| 1 | ! Copyright (c) Université de Reims Champagnne-Ardenne (2010-2015) |
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| 2 | ! Contributor: Jérémie Burgalat (jeremie.burgalat@univ-reims.fr) |
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| 3 | ! |
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| 4 | ! This software is a computer program whose purpose is to compute multi-variate |
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| 5 | ! linear interpolation. |
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| 6 | ! |
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| 7 | ! This software is governed by the CeCILL-B license under French law and |
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| 8 | ! abiding by the rules of distribution of free software. You can use, |
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| 9 | ! modify and/ or redistribute the software under the terms of the CeCILL-B |
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| 10 | ! license as circulated by CEA, CNRS and INRIA at the following URL |
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| 11 | ! "http://www.cecill.info". |
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| 12 | ! |
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| 13 | ! As a counterpart to the access to the source code and rights to copy, |
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| 14 | ! modify and redistribute granted by the license, users are provided only |
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| 15 | ! with a limited warranty and the software's author, the holder of the |
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| 16 | ! economic rights, and the successive licensors have only limited |
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| 17 | ! liability. |
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| 18 | ! |
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| 19 | ! In this respect, the user's attention is drawn to the risks associated |
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| 20 | ! with loading, using, modifying and/or developing or reproducing the |
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| 21 | ! software by the user in light of its specific status of free software, |
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| 22 | ! that may mean that it is complicated to manipulate, and that also |
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| 23 | ! therefore means that it is reserved for developers and experienced |
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| 24 | ! professionals having in-depth computer knowledge. Users are therefore |
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| 25 | ! encouraged to load and test the software's suitability as regards their |
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| 26 | ! requirements in conditions enabling the security of their systems and/or |
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| 27 | ! data to be ensured and, more generally, to use and operate it in the |
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| 28 | ! same conditions as regards security. |
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| 29 | ! |
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| 30 | ! The fact that you are presently reading this means that you have had |
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| 31 | ! knowledge of the CeCILL-B license and that you accept its terms. |
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| 32 | |
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| 33 | !! File: lint_gen.F90 |
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| 34 | !! Summary: Linear interpolation generic interfaces |
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| 35 | !! Author: J. Burgalat |
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| 36 | !! Date: 2010-2014 |
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| 37 | |
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| 38 | MODULE LINT_GEN |
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| 39 | !! Generic linear interpolation module |
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| 40 | USE LINT_PREC |
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| 41 | USE LINT_CORE |
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| 42 | IMPLICIT NONE |
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| 43 | |
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| 44 | PUBLIC :: lintgen, hdcd_lint_gen |
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| 45 | PRIVATE |
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| 46 | |
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| 47 | !> Interface to multi-variate linear interpolation |
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| 48 | !! |
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| 49 | !! For __n__, the number of function's variables, user must provide: |
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| 50 | !! |
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| 51 | !! - __n__ scalar(s) with the coordinate(s) of the point to interpolate. |
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| 52 | !! - __n__ vector(s) with the tabulated values of each coordinate. |
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| 53 | !! - a single __n__-D array with the value of tabulated function at each |
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| 54 | !! tabulated coordinate. |
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| 55 | !! - A function, satisfying [[lintcore(module):locate(interface)]] interface, |
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| 56 | !! that locates the neighbourhood of the point to interpolate. |
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| 57 | !! - A scalar that stores the output value. |
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| 58 | INTERFACE lintgen |
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| 59 | MODULE PROCEDURE l1d_gen_sc,l2d_gen_sc,l3d_gen_sc,l4d_gen_sc,l5d_gen_sc |
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| 60 | MODULE PROCEDURE l1d_gen_ve,l2d_gen_ve,l3d_gen_ve,l4d_gen_ve,l5d_gen_ve |
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| 61 | END INTERFACE |
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| 62 | |
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| 63 | !> Interface to multi-variate hard-coded linear interpolation |
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| 64 | !! |
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| 65 | !! Same remarks as in [[lint_gen(module):lintgen(interface)]] apply here. |
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| 66 | INTERFACE hdcd_lint_gen |
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| 67 | MODULE PROCEDURE hdcdl1d_gen_sc, hdcdl2d_gen_sc, hdcdl3d_gen_sc, & |
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| 68 | hdcdl4d_gen_sc, hdcdl5d_gen_sc |
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| 69 | MODULE PROCEDURE hdcdl1d_gen_ve, hdcdl2d_gen_ve, hdcdl3d_gen_ve, & |
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| 70 | hdcdl4d_gen_ve, hdcdl5d_gen_ve |
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| 71 | END INTERFACE |
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| 72 | |
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| 73 | CONTAINS |
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| 74 | |
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| 75 | ! GENERIC versions |
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| 76 | ! ---------------- |
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| 77 | |
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| 78 | FUNCTION l1d_gen_sc(x,cx,cv, locator,res) RESULT(ret) |
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| 79 | !! Wrapper interface for 1D linear interpolation (scalar) |
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| 80 | !! |
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| 81 | !! @warning |
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| 82 | !! On error, __res__ output value is undefined. |
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| 83 | REAL(kind=wp), INTENT(in) :: x !! X coordinate of the point to interpolate |
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| 84 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cx !! Tabulated function X coordinates |
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| 85 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cv !! Tabulated function values |
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| 86 | REAL(kind=wp), INTENT(out) :: res !! Interpolated value |
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| 87 | PROCEDURE(locate) :: locator !! Locator function |
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| 88 | LOGICAL :: ret !! .true. on success, .false. otherwise |
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| 89 | REAL(kind=wp), DIMENSION(2,2) :: g1d |
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| 90 | INTEGER :: i,ix |
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| 91 | ret = .false. |
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| 92 | ix = locator(x,cx) ; IF (ix == 0) RETURN |
