Return the (weighted) merged variance and mean of a complex or real sample resulting from the merger of two separate (weighted) samples \(A\) and \(B\).
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Detailed Description

Return the (weighted) merged variance and mean of a complex or real sample resulting from the merger of two separate (weighted) samples \(A\) and \(B\).

See the documentation of pm_sampleVar and pm_sampleMean for more information and definition online updating of sample variance and mean.

Note: The input and output variances of this generic interface are all biased variances.
A biased variance can be readily unbiased by multiplying it with the appropriate bias-correction factors detailed in the documentation of pm_sampleVar.

Parameters

[out]	varMerged	: The output object of the same type and kind and rank and shape as `meanA`, containing the biased variance of the sample resulting form the merger of the two samples. (optional. If missing, the resulting merged variance will be written to the argument `varB`.)
[out]	meanMerged	: The output object of the same type and kind and rank and shape as `meanA`, containing the mean of the sample resulting form the merger of the two samples. (optional. If missing, the resulting merged mean will be written to the argument `meanB`.)
[in,out]	varB	: The input or input/output object of type `real` of the same kind and rank and shape as the input argument `meanA`, containing the biased variance of the second sample that must be merged with the first sample. If the input argument `varMerged` is missing, then `varB` contains the updated biased variance of the merged sample on return. Otherwise, the contents of `varB` remain intact upon return.
[in,out]	meanB	: The input or input/output object of the same type and kind and rank and shape as the input argument `meanA`, containing the mean of the second sample that must be merged with the first sample. If the input argument `meanMerged` is missing, then `meanB` contains the updated mean of the merged sample on return. Otherwise, the contents of `meanB` remain intact upon return.
[in]	varA	: The input scalar or `contiguous` vector of shape `(1:ndim)` of type `real` of the same kind as the kind of the input argument `meanA`, containing the biased variance of the first sample that must be merged with the second sample.
[in]	meanA	: The input scalar or `contiguous` vector of shape `(1:ndim)` of, type `complex` of kind any supported by the processor (e.g., CK, CK32, CK64, or CK128), type `real` of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128), containing the mean of the first sample that must be merged with the second sample.
[in]	fracA	: The input scalar of type `real` of the same kind as kind of `varA`, containing the ratio of the sum of the weights of all points in sample \(A\) to sum of weights of all points in the merged sample. If the sample is unweighted, then `fracA` is simply `size(sampleA) / (size(sampleA) + size(sampleB))`.

Possible calling interfaces ⛓

: use pm_sampleVar, only: setVarMeanMerged

! univariate sample

call setVarMeanMerged(varB, meanB, varA, meanA, fracA)

call setVarMeanMerged(varMerged, meanMerged, varB, meanB, varA, meanA, fracA)

! ndim-dimensional sample

call setVarMeanMerged(varB(1:ndim), varA(1:ndim), meanDiff(1:ndim), fracA)

call setVarMeanMerged(varMerged(1:ndim), varB(1:ndim), varA(1:ndim), meanDiff(1:ndim), fracA)

pm_sampleVar::setVarMeanMerged
Return the (weighted) merged variance and mean of a complex or real sample resulting from the merger ...
Definition: pm_sampleVar.F90:9374

pm_sampleVar
This module contains classes and procedures for computing the properties related to the covariance ma...
Definition: pm_sampleVar.F90:394

Warning: The condition 0 < fracA .and. fracA < 1 must hold for the corresponding input arguments.
The condition size(varB) == size(varA) must hold for the corresponding input arguments.
The condition size(varA) == size(meanA) must hold for the corresponding input arguments.
The condition size(varA) == size(meanB) must hold for the corresponding input arguments.
The condition size(varA) == size(varMearged) must hold for the corresponding input arguments.
The condition size(varA) == size(meanMearged) must hold for the corresponding input arguments.
These conditions are verified only if the library is built with the preprocessor macro CHECK_ENABLED=1.; The pure procedure(s) documented herein become impure when the ParaMonte library is compiled with preprocessor macro CHECK_ENABLED=1.
By default, these procedures are pure in release build and impure in debug and testing builds.

See also: getCor
setCor
getCov
setCov
getVar
setVar
getMean
setMean
getCovMerged
setCovMerged
getVarMerged
setVarMerged
getMeanMerged
setMeanMerged
setVarMeanMerged
setVarMeanMerged

Example usage ⛓

: 1program example

2

3 use pm_kind, only: SK, IK

4 use pm_kind, only: TKG => RKS ! All other real types are also supported.

5 use pm_sampleVar, only: getVar

6 use pm_sampleMean, only: getMean

7 use pm_sampleVar, only: setVarMeanMerged

8 use pm_arrayRebind, only: setRebound

9 use pm_arrayResize, only: setResized

10 use pm_distUnif, only: getUnifRand

11 use pm_arrayRange, only: getRange

12 use pm_io, only: display_type

13

14 implicit none

15

16 integer(IK), parameter :: nsam = 2

17 integer(IK), allocatable :: iweight(:)

18 integer(IK) :: isam, ndim, lb(nsam), ub(nsam)

19 integer(IK) :: dim, itry, ntry = 5

20 type(display_type) :: disp

21 disp = display_type(file = "main.out.F90")

22

23 call disp%skip()

24 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

25 call disp%show("!Compute the biased merged variance and mean of a univariate sample.")

26 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

27 call disp%skip()

28

29 block

30 real(TKG) :: mean(0:nsam), meanMerged

31 real(TKG), allocatable :: sample(:)

32 real(TKG) :: var(0:nsam), varMerged

33 do itry = 1, ntry

34 call disp%skip()

35 call disp%show("lb(1) = 1; ub(1) = getUnifRand(2, 7)")

36 lb(1) = 1; ub(1) = getUnifRand(2, 7)

37 call disp%show("do isam = 2, nsam")

38 call disp%show(" lb(isam) = ub(isam - 1) + 1")

39 call disp%show(" ub(isam) = ub(isam - 1) + getUnifRand(2, 7)")

40 call disp%show("end do")

41 do isam = 2, nsam

42 lb(isam) = ub(isam - 1) + 1

43 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

44 end do

45 call disp%show("lb")

46 call disp%show( lb )

47 call disp%show("ub")

48 call disp%show( ub )

49 call disp%show("sample = getUnifRand(0., 1., ub(nsam))")

50 sample = getUnifRand(0., 1., ub(nsam))

51 call disp%show("sample")

52 call disp%show( sample )

53 call disp%show("mean(0) = getMean(sample)")

54 mean(0) = getMean(sample)

55 call disp%show("mean(0) ! reference")

56 call disp%show( mean(0) )

57 call disp%show("var(0) = getVar(sample)")

58 var(0) = getVar(sample)

59 call disp%show("var(0) ! reference")

60 call disp%show( var(0) )

61 call disp%show("do isam = 1, nsam")

62 call disp%show(" var(isam) = getVar(sample(lb(isam):ub(isam)))")

63 call disp%show(" mean(isam) = getMean(sample(lb(isam):ub(isam)))")

64 call disp%show("end do")

65 do isam = 1, nsam

66 var(isam) = getVar(sample(lb(isam):ub(isam)))

67 mean(isam) = getMean(sample(lb(isam):ub(isam)))

68 end do

69 call disp%show("call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), ub(1) / real(ub(2), TKG))")

70 call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), ub(1) / real(ub(2), TKG))

71 call disp%show("meanMerged")

72 call disp%show( meanMerged )

73 call disp%show("varMerged")

74 call disp%show( varMerged )

75 call disp%show("call setVarMeanMerged(var(2), mean(2), var(1), mean(1), ub(1) / real(ub(2), TKG))")

76 call setVarMeanMerged(var(2), mean(2), var(1), mean(1), ub(1) / real(ub(2), TKG))

77 call disp%show("mean(2)")

78 call disp%show( mean(2) )

79 call disp%show("mean(0) ! reference")

80 call disp%show( mean(0) )

81 call disp%show("var(2)")

82 call disp%show( var(2) )

83 call disp%show("var(0) ! reference")

84 call disp%show( var(0) )

85 call disp%skip()

86 end do

87 end block

88

89 block

90 complex(TKG) :: mean(0:nsam), meanMerged

91 complex(TKG), allocatable :: sample(:)

92 real(TKG) :: var(0:nsam), varMerged

93 do itry = 1, ntry

94 call disp%skip()

95 call disp%show("lb(1) = 1; ub(1) = getUnifRand(2, 7)")

96 lb(1) = 1; ub(1) = getUnifRand(2, 7)

97 call disp%show("do isam = 2, nsam")

98 call disp%show(" lb(isam) = ub(isam - 1) + 1")

99 call disp%show(" ub(isam) = ub(isam - 1) + getUnifRand(2, 7)")

100 call disp%show("end do")

101 do isam = 2, nsam

102 lb(isam) = ub(isam - 1) + 1

103 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

104 end do

105 call disp%show("lb")

106 call disp%show( lb )

107 call disp%show("ub")

108 call disp%show( ub )

109 call disp%show("sample = cmplx(getUnifRand(-1., +1., ub(nsam)), getUnifRand(-1., +1., ub(nsam)), TKG)")

110 sample = cmplx(getUnifRand(-1., +1., ub(nsam)), getUnifRand(-1., +1., ub(nsam)), TKG)

111 call disp%show("sample")

112 call disp%show( sample )

113 call disp%show("mean(0) = getMean(sample)")

114 mean(0) = getMean(sample)

115 call disp%show("mean(0) ! reference")

116 call disp%show( mean(0) )

117 call disp%show("var(0) = getVar(sample)")

118 var(0) = getVar(sample)

119 call disp%show("var(0) ! reference")

120 call disp%show( var(0) )

121 call disp%show("do isam = 1, nsam")

122 call disp%show(" var(isam) = getVar(sample(lb(isam):ub(isam)))")

123 call disp%show(" mean(isam) = getMean(sample(lb(isam):ub(isam)))")

124 call disp%show("end do")

125 do isam = 1, nsam

126 var(isam) = getVar(sample(lb(isam):ub(isam)))

127 mean(isam) = getMean(sample(lb(isam):ub(isam)))

128 end do

129 call disp%show("call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), ub(1) / real(ub(2), TKG))")

130 call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), ub(1) / real(ub(2), TKG))

131 call disp%show("meanMerged")

132 call disp%show( meanMerged )

133 call disp%show("varMerged")

134 call disp%show( varMerged )

135 call disp%show("call setVarMeanMerged(var(2), mean(2), var(1), mean(1), ub(1) / real(ub(2), TKG))")

136 call setVarMeanMerged(var(2), mean(2), var(1), mean(1), ub(1) / real(ub(2), TKG))

137 call disp%show("mean(2)")

138 call disp%show( mean(2) )

139 call disp%show("mean(0) ! reference")

140 call disp%show( mean(0) )

141 call disp%show("var(2)")

142 call disp%show( var(2) )

143 call disp%show("var(0) ! reference")

144 call disp%show( var(0) )

145 call disp%skip()

146 end do

147 end block

148

149 call disp%skip()

150 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

151 call disp%show("!Compute the biased merged variance and mean of a frequency weighted univariate sample.")

