1Primitive(3) User Contributed Perl Documentation Primitive(3)
2
6 PDL::Primitive - primitive operations for pdl
7
9 This module provides some primitive and useful functions defined using
10 PDL::PP and able to use the new indexing tricks.
11 See PDL::Indexing for how to use indices creatively. For explanation
13 of the signature format, see PDL::PP.
14
16 # Pulls in PDL::Primitive, among other modules.
17 use PDL;
18 # Only pull in PDL::Primitive:
20 use PDL::Primitive;
21
23 inner
24 Signature: (a(n); b(n); [o]c())
25 Inner product over one dimension
27 c = sum_i a_i * b_i
29 If "a() * b()" contains only bad data, c() is set bad. Otherwise c()
31 will have its bad flag cleared, as it will not contain any bad values.
32 outer
34 Signature: (a(n); b(m); [o]c(n,m))
35 outer product over one dimension
37 Naturally, it is possible to achieve the effects of outer product
39 simply by broadcasting over the ""*"" operator but this function is
40 provided for convenience.
41 outer processes bad values. It will set the bad-value flag of all
43 output ndarrays if the flag is set for any of the input ndarrays.
44 x
46 Signature: (a(i,z), b(x,i),[o]c(x,z))
47 Matrix multiplication
49 PDL overloads the "x" operator (normally the repeat operator) for
51 matrix multiplication. The number of columns (size of the 0 dimension)
52 in the left-hand argument must normally equal the number of rows (size
53 of the 1 dimension) in the right-hand argument.
54 Row vectors are represented as (N x 1) two-dimensional PDLs, or you may
56 be sloppy and use a one-dimensional PDL. Column vectors are
57 represented as (1 x N) two-dimensional PDLs.
58 Broadcasting occurs in the usual way, but as both the 0 and 1 dimension
60 (if present) are included in the operation, you must be sure that you
61 don't try to broadcast over either of those dims.
62 Of note, due to how Perl v5.14.0 and above implement operator
64 overloading of the "x" operator, the use of parentheses for the left
65 operand creates a list context, that is
66 pdl> ( $x * $y ) x $z
68 ERROR: Argument "..." isn't numeric in repeat (x) ...
69 treats $z as a numeric count for the list repeat operation and does not
71 call the scalar form of the overloaded operator. To use the operator in
72 this case, use a scalar context:
73 pdl> scalar( $x * $y ) x $z
75 or by calling "matmult" directly:
77 pdl> ( $x * $y )->matmult( $z )
79 EXAMPLES
81 Here are some simple ways to define vectors and matrices:
83 pdl> $r = pdl(1,2); # A row vector
85 pdl> $c = pdl([[3],[4]]); # A column vector
86 pdl> $c = pdl(3,4)->(*1); # A column vector, using NiceSlice
87 pdl> $m = pdl([[1,2],[3,4]]); # A 2x2 matrix
88 Now that we have a few objects prepared, here is how to matrix-multiply
90 them:
91 pdl> print $r x $m # row x matrix = row
93 [
94 [ 7 10]
95 ]
96 pdl> print $m x $r # matrix x row = ERROR
98 PDL: Dim mismatch in matmult of [2x2] x [2x1]: 2 != 1
99 pdl> print $m x $c # matrix x column = column
101 [
102 [ 5]
103 [11]
104 ]
105 pdl> print $m x 2 # Trivial case: scalar mult.
107 [
108 [2 4]
109 [6 8]
110 ]
111 pdl> print $r x $c # row x column = scalar
113 [
114 [11]
115 ]
116 pdl> print $c x $r # column x row = matrix
118 [
119 [3 6]
120 [4 8]
121 ]
122 INTERNALS
124 The mechanics of the multiplication are carried out by the "matmult"
126 method.
127 matmult
129 Signature: (a(t,h); b(w,t); [o]c(w,h))
130 Matrix multiplication
132 Notionally, matrix multiplication $x x $y is equivalent to the
134 broadcasting expression
135 $x->dummy(1)->inner($y->xchg(0,1)->dummy(2),$c);
137 but for large matrices that breaks CPU cache and is slow. Instead,
139 matmult calculates its result in 32x32x32 tiles, to keep the memory
140 footprint within cache as long as possible on most modern CPUs.
141 For usage, see "x", a description of the overloaded 'x' operator
143 matmult ignores the bad-value flag of the input ndarrays. It will set
145 the bad-value flag of all output ndarrays if the flag is set for any of
146 the input ndarrays.
147 innerwt
149 Signature: (a(n); b(n); c(n); [o]d())
150 Weighted (i.e. triple) inner product
152 d = sum_i a(i) b(i) c(i)
154 innerwt processes bad values. It will set the bad-value flag of all
156 output ndarrays if the flag is set for any of the input ndarrays.
157 inner2
159 Signature: (a(n); b(n,m); c(m); [o]d())
160 Inner product of two vectors and a matrix
162 d = sum_ij a(i) b(i,j) c(j)
164 Note that you should probably not broadcast over "a" and "c" since that
166 would be very wasteful. Instead, you should use a temporary for "b*c".
167 inner2 processes bad values. It will set the bad-value flag of all
169 output ndarrays if the flag is set for any of the input ndarrays.
170 inner2d
172 Signature: (a(n,m); b(n,m); [o]c())
173 Inner product over 2 dimensions.
175 Equivalent to
177 $c = inner($x->clump(2), $y->clump(2))
179 inner2d processes bad values. It will set the bad-value flag of all
181 output ndarrays if the flag is set for any of the input ndarrays.
182 inner2t
184 Signature: (a(j,n); b(n,m); c(m,k); [t]tmp(n,k); [o]d(j,k)))
185 Efficient Triple matrix product "a*b*c"
187 Efficiency comes from by using the temporary "tmp". This operation only
189 scales as "N**3" whereas broadcasting using "inner2" would scale as
190 "N**4".
191 The reason for having this routine is that you do not need to have the
193 same broadcast-dimensions for "tmp" as for the other arguments, which
194 in case of large numbers of matrices makes this much more memory-
195 efficient.
196 It is hoped that things like this could be taken care of as a kind of
198 closures at some point.
199 inner2t processes bad values. It will set the bad-value flag of all
201 output ndarrays if the flag is set for any of the input ndarrays.
202 crossp
204 Signature: (a(tri=3); b(tri); [o] c(tri))
205 Cross product of two 3D vectors
207 After
209 $c = crossp $x, $y
211 the inner product "$c*$x" and "$c*$y" will be zero, i.e. $c is
213 orthogonal to $x and $y
214 crossp does not process bad values. It will set the bad-value flag of
216 all output ndarrays if the flag is set for any of the input ndarrays.
217 norm
219 Signature: (vec(n); [o] norm(n))
220 Normalises a vector to unit Euclidean length
222 norm processes bad values. It will set the bad-value flag of all
224 output ndarrays if the flag is set for any of the input ndarrays.
225 indadd
227 Signature: (input(n); indx ind(n); [io] sum(m))
228 Broadcasting index add: add "input" to the "ind" element of "sum", i.e:
230 sum(ind) += input
232 Simple example:
234 $x = 2;
236 $ind = 3;
237 $sum = zeroes(10);
238 indadd($x,$ind, $sum);
239 print $sum
240 #Result: ( 2 added to element 3 of $sum)
241 # [0 0 0 2 0 0 0 0 0 0]
242 Broadcasting example:
244 $x = pdl( 1,2,3);
246 $ind = pdl( 1,4,6);
247 $sum = zeroes(10);
248 indadd($x,$ind, $sum);
249 print $sum."\n";
250 #Result: ( 1, 2, and 3 added to elements 1,4,6 $sum)
251 # [0 1 0 0 2 0 3 0 0 0]
252 The routine barfs on bad indices, and bad inputs set target outputs
254 bad.
