| 1 | |
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| 2 | ! |
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| 3 | ! This program may be freely redistributed under the |
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| 4 | ! condition that the copyright notices (including this |
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| 5 | ! entire header) are not removed, and no compensation |
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| 6 | ! is received through use of the software. Private, |
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| 7 | ! research, and institutional use is free. You may |
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| 8 | ! distribute modified versions of this code UNDER THE |
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| 9 | ! CONDITION THAT THIS CODE AND ANY MODIFICATIONS MADE |
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| 10 | ! TO IT IN THE SAME FILE REMAIN UNDER COPYRIGHT OF THE |
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| 11 | ! ORIGINAL AUTHOR, BOTH SOURCE AND OBJECT CODE ARE |
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| 12 | ! MADE FREELY AVAILABLE WITHOUT CHARGE, AND CLEAR |
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| 13 | ! NOTICE IS GIVEN OF THE MODIFICATIONS. Distribution |
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| 14 | ! of this code as part of a commercial system is |
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| 15 | ! permissible ONLY BY DIRECT ARRANGEMENT WITH THE |
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| 16 | ! AUTHOR. (If you are not directly supplying this |
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| 17 | ! code to a customer, and you are instead telling them |
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| 18 | ! how they can obtain it for free, then you are not |
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| 19 | ! required to make any arrangement with me.) |
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| 20 | ! |
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| 21 | ! Disclaimer: Neither I nor: Columbia University, the |
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| 22 | ! National Aeronautics and Space Administration, nor |
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| 23 | ! the Massachusetts Institute of Technology warrant |
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| 24 | ! or certify this code in any way whatsoever. This |
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| 25 | ! code is provided "as-is" to be used at your own risk. |
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| 26 | ! |
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| 27 | ! |
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| 28 | |
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| 29 | ! |
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| 30 | ! BFUN1D.h90: poly. basis-functions for reconstruction. |
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| 31 | ! |
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| 32 | ! Darren Engwirda |
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| 33 | ! 07-Sep-2016 |
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| 34 | ! de2363 [at] columbia [dot] edu |
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| 35 | ! |
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| 36 | ! |
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| 37 | |
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| 38 | pure subroutine bfun1d(isel,ndof,sval,bfun) |
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| 39 | |
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| 40 | ! |
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| 41 | ! ISEL basis-function "order", -1 => integral-basis , |
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| 42 | ! +0 => function-basis, +1 => 1st deriv.-basis , |
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| 43 | ! +2 => 2nd deriv.-basis. |
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| 44 | ! NDOF no. degrees-of-freedom in basis. |
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| 45 | ! SVAL local coord. at which to evaluate basis-func., |
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| 46 | ! such that -1.0 <= SVAL <= +1.0 . |
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| 47 | ! BFUN basis-vector evaluated at SVAL . |
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| 48 | ! |
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| 49 | |
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| 50 | implicit none |
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| 51 | |
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| 52 | !------------------------------------------- arguments ! |
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| 53 | integer, intent( in) :: isel,ndof |
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| 54 | real*8 , intent( in) :: sval |
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| 55 | real*8 , intent(out) :: bfun(:) |
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| 56 | |
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| 57 | select case (isel) |
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| 58 | case (-1) |
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| 59 | !------------------------------------ -1th-order basis ! |
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| 60 | select case (ndof) |
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| 61 | case (+1) |
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| 62 | bfun(1) = sval**1 / 1.e0 |
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| 63 | |
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| 64 | case (+2) |
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| 65 | bfun(1) = sval**1 / 1.e0 |
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| 66 | bfun(2) = sval**2 / 2.e0 |
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| 67 | |
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| 68 | case (+3) |
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| 69 | bfun(1) = sval**1 / 1.e0 |
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| 70 | bfun(2) = sval**2 / 2.e0 |
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| 71 | bfun(3) = sval**3 / 3.e0 |
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| 72 | |
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| 73 | case (+4) |
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| 74 | bfun(1) = sval**1 / 1.e0 |
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| 75 | bfun(2) = sval**2 / 2.e0 |
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| 76 | bfun(3) = sval**3 / 3.e0 |
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| 77 | bfun(4) = sval**4 / 4.e0 |