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| 93 | DO i=0,1 |
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| 94 | g1d(i+1,1) = cx(ix+i) |
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| 95 | g1d(i+1,2) = cv(ix+i) |
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| 96 | ENDDO |
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| 97 | res = lintc_((/x/),g1d) |
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| 98 | ret = .true. |
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| 99 | END FUNCTION l1d_gen_sc |
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| 100 | |
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| 101 | FUNCTION l2d_gen_sc(x,y,cx,cy,cv,locator,res) RESULT(ret) |
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| 102 | !! Wrapper interface for 2D linear interpolation (scalar) |
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| 103 | !! |
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| 104 | !! @warning |
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| 105 | !! On error, __res__ output value is undefined. |
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| 106 | REAL(kind=wp), INTENT(in) :: x !! X coordinate of the point to interpolate |
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| 107 | REAL(kind=wp), INTENT(in) :: y !! Y coordinate of the point to interpolate |
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| 108 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cx !! Tabulated function X coordinates |
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| 109 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cy !! Tabulated function Y coordinates |
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| 110 | REAL(kind=wp), INTENT(in), DIMENSION(:,:) :: cv !! Tabulated function values |
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| 111 | REAL(kind=wp), INTENT(out) :: res !! Interpolated value |
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| 112 | PROCEDURE(locate) :: locator !! Locator function |
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| 113 | LOGICAL :: ret !! .true. on success, .false. otherwise |
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| 114 | REAL(kind=wp), DIMENSION(4,3) :: g2d |
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| 115 | INTEGER :: ix0,iy0,i,a,b |
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| 116 | ret = .false. |
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| 117 | ix0 = locator(x,cx) ; IF (ix0 == 0) RETURN |
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| 118 | iy0 = locator(y,cy) ; IF (iy0 == 0) RETURN |
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| 119 | DO i=1,4 |
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| 120 | a=ix0+MOD((i-1),2) ; g2d(i,1) = cx(a) |
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| 121 | b=iy0+MOD((i-1)/2,2) ; g2d(i,2) = cy(b) |
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| 122 | g2d(i,3) = cv(a,b) |
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| 123 | ENDDO |
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| 124 | res = lintc_((/x,y/),g2d) |
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| 125 | ret = .true. |
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| 126 | END FUNCTION l2d_gen_sc |
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| 127 | |
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| 128 | FUNCTION l3d_gen_sc(x,y,z,cx,cy,cz,cv,locator,res) RESULT(ret) |
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| 129 | !! Wrapper interface for 3D linear interpolation (scalar) |
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| 130 | !! |
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| 131 | !! @warning |
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| 132 | !! On error, __res__ output value is undefined. |
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| 133 | REAL(kind=wp), INTENT(in) :: x !! X coordinate of the point to interpolate |
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| 134 | REAL(kind=wp), INTENT(in) :: y !! Y coordinate of the point to interpolate |
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| 135 | REAL(kind=wp), INTENT(in) :: z !! Z coordinate of the point to interpolate |
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| 136 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cx !! Tabulated function X coordinates |
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| 137 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cy !! Tabulated function Y coordinates |
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| 138 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cz !! Tabulated function Z coordinates |
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| 139 | REAL(kind=wp), INTENT(in), DIMENSION(:,:,:) :: cv !! Tabulated function values |
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| 140 | REAL(kind=wp), INTENT(out) :: res !! Interpolated value |
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| 141 | PROCEDURE(locate) :: locator !! Locator function |
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| 142 | LOGICAL :: ret !! .true. on success, .false. otherwise |
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| 143 | REAL(kind=wp), DIMENSION(8,4) :: g3d |
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| 144 | INTEGER :: ix0,iy0,iz0,i,a,b,c |
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| 145 | ret = .false. |
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| 146 | ix0 = locator(x,cx) ; IF (ix0 == 0) RETURN |
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| 147 | iy0 = locator(y,cy) ; IF (iy0 == 0) RETURN |
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| 148 | iz0 = locator(z,cz) ; IF (iz0 == 0) RETURN |
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| 149 | DO i=1,8 |
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| 150 | a=ix0+MOD((i-1),2) ; g3d(i,1) = cx(a) |
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| 151 | b=iy0+MOD((i-1)/2,2) ; g3d(i,2) = cy(b) |
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| 152 | c=iz0+MOD((i-1)/4,2) ; g3d(i,3) = cz(c) |
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| 153 | g3d(i,4) = cv(a,b,c) |
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| 154 | ENDDO |
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| 155 | res = lintc_((/x,y,z/),g3d) |
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| 156 | ret = .true. |
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| 157 | END FUNCTION l3d_gen_sc |
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| 158 | |
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| 159 | FUNCTION l4d_gen_sc(x,y,z,t,cx,cy,cz,ct,cv,locator,res) RESULT(ret) |
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| 160 | !! Wrapper interface for 4D linear interpolation (scalar) |
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| 161 | !! |
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| 162 | !! @warning |
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| 163 | !! On error, __res__ output value is undefined. |
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| 164 | REAL(kind=wp), INTENT(in) :: x !! X coordinate of the point to interpolate |
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| 165 | REAL(kind=wp), INTENT(in) :: y !! Y coordinate of the point to interpolate |
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| 166 | REAL(kind=wp), INTENT(in) :: z !! Z coordinate of the point to interpolate |
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| 167 | REAL(kind=wp), INTENT(in) :: t !! T coordinate of the point to interpolate |
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| 168 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cx !! Tabulated function X coordinates |
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| 169 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cy !! Tabulated function Y coordinates |
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| 170 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cz !! Tabulated function Z coordinates |
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| 171 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: ct !! Tabulated function T coordinates |
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| 172 | REAL(kind=wp), INTENT(in), DIMENSION(:,:,:,:) :: cv !! Tabulated function values |
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| 173 | REAL(kind=wp), INTENT(out) :: res !! Interpolated value |
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| 174 | PROCEDURE(locate) :: locator !! Locator function |
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| 175 | LOGICAL :: ret !! .true. on success, .false. otherwise |
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| 176 | REAL(kind=wp), DIMENSION(16,5) :: g4d |
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| 177 | INTEGER :: ix0,iy0,iz0,it0 |
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| 178 | INTEGER :: i,a,b,c,d |
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| 179 | ret = .false. |
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| 180 | ix0 = locator(x,cx) ; IF (ix0 == 0) RETURN |