152 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

153 call disp%skip()

154

155 block

156 real(TKG) :: mean(0:nsam), meanMerged

157 real(TKG), allocatable :: sample(:)

158 real(TKG) :: var(0:nsam), varMerged

159 do itry = 1, ntry

160 call disp%skip()

161 call disp%show("lb(1) = 1; ub(1) = getUnifRand(2, 7)")

162 lb(1) = 1; ub(1) = getUnifRand(2, 7)

163 call disp%show("do isam = 2, nsam")

164 call disp%show(" lb(isam) = ub(isam - 1) + 1")

165 call disp%show(" ub(isam) = ub(isam - 1) + getUnifRand(2, 7)")

166 call disp%show("end do")

167 do isam = 2, nsam

168 lb(isam) = ub(isam - 1) + 1

169 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

170 end do

171 call disp%show("lb")

172 call disp%show( lb )

173 call disp%show("ub")

174 call disp%show( ub )

175 call disp%show("sample = getUnifRand(0., 1., ub(nsam))")

176 sample = getUnifRand(0., 1., ub(nsam))

177 call disp%show("sample")

178 call disp%show( sample )

179 call disp%show("iweight = getUnifRand(1, 10, size(sample, 1, IK))")

180 iweight = getUnifRand(1, 10, size(sample, 1, IK))

181 call disp%show("iweight")

182 call disp%show( iweight )

183 call disp%show("mean(0) = getMean(sample, iweight)")

184 mean(0) = getMean(sample, iweight)

185 call disp%show("mean(0) ! reference")

186 call disp%show( mean(0) )

187 call disp%show("var(0) = getVar(sample, iweight)")

188 var(0) = getVar(sample, iweight)

189 call disp%show("var(0) ! reference")

190 call disp%show( var(0) )

191 call disp%show("do isam = 1, nsam")

192 call disp%show(" var(isam) = getVar(sample(lb(isam):ub(isam)), iweight(lb(isam):ub(isam)))")

193 call disp%show(" mean(isam) = getMean(sample(lb(isam):ub(isam)), iweight(lb(isam):ub(isam)))")

194 call disp%show("end do")

195 do isam = 1, nsam

196 var(isam) = getVar(sample(lb(isam):ub(isam)), iweight(lb(isam):ub(isam)))

197 mean(isam) = getMean(sample(lb(isam):ub(isam)), iweight(lb(isam):ub(isam)))

198 end do

199 call disp%show("call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))")

200 call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))

201 call disp%show("meanMerged")

202 call disp%show( meanMerged )

203 call disp%show("varMerged")

204 call disp%show( varMerged )

205 call disp%show("call setVarMeanMerged(var(2), mean(2), var(1), mean(1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))")

206 call setVarMeanMerged(var(2), mean(2), var(1), mean(1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))

207 call disp%show("mean(2)")

208 call disp%show( mean(2) )

209 call disp%show("mean(0) ! reference")

210 call disp%show( mean(0) )

211 call disp%show("var(2)")

212 call disp%show( var(2) )

213 call disp%show("var(0) ! reference")

214 call disp%show( var(0) )

215 call disp%skip()

216 end do

217 end block

218

219 block

220 complex(TKG) :: mean(0:nsam), meanMerged

221 complex(TKG), allocatable :: sample(:)

222 real(TKG) :: var(0:nsam), varMerged

223 do itry = 1, ntry

224 call disp%skip()

225 call disp%show("lb(1) = 1; ub(1) = getUnifRand(2, 7)")

226 lb(1) = 1; ub(1) = getUnifRand(2, 7)

227 call disp%show("do isam = 2, nsam")

228 call disp%show(" lb(isam) = ub(isam - 1) + 1")

229 call disp%show(" ub(isam) = ub(isam - 1) + getUnifRand(2, 7)")

230 call disp%show("end do")

231 do isam = 2, nsam

232 lb(isam) = ub(isam - 1) + 1

233 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

234 end do

235 call disp%show("lb")

236 call disp%show( lb )

237 call disp%show("ub")

238 call disp%show( ub )

239 call disp%show("sample = cmplx(getUnifRand(0., 1., ub(nsam)), -getUnifRand(0., 1., ub(nsam)), TKG)")

240 sample = cmplx(getUnifRand(0., 1., ub(nsam)), -getUnifRand(0., 1., ub(nsam)), TKG)

241 call disp%show("sample")

242 call disp%show( sample )

243 call disp%show("iweight = getUnifRand(1, 10, size(sample, 1, IK))")

244 iweight = getUnifRand(1, 10, size(sample, 1, IK))

245 call disp%show("iweight")

246 call disp%show( iweight )

247 call disp%show("mean(0) = getMean(sample, iweight)")

248 mean(0) = getMean(sample, iweight)

249 call disp%show("mean(0) ! reference")

250 call disp%show( mean(0) )

251 call disp%show("var(0) = getVar(sample, iweight)")

252 var(0) = getVar(sample, iweight)

253 call disp%show("var(0) ! reference")

254 call disp%show( var(0) )

255 call disp%show("do isam = 1, nsam")

256 call disp%show(" var(isam) = getVar(sample(lb(isam):ub(isam)), iweight(lb(isam):ub(isam)))")

257 call disp%show(" mean(isam) = getMean(sample(lb(isam):ub(isam)), iweight(lb(isam):ub(isam)))")

258 call disp%show("end do")

259 do isam = 1, nsam

260 var(isam) = getVar(sample(lb(isam):ub(isam)), iweight(lb(isam):ub(isam)))

261 mean(isam) = getMean(sample(lb(isam):ub(isam)), iweight(lb(isam):ub(isam)))

262 end do

263 call disp%show("call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))")

264 call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))

265 call disp%show("meanMerged")

266 call disp%show( meanMerged )

267 call disp%show("varMerged")

268 call disp%show( varMerged )

269 call disp%show("call setVarMeanMerged(var(2), mean(2), var(1), mean(1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))")

270 call setVarMeanMerged(var(2), mean(2), var(1), mean(1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))

271 call disp%show("mean(2)")

272 call disp%show( mean(2) )

273 call disp%show("mean(0) ! reference")

274 call disp%show( mean(0) )

275 call disp%show("var(2)")

276 call disp%show( var(2) )

277 call disp%show("var(0) ! reference")

278 call disp%show( var(0) )

279 call disp%skip()

280 end do

281 end block

282

283 call disp%skip()

284 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

285 call disp%show("!Compute the biased merged variance and mean of a reliability weighted univariate sample.")

286 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

287 call disp%skip()

288

289 block

290 real(TKG) :: mean(0:nsam), meanMerged

291 real(TKG), allocatable :: sample(:)

292 real(TKG), allocatable :: rweight(:)

293 real(TKG) :: var(0:nsam), varMerged

294 do itry = 1, ntry

295 call disp%skip()

296 call disp%show("lb(1) = 1; ub(1) = getUnifRand(2, 7)")

297 lb(1) = 1; ub(1) = getUnifRand(2, 7)

298 call disp%show("do isam = 2, nsam")

299 call disp%show(" lb(isam) = ub(isam - 1) + 1")

300 call disp%show(" ub(isam) = ub(isam - 1) + getUnifRand(2, 7)")

301 call disp%show("end do")

302 do isam = 2, nsam

303 lb(isam) = ub(isam - 1) + 1

304 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

305 end do

306 call disp%show("lb")

307 call disp%show( lb )

308 call disp%show("ub")

309 call disp%show( ub )

310 call disp%show("sample = getUnifRand(0., 1., ub(nsam))")

311 sample = getUnifRand(0., 1., ub(nsam))

312 call disp%show("sample")

313 call disp%show( sample )

314 call disp%show("rweight = getUnifRand(1., 2., size(sample, 1, IK))")

315 rweight = getUnifRand(1., 2., size(sample, 1, IK))

316 call disp%show("rweight")

317 call disp%show( rweight )

318 call disp%show("mean(0) = getMean(sample, rweight)")

319 mean(0) = getMean(sample, rweight)

320 call disp%show("mean(0) ! reference")

321 call disp%show( mean(0) )

322 call disp%show("var(0) = getVar(sample, rweight)")

323 var(0) = getVar(sample, rweight)

324 call disp%show("var(0) ! reference")

325 call disp%show( var(0) )

326 call disp%show("do isam = 1, nsam")

327 call disp%show(" var(isam) = getVar(sample(lb(isam):ub(isam)), rweight(lb(isam):ub(isam)))")

328 call disp%show(" mean(isam) = getMean(sample(lb(isam):ub(isam)), rweight(lb(isam):ub(isam)))")

329 call disp%show("end do")

330 do isam = 1, nsam

331 var(isam) = getVar(sample(lb(isam):ub(isam)), rweight(lb(isam):ub(isam)))

332 mean(isam) = getMean(sample(lb(isam):ub(isam)), rweight(lb(isam):ub(isam)))

333 end do

334 call disp%show("call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))")

335 call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))

336 call disp%show("meanMerged")

337 call disp%show( meanMerged )

338 call disp%show("varMerged")

339 call disp%show( varMerged )

340 call disp%show("call setVarMeanMerged(var(2), mean(2), var(1), mean(1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))")

341 call setVarMeanMerged(var(2), mean(2), var(1), mean(1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))

342 call disp%show("mean(2)")

343 call disp%show( mean(2) )

344 call disp%show("mean(0) ! reference")

345 call disp%show( mean(0) )

346 call disp%show("var(2)")

347 call disp%show( var(2) )

348 call disp%show("var(0) ! reference")

349 call disp%show( var(0) )

350 call disp%skip()

351 end do

352 end block

353

354 block

355 complex(TKG) :: mean(0:nsam), meanMerged

356 complex(TKG), allocatable :: sample(:)

357 real(TKG), allocatable :: rweight(:)

358 real(TKG) :: var(0:nsam), varMerged

359 do itry = 1, ntry

360 call disp%skip()

361 call disp%show("lb(1) = 1; ub(1) = getUnifRand(2, 7)")

362 lb(1) = 1; ub(1) = getUnifRand(2, 7)

363 call disp%show("do isam = 2, nsam")

364 call disp%show(" lb(isam) = ub(isam - 1) + 1")

365 call disp%show(" ub(isam) = ub(isam - 1) + getUnifRand(2, 7)")

366 call disp%show("end do")

367 do isam = 2, nsam

368 lb(isam) = ub(isam - 1) + 1

369 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

370 end do

371 call disp%show("lb")

372 call disp%show( lb )

373 call disp%show("ub")

374 call disp%show( ub )

375 call disp%show("sample = cmplx(getUnifRand(0., 1., ub(nsam)), -getUnifRand(0., 1., ub(nsam)), TKG)")

376 sample = cmplx(getUnifRand(0., 1., ub(nsam)), -getUnifRand(0., 1., ub(nsam)), TKG)

377 call disp%show("sample")

378 call disp%show( sample )

379 call disp%show("rweight = getUnifRand(1., 2., size(sample, 1, IK))")

380 rweight = getUnifRand(1., 2., size(sample, 1, IK))

381 call disp%show("rweight")

382 call disp%show( rweight )

383 call disp%show("mean(0) = getMean(sample, rweight)")

384 mean(0) = getMean(sample, rweight)

385 call disp%show("mean(0) ! reference")

386 call disp%show( mean(0) )

387 call disp%show("var(0) = getVar(sample, rweight)")

388 var(0) = getVar(sample, rweight)

389 call disp%show("var(0) ! reference")

390 call disp%show( var(0) )

391 call disp%show("do isam = 1, nsam")

392 call disp%show(" var(isam) = getVar(sample(lb(isam):ub(isam)), rweight(lb(isam):ub(isam)))")

393 call disp%show(" mean(isam) = getMean(sample(lb(isam):ub(isam)), rweight(lb(isam):ub(isam)))")

394 call disp%show("end do")

395 do isam = 1, nsam

396 var(isam) = getVar(sample(lb(isam):ub(isam)), rweight(lb(isam):ub(isam)))

397 mean(isam) = getMean(sample(lb(isam):ub(isam)), rweight(lb(isam):ub(isam)))

398 end do

399 call disp%show("call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))")

400 call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))

401 call disp%show("meanMerged")

402 call disp%show( meanMerged )

403 call disp%show("varMerged")

404 call disp%show( varMerged )

405 call disp%show("call setVarMeanMerged(var(2), mean(2), var(1), mean(1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))")

406 call setVarMeanMerged(var(2), mean(2), var(1), mean(1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))

407 call disp%show("mean(2)")

408 call disp%show( mean(2) )

409 call disp%show("mean(0) ! reference")

410 call disp%show( mean(0) )

411 call disp%show("var(2)")

412 call disp%show( var(2) )

413 call disp%show("var(0) ! reference")

414 call disp%show( var(0) )

415 call disp%skip()

416 end do

417 end block

418

419 call disp%skip()

420 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

421 call disp%show("!Compute the biased merged variance and mean of a multivariate sample.")