255 conv1d
257 Signature: (a(m); kern(p); [o]b(m); int reflect)
258 1D convolution along first dimension
260 The m-th element of the discrete convolution of an input ndarray $a of
262 size $M, and a kernel ndarray $kern of size $P, is calculated as
263 n = ($P-1)/2
265 ====
266 \
267 ($a conv1d $kern)[m] = > $a_ext[m - n] * $kern[n]
268 /
269 ====
270 n = -($P-1)/2
271 where $a_ext is either the periodic (or reflected) extension of $a so
273 it is equal to $a on " 0..$M-1 " and equal to the corresponding
274 periodic/reflected image of $a outside that range.
275 $con = conv1d sequence(10), pdl(-1,0,1);
277 $con = conv1d sequence(10), pdl(-1,0,1), {Boundary => 'reflect'};
279 By default, periodic boundary conditions are assumed (i.e. wrap
281 around). Alternatively, you can request reflective boundary conditions
282 using the "Boundary" option:
283 {Boundary => 'reflect'} # case in 'reflect' doesn't matter
285 The convolution is performed along the first dimension. To apply it
287 across another dimension use the slicing routines, e.g.
288 $y = $x->mv(2,0)->conv1d($kernel)->mv(0,2); # along third dim
290 This function is useful for broadcasted filtering of 1D signals.
292 Compare also conv2d, convolve, fftconvolve, fftwconv, rfftwconv
294 WARNING: "conv1d" processes bad values in its inputs as the numeric
296 value of "$pdl->badvalue" so it is not recommended for processing pdls
297 with bad values in them unless special care is taken.
298 conv1d ignores the bad-value flag of the input ndarrays. It will set
300 the bad-value flag of all output ndarrays if the flag is set for any of
301 the input ndarrays.
302 in
304 Signature: (a(); b(n); [o] c())
305 test if a is in the set of values b
307 $goodmsk = $labels->in($goodlabels);
309 print pdl(3,1,4,6,2)->in(pdl(2,3,3));
310 [1 0 0 0 1]
311 "in" is akin to the is an element of of set theory. In principle, PDL
313 broadcasting could be used to achieve its functionality by using a
314 construct like
315 $msk = ($labels->dummy(0) == $goodlabels)->orover;
317 However, "in" doesn't create a (potentially large) intermediate and is
319 generally faster.
320 in does not process bad values. It will set the bad-value flag of all
322 output ndarrays if the flag is set for any of the input ndarrays.
323 uniq
325 return all unique elements of an ndarray
326 The unique elements are returned in ascending order.
328 PDL> p pdl(2,2,2,4,0,-1,6,6)->uniq
330 [-1 0 2 4 6] # 0 is returned 2nd (sorted order)
331 PDL> p pdl(2,2,2,4,nan,-1,6,6)->uniq
333 [-1 2 4 6 nan] # NaN value is returned at end
334 Note: The returned pdl is 1D; any structure of the input ndarray is
336 lost. "NaN" values are never compare equal to any other values, even
337 themselves. As a result, they are always unique. "uniq" returns the
338 NaN values at the end of the result ndarray. This follows the Matlab
339 usage.
340 See "uniqind" if you need the indices of the unique elements rather
342 than the values.
343 Bad values are not considered unique by uniq and are ignored.
345 $x=sequence(10);
347 $x=$x->setbadif($x%3);
348 print $x->uniq;
349 [0 3 6 9]
350 uniqind
352 Return the indices of all unique elements of an ndarray The order is in
353 the order of the values to be consistent with uniq. "NaN" values never
354 compare equal with any other value and so are always unique. This
355 follows the Matlab usage.
356 PDL> p pdl(2,2,2,4,0,-1,6,6)->uniqind
358 [5 4 1 3 6] # the 0 at index 4 is returned 2nd, but...
359 PDL> p pdl(2,2,2,4,nan,-1,6,6)->uniqind
361 [5 1 3 6 4] # ...the NaN at index 4 is returned at end
362 Note: The returned pdl is 1D; any structure of the input ndarray is
364 lost.
365 See "uniq" if you want the unique values instead of the indices.
367 Bad values are not considered unique by uniqind and are ignored.
369 uniqvec
371 Return all unique vectors out of a collection
372 NOTE: If any vectors in the input ndarray have NaN values
374 they are returned at the end of the non-NaN ones. This is
375 because, by definition, NaN values never compare equal with
376 any other value.
377 NOTE: The current implementation does not sort the vectors
379 containing NaN values.
380 The unique vectors are returned in lexicographically sorted ascending
382 order. The 0th dimension of the input PDL is treated as a dimensional
383 index within each vector, and the 1st and any higher dimensions are
384 taken to run across vectors. The return value is always 2D; any
385 structure of the input PDL (beyond using the 0th dimension for vector
386 index) is lost.
387 See also "uniq" for a unique list of scalars; and qsortvec for sorting
389 a list of vectors lexicographcally.
390 If a vector contains all bad values, it is ignored as in "uniq". If
392 some of the values are good, it is treated as a normal vector. For
393 example, [1 2 BAD] and [BAD 2 3] could be returned, but [BAD BAD BAD]
394 could not. Vectors containing BAD values will be returned after any
395 non-NaN and non-BAD containing vectors, followed by the NaN vectors.
396 hclip
398 Signature: (a(); b(); [o] c())
399 clip (threshold) $a by $b ($b is upper bound)
401 hclip processes bad values. It will set the bad-value flag of all
403 output ndarrays if the flag is set for any of the input ndarrays.
404 lclip
406 Signature: (a(); b(); [o] c())
407 clip (threshold) $a by $b ($b is lower bound)
409 lclip processes bad values. It will set the bad-value flag of all
411 output ndarrays if the flag is set for any of the input ndarrays.
412 clip
414 Clip (threshold) an ndarray by (optional) upper or lower bounds.
415 $y = $x->clip(0,3);
417 $c = $x->clip(undef, $x);
418 clip handles bad values since it is just a wrapper around "hclip" and
420 "lclip".
421 clip
423 Signature: (a(); l(); h(); [o] c())
424 info not available
426 clip processes bad values. It will set the bad-value flag of all
428 output ndarrays if the flag is set for any of the input ndarrays.
429 wtstat
431 Signature: (a(n); wt(n); avg(); [o]b(); int deg)
432 Weighted statistical moment of given degree
434 This calculates a weighted statistic over the vector "a". The formula
436 is
437 b() = (sum_i wt_i * (a_i ** degree - avg)) / (sum_i wt_i)
439 Bad values are ignored in any calculation; $b will only have its bad
441 flag set if the output contains any bad data.
442 statsover
444 Signature: (a(n); w(n); float+ [o]avg(); float+ [o]prms(); int+ [o]median(); int+ [o]min(); int+ [o]max(); float+ [o]adev(); float+ [o]rms())
445 Calculate useful statistics over a dimension of an ndarray
447 ($mean,$prms,$median,$min,$max,$adev,$rms) = statsover($ndarray, $weights);
449 This utility function calculates various useful quantities of an
451 ndarray. These are:
452 • the mean:
454 MEAN = sum (x)/ N
456 with "N" being the number of elements in x
458 • the population RMS deviation from the mean:
460 PRMS = sqrt( sum( (x-mean(x))^2 )/(N-1)
462 The population deviation is the best-estimate of the deviation of
464 the population from which a sample is drawn.
465 • the median
467 The median is the 50th percentile data value. Median is found by
469 medover, so WEIGHTING IS IGNORED FOR THE MEDIAN CALCULATION.
