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12 RANDLIB |
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13 |
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14 Library of Fortran Routines for Random Number Generation |
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17 Version 1.3 -- August, 1997 |
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22 README |
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23 |
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30 |
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31 Compiled and Written by: |
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32 |
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33 Barry W. Brown |
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34 James Lovato |
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35 Kathy Russell |
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36 John Venier |
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46 Department of Biomathematics, Box 237 |
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47 The University of Texas, M.D. Anderson Cancer Center |
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48 1515 Holcombe Boulevard |
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49 Houston, TX 77030 |
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50 |
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51 |
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52 This work was supported by grant CA-16672 from the National Cancer Institute. |
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53 |
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54 |
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55 |
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56 THANKS TO OUR SUPPORTERS |
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57 |
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58 This work was supported in part by grant CA-16672 from the National |
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59 Cancer Institute. We are grateful to Larry and Pat McNeil of Corpus |
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60 Cristi for their generous support. Some equipment used in this effort |
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61 was provided by IBM as part of a cooperative study agreement; we thank |
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62 them. |
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63 |
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64 |
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65 SUMMARY OF RANDLIB |
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66 |
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67 The bottom level routines provide 32 virtual random number generators. |
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68 Each generator can provide 1,048,576 blocks of numbers, and each block |
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69 is of length 1,073,741,824. Any generator can be set to the beginning |
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70 or end of the current block or to its starting value. Packaging is |
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71 provided so that if these capabilities are not needed, a single |
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72 generator with period 2.3 X 10^18 is seen. |
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73 |
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74 Using this base, routines are provided that return: |
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75 (1) Beta random deviates |
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76 (2) Chi-square random deviates |
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77 (3) Exponential random deviates |
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78 (4) F random deviates |
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79 (5) Gamma random deviates |
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80 (6) Multivariate normal random deviates (mean and covariance |
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81 matrix specified) |
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82 (7) Noncentral chi-square random deviates |
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83 (8) Noncentral F random deviates |
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84 (9) Univariate normal random deviates |
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85 (10) Random permutations of an integer array |
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86 (11) Real uniform random deviates between specified limits |
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87 (12) Binomial random deviates |
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88 (13) Negative Binomial random deviates |
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89 (14) Multinomial random deviates |
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90 (15) Poisson random deviates |
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91 (16) Integer uniform deviates between specified limits |
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92 (17) Seeds for the random number generator calculated from a |
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93 character string |
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94 |
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95 INSTALLATION |
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96 |
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97 Directory src contains the Fortran source. The Fortran code from this |
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98 directory should be compiled and placed in a library. Directory test |
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99 contains three test programs for this code. |
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100 |
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101 |
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102 |
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103 |
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104 |
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105 |
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106 DOCUMENTATION |
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107 |
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108 Documentation is on directory doc on the distribution. All of the |
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109 documentation is in the form of character (ASCII) files. An |
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110 explanation of the concepts involved in the base generator and details |
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111 of its implementation are contained in Basegen.doc. A summary of all |
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112 of the available routines is contained in randlib.chs (chs is an |
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113 abbreviation of 'cheat sheet'). The 'chs' file will probably be the |
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114 reference to randlib that is primarily used. The file, randlib.fdoc, |
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115 contains all comments heading each routine. There is somewhat more |
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116 information in 'fdoc' than 'chs', but the additional information |
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117 consists primarily of references to the literature. |
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118 |
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119 |
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120 |
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121 SOURCES |
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122 |
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123 The following routines, which were written by others and lightly |
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124 modified for consistency in packaging, are included in RANDLIB. |
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125 |
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126 Bottom Level Routines |
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127 |
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128 These routines are a transliteration of the Pascal in the reference to |
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129 Fortran. |
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130 |
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131 L'Ecuyer, P. and Cote, S. "Implementing a Random Number Package with |
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132 Splitting Facilities." ACM Transactions on Mathematical Software, |
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133 17:98-111 (1991) |
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134 |
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135 Exponential |
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136 |
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137 This code was obtained from Netlib. |
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138 |
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139 Ahrens, J.H. and Dieter, U. Computer Methods for Sampling From the |
