| @@ -1,566 +1,566 | |||||
| 1 | subroutine lagp(plag,wl,r0,dr,nl,nrange) |
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1 | subroutine lagp(plag,wl,r0,dr,nl,nrange) | |
| 2 | c |
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2 | c | |
| 3 | c predict lagged product matrix using state parameters stored |
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3 | c predict lagged product matrix using state parameters stored | |
| 4 | c as cubic b-splines |
|
4 | c as cubic b-splines | |
| 5 | c read weights for numeric integration from a file |
|
5 | c read weights for numeric integration from a file | |
| 6 | c |
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6 | c | |
| 7 | c faster version - assumes samples taken at half-integer lags, ranges |
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7 | c faster version - assumes samples taken at half-integer lags, ranges | |
| 8 | c |
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8 | c | |
| 9 | include 'fitter.h' |
|
9 | include 'fitter.h' | |
| 10 | include 'spline.h' |
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10 | include 'spline.h' | |
| 11 | include 'bfield.h' |
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11 | include 'bfield.h' | |
| 12 | integer nl,nrange |
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12 | integer nl,nrange | |
| 13 | real plag(nl,nrange),taus(nl) |
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13 | real plag(nl,nrange),taus(nl) | |
| 14 | parameter(nw=1000) |
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14 | parameter(nw=1000) | |
| 15 | integer ilag(nw) |
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15 | integer ilag(nw) | |
| 16 | real weight(nw),dtau(nw),drange(nw) |
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16 | real weight(nw),dtau(nw),drange(nw) | |
| 17 | logical first |
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17 | logical first | |
| 18 | real store(2*nl,2*nrange,2) |
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18 | real store(2*nl,2*nrange,2) | |
| 19 |
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19 | |||
| 20 | character(1024) :: fqual_temp |
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20 | character(1024) :: fqual_temp | |
| 21 | character(:), allocatable :: fqual |
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21 | character(:), allocatable :: fqual | |
| 22 |
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22 | |||
| 23 | data first/.true./ |
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23 | data first/.true./ | |
| 24 | c |
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24 | c | |
| 25 |
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25 | |||
| 26 | c write(*,*) "dens_before: ",dens |
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26 | c write(*,*) "dens_before: ",dens | |
| 27 | c call exit |
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27 | c call exit | |
| 28 | c zero out array |
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28 | c zero out array | |
| 29 | c write(*,*) "Starting lagp" |
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29 | c write(*,*) "Starting lagp" | |
| 30 | do i=1,nrange |
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30 | do i=1,nrange | |
| 31 | do j=1,nl |
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31 | do j=1,nl | |
| 32 | plag(j,i)=0.0 |
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32 | plag(j,i)=0.0 | |
| 33 | end do |
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33 | end do | |
| 34 | end do |
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34 | end do | |
| 35 |
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35 | |||
| 36 | c |
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36 | c | |
| 37 | c compute all required acfs |
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37 | c compute all required acfs | |
| 38 | c |
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38 | c | |
| 39 | do i=1,2*nrange |
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39 | do i=1,2*nrange | |
| 40 | ii=(i-1)/2+1 |
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40 | ii=(i-1)/2+1 | |
| 41 | alt=r0+float(i-1)*dr*0.5 ! half integer ranges |
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41 | alt=r0+float(i-1)*dr*0.5 ! half integer ranges | |
| 42 | c write(*,*) "dens_before: ",dens |
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42 | c write(*,*) "dens_before: ",dens | |
| 43 | c call exit |
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43 | c call exit | |
| 44 | c write(*,*) "alt: ",alt |
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44 | c write(*,*) "alt: ",alt | |
| 45 | c write(*,*) "dens: ",dens |
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45 | c write(*,*) "dens: ",dens | |
| 46 | c write(*,*) "te: ",te |
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46 | c write(*,*) "te: ",te | |
| 47 | c write(*,*) "ti1: ",ti1 |
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47 | c write(*,*) "ti1: ",ti1 | |
| 48 | c write(*,*) "hf: ",hf |
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48 | c write(*,*) "hf: ",hf | |
| 49 | c write(*,*) "hef: ",hef |
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49 | c write(*,*) "hef: ",hef | |
| 50 | c call exit |
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50 | c call exit | |
| 51 | call get_spline(alt,dens,te,ti1,hf,hef) |
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51 | call get_spline(alt,dens,te,ti1,hf,hef) | |
| 52 | c write(*,*) "dens_after: ",dens |
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52 | c write(*,*) "dens_after: ",dens | |
| 53 | c call exit |
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53 | c call exit | |
| 54 | do k=1,nion |
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54 | do k=1,nion | |
| 55 | ti(k)=ti1 |
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55 | ti(k)=ti1 | |
| 56 | end do |
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56 | end do | |
| 57 | fi(2)=hf |
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57 | fi(2)=hf | |
| 58 | fi(3)=hef |
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58 | fi(3)=hef | |
| 59 | fi(1)=1.0-hf-hef |
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59 | fi(1)=1.0-hf-hef | |
| 60 |
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60 | |||
| 61 | do j=1,2*nl |
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61 | do j=1,2*nl | |
| 62 | tau=float(j-1)*(dr/1.5e5)*0.5 ! half integer lags |