422 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

423 call disp%skip()

424

425 block

426 real(TKG), allocatable :: sample(:,:)

427 real(TKG), allocatable :: mean(:,:), meanMerged(:)

428 real(TKG), allocatable :: var(:,:), varMerged(:)

429 do itry = 1, ntry

430 call disp%skip()

431 call disp%show("dim = 2; lb(1) = 1; ub(1) = getUnifRand(2, 7)")

432 dim = 2; lb(1) = 1; ub(1) = getUnifRand(2, 7)

433 call disp%show("do isam = 2, nsam")

434 call disp%show(" lb(isam) = ub(isam - 1) + 1")

435 call disp%show(" ub(isam) = ub(isam - 1) + getUnifRand(2, 7)")

436 call disp%show("end do")

437 do isam = 2, nsam

438 lb(isam) = ub(isam - 1) + 1

439 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

440 end do

441 call disp%show("lb")

442 call disp%show( lb )

443 call disp%show("ub")

444 call disp%show( ub )

445 call disp%show("ndim = getUnifRand(1, minval(ub - lb + 1, 1))")

446 ndim = getUnifRand(1, minval(ub - lb + 1, 1))

447 call disp%show("call setRebound(var, [1_IK, 0_IK], [ndim, nsam])")

448 call setRebound(var, [1_IK, 0_IK], [ndim, nsam])

449 call disp%show("call setRebound(mean, [1_IK, 0_IK], [ndim, nsam])")

450 call setRebound(mean, [1_IK, 0_IK], [ndim, nsam])

451 call disp%show("call setResized(meanMerged, ndim)")

452 call setResized(meanMerged, ndim)

453 call disp%show("call setResized(varMerged, ndim)")

454 call setResized(varMerged, ndim)

455 call disp%show("sample = getUnifRand(-1., +1., ndim, ub(nsam))")

456 sample = getUnifRand(-1., +1., ndim, ub(nsam))

457 call disp%show("sample")

458 call disp%show( sample )

459 call disp%show("mean(:,0) = getVar(sample, dim)")

460 mean(:,0) = getVar(sample, dim)

461 call disp%show("mean(:,0) ! reference")

462 call disp%show( mean(:,0) )

463 call disp%show("var(:,0) = getVar(sample, dim)")

464 var(:,0) = getVar(sample, dim)

465 call disp%show("var(:,0) ! reference")

466 call disp%show( var(:,0) )

467 call disp%show("do isam = 1, nsam")

468 call disp%show(" var(:,isam) = getVar(sample(:,lb(isam):ub(isam)), dim)")

469 call disp%show(" mean(:,isam) = getMean(sample(:,lb(isam):ub(isam)), dim)")

470 call disp%show("end do")

471 do isam = 1, nsam

472 var(:,isam) = getVar(sample(:,lb(isam):ub(isam)), dim)

473 mean(:,isam) = getMean(sample(:,lb(isam):ub(isam)), dim)

474 end do

475 call disp%show("call setVarMeanMerged(varMerged, meanMerged, var(:,2), mean(:,2), var(:,1), mean(:,1), real(ub(1), TKG) / real(ub(2), TKG))")

476 call setVarMeanMerged(varMerged, meanMerged, var(:,2), mean(:,2), var(:,1), mean(:,1), real(ub(1), TKG) / real(ub(2), TKG))

477 call disp%show("meanMerged")

478 call disp%show( meanMerged )

479 call disp%show("varMerged")

480 call disp%show( varMerged )

481 call disp%show("call setVarMeanMerged(var(:,2), mean(:,2), var(:,1), mean(:,1), real(ub(1), TKG) / real(ub(2), TKG))")

482 call setVarMeanMerged(var(:,2), mean(:,2), var(:,1), mean(:,1), real(ub(1), TKG) / real(ub(2), TKG))

483 call disp%show("mean(:,2)")

484 call disp%show( mean(:,2) )

485 call disp%show("mean(:,0) ! reference")

486 call disp%show( mean(:,0) )

487 call disp%show("var(:,2)")

488 call disp%show( var(:,2) )

489 call disp%show("var(:,0) ! reference")

490 call disp%show( var(:,0) )

491 call disp%skip()

492 end do

493 end block

494

495 block

496 complex(TKG), allocatable :: sample(:,:)

497 complex(TKG), allocatable :: mean(:,:), meanMerged(:)

498 real(TKG), allocatable :: var(:,:), varMerged(:)

499 do itry = 1, ntry

500 call disp%skip()

501 call disp%show("dim = 2; lb(1) = 1; ub(1) = getUnifRand(2, 7)")

502 dim = 2; lb(1) = 1; ub(1) = getUnifRand(2, 7)

503 call disp%show("do isam = 2, nsam")

504 call disp%show(" lb(isam) = ub(isam - 1) + 1")

505 call disp%show(" ub(isam) = ub(isam - 1) + getUnifRand(2, 7)")

506 call disp%show("end do")

507 do isam = 2, nsam

508 lb(isam) = ub(isam - 1) + 1

509 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

510 end do

511 call disp%show("lb")

512 call disp%show( lb )

513 call disp%show("ub")

514 call disp%show( ub )

515 call disp%show("ndim = getUnifRand(1, minval(ub - lb + 1, 1))")

516 ndim = getUnifRand(1, minval(ub - lb + 1, 1))

517 call disp%show("call setRebound(var, [1_IK, 0_IK], [ndim, nsam])")

518 call setRebound(var, [1_IK, 0_IK], [ndim, nsam])

519 call disp%show("call setRebound(mean, [1_IK, 0_IK], [ndim, nsam])")

520 call setRebound(mean, [1_IK, 0_IK], [ndim, nsam])

521 call disp%show("call setResized(meanMerged, ndim)")

522 call setResized(meanMerged, ndim)

523 call disp%show("call setResized(varMerged, ndim)")

524 call setResized(varMerged, ndim)

525 call disp%show("sample = cmplx(getUnifRand(-1., +1., ndim, ub(nsam)), -getUnifRand(-1., +1., ndim, ub(nsam)), TKG)")

526 sample = cmplx(getUnifRand(-1., +1., ndim, ub(nsam)), -getUnifRand(-1., +1., ndim, ub(nsam)), TKG)

527 call disp%show("sample")

528 call disp%show( sample )

529 call disp%show("mean(:,0) = getVar(sample, dim)")

530 mean(:,0) = getVar(sample, dim)

531 call disp%show("mean(:,0) ! reference")

532 call disp%show( mean(:,0) )

533 call disp%show("var(:,0) = getVar(sample, dim)")

534 var(:,0) = getVar(sample, dim)

535 call disp%show("var(:,0) ! reference")

536 call disp%show( var(:,0) )

537 call disp%show("do isam = 1, nsam")

538 call disp%show(" var(:,isam) = getVar(sample(:,lb(isam):ub(isam)), dim)")

539 call disp%show(" mean(:,isam) = getMean(sample(:,lb(isam):ub(isam)), dim)")

540 call disp%show("end do")

541 do isam = 1, nsam

542 var(:,isam) = getVar(sample(:,lb(isam):ub(isam)), dim)

543 mean(:,isam) = getMean(sample(:,lb(isam):ub(isam)), dim)

544 end do

545 call disp%show("call setVarMeanMerged(varMerged, meanMerged, var(:,2), mean(:,2), var(:,1), mean(:,1), real(ub(1), TKG) / real(ub(2), TKG))")

546 call setVarMeanMerged(varMerged, meanMerged, var(:,2), mean(:,2), var(:,1), mean(:,1), real(ub(1), TKG) / real(ub(2), TKG))

547 call disp%show("meanMerged")

548 call disp%show( meanMerged )

549 call disp%show("varMerged")

550 call disp%show( varMerged )

551 call disp%show("call setVarMeanMerged(var(:,2), mean(:,2), var(:,1), mean(:,1), real(ub(1), TKG) / real(ub(2), TKG))")

552 call setVarMeanMerged(var(:,2), mean(:,2), var(:,1), mean(:,1), real(ub(1), TKG) / real(ub(2), TKG))

553 call disp%show("mean(:,2)")

554 call disp%show( mean(:,2) )

555 call disp%show("mean(:,0) ! reference")

556 call disp%show( mean(:,0) )

557 call disp%show("var(:,2)")

558 call disp%show( var(:,2) )

559 call disp%show("var(:,0) ! reference")

560 call disp%show( var(:,0) )

561 call disp%skip()

562 end do

563 end block

564

565 call disp%skip()

566 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

567 call disp%show("!Compute the biased merged variance and mean of a frequency weighted multivariate sample.")

568 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

569 call disp%skip()

570

571 block

572 real(TKG), allocatable :: sample(:,:)

573 real(TKG), allocatable :: mean(:,:), meanMerged(:)

574 real(TKG), allocatable :: var(:,:), varMerged(:)

575 do itry = 1, ntry

576 call disp%skip()

577 call disp%show("dim = 2; lb(1) = 1; ub(1) = getUnifRand(2, 7)")

578 dim = 2; lb(1) = 1; ub(1) = getUnifRand(2, 7)

579 call disp%show("do isam = 2, nsam")

580 call disp%show(" lb(isam) = ub(isam - 1) + 1")

581 call disp%show(" ub(isam) = ub(isam - 1) + getUnifRand(2, 7)")

582 call disp%show("end do")

583 do isam = 2, nsam

584 lb(isam) = ub(isam - 1) + 1

585 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

586 end do

587 call disp%show("lb")

588 call disp%show( lb )

589 call disp%show("ub")

590 call disp%show( ub )

591 call disp%show("ndim = getUnifRand(1, minval(ub - lb + 1, 1))")

592 ndim = getUnifRand(1, minval(ub - lb + 1, 1))

593 call disp%show("call setRebound(var, [1_IK, 0_IK], [ndim, nsam])")

594 call setRebound(var, [1_IK, 0_IK], [ndim, nsam])

595 call disp%show("call setRebound(mean, [1_IK, 0_IK], [ndim, nsam])")

596 call setRebound(mean, [1_IK, 0_IK], [ndim, nsam])

597 call disp%show("call setResized(meanMerged, ndim)")

598 call setResized(meanMerged, ndim)

599 call disp%show("call setResized(varMerged, ndim)")

600 call setResized(varMerged, ndim)

601 call disp%show("sample = getUnifRand(-1., +1., ndim, ub(nsam))")

602 sample = getUnifRand(-1., +1., ndim, ub(nsam))

603 call disp%show("sample")

604 call disp%show( sample )

605 call disp%show("iweight = getUnifRand(1, 10, size(sample, dim, IK))")

606 iweight = getUnifRand(1, 10, size(sample, dim, IK))

607 call disp%show("iweight")

608 call disp%show( iweight )

609 call disp%show("mean(:,0) = getVar(sample, 2_IK, iweight)")

610 mean(:,0) = getVar(sample, 2_IK, iweight)

611 call disp%show("mean(:,0) ! reference")

612 call disp%show( mean(:,0) )

613 call disp%show("var(:,0) = getVar(sample, 2_IK, iweight)")

614 var(:,0) = getVar(sample, 2_IK, iweight)

615 call disp%show("var(:,0) ! reference")

616 call disp%show( var(:,0) )

617 call disp%show("do isam = 1, nsam")

618 call disp%show(" var(:,isam) = getVar(sample(:,lb(isam):ub(isam)), 2_IK, iweight(lb(isam):ub(isam)))")

619 call disp%show(" mean(:,isam) = getMean(sample(:,lb(isam):ub(isam)), 2_IK, iweight(lb(isam):ub(isam)))")

620 call disp%show("end do")

621 do isam = 1, nsam

622 var(:,isam) = getVar(sample(:,lb(isam):ub(isam)), 2_IK, iweight(lb(isam):ub(isam)))

623 mean(:,isam) = getMean(sample(:,lb(isam):ub(isam)), 2_IK, iweight(lb(isam):ub(isam)))

624 end do

625 call disp%show("call setVarMeanMerged(varMerged, meanMerged, var(:,2), mean(:,2), var(:,1), mean(:,1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))")

626 call setVarMeanMerged(varMerged, meanMerged, var(:,2), mean(:,2), var(:,1), mean(:,1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))

627 call disp%show("meanMerged")

628 call disp%show( meanMerged )

629 call disp%show("varMerged")

630 call disp%show( varMerged )

631 call disp%show("call setVarMeanMerged(var(:,2), mean(:,2), var(:,1), mean(:,1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))")

632 call setVarMeanMerged(var(:,2), mean(:,2), var(:,1), mean(:,1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))

633 call disp%show("mean(:,2)")

634 call disp%show( mean(:,2) )

635 call disp%show("mean(:,0) ! reference")

636 call disp%show( mean(:,0) )

637 call disp%show("var(:,2)")

638 call disp%show( var(:,2) )

639 call disp%show("var(:,0) ! reference")

640 call disp%show( var(:,0) )

641 call disp%skip()

642 end do

643 end block

644

645 block

646 complex(TKG), allocatable :: sample(:,:)

647 complex(TKG), allocatable :: mean(:,:), meanMerged(:)

648 real(TKG), allocatable :: var(:,:), varMerged(:)

649 do itry = 1, ntry

650 call disp%skip()

651 call disp%show("dim = 2; lb(1) = 1; ub(1) = getUnifRand(2, 7)")

652 dim = 2; lb(1) = 1; ub(1) = getUnifRand(2, 7)

653 call disp%show("do isam = 2, nsam")

654 call disp%show(" lb(isam) = ub(isam - 1) + 1")

655 call disp%show(" ub(isam) = ub(isam - 1) + getUnifRand(2, 7)")

656 call disp%show("end do")

657 do isam = 2, nsam

658 lb(isam) = ub(isam - 1) + 1

659 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

660 end do

661 call disp%show("lb")

662 call disp%show( lb )

663 call disp%show("ub")

664 call disp%show( ub )

665 call disp%show("ndim = getUnifRand(1, minval(ub - lb + 1, 1))")

666 ndim = getUnifRand(1, minval(ub - lb + 1, 1))

667 call disp%show("call setRebound(var, [1_IK, 0_IK], [ndim, nsam])")

668 call setRebound(var, [1_IK, 0_IK], [ndim, nsam])

669 call disp%show("call setRebound(mean, [1_IK, 0_IK], [ndim, nsam])")

