumover processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
cumusumover
Signature: (a(n); int+ [o]b(n))
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble cfloat cdouble cldouble)$b = cumusumover($a);
cumusumover($a, $b); # all arguments given
$b = $a->cumusumover; # method call
$a->cumusumover($b);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.
Broadcasts over its inputs.
cumusumover processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
dcumusumover
Signature: (a(n); double [o]b(n))
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble)$b = dcumusumover($a);
dcumusumover($a, $b); # all arguments given
$b = $a->dcumusumover; # method call
$a->dcumusumover($b);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.
Unlike "cumusumover", the calculations are performed in double precision.
Broadcasts over its inputs.
dcumusumover processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
andover
Signature: (a(n); int+ [o]b())
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble cfloat cdouble cldouble)$b = andover($a);
andover($a, $b); # all arguments given
$b = $a->andover; # method call
$a->andover($b);Project via and to N-1 dimensions
This function reduces the dimensionality of an ndarray by one by taking the and along the 1st dimension.
By using xchg etc. it is possible to use any dimension.
Broadcasts over its inputs.
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); [o]b())
Types: (sbyte byte short ushort long ulong indx ulonglong longlong)$b = bandover($a);
bandover($a, $b); # all arguments given
$b = $a->bandover; # method call
$a->bandover($b);Project via bitwise and to N-1 dimensions
This function reduces the dimensionality of an ndarray by one by taking the bitwise and along the 1st dimension.
By using xchg etc. it is possible to use any dimension.
Broadcasts over its inputs.
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); [o]b())
Types: (sbyte byte short ushort long ulong indx ulonglong longlong)$b = borover($a);
borover($a, $b); # all arguments given
$b = $a->borover; # method call
$a->borover($b);Project via bitwise or to N-1 dimensions
This function reduces the dimensionality of an ndarray by one by taking the bitwise or along the 1st dimension.
By using xchg etc. it is possible to use any dimension.
Broadcasts over its inputs.
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.
firstnonzeroover
Signature: (a(n); [o]b())
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble cfloat cdouble cldouble)$b = firstnonzeroover($a);
firstnonzeroover($a, $b); # all arguments given
$b = $a->firstnonzeroover; # method call
$a->firstnonzeroover($b);Project via first non-zero value to N-1 dimensions
This function reduces the dimensionality of an ndarray by one by taking the first non-zero value along the 1st dimension.
By using xchg etc. it is possible to use any dimension.
Broadcasts over its inputs.
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.
orover
Signature: (a(n); int+ [o]b())
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble cfloat cdouble cldouble)$b = orover($a);
orover($a, $b); # all arguments given
$b = $a->orover; # method call
$a->orover($b);Project via or to N-1 dimensions
This function reduces the dimensionality of an ndarray by one by taking the or along the 1st dimension.
By using xchg etc. it is possible to use any dimension.
Broadcasts over its inputs.
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())
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble cfloat cdouble cldouble)$b = zcover($a);
zcover($a, $b); # all arguments given
$b = $a->zcover; # method call
$a->zcover($b);Project via == 0 to N-1 dimensions
This function reduces the dimensionality of an ndarray by one by taking the == 0 along the 1st dimension.
By using xchg etc. it is possible to use any dimension.
Broadcasts over its inputs.
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.
numdiff
Signature: (x(t); [o]dx(t))
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble cfloat cdouble cldouble)$dx = numdiff($x);
numdiff($x, $dx); # all arguments given
$dx = $x->numdiff; # method call
$x->numdiff($dx);
$x->inplace->numdiff; # can be used inplace
numdiff($x->inplace);Numerical differencing. DX(t) = X(t) - X(t-1), DX(0) = X(0). Combined with slice('-1:0'), can be used for backward differencing.
Unlike "diff2", output vector is same length. Originally by Maggie J. Xiong.
Compare to "cumusumover", which acts as the converse of this. See also "diff2", "diffcentred", "partial", "pchip_chim" in PDL::Primitive.
