1Ufunc(3) User Contributed Perl Documentation Ufunc(3)
2
6 PDL::Ufunc - primitive ufunc operations for pdl
7
9 This module provides some primitive and useful functions defined using
10 PDL::PP based on functionality of what are sometimes called ufuncs (for
11 example NumPY and Mathematica talk about these). It collects all the
12 functions generally used to "reduce" or "accumulate" along a dimension.
13 These all do their job across the first dimension but by using the
14 slicing functions you can do it on any dimension.
15 The PDL::Reduce module provides an alternative interface to many of the
17 functions in this module.
18
20 use PDL::Ufunc;
21
23 prodover
24 Signature: (a(n); int+ [o]b())
25 Project via product to N-1 dimensions
27 This function reduces the dimensionality of an ndarray by one by taking
29 the product along the 1st dimension.
30 By using xchg etc. it is possible to use any dimension.
32 $y = prodover($x);
34 $spectrum = prodover $image->transpose
36 prodover processes bad values. It will set the bad-value flag of all
38 output ndarrays if the flag is set for any of the input ndarrays.
39 cprodover
41 Signature: (a(n); cdouble [o]b())
42 Project via product to N-1 dimensions
44 This function reduces the dimensionality of an ndarray by one by taking
46 the product along the 1st dimension.
47 By using xchg etc. it is possible to use any dimension.
49 $y = cprodover($x);
51 $spectrum = cprodover $image->transpose
53 Unlike "prodover", the calculations are performed in complex double
55 precision.
56 cprodover processes bad values. It will set the bad-value flag of all
58 output ndarrays if the flag is set for any of the input ndarrays.
59 dprodover
61 Signature: (a(n); double [o]b())
62 Project via product to N-1 dimensions
64 This function reduces the dimensionality of an ndarray by one by taking
66 the product along the 1st dimension.
67 By using xchg etc. it is possible to use any dimension.
69 $y = dprodover($x);
71 $spectrum = dprodover $image->transpose
73 Unlike "prodover", the calculations are performed in double precision.
75 dprodover processes bad values. It will set the bad-value flag of all
77 output ndarrays if the flag is set for any of the input ndarrays.
78 cumuprodover
80 Signature: (a(n); int+ [o]b(n))
81 Cumulative product
83 This function calculates the cumulative product along the 1st
85 dimension.
86 By using xchg etc. it is possible to use any dimension.
88 The sum is started so that the first element in the cumulative product
90 is the first element of the parameter.
91 $y = cumuprodover($x);
93 $spectrum = cumuprodover $image->transpose
95 cumuprodover processes bad values. It will set the bad-value flag of
97 all output ndarrays if the flag is set for any of the input ndarrays.
98 dcumuprodover
100 Signature: (a(n); double [o]b(n))
101 Cumulative product
103 This function calculates the cumulative product along the 1st
105 dimension.
106 By using xchg etc. it is possible to use any dimension.
108 The sum is started so that the first element in the cumulative product
110 is the first element of the parameter.
111 $y = dcumuprodover($x);
113 $spectrum = dcumuprodover $image->transpose
115 Unlike "cumuprodover", the calculations are performed in double
117 precision.
118 dcumuprodover processes bad values. It will set the bad-value flag of
120 all output ndarrays if the flag is set for any of the input ndarrays.
121 sumover
123 Signature: (a(n); int+ [o]b())
124 Project via sum to N-1 dimensions
126 This function reduces the dimensionality of an ndarray by one by taking
128 the sum along the 1st dimension.
129 By using xchg etc. it is possible to use any dimension.
131 $y = sumover($x);
133 $spectrum = sumover $image->transpose
135 sumover processes bad values. It will set the bad-value flag of all
137 output ndarrays if the flag is set for any of the input ndarrays.
138 csumover
140 Signature: (a(n); cdouble [o]b())
141 Project via sum to N-1 dimensions
143 This function reduces the dimensionality of an ndarray by one by taking
145 the sum along the 1st dimension.
146 By using xchg etc. it is possible to use any dimension.
148 $y = csumover($x);
150 $spectrum = csumover $image->transpose
152 Unlike "sumover", the calculations are performed in complex double
154 precision.
155 csumover processes bad values. It will set the bad-value flag of all
157 output ndarrays if the flag is set for any of the input ndarrays.
158 dsumover
160 Signature: (a(n); double [o]b())
161 Project via sum to N-1 dimensions
163 This function reduces the dimensionality of an ndarray by one by taking
165 the sum along the 1st dimension.
