Generate and return the approximate polynomial interpolation/extrapolation value of the input specified point x for the specified method. More...

Detailed Description

Generate and return the approximate polynomial interpolation/extrapolation value of the input specified point x for the specified method.

For polynomial interpolation/extrapolation, the computation relies on the Neville algorithm.
The extrapolation is done as if the out-of-bound query point is within the boundary (first or last) interpolation segment specified by the input (crdx, func) pairs of values.

Parameters

[in]	method	: The input scalar constant that can be, The scalar constant neimean or a scalar object of type neimean_type implying the use of the average of the `func` values of the two nearest neighbors of the input `queryx` smaller and larger than it as the output `extrap`. The scalar constant neinear or a scalar object of type neinear_type implying the use of the average of the `func` value of the `neinear` nearest neighbor of the input `queryx` as the output `extrap`. Note that the nearest neighbor in this case is measured by actual Euclidean distances of neighbors to the input `queryx`. The scalar constant neiprev or a scalar object of type neiprev_type implying the use of the `func` value of the largest abscissa in the input `crdx` smaller than the input `queryx` as the output `extrap`. The scalar constant neinext or a scalar object of type neinext_type implying the use of the `func` value of the smallest abscissa in the input `crdx` larger than the input `queryx` as the output `extrap`. The scalar constant piwilin or a scalar object of type piwilin_type implying the use of the linear interpolation/extrapolation of the `func` values of the two `crdx` points that bracket `queryx` as the output `extrap`. The linear interpolation/extrapolation implemented in this constructor is based on the Lagrange classical formula for linear interpolation/extrapolation. Suppose an input query point \(x\) falls between two nodes \(x_i\) and \(x_{i+1}\) with the corresponding function values \(y_i\) and \(y_{i+1}\) and we wish to estimate the corresponding interpolated/extrapolated value \(y(x)\), which can be computed as, \begin{equation} y(x) = \frac {x - x_{i+1}} {x_i - x_{i+1}} y_i + \frac {x - x_{i}} {x_{i+1} - x_{i}} y_{i+1} ~. \end{equation} The scalar constant monopol or a scalar object of type monopol_type implying the use of a single polynomial interpolation/extrapolation of highest degree `size(crdx) - 1` possible to all pairs of `(crdx, func)` for computing the output `extrap`. The Neville algorithm is used to approximate the polynomial interpolation/extrapolation.
[in]	crdx	: The input `contiguous` vector of type `real` of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128), containing the set of abscissa in strictly ascending order through which the constructed polynomial must pass. If needed, the input values for `crdx` and `sortedY` can be sorted in ascending order by calling either setSorted() or setSorted().
[in]	func	: The input `contiguous` vector of the same type, kind, and size as `crdx`, containing the set of function values corresponding to the input abscissa `crdx` through which the constructed polynomial must pass.
[in]	queryx	: The input scalar or vector of the same type and kind as `crdx`, containing the abscissa (x-value) of the queryx point.
[out]	extrap	: The output object of the same type, kind, rank, and shape as `queryx`, containing the (approximate) interpolated/extrapolated y-value(s) corresponding to the `queryx` point(s).
[out]	relerr	: The output scalar of the same type and kind as `crdx`, containing the estimated error in the output `extrap`. (optional. It can be present if and only the input argument `method` is set to monopol or a scalar object of type monopol_type .)

Possible calling interfaces ⛓

: use pm_polation, only: setExtrap

call setExtrap(method, crdx(1:nsam), func(1:nsam), queryx, extrap)

call setExtrap(method, crdx(1:nsam), func(1:nsam), queryx(1:nque), extrap(1:nque))

call setExtrap(method, crdx(1:nsam), func(1:nsam), queryx, extrap, relerr) ! method = monopol

call setExtrap(method, crdx(1:nsam), func(1:nsam), queryx(1:nque), extrap(1:nque), relerr(1:nque)) ! method = monopol

pm_polation::setExtrap
Generate and return the approximate polynomial interpolation/extrapolation value of the input specifi...
Definition: pm_polation.F90:3496

pm_polation
This module contains procedures and data types for interpolation of finite samples of data.
Definition: pm_polation.F90:142

pm_polation::monopol
type(monopol_type), parameter monopol
Definition: pm_polation.F90:359

Warning: The condition size(crdx) == size(func) must hold for the corresponding input arguments.
The condition all(shape(queryx) == shape(extrap)) must hold for the corresponding input arguments.
The condition all(shape(queryx) == shape(relerr)) must hold for the corresponding input arguments.
The condition isAscendingAll(crdx) .or. same_type_as(method, monopol_type()) 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: getExtrap
setExtrap
getInterp
setInterp
pm_sampleQuan
pm_arraySort
pm_quadRomb

Example usage ⛓

: 1program example

2

3 use pm_kind, only: SK, IK, LK

4 use pm_polation, only: setExtrap, neimean, neinear, neinext, neiprev, piwilin, monopol

5 use pm_arrayResize, only: setResized

6 use pm_arraySpace, only: getLinSpace

7 use pm_io, only: getErrTableWrite

8 use pm_io, only: display_type

9

10 implicit none

11

12 type(display_type) :: disp

13 integer(IK) :: itry, ntry = 5

14 integer(IK) :: dim, isam, ndim, nsam

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

16

17 call disp%skip()

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

19 call disp%show("!1D extrapolation.")