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62 | tau=float(j-1)*(dr/1.5e5)*0.5 ! half integer lags | |
| 63 |
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63 | |||
| 64 | c just consider a single azimuth angle for now |
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64 | c just consider a single azimuth angle for now | |
| 65 |
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65 | |||
| 66 | c call acf2(wl,tau,te,ti,fi,ven,vin,wi,nion, |
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66 | c call acf2(wl,tau,te,ti,fi,ven,vin,wi,nion, | |
| 67 | c & alpha_prof(ii)+1.74e-2,dens,bfld_prof(ii),rho) |
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67 | c & alpha_prof(ii)+1.74e-2,dens,bfld_prof(ii),rho) | |
| 68 | c store(j,i,1)=rho*dens*(100.0/alt)**2 |
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68 | c store(j,i,1)=rho*dens*(100.0/alt)**2 | |
| 69 |
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69 | |||
| 70 | c call acf2(wl,tau,te,ti,fi,ven,vin,wi,nion, |
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70 | c call acf2(wl,tau,te,ti,fi,ven,vin,wi,nion, | |
| 71 | c & alpha_prof(ii)-1.74e-2,dens,bfld_prof(ii),rho) |
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71 | c & alpha_prof(ii)-1.74e-2,dens,bfld_prof(ii),rho) | |
| 72 | c store(j,i,2)=rho*dens*(100.0/alt)**2 |
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72 | c store(j,i,2)=rho*dens*(100.0/alt)**2 | |
| 73 |
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73 | |||
| 74 | call acf2(wl,tau,te,ti,fi,ven,vin,wi,nion, |
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74 | call acf2(wl,tau,te,ti,fi,ven,vin,wi,nion, | |
| 75 | & alpha_prof(ii),dens,bfld_prof(ii),rho) |
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75 | & alpha_prof(ii),dens,bfld_prof(ii),rho) | |
| 76 | store(j,i,1)=rho*dens*(100.0/alt)**2 |
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76 | store(j,i,1)=rho*dens*(100.0/alt)**2 | |
| 77 | c write(*,*) "store", store(j,i,1) |
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77 | c write(*,*) "store", store(j,i,1) | |
| 78 | c call exit |
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78 | c call exit | |
| 79 | end do |
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79 | end do | |
| 80 | end do |
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80 | end do | |
| 81 |
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81 | |||
| 82 | c construct lagged products |
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82 | c construct lagged products | |
| 83 | c |
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83 | c | |
| 84 | c write(*,*) "before weights" |
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84 | c write(*,*) "before weights" | |
| 85 | c write(*,*) first |
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85 | c write(*,*) first | |
| 86 | c write(*,*) "weight before: ",weight |
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86 | c write(*,*) "weight before: ",weight | |
| 87 | c write(*,*) "BEFORE GET_PATH" |
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87 | c write(*,*) "BEFORE GET_PATH" | |
| 88 | call get_path(fqual_temp) |
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88 | call get_path(fqual_temp) | |
| 89 | c write(*,*) "L_BEF: ", fqual_temp, "L_BEF_end" |
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89 | c write(*,*) "L_BEF: ", fqual_temp, "L_BEF_end" | |
| 90 | fqual = TRIM(fqual_temp) |
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90 | fqual = TRIM(fqual_temp) | |
| 91 |
fqual = fqual//' |
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91 | fqual = fqual//'weights.dat' | |
| 92 | c write(*,*) "Final fqual",fqual,"FINAL" |
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92 | c write(*,*) "Final fqual",fqual,"FINAL" | |
| 93 |
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93 | |||
| 94 | if(first) then |
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94 | if(first) then | |
| 95 | open(unit=25,file=fqual, |
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95 | open(unit=25,file=fqual, | |
| 96 | & status='old') |
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96 | & status='old') | |
| 97 | read (25,*) nwt |
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97 | read (25,*) nwt | |
| 98 | do i=1,nwt |
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98 | do i=1,nwt | |
| 99 | read(25,*) weight(i),dtau(i),drange(i),ilag(i) |
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99 | read(25,*) weight(i),dtau(i),drange(i),ilag(i) | |
| 100 | c write(*,*) "ilag: ",ilag(i) |
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100 | c write(*,*) "ilag: ",ilag(i) | |
| 101 | end do |
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101 | end do | |
| 102 | c flush(25) |
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102 | c flush(25) | |
| 103 | close(25) |
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103 | close(25) | |
| 104 | c first=.false. |
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104 | c first=.false. | |
| 105 | end if |
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105 | end if | |
| 106 |
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106 | |||
| 107 | c write(*,*) "after weights" |
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107 | c write(*,*) "after weights" | |
| 108 |
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108 | |||
| 109 | c write(*,*) "weight(3): ",weight(3) |
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109 | c write(*,*) "weight(3): ",weight(3) | |
| 110 | c call exit |
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110 | c call exit | |
| 111 | c write(*,*) "nl: ",nl,"nrange: ",nrange,"nwt: ",nwt |
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111 | c write(*,*) "nl: ",nl,"nrange: ",nrange,"nwt: ",nwt | |
| 112 |
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112 | |||
| 113 | do i=1+nl,nrange ! don't worry about redundancy here |
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113 | do i=1+nl,nrange ! don't worry about redundancy here | |
| 114 |
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114 | |||
| 115 | do j=1,nwt |
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115 | do j=1,nwt | |
| 116 | c write(*,*) "j: ",j |
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116 | c write(*,*) "j: ",j | |
| 117 | alt=r0+(float(i-1)+drange(j))*dr |
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117 | alt=r0+(float(i-1)+drange(j))*dr | |