166 By using xchg etc. it is possible to use any dimension.
168 $y = dsumover($x);
170 $spectrum = dsumover $image->transpose
172 Unlike "sumover", the calculations are performed in double precision.
174 dsumover processes bad values. It will set the bad-value flag of all
176 output ndarrays if the flag is set for any of the input ndarrays.
177 cumusumover
179 Signature: (a(n); int+ [o]b(n))
180 Cumulative sum
182 This function calculates the cumulative sum along the 1st dimension.
184 By using xchg etc. it is possible to use any dimension.
186 The sum is started so that the first element in the cumulative sum is
188 the first element of the parameter.
189 $y = cumusumover($x);
191 $spectrum = cumusumover $image->transpose
193 cumusumover processes bad values. It will set the bad-value flag of
195 all output ndarrays if the flag is set for any of the input ndarrays.
196 dcumusumover
198 Signature: (a(n); double [o]b(n))
199 Cumulative sum
201 This function calculates the cumulative sum along the 1st dimension.
203 By using xchg etc. it is possible to use any dimension.
205 The sum is started so that the first element in the cumulative sum is
207 the first element of the parameter.
208 $y = dcumusumover($x);
210 $spectrum = dcumusumover $image->transpose
212 Unlike "cumusumover", the calculations are performed in double
214 precision.
215 dcumusumover processes bad values. It will set the bad-value flag of
217 all output ndarrays if the flag is set for any of the input ndarrays.
218 andover
220 Signature: (a(n); int+ [o]b())
221 Project via and to N-1 dimensions
223 This function reduces the dimensionality of an ndarray by one by taking
225 the and along the 1st dimension.
226 By using xchg etc. it is possible to use any dimension.
228 $y = andover($x);
230 $spectrum = andover $image->transpose
232 If "a()" contains only bad data (and its bad flag is set), "b()" is set
234 bad. Otherwise "b()" will have its bad flag cleared, as it will not
235 contain any bad values.
236 bandover
238 Signature: (a(n); [o]b())
239 Project via bitwise and to N-1 dimensions
241 This function reduces the dimensionality of an ndarray by one by taking
243 the bitwise and along the 1st dimension.
244 By using xchg etc. it is possible to use any dimension.
246 $y = bandover($x);
248 $spectrum = bandover $image->transpose
250 If "a()" contains only bad data (and its bad flag is set), "b()" is set
252 bad. Otherwise "b()" will have its bad flag cleared, as it will not
253 contain any bad values.
254 borover
256 Signature: (a(n); [o]b())
257 Project via bitwise or to N-1 dimensions
259 This function reduces the dimensionality of an ndarray by one by taking
261 the bitwise or along the 1st dimension.
262 By using xchg etc. it is possible to use any dimension.
264 $y = borover($x);
266 $spectrum = borover $image->transpose
268 If "a()" contains only bad data (and its bad flag is set), "b()" is set
270 bad. Otherwise "b()" will have its bad flag cleared, as it will not
271 contain any bad values.
272 orover
274 Signature: (a(n); int+ [o]b())
275 Project via or to N-1 dimensions
277 This function reduces the dimensionality of an ndarray by one by taking
279 the or along the 1st dimension.
280 By using xchg etc. it is possible to use any dimension.
282 $y = orover($x);
284 $spectrum = orover $image->transpose
286 If "a()" contains only bad data (and its bad flag is set), "b()" is set
288 bad. Otherwise "b()" will have its bad flag cleared, as it will not
289 contain any bad values.
290 zcover
292 Signature: (a(n); int+ [o]b())
293 Project via == 0 to N-1 dimensions
295 This function reduces the dimensionality of an ndarray by one by taking
297 the == 0 along the 1st dimension.
298 By using xchg etc. it is possible to use any dimension.
300 $y = zcover($x);
302 $spectrum = zcover $image->transpose
304 If "a()" contains only bad data (and its bad flag is set), "b()" is set
306 bad. Otherwise "b()" will have its bad flag cleared, as it will not
307 contain any bad values.
308 intover
310 Signature: (a(n); float+ [o]b())
311 Project via integral to N-1 dimensions
313 This function reduces the dimensionality of an ndarray by one by taking
315 the integral along the 1st dimension.
316 By using xchg etc. it is possible to use any dimension.
318 $y = intover($x);
320 $spectrum = intover $image->transpose
322 Notes:
324 "intover" uses a point spacing of one (i.e., delta-h==1). You will
326 need to scale the result to correct for the true point delta).