Broadcasts over its inputs.
numdiff does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
diffcentred
Signature: (a(n); [o]o(n))
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble cfloat cdouble cldouble)$o = diffcentred($a);
diffcentred($a, $o); # all arguments given
$o = $a->diffcentred; # method call
$a->diffcentred($o);Calculates centred differences along a vector's 0th dimension. Always periodic on boundaries; currently to change this, you must pad your data, and/or trim afterwards. This is so that when using with "partial", the size of data stays the same and therefore compatible if differentiated along different dimensions, e.g. calculating "curl".
By using "xchg" in PDL::Slices etc. it is possible to use any dimension.
See also "diff2", "partial", "numdiff", "pchip_chim" in PDL::Primitive.
Broadcasts over its inputs.
A bad value at n means the affected output values at n-2,n (if in boounds) are set bad.
partial
Take a numerical partial derivative along a given dimension, either forward, backward, or centred.
See also "numdiff", "diffcentred", "pchip_chim" in PDL::Primitive, "pchip_chsp" in PDL::Primitive, and "mv" in PDL::Slices, which are currently used to implement this.
Can be used to implement divergence and curl calculations (adapted from Luis Mochán's work at https://sourceforge.net/p/pdl/mailman/message/58843767/):
use v5.36;
use PDL;
sub curl ($f) {
my ($f0, $f1, $f2) = $f->using(0..2);
my $o = {dir=>'c'};
pdl(
$f2->partial(1,$o) - $f1->partial(2,$o),
$f0->partial(2,$o) - $f2->partial(0,$o),
$f1->partial(0,$o) - $f0->partial(1,$o),
)->mv(-1,0);
}
sub div ($f) {
my ($f0, $f1, $f2) = $f->using(0..2);
my $o = {dir=>'c'};
$f0->partial(0,$o) + $f1->partial(1,$o) + $f2->partial(2,$o);
}
sub trim3d ($f) { $f->slice(':,1:-2,1:-2,1:-2') } # adjust if change "dir"
my $z=zeroes(5,5,5);
my $v=pdl(-$z->yvals, $z->xvals, $z->zvals)->mv(-1,0);
say trim3d(curl($v));
say div($v);$pdl->partial(2); # along dim 2, centred
$pdl->partial(2, {d=>'c'}); # along dim 2, centred
$pdl->partial(2, {d=>'f'}); # along dim 2, forward
$pdl->partial(2, {d=>'b'}); # along dim 2, backward
$pdl->partial(2, {d=>'p'}); # along dim 2, piecewise cubic Hermite
$pdl->partial(2, {d=>'s'}); # along dim 2, cubic splinediff2
Signature: (a(n); [o]o(nminus1=CALC($SIZE(n) - 1)))
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble cfloat cdouble cldouble)$o = diff2($a);
diff2($a, $o); # all arguments given
$o = $a->diff2; # method call
$a->diff2($o);Numerically forward differentiates a vector along 0th dimension.
By using "xchg" in PDL::Slices etc. it is possible to use any dimension. Unlike "numdiff", output vector is one shorter. Combined with slice('-1:0'), can be used for backward differencing.
See also "numdiff", "diffcentred", "partial", "pchip_chim" in PDL::Primitive.
print pdl(q[3 4 2 3 2 3 1])->diff2;
# [1 -2 1 -1 1 -2]Broadcasts over its inputs.
On bad value, output value is set bad. On next good value, output value is difference between that and last good value.
intover
Signature: (a(n); float+ [o]b())
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble)$b = intover($a);
intover($a, $b); # all arguments given
$b = $a->intover; # method call
$a->intover($b);Project via integral to N-1 dimensions
This function reduces the dimensionality of an ndarray by one by taking the integral along the 1st dimension.
By using xchg etc. it is possible to use any dimension.
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.
