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Last change
on this file since 6bd3a8d1 was
79492222,
checked in by krzywon, 10 years ago
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Changed the file and folder names to remove all SANS references.
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-
Property mode set to
100644
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File size:
1.8 KB
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| Rev | Line | |
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| [230f479] | 1 | /* yn.c |
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| 2 | * |
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| 3 | * Bessel function of second kind of integer order |
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| 4 | * |
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| 5 | * |
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| 6 | * |
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| 7 | * SYNOPSIS: |
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| 8 | * |
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| 9 | * double x, y, yn(); |
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| 10 | * int n; |
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| 11 | * |
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| 12 | * y = yn( n, x ); |
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| 13 | * |
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| 14 | * |
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| 15 | * |
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| 16 | * DESCRIPTION: |
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| 17 | * |
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| 18 | * Returns Bessel function of order n, where n is a |
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| 19 | * (possibly negative) integer. |
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| 20 | * |
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| 21 | * The function is evaluated by forward recurrence on |
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| 22 | * n, starting with values computed by the routines |
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| 23 | * y0() and y1(). |
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| 24 | * |
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| 25 | * If n = 0 or 1 the routine for y0 or y1 is called |
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| 26 | * directly. |
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| 27 | * |
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| 28 | * |
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| 29 | * |
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| 30 | * ACCURACY: |
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| 31 | * |
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| 32 | * |
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| 33 | * Absolute error, except relative |
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| 34 | * when y > 1: |
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| 35 | * arithmetic domain # trials peak rms |
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| 36 | * DEC 0, 30 2200 2.9e-16 5.3e-17 |
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| 37 | * IEEE 0, 30 30000 3.4e-15 4.3e-16 |
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| 38 | * |
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| 39 | * |
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| 40 | * ERROR MESSAGES: |
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| 41 | * |
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| 42 | * message condition value returned |
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| 43 | * yn singularity x = 0 MAXNUM |
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| 44 | * yn overflow MAXNUM |
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| 45 | * |
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| 46 | * Spot checked against tables for x, n between 0 and 100. |
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| 47 | * |
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| 48 | */ |
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| 49 | |
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| 50 | /* |
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| 51 | Cephes Math Library Release 2.8: June, 2000 |
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| 52 | Copyright 1984, 1987, 2000 by Stephen L. Moshier |
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| 53 | */ |
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| 54 | |
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| 55 | #include "mconf.h" |
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| 56 | #ifdef ANSIPROT |
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| 57 | extern double y0 ( double ); |
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| 58 | extern double y1 ( double ); |
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| 59 | extern double log ( double ); |
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| 60 | #else |
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| 61 | double y0(), y1(), log(); |
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| 62 | #endif |
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| 63 | extern double MAXNUM, MAXLOG; |
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| 64 | |
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| 65 | double yn( n, x ) |
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| 66 | int n; |
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| 67 | double x; |
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| 68 | { |
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| 69 | double an, anm1, anm2, r; |
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| 70 | int k, sign; |
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| 71 | |
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| 72 | if( n < 0 ) |
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| 73 | { |
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| 74 | n = -n; |
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| 75 | if( (n & 1) == 0 ) /* -1**n */ |
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| 76 | sign = 1; |
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| 77 | else |
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| 78 | sign = -1; |
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| 79 | } |
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| 80 | else |
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| 81 | sign = 1; |
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| 82 | |
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| 83 | |
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| 84 | if( n == 0 ) |
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| 85 | return( sign * y0(x) ); |
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| 86 | if( n == 1 ) |
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| 87 | return( sign * y1(x) ); |
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| 88 | |
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| 89 | /* test for overflow */ |
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| 90 | if( x <= 0.0 ) |
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| 91 | { |
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| 92 | mtherr( "yn", SING ); |
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| 93 | return( -MAXNUM ); |
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| 94 | } |
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| 95 | |
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| 96 | /* forward recurrence on n */ |
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| 97 | |
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| 98 | anm2 = y0(x); |
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| 99 | anm1 = y1(x); |
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| 100 | k = 1; |
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| 101 | r = 2 * k; |
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| 102 | do |
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| 103 | { |
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| 104 | an = r * anm1 / x - anm2; |
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| 105 | anm2 = anm1; |
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| 106 | anm1 = an; |
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| 107 | r += 2.0; |
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| 108 | ++k; |
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| 109 | } |
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| 110 | while( k < n ); |
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| 111 | |
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| 112 | |
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| 113 | return( sign * an ); |
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| 114 | } |
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