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1 | 1 | subroutine lagp(plag,wl,r0,dr,nl,nrange) |
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2 | 2 | c |
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3 | 3 | c predict lagged product matrix using state parameters stored |
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4 | 4 | c as cubic b-splines |
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5 | 5 | c read weights for numeric integration from a file |
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6 | 6 | c |
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7 | 7 | c faster version - assumes samples taken at half-integer lags, ranges |
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8 | 8 | c |
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9 | 9 | include 'fitter.h' |
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10 | 10 | include 'spline.h' |
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11 | 11 | include 'bfield.h' |
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12 | 12 | integer nl,nrange |
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13 | 13 | real plag(nl,nrange),taus(nl) |
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14 | 14 | parameter(nw=1000) |
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15 | 15 | integer ilag(nw) |
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16 | 16 | real weight(nw),dtau(nw),drange(nw) |
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17 | 17 | logical first |
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18 | 18 | real store(2*nl,2*nrange,2) |
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19 | 19 | |
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20 | 20 | character(1024) :: fqual_temp |
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21 | 21 | character(:), allocatable :: fqual |
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22 | 22 | character bfmodel_str*8 |
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23 | 23 | |
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24 | 24 | data first/.true./ |
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25 | 25 | c |
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26 | 26 | |
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27 | 27 | c write(*,*) "dens_before: ",dens |
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28 | 28 | c call exit |
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29 | 29 | c zero out array |
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30 | 30 | c write(*,*) "Starting lagp" |
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31 | 31 | do i=1,nrange |
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32 | 32 | do j=1,nl |
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33 | 33 | plag(j,i)=0.0 |
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34 | 34 | end do |
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35 | 35 | end do |
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36 | 36 | |
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37 | 37 | c |
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38 | 38 | c compute all required acfs |
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39 | 39 | c |
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40 | 40 | do i=1,2*nrange |
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41 | 41 | ii=(i-1)/2+1 |
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42 | 42 | alt=r0+float(i-1)*dr*0.5 ! half integer ranges |
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43 | 43 | c write(*,*) "dens_before: ",dens |
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44 | 44 | c call exit |
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45 | 45 | c write(*,*) "alt: ",alt |
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46 | 46 | c write(*,*) "dens: ",dens |
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47 | 47 | c write(*,*) "te: ",te |
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48 | 48 | c write(*,*) "ti1: ",ti1 |
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49 | 49 | c write(*,*) "hf: ",hf |
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50 | 50 | c write(*,*) "hef: ",hef |
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51 | 51 | c call exit |
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52 | 52 | call get_spline(alt,dens,te,ti1,hf,hef) |
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53 | 53 | c write(*,*) "dens_after: ",dens |
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54 | 54 | c call exit |
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55 | 55 | do k=1,nion |
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56 | 56 | ti(k)=ti1 |
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57 | 57 | end do |
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58 | 58 | fi(2)=hf |
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59 | 59 | fi(3)=hef |
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60 | 60 | fi(1)=1.0-hf-hef |
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61 | 61 | |
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62 | 62 | do j=1,2*nl |
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63 | 63 | tau=float(j-1)*(dr/1.5e5)*0.5 ! half integer lags |
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64 | 64 | |
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65 | 65 | c just consider a single azimuth angle for now |
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66 | 66 | |
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67 | 67 | c call acf2(wl,tau,te,ti,fi,ven,vin,wi,nion, |
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68 | 68 | c & alpha_prof(ii)+1.74e-2,dens,bfld_prof(ii),rho) |
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69 | 69 | c store(j,i,1)=rho*dens*(100.0/alt)**2 |
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70 | 70 | |
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71 | 71 | c call acf2(wl,tau,te,ti,fi,ven,vin,wi,nion, |
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72 | 72 | c & alpha_prof(ii)-1.74e-2,dens,bfld_prof(ii),rho) |
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73 | 73 | c store(j,i,2)=rho*dens*(100.0/alt)**2 |
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74 | 74 | |
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75 | 75 | call acf2(wl,tau,te,ti,fi,ven,vin,wi,nion, |
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76 | 76 | & alpha_prof(ii),dens,bfld_prof(ii),rho) |