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

21 call disp%skip()

22

23 block

24 use pm_kind, only: RKG => RKS ! all processor kinds are supported.

25 use pm_mathConst, only: PI_RKH => PI

26 real(RKG), parameter :: PI = PI_RKH

27 real(RKG), allocatable :: crdx(:), func(:), queryx(:), extrap(:), relerr(:)

28 integer(IK) :: ncrd, nquery

29 call disp%skip()

30 call disp%show("ncrd = 9; nquery = 33")

31 ncrd = 9; nquery = 33

32 call disp%show("crdx = getLinSpace(0._RKG, 2 * PI, ncrd)")

33 crdx = getLinSpace(0._RKG, 2 * PI, ncrd)

34 call disp%show("crdx")

35 call disp%show( crdx )

36 call disp%show("func = sin(crdx)")

37 func = sin(crdx)

38 call disp%show("func")

39 call disp%show( func )

40 call disp%show("queryx = getLinSpace(-PI/2, 5 * PI/2, nquery)")

41 queryx = getLinSpace(-PI/2, 5 * PI/2, nquery)

42 call disp%show("queryx")

43 call disp%show( queryx )

44 call disp%show("call setResized(extrap, size(queryx, 1, IK))")

45 call setResized(extrap, size(queryx, 1, IK))

46 call disp%show("call setResized(relerr, size(queryx, 1, IK))")

47 call setResized(relerr, size(queryx, 1, IK))

48 call disp%skip()

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

50 call disp%show("!1D mean neighbors extrapolation.")

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

52 call disp%skip()

53 call disp%show("if (0 /= getErrTableWrite(SK_'setExtrap.neimean.crd.txt', reshape([crdx, func], [ncrd, 2_IK]), header = SK_'crdx,func')) error stop 'extrapolation node outputting failed.'")

54 if (0 /= getErrTableWrite(SK_'setExtrap.neimean.crd.txt', reshape([crdx, func], [ncrd, 2_IK]), header = SK_'crdx,func')) error stop 'extrapolation node outputting failed.'

55 call disp%show("call setExtrap(neimean, crdx, func, queryx, extrap)")

56 call setExtrap(neimean, crdx, func, queryx, extrap)

57 call disp%show("extrap")

58 call disp%show( extrap )

59 call disp%show("if (0 /= getErrTableWrite(SK_'setExtrap.neimean.extrap.txt', reshape([queryx, extrap], [nquery, 2_IK]), header = SK_'queryx,extrap')) error stop 'extrapolation outputting failed.'")

60 if (0 /= getErrTableWrite(SK_'setExtrap.neimean.extrap.txt', reshape([queryx, extrap], [nquery, 2_IK]), header = SK_'queryx,extrap')) error stop 'extrapolation outputting failed.'

61 call disp%skip()

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

63 call disp%show("!1D nearest neighbor extrapolation.")

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

65 call disp%skip()

66 call disp%show("if (0 /= getErrTableWrite(SK_'setExtrap.neinear.crd.txt', reshape([crdx, func], [ncrd, 2_IK]), header = SK_'crdx,func')) error stop 'extrapolation node outputting failed.'")

67 if (0 /= getErrTableWrite(SK_'setExtrap.neinear.crd.txt', reshape([crdx, func], [ncrd, 2_IK]), header = SK_'crdx,func')) error stop 'extrapolation node outputting failed.'

68 call disp%show("call setExtrap(neinear, crdx, func, queryx, extrap)")

69 call setExtrap(neinear, crdx, func, queryx, extrap)

70 call disp%show("extrap")

71 call disp%show( extrap )

72 call disp%show("if (0 /= getErrTableWrite(SK_'setExtrap.neinear.extrap.txt', reshape([queryx, extrap], [nquery, 2_IK]), header = SK_'queryx,extrap')) error stop 'extrapolation outputting failed.'")

73 if (0 /= getErrTableWrite(SK_'setExtrap.neinear.extrap.txt', reshape([queryx, extrap], [nquery, 2_IK]), header = SK_'queryx,extrap')) error stop 'extrapolation outputting failed.'

74 call disp%skip()

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

76 call disp%show("!1D next neighbor extrapolation.")

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

78 call disp%skip()

79 call disp%show("if (0 /= getErrTableWrite(SK_'setExtrap.neinext.crd.txt', reshape([crdx, func], [ncrd, 2_IK]), header = SK_'crdx,func')) error stop 'extrapolation node outputting failed.'")

80 if (0 /= getErrTableWrite(SK_'setExtrap.neinext.crd.txt', reshape([crdx, func], [ncrd, 2_IK]), header = SK_'crdx,func')) error stop 'extrapolation node outputting failed.'

81 call disp%show("call setExtrap(neinext, crdx, func, queryx, extrap)")

82 call setExtrap(neinext, crdx, func, queryx, extrap)

83 call disp%show("extrap")

84 call disp%show( extrap )

85 call disp%show("if (0 /= getErrTableWrite(SK_'setExtrap.neinext.extrap.txt', reshape([queryx, extrap], [nquery, 2_IK]), header = SK_'queryx,extrap')) error stop 'extrapolation outputting failed.'")