327 For "n > 3", these are all "O(h^4)" (like Simpson's rule), but are
329 integrals between the end points assuming the pdl gives values just at
330 these centres: for such `functions', sumover is correct to O(h), but is
331 the natural (and correct) choice for binned data, of course.
332 intover ignores the bad-value flag of the input ndarrays. It will set
334 the bad-value flag of all output ndarrays if the flag is set for any of
335 the input ndarrays.
336 average
338 Signature: (a(n); int+ [o]b())
339 Project via average to N-1 dimensions
341 This function reduces the dimensionality of an ndarray by one by taking
343 the average along the 1st dimension.
344 By using xchg etc. it is possible to use any dimension.
346 $y = average($x);
348 $spectrum = average $image->transpose
350 average processes bad values. It will set the bad-value flag of all
352 output ndarrays if the flag is set for any of the input ndarrays.
353 avgover
355 Synonym for average.
356 caverage
358 Signature: (a(n); cdouble [o]b())
359 Project via average to N-1 dimensions
361 This function reduces the dimensionality of an ndarray by one by taking
363 the average along the 1st dimension.
364 By using xchg etc. it is possible to use any dimension.
366 $y = caverage($x);
368 $spectrum = caverage $image->transpose
370 Unlike average, the calculation is performed in complex double
372 precision.
373 caverage processes bad values. It will set the bad-value flag of all
375 output ndarrays if the flag is set for any of the input ndarrays.
376 cavgover
378 Synonym for caverage.
379 daverage
381 Signature: (a(n); double [o]b())
382 Project via average to N-1 dimensions
384 This function reduces the dimensionality of an ndarray by one by taking
386 the average along the 1st dimension.
387 By using xchg etc. it is possible to use any dimension.
389 $y = daverage($x);
391 $spectrum = daverage $image->transpose
393 Unlike average, the calculation is performed in double precision.
395 daverage processes bad values. It will set the bad-value flag of all
397 output ndarrays if the flag is set for any of the input ndarrays.
398 davgover
400 Synonym for daverage.
401 minimum
403 Signature: (a(n); [o]c())
404 Project via minimum to N-1 dimensions
406 This function reduces the dimensionality of an ndarray by one by taking
408 the minimum along the 1st dimension.
409 By using xchg etc. it is possible to use any dimension.
411 $y = minimum($x);
413 $spectrum = minimum $image->transpose
415 Output is set bad if no elements of the input are non-bad, otherwise
417 the bad flag is cleared for the output ndarray.
418 Note that "NaNs" are considered to be valid values and will "win" over
420 non-"NaN"; see isfinite and badmask for ways of masking NaNs.
421 minover
423 Synonym for minimum.
424 minimum_ind
426 Signature: (a(n); indx [o] c())
427 Like minimum but returns the index rather than the value
429 Output is set bad if no elements of the input are non-bad, otherwise
431 the bad flag is cleared for the output ndarray.
432 Note that "NaNs" are considered to be valid values and will "win" over
434 non-"NaN"; see isfinite and badmask for ways of masking NaNs.
435 minover_ind
437 Synonym for minimum_ind.
438 minimum_n_ind
440 Signature: (a(n); indx [o]c(m); PDL_Indx m_size => m)
441 Returns the index of "m_size" minimum elements. As of 2.077, you can
443 specify how many by either passing in an ndarray of the given size
444 (DEPRECATED - will be converted to indx if needed and the input arg
445 will be set to that), or just the size, or a null and the size.
446 minimum_n_ind($pdl, $out = zeroes(5)); # DEPRECATED
448 $out = minimum_n_ind($pdl, 5);
449 minimum_n_ind($pdl, $out = null, 5);
450 Output bad flag is cleared for the output ndarray if sufficient non-bad
452 elements found, else remaining slots in "$c()" are set bad.
453 Note that "NaNs" are considered to be valid values and will "win" over
455 non-"NaN"; see isfinite and badmask for ways of masking NaNs.
456 minover_n_ind
458 Synonym for minimum_n_ind.
459 maximum
461 Signature: (a(n); [o]c())
462 Project via maximum to N-1 dimensions
464 This function reduces the dimensionality of an ndarray by one by taking
466 the maximum along the 1st dimension.
467 By using xchg etc. it is possible to use any dimension.
469 $y = maximum($x);
471 $spectrum = maximum $image->transpose
473 Output is set bad if no elements of the input are non-bad, otherwise
475 the bad flag is cleared for the output ndarray.