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77 | 77 | store(j,i,1)=rho*dens*(100.0/alt)**2 |
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78 | 78 | c write(*,*) "store", store(j,i,1) |
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79 | 79 | c call exit |
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80 | 80 | end do |
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81 | 81 | end do |
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82 | 82 | |
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83 | 83 | c construct lagged products |
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84 | 84 | c |
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85 | 85 | c write(*,*) "before weights" |
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86 | 86 | c write(*,*) first |
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87 | 87 | c write(*,*) "weight before: ",weight |
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88 | 88 | c write(*,*) "BEFORE GET_PATH" |
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89 | 89 | call get_path(fqual_temp) |
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90 | 90 | c write(*,*) "L_BEF: ", fqual_temp, "L_BEF_end" |
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91 | 91 | fqual = TRIM(fqual_temp) |
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92 | 92 | bfmodel_str = 'bfmodel/' |
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93 |
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93 | write(*,*) "bfmodel_str: ", bfmodel_str | |
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94 | 94 | c fqual(1:len_trim(fqual)-len_trim(bfmodel_str)) |
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95 | 95 | fqual = fqual(1:index(fqual, bfmodel_str))//'weights.da' |
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96 | write(*,*) "fqual: ", fqual | |
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96 | 97 | c write(*,*) "Final fqual",fqual,"FINAL" |
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97 | 98 | c call exit |
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98 | 99 | if(first) then |
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99 | 100 | open(unit=25,file=fqual, |
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100 | 101 | & status='old') |
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101 | 102 | read (25,*) nwt |
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102 | 103 | do i=1,nwt |
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103 | 104 | read(25,*) weight(i),dtau(i),drange(i),ilag(i) |
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104 | 105 | c write(*,*) "ilag: ",ilag(i) |
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105 | 106 | end do |
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106 | 107 | c flush(25) |
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107 | 108 | close(25) |
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108 | 109 | c first=.false. |
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109 | 110 | end if |
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110 | 111 | |
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111 | 112 | c write(*,*) "after weights" |
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112 | 113 | |
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113 | 114 | c write(*,*) "weight(3): ",weight(3) |
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114 | 115 | c call exit |
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115 | 116 | c write(*,*) "nl: ",nl,"nrange: ",nrange,"nwt: ",nwt |
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116 | 117 | |
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117 | 118 | do i=1+nl,nrange ! don't worry about redundancy here |
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118 | 119 | |
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119 | 120 | do j=1,nwt |
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120 | 121 | c write(*,*) "j: ",j |
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121 | 122 | alt=r0+(float(i-1)+drange(j))*dr |
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122 | 123 | tau=abs(dtau(j)*dr/1.5e5) |
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123 | 124 | lag=ilag(j)+1 |
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124 | 125 | c write(*,*) tau |
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125 | 126 | |
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126 | 127 | k=1+2.0*(tau/(dr/1.5e5)) |
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127 | 128 | l=1+2.0*(alt-r0)/dr |
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128 | 129 | |
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129 | 130 | do m=1,1 ! 2 |
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130 | 131 | |
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131 | 132 | c call exit |
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132 | 133 | c write(*,*) i |
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133 | 134 | c call exit |
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134 | 135 | c if (i .eq. nrange) then |
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135 | 136 | c if (j .eq. 227) then |
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136 | 137 | |
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137 | 138 | c write(*,*) "lag: ",lag |
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138 | 139 | c write(*,*) "ilag: ",ilag(j) |
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139 | 140 | c call exit |
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140 | 141 | c write(*,*) "plag: ",plag(lag,i) |
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141 | 142 | c write(*,*) "weight: ",weight |
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142 | 143 | c |
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143 | 144 | c write(*,*) "weight: ",weight(j) |
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144 | 145 | c write(*,*) "store: ",store(k,l,m) |
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145 | 146 | c call exit |
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146 | 147 | c end if |
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147 | 148 | c end if |
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148 | 149 | plag(lag,i)=plag(lag,i)+weight(j)*store(k,l,m) |
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149 | 150 | c if (i .eq. nrange) then |