86 if (0 /= getErrTableWrite(SK_'setExtrap.neinext.extrap.txt', reshape([queryx, extrap], [nquery, 2_IK]), header = SK_'queryx,extrap')) error stop 'extrapolation outputting failed.'

87 call disp%skip()

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

89 call disp%show("!1D previous neighbor extrapolation.")

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

91 call disp%skip()

92 call disp%show("if (0 /= getErrTableWrite(SK_'setExtrap.neiprev.crd.txt', reshape([crdx, func], [ncrd, 2_IK]), header = SK_'crdx,func')) error stop 'extrapolation node outputting failed.'")

93 if (0 /= getErrTableWrite(SK_'setExtrap.neiprev.crd.txt', reshape([crdx, func], [ncrd, 2_IK]), header = SK_'crdx,func')) error stop 'extrapolation node outputting failed.'

94 call disp%show("call setExtrap(neiprev, crdx, func, queryx, extrap)")

95 call setExtrap(neiprev, crdx, func, queryx, extrap)

96 call disp%show("extrap")

97 call disp%show( extrap )

98 call disp%show("if (0 /= getErrTableWrite(SK_'setExtrap.neiprev.extrap.txt', reshape([queryx, extrap], [nquery, 2_IK]), header = SK_'queryx,extrap')) error stop 'extrapolation outputting failed.'")

99 if (0 /= getErrTableWrite(SK_'setExtrap.neiprev.extrap.txt', reshape([queryx, extrap], [nquery, 2_IK]), header = SK_'queryx,extrap')) error stop 'extrapolation outputting failed.'

100 call disp%skip()

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

102 call disp%show("!1D piecewise linear extrapolation.")

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

104 call disp%skip()

105 call disp%show("if (0 /= getErrTableWrite(SK_'setExtrap.piwilin.crd.txt', reshape([crdx, func], [ncrd, 2_IK]), header = SK_'crdx,func')) error stop 'extrapolation node outputting failed.'")

106 if (0 /= getErrTableWrite(SK_'setExtrap.piwilin.crd.txt', reshape([crdx, func], [ncrd, 2_IK]), header = SK_'crdx,func')) error stop 'extrapolation node outputting failed.'

107 call disp%show("call setExtrap(piwilin, crdx, func, queryx, extrap)")

108 call setExtrap(piwilin, crdx, func, queryx, extrap)

109 call disp%show("extrap")

110 call disp%show( extrap )

111 call disp%show("if (0 /= getErrTableWrite(SK_'setExtrap.piwilin.extrap.txt', reshape([queryx, extrap], [nquery, 2_IK]), header = SK_'queryx,extrap')) error stop 'extrapolation outputting failed.'")

112 if (0 /= getErrTableWrite(SK_'setExtrap.piwilin.extrap.txt', reshape([queryx, extrap], [nquery, 2_IK]), header = SK_'queryx,extrap')) error stop 'extrapolation outputting failed.'

113 call disp%skip()

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

115 call disp%show("!1D single polynomial extrapolation.")

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

117 call disp%skip()

118 call disp%show("if (0 /= getErrTableWrite(SK_'setExtrap.monopol.crd.txt', reshape([crdx, func], [ncrd, 2_IK]), header = SK_'crdx,func')) error stop 'extrapolation node outputting failed.'")

119 if (0 /= getErrTableWrite(SK_'setExtrap.monopol.crd.txt', reshape([crdx, func], [ncrd, 2_IK]), header = SK_'crdx,func')) error stop 'extrapolation node outputting failed.'

120 call disp%show("call setExtrap(monopol, crdx, func, queryx, extrap, relerr)")

121 call setExtrap(monopol, crdx, func, queryx, extrap, relerr)

122 call disp%show("extrap")

123 call disp%show( extrap )

124 call disp%show("relerr")

125 call disp%show( relerr )

126 call disp%show("if (0 /= getErrTableWrite(SK_'setExtrap.monopol.extrap.txt', reshape([queryx, extrap], [nquery, 2_IK]), header = SK_'queryx,extrap')) error stop 'extrapolation outputting failed.'")

127 if (0 /= getErrTableWrite(SK_'setExtrap.monopol.extrap.txt', reshape([queryx, extrap], [nquery, 2_IK]), header = SK_'queryx,extrap')) error stop 'extrapolation outputting failed.'

128 call disp%skip()

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

130 call disp%show("!1D single polynomial extrapolation showing Runge effect.")

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

132 call disp%skip()

133 block

134 use pm_distNorm, only: getNormLogPDF

135 call disp%show("ncrd = 9; nquery = 50 * ncrd")

136 ncrd = 9; nquery = 50 * ncrd

137 call disp%show("crdx = getLinSpace(-5., +5., ncrd)")

138 crdx = getLinSpace(-5., +5., ncrd)

139 call disp%show("crdx")

140 call disp%show( crdx )

141 call disp%show("func = exp(getNormLogPDF(crdx))")

142 func = exp(getNormLogPDF(crdx))

143 call disp%show("func")

144 call disp%show( func )

145 call disp%show("if (0 /= getErrTableWrite(SK_'setExtrap.rungeEffect.crd.txt', reshape([crdx, func], [ncrd, 2_IK]), header = SK_'crdx,func')) error stop 'extrapolation node outputting failed.'")

