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annotate liboctave/cruft/quadpack/qagi.f @ 20595:c1a6c31ac29a

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eliminate more simple uses of error_state * ov-classdef.cc: Eliminate simple uses of error_state.
author John W. Eaton <jwe@octave.org>
date Tue, 06 Oct 2015 00:20:02 -0400
parents 648dabbb4c6b
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
7793
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1 subroutine qagi(f,bound,inf,epsabs,epsrel,result,abserr,neval,
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2 * ier,limit,lenw,last,iwork,work)
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3 c***begin prologue qagi
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4 c***date written 800101 (yymmdd)
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5 c***revision date 830518 (yymmdd)
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6 c***category no. h2a3a1,h2a4a1
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7 c***keywords automatic integrator, infinite intervals,
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8 c general-purpose, transformation, extrapolation,
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9 c globally adaptive
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10 c***author piessens,robert,appl. math. & progr. div. - k.u.leuven
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11 c de doncker,elise,appl. math. & progr. div. -k.u.leuven
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12 c***purpose the routine calculates an approximation result to a given
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13 c integral i = integral of f over (bound,+infinity)
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14 c or i = integral of f over (-infinity,bound)
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15 c or i = integral of f over (-infinity,+infinity)
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16 c hopefully satisfying following claim for accuracy
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17 c abs(i-result).le.max(epsabs,epsrel*abs(i)).
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18 c***description
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19 c
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20 c integration over infinite intervals
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21 c standard fortran subroutine
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22 c
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23 c parameters
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24 c on entry
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25 c f - subroutine f(x,result) defining the integrand
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26 c function f(x). the actual name for f needs to be
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27 c declared e x t e r n a l in the driver program.
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28 c
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29 c bound - real
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30 c finite bound of integration range
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31 c (has no meaning if interval is doubly-infinite)
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32 c
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33 c inf - integer
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34 c indicating the kind of integration range involved
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35 c inf = 1 corresponds to (bound,+infinity),
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36 c inf = -1 to (-infinity,bound),
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37 c inf = 2 to (-infinity,+infinity).
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38 c
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39 c epsabs - real
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40 c absolute accuracy requested
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41 c epsrel - real
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42 c relative accuracy requested
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43 c if epsabs.le.0
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44 c and epsrel.lt.max(50*rel.mach.acc.,0.5d-28),
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45 c the routine will end with ier = 6.
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46 c
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47 c
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48 c on return
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49 c result - real
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50 c approximation to the integral
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51 c
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52 c abserr - real
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53 c estimate of the modulus of the absolute error,
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54 c which should equal or exceed abs(i-result)
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55 c
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56 c neval - integer
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57 c number of integrand evaluations
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58 c
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59 c ier - integer
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60 c ier = 0 normal and reliable termination of the
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61 c routine. it is assumed that the requested
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62 c accuracy has been achieved.
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63 c - ier.gt.0 abnormal termination of the routine. the
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64 c estimates for result and error are less
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65 c reliable. it is assumed that the requested
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66 c accuracy has not been achieved.
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67 c error messages
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68 c ier = 1 maximum number of subdivisions allowed
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69 c has been achieved. one can allow more
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70 c subdivisions by increasing the value of
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71 c limit (and taking the according dimension
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72 c adjustments into account). however, if
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73 c this yields no improvement it is advised
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74 c to analyze the integrand in order to
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75 c determine the integration difficulties. if
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76 c the position of a local difficulty can be
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77 c determined (e.g. singularity,
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78 c discontinuity within the interval) one
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79 c will probably gain from splitting up the
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80 c interval at this point and calling the
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81 c integrator on the subranges. if possible,
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82 c an appropriate special-purpose integrator
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83 c should be used, which is designed for
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84 c handling the type of difficulty involved.
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85 c = 2 the occurrence of roundoff error is
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86 c detected, which prevents the requested
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87 c tolerance from being achieved.
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88 c the error may be under-estimated.