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140 Exponential and Normal Distributions. Comm. ACM, 15,10 (Oct. 1972), |
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141 873 - 882. |
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142 |
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143 Gamma |
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144 |
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145 (Case R >= 1.0) |
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146 |
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147 Ahrens, J.H. and Dieter, U. Generating Gamma Variates by a Modified |
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148 Rejection Technique. Comm. ACM, 25,1 (Jan. 1982), 47 - 54. |
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149 Algorithm GD |
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150 |
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151 (Case 0.0 <= R <= 1.0) |
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152 |
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153 Ahrens, J.H. and Dieter, U. Computer Methods for Sampling from Gamma, |
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154 Beta, Poisson and Binomial Distributions. Computing, 12 (1974), |
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155 223-246. Adaptation of algorithm GS. |
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156 |
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157 |
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158 |
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159 |
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160 |
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161 |
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162 Normal |
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163 |
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164 This code was obtained from netlib. |
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165 |
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166 Ahrens, J.H. and Dieter, U. Extensions of Forsythe's Method for |
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167 Random Sampling from the Normal Distribution. Math. Comput., 27,124 |
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168 (Oct. 1973), 927 - 937. |
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169 |
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170 Binomial |
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171 |
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172 This code was kindly sent me by Dr. Kachitvichyanukul. |
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173 |
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174 Kachitvichyanukul, V. and Schmeiser, B. W. Binomial Random Variate |
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175 Generation. Communications of the ACM, 31, 2 (February, 1988) 216. |
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176 |
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177 |
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178 Poisson |
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179 |
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180 This code was obtained from netlib. |
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181 |
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182 Ahrens, J.H. and Dieter, U. Computer Generation of Poisson Deviates |
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183 From Modified Normal Distributions. ACM Trans. Math. Software, 8, 2 |
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184 (June 1982),163-179 |
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185 |
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186 Beta |
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187 |
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188 This code was written by us following the recipe in the following. |
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189 |
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190 R. C. H. Cheng Generating Beta Variables with Nonintegral Shape |
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191 Parameters. Communications of the ACM, 21:317-322 (1978) (Algorithms |
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192 BB and BC) |
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193 |
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194 Linpack |
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195 |
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196 Routines SPOFA and SDOT are used to perform the Cholesky decomposition |
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197 of the covariance matrix in SETGMN (used for the generation of |
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198 multivariate normal deviates). |
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199 |
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200 Dongarra, J. J., Moler, C. B., Bunch, J. R. and Stewart, G. W. |
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201 Linpack User's Guide. SIAM Press, Philadelphia. (1979) |
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202 |
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203 |
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204 |
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205 |
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206 LEGALITIES |
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207 |
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208 Code that appeared in an ACM publication is subject to their |
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209 algorithms policy: |
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210 |
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211 Submittal of an algorithm for publication in one of the ACM |
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212 Transactions implies that unrestricted use of the algorithm within a |
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213 computer is permissible. General permission to copy and distribute |
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214 the algorithm without fee is granted provided that the copies are not |
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215 made or distributed for direct commercial advantage. The ACM |
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216 copyright notice and the title of the publication and its date appear, |
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217 and notice is given that copying is by permission of the Association |
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218 for Computing Machinery. To copy otherwise, or to republish, requires |
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219 a fee and/or specific permission. |
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220 |
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221 Krogh, F. Algorithms Policy. ACM Tran. Math. Softw. 13(1987), |
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222 183-186. |
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223 |
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224 We place the Randlib code that we have written in the public domain. |
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225 |
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226 NO WARRANTY |
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227 |
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228 WE PROVIDE ABSOLUTELY NO WARRANTY OF ANY KIND EITHER EXPRESSED OR |
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229 IMPLIED, INCLUDING BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF |
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230 MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK |
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231 AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD |
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232 THIS PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY |
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233 SERVICING, REPAIR OR CORRECTION. |
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234 |
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235 IN NO EVENT SHALL THE UNIVERSITY OF TEXAS OR ANY OF ITS COMPONENT |
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236 INSTITUTIONS INCLUDING M. D. ANDERSON HOSPITAL BE LIABLE TO YOU FOR |
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237 DAMAGES, INCLUDING ANY LOST PROFITS, LOST MONIES, OR OTHER SPECIAL, |
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238 INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR |
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239 INABILITY TO USE (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA OR |
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240 ITS ANALYSIS BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY THIRD |
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241 PARTIES) THE PROGRAM. |
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242 |
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243 (Above NO WARRANTY modified from the GNU NO WARRANTY statement.) |
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244 |