476 Note that "NaNs" are considered to be valid values and will "win" over
478 non-"NaN"; see isfinite and badmask for ways of masking NaNs.
479 maxover
481 Synonym for maximum.
482 maximum_ind
484 Signature: (a(n); indx [o] c())
485 Like maximum but returns the index rather than the value
487 Output is set bad if no elements of the input are non-bad, otherwise
489 the bad flag is cleared for the output ndarray.
490 Note that "NaNs" are considered to be valid values and will "win" over
492 non-"NaN"; see isfinite and badmask for ways of masking NaNs.
493 maxover_ind
495 Synonym for maximum_ind.
496 maximum_n_ind
498 Signature: (a(n); indx [o]c(m); PDL_Indx m_size => m)
499 Returns the index of "m_size" maximum elements. As of 2.077, you can
501 specify how many by either passing in an ndarray of the given size
502 (DEPRECATED - will be converted to indx if needed and the input arg
503 will be set to that), or just the size, or a null and the size.
504 maximum_n_ind($pdl, $out = zeroes(5)); # DEPRECATED
506 $out = maximum_n_ind($pdl, 5);
507 maximum_n_ind($pdl, $out = null, 5);
508 Output bad flag is cleared for the output ndarray if sufficient non-bad
510 elements found, else remaining slots in "$c()" are set bad.
511 Note that "NaNs" are considered to be valid values and will "win" over
513 non-"NaN"; see isfinite and badmask for ways of masking NaNs.
514 maxover_n_ind
516 Synonym for maximum_n_ind.
517 minmaximum
519 Signature: (a(n); [o]cmin(); [o] cmax(); indx [o]cmin_ind(); indx [o]cmax_ind())
520 Find minimum and maximum and their indices for a given ndarray;
522 pdl> $x=pdl [[-2,3,4],[1,0,3]]
524 pdl> ($min, $max, $min_ind, $max_ind)=minmaximum($x)
525 pdl> p $min, $max, $min_ind, $max_ind
526 [-2 0] [4 3] [0 1] [2 2]
527 See also "minmax", which clumps the ndarray together.
529 If "a()" contains only bad data, then the output ndarrays will be set
531 bad, along with their bad flag. Otherwise they will have their bad
532 flags cleared, since they will not contain any bad values.
533 minmaxover
535 Synonym for minmaximum.
536 avg
538 Return the average of all elements in an ndarray.
539 See the documentation for "average" for more information.
541 $x = avg($data);
543 This routine handles bad values.
545 sum
547 Return the sum of all elements in an ndarray.
548 See the documentation for "sumover" for more information.
550 $x = sum($data);
552 This routine handles bad values.
554 prod
556 Return the product of all elements in an ndarray.
557 See the documentation for "prodover" for more information.
559 $x = prod($data);
561 This routine handles bad values.
563 davg
565 Return the average (in double precision) of all elements in an ndarray.
566 See the documentation for "daverage" for more information.
568 $x = davg($data);
570 This routine handles bad values.
572 dsum
574 Return the sum (in double precision) of all elements in an ndarray.
575 See the documentation for "dsumover" for more information.
577 $x = dsum($data);
579 This routine handles bad values.
581 dprod
583 Return the product (in double precision) of all elements in an ndarray.
584 See the documentation for "dprodover" for more information.
586 $x = dprod($data);
588 This routine handles bad values.
590 zcheck
592 Return the check for zero of all elements in an ndarray.
593 See the documentation for "zcover" for more information.
595 $x = zcheck($data);
597 This routine handles bad values.
599 and
601 Return the logical and of all elements in an ndarray.
602 See the documentation for "andover" for more information.
604 $x = and($data);
606 This routine handles bad values.
608 band
610 Return the bitwise and of all elements in an ndarray.
611 See the documentation for "bandover" for more information.
613 $x = band($data);
615 This routine handles bad values.
617 or
619 Return the logical or of all elements in an ndarray.
620 See the documentation for "orover" for more information.
622 $x = or($data);
624 This routine handles bad values.
626 bor
628 Return the bitwise or of all elements in an ndarray.
629 See the documentation for "borover" for more information.
631 $x = bor($data);
633 This routine handles bad values.
635 min
637 Return the minimum of all elements in an ndarray.
638 See the documentation for "minimum" for more information.
640 $x = min($data);
