This is the indicator type for generating instances of objects that indicate the integration interval is open and, the intervals should be spaced assuming an integrand that behaves like a Negative-Exponent Exponential (NEXP), such that the upper limit of integration is allowed to be \(b = +\infty\). More...

Detailed Description

This is the indicator type for generating instances of objects that indicate the integration interval is open and, the intervals should be spaced assuming an integrand that behaves like a Negative-Exponent Exponential (NEXP), such that the upper limit of integration is allowed to be \(b = +\infty\).

This is an empty derived type that exists solely for generating unique objects that are distinguishable as input arguments to procedures under the generic interface getQuadRomb.

Possible calling interfaces ⛓

: use pm_quadRomb, only: nexp_type

type(nexp_type) :: NEXP

pm_quadRomb
This module contains classes and procedures to perform numerical integrations.
Definition: pm_quadRomb.F90:31

pm_quadRomb::nexp_type
This is the indicator type for generating instances of objects that indicate the integration interval...
Definition: pm_quadRomb.F90:169

See also: lbis_type
nexp_type
open_type
pexp_type
pwrl_type
ubis_type
getQuadRomb

Example usage ⛓

: 1program example

2

3 use pm_kind, only: SK, IK, SP => RKS, DP => RKD, QP => RKH ! all real kinds are supported.

4 use pm_mathGamma, only: getGammaIncLow

5 use pm_distExp, only: getExpCDF

6 use pm_distExp, only: getExpLogPDF

7 use pm_distGamma, only: getGammaLogPDF

8 use pm_quadRomb, only: getQuadRomb, nexp_type

9 use pm_io, only: display_type

10

11 implicit none

12

13 integer(IK) :: neval

14

15 real(SP) :: quad_SP, quadref_SP, relerr_SP, kappa_SP, invSigma_SP

16 real(DP) :: quad_DP, quadref_DP, relerr_DP, kappa_DP, invSigma_DP

17 real(QP) :: quad_QP, quadref_QP, relerr_QP, kappa_QP, invSigma_QP

18

19 type(display_type) :: disp

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

21

22 call disp%skip()

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

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

25 call disp%show("! Compute the Cumulative Distribution Function (CDF) over the semi-infinite interval of Exponential distribution.")

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

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

28 call disp%skip()

29

30 call disp%skip()

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

32 call disp%show("! Compute the numerical integration with single precision.")

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

34 call disp%skip()

35

36 call disp%skip()

37 call disp%show("invSigma_SP = 3._SP")

38 invSigma_SP = 3._SP

39 call disp%show("quadref_SP = getExpCDF(x = log(huge(0._SP)), invSigma = invSigma_SP)")

40 quadref_SP = getExpCDF(x = log(huge(0._SP)), invSigma = invSigma_SP)

41 call disp%show("quadref_SP")

42 call disp%show( quadref_SP )

43 call disp%show("quad_SP = getQuadRomb(getFunc = getExpPDF_SP, lb = 0._SP, ub = huge(0._SP), tol = epsilon(1._SP) * 100, nref = 4_IK, interval = nexp_type(), relerr = relerr_SP, neval = neval)")

44 quad_SP = getQuadRomb(getFunc = getExpPDF_SP, lb = 0._SP, ub = huge(0._SP), tol = epsilon(1._SP) * 100, nref = 4_IK, interval = nexp_type(), relerr = relerr_SP, neval = neval)

45 call disp%show("if (relerr_SP < 0._SP) error stop 'Integration failed to converge.'")

46 if (relerr_SP < 0._SP) error stop 'Integration failed to converge.'

47 call disp%show("relerr_SP ! < 0. if integration fails.")

48 call disp%show( relerr_SP )

49 call disp%show("neval ! # calls to the integrand.")

50 call disp%show( neval )

51 call disp%show("quad_SP ! integral")

52 call disp%show( quad_SP )

53 call disp%skip()

54

55 call disp%skip()

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

57 call disp%show("! Compute the numerical integration with double precision.")