146 if (0 /= getErrTableWrite(SK_'setExtrap.rungeEffect.crd.txt', reshape([crdx, func], [ncrd, 2_IK]), header = SK_'crdx,func')) error stop 'extrapolation node outputting failed.'

147 call disp%show("queryx = getLinSpace(1.1 * minval(crdx, 1), 1.1 * maxval(crdx, 1), nquery)")

148 queryx = getLinSpace(1.1 * minval(crdx, 1), 1.1 * maxval(crdx, 1), nquery)

149 call disp%show("queryx")

150 call disp%show( queryx )

151 call disp%show("call setResized(extrap, size(queryx, 1, IK))")

152 call setResized(extrap, size(queryx, 1, IK))

153 call disp%show("call setResized(relerr, size(queryx, 1, IK))")

154 call setResized(relerr, size(queryx, 1, IK))

155 call disp%show("call setExtrap(monopol, crdx, func, queryx, extrap, relerr)")

156 call setExtrap(monopol, crdx, func, queryx, extrap, relerr)

157 call disp%show("extrap")

158 call disp%show( extrap )

159 call disp%show("relerr")

160 call disp%show( relerr )

161 call disp%show("if (0 /= getErrTableWrite(SK_'setExtrap.rungeEffect.extrap.txt', reshape([queryx, extrap], [nquery, 2_IK]), header = SK_'queryx,extrap')) error stop 'extrapolation outputting failed.'")

162 if (0 /= getErrTableWrite(SK_'setExtrap.rungeEffect.extrap.txt', reshape([queryx, extrap], [nquery, 2_IK]), header = SK_'queryx,extrap')) error stop 'extrapolation outputting failed.'

163 call disp%skip()

164 end block

165 end block

166

167end program example

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_arraySpace::getLinSpace
Generate count evenly spaced points over the interval [x1, x2] if x1 < x2, or [x2,...
Definition: pm_arraySpace.F90:108

pm_distNorm::getNormLogPDF
Generate the natural logarithm of probability density function (PDF) of the univariate Normal distrib...
Definition: pm_distNorm.F90:294

pm_io::getErrTableWrite
Generate and return the iostat code resulting from writing the input table of rank 1 or 2 to the spec...
Definition: pm_io.F90:5940

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

pm_arraySpace
This module contains procedures and generic interfaces for generating arrays with linear or logarithm...
Definition: pm_arraySpace.F90:33

pm_distNorm
This module contains classes and procedures for computing various statistical quantities related to t...
Definition: pm_distNorm.F90:179

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::LK
integer, parameter LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
Definition: pm_kind.F90:541

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_mathConst
This module contains relevant mathematical constants.
Definition: pm_mathConst.F90:36

pm_mathConst::PI
real(RKB), parameter PI
The scalar real constant of kind with highest available precision RKB representing the irrational num...
Definition: pm_mathConst.F90:48

pm_polation::piwilin
type(piwilin_type), parameter piwilin
Definition: pm_polation.F90:324

pm_polation::neiprev
type(neiprev_type), parameter neiprev
Definition: pm_polation.F90:289

pm_polation::neinext
type(neinext_type), parameter neinext
Definition: pm_polation.F90:253

pm_polation::neinear
type(neinear_type), parameter neinear
Definition: pm_polation.F90:217

pm_polation::neimean
type(neimean_type), parameter neimean
Definition: pm_polation.F90:181

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!1D extrapolation.

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

5

6

7ncrd = 9; nquery = 33

8crdx = getLinSpace(0._RKG, 2 * PI, ncrd)

9crdx

10+0.00000000, +0.785398185, +1.57079637, +2.35619450, +3.14159274, +3.92699099, +4.71238899, +5.49778748, +6.28318548

11func = sin(crdx)

12func

13+0.00000000, +0.707106769, +1.00000000, +0.707106769, -0.874227766E-7, -0.707106888, -1.00000000, -0.707106531, +0.174845553E-6

14queryx = getLinSpace(-PI/2, 5 * PI/2, nquery)

15queryx

16-1.57079637, -1.27627206, -0.981747746, -0.687223434, -0.392699122, -0.981748104E-1, +0.196349502, +0.490873933, +0.785398126, +1.07992232, +1.37444675, +1.66897118, +1.96349537, +2.25801945, +2.55254412, +2.84706831, +3.14159250, +3.43611670, +3.73064089, +4.02516556, +4.31968975, +4.61421394, +4.90873861, +5.20326281, +5.49778700, +5.79231119, +6.08683538, +6.38136005, +6.67588472, +6.97040892, +7.26493311, +7.55945730, +7.85398197

17call setResized(extrap, size(queryx, 1, IK))

18call setResized(relerr, size(queryx, 1, IK))

19

20!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

21!1D mean neighbors extrapolation.

22!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

23

24if (0 /= getErrTableWrite(SK_'setExtrap.neimean.crd.txt', reshape([crdx, func], [ncrd, 2_IK]), header = SK_'crdx,func')) error stop 'extrapolation node outputting failed.'