| 118 | tau=abs(dtau(j)*dr/1.5e5) |
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118 | tau=abs(dtau(j)*dr/1.5e5) | |
| 119 | lag=ilag(j)+1 |
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119 | lag=ilag(j)+1 | |
| 120 | c write(*,*) tau |
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120 | c write(*,*) tau | |
| 121 |
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121 | |||
| 122 | k=1+2.0*(tau/(dr/1.5e5)) |
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122 | k=1+2.0*(tau/(dr/1.5e5)) | |
| 123 | l=1+2.0*(alt-r0)/dr |
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123 | l=1+2.0*(alt-r0)/dr | |
| 124 |
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124 | |||
| 125 | do m=1,1 ! 2 |
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125 | do m=1,1 ! 2 | |
| 126 |
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126 | |||
| 127 | c call exit |
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127 | c call exit | |
| 128 | c write(*,*) i |
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128 | c write(*,*) i | |
| 129 | c call exit |
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129 | c call exit | |
| 130 | c if (i .eq. nrange) then |
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130 | c if (i .eq. nrange) then | |
| 131 | c if (j .eq. 227) then |
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131 | c if (j .eq. 227) then | |
| 132 |
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132 | |||
| 133 | c write(*,*) "lag: ",lag |
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133 | c write(*,*) "lag: ",lag | |
| 134 | c write(*,*) "ilag: ",ilag(j) |
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134 | c write(*,*) "ilag: ",ilag(j) | |
| 135 | c call exit |
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135 | c call exit | |
| 136 | c write(*,*) "plag: ",plag(lag,i) |
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136 | c write(*,*) "plag: ",plag(lag,i) | |
| 137 | c write(*,*) "weight: ",weight |
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137 | c write(*,*) "weight: ",weight | |
| 138 | c |
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138 | c | |
| 139 | c write(*,*) "weight: ",weight(j) |
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139 | c write(*,*) "weight: ",weight(j) | |
| 140 | c write(*,*) "store: ",store(k,l,m) |
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140 | c write(*,*) "store: ",store(k,l,m) | |
| 141 | c call exit |
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141 | c call exit | |
| 142 | c end if |
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142 | c end if | |
| 143 | c end if |
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143 | c end if | |
| 144 | plag(lag,i)=plag(lag,i)+weight(j)*store(k,l,m) |
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144 | plag(lag,i)=plag(lag,i)+weight(j)*store(k,l,m) | |
| 145 | c if (i .eq. nrange) then |
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145 | c if (i .eq. nrange) then | |
| 146 | c write(*,*) "lag: ",lag |
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146 | c write(*,*) "lag: ",lag | |
| 147 | c write(*,*) "plag: ",plag(lag,i) |
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147 | c write(*,*) "plag: ",plag(lag,i) | |
| 148 | c write(*,*) "plag: ",plag(lag,i) |
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148 | c write(*,*) "plag: ",plag(lag,i) | |
| 149 | c call exit |
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149 | c call exit | |
| 150 | c end if |
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150 | c end if | |
| 151 | end do |
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151 | end do | |
| 152 | c write(*,*) "plag: ",plag(lag,i) |
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152 | c write(*,*) "plag: ",plag(lag,i) | |
| 153 | c write(*,*) "plag: ",plag(12,72) |
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153 | c write(*,*) "plag: ",plag(12,72) | |
| 154 | c call exit |
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154 | c call exit | |
| 155 | end do |
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155 | end do | |
| 156 | c call exit |
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156 | c call exit | |
| 157 | c write(*,*) "plag: ",plag(12,72) |
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157 | c write(*,*) "plag: ",plag(12,72) | |
| 158 | end do |
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158 | end do | |
| 159 | c write(*,*) "plag: ",plag(12,72) |
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159 | c write(*,*) "plag: ",plag(12,72) | |
| 160 | c call exit |
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160 | c call exit | |
| 161 | c write(*,*) "End LAGP" |
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161 | c write(*,*) "End LAGP" | |
| 162 | return |
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162 | return | |
| 163 | end |
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163 | end | |
| 164 |
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164 | |||
| 165 | subroutine lagp_old(plag,wl,r0,dr,nl,nrange) |
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165 | subroutine lagp_old(plag,wl,r0,dr,nl,nrange) | |
| 166 | c |
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166 | c | |
| 167 | c predict lagged product matrix using state parameters stored |
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167 | c predict lagged product matrix using state parameters stored | |
| 168 | c as cubic b-splines |
|
168 | c as cubic b-splines | |
| 169 | c read weights for numeric integration from a file |
|
169 | c read weights for numeric integration from a file | |
| 170 | c |
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170 | c | |
| 171 | c general version - samples can be anywhere |
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171 | c general version - samples can be anywhere | |
| 172 | c |
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172 | c | |
| 173 | include 'fitter.h' |
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173 | include 'fitter.h' | |
| 174 | include 'spline.h' |
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174 | include 'spline.h' | |
| 175 | include 'bfield.h' |
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175 | include 'bfield.h' | |
| 176 | integer nl,nrange |
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176 | integer nl,nrange | |
| 177 | real plag(nl,nrange),taus(nl) |