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

59 call disp%skip()

60

61 call disp%skip()

62 call disp%show("invSigma_DP = 3._DP")

63 invSigma_DP = 3._DP

64 call disp%show("quadref_DP = getExpCDF(x = log(huge(0._DP)), invSigma = invSigma_DP)")

65 quadref_DP = getExpCDF(x = log(huge(0._DP)), invSigma = invSigma_DP)

66 call disp%show("quadref_DP")

67 call disp%show( quadref_DP )

68 call disp%show("quad_DP = getQuadRomb(getFunc = getExpPDF_DP, lb = 0._DP, ub = huge(0._DP), tol = epsilon(1._DP) * 100, nref = 4_IK, interval = nexp_type(), relerr = relerr_DP, neval = neval)")

69 quad_DP = getQuadRomb(getFunc = getExpPDF_DP, lb = 0._DP, ub = huge(0._DP), tol = epsilon(1._DP) * 100, nref = 4_IK, interval = nexp_type(), relerr = relerr_DP, neval = neval)

70 call disp%show("if (relerr_DP < 0.) error stop 'Integration failed to converge.'")

71 if (relerr_DP < 0.) error stop 'Integration failed to converge.'

72 call disp%show("relerr_DP ! < 0. if integration fails.")

73 call disp%show( relerr_DP )

74 call disp%show("neval ! # calls to the integrand.")

75 call disp%show( neval )

76 call disp%show("quad_DP ! integral")

77 call disp%show( quad_DP )

78 call disp%skip()

79

80 call disp%skip()

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

82 call disp%show("! Compute the numerical integration with double precision.")

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

84 call disp%skip()

85

86 call disp%skip()

87 call disp%show("invSigma_QP = 3._QP")

88 invSigma_QP = 3._QP

89 call disp%show("quadref_QP = getExpCDF(x = log(huge(0._QP)), invSigma = invSigma_QP)")

90 quadref_QP = getExpCDF(x = log(huge(0._QP)), invSigma = invSigma_QP)

91 call disp%show("quadref_QP")

92 call disp%show( quadref_QP )

93 call disp%show("quad_QP = getQuadRomb(getFunc = getExpPDF_QP, lb = 0._QP, ub = huge(0._QP), tol = epsilon(1._QP) * 100, nref = 4_IK, interval = nexp_type(), relerr = relerr_QP, neval = neval)")

94 quad_QP = getQuadRomb(getFunc = getExpPDF_QP, lb = 0._QP, ub = huge(0._QP), tol = epsilon(1._QP) * 100, nref = 4_IK, interval = nexp_type(), relerr = relerr_QP, neval = neval)

95 call disp%show("if (relerr_QP < 0.) error stop 'Integration failed to converge.'")

96 if (relerr_QP < 0.) error stop 'Integration failed to converge.'

97 call disp%show("relerr_QP ! < 0. if integration fails.")

98 call disp%show( relerr_QP )

99 call disp%show("neval ! # calls to the integrand.")

100 call disp%show( neval )

101 call disp%show("quad_QP ! integral")

102 call disp%show( quad_QP )

103 call disp%skip()

104

105 call disp%skip()

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

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

108 call disp%show("! Compute the Cumulative Distribution Function (CDF) over the semi-infinite interval of Gamma distribution whose tail decays exponentially.")

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

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

111 call disp%skip()

112

113 call disp%skip()

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

115 call disp%show("! Compute the numerical integration with single precision.")

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

117 call disp%skip()

118

119 call disp%skip()

120 call disp%show("kappa_SP = 2._SP")

121 kappa_SP = 2._SP

122 call disp%show("invSigma_SP = 2._SP")

123 invSigma_SP = 2._SP

124 call disp%show("quadref_SP = getGammaIncLow(log(huge(0._SP)), kappa = kappa_SP) - getGammaIncLow(0._SP, kappa = kappa_SP)")

125 quadref_SP = getGammaIncLow(log(huge(0._SP)), kappa = kappa_SP) - getGammaIncLow(0._SP, kappa = kappa_SP)

126 call disp%show("quadref_SP")

127 call disp%show( quadref_SP )

128 call disp%show("quad_SP = getQuadRomb(getFunc = getGammaPDF_SP, lb = 0._SP, ub = huge(0._SP), tol = epsilon(1._SP) * 100, nref = 4_IK, interval = nexp_type(), relerr = relerr_SP, neval = neval)")

129 quad_SP = getQuadRomb(getFunc = getGammaPDF_SP, lb = 0._SP, ub = huge(0._SP), tol = epsilon(1._SP) * 100, nref = 4_IK, interval = nexp_type(), relerr = relerr_SP, neval = neval)

130 call disp%show("if (relerr_SP < 0._SP) error stop 'Integration failed to converge.'")

131 if (relerr_SP < 0._SP) error stop 'Integration failed to converge.'

132 call disp%show("relerr_SP ! < 0. if integration fails.")