25call setExtrap(neimean, crdx, func, queryx, extrap)

26extrap

27+0.00000000, +0.00000000, +0.00000000, +0.00000000, +0.00000000, +0.00000000, +0.353553385, +0.353553385, +0.353553385, +0.853553414, +0.853553414, +0.853553414, +0.853553414, +0.853553414, +0.353553355, +0.353553355, +0.353553355, -0.353553474, -0.353553474, -0.853553414, -0.853553414, -0.853553414, -0.853553295, -0.853553295, -0.853553295, -0.353553176, -0.353553176, +0.174845553E-6, +0.174845553E-6, +0.174845553E-6, +0.174845553E-6, +0.174845553E-6, +0.174845553E-6

28if (0 /= getErrTableWrite(SK_'setExtrap.neimean.extrap.txt', reshape([queryx, extrap], [nquery, 2_IK]), header = SK_'queryx,extrap')) error stop 'extrapolation outputting failed.'

29

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

31!1D nearest neighbor extrapolation.

32!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

33

34if (0 /= getErrTableWrite(SK_'setExtrap.neinear.crd.txt', reshape([crdx, func], [ncrd, 2_IK]), header = SK_'crdx,func')) error stop 'extrapolation node outputting failed.'

35call setExtrap(neinear, crdx, func, queryx, extrap)

36extrap

37+0.00000000, +0.00000000, +0.00000000, +0.00000000, +0.00000000, +0.00000000, +0.00000000, +0.707106769, +0.707106769, +0.707106769, +1.00000000, +1.00000000, +1.00000000, +0.707106769, +0.707106769, -0.874227766E-7, -0.874227766E-7, -0.874227766E-7, -0.707106888, -0.707106888, -0.707106888, -1.00000000, -1.00000000, -0.707106531, -0.707106531, -0.707106531, +0.174845553E-6, +0.174845553E-6, +0.174845553E-6, +0.174845553E-6, +0.174845553E-6, +0.174845553E-6, +0.174845553E-6

38if (0 /= getErrTableWrite(SK_'setExtrap.neinear.extrap.txt', reshape([queryx, extrap], [nquery, 2_IK]), header = SK_'queryx,extrap')) error stop 'extrapolation outputting failed.'

39

40!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

41!1D next neighbor extrapolation.

42!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

43

44if (0 /= getErrTableWrite(SK_'setExtrap.neinext.crd.txt', reshape([crdx, func], [ncrd, 2_IK]), header = SK_'crdx,func')) error stop 'extrapolation node outputting failed.'

45call setExtrap(neinext, crdx, func, queryx, extrap)

46extrap

47+0.00000000, +0.00000000, +0.00000000, +0.00000000, +0.00000000, +0.00000000, +0.707106769, +0.707106769, +0.707106769, +1.00000000, +1.00000000, +0.707106769, +0.707106769, +0.707106769, -0.874227766E-7, -0.874227766E-7, -0.874227766E-7, -0.707106888, -0.707106888, -1.00000000, -1.00000000, -1.00000000, -0.707106531, -0.707106531, -0.707106531, +0.174845553E-6, +0.174845553E-6, +0.174845553E-6, +0.174845553E-6, +0.174845553E-6, +0.174845553E-6, +0.174845553E-6, +0.174845553E-6

48if (0 /= getErrTableWrite(SK_'setExtrap.neinext.extrap.txt', reshape([queryx, extrap], [nquery, 2_IK]), header = SK_'queryx,extrap')) error stop 'extrapolation outputting failed.'

49

50!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

51!1D previous neighbor extrapolation.

52!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

53

54if (0 /= getErrTableWrite(SK_'setExtrap.neiprev.crd.txt', reshape([crdx, func], [ncrd, 2_IK]), header = SK_'crdx,func')) error stop 'extrapolation node outputting failed.'

55call setExtrap(neiprev, crdx, func, queryx, extrap)

56extrap

57+0.00000000, +0.00000000, +0.00000000, +0.00000000, +0.00000000, +0.00000000, +0.00000000, +0.00000000, +0.00000000, +0.707106769, +0.707106769, +1.00000000, +1.00000000, +1.00000000, +0.707106769, +0.707106769, +0.707106769, -0.874227766E-7, -0.874227766E-7, -0.707106888, -0.707106888, -0.707106888, -1.00000000, -1.00000000, -1.00000000, -0.707106531, -0.707106531, +0.174845553E-6, +0.174845553E-6, +0.174845553E-6, +0.174845553E-6, +0.174845553E-6, +0.174845553E-6

58if (0 /= getErrTableWrite(SK_'setExtrap.neiprev.extrap.txt', reshape([queryx, extrap], [nquery, 2_IK]), header = SK_'queryx,extrap')) error stop 'extrapolation outputting failed.'

59

60!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

61!1D piecewise linear extrapolation.

62!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

63

64if (0 /= getErrTableWrite(SK_'setExtrap.piwilin.crd.txt', reshape([crdx, func], [ncrd, 2_IK]), header = SK_'crdx,func')) error stop 'extrapolation node outputting failed.'