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150 | 151 | c write(*,*) "lag: ",lag |
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151 | 152 | c write(*,*) "plag: ",plag(lag,i) |
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152 | 153 | c write(*,*) "plag: ",plag(lag,i) |
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153 | 154 | c call exit |
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154 | 155 | c end if |
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155 | 156 | end do |
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156 | 157 | c write(*,*) "plag: ",plag(lag,i) |
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157 | 158 | c write(*,*) "plag: ",plag(12,72) |
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158 | 159 | c call exit |
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159 | 160 | end do |
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160 | 161 | c call exit |
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161 | 162 | c write(*,*) "plag: ",plag(12,72) |
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162 | 163 | end do |
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163 | 164 | c write(*,*) "plag: ",plag(12,72) |
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164 | 165 | c call exit |
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165 | 166 | c write(*,*) "End LAGP" |
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166 | 167 | return |
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167 | 168 | end |
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168 | 169 | |
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169 | 170 | subroutine lagp_old(plag,wl,r0,dr,nl,nrange) |
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170 | 171 | c |
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171 | 172 | c predict lagged product matrix using state parameters stored |
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172 | 173 | c as cubic b-splines |
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173 | 174 | c read weights for numeric integration from a file |
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174 | 175 | c |
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175 | 176 | c general version - samples can be anywhere |
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176 | 177 | c |
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177 | 178 | include 'fitter.h' |
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178 | 179 | include 'spline.h' |
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179 | 180 | include 'bfield.h' |
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180 | 181 | integer nl,nrange |
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181 | 182 | real plag(nl,nrange),taus(nl) |
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182 | 183 | parameter(nw=1000) |
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183 | 184 | integer ilag(nw) |
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184 | 185 | real weight(nw),dtau(nw),drange(nw) |
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185 | 186 | logical first |
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186 | 187 | data first/.true./ |
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187 | 188 | c |
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188 | 189 | |
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189 | 190 | c zero out array |
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190 | 191 | |
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191 | 192 | do i=1,nrange |
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192 | 193 | do j=1,nl |
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193 | 194 | plag(j,i)=0.0 |
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194 | 195 | end do |
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195 | 196 | end do |
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196 | 197 | |
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197 | 198 | c |
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198 | 199 | c construct lagged products |
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199 | 200 | c |
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200 | 201 | |
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201 | 202 | if(first) then |
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202 | 203 | open(unit=25,file='weights.dat',status='old') |
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203 | 204 | read (25,*) nwt |
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204 | 205 | do i=1,nwt |
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205 | 206 | read(25,*) weight(i),dtau(i),drange(i),ilag(i) |
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206 | 207 | end do |
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207 | 208 | close(25) |
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208 | 209 | first=.false. |
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209 | 210 | end if |
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210 | 211 | |
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211 | 212 | c can avoid recalculating splines and/or ACFs when parameters repeat |
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212 | 213 | |
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213 | 214 | altp=-1.0 |
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214 | 215 | taup=-1.0 |
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215 | 216 | |
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216 | 217 | do i=1+nl,nrange |
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217 | 218 | do j=1,nwt |
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218 | 219 | alt=r0+(float(i-1)+drange(j))*dr |
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219 | 220 | ii=(alt-r0)/dr+1 |
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220 | 221 | |
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221 | 222 | if(alt.ne.altp) then |
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222 | 223 | call get_spline(alt,dens,te,ti1,hf,hef) |
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223 | 224 | |
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224 | 225 | c write(*,*) alt,dens,te,ti1,hf,hef |
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225 | 226 | |
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226 | 227 | do k=1,nion |
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227 | 228 | ti(k)=ti1 |
