1Ufunc(3) User Contributed Perl Documentation Ufunc(3)
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6 PDL::Ufunc - primitive ufunc operations for pdl
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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())
26 Project via product to N-1 dimensions
28 This function reduces the dimensionality of a piddle by one by taking
30 the product along the 1st dimension.
31 By using xchg etc. it is possible to use any dimension.
33 $a = prodover($b);
35 $spectrum = prodover $image->xchg(0,1)
37 dprodover
39 Signature: (a(n); double [o]b())
41 Project via product to N-1 dimensions
43 This function reduces the dimensionality of a piddle by one by taking
45 the product along the 1st dimension.
46 By using xchg etc. it is possible to use any dimension.
48 $a = dprodover($b);
50 $spectrum = dprodover $image->xchg(0,1)
52 Unlike prodover, the calculations are performed in double precision.
54 cumuprodover
56 Signature: (a(n); int+ [o]b(n))
58 Cumulative product
60 This function calculates the cumulative product along the 1st dimen‐
62 sion.
63 By using xchg etc. it is possible to use any dimension.
65 The sum is started so that the first element in the cumulative product
67 is the first element of the parameter.
68 $a = cumuprodover($b);
70 $spectrum = cumuprodover $image->xchg(0,1)
72 dcumuprodover
74 Signature: (a(n); double [o]b(n))
76 Cumulative product
78 This function calculates the cumulative product along the 1st dimen‐
80 sion.
81 By using xchg etc. it is possible to use any dimension.
83 The sum is started so that the first element in the cumulative product
85 is the first element of the parameter.
86 $a = cumuprodover($b);
88 $spectrum = cumuprodover $image->xchg(0,1)
90 Unlike cumuprodover, the calculations are performed in double preci‐
92 sion.
93 sumover
95 Signature: (a(n); int+ [o]b())
97 Project via sum to N-1 dimensions
99 This function reduces the dimensionality of a piddle by one by taking
101 the sum along the 1st dimension.
102 By using xchg etc. it is possible to use any dimension.
104 $a = sumover($b);
106 $spectrum = sumover $image->xchg(0,1)
108 dsumover
110 Signature: (a(n); double [o]b())
112 Project via sum to N-1 dimensions
114 This function reduces the dimensionality of a piddle by one by taking
116 the sum along the 1st dimension.
117 By using xchg etc. it is possible to use any dimension.
119 $a = dsumover($b);
121 $spectrum = dsumover $image->xchg(0,1)
123 Unlike sumover, the calculations are performed in double precision.
125 cumusumover
127 Signature: (a(n); int+ [o]b(n))
129 Cumulative sum
131 This function calculates the cumulative sum along the 1st dimension.
133 By using xchg etc. it is possible to use any dimension.
135 The sum is started so that the first element in the cumulative sum is
137 the first element of the parameter.
138 $a = cumusumover($b);
140 $spectrum = cumusumover $image->xchg(0,1)
142 dcumusumover
144 Signature: (a(n); double [o]b(n))
146 Cumulative sum
148 This function calculates the cumulative sum along the 1st dimension.
150 By using xchg etc. it is possible to use any dimension.
152 The sum is started so that the first element in the cumulative sum is
154 the first element of the parameter.
155 $a = cumusumover($b);
157 $spectrum = cumusumover $image->xchg(0,1)
159 Unlike cumusumover, the calculations are performed in double precision.
161 orover
163 Signature: (a(n); int+ [o]b())
165 Project via or to N-1 dimensions
167 This function reduces the dimensionality of a piddle by one by taking
169 the or along the 1st dimension.
170 By using xchg etc. it is possible to use any dimension.
172 $a = orover($b);
174 $spectrum = orover $image->xchg(0,1)
176 bandover
178 Signature: (a(n); int+ [o]b())
180 Project via bitwise and to N-1 dimensions
182 This function reduces the dimensionality of a piddle by one by taking
184 the bitwise and along the 1st dimension.
185 By using xchg etc. it is possible to use any dimension.
187 $a = bandover($b);
189 $spectrum = bandover $image->xchg(0,1)
191 borover
193 Signature: (a(n); int+ [o]b())
195 Project via bitwise or to N-1 dimensions
197 This function reduces the dimensionality of a piddle by one by taking
199 the bitwise or along the 1st dimension.
200 By using xchg etc. it is possible to use any dimension.
202 $a = borover($b);
204 $spectrum = borover $image->xchg(0,1)
206 zcover
208 Signature: (a(n); int+ [o]b())
210 Project via == 0 to N-1 dimensions
212 This function reduces the dimensionality of a piddle by one by taking
214 the == 0 along the 1st dimension.