470 • the minimum
472 • the maximum
474 • the average absolute deviation:
476 AADEV = sum( abs(x-mean(x)) )/N
478 • RMS deviation from the mean:
480 RMS = sqrt(sum( (x-mean(x))^2 )/N)
482 (also known as the root-mean-square deviation, or the square root of
484 the variance)
485 This operator is a projection operator so the calculation will take
487 place over the final dimension. Thus if the input is N-dimensional each
488 returned value will be N-1 dimensional, to calculate the statistics for
489 the entire ndarray either use clump(-1) directly on the ndarray or call
490 "stats".
491 Bad values are simply ignored in the calculation, effectively reducing
493 the sample size. If all data are bad then the output data are marked
494 bad.
495 stats
497 Calculates useful statistics on an ndarray
498 ($mean,$prms,$median,$min,$max,$adev,$rms) = stats($ndarray,[$weights]);
500 This utility calculates all the most useful quantities in one call. It
502 works the same way as "statsover", except that the quantities are
503 calculated considering the entire input PDL as a single sample, rather
504 than as a collection of rows. See "statsover" for definitions of the
505 returned quantities.
506 Bad values are handled; if all input values are bad, then all of the
508 output values are flagged bad.
509 histogram
511 Signature: (in(n); int+[o] hist(m); double step; double min; int msize => m)
512 Calculates a histogram for given stepsize and minimum.
514 $h = histogram($data, $step, $min, $numbins);
516 $hist = zeroes $numbins; # Put histogram in existing ndarray.
517 histogram($data, $hist, $step, $min, $numbins);
518 The histogram will contain $numbins bins starting from $min, each $step
520 wide. The value in each bin is the number of values in $data that lie
521 within the bin limits.
522 Data below the lower limit is put in the first bin, and data above the
524 upper limit is put in the last bin.
525 The output is reset in a different broadcastloop so that you can take a
527 histogram of "$a(10,12)" into $b(15) and get the result you want.
528 For a higher-level interface, see hist.
530 pdl> p histogram(pdl(1,1,2),1,0,3)
532 [0 2 1]
533 histogram processes bad values. It will set the bad-value flag of all
535 output ndarrays if the flag is set for any of the input ndarrays.
536 whistogram
538 Signature: (in(n); float+ wt(n);float+[o] hist(m); double step; double min; int msize => m)
539 Calculates a histogram from weighted data for given stepsize and
541 minimum.
542 $h = whistogram($data, $weights, $step, $min, $numbins);
544 $hist = zeroes $numbins; # Put histogram in existing ndarray.
545 whistogram($data, $weights, $hist, $step, $min, $numbins);
546 The histogram will contain $numbins bins starting from $min, each $step
548 wide. The value in each bin is the sum of the values in $weights that
549 correspond to values in $data that lie within the bin limits.
550 Data below the lower limit is put in the first bin, and data above the
552 upper limit is put in the last bin.
553 The output is reset in a different broadcastloop so that you can take a
555 histogram of "$a(10,12)" into $b(15) and get the result you want.
556 pdl> p whistogram(pdl(1,1,2), pdl(0.1,0.1,0.5), 1, 0, 4)
558 [0 0.2 0.5 0]
559 whistogram processes bad values. It will set the bad-value flag of all
561 output ndarrays if the flag is set for any of the input ndarrays.
562 histogram2d
564 Signature: (ina(n); inb(n); int+[o] hist(ma,mb); double stepa; double mina; int masize => ma;
565 double stepb; double minb; int mbsize => mb;)
566 Calculates a 2d histogram.
568 $h = histogram2d($datax, $datay, $stepx, $minx,
570 $nbinx, $stepy, $miny, $nbiny);
571 $hist = zeroes $nbinx, $nbiny; # Put histogram in existing ndarray.
572 histogram2d($datax, $datay, $hist, $stepx, $minx,
573 $nbinx, $stepy, $miny, $nbiny);
574 The histogram will contain $nbinx x $nbiny bins, with the lower limits
576 of the first one at "($minx, $miny)", and with bin size "($stepx,
577 $stepy)". The value in each bin is the number of values in $datax and
578 $datay that lie within the bin limits.
579 Data below the lower limit is put in the first bin, and data above the
581 upper limit is put in the last bin.
582 pdl> p histogram2d(pdl(1,1,1,2,2),pdl(2,1,1,1,1),1,0,3,1,0,3)
584 [
585 [0 0 0]
586 [0 2 2]
587 [0 1 0]
588 ]
589 histogram2d processes bad values. It will set the bad-value flag of
591 all output ndarrays if the flag is set for any of the input ndarrays.
592 whistogram2d
594 Signature: (ina(n); inb(n); float+ wt(n);float+[o] hist(ma,mb); double stepa; double mina; int masize => ma;
595 double stepb; double minb; int mbsize => mb;)
596 Calculates a 2d histogram from weighted data.
598 $h = whistogram2d($datax, $datay, $weights,
600 $stepx, $minx, $nbinx, $stepy, $miny, $nbiny);
601 $hist = zeroes $nbinx, $nbiny; # Put histogram in existing ndarray.
602 whistogram2d($datax, $datay, $weights, $hist,
603 $stepx, $minx, $nbinx, $stepy, $miny, $nbiny);
604 The histogram will contain $nbinx x $nbiny bins, with the lower limits
606 of the first one at "($minx, $miny)", and with bin size "($stepx,
607 $stepy)". The value in each bin is the sum of the values in $weights
608 that correspond to values in $datax and $datay that lie within the bin
609 limits.
610 Data below the lower limit is put in the first bin, and data above the
612 upper limit is put in the last bin.
613 pdl> p whistogram2d(pdl(1,1,1,2,2),pdl(2,1,1,1,1),pdl(0.1,0.2,0.3,0.4,0.5),1,0,3,1,0,3)
615 [
616 [ 0 0 0]
617 [ 0 0.5 0.9]
618 [ 0 0.1 0]
619 ]
620 whistogram2d processes bad values. It will set the bad-value flag of
622 all output ndarrays if the flag is set for any of the input ndarrays.
623 fibonacci
625 Signature: (i(n); indx [o]x(n))
626 Constructor - a vector with Fibonacci's sequence
628 fibonacci does not process bad values. It will set the bad-value flag
630 of all output ndarrays if the flag is set for any of the input
631 ndarrays.
632 append
634 Signature: (a(n); b(m); [o] c(mn))
635 append two ndarrays by concatenating along their first dimensions
637 $x = ones(2,4,7);
639 $y = sequence 5;
640 $c = $x->append($y); # size of $c is now (7,4,7) (a jumbo-ndarray ;)
641 "append" appends two ndarrays along their first dimensions. The rest of
643 the dimensions must be compatible in the broadcasting sense. The
644 resulting size of the first dimension is the sum of the sizes of the
645 first dimensions of the two argument ndarrays - i.e. "n + m".
646 Similar functions include "glue" (below), which can append more than
648 two ndarrays along an arbitrary dimension, and cat, which can append
649 more than two ndarrays that all have the same sized dimensions.
650 append does not process bad values. It will set the bad-value flag of
652 all output ndarrays if the flag is set for any of the input ndarrays.
653 glue
655 $c = $x->glue(<dim>,$y,...)
656 Glue two or more PDLs together along an arbitrary dimension (N-D
658 "append").
659 Sticks $x, $y, and all following arguments together along the specified
661 dimension. All other dimensions must be compatible in the broadcasting
662 sense.
663 Glue is permissive, in the sense that every PDL is treated as having an
665 infinite number of trivial dimensions of order 1 -- so "$x->glue(3,$y)"
666 works, even if $x and $y are only one dimensional.
667 If one of the PDLs has no elements, it is ignored. Likewise, if one of
669 them is actually the undefined value, it is treated as if it had no
670 elements.
671 If the first parameter is a defined perl scalar rather than a pdl, then
673 it is taken as a dimension along which to glue everything else, so you
674 can say "$cube = PDL::glue(3,@image_list);" if you like.