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228 | 229 | end do |
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229 | 230 | fi(2)=hf |
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230 | 231 | fi(3)=hef |
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231 | 232 | fi(1)=1.0-hf-hef |
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232 | 233 | end if |
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233 | 234 | |
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234 | 235 | tau=abs(dtau(j)*dr/1.5e5) |
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235 | 236 | lag=ilag(j)+1 |
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236 | 237 | |
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237 | 238 | c write(*,*) i,alpha_prof(i),bfld_prof(i) |
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238 | 239 | |
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239 | 240 | if(tau.ne.taup.or.alt.ne.altp) then |
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240 | 241 | |
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241 | 242 | c two- or three- point Gauss Hermite quadrature rule |
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242 | 243 | |
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243 | 244 | c call acf2(wl,tau,te,ti,fi,ven,vin,wi,nion, |
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244 | 245 | c & alpha_prof(ii)+1.74e-2,dens,bfld_prof(ii),rho1) |
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245 | 246 | |
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246 | 247 | c call acf2(wl,tau,te,ti,fi,ven,vin,wi,nion, |
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247 | 248 | c & alpha_prof(ii)-1.74e-2,dens,bfld_prof(ii),rho2) |
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248 | 249 | |
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249 | 250 | c call acf2(wl,tau,te,ti,fi,ven,vin,wi,nion, |
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250 | 251 | c & alpha_prof(ii),dens,bfld_prof(ii),rho1) |
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251 | 252 | |
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252 | 253 | c call acf2(wl,tau,te,ti,fi,ven,vin,wi,nion, |
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253 | 254 | c & alpha_prof(ii)+1.9e-2,dens,bfld_prof(ii),rho2) |
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254 | 255 | |
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255 | 256 | c call acf2(wl,tau,te,ti,fi,ven,vin,wi,nion, |
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256 | 257 | c & alpha_prof(ii)-1.9e-2,dens,bfld_prof(ii),rho3) |
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257 | 258 | |
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258 | 259 | call acf2(wl,tau,te,ti,fi,ven,vin,wi,nion, |
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259 | 260 | & alpha_prof(ii),dens,bfld_prof(ii),rho) |
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260 | 261 | |
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261 | 262 | c rho=(rho1+rho2)/2.0 |
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262 | 263 | c rho=(rho2+rho3)*0.29541+rho1*1.18164)/1.77246 |
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263 | 264 | |
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264 | 265 | end if |
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265 | 266 | |
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266 | 267 | plag(lag,i)=plag(lag,i)+weight(j)*rho*dens*(100.0/alt)**2 |
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267 | 268 | |
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268 | 269 | altp=alt |
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269 | 270 | taup=tau |
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270 | 271 | |
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271 | 272 | end do |
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272 | 273 | end do |
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273 | 274 | |
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274 | 275 | return |
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275 | 276 | end |
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276 | 277 | |
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277 | 278 | function atanh(x) |
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278 | 279 | c |
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279 | 280 | real atanh,x |
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280 | 281 | c |
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281 | 282 | atanh=log(sqrt((1.+x)/(1.-x))) |
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282 | 283 | return |
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283 | 284 | end |
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284 | 285 | |
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285 | 286 | subroutine get_spline(alt,dens,te,ti,hf,hef) |
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286 | 287 | c |
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287 | 288 | c routines for handling cubic b-spline interpolation |
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288 | 289 | c gets values consistent with stored coefficients |
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289 | 290 | c |
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290 | 291 | |
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291 | 292 | include 'spline.h' |
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292 | 293 | |
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293 | 294 | c |
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294 | 295 | c bspline values from 200-1500 km in 15-km intervals |
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295 | 296 | c must specify five knots above ceiling |
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296 | 297 | c note offset ... start accessing splines above bottom two knots |
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297 | 298 | c |
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298 | 299 | c five banks of splines, for Ne, Te, Ti, H+, and He+ versus altitude |
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299 | 300 | c need to initialize ta somewhere |
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300 | 301 | c |
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301 | 302 | c write(*,*) "ta: ",ta |
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302 | 303 | c write(*,*) "bcoef(1,1): ",bcoef(1,1) |