670 call setRebound(mean, [1_IK, 0_IK], [ndim, nsam])

671 call disp%show("call setResized(meanMerged, ndim)")

672 call setResized(meanMerged, ndim)

673 call disp%show("call setResized(varMerged, ndim)")

674 call setResized(varMerged, ndim)

675 call disp%show("sample = cmplx(getUnifRand(-1., +1., ndim, ub(nsam)), getUnifRand(-1., +1., ndim, ub(nsam)), TKG)")

676 sample = cmplx(getUnifRand(-1., +1., ndim, ub(nsam)), getUnifRand(-1., +1., ndim, ub(nsam)), TKG)

677 call disp%show("sample")

678 call disp%show( sample )

679 call disp%show("iweight = getUnifRand(1, 10, size(sample, dim, IK))")

680 iweight = getUnifRand(1, 10, size(sample, dim, IK))

681 call disp%show("iweight")

682 call disp%show( iweight )

683 call disp%show("mean(:,0) = getVar(sample, 2_IK, iweight)")

684 mean(:,0) = getVar(sample, 2_IK, iweight)

685 call disp%show("mean(:,0) ! reference")

686 call disp%show( mean(:,0) )

687 call disp%show("var(:,0) = getVar(sample, 2_IK, iweight)")

688 var(:,0) = getVar(sample, 2_IK, iweight)

689 call disp%show("var(:,0) ! reference")

690 call disp%show( var(:,0) )

691 call disp%show("do isam = 1, nsam")

692 call disp%show(" var(:,isam) = getVar(sample(:,lb(isam):ub(isam)), 2_IK, iweight(lb(isam):ub(isam)))")

693 call disp%show(" mean(:,isam) = getMean(sample(:,lb(isam):ub(isam)), 2_IK, iweight(lb(isam):ub(isam)))")

694 call disp%show("end do")

695 do isam = 1, nsam

696 var(:,isam) = getVar(sample(:,lb(isam):ub(isam)), 2_IK, iweight(lb(isam):ub(isam)))

697 mean(:,isam) = getMean(sample(:,lb(isam):ub(isam)), 2_IK, iweight(lb(isam):ub(isam)))

698 end do

699 call disp%show("call setVarMeanMerged(varMerged, meanMerged, var(:,2), mean(:,2), var(:,1), mean(:,1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))")

700 call setVarMeanMerged(varMerged, meanMerged, var(:,2), mean(:,2), var(:,1), mean(:,1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))

701 call disp%show("meanMerged")

702 call disp%show( meanMerged )

703 call disp%show("varMerged")

704 call disp%show( varMerged )

705 call disp%show("call setVarMeanMerged(var(:,2), mean(:,2), var(:,1), mean(:,1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))")

706 call setVarMeanMerged(var(:,2), mean(:,2), var(:,1), mean(:,1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))

707 call disp%show("mean(:,2)")

708 call disp%show( mean(:,2) )

709 call disp%show("mean(:,0) ! reference")

710 call disp%show( mean(:,0) )

711 call disp%show("var(:,2)")

712 call disp%show( var(:,2) )

713 call disp%show("var(:,0) ! reference")

714 call disp%show( var(:,0) )

715 call disp%skip()

716 end do

717 end block

718

719 call disp%skip()

720 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

721 call disp%show("!Compute the biased merged variance and mean of a reliability weighted multivariate sample.")

722 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

723 call disp%skip()

724

725 block

726 real(TKG), allocatable :: sample(:,:)

727 real(TKG), allocatable :: mean(:,:), meanMerged(:)

728 real(TKG), allocatable :: var(:,:), varMerged(:)

729 real(TKG), allocatable :: rweight(:)

730 do itry = 1, ntry

731 call disp%skip()

732 call disp%show("dim = 2; lb(1) = 1; ub(1) = getUnifRand(2, 7)")

733 dim = 2; lb(1) = 1; ub(1) = getUnifRand(2, 7)

734 call disp%show("do isam = 2, nsam")

735 call disp%show(" lb(isam) = ub(isam - 1) + 1")

736 call disp%show(" ub(isam) = ub(isam - 1) + getUnifRand(2, 7)")

737 call disp%show("end do")

738 do isam = 2, nsam

739 lb(isam) = ub(isam - 1) + 1

740 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

741 end do

742 call disp%show("lb")

743 call disp%show( lb )

744 call disp%show("ub")

745 call disp%show( ub )

746 call disp%show("ndim = getUnifRand(1, minval(ub - lb + 1, 1))")

747 ndim = getUnifRand(1, minval(ub - lb + 1, 1))

748 call disp%show("call setRebound(var, [1_IK, 0_IK], [ndim, nsam])")

749 call setRebound(var, [1_IK, 0_IK], [ndim, nsam])

750 call disp%show("call setRebound(mean, [1_IK, 0_IK], [ndim, nsam])")

751 call setRebound(mean, [1_IK, 0_IK], [ndim, nsam])

752 call disp%show("call setResized(meanMerged, ndim)")

753 call setResized(meanMerged, ndim)

754 call disp%show("call setResized(varMerged, ndim)")

755 call setResized(varMerged, ndim)

756 call disp%show("sample = getUnifRand(-1., +1., ndim, ub(nsam))")

757 sample = getUnifRand(-1., +1., ndim, ub(nsam))

758 call disp%show("sample")

759 call disp%show( sample )

760 call disp%show("rweight = getUnifRand(1., 2., size(sample, dim, IK))")

761 rweight = getUnifRand(1., 2., size(sample, dim, IK))

762 call disp%show("rweight")

763 call disp%show( rweight )

764 call disp%show("mean(:,0) = getVar(sample, 2_IK, rweight)")

765 mean(:,0) = getVar(sample, 2_IK, rweight)

766 call disp%show("mean(:,0) ! reference")

767 call disp%show( mean(:,0) )

768 call disp%show("var(:,0) = getVar(sample, 2_IK, rweight)")

769 var(:,0) = getVar(sample, 2_IK, rweight)

770 call disp%show("var(:,0) ! reference")

771 call disp%show( var(:,0) )

772 call disp%show("do isam = 1, nsam")

773 call disp%show(" var(:,isam) = getVar(sample(:,lb(isam):ub(isam)), 2_IK, rweight(lb(isam):ub(isam)))")

774 call disp%show(" mean(:,isam) = getMean(sample(:,lb(isam):ub(isam)), 2_IK, rweight(lb(isam):ub(isam)))")

775 call disp%show("end do")

776 do isam = 1, nsam

777 var(:,isam) = getVar(sample(:,lb(isam):ub(isam)), 2_IK, rweight(lb(isam):ub(isam)))

778 mean(:,isam) = getMean(sample(:,lb(isam):ub(isam)), 2_IK, rweight(lb(isam):ub(isam)))

779 end do

780 call disp%show("call setVarMeanMerged(varMerged, meanMerged, var(:,2), mean(:,2), var(:,1), mean(:,1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))")

781 call setVarMeanMerged(varMerged, meanMerged, var(:,2), mean(:,2), var(:,1), mean(:,1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))

782 call disp%show("meanMerged")

783 call disp%show( meanMerged )

784 call disp%show("varMerged")

785 call disp%show( varMerged )

786 call disp%show("call setVarMeanMerged(var(:,2), mean(:,2), var(:,1), mean(:,1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))")

787 call setVarMeanMerged(var(:,2), mean(:,2), var(:,1), mean(:,1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))

788 call disp%show("mean(:,2)")

789 call disp%show( mean(:,2) )

790 call disp%show("mean(:,0) ! reference")

791 call disp%show( mean(:,0) )

792 call disp%show("var(:,2)")

793 call disp%show( var(:,2) )

794 call disp%show("var(:,0) ! reference")

795 call disp%show( var(:,0) )

796 call disp%skip()

797 end do

798 end block

799

800 block

801 complex(TKG), allocatable :: sample(:,:)

802 complex(TKG), allocatable :: mean(:,:), meanMerged(:)

803 real(TKG), allocatable :: var(:,:), varMerged(:)

804 real(TKG), allocatable :: rweight(:)

805 do itry = 1, ntry

806 call disp%skip()

807 call disp%show("dim = 2; lb(1) = 1; ub(1) = getUnifRand(2, 7)")

808 dim = 2; lb(1) = 1; ub(1) = getUnifRand(2, 7)

809 call disp%show("do isam = 2, nsam")

810 call disp%show(" lb(isam) = ub(isam - 1) + 1")

811 call disp%show(" ub(isam) = ub(isam - 1) + getUnifRand(2, 7)")

812 call disp%show("end do")

813 do isam = 2, nsam

814 lb(isam) = ub(isam - 1) + 1

815 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

816 end do

817 call disp%show("lb")

818 call disp%show( lb )

819 call disp%show("ub")

820 call disp%show( ub )

821 call disp%show("ndim = getUnifRand(1, minval(ub - lb + 1, 1))")

822 ndim = getUnifRand(1, minval(ub - lb + 1, 1))

823 call disp%show("call setRebound(var, [1_IK, 0_IK], [ndim, nsam])")

824 call setRebound(var, [1_IK, 0_IK], [ndim, nsam])

825 call disp%show("call setRebound(mean, [1_IK, 0_IK], [ndim, nsam])")

826 call setRebound(mean, [1_IK, 0_IK], [ndim, nsam])

827 call disp%show("call setResized(meanMerged, ndim)")

828 call setResized(meanMerged, ndim)

829 call disp%show("call setResized(varMerged, ndim)")

830 call setResized(varMerged, ndim)

831 call disp%show("sample = cmplx(getUnifRand(-1., +1., ndim, ub(nsam)), getUnifRand(-1., +1., ndim, ub(nsam)), TKG)")

832 sample = cmplx(getUnifRand(-1., +1., ndim, ub(nsam)), getUnifRand(-1., +1., ndim, ub(nsam)), TKG)

833 call disp%show("sample")

834 call disp%show( sample )

835 call disp%show("rweight = getUnifRand(1., 2., size(sample, dim, IK))")

836 rweight = getUnifRand(1., 2., size(sample, dim, IK))

837 call disp%show("rweight")

838 call disp%show( rweight )

839 call disp%show("mean(:,0) = getVar(sample, 2_IK, rweight)")

840 mean(:,0) = getVar(sample, 2_IK, rweight)

841 call disp%show("mean(:,0) ! reference")

842 call disp%show( mean(:,0) )

843 call disp%show("var(:,0) = getVar(sample, 2_IK, rweight)")

844 var(:,0) = getVar(sample, 2_IK, rweight)

845 call disp%show("var(:,0) ! reference")

846 call disp%show( var(:,0) )

847 call disp%show("do isam = 1, nsam")

848 call disp%show(" var(:,isam) = getVar(sample(:,lb(isam):ub(isam)), 2_IK, rweight(lb(isam):ub(isam)))")

849 call disp%show(" mean(:,isam) = getMean(sample(:,lb(isam):ub(isam)), 2_IK, rweight(lb(isam):ub(isam)))")

850 call disp%show("end do")

851 do isam = 1, nsam

852 var(:,isam) = getVar(sample(:,lb(isam):ub(isam)), 2_IK, rweight(lb(isam):ub(isam)))

853 mean(:,isam) = getMean(sample(:,lb(isam):ub(isam)), 2_IK, rweight(lb(isam):ub(isam)))

854 end do

855 call disp%show("call setVarMeanMerged(varMerged, meanMerged, var(:,2), mean(:,2), var(:,1), mean(:,1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))")

856 call setVarMeanMerged(varMerged, meanMerged, var(:,2), mean(:,2), var(:,1), mean(:,1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))

857 call disp%show("meanMerged")

858 call disp%show( meanMerged )

859 call disp%show("varMerged")

860 call disp%show( varMerged )

861 call disp%show("call setVarMeanMerged(var(:,2), mean(:,2), var(:,1), mean(:,1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))")

862 call setVarMeanMerged(var(:,2), mean(:,2), var(:,1), mean(:,1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))

863 call disp%show("mean(:,2)")

864 call disp%show( mean(:,2) )

865 call disp%show("mean(:,0) ! reference")

866 call disp%show( mean(:,0) )

867 call disp%show("var(:,2)")

868 call disp%show( var(:,2) )

869 call disp%show("var(:,0) ! reference")

870 call disp%show( var(:,0) )

871 call disp%skip()