675 "glue" is implemented in pdl, using a combination of xchg and "append".
677 It should probably be updated (one day) to a pure PP function.
678 Similar functions include "append" (above), which appends only two
680 ndarrays along their first dimension, and cat, which can append more
681 than two ndarrays that all have the same sized dimensions.
682 cmpvec
684 Signature: (a(n); b(n); sbyte [o]c())
685 Compare two vectors lexicographically.
687 Returns -1 if a is less, 1 if greater, 0 if equal.
689 The output is bad if any input values up to the point of inequality are
691 bad - any after are ignored.
692 eqvec
694 Signature: (a(n); b(n); sbyte [o]c())
695 Compare two vectors, returning 1 if equal, 0 if not equal.
697 The output is bad if any input values are bad.
699 enumvec
701 Signature: (v(M,N); indx [o]k(N))
702 Enumerate a list of vectors with locally unique keys.
704 Given a sorted list of vectors $v, generate a vector $k containing
706 locally unique keys for the elements of $v (where an "element" is a
707 vector of length $M occurring in $v).
708 Note that the keys returned in $k are only unique over a run of a
710 single vector in $v, so that each unique vector in $v has at least one
711 0 (zero) index in $k associated with it. If you need global keys, see
712 enumvecg().
713 Contributed by Bryan Jurish <moocow@cpan.org>.
715 enumvec does not process bad values. It will set the bad-value flag of
717 all output ndarrays if the flag is set for any of the input ndarrays.
718 enumvecg
720 Signature: (v(M,N); indx [o]k(N))
721 Enumerate a list of vectors with globally unique keys.
723 Given a sorted list of vectors $v, generate a vector $k containing
725 globally unique keys for the elements of $v (where an "element" is a
726 vector of length $M occurring in $v). Basically does the same thing
727 as:
728 $k = $v->vsearchvec($v->uniqvec);
730 ... but somewhat more efficiently.
732 Contributed by Bryan Jurish <moocow@cpan.org>.
734 enumvecg does not process bad values. It will set the bad-value flag
736 of all output ndarrays if the flag is set for any of the input
737 ndarrays.
738 vsearchvec
740 Signature: (find(M); which(M,N); indx [o]found())
741 Routine for searching N-dimensional values - akin to vsearch() for
743 vectors.
744 $found = vsearchvec($find, $which);
746 $nearest = $which->dice_axis(1,$found);
747 Returns for each row-vector in $find the index along dimension N of the
749 least row vector of $which greater or equal to it. $which should be
750 sorted in increasing order. If the value of $find is larger than any
751 member of $which, the index to the last element of $which is returned.
752 See also: "vsearch". Contributed by Bryan Jurish <moocow@cpan.org>.
754 vsearchvec does not process bad values. It will set the bad-value flag
756 of all output ndarrays if the flag is set for any of the input
757 ndarrays.
758 unionvec
760 Signature: (a(M,NA); b(M,NB); [o]c(M,NC); indx [o]nc())
761 Union of two vector-valued PDLs.
763 Input PDLs $a() and $b() MUST be sorted in lexicographic order. On
765 return, $nc() holds the actual number of vector-values in the union.
766 In scalar context, slices $c() to the actual number of elements in the
768 union and returns the sliced PDL.
769 Contributed by Bryan Jurish <moocow@cpan.org>.
771 unionvec does not process bad values. It will set the bad-value flag
773 of all output ndarrays if the flag is set for any of the input
774 ndarrays.
775 intersectvec
777 Signature: (a(M,NA); b(M,NB); [o]c(M,NC); indx [o]nc())
778 Intersection of two vector-valued PDLs. Input PDLs $a() and $b() MUST
780 be sorted in lexicographic order. On return, $nc() holds the actual
781 number of vector-values in the intersection.
782 In scalar context, slices $c() to the actual number of elements in the
784 intersection and returns the sliced PDL.
785 Contributed by Bryan Jurish <moocow@cpan.org>.
787 intersectvec does not process bad values. It will set the bad-value
789 flag of all output ndarrays if the flag is set for any of the input
790 ndarrays.
791 setdiffvec
793 Signature: (a(M,NA); b(M,NB); [o]c(M,NC); indx [o]nc())
794 Set-difference ($a() \ $b()) of two vector-valued PDLs.
796 Input PDLs $a() and $b() MUST be sorted in lexicographic order. On
798 return, $nc() holds the actual number of vector-values in the computed
799 vector set.
800 In scalar context, slices $c() to the actual number of elements in the
802 output vector set and returns the sliced PDL.
803 Contributed by Bryan Jurish <moocow@cpan.org>.
805 setdiffvec does not process bad values. It will set the bad-value flag
807 of all output ndarrays if the flag is set for any of the input
808 ndarrays.
809 union_sorted
811 Signature: (a(NA); b(NB); [o]c(NC); indx [o]nc())
812 Union of two flat sorted unique-valued PDLs. Input PDLs $a() and $b()
814 MUST be sorted in lexicographic order and contain no duplicates. On
815 return, $nc() holds the actual number of values in the union.
816 In scalar context, reshapes $c() to the actual number of elements in
818 the union and returns it.
819 Contributed by Bryan Jurish <moocow@cpan.org>.
821 union_sorted does not process bad values. It will set the bad-value
823 flag of all output ndarrays if the flag is set for any of the input
824 ndarrays.
825 intersect_sorted
827 Signature: (a(NA); b(NB); [o]c(NC); indx [o]nc())
828 Intersection of two flat sorted unique-valued PDLs. Input PDLs $a()
830 and $b() MUST be sorted in lexicographic order and contain no
831 duplicates. On return, $nc() holds the actual number of values in the
832 intersection.
833 In scalar context, reshapes $c() to the actual number of elements in
835 the intersection and returns it.
836 Contributed by Bryan Jurish <moocow@cpan.org>.
838 intersect_sorted does not process bad values. It will set the bad-
840 value flag of all output ndarrays if the flag is set for any of the
841 input ndarrays.
842 setdiff_sorted
844 Signature: (a(NA); b(NB); [o]c(NC); indx [o]nc())
845 Set-difference ($a() \ $b()) of two flat sorted unique-valued PDLs.
847 Input PDLs $a() and $b() MUST be sorted in lexicographic order and
849 contain no duplicate values. On return, $nc() holds the actual number
850 of values in the computed vector set.
851 In scalar context, reshapes $c() to the actual number of elements in
853 the difference set and returns it.
854 Contributed by Bryan Jurish <moocow@cpan.org>.
856 setdiff_sorted does not process bad values. It will set the bad-value
858 flag of all output ndarrays if the flag is set for any of the input
859 ndarrays.
860 srand
862 Signature: (a())
863 Seed random-number generator with a 64-bit int. Will generate seed data
865 for a number of threads equal to the return-value of "online_cpus" in
866 PDL::Core.
867 srand(); # uses current time
869 srand(5); # fixed number e.g. for testing
870 srand does not process bad values. It will set the bad-value flag of
872 all output ndarrays if the flag is set for any of the input ndarrays.
873 random
875 Signature: (a())
876 Constructor which returns ndarray of random numbers
878 $x = random([type], $nx, $ny, $nz,...);
880 $x = random $y;
881 etc (see zeroes).
883 This is the uniform distribution between 0 and 1 (assumedly excluding 1
885 itself). The arguments are the same as "zeroes" (q.v.) - i.e. one can
886 specify dimensions, types or give a template.
887 You can use the PDL function "srand" to seed the random generator. If
889 it has not been called yet, it will be with the current time.
890 random does not process bad values. It will set the bad-value flag of
892 all output ndarrays if the flag is set for any of the input ndarrays.
893 randsym
895 Signature: (a())
896 Constructor which returns ndarray of random numbers
898 $x = randsym([type], $nx, $ny, $nz,...);
900 $x = randsym $y;
901 etc (see zeroes).