215 By using xchg etc. it is possible to use any dimension.
217 $a = zcover($b);
219 $spectrum = zcover $image->xchg(0,1)
221 andover
223 Signature: (a(n); int+ [o]b())
225 Project via and to N-1 dimensions
227 This function reduces the dimensionality of a piddle by one by taking
229 the and along the 1st dimension.
230 By using xchg etc. it is possible to use any dimension.
232 $a = andover($b);
234 $spectrum = andover $image->xchg(0,1)
236 intover
238 Signature: (a(n); int+ [o]b())
240 Project via integral to N-1 dimensions
242 This function reduces the dimensionality of a piddle by one by taking
244 the integral along the 1st dimension.
245 By using xchg etc. it is possible to use any dimension.
247 $a = intover($b);
249 $spectrum = intover $image->xchg(0,1)
251 Notes:
253 For "n > 3", these are all "O(h^4)" (like Simpson's rule), but are
255 integrals between the end points assuming the pdl gives values just at
256 these centres: for such `functions', sumover is correct to O(h), but is
257 the natural (and correct) choice for binned data, of course.
258 average
260 Signature: (a(n); int+ [o]b())
262 Project via average to N-1 dimensions
264 This function reduces the dimensionality of a piddle by one by taking
266 the average along the 1st dimension.
267 By using xchg etc. it is possible to use any dimension.
269 $a = average($b);
271 $spectrum = average $image->xchg(0,1)
273 daverage
275 Signature: (a(n); double [o]b())
277 Project via average to N-1 dimensions
279 This function reduces the dimensionality of a piddle by one by taking
281 the average along the 1st dimension.
282 By using xchg etc. it is possible to use any dimension.
284 $a = daverage($b);
286 $spectrum = daverage $image->xchg(0,1)
288 Unlike average, the calculation is performed in double precision.
290 medover
292 Signature: (a(n); [o]b(); [t]tmp(n))
294 Project via median to N-1 dimensions
296 This function reduces the dimensionality of a piddle by one by taking
298 the median along the 1st dimension.
299 By using xchg etc. it is possible to use any dimension.
301 $a = medover($b);
303 $spectrum = medover $image->xchg(0,1)
305 oddmedover
307 Signature: (a(n); [o]b(); [t]tmp(n))
309 Project via oddmedian to N-1 dimensions
311 This function reduces the dimensionality of a piddle by one by taking
313 the oddmedian along the 1st dimension.
314 By using xchg etc. it is possible to use any dimension.
316 $a = oddmedover($b);
318 $spectrum = oddmedover $image->xchg(0,1)
320 The median is sometimes not a good choice as if the array has an even
322 number of elements it lies half-way between the two middle values -
323 thus it does not always correspond to a data value. The lower-odd
324 median is just the lower of these two values and so it ALWAYS sits on
325 an actual data value which is useful in some circumstances.
326 pctover
328 Signature: (a(n); p(); [o]b(); [t]tmp(n))
330 Project via percentile to N-1 dimensions
332 This function reduces the dimensionality of a piddle by one by finding
334 the specified percentile (p) along the 1st dimension. The specified
335 percentile must be between 0.0 and 1.0. When the specified percentile
336 falls between data points, the result is interpolated.
337 By using xchg etc. it is possible to use any dimension.
339 $a = pctover($b, $p);
341 $spectrum = pctover $image->xchg(0,1) $p
343 oddpctover
345 Signature: (a(n); p(); [o]b(); [t]tmp(n))
347 Project via percentile to N-1 dimensions
349 This function reduces the dimensionality of a piddle by one by finding
351 the specified percentile along the 1st dimension. The specified per‐
352 centile must be between 0.0 and 1.0. When the specified percentile
353 falls between two values, the nearest data value is the result.
354 By using xchg etc. it is possible to use any dimension.
356 $a = oddpctover($b, $p);
358 $spectrum = oddpctover $image->xchg(0,1) $p
360 pct
362 Return the specified percentile of all elements in a piddle. The speci‐
364 fied percentile (p) must be between 0.0 and 1.0. When the specified
365 percentile falls between data points, the result is interpolated.
366 $x = pct($data, $pct);
368 oddpct
370 Return the specified percentile of all elements in a piddle. The speci‐
372 fied percentile must be between 0.0 and 1.0. When the specified per‐
373 centile falls between two values, the nearest data value is the result.