872 end do

873 end block

874

875end program example

pm_arrayRange::getRange
Generate minimally-spaced character, integer, real sequences or sequences at fixed intervals of size ...
Definition: pm_arrayRange.F90:135

pm_arrayRebind::setRebound
Resize (shrink or expand) an input allocatable array of rank 1..3 to arbitrary new lower and upper bo...
Definition: pm_arrayRebind.F90:218

pm_arrayResize::setResized
Allocate or resize (shrink or expand) an input allocatable scalar string or array of rank 1....
Definition: pm_arrayResize.F90:249

pm_distUnif::getUnifRand
Generate and return a scalar or a contiguous array of rank 1 of length s1 of randomly uniformly distr...
Definition: pm_distUnif.F90:4150

pm_io::show
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11726

pm_io::skip
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11508

pm_sampleMean::getMean
Generate and return the (weighted) mean of an input sample of nsam observations with ndim = 1 or 2 at...
Definition: pm_sampleMean.F90:229

pm_sampleVar::getVar
Generate and return the variance of the input sample of type complex or real of shape (nsam) or (ndim...
Definition: pm_sampleVar.F90:715

pm_arrayRange
This module contains procedures and generic interfaces for generating ranges of discrete character,...
Definition: pm_arrayRange.F90:36

pm_arrayRebind
This module contains procedures and generic interfaces for resizing allocatable arrays of various typ...
Definition: pm_arrayRebind.F90:64

pm_arrayResize
This module contains procedures and generic interfaces for resizing allocatable arrays of various typ...
Definition: pm_arrayResize.F90:81

pm_distUnif
This module contains classes and procedures for computing various statistical quantities related to t...
Definition: pm_distUnif.F90:274

pm_io
This module contains classes and procedures for input/output (IO) or generic display operations on st...
Definition: pm_io.F90:252

pm_io::disp
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
Definition: pm_io.F90:11393

pm_kind
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
Definition: pm_kind.F90:268

pm_kind::IK
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in C-Fortran Interoper...
Definition: pm_kind.F90:540

pm_kind::SK
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in C-Fortran Intero...
Definition: pm_kind.F90:539

pm_kind::RKS
integer, parameter RKS
The single-precision real kind in Fortran mode. On most platforms, this is an 32-bit real kind.
Definition: pm_kind.F90:567

pm_sampleMean
This module contains classes and procedures for computing the first moment (i.e., the statistical mea...
Definition: pm_sampleMean.F90:104

pm_io::display_type
Generate and return an object of type display_type.
Definition: pm_io.F90:10282

Example Unix compile command via Intel ifort compiler ⛓
1#!/usr/bin/env sh

2rm main.exe

3ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe

4./main.exe

Example Windows Batch compile command via Intel ifort compiler ⛓
1del main.exe

2set PATH=..\..\..\lib;%PATH%

3ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe

4main.exe

Example Unix / MinGW compile command via GNU gfortran compiler ⛓
1#!/usr/bin/env sh

2rm main.exe

3gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe

4./main.exe

Example output ⛓
1

2!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

3!Compute the biased merged variance and mean of a univariate sample.

4!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

5

6

7lb(1) = 1; ub(1) = getUnifRand(2, 7)

8do isam = 2, nsam

9 lb(isam) = ub(isam - 1) + 1

10 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

11end do

12lb

13+1, +4

14ub

15+3, +6

16sample = getUnifRand(0., 1., ub(nsam))

17sample

18+0.300738692, +0.826546073, +0.904453993, +0.388791502, +0.707582772, +0.952494144

19mean(0) = getMean(sample)

20mean(0) ! reference

21+0.680101216

22var(0) = getVar(sample)

23var(0) ! reference

24+0.625851229E-1

25do isam = 1, nsam

26 var(isam) = getVar(sample(lb(isam):ub(isam)))

27 mean(isam) = getMean(sample(lb(isam):ub(isam)))

28end do

29call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), ub(1) / real(ub(2), TKG))

30meanMerged

31+0.680101216

32varMerged

33+0.625851154E-1

34call setVarMeanMerged(var(2), mean(2), var(1), mean(1), ub(1) / real(ub(2), TKG))

35mean(2)

36+0.680101216

37mean(0) ! reference

38+0.680101216

39var(2)

40+0.625851154E-1

41var(0) ! reference

42+0.625851229E-1

43

44

45lb(1) = 1; ub(1) = getUnifRand(2, 7)

46do isam = 2, nsam

47 lb(isam) = ub(isam - 1) + 1

48 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

49end do

50lb

51+1, +3

52ub

53+2, +4

54sample = getUnifRand(0., 1., ub(nsam))

55sample

56+0.451598644, +0.816199720, +0.182628632E-3, +0.347925842

57mean(0) = getMean(sample)

58mean(0) ! reference

59+0.403976738

60var(0) = getVar(sample)

61var(0) ! reference

62+0.845967531E-1

63do isam = 1, nsam

64 var(isam) = getVar(sample(lb(isam):ub(isam)))

65 mean(isam) = getMean(sample(lb(isam):ub(isam)))

66end do

67call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), ub(1) / real(ub(2), TKG))

68meanMerged

69+0.403976738

70varMerged

71+0.845967606E-1

72call setVarMeanMerged(var(2), mean(2), var(1), mean(1), ub(1) / real(ub(2), TKG))

73mean(2)

74+0.403976738

75mean(0) ! reference

76+0.403976738

77var(2)

78+0.845967606E-1

79var(0) ! reference

80+0.845967531E-1

81

82

83lb(1) = 1; ub(1) = getUnifRand(2, 7)

84do isam = 2, nsam

85 lb(isam) = ub(isam - 1) + 1

86 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

87end do

88lb

89+1, +5

90ub

91+4, +7

92sample = getUnifRand(0., 1., ub(nsam))

93sample

94+0.912773132, +0.402607918, +0.374722421, +0.778887272E-1, +0.958424330, +0.178530216, +0.515347719

95mean(0) = getMean(sample)

96mean(0) ! reference

97+0.488613516

98var(0) = getVar(sample)

99var(0) ! reference

100+0.980804190E-1

101do isam = 1, nsam

102 var(isam) = getVar(sample(lb(isam):ub(isam)))

103 mean(isam) = getMean(sample(lb(isam):ub(isam)))

104end do

105call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), ub(1) / real(ub(2), TKG))

106meanMerged

107+0.488613486

108varMerged

109+0.980804190E-1

110call setVarMeanMerged(var(2), mean(2), var(1), mean(1), ub(1) / real(ub(2), TKG))

111mean(2)

112+0.488613486

113mean(0) ! reference

114+0.488613516

115var(2)

116+0.980804190E-1

117var(0) ! reference

118+0.980804190E-1

119

120

121lb(1) = 1; ub(1) = getUnifRand(2, 7)

122do isam = 2, nsam

123 lb(isam) = ub(isam - 1) + 1

124 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

125end do

126lb

127+1, +7

128ub

129+6, +12

130sample = getUnifRand(0., 1., ub(nsam))

131sample

132+0.579243839, +0.365756810, +0.975298882, +0.150066078, +0.794467330E-1, +0.588669062, +0.288138032, +0.895552337, +0.190088153, +0.616138697, +0.854666471, +0.493799806

133mean(0) = getMean(sample)

134mean(0) ! reference

135+0.506405413

136var(0) = getVar(sample)

137var(0) ! reference

138+0.828004852E-1

139do isam = 1, nsam

140 var(isam) = getVar(sample(lb(isam):ub(isam)))

141 mean(isam) = getMean(sample(lb(isam):ub(isam)))

142end do

143call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), ub(1) / real(ub(2), TKG))

144meanMerged

145+0.506405413

146varMerged

147+0.828004852E-1

148call setVarMeanMerged(var(2), mean(2), var(1), mean(1), ub(1) / real(ub(2), TKG))

149mean(2)

150+0.506405413

151mean(0) ! reference

152+0.506405413

153var(2)

154+0.828004852E-1

155var(0) ! reference

156+0.828004852E-1

157

158

159lb(1) = 1; ub(1) = getUnifRand(2, 7)

160do isam = 2, nsam

161 lb(isam) = ub(isam - 1) + 1

162 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

163end do

164lb

165+1, +8

166ub

167+7, +11

168sample = getUnifRand(0., 1., ub(nsam))

169sample

170+0.444651842E-1, +0.178797841E-1, +0.486887693E-1, +0.292090833, +0.113872349, +0.828850269, +0.783131242, +0.673079848, +0.489113569, +0.925929666, +0.946931660

171mean(0) = getMean(sample)

172mean(0) ! reference

173+0.469457597

174var(0) = getVar(sample)

175var(0) ! reference

176+0.129567116

177do isam = 1, nsam

178 var(isam) = getVar(sample(lb(isam):ub(isam)))

179 mean(isam) = getMean(sample(lb(isam):ub(isam)))

180end do

181call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), ub(1) / real(ub(2), TKG))

182meanMerged

183+0.469457567

184varMerged

185+0.129567102

186call setVarMeanMerged(var(2), mean(2), var(1), mean(1), ub(1) / real(ub(2), TKG))

187mean(2)

188+0.469457567

189mean(0) ! reference

190+0.469457597

191var(2)

192+0.129567102

193var(0) ! reference

194+0.129567116

195

196

197lb(1) = 1; ub(1) = getUnifRand(2, 7)

198do isam = 2, nsam

199 lb(isam) = ub(isam - 1) + 1

200 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

201end do

202lb

203+1, +7

204ub

205+6, +12

206sample = cmplx(getUnifRand(-1., +1., ub(nsam)), getUnifRand(-1., +1., ub(nsam)), TKG)

207sample

208(+0.801158905, +0.962853432E-3), (+0.210760355, +0.602453232), (-0.984127879, +0.956022024), (+0.110168099, -0.636793494), (-0.704571128, -0.118475676), (-0.509290576, -0.652885079), (-0.427154779, +0.631077290E-1), (-0.708558559E-1, +0.205811262E-1), (-0.694830179, -0.457609057), (+0.292301059, -0.659750700E-1), (-0.781919956, +0.835206509), (+0.727935791, -0.540279627)

209mean(0) = getMean(sample)

210mean(0) ! reference

211(-0.169202164, +0.526289165E-3)

212var(0) = getVar(sample)

213var(0) ! reference

214+0.608877420

215do isam = 1, nsam

216 var(isam) = getVar(sample(lb(isam):ub(isam)))

217 mean(isam) = getMean(sample(lb(isam):ub(isam)))

218end do

219call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), ub(1) / real(ub(2), TKG))

220meanMerged

221(-0.169202179, +0.526289456E-3)

222varMerged

223+0.608877480

224call setVarMeanMerged(var(2), mean(2), var(1), mean(1), ub(1) / real(ub(2), TKG))

225mean(2)

226(-0.169202179, +0.526289456E-3)

227mean(0) ! reference

228(-0.169202164, +0.526289165E-3)

229var(2)

230+0.608877480

231var(0) ! reference

232+0.608877420

233

234

235lb(1) = 1; ub(1) = getUnifRand(2, 7)

236do isam = 2, nsam

237 lb(isam) = ub(isam - 1) + 1

238 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

239end do

240lb

241+1, +5

242ub

243+4, +8

244sample = cmplx(getUnifRand(-1., +1., ub(nsam)), getUnifRand(-1., +1., ub(nsam)), TKG)

245sample

246(+0.529052019, -0.868605375E-1), (-0.493851066, -0.366667509E-1), (-0.260193944, +0.392078161), (-0.200027227E-1, +0.929609656), (-0.612545013, +0.222085357), (-0.443601847, +0.670454979), (-0.545647740, +0.533435345), (-0.352996111, -0.934483647)

247mean(0) = getMean(sample)

248mean(0) ! reference

249(-0.274973303, +0.211206570)

250var(0) = getVar(sample)

251var(0) ! reference

252+0.413487852

253do isam = 1, nsam

254 var(isam) = getVar(sample(lb(isam):ub(isam)))

255 mean(isam) = getMean(sample(lb(isam):ub(isam)))

256end do

257call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), ub(1) / real(ub(2), TKG))

258meanMerged

259(-0.274973303, +0.211206570)

260varMerged

261+0.413487792

262call setVarMeanMerged(var(2), mean(2), var(1), mean(1), ub(1) / real(ub(2), TKG))

263mean(2)

264(-0.274973303, +0.211206570)

265mean(0) ! reference

266(-0.274973303, +0.211206570)

267var(2)

268+0.413487792

269var(0) ! reference

270+0.413487852

271

272

273lb(1) = 1; ub(1) = getUnifRand(2, 7)

274do isam = 2, nsam

275 lb(isam) = ub(isam - 1) + 1

276 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

277end do

278lb

279+1, +7

280ub

281+6, +8

282sample = cmplx(getUnifRand(-1., +1., ub(nsam)), getUnifRand(-1., +1., ub(nsam)), TKG)

283sample

284(-0.806439161, -0.688816190), (+0.126288772, +0.262729406), (-0.130549192, -0.820411921), (+0.512068272E-1, +0.401137114), (+0.659992576, +0.424023509), (+0.516079664, +0.233240485), (-0.906788826, +0.970872045), (-0.495441437, -0.576867700)

