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1 SUBROUTINE PREPJ (NEQ, Y, YH, NYH, EWT, FTEM, SAVF, WM, IWM, |
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2 1 F, JAC, IERR) |
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3 CLLL. OPTIMIZE |
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4 EXTERNAL F, JAC |
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5 INTEGER NEQ, NYH, IWM |
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6 INTEGER IOWND, IOWNS, |
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7 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, METH, MITER, |
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8 2 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU |
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9 INTEGER I, I1, I2, IER, II, J, J1, JJ, LENP, |
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10 1 MBA, MBAND, MEB1, MEBAND, ML, ML3, MU, NP1 |
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11 DOUBLE PRECISION Y, YH, EWT, FTEM, SAVF, WM |
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12 DOUBLE PRECISION ROWNS, |
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13 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND |
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14 DOUBLE PRECISION CON, DI, FAC, HL0, R, R0, SRUR, YI, YJ, YJJ, |
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15 1 VNORM |
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16 DIMENSION NEQ(*), Y(*), YH(NYH,*), EWT(*), FTEM(*), SAVF(*), |
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17 1 WM(*), IWM(*) |
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18 COMMON /LS0001/ ROWNS(209), |
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19 2 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, |
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20 3 IOWND(14), IOWNS(6), |
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21 4 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, METH, MITER, |
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22 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU |
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23 C----------------------------------------------------------------------- |
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24 C PREPJ IS CALLED BY STODE TO COMPUTE AND PROCESS THE MATRIX |
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25 C P = I - H*EL(1)*J , WHERE J IS AN APPROXIMATION TO THE JACOBIAN. |
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26 C HERE J IS COMPUTED BY THE USER-SUPPLIED ROUTINE JAC IF |
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27 C MITER = 1 OR 4, OR BY FINITE DIFFERENCING IF MITER = 2, 3, OR 5. |
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28 C IF MITER = 3, A DIAGONAL APPROXIMATION TO J IS USED. |
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29 C J IS STORED IN WM AND REPLACED BY P. IF MITER .NE. 3, P IS THEN |
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30 C SUBJECTED TO LU DECOMPOSITION IN PREPARATION FOR LATER SOLUTION |
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31 C OF LINEAR SYSTEMS WITH P AS COEFFICIENT MATRIX. THIS IS DONE |
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32 C BY DGETRF IF MITER = 1 OR 2, AND BY DGBTRF IF MITER = 4 OR 5. |
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33 C |
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34 C IN ADDITION TO VARIABLES DESCRIBED PREVIOUSLY, COMMUNICATION |
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35 C WITH PREPJ USES THE FOLLOWING.. |
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36 C Y = ARRAY CONTAINING PREDICTED VALUES ON ENTRY. |
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37 C FTEM = WORK ARRAY OF LENGTH N (ACOR IN STODE). |
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38 C SAVF = ARRAY CONTAINING F EVALUATED AT PREDICTED Y. |
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39 C WM = REAL WORK SPACE FOR MATRICES. ON OUTPUT IT CONTAINS THE |
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40 C INVERSE DIAGONAL MATRIX IF MITER = 3 AND THE LU DECOMPOSITION |
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41 C OF P IF MITER IS 1, 2 , 4, OR 5. |
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42 C STORAGE OF MATRIX ELEMENTS STARTS AT WM(3). |
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43 C WM ALSO CONTAINS THE FOLLOWING MATRIX-RELATED DATA.. |
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44 C WM(1) = SQRT(UROUND), USED IN NUMERICAL JACOBIAN INCREMENTS. |
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45 C WM(2) = H*EL0, SAVED FOR LATER USE IF MITER = 3. |
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46 C IWM = INTEGER WORK SPACE CONTAINING PIVOT INFORMATION, STARTING AT |
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47 C IWM(21), IF MITER IS 1, 2, 4, OR 5. IWM ALSO CONTAINS BAND |
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48 C PARAMETERS ML = IWM(1) AND MU = IWM(2) IF MITER IS 4 OR 5. |
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49 C EL0 = EL(1) (INPUT). |
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50 C IERPJ = OUTPUT ERROR FLAG, = 0 IF NO TROUBLE, .GT. 0 IF |
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51 C P MATRIX FOUND TO BE SINGULAR. |
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52 C JCUR = OUTPUT FLAG = 1 TO INDICATE THAT THE JACOBIAN MATRIX |
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53 C (OR APPROXIMATION) IS NOW CURRENT. |
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54 C THIS ROUTINE ALSO USES THE COMMON VARIABLES EL0, H, TN, UROUND, |
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55 C MITER, N, NFE, AND NJE. |
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56 C----------------------------------------------------------------------- |
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57 NJE = NJE + 1 |
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58 IERPJ = 0 |
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59 JCUR = 1 |
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60 HL0 = H*EL0 |
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61 GO TO (100, 200, 300, 400, 500), MITER |
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62 C IF MITER = 1, CALL JAC AND MULTIPLY BY SCALAR. ----------------------- |
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63 100 LENP = N*N |
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64 DO 110 I = 1,LENP |
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65 110 WM(I+2) = 0.0D0 |
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66 CALL JAC (NEQ, TN, Y, 0, 0, WM(3), N) |
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67 CON = -HL0 |
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68 DO 120 I = 1,LENP |
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69 120 WM(I+2) = WM(I+2)*CON |
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70 GO TO 240 |
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71 C IF MITER = 2, MAKE N CALLS TO F TO APPROXIMATE J. -------------------- |
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72 200 FAC = VNORM (N, SAVF, EWT) |
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73 R0 = 1000.0D0*DABS(H)*UROUND*DBLE(N)*FAC |
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74 IF (R0 .EQ. 0.0D0) R0 = 1.0D0 |
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75 SRUR = WM(1) |
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76 J1 = 2 |
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77 DO 230 J = 1,N |
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78 YJ = Y(J) |
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79 R = DMAX1(SRUR*DABS(YJ),R0/EWT(J)) |
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80 Y(J) = Y(J) + R |
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81 FAC = -HL0/R |