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245 |
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246 |
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247 WHAT'S NEW IN VERSION 1.1? |
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248 |
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249 |
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250 Random number generation for the Negative Binomial and Multinomial |
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251 distributions has been included. |
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252 |
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253 Two errors in the code which generates random numbers from the Gamma |
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254 distribution were fixed. |
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255 |
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256 |
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257 WHAT'S NEW IN VERSION 1.2? |
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258 |
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259 We changed the name of the package from 'ranlib' to 'randlib'. This |
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260 was done so that we can determine who archives it. 'ranlib' is the |
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261 name of a Unix utility which produces many spurious hits on a web |
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262 search engine. |
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263 |
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264 |
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265 The linpack routines are now housed in the /src directory. |
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266 |
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267 In several routines, some variables were given an explicit SAVE |
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268 attribute and some dummy initial values were changed to prevent |
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269 potential errors. |
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270 'genbet.f' 'ignbin.f' 'ignpoi.f' 'phrtsd.f' 'sexpo.f' 'sgamma.f' |
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271 'snorm.f' |
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272 |
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273 In several routines, argument checking was implemented; the code now |
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274 breaks if inappropriate values are passed to it. |
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275 'genbet.f' A and B must be >= 1.0E-37 instead of 0.0 |
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276 'genexp.f' AV must be >= 0.0 |
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277 'gengam.f' A and R both must be > 0.0 |
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278 'gennor.f' SD must be >= 0.0 |
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279 'ignbin.f' N must be >= 0, and 0.0 <= PP <= 1.0. |
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280 'ignnbn.f' N must be > 0, 0.0 < P < 1.0 (previously allowed N = 0) |
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281 'ignpoi.f' MU must be >= 0.0 |
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282 |
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283 For the Non-Central Chi-Squared and Non-Central F distributions, the |
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284 case DF = 1.0 (DFN = 1.0 for the F) is now allowed. |
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285 'gennch.f' 'gennf.f' |
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286 |
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287 Wherever possible, the user-accessible code now calls the base |
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288 generators directly. This means improved performance and fewer |
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289 dependencies, but the routines should work exactly as before from the |
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290 user's point of view. |
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291 'genchi.f' 'genf.f' 'gennch.f' 'gennf.f' 'ignnbn.f' |
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292 |
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293 Many minor modifications have been made which should make the code |
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294 more robust, without changing how the code is used. |
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295 'genbet.f' 'gengam.f' 'ignpoi.f' 'ignuin.f' 'sgamma.f' 'tstmid.f' |
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296 |
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297 Finally, five distributions have been added to the mid-level tester, |
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298 which test the Exponential, Gamma, Multinomial, Negative Binomial, and |
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299 Normal distributions. |
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300 'tstmid.f' |
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301 |
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302 |
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303 |
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304 |
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305 WHAT'S NOT NEW IN VERSION 1.2 ? |
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306 |
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307 No calling sequences have changed. |
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308 |
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309 WHAT'S NEW IN VERSION 1.3? |
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310 |
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311 The calling sequence of SETGMN has been changed! We added an argument |
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312 (INTEGER LDCOVM) representing the leading actual dimension of COVM, to |
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313 allow the user to use this routine in the case that COVM is contained |
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314 in a larger array. This change also makes the routine more compatible |
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315 with LINPACK routines. See the following files for details: |
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316 'setgmn.f' in the /src directory, and 'randlib.fdoc' and 'randlib.chs' |
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317 in the /doc directory. |
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318 |
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319 Briefly, the declaration of SETGMN has been changed |
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320 from: |
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321 SUBROUTINE setgmn(meanv,covm,p,parm) |
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322 to: |
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323 SUBROUTINE setgmn(meanv,covm,ldcovm,p,parm) |
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324 |
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325 The program 'tstgmn.f' (in the /test directory) was changed to reflect |
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326 the change in the calling sequence of SETGMN. |
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327 |
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328 'randlib.fdoc' and 'randlib.chs' in the /doc directory were changed to |
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329 relect the change in the calling sequence of SETGMN. |
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330 |
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331 Minor changes were made in two routines ('sgamma.f' and 'sexpo.f') to |
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332 fix unusual bugs. |
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333 |
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334 The protection from overflow in deviate generation in two routines |
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335 ('genf.f' and 'gennf.f') was changed to prevent a constant from |
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336 underflowing at compile time. |
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337 |
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338 WHAT'S NOT NEW IN VERSION 1.3 ? |
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339 |
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340 No calling sequences (other than SETGMN) have changed. |
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341 |
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342 MANY THANKS |
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343 |
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344 The authors would like to thank the many users who have reported bugs |
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345 and suggested improvements; Randlib would not be the same today |
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346 without them. We heartily encourage others to join them. |