Broadcasts over its inputs.
intover ignores the bad-value flag of the input ndarrays. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
average
Signature: (a(n); int+ [o]b())
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble)$b = average($a);
average($a, $b); # all arguments given
$b = $a->average; # method call
$a->average($b);Project via average to N-1 dimensions
This function reduces the dimensionality of an ndarray by one by taking the average along the 1st dimension.
By using xchg etc. it is possible to use any dimension.
Broadcasts over its inputs.
average processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
avgover
Synonym for "average".
caverage
Signature: (a(n); cdouble [o]b())
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble)$b = caverage($a);
caverage($a, $b); # all arguments given
$b = $a->caverage; # method call
$a->caverage($b);Project via average to N-1 dimensions
This function reduces the dimensionality of an ndarray by one by taking the average along the 1st dimension.
By using xchg etc. it is possible to use any dimension.
Unlike average, the calculation is performed in complex double precision.
Broadcasts over its inputs.
caverage processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
cavgover
Synonym for "caverage".
daverage
Signature: (a(n); double [o]b())
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble)$b = daverage($a);
daverage($a, $b); # all arguments given
$b = $a->daverage; # method call
$a->daverage($b);Project via average to N-1 dimensions
This function reduces the dimensionality of an ndarray by one by taking the average along the 1st dimension.
By using xchg etc. it is possible to use any dimension.
Unlike average, the calculation is performed in double precision.
Broadcasts over its inputs.
daverage processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
davgover
Synonym for "daverage".
minimum
Signature: (a(n); [o]c())
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble)$c = minimum($a);
minimum($a, $c); # all arguments given
$c = $a->minimum; # method call
$a->minimum($c);Project via minimum to N-1 dimensions
This function reduces the dimensionality of an ndarray by one by taking the minimum along the 1st dimension.
By using xchg etc. it is possible to use any dimension.
Broadcasts over its inputs.
Output is set bad if no elements of the input are non-bad, otherwise the bad flag is cleared for the output ndarray.
Note that NaNs are considered to be valid values and will "win" over non-NaN; see isfinite and badmask for ways of masking NaNs.
minover
Synonym for "minimum".
minimum_ind
Signature: (a(n); indx [o] c())
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble)$c = minimum_ind($a);
minimum_ind($a, $c); # all arguments given
$c = $a->minimum_ind; # method call
$a->minimum_ind($c);Like minimum but returns the first matching index rather than the value
Broadcasts over its inputs.
Output is set bad if no elements of the input are non-bad, otherwise the bad flag is cleared for the output ndarray.
Note that NaNs are considered to be valid values and will "win" over non-NaN; see isfinite and badmask for ways of masking NaNs.
minover_ind
Synonym for "minimum_ind".
minimum_n_ind
Signature: (a(n); indx [o]c(m); PDL_Indx m_size => m)
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble)Returns the index of first m_size minimum elements. As of 2.077, you can specify how many by either passing in an ndarray of the given size (DEPRECATED - will be converted to indx if needed and the input arg will be set to that), or just the size, or a null and the size.
minimum_n_ind($pdl, $out = zeroes(5)); # DEPRECATED
$out = minimum_n_ind($pdl, 5);
minimum_n_ind($pdl, $out = null, 5);Broadcasts over its inputs.
Output bad flag is cleared for the output ndarray if sufficient non-bad elements found, else remaining slots in $c() are set bad.
Note that NaNs are considered to be valid values and will "win" over non-NaN; see isfinite and badmask for ways of masking NaNs.
minover_n_ind
Synonym for "minimum_n_ind".
maximum
Signature: (a(n); [o]c())
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble)$c = maximum($a);
maximum($a, $c); # all arguments given
$c = $a->maximum; # method call
$a->maximum($c);Project via maximum to N-1 dimensions
This function reduces the dimensionality of an ndarray by one by taking the maximum along the 1st dimension.
By using xchg etc. it is possible to use any dimension.
Broadcasts over its inputs.
Output is set bad if no elements of the input are non-bad, otherwise the bad flag is cleared for the output ndarray.