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303 | 304 | c write(*,*) "nspline: ",nspline |
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304 | 305 | c write(*,*) "norder: ",norder |
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305 | 306 | c write(*,*) "alt: ",alt |
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306 | 307 | dens=bvalue(ta,bcoef(1,1),nspline,norder,alt,0) |
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307 | 308 | c write(*,*) "dens_inside_get_spline: ",dens |
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308 | 309 | c write(*,*) dens |
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309 | 310 | c call exit |
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310 | 311 | dens=10.0**MAX(dens,2.0) |
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311 | 312 | c write(*,*) dens |
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312 | 313 | c call exit |
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313 | 314 | te=bvalue(ta,bcoef(1,2),nspline,norder,alt,0) |
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314 | 315 | te=t0+t1*(1.0+tanh(te))/2.0 ! DLH 10/14 was 3500 |
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315 | 316 | c tr=bvalue(ta,bcoef(1,3),nspline,norder,alt,0) |
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316 | 317 | c tr=exp(tr) |
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317 | 318 | c ti=te/tr |
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318 | 319 | ti=bvalue(ta,bcoef(1,3),nspline,norder,alt,0) |
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319 | 320 | ti=t0+t1*(1.0+tanh(ti))/2.0 ! DLH 10/14 was 3500 |
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320 | 321 | hf=bvalue(ta,bcoef(1,4),nspline,norder,alt,0) |
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321 | 322 | hf=(1.0+tanh(hf))/2.0 |
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322 | 323 | hef=bvalue(ta,bcoef(1,5),nspline,norder,alt,0) |
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323 | 324 | hef=(1.0+tanh(hef))/2.0 |
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324 | 325 | return |
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325 | 326 | end |
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326 | 327 | |
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327 | 328 | |
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328 | 329 | real function bvalue ( t, bcoef, n, k, x, jderiv ) |
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329 | 330 | c from * a practical guide to splines * by c. de boor |
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330 | 331 | calls interv |
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331 | 332 | c |
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332 | 333 | calculates value at x of jderiv-th derivative of spline from b-repr. |
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333 | 334 | c the spline is taken to be continuous from the right, EXCEPT at the |
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334 | 335 | c rightmost knot, where it is taken to be continuous from the left. |
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335 | 336 | c |
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336 | 337 | c****** i n p u t ****** |
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337 | 338 | c t, bcoef, n, k......forms the b-representation of the spline f to |
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338 | 339 | c be evaluated. specifically, |
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339 | 340 | c t.....knot sequence, of length n+k, assumed nondecreasing. |
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340 | 341 | c bcoef.....b-coefficient sequence, of length n . |
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341 | 342 | c n.....length of bcoef and dimension of spline(k,t), |
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342 | 343 | c a s s u m e d positive . |
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343 | 344 | c k.....order of the spline . |
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344 | 345 | c |
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345 | 346 | c w a r n i n g . . . the restriction k .le. kmax (=20) is imposed |
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346 | 347 | c arbitrarily by the dimension statement for aj, dl, dr below, |
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347 | 348 | c but is n o w h e r e c h e c k e d for. |
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348 | 349 | c |
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349 | 350 | c x.....the point at which to evaluate . |
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350 | 351 | c jderiv.....integer giving the order of the derivative to be evaluated |
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351 | 352 | c a s s u m e d to be zero or positive. |
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352 | 353 | c |
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353 | 354 | c****** o u t p u t ****** |
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354 | 355 | c bvalue.....the value of the (jderiv)-th derivative of f at x . |
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355 | 356 | c |
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356 | 357 | c****** m e t h o d ****** |
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357 | 358 | c The nontrivial knot interval (t(i),t(i+1)) containing x is lo- |
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358 | 359 | c cated with the aid of interv . The k b-coeffs of f relevant for |
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359 | 360 | c this interval are then obtained from bcoef (or taken to be zero if |
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360 | 361 | c not explicitly available) and are then differenced jderiv times to |
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361 | 362 | c obtain the b-coeffs of (d**jderiv)f relevant for that interval. |
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362 | 363 | c Precisely, with j = jderiv, we have from x.(12) of the text that |
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363 | 364 | c |
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364 | 365 | c (d**j)f = sum ( bcoef(.,j)*b(.,k-j,t) ) |
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365 | 366 | c |
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366 | 367 | c where |