642 This routine handles bad values.
644 max
646 Return the maximum of all elements in an ndarray.
647 See the documentation for "maximum" for more information.
649 $x = max($data);
651 This routine handles bad values.
653 median
655 Return the median of all elements in an ndarray.
656 See the documentation for "medover" for more information.
658 $x = median($data);
660 This routine handles bad values.
662 mode
664 Return the mode of all elements in an ndarray.
665 See the documentation for "modeover" for more information.
667 $x = mode($data);
669 This routine handles bad values.
671 oddmedian
673 Return the oddmedian of all elements in an ndarray.
674 See the documentation for "oddmedover" for more information.
676 $x = oddmedian($data);
678 This routine handles bad values.
680 any
682 Return true if any element in ndarray set
683 Useful in conditional expressions:
685 if (any $x>15) { print "some values are greater than 15\n" }
687 See "or" for comments on what happens when all elements in the check
689 are bad.
690 all
692 Return true if all elements in ndarray set
693 Useful in conditional expressions:
695 if (all $x>15) { print "all values are greater than 15\n" }
697 See "and" for comments on what happens when all elements in the check
699 are bad.
700 minmax
702 Returns a list with minimum and maximum values of an ndarray.
703 ($mn, $mx) = minmax($pdl);
705 This routine does not broadcast over the dimensions of $pdl; it returns
707 the minimum and maximum values of the whole ndarray. See "minmaximum"
708 if this is not what is required. The two values are returned as Perl
709 scalars, and therefore ignore whether the values are bad.
710 pdl> $x = pdl [1,-2,3,5,0]
712 pdl> ($min, $max) = minmax($x);
713 pdl> p "$min $max\n";
714 -2 5
715 medover
717 Signature: (a(n); [o]b(); [t]tmp(n))
718 Project via median to N-1 dimensions
720 This function reduces the dimensionality of an ndarray by one by taking
722 the median along the 1st dimension.
723 By using xchg etc. it is possible to use any dimension.
725 $y = medover($x);
727 $spectrum = medover $image->transpose
729 medover processes bad values. It will set the bad-value flag of all
731 output ndarrays if the flag is set for any of the input ndarrays.
732 oddmedover
734 Signature: (a(n); [o]b(); [t]tmp(n))
735 Project via oddmedian to N-1 dimensions
737 This function reduces the dimensionality of an ndarray by one by taking
739 the oddmedian along the 1st dimension.
740 By using xchg etc. it is possible to use any dimension.
742 $y = oddmedover($x);
744 $spectrum = oddmedover $image->transpose
746 The median is sometimes not a good choice as if the array has an even
748 number of elements it lies half-way between the two middle values -
749 thus it does not always correspond to a data value. The lower-odd
750 median is just the lower of these two values and so it ALWAYS sits on
751 an actual data value which is useful in some circumstances.
752 oddmedover processes bad values. It will set the bad-value flag of all
754 output ndarrays if the flag is set for any of the input ndarrays.
755 modeover
757 Signature: (data(n); [o]out(); [t]sorted(n))
758 Project via mode to N-1 dimensions
760 This function reduces the dimensionality of an ndarray by one by taking
762 the mode along the 1st dimension.
763 By using xchg etc. it is possible to use any dimension.
765 $y = modeover($x);
767 $spectrum = modeover $image->transpose
769 The mode is the single element most frequently found in a discrete data
771 set.
772 It only makes sense for integer data types, since floating-point types
774 are demoted to integer before the mode is calculated.
775 "modeover" treats BAD the same as any other value: if BAD is the most
777 common element, the returned value is also BAD.
778 modeover does not process bad values. It will set the bad-value flag
780 of all output ndarrays if the flag is set for any of the input
781 ndarrays.
782 pctover
784 Signature: (a(n); p(); [o]b(); [t]tmp(n))
785 Project via specified percentile to N-1 dimensions
787 This function reduces the dimensionality of an ndarray by one by taking
789 the specified percentile along the 1st dimension.
790 By using xchg etc. it is possible to use any dimension.
792 $y = pctover($x);
794 $spectrum = pctover $image->transpose
796 The specified percentile must be between 0.0 and 1.0. When the
798 specified percentile falls between data points, the result is
799 interpolated. Values outside the allowed range are clipped to 0.0 or
800 1.0 respectively. The algorithm implemented here is based on the
801 interpolation variant described at
802 <http://en.wikipedia.org/wiki/Percentile> as used by Microsoft Excel
803 and recommended by NIST.
804 pctover processes bad values. It will set the bad-value flag of all
806 output ndarrays if the flag is set for any of the input ndarrays.