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| 78 | |
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| 79 | case (+5) |
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| 80 | bfun(1) = sval**1 / 1.e0 |
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| 81 | bfun(2) = sval**2 / 2.e0 |
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| 82 | bfun(3) = sval**3 / 3.e0 |
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| 83 | bfun(4) = sval**4 / 4.e0 |
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| 84 | bfun(5) = sval**5 / 5.e0 |
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| 85 | |
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| 86 | case (+6) |
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| 87 | bfun(1) = sval**1 / 1.e0 |
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| 88 | bfun(2) = sval**2 / 2.e0 |
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| 89 | bfun(3) = sval**3 / 3.e0 |
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| 90 | bfun(4) = sval**4 / 4.e0 |
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| 91 | bfun(5) = sval**5 / 5.e0 |
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| 92 | bfun(6) = sval**6 / 6.e0 |
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| 93 | |
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| 94 | case (+7) |
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| 95 | bfun(1) = sval**1 / 1.e0 |
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| 96 | bfun(2) = sval**2 / 2.e0 |
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| 97 | bfun(3) = sval**3 / 3.e0 |
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| 98 | bfun(4) = sval**4 / 4.e0 |
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| 99 | bfun(5) = sval**5 / 5.e0 |
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| 100 | bfun(6) = sval**6 / 6.e0 |
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| 101 | bfun(7) = sval**7 / 7.e0 |
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| 102 | |
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| 103 | end select |
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| 104 | |
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| 105 | case (+0) |
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| 106 | !------------------------------------ +0th-order basis ! |
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| 107 | select case (ndof) |
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| 108 | case (+1) |
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| 109 | bfun(1) = 1.e0 |
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| 110 | |
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| 111 | case (+2) |
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| 112 | bfun(1) = 1.e0 |
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| 113 | bfun(2) = sval**1 * 1.e0 |
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| 114 | |
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| 115 | case (+3) |
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| 116 | bfun(1) = 1.e0 |
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| 117 | bfun(2) = sval**1 * 1.e0 |
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| 118 | bfun(3) = sval**2 * 1.e0 |
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| 119 | |
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| 120 | case (+4) |
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| 121 | bfun(1) = 1.e0 |
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| 122 | bfun(2) = sval**1 * 1.e0 |
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| 123 | bfun(3) = sval**2 * 1.e0 |
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| 124 | bfun(4) = sval**3 * 1.e0 |
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| 125 | |
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| 126 | case (+5) |
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| 127 | bfun(1) = 1.e0 |
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| 128 | bfun(2) = sval**1 * 1.e0 |
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| 129 | bfun(3) = sval**2 * 1.e0 |
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| 130 | bfun(4) = sval**3 * 1.e0 |
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| 131 | bfun(5) = sval**4 * 1.e0 |
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| 132 | |
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| 133 | case (+6) |
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| 134 | bfun(1) = 1.e0 |
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| 135 | bfun(2) = sval**1 * 1.e0 |
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| 136 | bfun(3) = sval**2 * 1.e0 |
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| 137 | bfun(4) = sval**3 * 1.e0 |
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| 138 | bfun(5) = sval**4 * 1.e0 |
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| 139 | bfun(6) = sval**5 * 1.e0 |
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| 140 | |
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| 141 | case (+7) |
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| 142 | bfun(1) = 1.e0 |
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| 143 | bfun(2) = sval**1 * 1.e0 |
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| 144 | bfun(3) = sval**2 * 1.e0 |
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| 145 | bfun(4) = sval**3 * 1.e0 |
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| 146 | bfun(5) = sval**4 * 1.e0 |
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| 147 | bfun(6) = sval**5 * 1.e0 |
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| 148 | bfun(7) = sval**6 * 1.e0 |
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| 149 | |
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| 150 | end select |
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| 151 | |
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| 152 | case (+1) |
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| 153 | !------------------------------------ +1st-order basis ! |
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| 154 | select case (ndof) |
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| 155 | case (+1) |
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| 156 | bfun(1) = 0.e0 |
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| 157 | |
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| 158 | case (+2) |
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| 159 | bfun(1) = 0.e0 |
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| 160 | bfun(2) = 1.e0 |
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| 161 | |
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| 162 | case (+3) |
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| 163 | bfun(1) = 0.e0 |
