| 1 | SUBROUTINE LEGTRI (PSIN,KCP,KDIM,PALP) |
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| 2 | |
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| 3 | !**** *LEGTRI* - *LEGENDRE FUNCTIONS FOR A TRIANGULAR TRUNCATION. |
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| 4 | |
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| 5 | ! J.F.GELEYN E.C.M.W.F. 03/06/82. |
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| 6 | |
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| 7 | ! PURPOSE. |
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| 8 | ! -------- |
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| 9 | |
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| 10 | ! THIS ROUTINE COMPUTES THE VALUES *PALP* FOR THE ARGUMENT |
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| 11 | ! *PSIN* OF THE NORMALISED *LEGENDRE ASSOCIATED FUNCTIONS IN THE |
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| 12 | ! ORDER ((JN1=JM1,KCP),JM1=1,KCP) FOR JN=JN1-1 AND JM=JM1-1 . |
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| 13 | |
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| 14 | !** INTERFACE. |
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| 15 | ! ---------- |
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| 16 | |
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| 17 | ! *LEGTRI* IS CALLED FROM *RADMOD*. |
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| 18 | ! THERE ARE THREE DUMMY ARGUMENTS: *PSIN* IS THE SINE OF |
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| 19 | ! LATITUDE. |
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| 20 | ! *KCP* IS ONE PLUS THE LIMIT |
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| 21 | ! WAVE NUMBER. |
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| 22 | ! *PALP* IS THE ARRAY OF THE |
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| 23 | ! RESULTS. |
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| 24 | |
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| 25 | ! METHOD. |
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| 26 | ! ------- |
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| 27 | |
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| 28 | ! SIMPLE RECURENCE FORMULA. |
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| 29 | |
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| 30 | ! EXTERNALS. |
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| 31 | ! ---------- |
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| 32 | |
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| 33 | ! NONE. |
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| 34 | |
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| 35 | ! REFERENCE. |
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| 36 | ! ---------- |
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| 37 | |
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| 38 | ! NONE. |
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| 39 | |
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| 40 | |
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| 41 | #include "tsmbkind.h" |
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| 42 | |
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| 43 | IMPLICIT NONE |
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| 44 | |
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| 45 | |
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| 46 | ! DUMMY INTEGER SCALARS |
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| 47 | INTEGER_M :: KCP |
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| 48 | INTEGER_M :: KDIM |
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| 49 | |
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| 50 | ! DUMMY REAL SCALARS |
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| 51 | REAL_B :: PSIN |
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| 52 | |
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| 53 | REAL_B :: PALP(KDIM) |
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| 54 | |
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| 55 | ! LOCAL INTEGER SCALARS |
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| 56 | INTEGER_M :: IC, ICP, II, IM, IM2, JM1, JN |
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| 57 | |
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| 58 | ! LOCAL REAL SCALARS |
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| 59 | REAL_B :: Z2M, ZCOS, ZE1, ZE2, ZF1M, ZF2M, ZM, ZN, ZN2, ZRE1, ZSIN |
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| 60 | |
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| 61 | |
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| 62 | ! ------------------------------------------------------------------ |
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| 63 | |
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| 64 | !* 1. PRELIMINARY SETTING. |
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| 65 | ! ----------- -------- |
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| 66 | |
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| 67 | |
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| 68 | ZSIN=PSIN |
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| 69 | ICP=KCP |
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| 70 | |
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| 71 | ! ------------------------------------------------------------------ |
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| 72 | |
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| 73 | !* 2. COMPUTATIONS. |
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| 74 | ! ------------- |
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| 75 | |
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| 76 | |
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| 77 | IC=ICP-1 |
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| 78 | ZCOS=SQRT(_ONE_-ZSIN**2) |
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| 79 | II=2 |
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| 80 | PALP(1)=_ONE_ |
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| 81 | ZF1M=SQRT(3._JPRB) |
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| 82 | PALP(2)=ZF1M*ZSIN |
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| 83 | DO JM1=1,ICP |
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| 84 | IM=JM1-1 |
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| 85 | ZM=IM |
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| 86 | Z2M=ZM+ZM |
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| 87 | ZRE1=SQRT(Z2M+3._JPRB) |
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| 88 | ZE1=_ONE_/ZRE1 |
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| 89 | IF(IM == 0) GO TO 201 |
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| 90 | ZF2M=ZF1M*ZCOS/SQRT(Z2M) |
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| 91 | ZF1M=ZF2M*ZRE1 |
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| 92 | II=II+1 |
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| 93 | PALP(II)=ZF2M |
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| 94 | IF(IM == IC) GO TO 203 |
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| 95 | II=II+1 |
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| 96 | PALP(II)=ZF1M*ZSIN |
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| 97 | IF(JM1 == IC) GO TO 203 |
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| 98 | 201 CONTINUE |
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| 99 | IM2=IM+2 |
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| 100 | DO JN=IM2,IC |
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| 101 | ZN=JN |
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| 102 | ZN2=ZN**2 |
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| 103 | ZE2=SQRT((4._JPRB*ZN2-_ONE_)/(ZN2-ZM**2)) |
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| 104 | II=II+1 |
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| 105 | PALP(II)=ZE2*(ZSIN*PALP(II-1)-ZE1*PALP(II-2)) |
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| 106 | ZE1=_ONE_/ZE2 |
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| 107 | ENDDO |
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| 108 | 203 continue |
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| 109 | ENDDO |
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| 110 | |
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| 111 | ! ------------------------------------------------------------------ |
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| 112 | |
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| 113 | !* 3. RETURN. |
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| 114 | ! ------- |
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| 115 | |
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| 116 | |
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| 117 | RETURN |
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| 118 | END SUBROUTINE LEGTRI |
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| 119 | |
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| 120 | |
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| 121 | |
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