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| 181 | iy0 = locator(y,cy) ; IF (iy0 == 0) RETURN |
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| 182 | iz0 = locator(z,cz) ; IF (iz0 == 0) RETURN |
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| 183 | it0 = locator(t,ct) ; IF (it0 == 0) RETURN |
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| 184 | DO i=1,16 |
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| 185 | a=ix0+MOD((i-1),2) ; g4d(i,1) = cx(a) |
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| 186 | b=iy0+MOD((i-1)/2,2) ; g4d(i,2) = cy(b) |
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| 187 | c=iz0+MOD((i-1)/4,2) ; g4d(i,3) = cz(c) |
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| 188 | d=it0+MOD((i-1)/8,2) ; g4d(i,4) = ct(d) |
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| 189 | g4d(i,5) = cv(a,b,c,d) |
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| 190 | ENDDO |
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| 191 | res = lintc_((/x,y,z,t/),g4d) |
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| 192 | ret = .true. |
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| 193 | END FUNCTION l4d_gen_sc |
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| 194 | |
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| 195 | FUNCTION l5d_gen_sc(x,y,z,t,w,cx,cy,cz,ct,cw,cv,locator,res) RESULT(ret) |
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| 196 | !! Wrapper interface for 5D linear interpolation (scalar) |
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| 197 | !! |
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| 198 | !! @warning |
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| 199 | !! On error, __res__ output value is undefined. |
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| 200 | REAL(kind=wp), INTENT(in) :: x !! X coordinate of the point to interpolate |
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| 201 | REAL(kind=wp), INTENT(in) :: y !! Y coordinate of the point to interpolate |
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| 202 | REAL(kind=wp), INTENT(in) :: z !! Z coordinate of the point to interpolate |
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| 203 | REAL(kind=wp), INTENT(in) :: t !! T coordinate of the point to interpolate |
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| 204 | REAL(kind=wp), INTENT(in) :: w !! W coordinate of the point to interpolate |
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| 205 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cx !! Tabulated function X coordinates |
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| 206 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cy !! Tabulated function Y coordinates |
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| 207 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cz !! Tabulated function Z coordinates |
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| 208 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: ct !! Tabulated function T coordinates |
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| 209 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cw !! Tabulated function W coordinates |
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| 210 | REAL(kind=wp), INTENT(in), DIMENSION(:,:,:,:,:) :: cv !! Tabulated function values |
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| 211 | REAL(kind=wp), INTENT(out) :: res !! Interpolated value |
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| 212 | PROCEDURE(locate) :: locator !! Locator function |
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| 213 | LOGICAL :: ret !! .true. on success, .false. otherwise |
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| 214 | REAL(kind=wp), DIMENSION(32,6) :: g5d |
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| 215 | INTEGER :: ix0,iy0,iz0,it0,iw0 |
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| 216 | INTEGER :: i,a,b,c,d,e |
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| 217 | ret = .false. |
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| 218 | ix0 = locator(x,cx) ; IF (ix0 == 0) RETURN |
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| 219 | iy0 = locator(y,cy) ; IF (iy0 == 0) RETURN |
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| 220 | iz0 = locator(z,cz) ; IF (iz0 == 0) RETURN |
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| 221 | it0 = locator(t,ct) ; IF (it0 == 0) RETURN |
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| 222 | iw0 = locator(w,cw) ; IF (iw0 == 0) RETURN |
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| 223 | DO i=1,32 |
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| 224 | a=ix0+MOD((i-1),2) ; g5d(i,1) = cx(a) |
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| 225 | b=iy0+MOD((i-1)/2,2) ; g5d(i,2) = cy(b) |
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| 226 | c=iz0+MOD((i-1)/4,2) ; g5d(i,3) = cz(c) |
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| 227 | d=it0+MOD((i-1)/8,2) ; g5d(i,4) = ct(d) |
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| 228 | e=iw0+MOD((i-1)/16,2) ; g5d(i,5) = cw(e) |
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| 229 | g5d(i,6) = cv(a,b,c,d,e) |
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| 230 | ENDDO |
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| 231 | res = lintc_((/x,y,z,t,w/),g5d) |
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| 232 | ret = .true. |
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| 233 | END FUNCTION l5d_gen_sc |
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| 234 | |
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| 235 | ! HARD-CODED versions |
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| 236 | ! ------------------- |
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| 237 | |
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| 238 | FUNCTION hdcdl1d_gen_sc(x,cx,cv,locator,res) RESULT(ret) |
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| 239 | !! Hard-coded 1D linear interpolation (scalar) |
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| 240 | !! |
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| 241 | !! @warning |
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| 242 | !! On error, __res__ output value is undefined. |
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| 243 | REAL(kind=wp), INTENT(in) :: x !! X coordinate of the point to interpolate |
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| 244 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cx !! Tabulated function X coordinates |
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| 245 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cv !! Tabulated function values |
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| 246 | REAL(kind=wp), INTENT(out) :: res !! Interpolated value |
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| 247 | PROCEDURE(locate) :: locator !! Locator function |
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| 248 | LOGICAL :: ret !! .true. on success, .false. otherwise |
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| 249 | REAL(kind=wp) :: xd |
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| 250 | INTEGER :: ix0,ix1 |
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| 251 | ret = .false. |
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| 252 | ix0 = locator(x,cx) ; IF (ix0 == 0) RETURN |
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| 253 | ix1 = ix0+1 |
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| 254 | xd = (x-cx(ix0))/(cx(ix1)-cx(ix0)) |
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| 255 | res = cv(ix0)*(1d0-xd)+cv(ix1)*xd |
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| 256 | ret = .true. |
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| 257 | END FUNCTION hdcdl1d_gen_sc |
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| 258 | |
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| 259 | FUNCTION hdcdl2d_gen_sc(x,y,cx,cy,cv,locator,res) RESULT(ret) |
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| 260 | !! Hard-coded 2D linear interpolation (scalar) |
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| 261 | !! |
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| 262 | !! @warning |
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| 263 | !! On error, __res__ output value is undefined. |
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| 264 | REAL(kind=wp), INTENT(in) :: x !! X coordinate of the point to interpolate |
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| 265 | REAL(kind=wp), INTENT(in) :: y !! Y coordinate of the point to interpolate |
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| 266 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cx !! Tabulated function X coordinates |
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| 267 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cy !! Tabulated function Y coordinates |
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| 268 | REAL(kind=wp), INTENT(in), DIMENSION(:,:) :: cv !! Tabulated function values |
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| 269 | REAL(kind=wp), INTENT(out) :: res !! Interpolated value |
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| 270 | PROCEDURE(locate) :: locator !! Locator function |