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177 | real plag(nl,nrange),taus(nl) | |
| 178 | parameter(nw=1000) |
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178 | parameter(nw=1000) | |
| 179 | integer ilag(nw) |
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179 | integer ilag(nw) | |
| 180 | real weight(nw),dtau(nw),drange(nw) |
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180 | real weight(nw),dtau(nw),drange(nw) | |
| 181 | logical first |
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181 | logical first | |
| 182 | data first/.true./ |
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182 | data first/.true./ | |
| 183 | c |
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183 | c | |
| 184 |
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184 | |||
| 185 | c zero out array |
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185 | c zero out array | |
| 186 |
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186 | |||
| 187 | do i=1,nrange |
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187 | do i=1,nrange | |
| 188 | do j=1,nl |
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188 | do j=1,nl | |
| 189 | plag(j,i)=0.0 |
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189 | plag(j,i)=0.0 | |
| 190 | end do |
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190 | end do | |
| 191 | end do |
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191 | end do | |
| 192 |
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192 | |||
| 193 | c |
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193 | c | |
| 194 | c construct lagged products |
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194 | c construct lagged products | |
| 195 | c |
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195 | c | |
| 196 |
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196 | |||
| 197 | if(first) then |
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197 | if(first) then | |
| 198 | open(unit=25,file='weights.dat',status='old') |
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198 | open(unit=25,file='weights.dat',status='old') | |
| 199 | read (25,*) nwt |
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199 | read (25,*) nwt | |
| 200 | do i=1,nwt |
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200 | do i=1,nwt | |
| 201 | read(25,*) weight(i),dtau(i),drange(i),ilag(i) |
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201 | read(25,*) weight(i),dtau(i),drange(i),ilag(i) | |
| 202 | end do |
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202 | end do | |
| 203 | close(25) |
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203 | close(25) | |
| 204 | first=.false. |
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204 | first=.false. | |
| 205 | end if |
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205 | end if | |
| 206 |
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206 | |||
| 207 | c can avoid recalculating splines and/or ACFs when parameters repeat |
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207 | c can avoid recalculating splines and/or ACFs when parameters repeat | |
| 208 |
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208 | |||
| 209 | altp=-1.0 |
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209 | altp=-1.0 | |
| 210 | taup=-1.0 |
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210 | taup=-1.0 | |
| 211 |
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211 | |||
| 212 | do i=1+nl,nrange |
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212 | do i=1+nl,nrange | |
| 213 | do j=1,nwt |
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213 | do j=1,nwt | |
| 214 | alt=r0+(float(i-1)+drange(j))*dr |
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214 | alt=r0+(float(i-1)+drange(j))*dr | |
| 215 | ii=(alt-r0)/dr+1 |
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215 | ii=(alt-r0)/dr+1 | |
| 216 |
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216 | |||
| 217 | if(alt.ne.altp) then |
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217 | if(alt.ne.altp) then | |
| 218 | call get_spline(alt,dens,te,ti1,hf,hef) |
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218 | call get_spline(alt,dens,te,ti1,hf,hef) | |
| 219 |
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219 | |||
| 220 | c write(*,*) alt,dens,te,ti1,hf,hef |
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220 | c write(*,*) alt,dens,te,ti1,hf,hef | |
| 221 |
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221 | |||
| 222 | do k=1,nion |
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222 | do k=1,nion | |
| 223 | ti(k)=ti1 |
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223 | ti(k)=ti1 | |
| 224 | end do |
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224 | end do | |
| 225 | fi(2)=hf |
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225 | fi(2)=hf | |
| 226 | fi(3)=hef |
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226 | fi(3)=hef | |
| 227 | fi(1)=1.0-hf-hef |
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227 | fi(1)=1.0-hf-hef | |
| 228 | end if |
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228 | end if | |
| 229 |
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229 | |||
| 230 | tau=abs(dtau(j)*dr/1.5e5) |
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230 | tau=abs(dtau(j)*dr/1.5e5) | |
| 231 | lag=ilag(j)+1 |
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231 | lag=ilag(j)+1 | |
| 232 |
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232 | |||
| 233 | c write(*,*) i,alpha_prof(i),bfld_prof(i) |
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233 | c write(*,*) i,alpha_prof(i),bfld_prof(i) | |
| 234 |
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234 | |||
| 235 | if(tau.ne.taup.or.alt.ne.altp) then |
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235 | if(tau.ne.taup.or.alt.ne.altp) then | |
| 236 |
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236 | |||
| 237 | c two- or three- point Gauss Hermite quadrature rule |
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237 | c two- or three- point Gauss Hermite quadrature rule | |
| 238 |
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238 | |||
| 239 | c call acf2(wl,tau,te,ti,fi,ven,vin,wi,nion, |
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239 | c call acf2(wl,tau,te,ti,fi,ven,vin,wi,nion, | |
| 240 | c & alpha_prof(ii)+1.74e-2,dens,bfld_prof(ii),rho1) |
|
240 | c & alpha_prof(ii)+1.74e-2,dens,bfld_prof(ii),rho1) | |
| 241 |
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241 | |||