285mean(0) = getMean(sample)

286mean(0) ! reference

287(-0.123206347, +0.257383436E-1)

288var(0) = getVar(sample)

289var(0) ! reference

290+0.651990533

291do isam = 1, nsam

292 var(isam) = getVar(sample(lb(isam):ub(isam)))

293 mean(isam) = getMean(sample(lb(isam):ub(isam)))

294end do

295call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), ub(1) / real(ub(2), TKG))

296meanMerged

297(-0.123206347, +0.257383436E-1)

298varMerged

299+0.651990414

300call setVarMeanMerged(var(2), mean(2), var(1), mean(1), ub(1) / real(ub(2), TKG))

301mean(2)

302(-0.123206347, +0.257383436E-1)

303mean(0) ! reference

304(-0.123206347, +0.257383436E-1)

305var(2)

306+0.651990414

307var(0) ! reference

308+0.651990533

309

310

311lb(1) = 1; ub(1) = getUnifRand(2, 7)

312do isam = 2, nsam

313 lb(isam) = ub(isam - 1) + 1

314 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

315end do

316lb

317+1, +6

318ub

319+5, +12

320sample = cmplx(getUnifRand(-1., +1., ub(nsam)), getUnifRand(-1., +1., ub(nsam)), TKG)

321sample

322(+0.540003300, +0.109041452), (-0.367841721E-1, +0.277980685), (+0.877188444, -0.245737076), (-0.336740017, -0.323849559), (-0.850127816, -0.184817672), (+0.687840700, -0.316632271), (+0.957695961, -0.303204417), (-0.897617340E-1, -0.770005941), (-0.925921321, -0.153110504), (+0.934314966, -0.251621485), (-0.526561618, -0.843809247), (+0.247843266E-1, -0.198450327)

323mean(0) = getMean(sample)

324mean(0) ! reference

325(+0.104660921, -0.267018020)

326var(0) = getVar(sample)

327var(0) ! reference

328+0.519154489

329do isam = 1, nsam

330 var(isam) = getVar(sample(lb(isam):ub(isam)))

331 mean(isam) = getMean(sample(lb(isam):ub(isam)))

332end do

333call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), ub(1) / real(ub(2), TKG))

334meanMerged

335(+0.104660928, -0.267018050)

336varMerged

337+0.519154489

338call setVarMeanMerged(var(2), mean(2), var(1), mean(1), ub(1) / real(ub(2), TKG))

339mean(2)

340(+0.104660928, -0.267018050)

341mean(0) ! reference

342(+0.104660921, -0.267018020)

343var(2)

344+0.519154489

345var(0) ! reference

346+0.519154489

347

348

349lb(1) = 1; ub(1) = getUnifRand(2, 7)

350do isam = 2, nsam

351 lb(isam) = ub(isam - 1) + 1

352 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

353end do

354lb

355+1, +5

356ub

357+4, +11

358sample = cmplx(getUnifRand(-1., +1., ub(nsam)), getUnifRand(-1., +1., ub(nsam)), TKG)

359sample

360(-0.469204903, -0.226135015), (-0.386271119, +0.397879481), (-0.199822664, -0.411331773), (+0.356772304, +0.825235963), (+0.310785055, -0.351433516), (-0.238024712, -0.188817978), (-0.478876948, -0.407534361), (-0.495306730, -0.966156840), (-0.424324989, +0.835064173), (+0.737160206, -0.971837282), (-0.949585438, +0.102951050)

361mean(0) = getMean(sample)

362mean(0) ! reference

363(-0.203336373, -0.123828739)

364var(0) = getVar(sample)

365var(0) ! reference

366+0.557901859

367do isam = 1, nsam

368 var(isam) = getVar(sample(lb(isam):ub(isam)))

369 mean(isam) = getMean(sample(lb(isam):ub(isam)))

370end do

371call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), ub(1) / real(ub(2), TKG))

372meanMerged

373(-0.203336358, -0.123828739)

374varMerged

375+0.557901859

376call setVarMeanMerged(var(2), mean(2), var(1), mean(1), ub(1) / real(ub(2), TKG))

377mean(2)

378(-0.203336358, -0.123828739)

379mean(0) ! reference

380(-0.203336373, -0.123828739)

381var(2)

382+0.557901859

383var(0) ! reference

384+0.557901859

385

386

387!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

388!Compute the biased merged variance and mean of a frequency weighted univariate sample.

389!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

390

391

392lb(1) = 1; ub(1) = getUnifRand(2, 7)

393do isam = 2, nsam

394 lb(isam) = ub(isam - 1) + 1

395 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

396end do

397lb

398+1, +6

399ub

400+5, +10

401sample = getUnifRand(0., 1., ub(nsam))

402sample

403+0.701505542E-1, +0.508313477, +0.663662851, +0.766035795, +0.129113495, +0.488194823E-1, +0.533005714, +0.840995431, +0.714910030E-1, +0.621918678

404iweight = getUnifRand(1, 10, size(sample, 1, IK))

405iweight

406+6, +6, +7, +10, +9, +3, +9, +7, +10, +6

407mean(0) = getMean(sample, iweight)

408mean(0) ! reference

409+0.441311032

410var(0) = getVar(sample, iweight)

411var(0) ! reference

412+0.869956687E-1

413do isam = 1, nsam

414 var(isam) = getVar(sample(lb(isam):ub(isam)), iweight(lb(isam):ub(isam)))

415 mean(isam) = getMean(sample(lb(isam):ub(isam)), iweight(lb(isam):ub(isam)))

416end do

417call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))

418meanMerged

419+0.441311061

420varMerged

421+0.869956613E-1

422call setVarMeanMerged(var(2), mean(2), var(1), mean(1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))

423mean(2)

424+0.441311061

425mean(0) ! reference

426+0.441311032

427var(2)

428+0.869956613E-1

429var(0) ! reference

430+0.869956687E-1

431

432

433lb(1) = 1; ub(1) = getUnifRand(2, 7)

434do isam = 2, nsam

435 lb(isam) = ub(isam - 1) + 1

436 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

437end do

438lb

439+1, +3

440ub

441+2, +6

442sample = getUnifRand(0., 1., ub(nsam))

443sample

444+0.596907258, +0.626886666, +0.858889878, +0.510622203, +0.609003961, +0.780717015

445iweight = getUnifRand(1, 10, size(sample, 1, IK))

446iweight

447+8, +5, +9, +1, +7, +4

448mean(0) = getMean(sample, iweight)

449mean(0) ! reference

450+0.692241669

451var(0) = getVar(sample, iweight)

452var(0) ! reference

453+0.134354997E-1

454do isam = 1, nsam

455 var(isam) = getVar(sample(lb(isam):ub(isam)), iweight(lb(isam):ub(isam)))

456 mean(isam) = getMean(sample(lb(isam):ub(isam)), iweight(lb(isam):ub(isam)))

457end do

458call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))

459meanMerged

460+0.692241669

461varMerged

462+0.134354997E-1

463call setVarMeanMerged(var(2), mean(2), var(1), mean(1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))

464mean(2)

465+0.692241669

466mean(0) ! reference

467+0.692241669

468var(2)

469+0.134354997E-1

470var(0) ! reference

471+0.134354997E-1

472

473

474lb(1) = 1; ub(1) = getUnifRand(2, 7)

475do isam = 2, nsam

476 lb(isam) = ub(isam - 1) + 1

477 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

478end do

479lb

480+1, +3

481ub

482+2, +7

483sample = getUnifRand(0., 1., ub(nsam))

484sample

485+0.335113466, +0.973845780, +0.818820000E-1, +0.996913373, +0.634366870, +0.131615400E-1, +0.471685588

486iweight = getUnifRand(1, 10, size(sample, 1, IK))

487iweight

488+5, +4, +1, +6, +2, +5, +5

489mean(0) = getMean(sample, iweight)

490mean(0) ! reference

491+0.547402918

492var(0) = getVar(sample, iweight)

493var(0) ! reference

494+0.137595579

495do isam = 1, nsam

496 var(isam) = getVar(sample(lb(isam):ub(isam)), iweight(lb(isam):ub(isam)))

497 mean(isam) = getMean(sample(lb(isam):ub(isam)), iweight(lb(isam):ub(isam)))

498end do

499call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))

500meanMerged

501+0.547402978

502varMerged

503+0.137595579

504call setVarMeanMerged(var(2), mean(2), var(1), mean(1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))

505mean(2)

506+0.547402978

507mean(0) ! reference

508+0.547402918

509var(2)

510+0.137595579

511var(0) ! reference

512+0.137595579

513

514

515lb(1) = 1; ub(1) = getUnifRand(2, 7)

516do isam = 2, nsam

517 lb(isam) = ub(isam - 1) + 1

518 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

519end do

520lb

521+1, +6

522ub

523+5, +11

524sample = getUnifRand(0., 1., ub(nsam))

525sample

526+0.422895610, +0.638454258, +0.829345107, +0.559985995, +0.598645210E-1, +0.914627314E-2, +0.829150975, +0.150096893, +0.981886268, +0.852020204, +0.153485954

527iweight = getUnifRand(1, 10, size(sample, 1, IK))

528iweight

529+4, +6, +4, +8, +2, +9, +1, +2, +5, +7, +4

530mean(0) = getMean(sample, iweight)

531mean(0) ! reference

532+0.502663136

533var(0) = getVar(sample, iweight)

534var(0) ! reference

535+0.115749151

536do isam = 1, nsam

537 var(isam) = getVar(sample(lb(isam):ub(isam)), iweight(lb(isam):ub(isam)))

538 mean(isam) = getMean(sample(lb(isam):ub(isam)), iweight(lb(isam):ub(isam)))

539end do

540call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))

541meanMerged

542+0.502663195

543varMerged

544+0.115749151

545call setVarMeanMerged(var(2), mean(2), var(1), mean(1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))

546mean(2)

547+0.502663195

548mean(0) ! reference

549+0.502663136

550var(2)

551+0.115749151

552var(0) ! reference

553+0.115749151

554

555

556lb(1) = 1; ub(1) = getUnifRand(2, 7)

557do isam = 2, nsam

558 lb(isam) = ub(isam - 1) + 1

559 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

560end do

561lb

562+1, +4

563ub

564+3, +5

565sample = getUnifRand(0., 1., ub(nsam))

566sample

567+0.173784912, +0.158469498, +0.739210546, +0.495084107, +0.337988734E-1

568iweight = getUnifRand(1, 10, size(sample, 1, IK))

569iweight

570+9, +1, +4, +8, +10

571mean(0) = getMean(sample, iweight)

572mean(0) ! reference

573+0.280563682

574var(0) = getVar(sample, iweight)

575var(0) ! reference

576+0.605009720E-1

577do isam = 1, nsam

578 var(isam) = getVar(sample(lb(isam):ub(isam)), iweight(lb(isam):ub(isam)))

579 mean(isam) = getMean(sample(lb(isam):ub(isam)), iweight(lb(isam):ub(isam)))

580end do

581call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))

582meanMerged

583+0.280563653

584varMerged

585+0.605009645E-1

586call setVarMeanMerged(var(2), mean(2), var(1), mean(1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))

587mean(2)

588+0.280563653

589mean(0) ! reference

590+0.280563682

591var(2)

592+0.605009645E-1

593var(0) ! reference

594+0.605009720E-1

595

596

597lb(1) = 1; ub(1) = getUnifRand(2, 7)

598do isam = 2, nsam

599 lb(isam) = ub(isam - 1) + 1

600 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

601end do

602lb

603+1, +3

604ub

605+2, +9

606sample = cmplx(getUnifRand(0., 1., ub(nsam)), -getUnifRand(0., 1., ub(nsam)), TKG)

607sample

608(+0.558308482, -0.966540754), (+0.431492269, -0.113531291), (+0.833939731, -0.940448761), (+0.305300236, -0.650056243), (+0.320975304, -0.355702698), (+0.492913067, -0.250933945), (+0.995503962, -0.222379148), (+0.487275422, -0.607189894), (+0.863998532, -0.644135475E-1)

609iweight = getUnifRand(1, 10, size(sample, 1, IK))

610iweight

611+6, +3, +4, +1, +2, +6, +1, +1, +2

612mean(0) = getMean(sample, iweight)

613mean(0) ! reference

614(+0.580599725, -0.527965188)

615var(0) = getVar(sample, iweight)

616var(0) ! reference

617+0.166873232

618do isam = 1, nsam

619 var(isam) = getVar(sample(lb(isam):ub(isam)), iweight(lb(isam):ub(isam)))

620 mean(isam) = getMean(sample(lb(isam):ub(isam)), iweight(lb(isam):ub(isam)))

621end do

622call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))

623meanMerged

624(+0.580599666, -0.527965188)

625varMerged

626+0.166873217

627call setVarMeanMerged(var(2), mean(2), var(1), mean(1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))