903 This is the uniform distribution between 0 and 1 (excluding both 0 and
905 1, cf "random"). The arguments are the same as "zeroes" (q.v.) - i.e.
906 one can specify dimensions, types or give a template.
907 You can use the PDL function "srand" to seed the random generator. If
909 it has not been called yet, it will be with the current time.
910 randsym does not process bad values. It will set the bad-value flag of
912 all output ndarrays if the flag is set for any of the input ndarrays.
913 grandom
915 Constructor which returns ndarray of Gaussian random numbers
916 $x = grandom([type], $nx, $ny, $nz,...);
918 $x = grandom $y;
919 etc (see zeroes).
921 This is generated using the math library routine "ndtri".
923 Mean = 0, Stddev = 1
925 You can use the PDL function "srand" to seed the random generator. If
927 it has not been called yet, it will be with the current time.
928 vsearch
930 Signature: ( vals(); xs(n); [o] indx(); [\%options] )
931 Efficiently search for values in a sorted ndarray, returning indices.
933 $idx = vsearch( $vals, $x, [\%options] );
935 vsearch( $vals, $x, $idx, [\%options ] );
936 vsearch performs a binary search in the ordered ndarray $x, for the
938 values from $vals ndarray, returning indices into $x. What is a
939 "match", and the meaning of the returned indices, are determined by the
940 options.
941 The "mode" option indicates which method of searching to use, and may
943 be one of:
944 "sample"
946 invoke vsearch_sample, returning indices appropriate for sampling
947 within a distribution.
948 "insert_leftmost"
950 invoke vsearch_insert_leftmost, returning the left-most possible
951 insertion point which still leaves the ndarray sorted.
952 "insert_rightmost"
954 invoke vsearch_insert_rightmost, returning the right-most possible
955 insertion point which still leaves the ndarray sorted.
956 "match"
958 invoke vsearch_match, returning the index of a matching element,
959 else -(insertion point + 1)
960 "bin_inclusive"
962 invoke vsearch_bin_inclusive, returning an index appropriate for
963 binning on a grid where the left bin edges are inclusive of the
964 bin. See below for further explanation of the bin.
965 "bin_exclusive"
967 invoke vsearch_bin_exclusive, returning an index appropriate for
968 binning on a grid where the left bin edges are exclusive of the
969 bin. See below for further explanation of the bin.
970 The default value of "mode" is "sample".
972 use PDL;
974 my @modes = qw( sample insert_leftmost insert_rightmost match
976 bin_inclusive bin_exclusive );
977 # Generate a sequence of 3 zeros, 3 ones, ..., 3 fours.
979 my $x = zeroes(3,5)->yvals->flat;
980 for my $mode ( @modes ) {
982 # if the value is in $x
983 my $contained = 2;
984 my $idx_contained = vsearch( $contained, $x, { mode => $mode } );
985 my $x_contained = $x->copy;
986 $x_contained->slice( $idx_contained ) .= 9;
987 # if the value is not in $x
989 my $not_contained = 1.5;
990 my $idx_not_contained = vsearch( $not_contained, $x, { mode => $mode } );
991 my $x_not_contained = $x->copy;
992 $x_not_contained->slice( $idx_not_contained ) .= 9;
993 print sprintf("%-23s%30s\n", '$x', $x);
995 print sprintf("%-23s%30s\n", "$mode ($contained)", $x_contained);
996 print sprintf("%-23s%30s\n\n", "$mode ($not_contained)", $x_not_contained);
997 }
998 # $x [0 0 0 1 1 1 2 2 2 3 3 3 4 4 4]
1000 # sample (2) [0 0 0 1 1 1 9 2 2 3 3 3 4 4 4]
1001 # sample (1.5) [0 0 0 1 1 1 9 2 2 3 3 3 4 4 4]
1002 #
1003 # $x [0 0 0 1 1 1 2 2 2 3 3 3 4 4 4]
1004 # insert_leftmost (2) [0 0 0 1 1 1 9 2 2 3 3 3 4 4 4]
1005 # insert_leftmost (1.5) [0 0 0 1 1 1 9 2 2 3 3 3 4 4 4]
1006 #
1007 # $x [0 0 0 1 1 1 2 2 2 3 3 3 4 4 4]
1008 # insert_rightmost (2) [0 0 0 1 1 1 2 2 2 9 3 3 4 4 4]
1009 # insert_rightmost (1.5) [0 0 0 1 1 1 9 2 2 3 3 3 4 4 4]
1010 #
1011 # $x [0 0 0 1 1 1 2 2 2 3 3 3 4 4 4]
1012 # match (2) [0 0 0 1 1 1 2 9 2 3 3 3 4 4 4]
1013 # match (1.5) [0 0 0 1 1 1 2 2 9 3 3 3 4 4 4]
1014 #
1015 # $x [0 0 0 1 1 1 2 2 2 3 3 3 4 4 4]
1016 # bin_inclusive (2) [0 0 0 1 1 1 2 2 9 3 3 3 4 4 4]
1017 # bin_inclusive (1.5) [0 0 0 1 1 9 2 2 2 3 3 3 4 4 4]
1018 #
1019 # $x [0 0 0 1 1 1 2 2 2 3 3 3 4 4 4]
1020 # bin_exclusive (2) [0 0 0 1 1 9 2 2 2 3 3 3 4 4 4]
1021 # bin_exclusive (1.5) [0 0 0 1 1 9 2 2 2 3 3 3 4 4 4]
1022 Also see vsearch_sample, vsearch_insert_leftmost,
1024 vsearch_insert_rightmost, vsearch_match, vsearch_bin_inclusive, and
1025 vsearch_bin_exclusive
1026 vsearch_sample
1028 Signature: (vals(); x(n); indx [o]idx())
1029 Search for values in a sorted array, return index appropriate for
1031 sampling from a distribution
1032 $idx = vsearch_sample($vals, $x);
1034 $x must be sorted, but may be in decreasing or increasing order.
1036 vsearch_sample returns an index I for each value V of $vals appropriate
1038 for sampling $vals
1039 I has the following properties:
1041 • if $x is sorted in increasing order
1043 V <= x[0] : I = 0
1045 x[0] < V <= x[-1] : I s.t. x[I-1] < V <= x[I]
1046 x[-1] < V : I = $x->nelem -1
1047 • if $x is sorted in decreasing order
1049 V > x[0] : I = 0
1051 x[0] >= V > x[-1] : I s.t. x[I] >= V > x[I+1]
1052 x[-1] >= V : I = $x->nelem - 1
1053 If all elements of $x are equal, I = $x->nelem - 1.
1055 If $x contains duplicated elements, I is the index of the leftmost (by
1057 position in array) duplicate if V matches.
1058 This function is useful e.g. when you have a list of probabilities for
1060 events and want to generate indices to events:
1061 $x = pdl(.01,.86,.93,1); # Barnsley IFS probabilities cumulatively
1063 $y = random 20;
1064 $c = vsearch_sample($y, $x); # Now, $c will have the appropriate distr.
1065 It is possible to use the cumusumover function to obtain cumulative
1067 probabilities from absolute probabilities.
1068 needs major (?) work to handles bad values
1070 vsearch_insert_leftmost
1072 Signature: (vals(); x(n); indx [o]idx())
1073 Determine the insertion point for values in a sorted array, inserting
1075 before duplicates.
1076 $idx = vsearch_insert_leftmost($vals, $x);
1078 $x must be sorted, but may be in decreasing or increasing order.
1080 vsearch_insert_leftmost returns an index I for each value V of $vals
1082 equal to the leftmost position (by index in array) within $x that V may
1083 be inserted and still maintain the order in $x.
1084 Insertion at index I involves shifting elements I and higher of $x to
1086 the right by one and setting the now empty element at index I to V.