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| 271 | LOGICAL :: ret !! .true. on success, .false. otherwise |
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| 272 | REAL(kind=wp) :: xd,yd |
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| 273 | REAL(kind=wp) :: f0,f1 |
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| 274 | INTEGER :: ix0,iy0,ix1,iy1 |
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| 275 | ret = .false. |
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| 276 | ix0 = locator(x,cx) ; IF (ix0 == 0) RETURN |
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| 277 | iy0 = locator(y,cy) ; IF (iy0 == 0) RETURN |
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| 278 | ix1 = ix0 + 1 ; iy1 = iy0 + 1 |
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| 279 | xd = (x-cx(ix0))/(cx(ix1)-cx(ix0)) |
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| 280 | yd = (y-cy(iy0))/(cy(iy1)-cy(iy0)) |
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| 281 | f0 = cv(ix0,iy0)*(1d0-xd)+cv(ix1,iy0)*xd |
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| 282 | f1 = cv(ix0,iy1)*(1d0-xd)+cv(ix1,iy1)*xd |
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| 283 | res = f0*(1d0-yd)+f1*yd |
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| 284 | ret = .true. |
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| 285 | END FUNCTION hdcdl2d_gen_sc |
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| 286 | |
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| 287 | FUNCTION hdcdl3d_gen_sc(x,y,z,cx,cy,cz,cv,locator,res) RESULT(ret) |
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| 288 | !! Hard-coded 3D linear interpolation (scalar) |
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| 289 | !! |
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| 290 | !! @warning |
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| 291 | !! On error, __res__ output value is undefined. |
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| 292 | REAL(kind=wp), INTENT(in) :: x !! X coordinate of the point to interpolate |
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| 293 | REAL(kind=wp), INTENT(in) :: y !! Y coordinate of the point to interpolate |
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| 294 | REAL(kind=wp), INTENT(in) :: z !! Z coordinate of the point to interpolate |
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| 295 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cx !! Tabulated function X coordinates |
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| 296 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cy !! Tabulated function Y coordinates |
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| 297 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cz !! Tabulated function Z coordinates |
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| 298 | REAL(kind=wp), INTENT(in), DIMENSION(:,:,:) :: cv !! Tabulated function values |
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| 299 | REAL(kind=wp), INTENT(out) :: res !! Interpolated value |
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| 300 | PROCEDURE(locate) :: locator !! Locator function |
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| 301 | LOGICAL :: ret !! .true. on success, .false. otherwise |
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| 302 | REAL(kind=wp) :: xd,yd,zd |
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| 303 | REAL(kind=wp) :: f00,f10,f01,f11,f0,f1 |
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| 304 | INTEGER :: ix0,iy0,iz0,ix1,iy1,iz1 |
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| 305 | ret = .false. |
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| 306 | ix0 = locator(x,cx) ; IF (ix0 == 0) RETURN |
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| 307 | iy0 = locator(y,cy) ; IF (iy0 == 0) RETURN |
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| 308 | iz0 = locator(z,cz) ; IF (iz0 == 0) RETURN |
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| 309 | ix1=ix0+1 ; iy1=iy0+1 ; iz1=iz0+1 |
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| 310 | xd = (x-cx(ix0))/(cx(ix1)-cx(ix0)) |
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| 311 | yd = (y-cy(iy0))/(cy(iy1)-cy(iy0)) |
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| 312 | zd = (z-cz(iz0))/(cz(iz1)-cz(iz0)) |
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| 313 | |
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| 314 | f00 = cv(ix0,iy0,iz0)*(1d0-xd)+cv(ix1,iy0,iz0)*xd |
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| 315 | f10 = cv(ix0,iy1,iz0)*(1d0-xd)+cv(ix1,iy1,iz0)*xd |
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| 316 | f01 = cv(ix0,iy0,iz1)*(1d0-xd)+cv(ix1,iy0,iz1)*xd |
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| 317 | f11 = cv(ix0,iy1,iz1)*(1d0-xd)+cv(ix1,iy1,iz1)*xd |
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| 318 | |
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| 319 | f0 = f00 *(1d0-yd)+f10*yd |
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| 320 | f1 = f00 *(1d0-yd)+f10*yd |
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| 321 | |
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| 322 | res = f0*(1d0-zd)+f1*zd |
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| 323 | ret = .true. |
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| 324 | END FUNCTION hdcdl3d_gen_sc |
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| 325 | |
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| 326 | FUNCTION hdcdl4d_gen_sc(x,y,z,t,cx,cy,cz,ct,cv,locator,res) RESULT(ret) |
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| 327 | !! Hard-coded 4D linear interpolation (scalar) |
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| 328 | !! |
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| 329 | !! @warning |
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| 330 | !! On error, __res__ output value is undefined. |
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| 331 | REAL(kind=wp), INTENT(in) :: x !! X coordinate of the point to interpolate |
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| 332 | REAL(kind=wp), INTENT(in) :: y !! Y coordinate of the point to interpolate |
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| 333 | REAL(kind=wp), INTENT(in) :: z !! Z coordinate of the point to interpolate |
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| 334 | REAL(kind=wp), INTENT(in) :: t !! T coordinate of the point to interpolate |
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| 335 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cx !! Tabulated function X coordinates |
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| 336 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cy !! Tabulated function Y coordinates |
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| 337 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cz !! Tabulated function Z coordinates |
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| 338 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: ct !! Tabulated function T coordinates |
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| 339 | REAL(kind=wp), INTENT(in), DIMENSION(:,:,:,:) :: cv !! Tabulated function values |
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| 340 | REAL(kind=wp), INTENT(out) :: res !! Interpolated value |
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| 341 | PROCEDURE(locate) :: locator !! Locator function |
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| 342 | LOGICAL :: ret !! .true. on success, .false. otherwise |
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| 343 | REAL(kind=wp) :: xd,yd,zd,td |
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| 344 | REAL(kind=wp) :: f000,f100,f010,f110,f001,f101,f011,f111, & |
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| 345 | f00,f10,f01,f11,f0,f1 |
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| 346 | INTEGER :: ix0,iy0,iz0,it0,ix1,iy1,iz1,it1 |
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| 347 | ret = .false. |
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| 348 | ix0 = locator(x,cx) ; IF (ix0 == 0) RETURN |
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| 349 | iy0 = locator(y,cy) ; IF (iy0 == 0) RETURN |
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| 350 | iz0 = locator(z,cz) ; IF (iz0 == 0) RETURN |
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| 351 | it0 = locator(t,ct) ; IF (it0 == 0) RETURN |
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| 352 | |
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| 353 | ix1=ix0+1 ; iy1=iy0+1 ; iz1=iz0+1 ; it1=it0+1 |
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| 354 | xd = (x-cx(ix0))/(cx(ix1)-cx(ix0)) |
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| 355 | yd = (y-cy(iy0))/(cy(iy1)-cy(iy0)) |
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| 356 | zd = (z-cz(iz0))/(cz(iz1)-cz(iz0)) |
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| 357 | td = (t-ct(it0))/(ct(it1)-ct(it0)) |
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| 358 | |
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| 359 | f000 = cv(ix0,iy0,iz0,it0)*(1d0-xd)+cv(ix1,iy0,iz0,it0)*xd |