807 oddpctover
809 Signature: (a(n); p(); [o]b(); [t]tmp(n))
810 Project via specified percentile to N-1 dimensions
812 This function reduces the dimensionality of an ndarray by one by taking
814 the specified percentile along the 1st dimension.
815 By using xchg etc. it is possible to use any dimension.
817 $y = oddpctover($x);
819 $spectrum = oddpctover $image->transpose
821 The specified percentile must be between 0.0 and 1.0. When the
823 specified percentile falls between two values, the nearest data value
824 is the result. The algorithm implemented is from the textbook version
825 described first at <http://en.wikipedia.org/wiki/Percentile>.
826 oddpctover processes bad values. It will set the bad-value flag of all
828 output ndarrays if the flag is set for any of the input ndarrays.
829 pct
831 Return the specified percentile of all elements in an ndarray. The
832 specified percentile (p) must be between 0.0 and 1.0. When the
833 specified percentile falls between data points, the result is
834 interpolated.
835 $x = pct($data, $pct);
837 oddpct
839 Return the specified percentile of all elements in an ndarray. The
840 specified percentile (p) must be between 0.0 and 1.0. When the
841 specified percentile falls between data points, the nearest data value
842 is the result.
843 $x = oddpct($data, $pct);
845 qsort
847 Signature: (a(n); [o]b(n))
848 Quicksort a vector into ascending order.
850 print qsort random(10);
852 Bad values are moved to the end of the array:
854 pdl> p $y
856 [42 47 98 BAD 22 96 74 41 79 76 96 BAD 32 76 25 59 BAD 96 32 BAD]
857 pdl> p qsort($y)
858 [22 25 32 32 41 42 47 59 74 76 76 79 96 96 96 98 BAD BAD BAD BAD]
859 qsorti
861 Signature: (a(n); indx [o]indx(n))
862 Quicksort a vector and return index of elements in ascending order.
864 $ix = qsorti $x;
866 print $x->index($ix); # Sorted list
867 Bad elements are moved to the end of the array:
869 pdl> p $y
871 [42 47 98 BAD 22 96 74 41 79 76 96 BAD 32 76 25 59 BAD 96 32 BAD]
872 pdl> p $y->index( qsorti($y) )
873 [22 25 32 32 41 42 47 59 74 76 76 79 96 96 96 98 BAD BAD BAD BAD]
874 qsortvec
876 Signature: (a(n,m); [o]b(n,m))
877 Sort a list of vectors lexicographically.
879 The 0th dimension of the source ndarray is dimension in the vector; the
881 1st dimension is list order. Higher dimensions are broadcasted over.
882 print qsortvec pdl([[1,2],[0,500],[2,3],[4,2],[3,4],[3,5]]);
884 [
885 [ 0 500]
886 [ 1 2]
887 [ 2 3]
888 [ 3 4]
889 [ 3 5]
890 [ 4 2]
891 ]
892 Vectors with bad components are moved to the end of the array:
894 pdl> p $p = pdl("[0 0] [-100 0] [BAD 0] [100 0]")->qsortvec
896 [
898 [-100 0]
899 [ 0 0]
900 [ 100 0]
901 [ BAD 0]
902 ]
903 qsortveci
905 Signature: (a(n,m); indx [o]indx(m))
906 Sort a list of vectors lexicographically, returning the indices of the
908 sorted vectors rather than the sorted list itself.
909 As with "qsortvec", the input PDL should be an NxM array containing M
911 separate N-dimensional vectors. The return value is an integer M-PDL
912 containing the M-indices of original array rows, in sorted order.
913 As with "qsortvec", the zeroth element of the vectors runs slowest in
915 the sorted list.
916 Additional dimensions are broadcasted over: each plane is sorted
918 separately, so qsortveci may be thought of as a collapse operator of
919 sorts (groan).
920 Vectors with bad components are moved to the end of the array as for
922 "qsortvec".
923
925 Copyright (C) Tuomas J. Lukka 1997 (lukka@husc.harvard.edu).
926 Contributions by Christian Soeller (c.soeller@auckland.ac.nz) and Karl
927 Glazebrook (kgb@aaoepp.aao.gov.au). All rights reserved. There is no
928 warranty. You are allowed to redistribute this software / documentation
929 under certain conditions. For details, see the file COPYING in the PDL
930 distribution. If this file is separated from the PDL distribution, the
931 copyright notice should be included in the file.
932perl v5.36.0 2022-07-22 Ufunc(3)