133 call disp%show( relerr_SP )

134 call disp%show("neval ! # calls to the integrand.")

135 call disp%show( neval )

136 call disp%show("quad_SP ! integral")

137 call disp%show( quad_SP )

138 call disp%skip()

139

140 call disp%skip()

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

142 call disp%show("! Compute the numerical integration with double precision.")

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

144 call disp%skip()

145

146 call disp%skip()

147 call disp%show("kappa_DP = 2._DP")

148 kappa_DP = 2._DP

149 call disp%show("invSigma_DP = 2._DP")

150 invSigma_DP = 2._DP

151 call disp%show("quadref_DP = getGammaIncLow(log(huge(0._DP)), kappa = kappa_DP) - getGammaIncLow(0._DP, kappa = kappa_DP)")

152 quadref_DP = getGammaIncLow(log(huge(0._DP)), kappa = kappa_DP) - getGammaIncLow(0._DP, kappa = kappa_DP)

153 call disp%show("quadref_DP")

154 call disp%show( quadref_DP )

155 call disp%show("quad_DP = getQuadRomb(getFunc = getGammaPDF_DP, lb = 0._DP, ub = huge(0._DP), tol = epsilon(1._DP) * 100, nref = 7_IK, interval = nexp_type(), relerr = relerr_DP, neval = neval)")

156 quad_DP = getQuadRomb(getFunc = getGammaPDF_DP, lb = 0._DP, ub = huge(0._DP), tol = epsilon(1._DP) * 100, nref = 7_IK, interval = nexp_type(), relerr = relerr_DP, neval = neval)

157 call disp%show("if (relerr_DP < 0._DP) error stop 'Integration failed to converge.'")

158 if (relerr_DP < 0._DP) error stop 'Integration failed to converge.'

159 call disp%show("relerr_DP ! < 0. if integration fails.")

160 call disp%show( relerr_DP )

161 call disp%show("neval ! # calls to the integrand.")

162 call disp%show( neval )

163 call disp%show("quad_DP ! integral")

164 call disp%show( quad_DP )

165 call disp%skip()

166

167 call disp%skip()

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

169 call disp%show("! Compute the numerical integration with quadro precision.")

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

171 call disp%skip()

172

173 call disp%skip()

174 call disp%show("kappa_QP = 2._QP")

175 kappa_QP = 2._QP

176 call disp%show("invSigma_QP = 2._QP")

177 invSigma_QP = 2._QP

178 call disp%show("quadref_QP = getGammaIncLow(log(huge(0._QP)), kappa = kappa_QP) - getGammaIncLow(0._QP, kappa = kappa_QP)")

179 quadref_QP = getGammaIncLow(log(huge(0._QP)), kappa = kappa_QP) - getGammaIncLow(0._QP, kappa = kappa_QP)

180 call disp%show("quadref_QP")

181 call disp%show( quadref_QP )

182 call disp%show("quad_QP = getQuadRomb(getFunc = getGammaPDF_QP, lb = 0._QP, ub = huge(0._QP), tol = sqrt(epsilon(1._QP)), nref = 10_IK, interval = nexp_type(), relerr = relerr_QP, neval = neval)")

183 quad_QP = getQuadRomb(getFunc = getGammaPDF_QP, lb = 0._QP, ub = huge(0._QP), tol = sqrt(epsilon(1._QP)), nref = 10_IK, interval = nexp_type(), relerr = relerr_QP, neval = neval)

184 call disp%show("if (relerr_QP < 0._QP) error stop 'Integration failed to converge.'")

185 if (relerr_QP < 0._QP) error stop 'Integration failed to converge.'

186 call disp%show("relerr_QP ! < 0. if integration fails.")

187 call disp%show( relerr_QP )

188 call disp%show("neval ! # calls to the integrand.")

