core_shell_microgelscostrafo411magnetic_modelrelease_v0.94release_v0.95ticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change
on this file since 3936ad3 was
3936ad3,
checked in by wojciech, 8 years ago
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Bessel functions from double-precison cephes has been added
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Property mode set to
100644
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File size:
1.8 KB
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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 | |
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49 | double jn( int n, double x ); |
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50 | #define MACHEP 1.11022302462515654042E-16 |
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51 | |
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52 | double jn( int n, double x ) |
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53 | { |
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54 | double pkm2, pkm1, pk, xk, r, ans; |
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55 | int k, sign; |
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56 | |
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57 | if( n < 0 ) |
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58 | { |
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59 | n = -n; |
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60 | if( (n & 1) == 0 ) /* -1**n */ |
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61 | sign = 1; |
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62 | else |
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63 | sign = -1; |
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64 | } |
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65 | else |
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66 | sign = 1; |
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67 | |
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68 | if( x < 0.0 ) |
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69 | { |
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70 | if( n & 1 ) |
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71 | sign = -sign; |
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72 | x = -x; |
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73 | } |
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74 | |
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75 | if( n == 0 ) |
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76 | return( sign * j0(x) ); |
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77 | if( n == 1 ) |
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78 | return( sign * j1(x) ); |
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79 | if( n == 2 ) |
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80 | return( sign * (2.0 * j1(x) / x - j0(x)) ); |
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81 | |
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82 | if( x < MACHEP ) |
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83 | return( 0.0 ); |
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84 | |
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85 | |
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86 | pk = 2 * (n + k); |
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87 | ans = pk; |
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88 | xk = x * x; |
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89 | |
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90 | do |
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91 | { |
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92 | pk -= 2.0; |
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93 | ans = pk - (xk/ans); |
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94 | } |
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95 | while( --k > 0 ); |
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96 | ans = x/ans; |
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97 | |
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98 | /* backward recurrence */ |
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99 | |
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100 | pk = 1.0; |
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101 | pkm1 = 1.0/ans; |
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102 | k = n-1; |
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103 | r = 2 * k; |
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104 | |
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105 | do |
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106 | { |
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107 | pkm2 = (pkm1 * r - pk * x) / x; |
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108 | pk = pkm1; |
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109 | pkm1 = pkm2; |
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110 | r -= 2.0; |
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111 | } |
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112 | while( --k > 0 ); |
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113 | |
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114 | if( fabs(pk) > fabs(pkm1) ) |
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115 | ans = j1(x)/pk; |
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116 | else |
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117 | ans = j0(x)/pkm1; |
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118 | return( sign * ans ); |
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119 | } |
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120 | |
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