| 242 | c call acf2(wl,tau,te,ti,fi,ven,vin,wi,nion, |
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242 | c call acf2(wl,tau,te,ti,fi,ven,vin,wi,nion, | |
| 243 | c & alpha_prof(ii)-1.74e-2,dens,bfld_prof(ii),rho2) |
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243 | c & alpha_prof(ii)-1.74e-2,dens,bfld_prof(ii),rho2) | |
| 244 |
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244 | |||
| 245 | c call acf2(wl,tau,te,ti,fi,ven,vin,wi,nion, |
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245 | c call acf2(wl,tau,te,ti,fi,ven,vin,wi,nion, | |
| 246 | c & alpha_prof(ii),dens,bfld_prof(ii),rho1) |
|
246 | c & alpha_prof(ii),dens,bfld_prof(ii),rho1) | |
| 247 |
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247 | |||
| 248 | c call acf2(wl,tau,te,ti,fi,ven,vin,wi,nion, |
|
248 | c call acf2(wl,tau,te,ti,fi,ven,vin,wi,nion, | |
| 249 | c & alpha_prof(ii)+1.9e-2,dens,bfld_prof(ii),rho2) |
|
249 | c & alpha_prof(ii)+1.9e-2,dens,bfld_prof(ii),rho2) | |
| 250 |
|
250 | |||
| 251 | c call acf2(wl,tau,te,ti,fi,ven,vin,wi,nion, |
|
251 | c call acf2(wl,tau,te,ti,fi,ven,vin,wi,nion, | |
| 252 | c & alpha_prof(ii)-1.9e-2,dens,bfld_prof(ii),rho3) |
|
252 | c & alpha_prof(ii)-1.9e-2,dens,bfld_prof(ii),rho3) | |
| 253 |
|
253 | |||
| 254 | call acf2(wl,tau,te,ti,fi,ven,vin,wi,nion, |
|
254 | call acf2(wl,tau,te,ti,fi,ven,vin,wi,nion, | |
| 255 | & alpha_prof(ii),dens,bfld_prof(ii),rho) |
|
255 | & alpha_prof(ii),dens,bfld_prof(ii),rho) | |
| 256 |
|
256 | |||
| 257 | c rho=(rho1+rho2)/2.0 |
|
257 | c rho=(rho1+rho2)/2.0 | |
| 258 | c rho=(rho2+rho3)*0.29541+rho1*1.18164)/1.77246 |
|
258 | c rho=(rho2+rho3)*0.29541+rho1*1.18164)/1.77246 | |
| 259 |
|
259 | |||
| 260 | end if |
|
260 | end if | |
| 261 |
|
261 | |||
| 262 | plag(lag,i)=plag(lag,i)+weight(j)*rho*dens*(100.0/alt)**2 |
|
262 | plag(lag,i)=plag(lag,i)+weight(j)*rho*dens*(100.0/alt)**2 | |
| 263 |
|
263 | |||
| 264 | altp=alt |
|
264 | altp=alt | |
| 265 | taup=tau |
|
265 | taup=tau | |
| 266 |
|
266 | |||
| 267 | end do |
|
267 | end do | |
| 268 | end do |
|
268 | end do | |
| 269 |
|
269 | |||
| 270 | return |
|
270 | return | |
| 271 | end |
|
271 | end | |
| 272 |
|
272 | |||
| 273 | function atanh(x) |
|
273 | function atanh(x) | |
| 274 | c |
|
274 | c | |
| 275 | real atanh,x |
|
275 | real atanh,x | |
| 276 | c |
|
276 | c | |
| 277 | atanh=log(sqrt((1.+x)/(1.-x))) |
|
277 | atanh=log(sqrt((1.+x)/(1.-x))) | |
| 278 | return |
|
278 | return | |
| 279 | end |
|
279 | end | |
| 280 |
|
280 | |||
| 281 | subroutine get_spline(alt,dens,te,ti,hf,hef) |
|
281 | subroutine get_spline(alt,dens,te,ti,hf,hef) | |
| 282 | c |
|
282 | c | |
| 283 | c routines for handling cubic b-spline interpolation |
|
283 | c routines for handling cubic b-spline interpolation | |
| 284 | c gets values consistent with stored coefficients |
|
284 | c gets values consistent with stored coefficients | |
| 285 | c |
|
285 | c | |
| 286 |
|
286 | |||
| 287 | include 'spline.h' |
|
287 | include 'spline.h' | |
| 288 |
|
288 | |||
| 289 | c |
|
289 | c | |
| 290 | c bspline values from 200-1500 km in 15-km intervals |
|
290 | c bspline values from 200-1500 km in 15-km intervals | |
| 291 | c must specify five knots above ceiling |
|
291 | c must specify five knots above ceiling | |
| 292 | c note offset ... start accessing splines above bottom two knots |
|
292 | c note offset ... start accessing splines above bottom two knots | |
| 293 | c |
|
293 | c | |
| 294 | c five banks of splines, for Ne, Te, Ti, H+, and He+ versus altitude |
|
294 | c five banks of splines, for Ne, Te, Ti, H+, and He+ versus altitude | |
| 295 | c need to initialize ta somewhere |
|
295 | c need to initialize ta somewhere | |
| 296 | c |
|
296 | c | |
| 297 | c write(*,*) "ta: ",ta |
|
297 | c write(*,*) "ta: ",ta | |
| 298 | c write(*,*) "bcoef(1,1): ",bcoef(1,1) |
|
298 | c write(*,*) "bcoef(1,1): ",bcoef(1,1) | |
| 299 | c write(*,*) "nspline: ",nspline |
|
299 | c write(*,*) "nspline: ",nspline | |
| 300 | c write(*,*) "norder: ",norder |
|
300 | c write(*,*) "norder: ",norder | |
| 301 | c write(*,*) "alt: ",alt |
|
301 | c write(*,*) "alt: ",alt | |
| 302 | dens=bvalue(ta,bcoef(1,1),nspline,norder,alt,0) |
|
302 | dens=bvalue(ta,bcoef(1,1),nspline,norder,alt,0) | |
| 303 | c write(*,*) "dens_inside_get_spline: ",dens |
|
303 | c write(*,*) "dens_inside_get_spline: ",dens | |
| 304 | c write(*,*) dens |
|
304 | c write(*,*) dens | |
| 305 | c call exit |
|
305 | c call exit | |
| 306 | dens=10.0**MAX(dens,2.0) |
|
306 | dens=10.0**MAX(dens,2.0) | |
| 307 | c write(*,*) dens |
|
307 | c write(*,*) dens | |
| 308 | c call exit |
|
308 | c call exit | |
| 309 | te=bvalue(ta,bcoef(1,2),nspline,norder,alt,0) |
|
309 | te=bvalue(ta,bcoef(1,2),nspline,norder,alt,0) | |
| 310 | te=t0+t1*(1.0+tanh(te))/2.0 ! DLH 10/14 was 3500 |
|
310 | te=t0+t1*(1.0+tanh(te))/2.0 ! DLH 10/14 was 3500 | |
| 311 | c tr=bvalue(ta,bcoef(1,3),nspline,norder,alt,0) |
|
311 | c tr=bvalue(ta,bcoef(1,3),nspline,norder,alt,0) | |
| 312 | c tr=exp(tr) |
|
312 | c tr=exp(tr) | |
| 313 | c ti=te/tr |
|
313 | c ti=te/tr | |
| 314 | ti=bvalue(ta,bcoef(1,3),nspline,norder,alt,0) |
|
314 | ti=bvalue(ta,bcoef(1,3),nspline,norder,alt,0) | |
| 315 | ti=t0+t1*(1.0+tanh(ti))/2.0 ! DLH 10/14 was 3500 |
|
315 | ti=t0+t1*(1.0+tanh(ti))/2.0 ! DLH 10/14 was 3500 | |
| 316 | hf=bvalue(ta,bcoef(1,4),nspline,norder,alt,0) |
|
316 | hf=bvalue(ta,bcoef(1,4),nspline,norder,alt,0) | |
| 317 | hf=(1.0+tanh(hf))/2.0 |
|
317 | hf=(1.0+tanh(hf))/2.0 | |
| 318 | hef=bvalue(ta,bcoef(1,5),nspline,norder,alt,0) |
|
318 | hef=bvalue(ta,bcoef(1,5),nspline,norder,alt,0) | |
| 319 | hef=(1.0+tanh(hef))/2.0 |
|
319 | hef=(1.0+tanh(hef))/2.0 | |
| 320 | return |
|
320 | return | |
| 321 | end |
|
321 | end | |
| 322 |
|
322 | |||
| 323 |
|
323 | |||
| 324 | real function bvalue ( t, bcoef, n, k, x, jderiv ) |
|
324 | real function bvalue ( t, bcoef, n, k, x, jderiv ) | |
| 325 | c from * a practical guide to splines * by c. de boor |
|
325 | c from * a practical guide to splines * by c. de boor | |
| 326 | calls interv |
|
326 | calls interv | |
| 327 | c |
|
327 | c | |
| 328 | calculates value at x of jderiv-th derivative of spline from b-repr. |
|
328 | calculates value at x of jderiv-th derivative of spline from b-repr. | |
| 329 | c the spline is taken to be continuous from the right, EXCEPT at the |
|
329 | c the spline is taken to be continuous from the right, EXCEPT at the | |
| 330 | c rightmost knot, where it is taken to be continuous from the left. |
|