374 $x = oddpct($data, $pct);
376 avg
378 Return the average of all elements in a piddle
380 $x = avg($data);
382 sum
384 Return the sum of all elements in a piddle
386 $x = sum($data);
388 prod
390 Return the product of all elements in a piddle
392 $x = prod($data);
394 davg
396 Return the average (in double precision) of all elements in a piddle
398 $x = davg($data);
400 dsum
402 Return the sum (in double precision) of all elements in a piddle
404 $x = dsum($data);
406 dprod
408 Return the product (in double precision) of all elements in a piddle
410 $x = dprod($data);
412 zcheck
414 Return the check for zero of all elements in a piddle
416 $x = zcheck($data);
418 and
420 Return the logical and of all elements in a piddle
422 $x = and($data);
424 band
426 Return the bitwise and of all elements in a piddle
428 $x = band($data);
430 or
432 Return the logical or of all elements in a piddle
434 $x = or($data);
436 bor
438 Return the bitwise or of all elements in a piddle
440 $x = bor($data);
442 min
444 Return the minimum of all elements in a piddle
446 $x = min($data);
448 max
450 Return the maximum of all elements in a piddle
452 $x = max($data);
454 median
456 Return the median of all elements in a piddle
458 $x = median($data);
460 oddmedian
462 Return the oddmedian of all elements in a piddle
464 $x = oddmedian($data);
466 any
468 Return true if any element in piddle set
470 Useful in conditional expressions:
472 if (any $a>15) { print "some values are greater than 15\n" }
474 all
476 Return true if all elements in piddle set
478 Useful in conditional expressions:
480 if (all $a>15) { print "all values are greater than 15\n" }
482 minmax
484 Returns an array with minimum and maximum values of a piddle.
486 ($mn, $mx) = minmax($pdl);
488 This routine does not thread over the dimensions of $pdl; it returns
490 the minimum and maximum values of the whole array. See minmaximum if
491 this is not what is required. The two values are returned as Perl
492 scalars similar to min/max.
493 perldl> $x = pdl [1,-2,3,5,0]
495 perldl> ($min, $max) = minmax($x);
496 perldl> p "$min $max\n";
497 -2 5
498 qsort
500 Signature: (a(n); [o]b(n))
502 Quicksort a vector into ascending order.
504 print qsort random(10);
506 qsorti
508 Signature: (a(n); int [o]indx(n))
510 Quicksort a vector and return index of elements in ascending order.
512 $ix = qsorti $a;
514 print $a->index($ix); # Sorted list
515 qsortvec
517 Signature: (a(n,m); [o]b(n,m))
519 Sort a list of vectors lexicographically.
521 The 0th dimension of the source piddle is dimension in the vector; the
523 1st dimension is list order. Higher dimensions are threaded over.
524 print qsortvec pdl([[1,2],[0,500],[2,3],[4,2],[3,4],[3,5]]);
526 [
527 [ 0 500]
528 [ 1 2]
529 [ 2 3]
530 [ 3 4]
531 [ 3 5]
532 [ 4 2]
533 ]
534 minimum
536 Signature: (a(n); [o]c())
538 Project via minimum to N-1 dimensions
540 This function reduces the dimensionality of a piddle by one by taking
542 the minimum along the 1st dimension.
543 By using xchg etc. it is possible to use any dimension.
545 $a = minimum($b);
547 $spectrum = minimum $image->xchg(0,1)
549 minimum_ind
551 Signature: (a(n); int [o] c())
553 Like minimum but returns the index rather than the value
555 minimum_n_ind
557 Signature: (a(n); int[o]c(m))
559 Returns the index of "m" minimum elements
561 maximum
563 Signature: (a(n); [o]c())
565 Project via maximum to N-1 dimensions
567 This function reduces the dimensionality of a piddle by one by taking
569 the maximum along the 1st dimension.
570 By using xchg etc. it is possible to use any dimension.
572 $a = maximum($b);
574 $spectrum = maximum $image->xchg(0,1)
576 maximum_ind
578 Signature: (a(n); int [o] c())
580 Like maximum but returns the index rather than the value
582 maximum_n_ind
584 Signature: (a(n); int[o]c(m))
586 Returns the index of "m" maximum elements
588 minmaximum
590 Signature: (a(n); [o]cmin(); [o] cmax(); int [o]cmin_ind(); int [o]cmax_ind())
592 Find minimum and maximum and their indices for a given piddle;
594 perldl> $a=pdl [[-2,3,4],[1,0,3]]
596 perldl> ($min, $max, $min_ind, $max_ind)=minmaximum($a)
597 perldl> p $min, $max, $min_ind, $max_ind
598 [-2 0] [4 3] [0 1] [2 2]
599 See also minmax, which clumps the piddle together.
601
603 Copyright (C) Tuomas J. Lukka 1997 (lukka@husc.harvard.edu). Contribu‐
604 tions by Christian Soeller (c.soeller@auckland.ac.nz) and Karl Glaze‐
605 brook (kgb@aaoepp.aao.gov.au). All rights reserved. There is no war‐
606 ranty. You are allowed to redistribute this software / documentation
607 under certain conditions. For details, see the file COPYING in the PDL
608 distribution. If this file is separated from the PDL distribution, the
609 copyright notice should be included in the file.
610perl v5.8.8 2006-12-02 Ufunc(3)