Note that NaNs are considered to be valid values and will "win" over non-NaN; see isfinite and badmask for ways of masking NaNs.
maxover
Synonym for "maximum".
maximum_ind
Signature: (a(n); indx [o] c())
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble)$c = maximum_ind($a);
maximum_ind($a, $c); # all arguments given
$c = $a->maximum_ind; # method call
$a->maximum_ind($c);Like maximum but returns the first matching index rather than the value
Broadcasts over its inputs.
Output is set bad if no elements of the input are non-bad, otherwise the bad flag is cleared for the output ndarray.
Note that NaNs are considered to be valid values and will "win" over non-NaN; see isfinite and badmask for ways of masking NaNs.
maxover_ind
Synonym for "maximum_ind".
maximum_n_ind
Signature: (a(n); indx [o]c(m); PDL_Indx m_size => m)
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble)Returns the index of first m_size maximum elements. As of 2.077, you can specify how many by either passing in an ndarray of the given size (DEPRECATED - will be converted to indx if needed and the input arg will be set to that), or just the size, or a null and the size.
maximum_n_ind($pdl, $out = zeroes(5)); # DEPRECATED
$out = maximum_n_ind($pdl, 5);
maximum_n_ind($pdl, $out = null, 5);Broadcasts over its inputs.
Output bad flag is cleared for the output ndarray if sufficient non-bad elements found, else remaining slots in $c() are set bad.
Note that NaNs are considered to be valid values and will "win" over non-NaN; see isfinite and badmask for ways of masking NaNs.
maxover_n_ind
Synonym for "maximum_n_ind".
minmaximum
Signature: (a(n); [o]cmin(); [o] cmax(); indx [o]cmin_ind(); indx [o]cmax_ind())
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble)($cmin, $cmax, $cmin_ind, $cmax_ind) = minmaximum($a);
minmaximum($a, $cmin, $cmax, $cmin_ind, $cmax_ind); # all arguments given
($cmin, $cmax, $cmin_ind, $cmax_ind) = $a->minmaximum; # method call
$a->minmaximum($cmin, $cmax, $cmin_ind, $cmax_ind);Find minimum and maximum and their indices for a given ndarray;
pdl> $x=pdl [[-2,3,4],[1,0,3]]
pdl> ($min, $max, $min_ind, $max_ind)=minmaximum($x)
pdl> p $min, $max, $min_ind, $max_ind
[-2 0] [4 3] [0 1] [2 2]See also "minmax", which clumps the ndarray together.
Broadcasts over its inputs.
If a() contains only bad data, then the output ndarrays 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.
minmaxover
Synonym for "minmaximum".
avg
Return the average of all elements in an ndarray.
See the documentation for "average" for more information.
$x = avg($data);This routine handles bad values.
sum
Return the sum of all elements in an ndarray.
See the documentation for "sumover" for more information.
$x = sum($data);This routine handles bad values.
prod
Return the product of all elements in an ndarray.
See the documentation for "prodover" for more information.
$x = prod($data);This routine handles bad values.
davg
Return the average (in double precision) of all elements in an ndarray.
See the documentation for "daverage" for more information.
$x = davg($data);This routine handles bad values.
dsum
Return the sum (in double precision) of all elements in an ndarray.
See the documentation for "dsumover" for more information.
$x = dsum($data);This routine handles bad values.
dprod
Return the product (in double precision) of all elements in an ndarray.
See the documentation for "dprodover" for more information.
$x = dprod($data);This routine handles bad values.
zcheck
Return the check for zero of all elements in an ndarray.
See the documentation for "zcover" for more information.
$x = zcheck($data);This routine handles bad values.
and
Return the logical and of all elements in an ndarray.
See the documentation for "andover" for more information.
$x = and($data);This routine handles bad values.
band
Return the bitwise and of all elements in an ndarray.
See the documentation for "bandover" for more information.
$x = band($data);This routine handles bad values.
or
Return the logical or of all elements in an ndarray.