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| 360 | f100 = cv(ix0,iy1,iz0,it0)*(1d0-xd)+cv(ix1,iy1,iz0,it0)*xd |
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| 361 | f010 = cv(ix0,iy0,iz1,it0)*(1d0-xd)+cv(ix1,iy0,iz1,it0)*xd |
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| 362 | f110 = cv(ix0,iy1,iz1,it0)*(1d0-xd)+cv(ix1,iy1,iz1,it0)*xd |
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| 363 | f001 = cv(ix0,iy0,iz0,it1)*(1d0-xd)+cv(ix1,iy0,iz0,it1)*xd |
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| 364 | f101 = cv(ix0,iy1,iz0,it1)*(1d0-xd)+cv(ix1,iy1,iz0,it1)*xd |
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| 365 | f011 = cv(ix0,iy0,iz1,it1)*(1d0-xd)+cv(ix1,iy0,iz1,it1)*xd |
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| 366 | f111 = cv(ix0,iy1,iz1,it1)*(1d0-xd)+cv(ix1,iy1,iz1,it1)*xd |
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| 367 | |
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| 368 | f00 = f000*(1d0-yd)+f100*yd |
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| 369 | f10 = f010*(1d0-yd)+f110*yd |
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| 370 | f01 = f001*(1d0-yd)+f101*yd |
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| 371 | f11 = f011*(1d0-yd)+f111*yd |
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| 372 | |
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| 373 | f0 = f00 *(1d0-zd)+f10*zd |
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| 374 | f1 = f01 *(1d0-zd)+f11*zd |
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| 375 | |
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| 376 | res = f0*(1d0-td)+f1*td |
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| 377 | ret = .true. |
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| 378 | END FUNCTION hdcdl4d_gen_sc |
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| 379 | |
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| 380 | FUNCTION hdcdl5d_gen_sc(x,y,z,t,w,cx,cy,cz,ct,cw,cv,locator,res) RESULT(ret) |
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| 381 | !! Hard-coded 5D linear interpolation (scalar) |
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| 382 | !! |
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| 383 | !! @warning |
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| 384 | !! On error, __res__ output value is undefined. |
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| 385 | REAL(kind=wp), INTENT(in) :: x !! X coordinate of the point to interpolate |
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| 386 | REAL(kind=wp), INTENT(in) :: y !! Y coordinate of the point to interpolate |
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| 387 | REAL(kind=wp), INTENT(in) :: z !! Z coordinate of the point to interpolate |
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| 388 | REAL(kind=wp), INTENT(in) :: t !! T coordinate of the point to interpolate |
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| 389 | REAL(kind=wp), INTENT(in) :: w !! W coordinate of the point to interpolate |
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| 390 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cx !! Tabulated function X coordinates |
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| 391 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cy !! Tabulated function Y coordinates |
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| 392 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cz !! Tabulated function Z coordinates |
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| 393 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: ct !! Tabulated function T coordinates |
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| 394 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cw !! Tabulated function W coordinates |
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| 395 | REAL(kind=wp), INTENT(in), DIMENSION(:,:,:,:,:) :: cv !! Tabulated function values |
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| 396 | REAL(kind=wp), INTENT(out) :: res !! Interpolated value |
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| 397 | PROCEDURE(locate) :: locator !! Locator function |
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| 398 | LOGICAL :: ret !! .true. on success, .false. otherwise |
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| 399 | REAL(kind=wp) :: xd,yd,zd,td,wd |
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| 400 | REAL(kind=wp) :: f0000,f1000,f0100,f1100,f0010,f1010,f0110,f1110, & |
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| 401 | f0001,f1001,f0101,f1101,f0011,f1011,f0111,f1111, & |
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| 402 | f000,f100,f010,f110,f001,f101,f011,f111, & |
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| 403 | f00,f10,f01,f11,f0,f1 |
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| 404 | INTEGER :: ix0,iy0,iz0,it0,iw0,ix1,iy1,iz1,it1,iw1 |
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| 405 | ret = .false. |
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| 406 | ix0 = locator(x,cx) ; IF (ix0 == 0) RETURN |
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| 407 | iy0 = locator(y,cy) ; IF (iy0 == 0) RETURN |
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| 408 | iz0 = locator(z,cz) ; IF (iz0 == 0) RETURN |
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| 409 | it0 = locator(t,ct) ; IF (it0 == 0) RETURN |
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| 410 | iw0 = locator(w,cw) ; IF (iw0 == 0) RETURN |
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| 411 | |
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| 412 | ix1=ix0+1 ; iy1=iy0+1 ; iz1=iz0+1 ; it1=it0+1 ; iw1=iw0+1 |
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| 413 | xd = (x-cx(ix0))/(cx(ix1)-cx(ix0)) |
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| 414 | yd = (y-cy(iy0))/(cy(iy1)-cy(iy0)) |
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| 415 | zd = (z-cz(iz0))/(cz(iz1)-cz(iz0)) |
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| 416 | td = (t-ct(it0))/(ct(it1)-ct(it0)) |
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| 417 | wd = (w-cw(iw0))/(cw(iw1)-cw(iw0)) |
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| 418 | |
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| 419 | f0000 = cv(ix0,iy0,iz0,it0,iw0)*(1d0-xd)+cv(ix1,iy0,iz0,it0,iw0)*xd |
|---|
| 420 | f1000 = cv(ix0,iy1,iz0,it0,iw0)*(1d0-xd)+cv(ix0,iy1,iz0,it0,iw0)*xd |
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| 421 | f0100 = cv(ix0,iy0,iz1,it0,iw0)*(1d0-xd)+cv(ix1,iy0,iz1,it0,iw0)*xd |
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| 422 | f1100 = cv(ix0,iy1,iz1,it0,iw0)*(1d0-xd)+cv(ix1,iy1,iz1,it0,iw0)*xd |
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| 423 | f0010 = cv(ix0,iy0,iz0,it1,iw0)*(1d0-xd)+cv(ix1,iy0,iz0,it1,iw0)*xd |
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| 424 | f1010 = cv(ix0,iy1,iz0,it1,iw0)*(1d0-xd)+cv(ix1,iy1,iz0,it1,iw0)*xd |
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| 425 | f0110 = cv(ix0,iy0,iz1,it1,iw0)*(1d0-xd)+cv(ix1,iy0,iz1,it1,iw0)*xd |
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| 426 | f1110 = cv(ix0,iy1,iz1,it1,iw0)*(1d0-xd)+cv(ix1,iy1,iz1,it1,iw0)*xd |
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| 427 | f0001 = cv(ix0,iy0,iz0,it0,iw1)*(1d0-xd)+cv(ix1,iy0,iz0,it0,iw1)*xd |
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| 428 | f1001 = cv(ix0,iy1,iz0,it0,iw1)*(1d0-xd)+cv(ix0,iy1,iz0,it0,iw1)*xd |
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| 429 | f0101 = cv(ix0,iy0,iz1,it0,iw1)*(1d0-xd)+cv(ix1,iy0,iz1,it0,iw1)*xd |
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| 430 | f1101 = cv(ix0,iy1,iz1,it0,iw1)*(1d0-xd)+cv(ix1,iy1,iz1,it0,iw1)*xd |
|---|
| 431 | f0011 = cv(ix0,iy0,iz0,it1,iw1)*(1d0-xd)+cv(ix1,iy0,iz0,it1,iw1)*xd |
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| 432 | f1011 = cv(ix0,iy1,iz0,it1,iw1)*(1d0-xd)+cv(ix1,iy1,iz0,it1,iw1)*xd |
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| 433 | f0111 = cv(ix0,iy0,iz1,it1,iw1)*(1d0-xd)+cv(ix1,iy0,iz1,it1,iw1)*xd |
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| 434 | f1111 = cv(ix0,iy1,iz1,it1,iw1)*(1d0-xd)+cv(ix1,iy1,iz1,it1,iw1)*xd |
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| 435 | |
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| 436 | f000 = f0000*(1d0-yd) + f1000*yd |
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| 437 | f100 = f0100*(1d0-yd) + f1100*yd |
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| 438 | f010 = f0010*(1d0-yd) + f1010*yd |
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| 439 | f110 = f0110*(1d0-yd) + f1110*yd |
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| 440 | f101 = f0101*(1d0-yd) + f1101*yd |
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| 441 | f011 = f0011*(1d0-yd) + f1011*yd |
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| 442 | f111 = f0111*(1d0-yd) + f1111*yd |
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| 443 | |
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| 444 | f00 = f000*(1d0-zd)+f100*zd |
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| 445 | f10 = f010*(1d0-zd)+f110*zd |
