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Last change
on this file since e8e3e38 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:
2.0 KB
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| Rev | Line | |
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| [230f479] | 1 | /* jn.c |
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| 2 | * |
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| 3 | * Bessel function 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 | * int n; |
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| 10 | * double x, y, jn(); |
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| 11 | * |
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| 12 | * y = jn( 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 ratio of jn(x) to j0(x) is computed by backward |
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| 22 | * recurrence. First the ratio jn/jn-1 is found by a |
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| 23 | * continued fraction expansion. Then the recurrence |
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| 24 | * relating successive orders is applied until j0 or j1 is |
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| 25 | * reached. |
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| 26 | * |
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| 27 | * If n = 0 or 1 the routine for j0 or j1 is called |
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| 28 | * directly. |
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| 29 | * |
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| 30 | * |
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| 31 | * |
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| 32 | * ACCURACY: |
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| 33 | * |
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| 34 | * Absolute error: |
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| 35 | * arithmetic range # trials peak rms |
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| 36 | * DEC 0, 30 5500 6.9e-17 9.3e-18 |
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| 37 | * IEEE 0, 30 5000 4.4e-16 7.9e-17 |
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| 38 | * |
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| 39 | * |
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| 40 | * Not suitable for large n or x. Use jv() instead. |
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| 41 | * |
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| 42 | */ |
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| 43 | |
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| 44 | /* jn.c |
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| 45 | Cephes Math Library Release 2.8: June, 2000 |
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| 46 | Copyright 1984, 1987, 2000 by Stephen L. Moshier |
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| 47 | */ |
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| 48 | #include "mconf.h" |
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| 49 | #ifdef ANSIPROT |
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| 50 | extern double fabs ( double ); |
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| 51 | extern double j0 ( double ); |
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| 52 | extern double j1 ( double ); |
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| 53 | #else |
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| 54 | double fabs(), j0(), j1(); |
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| 55 | #endif |
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| 56 | extern double MACHEP; |
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| 57 | |
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| 58 | double jn( n, x ) |
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| 59 | int n; |
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| 60 | double x; |
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| 61 | { |
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| 62 | double pkm2, pkm1, pk, xk, r, ans; |
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| 63 | int k, sign; |
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| 64 | |
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| 65 | if( n < 0 ) |
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| 66 | { |
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| 67 | n = -n; |
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| 68 | if( (n & 1) == 0 ) /* -1**n */ |
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| 69 | sign = 1; |
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| 70 | else |
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| 71 | sign = -1; |
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| 72 | } |
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| 73 | else |
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| 74 | sign = 1; |
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| 75 | |
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| 76 | if( x < 0.0 ) |
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| 77 | { |
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| 78 | if( n & 1 ) |
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| 79 | sign = -sign; |
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| 80 | x = -x; |
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| 81 | } |
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| 82 | |
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| 83 | if( n == 0 ) |
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| 84 | return( sign * j0(x) ); |
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| 85 | if( n == 1 ) |
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| 86 | return( sign * j1(x) ); |
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| 87 | if( n == 2 ) |
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| 88 | return( sign * (2.0 * j1(x) / x - j0(x)) ); |
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| 89 | |
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| 90 | if( x < MACHEP ) |
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| 91 | return( 0.0 ); |
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| 92 | |
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| 93 | /* continued fraction */ |
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| 94 | #ifdef DEC |
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| 95 | k = 56; |
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| 96 | #else |
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| 97 | k = 53; |
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| 98 | #endif |
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| 99 | |
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| 100 | pk = 2 * (n + k); |
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| 101 | ans = pk; |
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| 102 | xk = x * x; |
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| 103 | |
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| 104 | do |
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| 105 | { |
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| 106 | pk -= 2.0; |
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| 107 | ans = pk - (xk/ans); |
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| 108 | } |
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| 109 | while( --k > 0 ); |
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| 110 | ans = x/ans; |
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| 111 | |
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| 112 | /* backward recurrence */ |
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| 113 | |
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| 114 | pk = 1.0; |
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| 115 | pkm1 = 1.0/ans; |
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| 116 | k = n-1; |
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| 117 | r = 2 * k; |
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| 118 | |
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| 119 | do |
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| 120 | { |
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| 121 | pkm2 = (pkm1 * r - pk * x) / x; |
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| 122 | pk = pkm1; |
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| 123 | pkm1 = pkm2; |
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| 124 | r -= 2.0; |
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| 125 | } |
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| 126 | while( --k > 0 ); |
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| 127 | |
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| 128 | if( fabs(pk) > fabs(pkm1) ) |
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| 129 | ans = j1(x)/pk; |
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| 130 | else |
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| 131 | ans = j0(x)/pkm1; |
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| 132 | return( sign * ans ); |
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| 133 | } |
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