189 call disp%show( neval )

190 call disp%show("quad_QP ! integral")

191 call disp%show( quad_QP )

192 call disp%skip()

193

194contains

195

196 function getExpPDF_SP(x) result(expPDF)

197 real(SP), intent(in) :: x

198 real(SP) :: expPDF

199 expPDF = exp(getExpLogPDF(x, invSigma = invSigma_SP))

200 end function

201

202 function getExpPDF_DP(x) result(expPDF)

203 real(DP), intent(in) :: x

204 real(DP) :: expPDF

205 expPDF = exp(getExpLogPDF(x, invSigma = invSigma_DP))

206 end function

207

208 function getExpPDF_QP(x) result(expPDF)

209 real(QP), intent(in) :: x

210 real(QP) :: expPDF

211 expPDF = exp(getExpLogPDF(x, invSigma = invSigma_QP))

212 end function

213

214 function getGammaPDF_SP(x) result(gammaPDF)

215 real(SP), intent(in) :: x

216 real(SP) :: gammaPDF

217 gammaPDF = exp(getGammaLogPDF(x, kappa = kappa_SP, invSigma = invSigma_SP))

218 end function

219

220 function getGammaPDF_DP(x) result(gammaPDF)

221 real(DP), intent(in) :: x

222 real(DP) :: gammaPDF

223 gammaPDF = exp(getGammaLogPDF(x, kappa = kappa_DP, invSigma = invSigma_DP))

224 end function

225

226 function getGammaPDF_QP(x) result(gammaPDF)

227 real(QP), intent(in) :: x

228 real(QP) :: gammaPDF

229 gammaPDF = exp(getGammaLogPDF(x, kappa = kappa_QP, invSigma = invSigma_QP))

230 end function

231

232end program example

pm_distExp::getExpCDF
Generate and return the Cumulative Distribution Function (CDF) of the Exponential distribution for an...
Definition: pm_distExp.F90:655

pm_distExp::getExpLogPDF
Generate and return the natural logarithm of the Probability Density Function (PDF) of the Exponentia...
Definition: pm_distExp.F90:221

pm_distGamma::getGammaLogPDF
Generate and return the natural logarithm of the Probability Density Function (PDF) of the Gamma dist...
Definition: pm_distGamma.F90:392

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_mathGamma::getGammaIncLow
Generate and return the regularized Lower Incomplete Gamma function for the specified shape parameter...
Definition: pm_mathGamma.F90:124

pm_quadRomb::getQuadRomb
Generate and return the integral of the input function getFunc() in the closed range [lb,...
Definition: pm_quadRomb.F90:396

pm_distExp
This module contains classes and procedures for computing various statistical quantities related to t...
Definition: pm_distExp.F90:112

pm_distGamma
This module contains classes and procedures for computing various statistical quantities related to t...
Definition: pm_distGamma.F90:75

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::RKD
integer, parameter RKD
The double precision real kind in Fortran mode. On most platforms, this is an 64-bit real kind.
Definition: pm_kind.F90:568

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::RKH
integer, parameter RKH
The scalar integer constant of intrinsic default kind, representing the highest-precision real kind t...
Definition: pm_kind.F90:858

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_mathGamma
This module contains procedures and generic interfaces for the Lower and Upper Incomplete Gamma funct...
Definition: pm_mathGamma.F90:37

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!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

4! Compute the Cumulative Distribution Function (CDF) over the semi-infinite interval of Exponential distribution.

5!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

6!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

7

8

9!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

10! Compute the numerical integration with single precision.

11!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

12

13

14invSigma_SP = 3._SP

15quadref_SP = getExpCDF(x = log(huge(0._SP)), invSigma = invSigma_SP)

16quadref_SP

17+1.00000000

18quad_SP = getQuadRomb(getFunc = getExpPDF_SP, lb = 0._SP, ub = huge(0._SP), tol = epsilon(1._SP) * 100, nref = 4_IK, interval = nexp_type(), relerr = relerr_SP, neval = neval)

19if (relerr_SP < 0._SP) error stop 'Integration failed to converge.'

20relerr_SP ! < 0. if integration fails.

21+0.407197748E-9

22neval ! # calls to the integrand.

23+27

24quad_SP ! integral

25+0.999999940

26

27

28!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

29! Compute the numerical integration with double precision.

30!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

31

32

33invSigma_DP = 3._DP

34quadref_DP = getExpCDF(x = log(huge(0._DP)), invSigma = invSigma_DP)

35quadref_DP

36+1.0000000000000000

37quad_DP = getQuadRomb(getFunc = getExpPDF_DP, lb = 0._DP, ub = huge(0._DP), tol = epsilon(1._DP) * 100, nref = 4_IK, interval = nexp_type(), relerr = relerr_DP, neval = neval)

38if (relerr_DP < 0.) error stop 'Integration failed to converge.'

39relerr_DP ! < 0. if integration fails.

40+0.15679231417482677E-18

41neval ! # calls to the integrand.

42+27

43quad_DP ! integral

44+1.0000000000000000

45

46

47!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

48! Compute the numerical integration with double precision.