65call setExtrap(piwilin, crdx, func, queryx, extrap)

66extrap

67-1.41421354, -1.14904845, -0.883883417, -0.618718445, -0.353553385, -0.883883759E-1, +0.176776648, +0.441941768, +0.707106709, +0.816941619, +0.926776648, +0.963388324, +0.853553414, +0.743718565, +0.530330002, +0.265165061, +0.127229356E-6, -0.265164793, -0.530329704, -0.743718445, -0.853553414, -0.963388264, -0.926776648, -0.816941679, -0.707106709, -0.441942036, -0.176777050, +0.883883536E-1, +0.353553772, +0.618718803, +0.883883774, +1.14904869, +1.41421402

68if (0 /= getErrTableWrite(SK_'setExtrap.piwilin.extrap.txt', reshape([queryx, extrap], [nquery, 2_IK]), header = SK_'queryx,extrap')) error stop 'extrapolation outputting failed.'

69

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

71!1D single polynomial extrapolation.

72!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

73

74if (0 /= getErrTableWrite(SK_'setExtrap.monopol.crd.txt', reshape([crdx, func], [ncrd, 2_IK]), header = SK_'crdx,func')) error stop 'extrapolation node outputting failed.'

75call setExtrap(monopol, crdx, func, queryx, extrap, relerr)

76extrap

77-1.78382504, -1.33006334, -0.990992546, -0.692502201, -0.398540974, -0.996969119E-1, +0.196270004, +0.472104400, +0.707106769, +0.881702781, +0.980677783, +0.995225310, +0.923959136, +0.773035169, +0.555531383, +0.290238500, +0.150949504E-6, -0.290238202, -0.555531144, -0.773034930, -0.923959076, -0.995225310, -0.980677783, -0.881702840, -0.707106888, -0.472104609, -0.196270570, +0.996969715E-1, +0.398542523, +0.692507029, +0.991004944, +1.33009934, +1.78385079

78relerr

79+0.607967331E-5, +0.118650487E-4, +0.407919288E-5, +0.873580575E-6, +0.275671511E-6, +0.200234425E-7, -0.242143834E-7, -0.267755293E-7, -0.344169116E-14, +0.240106557E-8, +0.366708264E-8, -0.796262667E-9, -0.254658494E-8, -0.381760346E-9, +0.792169885E-9, +0.192540028E-8, +0.137390089E-14, -0.111413094E-9, -0.141699252E-8, +0.155682744E-8, +0.548243362E-8, +0.250065546E-8, -0.545696821E-8, -0.304644345E-7, -0.162425615E-12, +0.111613183E-6, -0.286382491E-7, +0.423750883E-7, +0.361353301E-6, +0.153202564E-5, +0.311061694E-5, +0.886246380E-5, +0.109672555E-4

80if (0 /= getErrTableWrite(SK_'setExtrap.monopol.extrap.txt', reshape([queryx, extrap], [nquery, 2_IK]), header = SK_'queryx,extrap')) error stop 'extrapolation outputting failed.'

81

82!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

83!1D single polynomial extrapolation showing Runge effect.

84!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

85

86ncrd = 9; nquery = 50 * ncrd

87crdx = getLinSpace(-5., +5., ncrd)

88crdx

89-5.00000000, -3.75000000, -2.50000000, -1.25000000, +0.00000000, +1.25000000, +2.50000000, +3.75000000, +5.00000000

90func = exp(getNormLogPDF(crdx))

91func

92+0.148671938E-5, +0.352595642E-3, +0.175282992E-1, +0.182649091, +0.398942292, +0.182649091, +0.175282992E-1, +0.352595642E-3, +0.148671938E-5

93if (0 /= getErrTableWrite(SK_'setExtrap.rungeEffect.crd.txt', reshape([crdx, func], [ncrd, 2_IK]), header = SK_'crdx,func')) error stop 'extrapolation node outputting failed.'

94queryx = getLinSpace(1.1 * minval(crdx, 1), 1.1 * maxval(crdx, 1), nquery)