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| 446 | f01 = f001*(1d0-zd)+f101*zd |
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| 447 | f11 = f011*(1d0-zd)+f111*zd |
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| 448 | |
|---|
| 449 | f0 = f00 *(1d0-td)+f10*td |
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| 450 | f1 = f01 *(1d0-td)+f11*td |
|---|
| 451 | |
|---|
| 452 | res = f0*(1d0-wd)+f1*wd |
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| 453 | ret = .true. |
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| 454 | END FUNCTION hdcdl5d_gen_sc |
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| 455 | |
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| 456 | !-------------------- |
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| 457 | ! VECTORIZED VERSIONS |
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| 458 | !-------------------- |
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| 459 | |
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| 460 | ! GENERIC versions |
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| 461 | ! ---------------- |
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| 462 | |
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| 463 | FUNCTION l1d_gen_ve(x,cx,cv,locator,res) RESULT(ret) |
|---|
| 464 | !! Wrapper interface for 1D linear interpolation (vector) |
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| 465 | !! |
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| 466 | !! @warning |
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| 467 | !! On error, __res__ output vector is undefined (i.e. not allocated). |
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| 468 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: x !! X coordinate of the points to interpolate |
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| 469 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cx !! Tabulated function X coordinates |
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| 470 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cv !! Tabulated function values |
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| 471 | REAL(kind=wp), INTENT(out), DIMENSION(:), ALLOCATABLE :: res !! Interpolated values |
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| 472 | PROCEDURE(locate) :: locator !! Locator function |
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| 473 | LOGICAL :: ret !! .true. on success, .false. otherwise |
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| 474 | REAL(kind=wp), DIMENSION(2,2) :: g1d |
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| 475 | INTEGER :: n,j,i,ix |
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| 476 | ret = .false. |
|---|
| 477 | n = SIZE(x) ; ALLOCATE(res(n)) |
|---|
| 478 | DO j=1,n |
|---|
| 479 | ix = locator(x(j),cx) |
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| 480 | IF (ix == 0) THEN |
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| 481 | DEALLOCATE(res) ; RETURN |
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| 482 | ENDIF |
|---|
| 483 | DO i=0,1 |
|---|
| 484 | g1d(i+1,1) = cx(ix+i) |
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| 485 | g1d(i+1,2) = cv(ix+i) |
|---|
| 486 | ENDDO |
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| 487 | res(j) = lintc_((/x(j)/),g1d) |
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| 488 | ENDDO |
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| 489 | ret = .true. |
|---|
| 490 | END FUNCTION l1d_gen_ve |
|---|
| 491 | |
|---|
| 492 | FUNCTION l2d_gen_ve(x,y,cx,cy,cv,locator,res) RESULT(ret) |
|---|
| 493 | !! Wrapper interface for 2D linear interpolation (vector) |
|---|
| 494 | !! |
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| 495 | !! @warning |
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| 496 | !! On error, __res__ output vector is undefined (i.e. not allocated). |
|---|
| 497 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: x !! X coordinate of the points to interpolate |
|---|
| 498 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: y !! Y coordinate of the points to interpolate |
|---|
| 499 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cx !! Tabulated function X coordinates |
|---|
| 500 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cy !! Tabulated function Y coordinates |
|---|
| 501 | REAL(kind=wp), INTENT(in), DIMENSION(:,:) :: cv !! Tabulated function values |
|---|
| 502 | REAL(kind=wp), INTENT(out), DIMENSION(:), ALLOCATABLE :: res !! Interpolated values |
|---|
| 503 | PROCEDURE(locate) :: locator !! Locator function |
|---|
| 504 | LOGICAL :: ret !! .true. on success, .false. otherwise |
|---|
| 505 | REAL(kind=wp), DIMENSION(4,3) :: g2d |
|---|
| 506 | INTEGER :: n,j,ix0,iy0,i,a,b |
|---|
| 507 | ret = .false. |
|---|
| 508 | n = SIZE(x) ; ALLOCATE(res(n)) |
|---|
| 509 | DO j=1,n |
|---|
| 510 | ix0 = locator(x(j),cx) |
|---|
| 511 | iy0 = locator(y(j),cy) |
|---|
| 512 | IF (ix0 == 0 .OR. iy0 == 0) THEN |
|---|
| 513 | DEALLOCATE(res) ; RETURN |
|---|
| 514 | ENDIF |
|---|
| 515 | DO i=1,4 |
|---|
| 516 | a=ix0+MOD((i-1),2) ; g2d(i,1) = cx(a) |
|---|
| 517 | b=iy0+MOD((i-1)/2,2) ; g2d(i,2) = cy(b) |
|---|
| 518 | g2d(i,3) = cv(a,b) |
|---|
| 519 | ENDDO |
|---|
| 520 | res(j) = lintc_((/x(j),y(j)/),g2d) |
|---|
| 521 | ENDDO |
|---|
| 522 | ret = .true. |
|---|
| 523 | END FUNCTION l2d_gen_ve |
|---|
| 524 | |
|---|
| 525 | FUNCTION l3d_gen_ve(x,y,z,cx,cy,cz,cv,locator,res) RESULT(ret) |
|---|
| 526 | !! Wrapper interface for 3D linear interpolation (vector) |
|---|
| 527 | !! |
|---|
| 528 | !! @warning |
|---|
| 529 | !! On error, __res__ output vector is undefined (i.e. not allocated). |
|---|
| 530 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: x !! X coordinate of the points to interpolate |
|---|
| 531 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: y !! Y coordinate of the points to interpolate |
|---|
| 532 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: z !! Z coordinate of the points to interpolate |
|---|
| 533 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cx !! Tabulated function X coordinates |
|---|
| 534 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cy !! Tabulated function Y coordinates |
|---|
| 535 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cz !! Tabulated function Z coordinates |
|---|
| 536 | REAL(kind=wp), INTENT(in), DIMENSION(:,:,:) :: cv !! Tabulated function values |
|---|
| 537 | REAL(kind=wp), INTENT(out), DIMENSION(:), ALLOCATABLE :: res !! Interpolated values |
|---|
| 538 | PROCEDURE(locate) :: locator !! Locator function |
|---|
| 539 | LOGICAL :: ret !! .true. on success, .false. otherwise |
|---|
| 540 | REAL(kind=wp), DIMENSION(8,4) :: g3d |
|---|
| 541 | INTEGER :: ix0,iy0,iz0 |
|---|
| 542 | INTEGER :: n,j,i,a,b,c |
|---|
| 543 | ret = .false. |
|---|
| 544 | n = SIZE(x) ; ALLOCATE(res(n)) |
|---|
| 545 | DO j=1,n |
|---|
| 546 | ix0 = locator(x(j),cx) |
|---|
| 547 | iy0 = locator(y(j),cy) |
|---|
| 548 | iz0 = locator(z(j),cz) |
|---|
| 549 | IF (ix0 == 0 .OR. iy0 == 0 .OR. iz0 == 0) THEN |
|---|
| 550 | DEALLOCATE(res) ; RETURN |
|---|
| 551 | ENDIF |
|---|
| 552 | DO i=1,8 |
|---|
| 553 | a=ix0+MOD((i-1),2) ; g3d(i,1) = cx(a) |
|---|
| 554 | b=iy0+MOD((i-1)/2,2) ; g3d(i,2) = cy(b) |
|---|
| 555 | c=iz0+MOD((i-1)/4,2) ; g3d(i,3) = cz(c) |
|---|
| 556 | g3d(i,4) = cv(a,b,c) |
|---|
| 557 | ENDDO |
|---|
| 558 | res(j) = lintc_((/x(j),y(j),z(j)/),g3d) |
|---|
| 559 | ENDDO |
|---|
| 560 | ret = .true. |
|---|
| 561 | END FUNCTION l3d_gen_ve |
|---|
| 562 | |
|---|
| 563 | FUNCTION l4d_gen_ve(x,y,z,t,cx,cy,cz,ct,cv,locator,res) RESULT(ret) |
|---|
| 564 | !! Wrapper interface for 4D linear interpolation (vector) |
|---|
| 565 | !! |
|---|
| 566 | !! @warning |
|---|
| 567 | !! On error, __res__ output vector is undefined (i.e. not allocated). |
|---|
| 568 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: x !! X coordinate of the points to interpolate |
|---|
| 569 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: y !! Y coordinate of the points to interpolate |
|---|
| 570 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: z !! Z coordinate of the points to interpolate |
|---|
| 571 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: t !! T coordinate of the points to interpolate |
|---|
| 572 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cx !! Tabulated function X coordinates |
|---|
| 573 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cy !! Tabulated function Y coordinates |
|---|
| 574 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cz !! Tabulated function Z coordinates |
|---|
| 575 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: ct !! Tabulated function T coordinates |
|---|
| 576 | REAL(kind=wp), INTENT(in), DIMENSION(:,:,:,:) :: cv !! Tabulated function values |
|---|
| 577 | REAL(kind=wp), INTENT(out), DIMENSION(:), ALLOCATABLE :: res !! Interpolated values |
|---|
| 578 | PROCEDURE(locate) :: locator !! Locator function |
|---|
| 579 | LOGICAL :: ret !! .true. on success, .false. otherwise |
|---|
| 580 | REAL(kind=wp), DIMENSION(16,5) :: g4d |
|---|
| 581 | INTEGER :: ix0,iy0,iz0,it0 |
|---|
| 582 | INTEGER :: n,j,i,a,b,c,d |
|---|
| 583 | ret = .false. |
|---|
| 584 | n = SIZE(x) ; ALLOCATE(res(n)) |
|---|
| 585 | DO j=1,n |
|---|
| 586 | ix0 = locator(x(j),cx) |