49!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

50

51

52invSigma_QP = 3._QP

53quadref_QP = getExpCDF(x = log(huge(0._QP)), invSigma = invSigma_QP)

54quadref_QP

55+1.00000000000000000000000000000000000

56quad_QP = getQuadRomb(getFunc = getExpPDF_QP, lb = 0._QP, ub = huge(0._QP), tol = epsilon(1._QP) * 100, nref = 4_IK, interval = nexp_type(), relerr = relerr_QP, neval = neval)

57if (relerr_QP < 0.) error stop 'Integration failed to converge.'

58relerr_QP ! < 0. if integration fails.

59+0.100451159285899950138381146936573719E-35

60neval ! # calls to the integrand.

61+27

62quad_QP ! integral

63+0.999999999999999999999999999999999422

64

65

66!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

67!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

68! Compute the Cumulative Distribution Function (CDF) over the semi-infinite interval of Gamma distribution whose tail decays exponentially.

69!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

70!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

71

72

73!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

74! Compute the numerical integration with single precision.

75!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

76

77

78kappa_SP = 2._SP

79invSigma_SP = 2._SP

80quadref_SP = getGammaIncLow(log(huge(0._SP)), kappa = kappa_SP) - getGammaIncLow(0._SP, kappa = kappa_SP)

81quadref_SP

82+1.00000000

83quad_SP = getQuadRomb(getFunc = getGammaPDF_SP, lb = 0._SP, ub = huge(0._SP), tol = epsilon(1._SP) * 100, nref = 4_IK, interval = nexp_type(), relerr = relerr_SP, neval = neval)

84if (relerr_SP < 0._SP) error stop 'Integration failed to converge.'

85relerr_SP ! < 0. if integration fails.

86+0.279331175E-5

87neval ! # calls to the integrand.

88+27

89quad_SP ! integral

90+1.00025165

91

92

93!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

94! Compute the numerical integration with double precision.

95!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

96

97

98kappa_DP = 2._DP

99invSigma_DP = 2._DP

100quadref_DP = getGammaIncLow(log(huge(0._DP)), kappa = kappa_DP) - getGammaIncLow(0._DP, kappa = kappa_DP)

101quadref_DP

102+1.0000000000000000

103quad_DP = getQuadRomb(getFunc = getGammaPDF_DP, lb = 0._DP, ub = huge(0._DP), tol = epsilon(1._DP) * 100, nref = 7_IK, interval = nexp_type(), relerr = relerr_DP, neval = neval)

104if (relerr_DP < 0._DP) error stop 'Integration failed to converge.'

105relerr_DP ! < 0. if integration fails.

106+0.71143903588068092E-14

107neval ! # calls to the integrand.

108+19683

109quad_DP ! integral

110+1.0000000004727598

111

112

113!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

114! Compute the numerical integration with quadro precision.

115!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

116

117

118kappa_QP = 2._QP

119invSigma_QP = 2._QP

120quadref_QP = getGammaIncLow(log(huge(0._QP)), kappa = kappa_QP) - getGammaIncLow(0._QP, kappa = kappa_QP)

121quadref_QP

122+1.00000000000000000000000000000000000

123quad_QP = getQuadRomb(getFunc = getGammaPDF_QP, lb = 0._QP, ub = huge(0._QP), tol = sqrt(epsilon(1._QP)), nref = 10_IK, interval = nexp_type(), relerr = relerr_QP, neval = neval)

124if (relerr_QP < 0._QP) error stop 'Integration failed to converge.'

125relerr_QP ! < 0. if integration fails.

126+0.975928566535230134937169834879257738E-17

127neval ! # calls to the integrand.

128+19683

129quad_QP ! integral

130+1.00000000047261839211598849473494003

131

132

Test:: test_pm_quadRomb

Final Remarks ⛓

If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.

If you use any parts or concepts from this library to any extent, please acknowledge the usage by citing the relevant publications of the ParaMonte library.
If you regenerate any parts/ideas from this library in a programming environment other than those currently supported by this ParaMonte library (i.e., other than C, C++, Fortran, MATLAB, Python, R), please also ask the end users to cite this original ParaMonte library.

This software is available to the public under a highly permissive license.
Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

Copyright: Computational Data Science Lab

Author:: Amir Shahmoradi, September 1, 2017, 12:00 AM, Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin

Definition at line 169 of file pm_quadRomb.F90.

The documentation for this type was generated from the following file:

src/fortran/main/pm_quadRomb.F90