1087 I has the following properties:
1089 • if $x is sorted in increasing order
1091 V <= x[0] : I = 0
1093 x[0] < V <= x[-1] : I s.t. x[I-1] < V <= x[I]
1094 x[-1] < V : I = $x->nelem
1095 • if $x is sorted in decreasing order
1097 V > x[0] : I = -1
1099 x[0] >= V >= x[-1] : I s.t. x[I] >= V > x[I+1]
1100 x[-1] >= V : I = $x->nelem -1
1101 If all elements of $x are equal,
1103 i = 0
1105 If $x contains duplicated elements, I is the index of the leftmost (by
1107 index in array) duplicate if V matches.
1108 needs major (?) work to handles bad values
1110 vsearch_insert_rightmost
1112 Signature: (vals(); x(n); indx [o]idx())
1113 Determine the insertion point for values in a sorted array, inserting
1115 after duplicates.
1116 $idx = vsearch_insert_rightmost($vals, $x);
1118 $x must be sorted, but may be in decreasing or increasing order.
1120 vsearch_insert_rightmost returns an index I for each value V of $vals
1122 equal to the rightmost position (by index in array) within $x that V
1123 may be inserted and still maintain the order in $x.
1124 Insertion at index I involves shifting elements I and higher of $x to
1126 the right by one and setting the now empty element at index I to V.
1127 I has the following properties:
1129 • if $x is sorted in increasing order
1131 V < x[0] : I = 0
1133 x[0] <= V < x[-1] : I s.t. x[I-1] <= V < x[I]
1134 x[-1] <= V : I = $x->nelem
1135 • if $x is sorted in decreasing order
1137 V >= x[0] : I = -1
1139 x[0] > V >= x[-1] : I s.t. x[I] >= V > x[I+1]
1140 x[-1] > V : I = $x->nelem -1
1141 If all elements of $x are equal,
1143 i = $x->nelem - 1
1145 If $x contains duplicated elements, I is the index of the leftmost (by
1147 index in array) duplicate if V matches.
1148 needs major (?) work to handles bad values
1150 vsearch_match
1152 Signature: (vals(); x(n); indx [o]idx())
1153 Match values against a sorted array.
1155 $idx = vsearch_match($vals, $x);
1157 $x must be sorted, but may be in decreasing or increasing order.
1159 vsearch_match returns an index I for each value V of $vals. If V
1161 matches an element in $x, I is the index of that element, otherwise it
1162 is -( insertion_point + 1 ), where insertion_point is an index in $x
1163 where V may be inserted while maintaining the order in $x. If $x has
1164 duplicated values, I may refer to any of them.
1165 needs major (?) work to handles bad values
1167 vsearch_bin_inclusive
1169 Signature: (vals(); x(n); indx [o]idx())
1170 Determine the index for values in a sorted array of bins, lower bound
1172 inclusive.
1173 $idx = vsearch_bin_inclusive($vals, $x);
1175 $x must be sorted, but may be in decreasing or increasing order.
1177 $x represents the edges of contiguous bins, with the first and last
1179 elements representing the outer edges of the outer bins, and the inner
1180 elements the shared bin edges.
1181 The lower bound of a bin is inclusive to the bin, its outer bound is
1183 exclusive to it. vsearch_bin_inclusive returns an index I for each
1184 value V of $vals
1185 I has the following properties:
1187 • if $x is sorted in increasing order
1189 V < x[0] : I = -1
1191 x[0] <= V < x[-1] : I s.t. x[I] <= V < x[I+1]
1192 x[-1] <= V : I = $x->nelem - 1
1193 • if $x is sorted in decreasing order
1195 V >= x[0] : I = 0
1197 x[0] > V >= x[-1] : I s.t. x[I+1] > V >= x[I]
1198 x[-1] > V : I = $x->nelem
1199 If all elements of $x are equal,
1201 i = $x->nelem - 1
1203 If $x contains duplicated elements, I is the index of the righmost (by
1205 index in array) duplicate if V matches.
1206 needs major (?) work to handles bad values
1208 vsearch_bin_exclusive
1210 Signature: (vals(); x(n); indx [o]idx())
1211 Determine the index for values in a sorted array of bins, lower bound
1213 exclusive.
1214 $idx = vsearch_bin_exclusive($vals, $x);
1216 $x must be sorted, but may be in decreasing or increasing order.
1218 $x represents the edges of contiguous bins, with the first and last
1220 elements representing the outer edges of the outer bins, and the inner
1221 elements the shared bin edges.
1222 The lower bound of a bin is exclusive to the bin, its upper bound is
1224 inclusive to it. vsearch_bin_exclusive returns an index I for each
1225 value V of $vals.
1226 I has the following properties:
1228 • if $x is sorted in increasing order
1230 V <= x[0] : I = -1
1232 x[0] < V <= x[-1] : I s.t. x[I] < V <= x[I+1]
1233 x[-1] < V : I = $x->nelem - 1
1234 • if $x is sorted in decreasing order
1236 V > x[0] : I = 0
1238 x[0] >= V > x[-1] : I s.t. x[I-1] >= V > x[I]
1239 x[-1] >= V : I = $x->nelem
1240 If all elements of $x are equal,
1242 i = $x->nelem - 1
1244 If $x contains duplicated elements, I is the index of the righmost (by
1246 index in array) duplicate if V matches.
1247 needs major (?) work to handles bad values
1249 interpolate
1251 Signature: (real xi(); real x(n); y(n); [o] yi(); int [o] err())
1252 routine for 1D linear interpolation
1254 ( $yi, $err ) = interpolate($xi, $x, $y)
1256 Given a set of points "($x,$y)", use linear interpolation to find the
1258 values $yi at a set of points $xi.
1259 "interpolate" uses a binary search to find the suspects, er...,
1261 interpolation indices and therefore abscissas (ie $x) have to be
1262 strictly ordered (increasing or decreasing). For interpolation at lots
1263 of closely spaced abscissas an approach that uses the last index found
1264 as a start for the next search can be faster (compare Numerical Recipes
1265 "hunt" routine). Feel free to implement that on top of the binary
1266 search if you like. For out of bounds values it just does a linear
1267 extrapolation and sets the corresponding element of $err to 1, which is
1268 otherwise 0.
1269 See also "interpol", which uses the same routine, differing only in the
1271 handling of extrapolation - an error message is printed rather than
1272 returning an error ndarray.
1273 Note that "interpolate" can use complex values for $y and $yi but $x
1275 and $xi must be real.
1276 needs major (?) work to handles bad values
1278 interpol
1280 Signature: (xi(); x(n); y(n); [o] yi())
1281 routine for 1D linear interpolation
1283 $yi = interpol($xi, $x, $y)
1285 "interpol" uses the same search method as "interpolate", hence $x must
1287 be strictly ordered (either increasing or decreasing). The difference
1288 occurs in the handling of out-of-bounds values; here an error message
1289 is printed.
1290 interpND
1292 Interpolate values from an N-D ndarray, with switchable method
1293 $source = 10*xvals(10,10) + yvals(10,10);
1295 $index = pdl([[2.2,3.5],[4.1,5.0]],[[6.0,7.4],[8,9]]);
1296 print $source->interpND( $index );
1297 InterpND acts like indexND, collapsing $index by lookup into $source;
1299 but it does interpolation rather than direct sampling. The
1300 interpolation method and boundary condition are switchable via an
1301 options hash.
1302 By default, linear or sample interpolation is used, with constant value
1304 outside the boundaries of the source pdl. No dataflow occurs, because
1305 in general the output is computed rather than indexed.
1306 All the interpolation methods treat the pixels as value-centered, so
1308 the "sample" method will return $a->(0) for coordinate values on the
1309 set [-0.5,0.5), and all methods will return $a->(1) for a coordinate
1310 value of exactly 1.