|---|
| 587 | iy0 = locator(y(j),cy) |
|---|
| 588 | iz0 = locator(z(j),cz) |
|---|
| 589 | it0 = locator(t(j),ct) |
|---|
| 590 | IF (ix0 == 0 .OR. iy0 == 0 .OR. iz0 == 0 .OR. it0 == 0) THEN |
|---|
| 591 | DEALLOCATE(res) ; RETURN |
|---|
| 592 | ENDIF |
|---|
| 593 | DO i=1,16 |
|---|
| 594 | a=ix0+MOD((i-1),2) ; g4d(i,1) = cx(a) |
|---|
| 595 | b=iy0+MOD((i-1)/2,2) ; g4d(i,2) = cy(b) |
|---|
| 596 | c=iz0+MOD((i-1)/4,2) ; g4d(i,3) = cz(c) |
|---|
| 597 | d=it0+MOD((i-1)/8,2) ; g4d(i,4) = ct(d) |
|---|
| 598 | g4d(i,5) = cv(a,b,c,d) |
|---|
| 599 | ENDDO |
|---|
| 600 | res(j) = lintc_((/x(j),y(j),z(j),t(j)/),g4d) |
|---|
| 601 | ENDDO |
|---|
| 602 | ret = .true. |
|---|
| 603 | END FUNCTION l4d_gen_ve |
|---|
| 604 | |
|---|
| 605 | FUNCTION l5d_gen_ve(x,y,z,t,w,cx,cy,cz,ct,cw,cv,locator,res) RESULT(ret) |
|---|
| 606 | !! Wrapper interface for 5D linear interpolation (vector) |
|---|
| 607 | !! |
|---|
| 608 | !! @warning |
|---|
| 609 | !! On error, __res__ output vector is undefined (i.e. not allocated). |
|---|
| 610 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: x !! X coordinate of the points to interpolate |
|---|
| 611 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: y !! Y coordinate of the points to interpolate |
|---|
| 612 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: z !! Z coordinate of the points to interpolate |
|---|
| 613 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: t !! T coordinate of the points to interpolate |
|---|
| 614 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: w !! W coordinate of the points to interpolate |
|---|
| 615 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cx !! Tabulated function X coordinates |
|---|
| 616 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cy !! Tabulated function Y coordinates |
|---|
| 617 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cz !! Tabulated function Z coordinates |
|---|
| 618 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: ct !! Tabulated function T coordinates |
|---|
| 619 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cw !! Tabulated function W coordinates |
|---|
| 620 | REAL(kind=wp), INTENT(in), DIMENSION(:,:,:,:,:) :: cv !! Tabulated function values |
|---|
| 621 | REAL(kind=wp), INTENT(out), DIMENSION(:), ALLOCATABLE :: res !! Interpolated values |
|---|
| 622 | PROCEDURE(locate) :: locator !! Locator function |
|---|
| 623 | LOGICAL :: ret !! .true. on success, .false. otherwise |
|---|
| 624 | REAL(kind=wp), DIMENSION(32,6) :: g5d |
|---|
| 625 | INTEGER :: ix0,iy0,iz0,it0,iw0 |
|---|
| 626 | INTEGER :: n,j,i,a,b,c,d,e |
|---|
| 627 | ret = .false. |
|---|
| 628 | n = SIZE(x) ; ALLOCATE(res(n)) |
|---|
| 629 | DO j=1,n |
|---|
| 630 | ix0 = locator(x(j),cx) |
|---|
| 631 | iy0 = locator(y(j),cy) |
|---|
| 632 | iz0 = locator(z(j),cz) |
|---|
| 633 | it0 = locator(t(j),ct) |
|---|
| 634 | iw0 = locator(w(j),cw) |
|---|
| 635 | IF (ix0 == 0 .OR. iy0 == 0 .OR. iz0 == 0 .OR. it0 == 0 .OR. iw0 == 0) THEN |
|---|
| 636 | DEALLOCATE(res) ; RETURN |
|---|
| 637 | ENDIF |
|---|
| 638 | DO i=1,32 |
|---|
| 639 | a=ix0+MOD((i-1),2) ; g5d(i,1) = cx(a) |
|---|
| 640 | b=iy0+MOD((i-1)/2,2) ; g5d(i,2) = cy(b) |
|---|
| 641 | c=iz0+MOD((i-1)/4,2) ; g5d(i,3) = cz(c) |
|---|
| 642 | d=it0+MOD((i-1)/8,2) ; g5d(i,4) = ct(d) |
|---|
| 643 | e=iw0+MOD((i-1)/16,2) ; g5d(i,5) = cw(e) |
|---|
| 644 | g5d(i,6) = cv(a,b,c,d,e) |
|---|
| 645 | ENDDO |
|---|
| 646 | res(j) = lintc_((/x,y,z,t,w/),g5d) |
|---|
| 647 | ENDDO |
|---|
| 648 | ret = .true. |
|---|
| 649 | END FUNCTION l5d_gen_ve |
|---|
| 650 | |
|---|
| 651 | ! HARD-CODED versions |
|---|
| 652 | ! ------------------- |
|---|
| 653 | |
|---|
| 654 | FUNCTION hdcdl1d_gen_ve(x,cx,cv,locator,res) RESULT(ret) |
|---|
| 655 | !! Hard-coded 1D linear interpolation (vector) |
|---|
| 656 | !! |
|---|
| 657 | !! @warning |
|---|
| 658 | !! On error, __res__ output vector is undefined (i.e. not allocated). |
|---|
| 659 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: x !! X coordinate of the points to interpolate |
|---|
| 660 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cx !! Tabulated function X coordinates |
|---|
| 661 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cv !! Tabulated function values |
|---|
| 662 | REAL(kind=wp), INTENT(out), DIMENSION(:), ALLOCATABLE :: res !! Interpolated values |
|---|
| 663 | PROCEDURE(locate) :: locator !! Locator function |
|---|
| 664 | LOGICAL :: ret !! .true. on success, .false. otherwise |
|---|
| 665 | REAL(kind=wp) :: xd |
|---|
| 666 | INTEGER :: ix0,ix1 |
|---|
| 667 | INTEGER :: n,j |
|---|
| 668 | ret = .false. |
|---|
| 669 | n = SIZE(x) ; ALLOCATE(res(n)) |
|---|
| 670 | DO j=1,n |
|---|
| 671 | ix0 = locator(x(j),cx) |
|---|
| 672 | IF (ix0 == 0) THEN |
|---|
| 673 | DEALLOCATE(res) ; RETURN |
|---|
| 674 | ENDIF |
|---|
| 675 | ix1 = ix0+1 |
|---|
| 676 | xd = (x(j)-cx(ix0))/(cx(ix1)-cx(ix0)) |
|---|
| 677 | res(j) = cv(ix0)*(1d0-xd)+cv(ix1)*xd |
|---|
| 678 | ENDDO |
|---|
| 679 | ret = .true. |
|---|
| 680 | END FUNCTION hdcdl1d_gen_ve |
|---|
| 681 | |
|---|
| 682 | FUNCTION hdcdl2d_gen_ve(x,y,cx,cy,cv,locator,res) RESULT(ret) |
|---|
| 683 | !! Hard-coded 2D linear interpolation (vector) |
|---|
| 684 | !! |
|---|
| 685 | !! @warning |
|---|
| 686 | !! On error, __res__ output vector is undefined (i.e. not allocated). |
|---|
| 687 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: x !! X coordinate of the points to interpolate |
|---|
| 688 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: y !! Y coordinate of the points to interpolate |
|---|
| 689 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cx !! Tabulated function X coordinates |
|---|
| 690 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cy !! Tabulated function Y coordinates |
|---|
| 691 | REAL(kind=wp), INTENT(in), DIMENSION(:,:) :: cv !! Tabulated function values |
|---|
| 692 | REAL(kind=wp), INTENT(out), DIMENSION(:), ALLOCATABLE :: res !! Interpolated values |
|---|
| 693 | PROCEDURE(locate) :: locator !! Locator function |
|---|
| 694 | LOGICAL :: ret !! .true. on success, .false. otherwise |
|---|
| 695 | REAL(kind=wp) :: xd,yd |
|---|
| 696 | REAL(kind=wp) :: f0,f1 |
|---|
| 697 | INTEGER :: ix0,iy0,ix1,iy1 |
|---|
| 698 | INTEGER :: n,j |
|---|
| 699 | ret = .false. |
|---|
| 700 | n = SIZE(x) ; ALLOCATE(res(n)) |
|---|
| 701 | DO j=1,n |
|---|
| 702 | ix0 = locator(x(j),cx) |
|---|
| 703 | iy0 = locator(y(j),cy) |
|---|
| 704 | IF (ix0 == 0 .OR. iy0 == 0) THEN |
|---|
| 705 | DEALLOCATE(res) ; RETURN |
|---|
| 706 | ENDIF |
|---|
| 707 | ix1 = ix0 + 1 ; iy1 = iy0 + 1 |
|---|
| 708 | xd = (x(j)-cx(ix0))/(cx(ix1)-cx(ix0)) |
|---|
| 709 | yd = (y(j)-cy(iy0))/(cy(iy1)-cy(iy0)) |
|---|
| 710 | f0 = cv(ix0,iy0)*(1d0-xd)+cv(ix1,iy0)*xd |
|---|
| 711 | f1 = cv(ix0,iy1)*(1d0-xd)+cv(ix1,iy1)*xd |
|---|
| 712 | res(j) = f0*(1d0-yd)+f1*yd |
|---|
| 713 | ENDDO |
|---|
| 714 | ret = .true. |
|---|
| 715 | END FUNCTION hdcdl2d_gen_ve |
|---|
| 716 | |
|---|
| 717 | FUNCTION hdcdl3d_gen_ve(x,y,z,cx,cy,cz,cv,locator,res) RESULT(ret) |
|---|
| 718 | !! Hard-coded 3D linear interpolation (vector) |
|---|
| 719 | !! |
|---|
| 720 | !! @warning |
|---|
| 721 | !! On error, __res__ output vector is undefined (i.e. not allocated). |
|---|
| 722 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: x !! X coordinate of the points to interpolate |
|---|
| 723 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: y !! Y coordinate of the points to interpolate |
|---|
| 724 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: z !! Z coordinate of the points to interpolate |
|---|
| 725 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cx !! Tabulated function X coordinates |
|---|
| 726 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cy !! Tabulated function Y coordinates |
|---|
| 727 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cz !! Tabulated function Z coordinates |
|---|
| 728 | REAL(kind=wp), INTENT(in), DIMENSION(:,:,:) :: cv !! Tabulated function values |
|---|
| 729 | REAL(kind=wp), INTENT(out), DIMENSION(:), ALLOCATABLE :: res !! Interpolated values |
|---|
| 730 | PROCEDURE(locate) :: locator !! Locator function |
|---|
| 731 | LOGICAL :: ret !! .true. on success, .false. otherwise |
|---|
| 732 | REAL(kind=wp) :: xd,yd,zd |
|---|
| 733 | REAL(kind=wp) :: f00,f10,f01,f11,f0,f1 |
|---|
| 734 | INTEGER :: ix0,iy0,iz0,ix1,iy1,iz1 |
|---|
| 735 | INTEGER :: n,j |
|---|
| 736 | ret = .false. |
|---|
| 737 | n = SIZE(x) ; ALLOCATE(res(n)) |
|---|
| 738 | DO j=1,n |
|---|
| 739 | ix0 = locator(x(j),cx) |
|---|
| 740 | iy0 = locator(y(j),cy) |
|---|
| 741 | iz0 = locator(z(j),cz) |
|---|
| 742 | IF (ix0 == 0 .OR. iy0 == 0 .OR. iz0 == 0) THEN |
|---|
| 743 | DEALLOCATE(res) ; RETURN |
|---|
| 744 | ENDIF |
|---|
| 745 | ix1=ix0+1 ; iy1=iy0+1 ; iz1=iz0+1 |
|---|
| 746 | xd = (x(j)-cx(ix0))/(cx(ix1)-cx(ix0)) |
|---|
| 747 | yd = (y(j)-cy(iy0))/(cy(iy1)-cy(iy0)) |
|---|
| 748 | zd = (z(j)-cz(iz0))/(cz(iz1)-cz(iz0)) |
|---|
| 749 | |
|---|
| 750 | f00 = cv(ix0,iy0,iz0)*(1d0-xd)+cv(ix1,iy0,iz0)*xd |
|---|
| 751 | f10 = cv(ix0,iy1,iz0)*(1d0-xd)+cv(ix1,iy1,iz0)*xd |
|---|
| 752 | f01 = cv(ix0,iy0,iz1)*(1d0-xd)+cv(ix1,iy0,iz1)*xd |
|---|
| 753 | f11 = cv(ix0,iy1,iz1)*(1d0-xd)+cv(ix1,iy1,iz1)*xd |
|---|
| 754 | |
|---|
| 755 | f0 = f00 *(1d0-yd)+f10*yd |
|---|