330 | c rightmost knot, where it is taken to be continuous from the left. | |
| 331 | c |
|
331 | c | |
| 332 | c****** i n p u t ****** |
|
332 | c****** i n p u t ****** | |
| 333 | c t, bcoef, n, k......forms the b-representation of the spline f to |
|
333 | c t, bcoef, n, k......forms the b-representation of the spline f to | |
| 334 | c be evaluated. specifically, |
|
334 | c be evaluated. specifically, | |
| 335 | c t.....knot sequence, of length n+k, assumed nondecreasing. |
|
335 | c t.....knot sequence, of length n+k, assumed nondecreasing. | |
| 336 | c bcoef.....b-coefficient sequence, of length n . |
|
336 | c bcoef.....b-coefficient sequence, of length n . | |
| 337 | c n.....length of bcoef and dimension of spline(k,t), |
|
337 | c n.....length of bcoef and dimension of spline(k,t), | |
| 338 | c a s s u m e d positive . |
|
338 | c a s s u m e d positive . | |
| 339 | c k.....order of the spline . |
|
339 | c k.....order of the spline . | |
| 340 | c |
|
340 | c | |
| 341 | c w a r n i n g . . . the restriction k .le. kmax (=20) is imposed |
|
341 | c w a r n i n g . . . the restriction k .le. kmax (=20) is imposed | |
| 342 | c arbitrarily by the dimension statement for aj, dl, dr below, |
|
342 | c arbitrarily by the dimension statement for aj, dl, dr below, | |
| 343 | c but is n o w h e r e c h e c k e d for. |
|
343 | c but is n o w h e r e c h e c k e d for. | |
| 344 | c |
|
344 | c | |
| 345 | c x.....the point at which to evaluate . |
|
345 | c x.....the point at which to evaluate . | |
| 346 | c jderiv.....integer giving the order of the derivative to be evaluated |
|
346 | c jderiv.....integer giving the order of the derivative to be evaluated | |
| 347 | c a s s u m e d to be zero or positive. |
|
347 | c a s s u m e d to be zero or positive. | |
| 348 | c |
|
348 | c | |
| 349 | c****** o u t p u t ****** |
|
349 | c****** o u t p u t ****** | |
| 350 | c bvalue.....the value of the (jderiv)-th derivative of f at x . |
|
350 | c bvalue.....the value of the (jderiv)-th derivative of f at x . | |
| 351 | c |
|
351 | c | |
| 352 | c****** m e t h o d ****** |
|
352 | c****** m e t h o d ****** | |
| 353 | c The nontrivial knot interval (t(i),t(i+1)) containing x is lo- |
|
353 | c The nontrivial knot interval (t(i),t(i+1)) containing x is lo- | |
| 354 | c cated with the aid of interv . The k b-coeffs of f relevant for |
|
354 | c cated with the aid of interv . The k b-coeffs of f relevant for | |
| 355 | c this interval are then obtained from bcoef (or taken to be zero if |
|
355 | c this interval are then obtained from bcoef (or taken to be zero if | |
| 356 | c not explicitly available) and are then differenced jderiv times to |
|
356 | c not explicitly available) and are then differenced jderiv times to | |
| 357 | c obtain the b-coeffs of (d**jderiv)f relevant for that interval. |
|
357 | c obtain the b-coeffs of (d**jderiv)f relevant for that interval. | |
| 358 | c Precisely, with j = jderiv, we have from x.(12) of the text that |
|
358 | c Precisely, with j = jderiv, we have from x.(12) of the text that | |
| 359 | c |
|
359 | c | |
| 360 | c (d**j)f = sum ( bcoef(.,j)*b(.,k-j,t) ) |
|
360 | c (d**j)f = sum ( bcoef(.,j)*b(.,k-j,t) ) | |
| 361 | c |
|
361 | c | |
| 362 | c where |
|
362 | c where | |
| 363 | c / bcoef(.), , j .eq. 0 |
|
363 | c / bcoef(.), , j .eq. 0 | |
| 364 | c / |
|
364 | c / | |
| 365 | c bcoef(.,j) = / bcoef(.,j-1) - bcoef(.-1,j-1) |
|
365 | c bcoef(.,j) = / bcoef(.,j-1) - bcoef(.-1,j-1) | |
| 366 | c / ----------------------------- , j .gt. 0 |
|
366 | c / ----------------------------- , j .gt. 0 | |
| 367 | c / (t(.+k-j) - t(.))/(k-j) |
|
367 | c / (t(.+k-j) - t(.))/(k-j) | |
| 368 | c |
|
368 | c | |
| 369 | c Then, we use repeatedly the fact that |
|
369 | c Then, we use repeatedly the fact that | |
| 370 | c |
|
370 | c | |
| 371 | c sum ( a(.)*b(.,m,t)(x) ) = sum ( a(.,x)*b(.,m-1,t)(x) ) |
|
371 | c sum ( a(.)*b(.,m,t)(x) ) = sum ( a(.,x)*b(.,m-1,t)(x) ) | |
| 372 | c with |
|
372 | c with | |
| 373 | c (x - t(.))*a(.) + (t(.+m-1) - x)*a(.-1) |
|
373 | c (x - t(.))*a(.) + (t(.+m-1) - x)*a(.-1) | |
| 374 | c a(.,x) = --------------------------------------- |
|
374 | c a(.,x) = --------------------------------------- | |
| 375 | c (x - t(.)) + (t(.+m-1) - x) |
|
375 | c (x - t(.)) + (t(.+m-1) - x) | |
| 376 | c |
|
376 | c | |
| 377 | c to write (d**j)f(x) eventually as a linear combination of b-splines |
|
377 | c to write (d**j)f(x) eventually as a linear combination of b-splines | |
| 378 | c of order 1 , and the coefficient for b(i,1,t)(x) must then be the |
|
378 | c of order 1 , and the coefficient for b(i,1,t)(x) must then be the | |
| 379 | c desired number (d**j)f(x). (see x.(17)-(19) of text). |
|
379 | c desired number (d**j)f(x). (see x.(17)-(19) of text). | |
| 380 | c |
|
380 | c | |
| 381 | parameter (kmax = 40) |
|
381 | parameter (kmax = 40) | |
| 382 | integer jderiv,k,n, i,ilo,imk,j,jc,jcmin,jcmax,jj,kmj,km1 |
|
382 | integer jderiv,k,n, i,ilo,imk,j,jc,jcmin,jcmax,jj,kmj,km1 | |
| 383 | * ,mflag,nmi,jdrvp1 |
|
383 | * ,mflag,nmi,jdrvp1 | |
| 384 | c integer kmax |
|
384 | c integer kmax | |
| 385 | C real bcoef(n),t(1),x, aj(20),dl(20),dr(20),fkmj |
|
385 | C real bcoef(n),t(1),x, aj(20),dl(20),dr(20),fkmj | |
| 386 | real bcoef(n),x, aj(kmax),dl(kmax),dr(kmax),fkmj |
|
386 | real bcoef(n),x, aj(kmax),dl(kmax),dr(kmax),fkmj | |
| 387 | dimension t(n+k) |
|
387 | dimension t(n+k) | |
| 388 | c former fortran standard made it impossible to specify the length of t |
|
388 | c former fortran standard made it impossible to specify the length of t | |
| 389 | c precisely without the introduction of otherwise superfluous addition- |
|
389 | c precisely without the introduction of otherwise superfluous addition- | |
| 390 | c al arguments. |
|
390 | c al arguments. | |
| 391 | bvalue = 0. |
|
391 | bvalue = 0. | |
| 392 | if (jderiv .ge. k) go to 99 |
|
392 | if (jderiv .ge. k) go to 99 | |
| 393 | c |
|
393 | c | |
| 394 | c *** Find i s.t. 1 .le. i .lt. n+k and t(i) .lt. t(i+1) and |
|
394 | c *** Find i s.t. 1 .le. i .lt. n+k and t(i) .lt. t(i+1) and | |
| 395 | c t(i) .le. x .lt. t(i+1) . If no such i can be found, x lies |
|
395 | c t(i) .le. x .lt. t(i+1) . If no such i can be found, x lies | |
| 396 | c outside the support of the spline f , hence bvalue = 0. |
|
396 | c outside the support of the spline f , hence bvalue = 0. | |
| 397 | c (The asymmetry in this choice of i makes f rightcontinuous, except |
|
397 | c (The asymmetry in this choice of i makes f rightcontinuous, except | |