1311 Recognized options:
1313 method
1315 Values can be:
1316 • 0, s, sample, Sample (default for integer source types)
1318 The nearest value is taken. Pixels are regarded as centered on
1320 their respective integer coordinates (no offset from the linear
1321 case).
1322 • 1, l, linear, Linear (default for floating point source types)
1324 The values are N-linearly interpolated from an N-dimensional cube
1326 of size 2.
1327 • 3, c, cube, cubic, Cubic
1329 The values are interpolated using a local cubic fit to the data.
1331 The fit is constrained to match the original data and its
1332 derivative at the data points. The second derivative of the fit
1333 is not continuous at the data points. Multidimensional datasets
1334 are interpolated by the successive-collapse method.
1335 (Note that the constraint on the first derivative causes a small
1337 amount of ringing around sudden features such as step functions).
1338 • f, fft, fourier, Fourier
1340 The source is Fourier transformed, and the interpolated values
1342 are explicitly calculated from the coefficients. The boundary
1343 condition option is ignored -- periodic boundaries are imposed.
1344 If you pass in the option "fft", and it is a list (ARRAY) ref,
1346 then it is a stash for the magnitude and phase of the source FFT.
1347 If the list has two elements then they are taken as already
1348 computed; otherwise they are calculated and put in the stash.
1349 b, bound, boundary, Boundary
1351 This option is passed unmodified into indexND, which is used as the
1352 indexing engine for the interpolation. Some current allowed values
1353 are 'extend', 'periodic', 'truncate', and 'mirror' (default is
1354 'truncate').
1355 bad
1357 contains the fill value used for 'truncate' boundary. (default 0)
1358 fft
1360 An array ref whose associated list is used to stash the FFT of the
1361 source data, for the FFT method.
1362 one2nd
1364 Converts a one dimensional index ndarray to a set of ND coordinates
1365 @coords=one2nd($x, $indices)
1367 returns an array of ndarrays containing the ND indexes corresponding to
1369 the one dimensional list indices. The indices are assumed to correspond
1370 to array $x clumped using clump(-1). This routine is used in the old
1371 vector form of "whichND", but is useful on its own occasionally.
1372 Returned ndarrays have the indx datatype. $indices can have values
1374 larger than "$x->nelem" but negative values in $indices will not give
1375 the answer you expect.
1376 pdl> $x=pdl [[[1,2],[-1,1]], [[0,-3],[3,2]]]; $c=$x->clump(-1)
1378 pdl> $maxind=maximum_ind($c); p $maxind;
1379 6
1380 pdl> print one2nd($x, maximum_ind($c))
1381 0 1 1
1382 pdl> p $x->at(0,1,1)
1383 3
1384 which
1386 Signature: (mask(n); indx [o] inds(n); indx [o]lastout())
1387 Returns indices of non-zero values from a 1-D PDL
1389 $i = which($mask);
1391 returns a pdl with indices for all those elements that are nonzero in
1393 the mask. Note that the returned indices will be 1D. If you feed in a
1394 multidimensional mask, it will be flattened before the indices are
1395 calculated. See also "whichND" for multidimensional masks.
1396 If you want to index into the original mask or a similar ndarray with
1398 output from "which", remember to flatten it before calling index:
1399 $data = random 5, 5;
1401 $idx = which $data > 0.5; # $idx is now 1D
1402 $bigsum = $data->flat->index($idx)->sum; # flatten before indexing
1403 Compare also "where" for similar functionality.
1405 SEE ALSO:
1407 "which_both" returns separately the indices of both nonzero and zero
1409 values in the mask.
1410 "where_both" returns separately slices of both nonzero and zero values
1412 in the mask.
1413 "where" returns associated values from a data PDL, rather than indices
1415 into the mask PDL.
1416 "whichND" returns N-D indices into a multidimensional PDL.
1418 pdl> $x = sequence(10); p $x
1420 [0 1 2 3 4 5 6 7 8 9]
1421 pdl> $indx = which($x>6); p $indx
1422 [7 8 9]
1423 which processes bad values. It will set the bad-value flag of all
1425 output ndarrays if the flag is set for any of the input ndarrays.
1426 which_both
1428 Signature: (mask(n); indx [o] inds(n); indx [o]notinds(n); indx [o]lastout(); indx [o]lastoutn())
1429 Returns indices of nonzero and zero values in a mask PDL
1431 ($i, $c_i) = which_both($mask);
1433 This works just as "which", but the complement of $i will be in $c_i.
1435 pdl> p $x = sequence(10)
1437 [0 1 2 3 4 5 6 7 8 9]
1438 pdl> ($big, $small) = which_both($x >= 5); p "$big\n$small"
1439 [5 6 7 8 9]
1440 [0 1 2 3 4]
1441 which_both processes bad values. It will set the bad-value flag of all
1443 output ndarrays if the flag is set for any of the input ndarrays.
1444 where
1446 Use a mask to select values from one or more data PDLs
1447 "where" accepts one or more data ndarrays and a mask ndarray. It
1449 returns a list of output ndarrays, corresponding to the input data
1450 ndarrays. Each output ndarray is a 1-dimensional list of values in its
1451 corresponding data ndarray. The values are drawn from locations where
1452 the mask is nonzero.
1453 The output PDLs are still connected to the original data PDLs, for the
1455 purpose of dataflow.
1456 "where" combines the functionality of "which" and index into a single
1458 operation.
1459 BUGS:
1461 While "where" works OK for most N-dimensional cases, it does not
1463 broadcast properly over (for example) the (N+1)th dimension in data
1464 that is compared to an N-dimensional mask. Use "whereND" for that.
1465 $i = $x->where($x+5 > 0); # $i contains those elements of $x
1467 # where mask ($x+5 > 0) is 1
1468 $i .= -5; # Set those elements (of $x) to -5. Together, these
1469 # commands clamp $x to a maximum of -5.
1470 It is also possible to use the same mask for several ndarrays with the
1472 same call:
1473 ($i,$j,$k) = where($x,$y,$z, $x+5>0);
1475 Note: $i is always 1-D, even if $x is >1-D.
1477 WARNING: The first argument (the values) and the second argument (the
1479 mask) currently have to have the exact same dimensions (or horrible
1480 things happen). You *cannot* broadcast over a smaller mask, for
1481 example.
1482 where_both
1484 Returns slices (non-zero in mask, zero) of an ndarray according to a
1485 mask
1486 ($match_vals, $non_match_vals) = where_both($pdl, $mask);
1488 This works like "which_both", but (flattened) data-flowing slices
1490 rather than index-sets are returned.
1491 pdl> p $x = sequence(10) + 2
1493 [2 3 4 5 6 7 8 9 10 11]
1494 pdl> ($big, $small) = where_both($x, $x > 5); p "$big\n$small"
1495 [6 7 8 9 10 11]
1496 [2 3 4 5]
1497 pdl> p $big += 2, $small -= 1
1498 [8 9 10 11 12 13] [1 2 3 4]
1499 pdl> p $x
1500 [1 2 3 4 8 9 10 11 12 13]
1501 whereND
1503 "where" with support for ND masks and broadcasting
1504 "whereND" accepts one or more data ndarrays and a mask ndarray. It
1506 returns a list of output ndarrays, corresponding to the input data
1507 ndarrays. The values are drawn from locations where the mask is
1508 nonzero.
1509 "whereND" differs from "where" in that the mask dimensionality is
1511 preserved which allows for proper broadcasting of the selection
1512 operation over higher dimensions.
1513 As with "where" the output PDLs are still connected to the original
1515 data PDLs, for the purpose of dataflow.