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| 164 | bfun(2) = 1.e0 |
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| 165 | bfun(3) = sval**1 * 2.e0 |
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| 166 | |
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| 167 | case (+4) |
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| 168 | bfun(1) = 0.e0 |
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| 169 | bfun(2) = 1.e0 |
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| 170 | bfun(3) = sval**1 * 2.e0 |
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| 171 | bfun(4) = sval**2 * 3.e0 |
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| 172 | |
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| 173 | case (+5) |
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| 174 | bfun(1) = 0.e0 |
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| 175 | bfun(2) = 1.e0 |
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| 176 | bfun(3) = sval**1 * 2.e0 |
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| 177 | bfun(4) = sval**2 * 3.e0 |
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| 178 | bfun(5) = sval**3 * 4.e0 |
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| 179 | |
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| 180 | case (+6) |
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| 181 | bfun(1) = 0.e0 |
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| 182 | bfun(2) = 1.e0 |
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| 183 | bfun(3) = sval**1 * 2.e0 |
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| 184 | bfun(4) = sval**2 * 3.e0 |
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| 185 | bfun(5) = sval**3 * 4.e0 |
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| 186 | bfun(6) = sval**4 * 5.e0 |
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| 187 | |
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| 188 | case (+7) |
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| 189 | bfun(1) = 0.e0 |
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| 190 | bfun(2) = 1.e0 |
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| 191 | bfun(3) = sval**1 * 2.e0 |
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| 192 | bfun(4) = sval**2 * 3.e0 |
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| 193 | bfun(5) = sval**3 * 4.e0 |
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| 194 | bfun(6) = sval**4 * 5.e0 |
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| 195 | bfun(7) = sval**5 * 6.e0 |
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| 196 | |
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| 197 | end select |
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| 198 | |
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| 199 | case (+2) |
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| 200 | !------------------------------------ +2nd-order basis ! |
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| 201 | select case (ndof) |
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| 202 | case (+1) |
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| 203 | bfun(1) = 0.e0 |
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| 204 | |
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| 205 | case (+2) |
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| 206 | bfun(1) = 0.e0 |
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| 207 | bfun(2) = 0.e0 |
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| 208 | |
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| 209 | case (+3) |
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| 210 | bfun(1) = 0.e0 |
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| 211 | bfun(2) = 0.e0 |
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| 212 | bfun(3) = 2.e0 |
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| 213 | |
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| 214 | case (+4) |
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| 215 | bfun(1) = 0.e0 |
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| 216 | bfun(2) = 0.e0 |
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| 217 | bfun(3) = 2.e0 |
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| 218 | bfun(4) = sval**1 * 6.e0 |
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| 219 | |
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| 220 | case (+5) |
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| 221 | bfun(1) = 0.e0 |
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| 222 | bfun(2) = 0.e0 |
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| 223 | bfun(3) = 2.e0 |
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| 224 | bfun(4) = sval**1 * 6.e0 |
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| 225 | bfun(5) = sval**2 *12.e0 |
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| 226 | |
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| 227 | case (+6) |
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| 228 | bfun(1) = 0.e0 |
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| 229 | bfun(2) = 0.e0 |
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| 230 | bfun(3) = 2.e0 |
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| 231 | bfun(4) = sval**1 * 6.e0 |
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| 232 | bfun(5) = sval**2 *12.e0 |
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| 233 | bfun(6) = sval**3 *20.e0 |
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| 234 | |
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| 235 | case (+7) |
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| 236 | bfun(1) = 0.e0 |
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| 237 | bfun(2) = 0.e0 |
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| 238 | bfun(3) = 2.e0 |
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| 239 | bfun(4) = sval**1 * 6.e0 |
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| 240 | bfun(5) = sval**2 *12.e0 |
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| 241 | bfun(6) = sval**3 *20.e0 |
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| 242 | bfun(7) = sval**4 *30.e0 |
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| 243 | |
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| 244 | end select |
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| 245 | |
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| 246 | end select |
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| 247 | |
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| 248 | end subroutine |
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| 249 | |
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| 250 | |
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| 251 | |
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