See the documentation for "orover" for more information.
$x = or($data);This routine handles bad values.
bor
Return the bitwise or of all elements in an ndarray.
See the documentation for "borover" for more information.
$x = bor($data);This routine handles bad values.
min
Return the minimum of all elements in an ndarray.
See the documentation for "minimum" for more information.
$x = min($data);This routine handles bad values.
max
Return the maximum of all elements in an ndarray.
See the documentation for "maximum" for more information.
$x = max($data);This routine handles bad values.
median
Return the median of all elements in an ndarray.
See the documentation for "medover" for more information.
$x = median($data);This routine handles bad values.
mode
Return the mode of all elements in an ndarray.
See the documentation for "modeover" for more information.
$x = mode($data);This routine handles bad values.
oddmedian
Return the oddmedian of all elements in an ndarray.
See the documentation for "oddmedover" for more information.
$x = oddmedian($data);This routine handles bad values.
any
Return true if any element in ndarray set
Useful in conditional expressions:
if (any $x>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 ndarray set
Useful in conditional expressions:
if (all $x>15) { print "all values are greater than 15\n" }See "and" for comments on what happens when all elements in the check are bad.
minmax
Returns a list with minimum and maximum values of an ndarray.
($mn, $mx) = minmax($pdl);This routine does not broadcast over the dimensions of $pdl; it returns the minimum and maximum values of the whole ndarray. See "minmaximum" if this is not what is required. The two values are returned as Perl scalars, and therefore ignore whether the values are bad.
pdl> $x = pdl [1,-2,3,5,0]
pdl> ($min, $max) = minmax($x);
pdl> p "$min $max\n";
-2 5medover
Signature: (a(n); [o]b(); [t]tmp(n))
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble)$b = medover($a);
medover($a, $b); # all arguments given
$b = $a->medover; # method call
$a->medover($b);Project via median to N-1 dimensions
This function reduces the dimensionality of an ndarray by one by taking the median along the 1st dimension.
By using xchg etc. it is possible to use any dimension.
Broadcasts over its inputs.
medover processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
oddmedover
Signature: (a(n); [o]b(); [t]tmp(n))
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble)$b = oddmedover($a);
oddmedover($a, $b); # all arguments given
$b = $a->oddmedover; # method call
$a->oddmedover($b);Project via oddmedian to N-1 dimensions
This function reduces the dimensionality of an ndarray by one by taking the oddmedian along the 1st dimension.
By using xchg etc. it is possible to use any dimension.
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.
Broadcasts over its inputs.
oddmedover processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
modeover
Signature: (data(n); [o]out(); [t]sorted(n))
Types: (sbyte byte short ushort long ulong indx ulonglong longlong)$out = modeover($data);
modeover($data, $out); # all arguments given
$out = $data->modeover; # method call
$data->modeover($out);Project via mode to N-1 dimensions
This function reduces the dimensionality of an ndarray by one by taking the mode along the 1st dimension.
By using xchg etc. it is possible to use any dimension.
The mode is the single element most frequently found in a discrete data set.
It only makes sense for integer data types, since floating-point types are demoted to integer before the mode is calculated.
modeover treats BAD the same as any other value: if BAD is the most common element, the returned value is also BAD.
Broadcasts over its inputs.
modeover does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
pctover
Signature: (a(n); p(); [o]b(); [t]tmp(n))
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble)$b = pctover($a, $p);
pctover($a, $p, $b); # all arguments given
$b = $a->pctover($p); # method call
$a->pctover($p, $b);Project via specified percentile to N-1 dimensions
This function reduces the dimensionality of an ndarray by one by taking the specified percentile along the 1st dimension.
By using xchg etc. it is possible to use any dimension.
The specified percentile must be between 0.0 and 1.0. When the specified percentile falls between data points, the result is interpolated. Values outside the allowed range are clipped to 0.0 or 1.0 respectively. The algorithm implemented here is based on the interpolation variant described at http://en.wikipedia.org/wiki/Percentile as used by Microsoft Excel and recommended by NIST.