1516 $sdata = whereND $data, $mask
1518 ($s1, $s2, ..., $sn) = whereND $d1, $d2, ..., $dn, $mask
1519 where
1521 $data is M dimensional
1523 $mask is N < M dimensional
1524 dims($data) 1..N == dims($mask) 1..N
1525 with broadcasting over N+1 to M dimensions
1526 $data = sequence(4,3,2); # example data array
1528 $mask4 = (random(4)>0.5); # example 1-D mask array, has $n4 true values
1529 $mask43 = (random(4,3)>0.5); # example 2-D mask array, has $n43 true values
1530 $sdat4 = whereND $data, $mask4; # $sdat4 is a [$n4,3,2] pdl
1531 $sdat43 = whereND $data, $mask43; # $sdat43 is a [$n43,2] pdl
1532 Just as with "where", you can use the returned value in an assignment.
1534 That means that both of these examples are valid:
1535 # Used to create a new slice stored in $sdat4:
1537 $sdat4 = $data->whereND($mask4);
1538 $sdat4 .= 0;
1539 # Used in lvalue context:
1540 $data->whereND($mask4) .= 0;
1541 SEE ALSO:
1543 "whichND" returns N-D indices into a multidimensional PDL, from a mask.
1545 whichND
1547 Return the coordinates of non-zero values in a mask.
1548 WhichND returns the N-dimensional coordinates of each nonzero value in
1550 a mask PDL with any number of dimensions. The returned values arrive
1551 as an array-of-vectors suitable for use in indexND or range.
1552 $coords = whichND($mask);
1554 returns a PDL containing the coordinates of the elements that are non-
1556 zero in $mask, suitable for use in "indexND" in PDL::Slices. The 0th
1557 dimension contains the full coordinate listing of each point; the 1st
1558 dimension lists all the points. For example, if $mask has rank 4 and
1559 100 matching elements, then $coords has dimension 4x100.
1560 If no such elements exist, then whichND returns a structured empty PDL:
1562 an Nx0 PDL that contains no values (but matches, broadcasting-wise,
1563 with the vectors that would be produced if such elements existed).
1564 DEPRECATED BEHAVIOR IN LIST CONTEXT:
1566 whichND once delivered different values in list context than in scalar
1568 context, for historical reasons. In list context, it returned the
1569 coordinates transposed, as a collection of 1-PDLs (one per dimension)
1570 in a list. This usage is deprecated in PDL 2.4.10, and will cause a
1571 warning to be issued every time it is encountered. To avoid the
1572 warning, you can set the global variable "$PDL::whichND" to 's' to get
1573 scalar behavior in all contexts, or to 'l' to get list behavior in list
1574 context.
1575 In later versions of PDL, the deprecated behavior will disappear.
1577 Deprecated list context whichND expressions can be replaced with:
1578 @list = $x->whichND->mv(0,-1)->dog;
1580 SEE ALSO:
1582 "which" finds coordinates of nonzero values in a 1-D mask.
1584 "where" extracts values from a data PDL that are associated with
1586 nonzero values in a mask PDL.
1587 "indexND" in PDL::Slices can be fed the coordinates to return the
1589 values.
1590 pdl> $s=sequence(10,10,3,4)
1592 pdl> ($x, $y, $z, $w)=whichND($s == 203); p $x, $y, $z, $w
1593 [3] [0] [2] [0]
1594 pdl> print $s->at(list(cat($x,$y,$z,$w)))
1595 203
1596 setops
1598 Implements simple set operations like union and intersection
1599 Usage: $set = setops($x, <OPERATOR>, $y);
1601 The operator can be "OR", "XOR" or "AND". This is then applied to $x
1603 viewed as a set and $y viewed as a set. Set theory says that a set may
1604 not have two or more identical elements, but setops takes care of this
1605 for you, so "$x=pdl(1,1,2)" is OK. The functioning is as follows:
1606 "OR"
1608 The resulting vector will contain the elements that are either in
1609 $x or in $y or both. This is the union in set operation terms
1610 "XOR"
1612 The resulting vector will contain the elements that are either in
1613 $x or $y, but not in both. This is
1614 Union($x, $y) - Intersection($x, $y)
1616 in set operation terms.
1618 "AND"
1620 The resulting vector will contain the intersection of $x and $y, so
1621 the elements that are in both $x and $y. Note that for convenience
1622 this operation is also aliased to "intersect".
1623 It should be emphasized that these routines are used when one or both
1625 of the sets $x, $y are hard to calculate or that you get from a
1626 separate subroutine.
1627 Finally IDL users might be familiar with Craig Markwardt's
1629 "cmset_op.pro" routine which has inspired this routine although it was
1630 written independently However the present routine has a few less
1631 options (but see the examples)
1632 You will very often use these functions on an index vector, so that is
1634 what we will show here. We will in fact something slightly silly. First
1635 we will find all squares that are also cubes below 10000.
1636 Create a sequence vector:
1638 pdl> $x = sequence(10000)
1640 Find all odd and even elements:
1642 pdl> ($even, $odd) = which_both( ($x % 2) == 0)
1644 Find all squares
1646 pdl> $squares= which(ceil(sqrt($x)) == floor(sqrt($x)))
1648 Find all cubes (being careful with roundoff error!)
1650 pdl> $cubes= which(ceil($x**(1.0/3.0)) == floor($x**(1.0/3.0)+1e-6))
1652 Then find all squares that are cubes:
1654 pdl> $both = setops($squares, 'AND', $cubes)
1656 And print these (assumes that "PDL::NiceSlice" is loaded!)
1658 pdl> p $x($both)
1660 [0 1 64 729 4096]
1661 Then find all numbers that are either cubes or squares, but not both:
1663 pdl> $cube_xor_square = setops($squares, 'XOR', $cubes)
1665 pdl> p $cube_xor_square->nelem()
1667 112
1668 So there are a total of 112 of these!
1670 Finally find all odd squares:
1672 pdl> $odd_squares = setops($squares, 'AND', $odd)
1674 Another common occurrence is to want to get all objects that are in $x
1676 and in the complement of $y. But it is almost always best to create the
1677 complement explicitly since the universe that both are taken from is
1678 not known. Thus use "which_both" if possible to keep track of
1679 complements.
1680 If this is impossible the best approach is to make a temporary:
1682 This creates an index vector the size of the universe of the sets and
1684 set all elements in $y to 0
1685 pdl> $tmp = ones($n_universe); $tmp($y) .= 0;
1687 This then finds the complement of $y
1689 pdl> $C_b = which($tmp == 1);
1691 and this does the final selection:
1693 pdl> $set = setops($x, 'AND', $C_b)
1695 intersect
1697 Calculate the intersection of two ndarrays
1698 Usage: $set = intersect($x, $y);
1700 This routine is merely a simple interface to "setops". See that for
1702 more information
1703 Find all numbers less that 100 that are of the form 2*y and 3*x
1705 pdl> $x=sequence(100)
1707 pdl> $factor2 = which( ($x % 2) == 0)
1708 pdl> $factor3 = which( ($x % 3) == 0)
1709 pdl> $ii=intersect($factor2, $factor3)
1710 pdl> p $x($ii)
1711 [0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96]
1712
1714 Copyright (C) Tuomas J. Lukka 1997 (lukka@husc.harvard.edu).
1715 Contributions by Christian Soeller (c.soeller@auckland.ac.nz), Karl
1716 Glazebrook (kgb@aaoepp.aao.gov.au), Craig DeForest
1717 (deforest@boulder.swri.edu) and Jarle Brinchmann (jarle@astro.up.pt)
1718 All rights reserved. There is no warranty. You are allowed to
1719 redistribute this software / documentation under certain conditions.
1720 For details, see the file COPYING in the PDL distribution. If this file
1721 is separated from the PDL distribution, the copyright notice should be
1722 included in the file.
1723 Updated for CPAN viewing compatibility by David Mertens.
1725perl v5.36.0 2023-01-20 Primitive(3)