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367 | 368 | c / bcoef(.), , j .eq. 0 |
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368 | 369 | c / |
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369 | 370 | c bcoef(.,j) = / bcoef(.,j-1) - bcoef(.-1,j-1) |
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370 | 371 | c / ----------------------------- , j .gt. 0 |
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371 | 372 | c / (t(.+k-j) - t(.))/(k-j) |
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372 | 373 | c |
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373 | 374 | c Then, we use repeatedly the fact that |
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374 | 375 | c |
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375 | 376 | c sum ( a(.)*b(.,m,t)(x) ) = sum ( a(.,x)*b(.,m-1,t)(x) ) |
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376 | 377 | c with |
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377 | 378 | c (x - t(.))*a(.) + (t(.+m-1) - x)*a(.-1) |
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378 | 379 | c a(.,x) = --------------------------------------- |
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379 | 380 | c (x - t(.)) + (t(.+m-1) - x) |
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380 | 381 | c |
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381 | 382 | c to write (d**j)f(x) eventually as a linear combination of b-splines |
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382 | 383 | c of order 1 , and the coefficient for b(i,1,t)(x) must then be the |
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383 | 384 | c desired number (d**j)f(x). (see x.(17)-(19) of text). |
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384 | 385 | c |
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385 | 386 | parameter (kmax = 40) |
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386 | 387 | integer jderiv,k,n, i,ilo,imk,j,jc,jcmin,jcmax,jj,kmj,km1 |
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387 | 388 | * ,mflag,nmi,jdrvp1 |
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388 | 389 | c integer kmax |
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389 | 390 | C real bcoef(n),t(1),x, aj(20),dl(20),dr(20),fkmj |
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390 | 391 | real bcoef(n),x, aj(kmax),dl(kmax),dr(kmax),fkmj |
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391 | 392 | dimension t(n+k) |
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392 | 393 | c former fortran standard made it impossible to specify the length of t |
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393 | 394 | c precisely without the introduction of otherwise superfluous addition- |
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394 | 395 | c al arguments. |
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395 | 396 | bvalue = 0. |
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396 | 397 | if (jderiv .ge. k) go to 99 |
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397 | 398 | c |
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398 | 399 | c *** Find i s.t. 1 .le. i .lt. n+k and t(i) .lt. t(i+1) and |
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399 | 400 | c t(i) .le. x .lt. t(i+1) . If no such i can be found, x lies |
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400 | 401 | c outside the support of the spline f , hence bvalue = 0. |
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401 | 402 | c (The asymmetry in this choice of i makes f rightcontinuous, except |
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402 | 403 | c at t(n+k) where it is leftcontinuous.) |
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403 | 404 | call interv ( t, n+k, x, i, mflag ) |
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404 | 405 | if (mflag .ne. 0) go to 99 |
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405 | 406 | c *** if k = 1 (and jderiv = 0), bvalue = bcoef(i). |
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406 | 407 | km1 = k - 1 |
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407 | 408 | if (km1 .gt. 0) go to 1 |
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408 | 409 | bvalue = bcoef(i) |
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409 | 410 | go to 99 |
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410 | 411 | c |
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411 | 412 | c *** store the k b-spline coefficients relevant for the knot interval |
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412 | 413 | c (t(i),t(i+1)) in aj(1),...,aj(k) and compute dl(j) = x - t(i+1-j), |
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413 | 414 | c dr(j) = t(i+j) - x, j=1,...,k-1 . set any of the aj not obtainable |
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414 | 415 | c from input to zero. set any t.s not obtainable equal to t(1) or |
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415 | 416 | c to t(n+k) appropriately. |
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416 | 417 | 1 jcmin = 1 |
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417 | 418 | imk = i - k |
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418 | 419 | if (imk .ge. 0) go to 8 |
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419 | 420 | jcmin = 1 - imk |
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420 | 421 | do 5 j=1,i |
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421 | 422 | 5 dl(j) = x - t(i+1-j) |
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422 | 423 | do 6 j=i,km1 |
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423 | 424 | aj(k-j) = 0. |
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424 | 425 | 6 dl(j) = dl(i) |
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425 | 426 | go to 10 |
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426 | 427 | 8 do 9 j=1,km1 |
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427 | 428 | 9 dl(j) = x - t(i+1-j) |
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428 | 429 | c |
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429 | 430 | 10 jcmax = k |
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430 | 431 | nmi = n - i |
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431 | 432 | if (nmi .ge. 0) go to 18 |
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432 | 433 | jcmax = k + nmi |
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433 | 434 | do 15 j=1,jcmax |