95queryx

96-5.50000000, -5.47550106, -5.45100212, -5.42650318, -5.40200424, -5.37750578, -5.35300684, -5.32850790, -5.30400896, -5.27951002, -5.25501108, -5.23051214, -5.20601320, -5.18151474, -5.15701580, -5.13251686, -5.10801792, -5.08351898, -5.05902004, -5.03452110, -5.01002216, -4.98552322, -4.96102428, -4.93652582, -4.91202688, -4.88752794, -4.86302900, -4.83853006, -4.81403112, -4.78953218, -4.76503325, -4.74053478, -4.71603584, -4.69153690, -4.66703796, -4.64253902, -4.61804008, -4.59354115, -4.56904221, -4.54454327, -4.52004433, -4.49554586, -4.47104692, -4.44654799, -4.42204905, -4.39755011, -4.37305117, -4.34855223, -4.32405376, -4.29955482, -4.27505589, -4.25055695, -4.22605801, -4.20155907, -4.17706013, -4.15256119, -4.12806225, -4.10356331, -4.07906437, -4.05456591, -4.03006697, -4.00556803, -3.98106909, -3.95657015, -3.93207121, -3.90757227, -3.88307357, -3.85857463, -3.83407593, -3.80957699, -3.78507805, -3.76057911, -3.73608017, -3.71158123, -3.68708253, -3.66258359, -3.63808465, -3.61358595, -3.58908701, -3.56458807, -3.54008913, -3.51559019, -3.49109149, -3.46659255, -3.44209361, -3.41759467, -3.39309573, -3.36859703, -3.34409809, -3.31959915, -3.29510021, -3.27060151, -3.24610257, -3.22160363, -3.19710469, -3.17260599, -3.14810705, -3.12360811, -3.09910917, -3.07461023, -3.05011153, -3.02561259, -3.00111365, -2.97661471, -2.95211601, -2.92761707, -2.90311813, -2.87861919, -2.85412025, -2.82962155, -2.80512261, -2.78062367, -2.75612473, -2.73162603, -2.70712709, -2.68262815, -2.65812922, -2.63363051, -2.60913157, -2.58463264, -2.56013370, -2.53563476, -2.51113605, -2.48663712, -2.46213818, -2.43763924, -2.41314054, -2.38864160, -2.36414266, -2.33964372, -2.31514478, -2.29064608, -2.26614714, -2.24164820, -2.21714926, -2.19265056, -2.16815162, -2.14365268, -2.11915374, -2.09465480, -2.07015610, -2.04565716, -2.02115822, -1.99665928, -1.97216058, -1.94766164, -1.92316270, -1.89866376, -1.87416506, -1.84966612, -1.82516718, -1.80066824, -1.77616930, -1.75167060, -1.72717166, -1.70267272, -1.67817378, -1.65367508, -1.62917614, -1.60467720, -1.58017826, -1.55567932, -1.53118062, -1.50668168, -1.48218298, -1.45768404, -1.43318510, -1.40868616, -1.38418722, -1.35968828, -1.33518934, -1.31069040, -1.28619146, -1.26169300, -1.23719406, -1.21269512, -1.18819618, -1.16369724, -1.13919830, -1.11469936, -1.09020042, -1.06570196, -1.04120302, -1.01670408, -0.992205143, -0.967706203, -0.943207264, -0.918708324, -0.894209385, -0.869710445, -0.845211983, -0.820713043, -0.796214104, -0.771715164, -0.747216225, -0.722717285, -0.698218346, -0.673719406, -0.649220467, -0.624722004, -0.600223064, -0.575724125, -0.551225185, -0.526726246, -0.502227306, -0.477728367, -0.453229427, -0.428730488, -0.404232025, -0.379733086, -0.355234146, -0.330735207, -0.306236267, -0.281737328, -0.257238388, -0.232739449, -0.208240509, -0.183742046, -0.159243107, -0.134744167, -0.110245228, -0.857462883E-1, -0.612473488E-1, -0.367484093E-1, -0.122494698E-1, +0.122494698E-1, +0.367479324E-1, +0.612468719E-1, +0.857458115E-1, +0.110244751, +0.134743690, +0.159242630, +0.183741570, +0.208240509, +0.232738972, +0.257237911, +0.281736851, +0.306235790, +0.330734730, +0.355233669, +0.379732609, +0.404231548, +0.428730488, +0.453228951, +0.477727890, +0.502226830, +0.526725769, +0.551224709, +0.575723648, +0.600222588, +0.624721527, +0.649220467, +0.673718929, +0.698217869, +0.722716808, +0.747215748, +0.771714687, +0.796213627, +0.820712566, +0.845211506, +0.869710445, +0.894208908, +0.918707848, +0.943206787, +0.967705727, +0.992204666, +1.01670361, +1.04120255, +1.06570148, +1.09020042, +1.11469889, +1.13919783, +1.16369677, +1.18819571, +1.21269464, +1.23719358, +1.26169252, +1.28619146, +1.31069040, +1.33518887, +1.35968781, +1.38418674, +1.40868568, +1.43318462, +1.45768356, +1.48218250, +1.50668144, +1.53117990, +1.55567884, +1.58017778, +1.60467672, +1.62917566, +1.65367460, +1.67817354, +1.70267248, +1.72717142, +1.75166988, +1.77616882, +1.80066776, +1.82516670, +1.84966564, +1.87416458, +1.89866352, +1.92316246, +1.94766140, +1.97215986, +1.99665880, +2.02115774, +2.04565668, +2.07015562, +2.09465456, +2.11915350, +2.14365244, +2.16815138, +2.19264984, +2.21714878, +2.24164772, +2.26614666, +2.29064560, +2.31514454, +2.33964348, +2.36414242, +2.38864136, +2.41313982, +2.43763876, +2.46213770, +2.48663664, +2.51113510, +2.53563404, +2.56013298, +2.58463192, +2.60913086, +2.63362980, +2.65812874, +2.68262768, +2.70712662, +2.73162556, +2.75612450, +2.78062344, +2.80512238, +2.82962132, +2.85412025, +2.87861919, +2.90311813, +2.92761707, +2.95211506, +2.97661400, +3.00111294, +3.02561188, +3.05011082, +3.07460976, +3.09910870, +3.12360764, +3.14810658, +3.17260551, +3.19710445, +3.22160339, +3.24610233, +3.27060127, +3.29510021, +3.31959915, +3.34409809, +3.36859608, +3.39309502, +3.41759396, +3.44209290, +3.46659184, +3.49109077, +3.51558971, +3.54008865, +3.56458759, +3.58908653, +3.61358547, +3.63808441, +3.66258335, +3.68708229, +3.71158123, +3.73608017, +3.76057911, +3.78507805, +3.80957603, +3.83407497, +3.85857391, +3.88307285, +3.90757179, +3.93207073, +3.95656967, +3.98106861, +4.00556755, +4.03006649, +4.05456543, +4.07906437, +4.10356331, +4.12806225, +4.15256119, +4.17706013, +4.20155907, +4.22605801, +4.25055599, +4.27505493, +4.29955387, +4.32405281, +4.34855175, +4.37305069, +4.39754963, +4.42204857, +4.44654751, +4.47104645, +4.49554539, +4.52004433, +4.54454327, +4.56904221, +4.59354115, +4.61804008, +4.64253902, +4.66703701, +4.69153595, +4.71603489, +4.74053383, +4.76503277, +4.78953171, +4.81403065, +4.83852959, +4.86302853, +4.88752747, +4.91202641, +4.93652534, +4.96102428, +4.98552322, +5.01002216, +5.03452110, +5.05902004, +5.08351898, +5.10801697, +5.13251591, +5.15701485, +5.18151379, +5.20601273, +5.23051167, +5.25501060, +5.27950954, +5.30400848, +5.32850742, +5.35300636, +5.37750530, +5.40200424, +5.42650318, +5.45100212, +5.47550106, +5.50000000