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82 IERR = 0 |
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83 CALL F (NEQ, TN, Y, FTEM, IERR) |
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84 IF (IERR .LT. 0) RETURN |
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85 DO 220 I = 1,N |
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86 220 WM(I+J1) = (FTEM(I) - SAVF(I))*FAC |
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87 Y(J) = YJ |
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88 J1 = J1 + N |
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89 230 CONTINUE |
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90 NFE = NFE + N |
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91 C ADD IDENTITY MATRIX. ------------------------------------------------- |
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92 240 J = 3 |
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93 NP1 = N + 1 |
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94 DO 250 I = 1,N |
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95 WM(J) = WM(J) + 1.0D0 |
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96 250 J = J + NP1 |
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97 C DO LU DECOMPOSITION ON P. -------------------------------------------- |
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98 CALL DGETRF ( N, N, WM(3), N, IWM(21), IER) |
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99 IF (IER .NE. 0) IERPJ = 1 |
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100 RETURN |
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101 C IF MITER = 3, CONSTRUCT A DIAGONAL APPROXIMATION TO J AND P. --------- |
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102 300 WM(2) = HL0 |
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103 R = EL0*0.1D0 |
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104 DO 310 I = 1,N |
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105 310 Y(I) = Y(I) + R*(H*SAVF(I) - YH(I,2)) |
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106 IERR = 0 |
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107 CALL F (NEQ, TN, Y, WM(3), IERR) |
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108 IF (IERR .LT. 0) RETURN |
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109 NFE = NFE + 1 |
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110 DO 320 I = 1,N |
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111 R0 = H*SAVF(I) - YH(I,2) |
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112 DI = 0.1D0*R0 - H*(WM(I+2) - SAVF(I)) |
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113 WM(I+2) = 1.0D0 |
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114 IF (DABS(R0) .LT. UROUND/EWT(I)) GO TO 320 |
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115 IF (DABS(DI) .EQ. 0.0D0) GO TO 330 |
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116 WM(I+2) = 0.1D0*R0/DI |
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117 320 CONTINUE |
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118 RETURN |
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119 330 IERPJ = 1 |
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120 RETURN |
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121 C IF MITER = 4, CALL JAC AND MULTIPLY BY SCALAR. ----------------------- |
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122 400 ML = IWM(1) |
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123 MU = IWM(2) |
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124 ML3 = ML + 3 |
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125 MBAND = ML + MU + 1 |
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126 MEBAND = MBAND + ML |
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127 LENP = MEBAND*N |
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128 DO 410 I = 1,LENP |
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129 410 WM(I+2) = 0.0D0 |
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130 CALL JAC (NEQ, TN, Y, ML, MU, WM(ML3), MEBAND) |
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131 CON = -HL0 |
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132 DO 420 I = 1,LENP |
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133 420 WM(I+2) = WM(I+2)*CON |
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134 GO TO 570 |
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135 C IF MITER = 5, MAKE MBAND CALLS TO F TO APPROXIMATE J. ---------------- |
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136 500 ML = IWM(1) |
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137 MU = IWM(2) |
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138 MBAND = ML + MU + 1 |
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139 MBA = MIN0(MBAND,N) |
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140 MEBAND = MBAND + ML |
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141 MEB1 = MEBAND - 1 |
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142 SRUR = WM(1) |
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143 FAC = VNORM (N, SAVF, EWT) |
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144 R0 = 1000.0D0*DABS(H)*UROUND*DBLE(N)*FAC |
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145 IF (R0 .EQ. 0.0D0) R0 = 1.0D0 |
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146 DO 560 J = 1,MBA |
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147 DO 530 I = J,N,MBAND |
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148 YI = Y(I) |
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149 R = DMAX1(SRUR*DABS(YI),R0/EWT(I)) |
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150 530 Y(I) = Y(I) + R |
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151 IERR = 0 |
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152 CALL F (NEQ, TN, Y, FTEM, IERR) |
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153 IF (IERR .LT. 0) RETURN |
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154 DO 550 JJ = J,N,MBAND |
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155 Y(JJ) = YH(JJ,1) |
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156 YJJ = Y(JJ) |
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157 R = DMAX1(SRUR*DABS(YJJ),R0/EWT(JJ)) |
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158 FAC = -HL0/R |
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159 I1 = MAX0(JJ-MU,1) |
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160 I2 = MIN0(JJ+ML,N) |
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161 II = JJ*MEB1 - ML + 2 |
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162 DO 540 I = I1,I2 |
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163 540 WM(II+I) = (FTEM(I) - SAVF(I))*FAC |
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164 550 CONTINUE |
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165 560 CONTINUE |
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166 NFE = NFE + MBA |
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167 C ADD IDENTITY MATRIX. ------------------------------------------------- |
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168 570 II = MBAND + 2 |
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169 DO 580 I = 1,N |
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170 WM(II) = WM(II) + 1.0D0 |
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171 580 II = II + MEBAND |
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172 C DO LU DECOMPOSITION OF P. -------------------------------------------- |
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173 CALL DGBTRF ( N, N, ML, MU, WM(3), MEBAND, IWM(21), IER) |
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174 IF (IER .NE. 0) IERPJ = 1 |
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175 RETURN |
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176 C----------------------- END OF SUBROUTINE PREPJ ----------------------- |
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177 END |