Broadcasts over its inputs.
pctover processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
oddpctover
Signature: (a(n); p(); [o]b(); [t]tmp(n))
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble)$b = oddpctover($a, $p);
oddpctover($a, $p, $b); # all arguments given
$b = $a->oddpctover($p); # method call
$a->oddpctover($p, $b);Project via specified percentile to N-1 dimensions
This function reduces the dimensionality of an ndarray by one by taking the specified percentile along the 1st dimension.
By using xchg etc. it is possible to use any 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 http://en.wikipedia.org/wiki/Percentile.
Broadcasts over its inputs.
oddpctover processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
pct
Return the specified percentile of all elements in an ndarray. 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 an ndarray. The specified percentile (p) must be between 0.0 and 1.0. When the specified percentile falls between data points, the nearest data value is the result.
$x = oddpct($data, $pct);qsort
Signature: (a(n); [o]b(n))
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble)$b = qsort($a);
qsort($a, $b); # all arguments given
$b = $a->qsort; # method call
$a->qsort($b);
$a->inplace->qsort; # can be used inplace
qsort($a->inplace);Quicksort a vector into ascending order.
Broadcasts over its inputs.
Bad values are moved to the end of the array:
pdl> p $y
[42 47 98 BAD 22 96 74 41 79 76 96 BAD 32 76 25 59 BAD 96 32 BAD]
pdl> p qsort($y)
[22 25 32 32 41 42 47 59 74 76 76 79 96 96 96 98 BAD BAD BAD BAD]qsorti
Signature: (a(n); indx [o]indx(n))
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble)$indx = qsorti($a);
qsorti($a, $indx); # all arguments given
$indx = $a->qsorti; # method call
$a->qsorti($indx);Quicksort a vector and return index of elements in ascending order.
$ix = qsorti $x;
print $x->index($ix); # Sorted listBroadcasts over its inputs.
Bad elements are moved to the end of the array:
pdl> p $y
[42 47 98 BAD 22 96 74 41 79 76 96 BAD 32 76 25 59 BAD 96 32 BAD]
pdl> p $y->index( qsorti($y) )
[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))
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble)$b = qsortvec($a);
qsortvec($a, $b); # all arguments given
$b = $a->qsortvec; # method call
$a->qsortvec($b);
$a->inplace->qsortvec; # can be used inplace
qsortvec($a->inplace);Sort a list of vectors lexicographically.
The 0th dimension of the source ndarray is dimension in the vector; the 1st dimension is list order. Higher dimensions are broadcasted 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]
]Broadcasts over its inputs.
Vectors with bad components are moved to the end of the array:
pdl> p $p = pdl("[0 0] [-100 0] [BAD 0] [100 0]")->qsortvec
[
[-100 0]
[ 0 0]
[ 100 0]
[ BAD 0]
]qsortveci
Signature: (a(n,m); indx [o]indx(m))
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble)$indx = qsortveci($a);
qsortveci($a, $indx); # all arguments given
$indx = $a->qsortveci; # method call
$a->qsortveci($indx);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 broadcasted over: each plane is sorted separately, so qsortveci may be thought of as a collapse operator of sorts (groan).
Broadcasts over its inputs.
Vectors with bad components are moved to the end of the array as for "qsortvec".
magnover
Signature: (a(n); float+ [o]b())
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
float double ldouble cfloat cdouble cldouble)$b = magnover($a);
magnover($a, $b); # all arguments given
$b = $a->magnover; # method call
$a->magnover($b);Project via Euclidean (aka Pythagorean) distance to N-1 dimensions
This function reduces the dimensionality of an ndarray by one by taking the Euclidean (aka Pythagorean) distance along the 1st dimension.
By using xchg etc. it is possible to use any dimension.
Minimum float precision output. See also "inner" in PDL::Primitive, "norm" in PDL::Primitive.
Broadcasts over its inputs.
magnover processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
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.