628mean(2)

629(+0.580599666, -0.527965188)

630mean(0) ! reference

631(+0.580599725, -0.527965188)

632var(2)

633+0.166873217

634var(0) ! reference

635+0.166873232

636

637

638lb(1) = 1; ub(1) = getUnifRand(2, 7)

639do isam = 2, nsam

640 lb(isam) = ub(isam - 1) + 1

641 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

642end do

643lb

644+1, +3

645ub

646+2, +6

647sample = cmplx(getUnifRand(0., 1., ub(nsam)), -getUnifRand(0., 1., ub(nsam)), TKG)

648sample

649(+0.358182371, -0.448367715), (+0.775513649, -0.144074440), (+0.779866338, -0.909540296), (+0.611526370E-1, -0.319255292), (+0.598419309E-1, -0.532354891), (+0.359419882, -0.894570708)

650iweight = getUnifRand(1, 10, size(sample, 1, IK))

651iweight

652+10, +1, +3, +6, +2, +2

653mean(0) = getMean(sample, iweight)

654mean(0) ! reference

655(+0.329265654, -0.505239785)

656var(0) = getVar(sample, iweight)

657var(0) ! reference

658+0.106677353

659do isam = 1, nsam

660 var(isam) = getVar(sample(lb(isam):ub(isam)), iweight(lb(isam):ub(isam)))

661 mean(isam) = getMean(sample(lb(isam):ub(isam)), iweight(lb(isam):ub(isam)))

662end do

663call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))

664meanMerged

665(+0.329265654, -0.505239785)

666varMerged

667+0.106677361

668call setVarMeanMerged(var(2), mean(2), var(1), mean(1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))

669mean(2)

670(+0.329265654, -0.505239785)

671mean(0) ! reference

672(+0.329265654, -0.505239785)

673var(2)

674+0.106677361

675var(0) ! reference

676+0.106677353

677

678

679lb(1) = 1; ub(1) = getUnifRand(2, 7)

680do isam = 2, nsam

681 lb(isam) = ub(isam - 1) + 1

682 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

683end do

684lb

685+1, +4

686ub

687+3, +8

688sample = cmplx(getUnifRand(0., 1., ub(nsam)), -getUnifRand(0., 1., ub(nsam)), TKG)

689sample

690(+0.711909115, -0.841032982), (+0.269236028, -0.573951840), (+0.687201858, -0.726742506), (+0.318318903, -0.564504802), (+0.490798354E-1, -0.957034111), (+0.461083829, -0.359048188), (+0.902928472, -0.827983439), (+0.382648230, -0.613879204)

691iweight = getUnifRand(1, 10, size(sample, 1, IK))

692iweight

693+7, +6, +7, +8, +8, +4, +10, +9

694mean(0) = getMean(sample, iweight)

695mean(0) ! reference

696(+0.485861659, -0.709006667)

697var(0) = getVar(sample, iweight)

698var(0) ! reference

699+0.103683129

700do isam = 1, nsam

701 var(isam) = getVar(sample(lb(isam):ub(isam)), iweight(lb(isam):ub(isam)))

702 mean(isam) = getMean(sample(lb(isam):ub(isam)), iweight(lb(isam):ub(isam)))

703end do

704call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))

705meanMerged

706(+0.485861659, -0.709006667)

707varMerged

708+0.103683144

709call setVarMeanMerged(var(2), mean(2), var(1), mean(1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))

710mean(2)

711(+0.485861659, -0.709006667)

712mean(0) ! reference

713(+0.485861659, -0.709006667)

714var(2)

715+0.103683144

716var(0) ! reference

717+0.103683129

718

719

720lb(1) = 1; ub(1) = getUnifRand(2, 7)

721do isam = 2, nsam

722 lb(isam) = ub(isam - 1) + 1

723 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

724end do

725lb

726+1, +7

727ub

728+6, +11

729sample = cmplx(getUnifRand(0., 1., ub(nsam)), -getUnifRand(0., 1., ub(nsam)), TKG)

730sample

731(+0.987938046E-1, -0.979642093), (+0.266931891, -0.334516943), (+0.602450013, -0.584214926E-2), (+0.656891644, -0.182013988), (+0.396838129, -0.253311217), (+0.639068127, -0.202912629), (+0.478952527E-1, -0.126890540), (+0.652961493, -0.565283179), (+0.987951398, -0.313381433), (+0.266513228, -0.516300797), (+0.464500844, -0.696025372)

732iweight = getUnifRand(1, 10, size(sample, 1, IK))

733iweight

734+9, +4, +1, +8, +4, +2, +3, +5, +4, +10, +4

735mean(0) = getMean(sample, iweight)

736mean(0) ! reference

737(+0.417840362, -0.471177638)

738var(0) = getVar(sample, iweight)

739var(0) ! reference

740+0.151217729

741do isam = 1, nsam

742 var(isam) = getVar(sample(lb(isam):ub(isam)), iweight(lb(isam):ub(isam)))

743 mean(isam) = getMean(sample(lb(isam):ub(isam)), iweight(lb(isam):ub(isam)))

744end do

745call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))

746meanMerged

747(+0.417840362, -0.471177667)

748varMerged

749+0.151217729

750call setVarMeanMerged(var(2), mean(2), var(1), mean(1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))

751mean(2)

752(+0.417840362, -0.471177667)

753mean(0) ! reference

754(+0.417840362, -0.471177638)

755var(2)

756+0.151217729

757var(0) ! reference

758+0.151217729

759

760

761lb(1) = 1; ub(1) = getUnifRand(2, 7)

762do isam = 2, nsam

763 lb(isam) = ub(isam - 1) + 1

764 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

765end do

766lb

767+1, +5

768ub

769+4, +7

770sample = cmplx(getUnifRand(0., 1., ub(nsam)), -getUnifRand(0., 1., ub(nsam)), TKG)

771sample

772(+0.255483687, -0.863725185), (+0.252958536E-1, -0.131093144), (+0.827879131, -0.233905315E-1), (+0.141663313, -0.838022411), (+0.123178959E-1, -0.273090243), (+0.521687031, -0.840979874), (+0.168640614, -0.666367531)

773iweight = getUnifRand(1, 10, size(sample, 1, IK))

774iweight

775+4, +6, +10, +3, +8, +6, +1

776mean(0) = getMean(sample, iweight)

777mean(0) ! reference

778(+0.349336773, -0.391747385)

779var(0) = getVar(sample, iweight)

780var(0) ! reference

781+0.233056664

782do isam = 1, nsam

783 var(isam) = getVar(sample(lb(isam):ub(isam)), iweight(lb(isam):ub(isam)))

784 mean(isam) = getMean(sample(lb(isam):ub(isam)), iweight(lb(isam):ub(isam)))

785end do

786call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))

787meanMerged

788(+0.349336773, -0.391747385)

789varMerged

790+0.233056650

791call setVarMeanMerged(var(2), mean(2), var(1), mean(1), real(sum(iweight(:ub(1))), TKG) / real(sum(iweight), TKG))

792mean(2)

793(+0.349336773, -0.391747385)

794mean(0) ! reference

795(+0.349336773, -0.391747385)

796var(2)

797+0.233056650

798var(0) ! reference

799+0.233056664

800

801

802!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

803!Compute the biased merged variance and mean of a reliability weighted univariate sample.

804!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

805

806

807lb(1) = 1; ub(1) = getUnifRand(2, 7)

808do isam = 2, nsam

809 lb(isam) = ub(isam - 1) + 1

810 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

811end do

812lb

813+1, +8

814ub

815+7, +14

816sample = getUnifRand(0., 1., ub(nsam))

817sample

818+0.132835269, +0.871566176, +0.775098443, +0.907114089, +0.543647945, +0.767972767, +0.747309387, +0.377118051, +0.887677670, +0.682251513, +0.542521238, +0.744446516E-1, +0.393683314, +0.756820977

819rweight = getUnifRand(1., 2., size(sample, 1, IK))

820rweight

821+1.22699714, +1.18399847, +1.77490568, +1.27476716, +1.69784927, +1.09041381, +1.34542489, +1.66541398, +1.75653911, +1.59754062, +1.79350400, +1.21765828, +1.75040889, +1.15708590

822mean(0) = getMean(sample, rweight)

823mean(0) ! reference

824+0.603851974

825var(0) = getVar(sample, rweight)

826var(0) ! reference

827+0.622879639E-1

828do isam = 1, nsam

829 var(isam) = getVar(sample(lb(isam):ub(isam)), rweight(lb(isam):ub(isam)))

830 mean(isam) = getMean(sample(lb(isam):ub(isam)), rweight(lb(isam):ub(isam)))

831end do

832call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))

833meanMerged

834+0.603851974

835varMerged

836+0.622879639E-1

837call setVarMeanMerged(var(2), mean(2), var(1), mean(1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))

838mean(2)

839+0.603851974

840mean(0) ! reference

841+0.603851974

842var(2)

843+0.622879639E-1

844var(0) ! reference

845+0.622879639E-1

846

847

848lb(1) = 1; ub(1) = getUnifRand(2, 7)

849do isam = 2, nsam

850 lb(isam) = ub(isam - 1) + 1

851 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

852end do

853lb

854+1, +7

855ub

856+6, +12

857sample = getUnifRand(0., 1., ub(nsam))

858sample

859+0.385523200, +0.151785374, +0.892585039, +0.805965960, +0.524945855, +0.951787770, +0.701613188, +0.747123420, +0.696798205, +0.673267841E-1, +0.535488605, +0.402875066

860rweight = getUnifRand(1., 2., size(sample, 1, IK))

861rweight

862+1.49040484, +1.00088000, +1.05744600, +1.19077814, +1.57509434, +1.39221954, +1.51680493, +1.29833269, +1.62845206, +1.46337569, +1.35242033, +1.58305430

863mean(0) = getMean(sample, rweight)

864mean(0) ! reference

865+0.568693519

866var(0) = getVar(sample, rweight)

867var(0) ! reference

868+0.674956143E-1

869do isam = 1, nsam

870 var(isam) = getVar(sample(lb(isam):ub(isam)), rweight(lb(isam):ub(isam)))

871 mean(isam) = getMean(sample(lb(isam):ub(isam)), rweight(lb(isam):ub(isam)))

872end do

873call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))

874meanMerged

875+0.568693519

876varMerged

877+0.674956143E-1

878call setVarMeanMerged(var(2), mean(2), var(1), mean(1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))

879mean(2)

880+0.568693519

881mean(0) ! reference

882+0.568693519

883var(2)

884+0.674956143E-1

885var(0) ! reference

886+0.674956143E-1

887

888

889lb(1) = 1; ub(1) = getUnifRand(2, 7)

890do isam = 2, nsam

891 lb(isam) = ub(isam - 1) + 1

892 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

893end do

894lb

895+1, +4

896ub

897+3, +8

898sample = getUnifRand(0., 1., ub(nsam))

899sample

900+0.396233797E-2, +0.786422789, +0.471328497E-1, +0.602182388, +0.485928059, +0.486149132, +0.131243944, +0.834346592

901rweight = getUnifRand(1., 2., size(sample, 1, IK))

902rweight

903+1.84344220, +1.58568430, +1.44832397, +1.95216489, +1.72541952, +1.59418809, +1.16701436, +1.19981599

904mean(0) = getMean(sample, rweight)

905mean(0) ! reference

906+0.420724869

907var(0) = getVar(sample, rweight)

908var(0) ! reference

909+0.891571492E-1

910do isam = 1, nsam

911 var(isam) = getVar(sample(lb(isam):ub(isam)), rweight(lb(isam):ub(isam)))

912 mean(isam) = getMean(sample(lb(isam):ub(isam)), rweight(lb(isam):ub(isam)))

913end do

914call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))

915meanMerged

916+0.420724869

917varMerged

918+0.891571566E-1

919call setVarMeanMerged(var(2), mean(2), var(1), mean(1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))

920mean(2)

921+0.420724869

922mean(0) ! reference

923+0.420724869

924var(2)

925+0.891571566E-1

926var(0) ! reference

927+0.891571492E-1

928

929

930lb(1) = 1; ub(1) = getUnifRand(2, 7)

931do isam = 2, nsam

932 lb(isam) = ub(isam - 1) + 1

933 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

934end do

935lb

936+1, +7

937ub

938+6, +10

939sample = getUnifRand(0., 1., ub(nsam))

940sample

941+0.205258787, +0.893208385E-1, +0.946596920, +0.893974543, +0.386933804, +0.815021157, +0.759558976, +0.529469252, +0.297594368, +0.870348871

942rweight = getUnifRand(1., 2., size(sample, 1, IK))

943rweight

944+1.13571191, +1.66045403, +1.64836907, +1.13851058, +1.44940674, +1.60287857, +1.35368907, +1.59423661, +1.40005064, +1.72472763

