1Math(3)               User Contributed Perl Documentation              Math(3)
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NAME

6       PDL::Math - extended mathematical operations and special functions
7

SYNOPSIS

9        use PDL::Math;
10
11        use PDL::Graphics::TriD;
12        imag3d [SURF2D,bessj0(rvals(zeroes(50,50))/2)];
13

DESCRIPTION

15       This module extends PDL with more advanced mathematical functions than
16       provided by standard Perl.
17
18       All the functions have one input pdl, and one output, unless otherwise
19       stated.
20
21       Many of the functions are linked from the system maths library or the
22       Cephes maths library (determined when PDL is compiled); a few are
23       implemented entirely in PDL.
24

FUNCTIONS

26   acos
27         Signature: (a(); [o]b())
28
29       The usual trigonometric function. Works inplace.
30
31       acos processes bad values.  It will set the bad-value flag of all
32       output piddles if the flag is set for any of the input piddles.
33
34   asin
35         Signature: (a(); [o]b())
36
37       The usual trigonometric function. Works inplace.
38
39       asin processes bad values.  It will set the bad-value flag of all
40       output piddles if the flag is set for any of the input piddles.
41
42   atan
43         Signature: (a(); [o]b())
44
45       The usual trigonometric function. Works inplace.
46
47       atan processes bad values.  It will set the bad-value flag of all
48       output piddles if the flag is set for any of the input piddles.
49
50   cosh
51         Signature: (a(); [o]b())
52
53       The standard hyperbolic function. Works inplace.
54
55       cosh processes bad values.  It will set the bad-value flag of all
56       output piddles if the flag is set for any of the input piddles.
57
58   sinh
59         Signature: (a(); [o]b())
60
61       The standard hyperbolic function. Works inplace.
62
63       sinh processes bad values.  It will set the bad-value flag of all
64       output piddles if the flag is set for any of the input piddles.
65
66   tan
67         Signature: (a(); [o]b())
68
69       The usual trigonometric function. Works inplace.
70
71       tan processes bad values.  It will set the bad-value flag of all output
72       piddles if the flag is set for any of the input piddles.
73
74   tanh
75         Signature: (a(); [o]b())
76
77       The standard hyperbolic function. Works inplace.
78
79       tanh processes bad values.  It will set the bad-value flag of all
80       output piddles if the flag is set for any of the input piddles.
81
82   ceil
83         Signature: (a(); [o]b())
84
85       Round to integer values in floating-point format. Works inplace.
86
87       ceil processes bad values.  It will set the bad-value flag of all
88       output piddles if the flag is set for any of the input piddles.
89
90   floor
91         Signature: (a(); [o]b())
92
93       Round to integer values in floating-point format. Works inplace.
94
95       floor processes bad values.  It will set the bad-value flag of all
96       output piddles if the flag is set for any of the input piddles.
97
98   rint
99         Signature: (a(); [o]b())
100
101       Round to integer values in floating-point format.
102
103       rint uses the 'round half to even' rounding method (also known as
104       banker's rounding).  Half-integers are rounded to the nearest even
105       number. This avoids a slight statistical bias inherent in always
106       rounding half-integers up or away from zero.
107
108       If you are looking to round half-integers up (regardless of sign), try
109       "floor($x+0.5)".  If you want to round half-integers away from zero,
110       try "floor(abs($x)+0.5)*($x<=>0)". Works inplace.
111
112       rint processes bad values.  It will set the bad-value flag of all
113       output piddles if the flag is set for any of the input piddles.
114
115   pow
116         Signature: (a(); b(); [o]c())
117
118       Synonym for `**'. Works inplace.
119
120       pow processes bad values.  It will set the bad-value flag of all output
121       piddles if the flag is set for any of the input piddles.
122
123   acosh
124         Signature: (a(); [o]b())
125
126       The standard hyperbolic function. Works inplace.
127
128       acosh processes bad values.  It will set the bad-value flag of all
129       output piddles if the flag is set for any of the input piddles.
130
131   asinh
132         Signature: (a(); [o]b())
133
134       The standard hyperbolic function. Works inplace.
135
136       asinh processes bad values.  It will set the bad-value flag of all
137       output piddles if the flag is set for any of the input piddles.
138
139   atanh
140         Signature: (a(); [o]b())
141
142       The standard hyperbolic function. Works inplace.
143
144       atanh processes bad values.  It will set the bad-value flag of all
145       output piddles if the flag is set for any of the input piddles.
146
147   erf
148         Signature: (a(); [o]b())
149
150       The error function. Works inplace.
151
152       erf processes bad values.  It will set the bad-value flag of all output
153       piddles if the flag is set for any of the input piddles.
154
155   erfc