| 756 | f1 = f00 *(1d0-yd)+f10*yd |
|---|
| 757 | |
|---|
| 758 | res(j) = f0*(1d0-zd)+f1*zd |
|---|
| 759 | ENDDO |
|---|
| 760 | ret = .true. |
|---|
| 761 | END FUNCTION hdcdl3d_gen_ve |
|---|
| 762 | |
|---|
| 763 | FUNCTION hdcdl4d_gen_ve(x,y,z,t,cx,cy,cz,ct,cv,locator,res) RESULT(ret) |
|---|
| 764 | !! Hard-coded 4D linear interpolation (vector) |
|---|
| 765 | !! |
|---|
| 766 | !! @warning |
|---|
| 767 | !! On error, __res__ output vector is undefined (i.e. not allocated). |
|---|
| 768 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: x !! X coordinate of the points to interpolate |
|---|
| 769 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: y !! Y coordinate of the points to interpolate |
|---|
| 770 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: z !! Z coordinate of the points to interpolate |
|---|
| 771 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: t !! T coordinate of the points to interpolate |
|---|
| 772 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cx !! Tabulated function X coordinates |
|---|
| 773 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cy !! Tabulated function Y coordinates |
|---|
| 774 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cz !! Tabulated function Z coordinates |
|---|
| 775 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: ct !! Tabulated function T coordinates |
|---|
| 776 | REAL(kind=wp), INTENT(in), DIMENSION(:,:,:,:) :: cv !! Tabulated function values |
|---|
| 777 | REAL(kind=wp), INTENT(out), DIMENSION(:), ALLOCATABLE :: res !! Interpolated values |
|---|
| 778 | PROCEDURE(locate) :: locator !! Locator function |
|---|
| 779 | LOGICAL :: ret !! .true. on success, .false. otherwise |
|---|
| 780 | REAL(kind=wp) :: xd,yd,zd,td |
|---|
| 781 | REAL(kind=wp) :: f000,f100,f010,f110,f001,f101,f011,f111, & |
|---|
| 782 | f00,f10,f01,f11,f0,f1 |
|---|
| 783 | INTEGER :: ix0,iy0,iz0,it0,ix1,iy1,iz1,it1 |
|---|
| 784 | INTEGER :: n,j |
|---|
| 785 | ret = .false. |
|---|
| 786 | n = SIZE(x) ; ALLOCATE(res(n)) |
|---|
| 787 | DO j=1,n |
|---|
| 788 | ix0 = locator(x(j),cx) |
|---|
| 789 | iy0 = locator(y(j),cy) |
|---|
| 790 | iz0 = locator(z(j),cz) |
|---|
| 791 | it0 = locator(t(j),ct) |
|---|
| 792 | IF (ix0 == 0 .OR. iy0 == 0 .OR. iz0 == 0 .OR. it0 == 0) THEN |
|---|
| 793 | DEALLOCATE(res) ; RETURN |
|---|
| 794 | ENDIF |
|---|
| 795 | ix1=ix0+1 ; iy1=iy0+1 ; iz1=iz0+1 ; it1=it0+1 |
|---|
| 796 | xd = (x(j)-cx(ix0))/(cx(ix1)-cx(ix0)) |
|---|
| 797 | yd = (y(j)-cy(iy0))/(cy(iy1)-cy(iy0)) |
|---|
| 798 | zd = (z(j)-cz(iz0))/(cz(iz1)-cz(iz0)) |
|---|
| 799 | td = (t(j)-ct(it0))/(ct(it1)-ct(it0)) |
|---|
| 800 | |
|---|
| 801 | f000 = cv(ix0,iy0,iz0,it0)*(1d0-xd)+cv(ix1,iy0,iz0,it0)*xd |
|---|
| 802 | f100 = cv(ix0,iy1,iz0,it0)*(1d0-xd)+cv(ix1,iy1,iz0,it0)*xd |
|---|
| 803 | f010 = cv(ix0,iy0,iz1,it0)*(1d0-xd)+cv(ix1,iy0,iz1,it0)*xd |
|---|
| 804 | f110 = cv(ix0,iy1,iz1,it0)*(1d0-xd)+cv(ix1,iy1,iz1,it0)*xd |
|---|
| 805 | f001 = cv(ix0,iy0,iz0,it1)*(1d0-xd)+cv(ix1,iy0,iz0,it1)*xd |
|---|
| 806 | f101 = cv(ix0,iy1,iz0,it1)*(1d0-xd)+cv(ix1,iy1,iz0,it1)*xd |
|---|
| 807 | f011 = cv(ix0,iy0,iz1,it1)*(1d0-xd)+cv(ix1,iy0,iz1,it1)*xd |
|---|
| 808 | f111 = cv(ix0,iy1,iz1,it1)*(1d0-xd)+cv(ix1,iy1,iz1,it1)*xd |
|---|
| 809 | |
|---|
| 810 | f00 = f000*(1d0-yd)+f100*yd |
|---|
| 811 | f10 = f010*(1d0-yd)+f110*yd |
|---|
| 812 | f01 = f001*(1d0-yd)+f101*yd |
|---|
| 813 | f11 = f011*(1d0-yd)+f111*yd |
|---|
| 814 | |
|---|
| 815 | f0 = f00 *(1d0-zd)+f10*zd |
|---|
| 816 | f1 = f01 *(1d0-zd)+f11*zd |
|---|
| 817 | |
|---|
| 818 | res(j) = f0*(1d0-td)+f1*td |
|---|
| 819 | ENDDO |
|---|
| 820 | ret = .true. |
|---|
| 821 | END FUNCTION hdcdl4d_gen_ve |
|---|
| 822 | |
|---|
| 823 | FUNCTION hdcdl5d_gen_ve(x,y,z,t,w,cx,cy,cz,ct,cw,cv,locator,res) RESULT(ret) |
|---|
| 824 | !! Hard-coded 5D linear interpolation (vector) |
|---|
| 825 | !! |
|---|
| 826 | !! @warning |
|---|
| 827 | !! On error, __res__ output vector is undefined (i.e. not allocated). |
|---|
| 828 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: x !! X coordinate of the points to interpolate |
|---|
| 829 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: y !! Y coordinate of the points to interpolate |
|---|
| 830 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: z !! Z coordinate of the points to interpolate |
|---|
| 831 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: t !! T coordinate of the points to interpolate |
|---|
| 832 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: w !! W coordinate of the points to interpolate |
|---|
| 833 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cx !! Tabulated function X coordinates |
|---|
| 834 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cy !! Tabulated function Y coordinates |
|---|
| 835 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cz !! Tabulated function Z coordinates |
|---|
| 836 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: ct !! Tabulated function T coordinates |
|---|
| 837 | REAL(kind=wp), INTENT(in), DIMENSION(:) :: cw !! Tabulated function W coordinates |
|---|
| 838 | REAL(kind=wp), INTENT(in), DIMENSION(:,:,:,:,:) :: cv !! Tabulated function values |
|---|
| 839 | REAL(kind=wp), INTENT(out), DIMENSION(:), ALLOCATABLE :: res !! Interpolated values |
|---|
| 840 | PROCEDURE(locate) :: locator !! Locator function |
|---|
| 841 | LOGICAL :: ret !! .true. on success, .false. otherwise |
|---|
| 842 | REAL(kind=wp) :: xd,yd,zd,td,wd |
|---|
| 843 | REAL(kind=wp) :: f0000,f1000,f0100,f1100,f0010,f1010,f0110,f1110, & |
|---|
| 844 | f0001,f1001,f0101,f1101,f0011,f1011,f0111,f1111, & |
|---|
| 845 | f000,f100,f010,f110,f001,f101,f011,f111, & |
|---|
| 846 | f00,f10,f01,f11,f0,f1 |
|---|
| 847 | INTEGER :: ix0,iy0,iz0,it0,iw0,ix1,iy1,iz1,it1,iw1 |
|---|
| 848 | INTEGER :: n,j |
|---|
| 849 | ret = .false. |
|---|
| 850 | n = SIZE(x) ; ALLOCATE(res(n)) |
|---|
| 851 | DO j=1,n |
|---|
| 852 | ix0 = locator(x(j),cx) |
|---|
| 853 | iy0 = locator(y(j),cy) |
|---|
| 854 | iz0 = locator(z(j),cz) |
|---|
| 855 | it0 = locator(t(j),ct) |
|---|
| 856 | iw0 = locator(w(j),cw) |
|---|
| 857 | IF (ix0 == 0 .OR. iy0 == 0 .OR. iz0 == 0 .OR. it0 == 0 .OR. iw0 == 0) THEN |
|---|
| 858 | DEALLOCATE(res) ; RETURN |
|---|
| 859 | ENDIF |
|---|
| 860 | ix1=ix0+1 ; iy1=iy0+1 ; iz1=iz0+1 ; |
|---|
| 861 | xd = (x(j)-cx(ix0))/(cx(ix1)-cx(ix0)) |
|---|
| 862 | yd = (y(j)-cy(iy0))/(cy(iy1)-cy(iy0)) |
|---|
| 863 | zd = (z(j)-cz(iz0))/(cz(iz1)-cz(iz0)) |
|---|
| 864 | td = (t(j)-ct(it0))/(ct(it1)-ct(it0)) |
|---|
| 865 | wd = (w(j)-cw(it0))/(cw(it1)-cw(it0)) |
|---|
| 866 | |
|---|
| 867 | f0000 = cv(ix0,iy0,iz0,it0,iw0)*(1d0-xd)+cv(ix1,iy0,iz0,it0,iw0)*xd |
|---|
| 868 | f1000 = cv(ix0,iy1,iz0,it0,iw0)*(1d0-xd)+cv(ix0,iy1,iz0,it0,iw0)*xd |
|---|
| 869 | f0100 = cv(ix0,iy0,iz1,it0,iw0)*(1d0-xd)+cv(ix1,iy0,iz1,it0,iw0)*xd |
|---|
| 870 | f1100 = cv(ix0,iy1,iz1,it0,iw0)*(1d0-xd)+cv(ix1,iy1,iz1,it0,iw0)*xd |
|---|
| 871 | f0010 = cv(ix0,iy0,iz0,it1,iw0)*(1d0-xd)+cv(ix1,iy0,iz0,it1,iw0)*xd |
|---|
| 872 | f1010 = cv(ix0,iy1,iz0,it1,iw0)*(1d0-xd)+cv(ix1,iy1,iz0,it1,iw0)*xd |
|---|
| 873 | f0110 = cv(ix0,iy0,iz1,it1,iw0)*(1d0-xd)+cv(ix1,iy0,iz1,it1,iw0)*xd |
|---|
| 874 | f1110 = cv(ix0,iy1,iz1,it1,iw0)*(1d0-xd)+cv(ix1,iy1,iz1,it1,iw0)*xd |
|---|
| 875 | f0001 = cv(ix0,iy0,iz0,it0,iw1)*(1d0-xd)+cv(ix1,iy0,iz0,it0,iw1)*xd |
|---|
| 876 | f1001 = cv(ix0,iy1,iz0,it0,iw1)*(1d0-xd)+cv(ix0,iy1,iz0,it0,iw1)*xd |
|---|
| 877 | f0101 = cv(ix0,iy0,iz1,it0,iw1)*(1d0-xd)+cv(ix1,iy0,iz1,it0,iw1)*xd |
|---|
| 878 | f1101 = cv(ix0,iy1,iz1,it0,iw1)*(1d0-xd)+cv(ix1,iy1,iz1,it0,iw1)*xd |
|---|
| 879 | f0011 = cv(ix0,iy0,iz0,it1,iw1)*(1d0-xd)+cv(ix1,iy0,iz0,it1,iw1)*xd |
|---|
| 880 | f1011 = cv(ix0,iy1,iz0,it1,iw1)*(1d0-xd)+cv(ix1,iy1,iz0,it1,iw1)*xd |
|---|
| 881 | f0111 = cv(ix0,iy0,iz1,it1,iw1)*(1d0-xd)+cv(ix1,iy0,iz1,it1,iw1)*xd |
|---|
| 882 | f1111 = cv(ix0,iy1,iz1,it1,iw1)*(1d0-xd)+cv(ix1,iy1,iz1,it1,iw1)*xd |
|---|
| 883 | |
|---|
| 884 | f000 = f0000*(1d0-yd) + f1000*yd |
|---|
| 885 | f100 = f0100*(1d0-yd) + f1100*yd |
|---|
| 886 | f010 = f0010*(1d0-yd) + f1010*yd |
|---|
| 887 | f110 = f0110*(1d0-yd) + f1110*yd |
|---|
| 888 | f101 = f0101*(1d0-yd) + f1101*yd |
|---|
| 889 | f011 = f0011*(1d0-yd) + f1011*yd |
|---|
| 890 | f111 = f0111*(1d0-yd) + f1111*yd |
|---|
| 891 | |
|---|
| 892 | f00 = f000*(1d0-zd)+f100*zd |
|---|
| 893 | f10 = f010*(1d0-zd)+f110*zd |
|---|
| 894 | f01 = f001*(1d0-zd)+f101*zd |
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| 895 | f11 = f011*(1d0-zd)+f111*zd |
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| 896 | |
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| 897 | f0 = f00 *(1d0-td)+f10*td |
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| 898 | f1 = f01 *(1d0-td)+f11*td |
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| 899 | |
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| 900 | res(j) = f0*(1d0-wd)+f1*wd |
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| 901 | ENDDO |
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| 902 | ret = .true. |
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| 903 | END FUNCTION hdcdl5d_gen_ve |
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| 904 | |
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| 905 | END MODULE LINT_GEN |
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