| 398 | c at t(n+k) where it is leftcontinuous.) |
|
398 | c at t(n+k) where it is leftcontinuous.) | |
| 399 | call interv ( t, n+k, x, i, mflag ) |
|
399 | call interv ( t, n+k, x, i, mflag ) | |
| 400 | if (mflag .ne. 0) go to 99 |
|
400 | if (mflag .ne. 0) go to 99 | |
| 401 | c *** if k = 1 (and jderiv = 0), bvalue = bcoef(i). |
|
401 | c *** if k = 1 (and jderiv = 0), bvalue = bcoef(i). | |
| 402 | km1 = k - 1 |
|
402 | km1 = k - 1 | |
| 403 | if (km1 .gt. 0) go to 1 |
|
403 | if (km1 .gt. 0) go to 1 | |
| 404 | bvalue = bcoef(i) |
|
404 | bvalue = bcoef(i) | |
| 405 | go to 99 |
|
405 | go to 99 | |
| 406 | c |
|
406 | c | |
| 407 | c *** store the k b-spline coefficients relevant for the knot interval |
|
407 | c *** store the k b-spline coefficients relevant for the knot interval | |
| 408 | c (t(i),t(i+1)) in aj(1),...,aj(k) and compute dl(j) = x - t(i+1-j), |
|
408 | c (t(i),t(i+1)) in aj(1),...,aj(k) and compute dl(j) = x - t(i+1-j), | |
| 409 | c dr(j) = t(i+j) - x, j=1,...,k-1 . set any of the aj not obtainable |
|
409 | c dr(j) = t(i+j) - x, j=1,...,k-1 . set any of the aj not obtainable | |
| 410 | c from input to zero. set any t.s not obtainable equal to t(1) or |
|
410 | c from input to zero. set any t.s not obtainable equal to t(1) or | |
| 411 | c to t(n+k) appropriately. |
|
411 | c to t(n+k) appropriately. | |
| 412 | 1 jcmin = 1 |
|
412 | 1 jcmin = 1 | |
| 413 | imk = i - k |
|
413 | imk = i - k | |
| 414 | if (imk .ge. 0) go to 8 |
|
414 | if (imk .ge. 0) go to 8 | |
| 415 | jcmin = 1 - imk |
|
415 | jcmin = 1 - imk | |
| 416 | do 5 j=1,i |
|
416 | do 5 j=1,i | |
| 417 | 5 dl(j) = x - t(i+1-j) |
|
417 | 5 dl(j) = x - t(i+1-j) | |
| 418 | do 6 j=i,km1 |
|
418 | do 6 j=i,km1 | |
| 419 | aj(k-j) = 0. |
|
419 | aj(k-j) = 0. | |
| 420 | 6 dl(j) = dl(i) |
|
420 | 6 dl(j) = dl(i) | |
| 421 | go to 10 |
|
421 | go to 10 | |
| 422 | 8 do 9 j=1,km1 |
|
422 | 8 do 9 j=1,km1 | |
| 423 | 9 dl(j) = x - t(i+1-j) |
|
423 | 9 dl(j) = x - t(i+1-j) | |
| 424 | c |
|
424 | c | |
| 425 | 10 jcmax = k |
|
425 | 10 jcmax = k | |
| 426 | nmi = n - i |
|
426 | nmi = n - i | |
| 427 | if (nmi .ge. 0) go to 18 |
|
427 | if (nmi .ge. 0) go to 18 | |
| 428 | jcmax = k + nmi |
|
428 | jcmax = k + nmi | |
| 429 | do 15 j=1,jcmax |
|
429 | do 15 j=1,jcmax | |
| 430 | 15 dr(j) = t(i+j) - x |
|
430 | 15 dr(j) = t(i+j) - x | |
| 431 | do 16 j=jcmax,km1 |
|
431 | do 16 j=jcmax,km1 | |
| 432 | aj(j+1) = 0. |
|
432 | aj(j+1) = 0. | |
| 433 | 16 dr(j) = dr(jcmax) |
|
433 | 16 dr(j) = dr(jcmax) | |
| 434 | go to 20 |
|
434 | go to 20 | |
| 435 | 18 do 19 j=1,km1 |
|
435 | 18 do 19 j=1,km1 | |
| 436 | 19 dr(j) = t(i+j) - x |
|
436 | 19 dr(j) = t(i+j) - x | |
| 437 | c |
|
437 | c | |
| 438 | 20 do 21 jc=jcmin,jcmax |
|
438 | 20 do 21 jc=jcmin,jcmax | |
| 439 | 21 aj(jc) = bcoef(imk + jc) |
|
439 | 21 aj(jc) = bcoef(imk + jc) | |
| 440 | c |
|
440 | c | |
| 441 | c *** difference the coefficients jderiv times. |
|
441 | c *** difference the coefficients jderiv times. | |
| 442 | if (jderiv .eq. 0) go to 30 |
|
442 | if (jderiv .eq. 0) go to 30 | |
| 443 | do 23 j=1,jderiv |
|
443 | do 23 j=1,jderiv | |
| 444 | kmj = k-j |
|
444 | kmj = k-j | |
| 445 | fkmj = float(kmj) |
|
445 | fkmj = float(kmj) | |
| 446 | ilo = kmj |
|
446 | ilo = kmj | |
| 447 | do 23 jj=1,kmj |
|
447 | do 23 jj=1,kmj | |
| 448 | aj(jj) = ((aj(jj+1) - aj(jj))/(dl(ilo) + dr(jj)))*fkmj |
|
448 | aj(jj) = ((aj(jj+1) - aj(jj))/(dl(ilo) + dr(jj)))*fkmj | |
| 449 | 23 ilo = ilo - 1 |
|
449 | 23 ilo = ilo - 1 | |
| 450 | c |
|
450 | c | |
| 451 | c *** compute value at x in (t(i),t(i+1)) of jderiv-th derivative, |
|
451 | c *** compute value at x in (t(i),t(i+1)) of jderiv-th derivative, | |
| 452 | c given its relevant b-spline coeffs in aj(1),...,aj(k-jderiv). |
|
452 | c given its relevant b-spline coeffs in aj(1),...,aj(k-jderiv). | |
| 453 | 30 if (jderiv .eq. km1) go to 39 |
|
453 | 30 if (jderiv .eq. km1) go to 39 | |
| 454 | jdrvp1 = jderiv + 1 |
|
454 | jdrvp1 = jderiv + 1 | |
| 455 | do 33 j=jdrvp1,km1 |
|
455 | do 33 j=jdrvp1,km1 | |
| 456 | kmj = k-j |
|
456 | kmj = k-j | |
| 457 | ilo = kmj |
|
457 | ilo = kmj | |
| 458 | do 33 jj=1,kmj |
|
458 | do 33 jj=1,kmj | |
| 459 | aj(jj) = (aj(jj+1)*dl(ilo) + aj(jj)*dr(jj))/(dl(ilo)+dr(jj)) |
|
459 | aj(jj) = (aj(jj+1)*dl(ilo) + aj(jj)*dr(jj))/(dl(ilo)+dr(jj)) | |
| 460 | 33 ilo = ilo - 1 |
|
460 | 33 ilo = ilo - 1 | |
| 461 | 39 bvalue = aj(1) |
|
461 | 39 bvalue = aj(1) | |
| 462 | c |
|
462 | c | |
| 463 | 99 return |
|
463 | 99 return | |
| 464 | end |
|
464 | end | |
| 465 | subroutine interv ( xt, lxt, x, left, mflag ) |
|
465 | subroutine interv ( xt, lxt, x, left, mflag ) | |
| 466 | c from * a practical guide to splines * by C. de Boor |
|
466 | c from * a practical guide to splines * by C. de Boor | |
| 467 | computes left = max( i : xt(i) .lt. xt(lxt) .and. xt(i) .le. x ) . |
|
467 | computes left = max( i : xt(i) .lt. xt(lxt) .and. xt(i) .le. x ) . | |
| 468 | c |
|
468 | c | |
| 469 | c****** i n p u t ****** |
|
469 | c****** i n p u t ****** | |
| 470 | c xt.....a real sequence, of length lxt , assumed to be nondecreasing |
|
470 | c xt.....a real sequence, of length lxt , assumed to be nondecreasing | |
| 471 | c lxt.....number of terms in the sequence xt . |
|
471 | c lxt.....number of terms in the sequence xt . | |
| 472 | c x.....the point whose location with respect to the sequence xt is |
|
472 | c x.....the point whose location with respect to the sequence xt is | |
| 473 | c to be determined. |
|
473 | c to be determined. | |
| 474 | c |
|
474 | c | |
| 475 | c****** o u t p u t ****** |
|
475 | c****** o u t p u t ****** | |
| 476 | c left, mflag.....both integers, whose value is |
|
476 | c left, mflag.....both integers, whose value is | |
| 477 | c |
|
477 | c | |
| 478 | c 1 -1 if x .lt. xt(1) |
|
478 | c 1 -1 if x .lt. xt(1) | |
| 479 | c i 0 if xt(i) .le. x .lt. xt(i+1) |
|
479 | c i 0 if xt(i) .le. x .lt. xt(i+1) | |
| 480 | c i 0 if xt(i) .lt. x .eq. xt(i+1) .eq. xt(lxt) |
|
480 | c i 0 if xt(i) .lt. x .eq. xt(i+1) .eq. xt(lxt) | |
| 481 | c i 1 if xt(i) .lt. xt(i+1) .eq. xt(lxt) .lt. x |
|
481 | c i 1 if xt(i) .lt. xt(i+1) .eq. xt(lxt) .lt. x | |
| 482 | c |
|
482 | c | |
| 483 | c In particular, mflag = 0 is the 'usual' case. mflag .ne. 0 |
|
483 | c In particular, mflag = 0 is the 'usual' case. mflag .ne. 0 | |
| 484 | c indicates that x lies outside the CLOSED interval |
|
484 | c indicates that x lies outside the CLOSED interval | |
| 485 | c xt(1) .le. y .le. xt(lxt) . The asymmetric treatment of the |
|