156         Signature: (a(); [o]b())
157
158       The complement of the error function. Works inplace.
159
160       erfc processes bad values.  It will set the bad-value flag of all
161       output piddles if the flag is set for any of the input piddles.
162
163   bessj0
164         Signature: (a(); [o]b())
165
166       The regular Bessel function of the first kind, J_n Works inplace.
167
168       bessj0 processes bad values.  It will set the bad-value flag of all
169       output piddles if the flag is set for any of the input piddles.
170
171   bessj1
172         Signature: (a(); [o]b())
173
174       The regular Bessel function of the first kind, J_n Works inplace.
175
176       bessj1 processes bad values.  It will set the bad-value flag of all
177       output piddles if the flag is set for any of the input piddles.
178
179   bessy0
180         Signature: (a(); [o]b())
181
182       The regular Bessel function of the second kind, Y_n. Works inplace.
183
184       bessy0 processes bad values.  It will set the bad-value flag of all
185       output piddles if the flag is set for any of the input piddles.
186
187   bessy1
188         Signature: (a(); [o]b())
189
190       The regular Bessel function of the second kind, Y_n. Works inplace.
191
192       bessy1 processes bad values.  It will set the bad-value flag of all
193       output piddles if the flag is set for any of the input piddles.
194
195   bessjn
196         Signature: (a(); int n(); [o]b())
197
198       The regular Bessel function of the first kind, J_n .  This takes a
199       second int argument which gives the order of the function required.
200        Works inplace.
201
202       bessjn processes bad values.  It will set the bad-value flag of all
203       output piddles if the flag is set for any of the input piddles.
204
205   bessyn
206         Signature: (a(); int n(); [o]b())
207
208       The regular Bessel function of the first kind, Y_n .  This takes a
209       second int argument which gives the order of the function required.
210        Works inplace.
211
212       bessyn processes bad values.  It will set the bad-value flag of all
213       output piddles if the flag is set for any of the input piddles.
214
215   lgamma
216         Signature: (a(); [o]b(); int[o]s())
217
218       log gamma function
219
220       This returns 2 piddles -- the first set gives the log(gamma) values,
221       while the second set, of integer values, gives the sign of the gamma
222       function.  This is useful for determining factorials, amongst other
223       things.
224
225       lgamma processes bad values.  It will set the bad-value flag of all
226       output piddles if the flag is set for any of the input piddles.
227
228   badmask
229         Signature: (a(); b(); [o]c())
230
231       Clears all "infs" and "nans" in $a to the corresponding value in $b.
232
233       badmask can be run with $x inplace:
234
235         badmask($x->inplace,0);
236         $x->inplace->badmask(0);
237
238       If bad values are present, these are also cleared.
239
240   isfinite
241         Signature: (a(); int [o]mask())
242
243       Sets $mask true if $a is not a "NaN" or "inf" (either positive or
244       negative). Works inplace.
245
246       Bad values are treated as "NaN" or "inf".
247
248   erfi
249         Signature: (a(); [o]b())
250
251       The inverse of the error function. Works inplace.
252
253       erfi processes bad values.  It will set the bad-value flag of all
254       output piddles if the flag is set for any of the input piddles.
255
256   ndtri
257         Signature: (a(); [o]b())
258
259       The value for which the area under the Gaussian probability density
260       function (integrated from minus infinity) is equal to the argument (cf
261       erfi). Works inplace.
262
263       ndtri processes bad values.  It will set the bad-value flag of all
264       output piddles if the flag is set for any of the input piddles.
265
266   polyroots
267         Signature: (cr(n); ci(n); [o]rr(m); [o]ri(m))
268
269       Complex roots of a complex polynomial, given coefficients in order of
270       decreasing powers.
271
272        ($rr, $ri) = polyroots($cr, $ci);
273
274       polyroots does not process bad values.  It will set the bad-value flag
275       of all output piddles if the flag is set for any of the input piddles.
276

BUGS

278       Hasn't been tested on all platforms to ensure Cephes versions are
279       picked up automatically and used correctly.
280

AUTHOR

282       Copyright (C) R.J.R. Williams 1997 (rjrw@ast.leeds.ac.uk), Karl
283       Glazebrook (kgb@aaoepp.aao.gov.au) and Tuomas J. Lukka
284       (Tuomas.Lukka@helsinki.fi).  Portions (C) Craig DeForest 2002
285       (deforest@boulder.swri.edu).
286
287       All rights reserved. There is no warranty. You are allowed to
288       redistribute this software / documentation under certain conditions.
289       For details, see the file COPYING in the PDL distribution. If this file
290       is separated from the PDL distribution, the PDL copyright notice should
291       be included in the file.
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295perl v5.32.0                      2020-09-17                           Math(3)