945mean(0) = getMean(sample, rweight)

946mean(0) ! reference

947+0.585859418

948var(0) = getVar(sample, rweight)

949var(0) ! reference

950+0.910973400E-1

951do isam = 1, nsam

952 var(isam) = getVar(sample(lb(isam):ub(isam)), rweight(lb(isam):ub(isam)))

953 mean(isam) = getMean(sample(lb(isam):ub(isam)), rweight(lb(isam):ub(isam)))

954end do

955call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))

956meanMerged

957+0.585859418

958varMerged

959+0.910973251E-1

960call setVarMeanMerged(var(2), mean(2), var(1), mean(1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))

961mean(2)

962+0.585859418

963mean(0) ! reference

964+0.585859418

965var(2)

966+0.910973251E-1

967var(0) ! reference

968+0.910973400E-1

969

970

971lb(1) = 1; ub(1) = getUnifRand(2, 7)

972do isam = 2, nsam

973 lb(isam) = ub(isam - 1) + 1

974 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

975end do

976lb

977+1, +3

978ub

979+2, +7

980sample = getUnifRand(0., 1., ub(nsam))

981sample

982+0.505931675, +0.527020872, +0.486540020, +0.537758350, +0.387741745, +0.720295787, +0.962912679

983rweight = getUnifRand(1., 2., size(sample, 1, IK))

984rweight

985+1.53134251, +1.26934409, +1.86794567, +1.85778236, +1.29841423, +1.20967221, +1.44157910

986mean(0) = getMean(sample, rweight)

987mean(0) ! reference

988+0.583661079

989var(0) = getVar(sample, rweight)

990var(0) ! reference

991+0.300327372E-1

992do isam = 1, nsam

993 var(isam) = getVar(sample(lb(isam):ub(isam)), rweight(lb(isam):ub(isam)))

994 mean(isam) = getMean(sample(lb(isam):ub(isam)), rweight(lb(isam):ub(isam)))

995end do

996call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))

997meanMerged

998+0.583661079

999varMerged

1000+0.300327390E-1

1001call setVarMeanMerged(var(2), mean(2), var(1), mean(1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))

1002mean(2)

1003+0.583661079

1004mean(0) ! reference

1005+0.583661079

1006var(2)

1007+0.300327390E-1

1008var(0) ! reference

1009+0.300327372E-1

1010

1011

1012lb(1) = 1; ub(1) = getUnifRand(2, 7)

1013do isam = 2, nsam

1014 lb(isam) = ub(isam - 1) + 1

1015 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

1016end do

1017lb

1018+1, +7

1019ub

1020+6, +9

1021sample = cmplx(getUnifRand(0., 1., ub(nsam)), -getUnifRand(0., 1., ub(nsam)), TKG)

1022sample

1023(+0.145176530, -0.660803080), (+0.692834854E-1, -0.524664700), (+0.921244144, -0.426119447), (+0.899475634, -0.535263300), (+0.473420918, -0.416758120), (+0.604838371, -0.511714697), (+0.342711806E-1, -0.805644035), (+0.487457275, -0.203567863), (+0.541109562, -0.115936935)

1024rweight = getUnifRand(1., 2., size(sample, 1, IK))

1025rweight

1026+1.60351181, +1.49233472, +1.12591147, +1.94855857, +1.01515245, +1.90431690, +1.26000714, +1.62076271, +1.59752035

1027mean(0) = getMean(sample, rweight)

1028mean(0) ! reference

1029(+0.475835502, -0.463820279)

1030var(0) = getVar(sample, rweight)

1031var(0) ! reference

1032+0.133821428

1033do isam = 1, nsam

1034 var(isam) = getVar(sample(lb(isam):ub(isam)), rweight(lb(isam):ub(isam)))

1035 mean(isam) = getMean(sample(lb(isam):ub(isam)), rweight(lb(isam):ub(isam)))

1036end do

1037call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))

1038meanMerged

1039(+0.475835532, -0.463820308)

1040varMerged

1041+0.133821428

1042call setVarMeanMerged(var(2), mean(2), var(1), mean(1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))

1043mean(2)

1044(+0.475835532, -0.463820308)

1045mean(0) ! reference

1046(+0.475835502, -0.463820279)

1047var(2)

1048+0.133821428

1049var(0) ! reference

1050+0.133821428

1051

1052

1053lb(1) = 1; ub(1) = getUnifRand(2, 7)

1054do isam = 2, nsam

1055 lb(isam) = ub(isam - 1) + 1

1056 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

1057end do

1058lb

1059+1, +7

1060ub

1061+6, +9

1062sample = cmplx(getUnifRand(0., 1., ub(nsam)), -getUnifRand(0., 1., ub(nsam)), TKG)

1063sample

1064(+0.241394639E-1, -0.748961091), (+0.253201246, -0.899627328), (+0.212384999, -0.271962345), (+0.300542712E-1, -0.374002814), (+0.996819735, -0.791645885), (+0.634574950, -0.480429113), (+0.174930692, -0.407218218), (+0.213004172, -0.684497714), (+0.827396333, -0.463329673)

1065rweight = getUnifRand(1., 2., size(sample, 1, IK))

1066rweight

1067+1.38830280, +1.45451522, +1.05288303, +1.00300562, +1.94611835, +1.98834896, +1.67692256, +1.29554772, +1.89863777

1068mean(0) = getMean(sample, rweight)

1069mean(0) ! reference

1070(+0.437634945, -0.580478609)

1071var(0) = getVar(sample, rweight)

1072var(0) ! reference

1073+0.159782201

1074do isam = 1, nsam

1075 var(isam) = getVar(sample(lb(isam):ub(isam)), rweight(lb(isam):ub(isam)))

1076 mean(isam) = getMean(sample(lb(isam):ub(isam)), rweight(lb(isam):ub(isam)))

1077end do

1078call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))

1079meanMerged

1080(+0.437634945, -0.580478609)

1081varMerged

1082+0.159782201

1083call setVarMeanMerged(var(2), mean(2), var(1), mean(1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))

1084mean(2)

1085(+0.437634945, -0.580478609)

1086mean(0) ! reference

1087(+0.437634945, -0.580478609)

1088var(2)

1089+0.159782201

1090var(0) ! reference

1091+0.159782201

1092

1093

1094lb(1) = 1; ub(1) = getUnifRand(2, 7)

1095do isam = 2, nsam

1096 lb(isam) = ub(isam - 1) + 1

1097 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

1098end do

1099lb

1100+1, +3

1101ub

1102+2, +4

1103sample = cmplx(getUnifRand(0., 1., ub(nsam)), -getUnifRand(0., 1., ub(nsam)), TKG)

1104sample

1105(+0.249018967, -0.886792243), (+0.673844218, -0.468544424), (+0.427544892, -0.629629791), (+0.420058727, -0.593061984)

1106rweight = getUnifRand(1., 2., size(sample, 1, IK))

1107rweight

1108+1.14002752, +1.65599191, +1.93492341, +1.00124562

1109mean(0) = getMean(sample, rweight)

1110mean(0) ! reference

1111(+0.461886048, -0.627850950)

1112var(0) = getVar(sample, rweight)

1113var(0) ! reference

1114+0.435736962E-1

1115do isam = 1, nsam

1116 var(isam) = getVar(sample(lb(isam):ub(isam)), rweight(lb(isam):ub(isam)))

1117 mean(isam) = getMean(sample(lb(isam):ub(isam)), rweight(lb(isam):ub(isam)))

1118end do

1119call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))

1120meanMerged

1121(+0.461885989, -0.627850771)

1122varMerged

1123+0.435736999E-1

1124call setVarMeanMerged(var(2), mean(2), var(1), mean(1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))

1125mean(2)

1126(+0.461885989, -0.627850771)

1127mean(0) ! reference

1128(+0.461886048, -0.627850950)

1129var(2)

1130+0.435736999E-1

1131var(0) ! reference

1132+0.435736962E-1

1133

1134

1135lb(1) = 1; ub(1) = getUnifRand(2, 7)

1136do isam = 2, nsam

1137 lb(isam) = ub(isam - 1) + 1

1138 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

1139end do

1140lb

1141+1, +4

1142ub

1143+3, +5

1144sample = cmplx(getUnifRand(0., 1., ub(nsam)), -getUnifRand(0., 1., ub(nsam)), TKG)

1145sample

1146(+0.250425339, -0.129961252), (+0.458485603, -0.416625142), (+0.632188916E-1, -0.594669700), (+0.932048678, -0.610012352), (+0.471760213, -0.339183271)

1147rweight = getUnifRand(1., 2., size(sample, 1, IK))

1148rweight

1149+1.15344775, +1.08451664, +1.01332998, +1.51756334, +1.98186207

1150mean(0) = getMean(sample, rweight)

1151mean(0) ! reference

1152(+0.473957717, -0.415108919)

1153var(0) = getVar(sample, rweight)

1154var(0) ! reference

1155+0.110039875

1156do isam = 1, nsam

1157 var(isam) = getVar(sample(lb(isam):ub(isam)), rweight(lb(isam):ub(isam)))

1158 mean(isam) = getMean(sample(lb(isam):ub(isam)), rweight(lb(isam):ub(isam)))

1159end do

1160call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))

1161meanMerged

1162(+0.473957747, -0.415108919)

1163varMerged

1164+0.110039860

1165call setVarMeanMerged(var(2), mean(2), var(1), mean(1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))

1166mean(2)

1167(+0.473957747, -0.415108919)

1168mean(0) ! reference

1169(+0.473957717, -0.415108919)

1170var(2)

1171+0.110039860

1172var(0) ! reference

1173+0.110039875

1174

1175

1176lb(1) = 1; ub(1) = getUnifRand(2, 7)

1177do isam = 2, nsam

1178 lb(isam) = ub(isam - 1) + 1

1179 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

1180end do

1181lb

1182+1, +8

1183ub

1184+7, +11

1185sample = cmplx(getUnifRand(0., 1., ub(nsam)), -getUnifRand(0., 1., ub(nsam)), TKG)

1186sample

1187(+0.696598232, -0.151467144), (+0.351984441, -0.814055145), (+0.195879579, -0.724640489E-1), (+0.489833176, -0.436737955), (+0.415061951, -0.887042761), (+0.775786877, -0.510850668), (+0.603616834E-1, -0.516502917), (+0.781464994, -0.820315003), (+0.767220140, -0.678626120), (+0.124815583, -0.825029254), (+0.707865298, -0.177748680)

1188rweight = getUnifRand(1., 2., size(sample, 1, IK))

1189rweight

1190+1.26175809, +1.50726783, +1.10619044, +1.21604908, +1.07151687, +1.50455964, +1.44589996, +1.75267696, +1.71240234, +1.86201596, +1.35395122

1191mean(0) = getMean(sample, rweight)

1192mean(0) ! reference

1193(+0.493553340, -0.561720431)

1194var(0) = getVar(sample, rweight)

1195var(0) ! reference

1196+0.148701340

1197do isam = 1, nsam

1198 var(isam) = getVar(sample(lb(isam):ub(isam)), rweight(lb(isam):ub(isam)))

1199 mean(isam) = getMean(sample(lb(isam):ub(isam)), rweight(lb(isam):ub(isam)))

1200end do

1201call setVarMeanMerged(varMerged, meanMerged, var(2), mean(2), var(1), mean(1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))

1202meanMerged

1203(+0.493553370, -0.561720490)

1204varMerged

1205+0.148701355

1206call setVarMeanMerged(var(2), mean(2), var(1), mean(1), real(sum(rweight(:ub(1))), TKG) / real(sum(rweight), TKG))

1207mean(2)

1208(+0.493553370, -0.561720490)

1209mean(0) ! reference

1210(+0.493553340, -0.561720431)

1211var(2)

1212+0.148701355

1213var(0) ! reference

1214+0.148701340

1215

1216

1217!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

1218!Compute the biased merged variance and mean of a multivariate sample.

1219!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

1220

1221

1222dim = 2; lb(1) = 1; ub(1) = getUnifRand(2, 7)

1223do isam = 2, nsam

1224 lb(isam) = ub(isam - 1) + 1

1225 ub(isam) = ub(isam - 1) + getUnifRand(2, 7)

1226end do

1227lb

1228+1, +7

1229ub

1230+6, +12

1231ndim = getUnifRand(1, minval(ub - lb + 1, 1))

1232call setRebound(var, [1_IK, 0_IK], [ndim, nsam])

1233call setRebound(mean, [1_IK, 0_IK], [ndim, nsam])

1234call setResized(meanMerged, ndim)

1235call setResized(varMerged, ndim)

1236sample = getUnifRand(-1., +1., ndim, ub(nsam))

1237sample

1238-0.570608616, +0.675416708, -0.1638094