485 | c xt(1) .le. y .le. xt(lxt) . The asymmetric treatment of the | |
| 486 | c intervals is due to the decision to make all pp functions cont- |
|
486 | c intervals is due to the decision to make all pp functions cont- | |
| 487 | c inuous from the right, but, by returning mflag = 0 even if |
|
487 | c inuous from the right, but, by returning mflag = 0 even if | |
| 488 | C x = xt(lxt), there is the option of having the computed pp function |
|
488 | C x = xt(lxt), there is the option of having the computed pp function | |
| 489 | c continuous from the left at xt(lxt) . |
|
489 | c continuous from the left at xt(lxt) . | |
| 490 | c |
|
490 | c | |
| 491 | c****** m e t h o d ****** |
|
491 | c****** m e t h o d ****** | |
| 492 | c The program is designed to be efficient in the common situation that |
|
492 | c The program is designed to be efficient in the common situation that | |
| 493 | c it is called repeatedly, with x taken from an increasing or decrea- |
|
493 | c it is called repeatedly, with x taken from an increasing or decrea- | |
| 494 | c sing sequence. This will happen, e.g., when a pp function is to be |
|
494 | c sing sequence. This will happen, e.g., when a pp function is to be | |
| 495 | c graphed. The first guess for left is therefore taken to be the val- |
|
495 | c graphed. The first guess for left is therefore taken to be the val- | |
| 496 | c ue returned at the previous call and stored in the l o c a l varia- |
|
496 | c ue returned at the previous call and stored in the l o c a l varia- | |
| 497 | c ble ilo . A first check ascertains that ilo .lt. lxt (this is nec- |
|
497 | c ble ilo . A first check ascertains that ilo .lt. lxt (this is nec- | |
| 498 | c essary since the present call may have nothing to do with the previ- |
|
498 | c essary since the present call may have nothing to do with the previ- | |
| 499 | c ous call). Then, if xt(ilo) .le. x .lt. xt(ilo+1), we set left = |
|
499 | c ous call). Then, if xt(ilo) .le. x .lt. xt(ilo+1), we set left = | |
| 500 | c ilo and are done after just three comparisons. |
|
500 | c ilo and are done after just three comparisons. | |
| 501 | c Otherwise, we repeatedly double the difference istep = ihi - ilo |
|
501 | c Otherwise, we repeatedly double the difference istep = ihi - ilo | |
| 502 | c while also moving ilo and ihi in the direction of x , until |
|
502 | c while also moving ilo and ihi in the direction of x , until | |
| 503 | c xt(ilo) .le. x .lt. xt(ihi) , |
|
503 | c xt(ilo) .le. x .lt. xt(ihi) , | |
| 504 | c after which we use bisection to get, in addition, ilo+1 = ihi . |
|
504 | c after which we use bisection to get, in addition, ilo+1 = ihi . | |
| 505 | c left = ilo is then returned. |
|
505 | c left = ilo is then returned. | |
| 506 | c |
|
506 | c | |
| 507 | integer left,lxt,mflag, ihi,ilo,istep,middle |
|
507 | integer left,lxt,mflag, ihi,ilo,istep,middle | |
| 508 | real x,xt(lxt) |
|
508 | real x,xt(lxt) | |
| 509 | data ilo /1/ |
|
509 | data ilo /1/ | |
| 510 | save ilo |
|
510 | save ilo | |
| 511 | ihi = ilo + 1 |
|
511 | ihi = ilo + 1 | |
| 512 | if (ihi .lt. lxt) go to 20 |
|
512 | if (ihi .lt. lxt) go to 20 | |
| 513 | if (x .ge. xt(lxt)) go to 110 |
|
513 | if (x .ge. xt(lxt)) go to 110 | |
| 514 | if (lxt .le. 1) go to 90 |
|
514 | if (lxt .le. 1) go to 90 | |
| 515 | ilo = lxt - 1 |
|
515 | ilo = lxt - 1 | |
| 516 | ihi = lxt |
|
516 | ihi = lxt | |
| 517 | c |
|
517 | c | |
| 518 | 20 if (x .ge. xt(ihi)) go to 40 |
|
518 | 20 if (x .ge. xt(ihi)) go to 40 | |
| 519 | if (x .ge. xt(ilo)) go to 100 |
|
519 | if (x .ge. xt(ilo)) go to 100 | |
| 520 | c |
|
520 | c | |
| 521 | c **** now x .lt. xt(ilo) . decrease ilo to capture x . |
|
521 | c **** now x .lt. xt(ilo) . decrease ilo to capture x . | |
| 522 | istep = 1 |
|
522 | istep = 1 | |
| 523 | 31 ihi = ilo |
|
523 | 31 ihi = ilo | |
| 524 | ilo = ihi - istep |
|
524 | ilo = ihi - istep | |
| 525 | if (ilo .le. 1) go to 35 |
|
525 | if (ilo .le. 1) go to 35 | |
| 526 | if (x .ge. xt(ilo)) go to 50 |
|
526 | if (x .ge. xt(ilo)) go to 50 | |
| 527 | istep = istep*2 |
|
527 | istep = istep*2 | |
| 528 | go to 31 |
|
528 | go to 31 | |
| 529 | 35 ilo = 1 |
|
529 | 35 ilo = 1 | |
| 530 | if (x .lt. xt(1)) go to 90 |
|
530 | if (x .lt. xt(1)) go to 90 | |
| 531 | go to 50 |
|
531 | go to 50 | |
| 532 | c **** now x .ge. xt(ihi) . increase ihi to capture x . |
|
532 | c **** now x .ge. xt(ihi) . increase ihi to capture x . | |
| 533 | 40 istep = 1 |
|
533 | 40 istep = 1 | |
| 534 | 41 ilo = ihi |
|
534 | 41 ilo = ihi | |
| 535 | ihi = ilo + istep |
|
535 | ihi = ilo + istep | |
| 536 | if (ihi .ge. lxt) go to 45 |
|
536 | if (ihi .ge. lxt) go to 45 | |
| 537 | if (x .lt. xt(ihi)) go to 50 |
|
537 | if (x .lt. xt(ihi)) go to 50 | |
| 538 | istep = istep*2 |
|
538 | istep = istep*2 | |
| 539 | go to 41 |
|
539 | go to 41 | |
| 540 | 45 if (x .ge. xt(lxt)) go to 110 |
|
540 | 45 if (x .ge. xt(lxt)) go to 110 | |
| 541 | ihi = lxt |
|
541 | ihi = lxt | |
| 542 | c |
|
542 | c | |
| 543 | c **** now xt(ilo) .le. x .lt. xt(ihi) . narrow the interval. |
|
543 | c **** now xt(ilo) .le. x .lt. xt(ihi) . narrow the interval. | |
| 544 | 50 middle = (ilo + ihi)/2 |
|
544 | 50 middle = (ilo + ihi)/2 | |
| 545 | if (middle .eq. ilo) go to 100 |
|
545 | if (middle .eq. ilo) go to 100 | |
| 546 | c note. it is assumed that middle = ilo in case ihi = ilo+1 . |
|
546 | c note. it is assumed that middle = ilo in case ihi = ilo+1 . | |
| 547 | if (x .lt. xt(middle)) go to 53 |
|
547 | if (x .lt. xt(middle)) go to 53 | |
| 548 | ilo = middle |
|
548 | ilo = middle | |
| 549 | go to 50 |
|
549 | go to 50 | |
| 550 | 53 ihi = middle |
|
550 | 53 ihi = middle | |
| 551 | go to 50 |
|
551 | go to 50 | |
| 552 | c**** set output and return. |
|
552 | c**** set output and return. | |
| 553 | 90 mflag = -1 |
|
553 | 90 mflag = -1 | |
| 554 | left = 1 |
|
554 | left = 1 | |
| 555 | return |
|
555 | return | |
| 556 | 100 mflag = 0 |
|
556 | 100 mflag = 0 | |
| 557 | left = ilo |
|
557 | left = ilo | |
| 558 | return |
|
558 | return | |
| 559 | 110 mflag = 1 |
|
559 | 110 mflag = 1 | |
| 560 | if (x .eq. xt(lxt)) mflag = 0 |
|
560 | if (x .eq. xt(lxt)) mflag = 0 | |
| 561 | left = lxt |
|
561 | left = lxt | |
| 562 | 111 if (left .eq. 1) return |
|
562 | 111 if (left .eq. 1) return | |
| 563 | left = left - 1 |
|
563 | left = left - 1 | |
| 564 | if (xt(left) .lt. xt(lxt)) return |
|
564 | if (xt(left) .lt. xt(lxt)) return | |
| 565 | go to 111 |
|
565 | go to 111 | |
| 566 | end |
|
566 | end | |
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