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434 | 435 | 15 dr(j) = t(i+j) - x |
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435 | 436 | do 16 j=jcmax,km1 |
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436 | 437 | aj(j+1) = 0. |
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437 | 438 | 16 dr(j) = dr(jcmax) |
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438 | 439 | go to 20 |
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439 | 440 | 18 do 19 j=1,km1 |
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440 | 441 | 19 dr(j) = t(i+j) - x |
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441 | 442 | c |
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442 | 443 | 20 do 21 jc=jcmin,jcmax |
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443 | 444 | 21 aj(jc) = bcoef(imk + jc) |
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444 | 445 | c |
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445 | 446 | c *** difference the coefficients jderiv times. |
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446 | 447 | if (jderiv .eq. 0) go to 30 |
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447 | 448 | do 23 j=1,jderiv |
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448 | 449 | kmj = k-j |
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449 | 450 | fkmj = float(kmj) |
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450 | 451 | ilo = kmj |
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451 | 452 | do 23 jj=1,kmj |
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452 | 453 | aj(jj) = ((aj(jj+1) - aj(jj))/(dl(ilo) + dr(jj)))*fkmj |
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453 | 454 | 23 ilo = ilo - 1 |
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454 | 455 | c |
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455 | 456 | c *** compute value at x in (t(i),t(i+1)) of jderiv-th derivative, |
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456 | 457 | c given its relevant b-spline coeffs in aj(1),...,aj(k-jderiv). |
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457 | 458 | 30 if (jderiv .eq. km1) go to 39 |
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458 | 459 | jdrvp1 = jderiv + 1 |
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459 | 460 | do 33 j=jdrvp1,km1 |
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460 | 461 | kmj = k-j |
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461 | 462 | ilo = kmj |
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462 | 463 | do 33 jj=1,kmj |
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463 | 464 | aj(jj) = (aj(jj+1)*dl(ilo) + aj(jj)*dr(jj))/(dl(ilo)+dr(jj)) |
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464 | 465 | 33 ilo = ilo - 1 |
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465 | 466 | 39 bvalue = aj(1) |
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466 | 467 | c |
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467 | 468 | 99 return |
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468 | 469 | end |
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469 | 470 | subroutine interv ( xt, lxt, x, left, mflag ) |
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470 | 471 | c from * a practical guide to splines * by C. de Boor |
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471 | 472 | computes left = max( i : xt(i) .lt. xt(lxt) .and. xt(i) .le. x ) . |
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472 | 473 | c |
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473 | 474 | c****** i n p u t ****** |
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474 | 475 | c xt.....a real sequence, of length lxt , assumed to be nondecreasing |
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475 | 476 | c lxt.....number of terms in the sequence xt . |
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476 | 477 | c x.....the point whose location with respect to the sequence xt is |
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477 | 478 | c to be determined. |
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478 | 479 | c |
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479 | 480 | c****** o u t p u t ****** |
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480 | 481 | c left, mflag.....both integers, whose value is |
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481 | 482 | c |
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482 | 483 | c 1 -1 if x .lt. xt(1) |
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483 | 484 | c i 0 if xt(i) .le. x .lt. xt(i+1) |
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484 | 485 | c i 0 if xt(i) .lt. x .eq. xt(i+1) .eq. xt(lxt) |
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485 | 486 | c i 1 if xt(i) .lt. xt(i+1) .eq. xt(lxt) .lt. x |
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486 | 487 | c |
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487 | 488 | c In particular, mflag = 0 is the 'usual' case. mflag .ne. 0 |
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488 | 489 | c indicates that x lies outside the CLOSED interval |
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489 | 490 | c xt(1) .le. y .le. xt(lxt) . The asymmetric treatment of the |
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490 | 491 | c intervals is due to the decision to make all pp functions cont- |
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491 | 492 | c inuous from the right, but, by returning mflag = 0 even if |
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492 | 493 | C x = xt(lxt), there is the option of having the computed pp function |
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493 | 494 | c continuous from the left at xt(lxt) . |
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494 | 495 | c |
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495 | 496 | c****** m e t h o d ****** |
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496 | 497 | c The program is designed to be efficient in the common situation that |
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497 | 498 | c it is called repeatedly, with x taken from an increasing or decrea- |
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498 | 499 | c sing sequence. This will happen, e.g., when a pp function is to be |
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499 | 500 | c graphed. The first guess for left is therefore taken to be the val- |