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89 c = 3 extremely bad integrand behaviour occurs
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90 c at some points of the integration
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91 c interval.
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92 c = 4 the algorithm does not converge.
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93 c roundoff error is detected in the
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94 c extrapolation table.
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95 c it is assumed that the requested tolerance
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96 c cannot be achieved, and that the returned
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97 c result is the best which can be obtained.
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98 c = 5 the integral is probably divergent, or
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99 c slowly convergent. it must be noted that
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100 c divergence can occur with any other value
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101 c of ier.
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102 c = 6 the input is invalid, because
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103 c (epsabs.le.0 and
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104 c epsrel.lt.max(50*rel.mach.acc.,0.5d-28))
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105 c or limit.lt.1 or leniw.lt.limit*4.
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106 c result, abserr, neval, last are set to
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107 c zero. exept when limit or leniw is
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108 c invalid, iwork(1), work(limit*2+1) and
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109 c work(limit*3+1) are set to zero, work(1)
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110 c is set to a and work(limit+1) to b.
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111 c
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112 c dimensioning parameters
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113 c limit - integer
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114 c dimensioning parameter for iwork
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115 c limit determines the maximum number of subintervals
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116 c in the partition of the given integration interval
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117 c (a,b), limit.ge.1.
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118 c if limit.lt.1, the routine will end with ier = 6.
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119 c
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120 c lenw - integer
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121 c dimensioning parameter for work
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122 c lenw must be at least limit*4.
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123 c if lenw.lt.limit*4, the routine will end
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124 c with ier = 6.
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125 c
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126 c last - integer
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127 c on return, last equals the number of subintervals
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128 c produced in the subdivision process, which
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129 c determines the number of significant elements
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130 c actually in the work arrays.
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131 c
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132 c work arrays
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133 c iwork - integer
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134 c vector of dimension at least limit, the first
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135 c k elements of which contain pointers
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136 c to the error estimates over the subintervals,
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137 c such that work(limit*3+iwork(1)),... ,
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138 c work(limit*3+iwork(k)) form a decreasing
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139 c sequence, with k = last if last.le.(limit/2+2), and
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140 c k = limit+1-last otherwise
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141 c
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142 c work - real
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143 c vector of dimension at least lenw
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144 c on return
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145 c work(1), ..., work(last) contain the left
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146 c end points of the subintervals in the
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147 c partition of (a,b),
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148 c work(limit+1), ..., work(limit+last) contain
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149 c the right end points,
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150 c work(limit*2+1), ...,work(limit*2+last) contain the
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151 c integral approximations over the subintervals,
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152 c work(limit*3+1), ..., work(limit*3)
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153 c contain the error estimates.
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154 c***references (none)
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155 c***routines called qagie,xerror
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156 c***end prologue qagi
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157 c
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158 real abserr, epsabs,epsrel,result,work
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159 integer ier,iwork, lenw,limit,lvl,l1,l2,l3,neval
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160 c
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161 dimension iwork(limit),work(lenw)
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162 c
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163 external f
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164 c
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165 c check validity of limit and lenw.
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166 c
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167 c***first executable statement qagi
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168 ier = 6
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169 neval = 0
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170 last = 0
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171 result = 0.0e+00
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172 abserr = 0.0e+00
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173 if(limit.lt.1.or.lenw.lt.limit*4) go to 10
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174 c
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175 c prepare call for qagie.
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176 c
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177 l1 = limit+1
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178 l2 = limit+l1
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179 l3 = limit+l2
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180 c
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181 call qagie(f,bound,inf,epsabs,epsrel,limit,result,abserr,
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182 * neval,ier,work(1),work(l1),work(l2),work(l3),iwork,last)
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183 c
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184 c call error handler if necessary.
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185 c
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186 lvl = 0
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187 10 if(ier.eq.6) lvl = 1
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188 if(ier.ne.0) call xerror('abnormal return from qagi',26,ier,lvl)
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189 return
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190 end