97call setResized(extrap, size(queryx, 1, IK))

98call setResized(relerr, size(queryx, 1, IK))

99call setExtrap(monopol, crdx, func, queryx, extrap, relerr)

100extrap

101+1.84591424, +1.68530297, +1.53404069, +1.39173245, +1.25799561, +1.13246179, +1.01476717, +0.904567301, +0.801525354, +0.705316544, +0.615625620, +0.532148898, +0.454591900, +0.382672310, +0.316112578, +0.254649341, +0.198026896, +0.145998508, +0.983262807E-1, +0.547808707E-1, +0.151412832E-1, -0.208053477E-1, -0.532639138E-1, -0.824311003E-1, -0.108497709, -0.131645471, -0.152049571, -0.169878244, -0.185293078, -0.198448911, -0.209494323, -0.218571454, -0.225816920, -0.231360912, -0.235328153, -0.237837821, -0.239003673, -0.238934264, -0.237732947, -0.235498562, -0.232324779, -0.228300989, -0.223511547, -0.218037084, -0.211953789, -0.205333769, -0.198245347, -0.190752536, -0.182916731, -0.174794674, -0.166440085, -0.157903701, -0.149232596, -0.140471071, -0.131660253, -0.122838601, -0.114041790, -0.105302736, -0.966518819E-1, -0.881173611E-1, -0.797245502E-1, -0.714969933E-1, -0.634558946E-1, -0.556204244E-1, -0.480078310E-1, -0.406333320E-1, -0.335105062E-1, -0.266509764E-1, 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104if (0 /= getErrTableWrite(SK_'setExtrap.rungeEffect.extrap.txt', reshape([queryx, extrap], [nquery, 2_IK]), header = SK_'queryx,extrap')) error stop 'extrapolation outputting failed.'

105

106

Postprocessing of the example output ⛓
1#!/usr/bin/env python

2

3import matplotlib.pyplot as plt

4import pandas as pd

5import numpy as np

6import glob

7import sys

8

9linewidth = 2

10fontsize = 17

11

12for kind in ["neimean", "neinear", "neinext", "neiprev", "piwilin", "monopol", "rungeEffect"]:

13

14 crd = pd.read_csv(glob.glob("*."+kind+".crd.txt")[0], delimiter = ",")

15 pattern = "*."+kind+".extrap.txt"

16 fileList = glob.glob(pattern)

17

18 for file in fileList:

19

20 df = pd.read_csv(file, delimiter = ",")

21

22 # start with a square Figure

23 fig = plt.figure(figsize = (8, 6))

24 ax = plt.subplot(1,1,1)

25

26 ax.scatter ( df.values[:, 0]

27 , df.values[:, 1]

28 , zorder = 1000

29 , c = "black"

30 , s = 8

31 )

32 ax.scatter ( crd.values[:, 0]

33 , crd.values[:,1]

34 , zorder = 1000

35 , c = "red"

36 , s = 20

37 )

38

39 plt.minorticks_on()

40 ax.set_xlabel("X", fontsize = 17)

41 ax.set_ylabel("Y", fontsize = 17)

42 plt.grid(visible = True, which = "both", axis = "both", color = "0.85", linestyle = "-")

43 ax.tick_params(axis = "x", which = "minor")

44 ax.tick_params(axis = "y", which = "minor")

45 ax.legend([file.split(".")[-3], "nodes"], fontsize = fontsize)

46

47 plt.tight_layout()

48 plt.savefig(file.replace(".txt",".png"))

Visualization of the example output ⛓

Test:: test_pm_polation

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 Austin

Definition at line 3496 of file pm_polation.F90.

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

src/fortran/main/pm_polation.F90