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500 | 501 | c ue returned at the previous call and stored in the l o c a l varia- |
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501 | 502 | c ble ilo . A first check ascertains that ilo .lt. lxt (this is nec- |
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502 | 503 | c essary since the present call may have nothing to do with the previ- |
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503 | 504 | c ous call). Then, if xt(ilo) .le. x .lt. xt(ilo+1), we set left = |
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504 | 505 | c ilo and are done after just three comparisons. |
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505 | 506 | c Otherwise, we repeatedly double the difference istep = ihi - ilo |
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506 | 507 | c while also moving ilo and ihi in the direction of x , until |
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507 | 508 | c xt(ilo) .le. x .lt. xt(ihi) , |
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508 | 509 | c after which we use bisection to get, in addition, ilo+1 = ihi . |
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509 | 510 | c left = ilo is then returned. |
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510 | 511 | c |
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511 | 512 | integer left,lxt,mflag, ihi,ilo,istep,middle |
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512 | 513 | real x,xt(lxt) |
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513 | 514 | data ilo /1/ |
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514 | 515 | save ilo |
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515 | 516 | ihi = ilo + 1 |
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516 | 517 | if (ihi .lt. lxt) go to 20 |
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517 | 518 | if (x .ge. xt(lxt)) go to 110 |
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518 | 519 | if (lxt .le. 1) go to 90 |
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519 | 520 | ilo = lxt - 1 |
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520 | 521 | ihi = lxt |
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521 | 522 | c |
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522 | 523 | 20 if (x .ge. xt(ihi)) go to 40 |
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523 | 524 | if (x .ge. xt(ilo)) go to 100 |
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524 | 525 | c |
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525 | 526 | c **** now x .lt. xt(ilo) . decrease ilo to capture x . |
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526 | 527 | istep = 1 |
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527 | 528 | 31 ihi = ilo |
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528 | 529 | ilo = ihi - istep |
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529 | 530 | if (ilo .le. 1) go to 35 |
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530 | 531 | if (x .ge. xt(ilo)) go to 50 |
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531 | 532 | istep = istep*2 |
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532 | 533 | go to 31 |
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533 | 534 | 35 ilo = 1 |
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534 | 535 | if (x .lt. xt(1)) go to 90 |
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535 | 536 | go to 50 |
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536 | 537 | c **** now x .ge. xt(ihi) . increase ihi to capture x . |
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537 | 538 | 40 istep = 1 |
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538 | 539 | 41 ilo = ihi |
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539 | 540 | ihi = ilo + istep |
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540 | 541 | if (ihi .ge. lxt) go to 45 |
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541 | 542 | if (x .lt. xt(ihi)) go to 50 |
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542 | 543 | istep = istep*2 |
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543 | 544 | go to 41 |
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544 | 545 | 45 if (x .ge. xt(lxt)) go to 110 |
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545 | 546 | ihi = lxt |
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546 | 547 | c |
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547 | 548 | c **** now xt(ilo) .le. x .lt. xt(ihi) . narrow the interval. |
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548 | 549 | 50 middle = (ilo + ihi)/2 |
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549 | 550 | if (middle .eq. ilo) go to 100 |
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550 | 551 | c note. it is assumed that middle = ilo in case ihi = ilo+1 . |
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551 | 552 | if (x .lt. xt(middle)) go to 53 |
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552 | 553 | ilo = middle |
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553 | 554 | go to 50 |
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554 | 555 | 53 ihi = middle |
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555 | 556 | go to 50 |
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556 | 557 | c**** set output and return. |
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557 | 558 | 90 mflag = -1 |
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558 | 559 | left = 1 |
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559 | 560 | return |
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560 | 561 | 100 mflag = 0 |
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561 | 562 | left = ilo |
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562 | 563 | return |
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563 | 564 | 110 mflag = 1 |
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564 | 565 | if (x .eq. xt(lxt)) mflag = 0 |
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565 | 566 | left = lxt |
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566 | 567 | 111 if (left .eq. 1) return |
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567 | 568 | left = left - 1 |
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568 | 569 | if (xt(left) .lt. xt(lxt)) return |
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569 | 570 | go to 111 |
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570 | 571 | end |
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