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1 SUBROUTINE DGEBAK( JOB, SIDE, N, ILO, IHI, SCALE, M, V, LDV, |
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2 $ INFO ) |
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3 * |
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7034
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4 * -- LAPACK routine (version 3.1) -- |
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5 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. |
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6 * November 2006 |
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2329
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7 * |
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8 * .. Scalar Arguments .. |
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9 CHARACTER JOB, SIDE |
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10 INTEGER IHI, ILO, INFO, LDV, M, N |
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11 * .. |
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12 * .. Array Arguments .. |
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13 DOUBLE PRECISION SCALE( * ), V( LDV, * ) |
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14 * .. |
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15 * |
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16 * Purpose |
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17 * ======= |
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18 * |
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19 * DGEBAK forms the right or left eigenvectors of a real general matrix |
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20 * by backward transformation on the computed eigenvectors of the |
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21 * balanced matrix output by DGEBAL. |
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22 * |
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23 * Arguments |
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24 * ========= |
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25 * |
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26 * JOB (input) CHARACTER*1 |
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27 * Specifies the type of backward transformation required: |
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28 * = 'N', do nothing, return immediately; |
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29 * = 'P', do backward transformation for permutation only; |
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30 * = 'S', do backward transformation for scaling only; |
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31 * = 'B', do backward transformations for both permutation and |
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32 * scaling. |
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33 * JOB must be the same as the argument JOB supplied to DGEBAL. |
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34 * |
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35 * SIDE (input) CHARACTER*1 |
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36 * = 'R': V contains right eigenvectors; |
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37 * = 'L': V contains left eigenvectors. |
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38 * |
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39 * N (input) INTEGER |
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40 * The number of rows of the matrix V. N >= 0. |
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41 * |
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42 * ILO (input) INTEGER |
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43 * IHI (input) INTEGER |
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44 * The integers ILO and IHI determined by DGEBAL. |
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45 * 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. |
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46 * |
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47 * SCALE (input) DOUBLE PRECISION array, dimension (N) |
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48 * Details of the permutation and scaling factors, as returned |
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49 * by DGEBAL. |
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50 * |
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51 * M (input) INTEGER |
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52 * The number of columns of the matrix V. M >= 0. |
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53 * |
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54 * V (input/output) DOUBLE PRECISION array, dimension (LDV,M) |
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55 * On entry, the matrix of right or left eigenvectors to be |
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56 * transformed, as returned by DHSEIN or DTREVC. |
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57 * On exit, V is overwritten by the transformed eigenvectors. |
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58 * |
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59 * LDV (input) INTEGER |
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60 * The leading dimension of the array V. LDV >= max(1,N). |
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61 * |
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62 * INFO (output) INTEGER |
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63 * = 0: successful exit |
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64 * < 0: if INFO = -i, the i-th argument had an illegal value. |
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65 * |
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66 * ===================================================================== |
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67 * |
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68 * .. Parameters .. |
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69 DOUBLE PRECISION ONE |
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70 PARAMETER ( ONE = 1.0D+0 ) |
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71 * .. |
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72 * .. Local Scalars .. |
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73 LOGICAL LEFTV, RIGHTV |
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74 INTEGER I, II, K |
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75 DOUBLE PRECISION S |
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76 * .. |
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77 * .. External Functions .. |
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78 LOGICAL LSAME |
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79 EXTERNAL LSAME |
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80 * .. |
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81 * .. External Subroutines .. |
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82 EXTERNAL DSCAL, DSWAP, XERBLA |
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83 * .. |
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84 * .. Intrinsic Functions .. |
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85 INTRINSIC MAX, MIN |
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86 * .. |
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87 * .. Executable Statements .. |
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88 * |
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89 * Decode and Test the input parameters |
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90 * |
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91 RIGHTV = LSAME( SIDE, 'R' ) |
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92 LEFTV = LSAME( SIDE, 'L' ) |
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93 * |
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94 INFO = 0 |
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95 IF( .NOT.LSAME( JOB, 'N' ) .AND. .NOT.LSAME( JOB, 'P' ) .AND. |
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96 $ .NOT.LSAME( JOB, 'S' ) .AND. .NOT.LSAME( JOB, 'B' ) ) THEN |
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97 INFO = -1 |
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98 ELSE IF( .NOT.RIGHTV .AND. .NOT.LEFTV ) THEN |
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99 INFO = -2 |
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100 ELSE IF( N.LT.0 ) THEN |
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101 INFO = -3 |
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102 ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN |
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103 INFO = -4 |
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104 ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN |
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105 INFO = -5 |
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106 ELSE IF( M.LT.0 ) THEN |
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107 INFO = -7 |
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108 ELSE IF( LDV.LT.MAX( 1, N ) ) THEN |
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109 INFO = -9 |
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110 END IF |
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111 IF( INFO.NE.0 ) THEN |
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112 CALL XERBLA( 'DGEBAK', -INFO ) |
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113 RETURN |
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114 END IF |
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115 * |
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116 * Quick return if possible |
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117 * |
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118 IF( N.EQ.0 ) |
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119 $ RETURN |
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120 IF( M.EQ.0 ) |
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121 $ RETURN |
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122 IF( LSAME( JOB, 'N' ) ) |
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123 $ RETURN |
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124 * |
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125 IF( ILO.EQ.IHI ) |
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126 $ GO TO 30 |
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127 * |
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128 * Backward balance |
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129 * |
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130 IF( LSAME( JOB, 'S' ) .OR. LSAME( JOB, 'B' ) ) THEN |
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131 * |
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132 IF( RIGHTV ) THEN |
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133 DO 10 I = ILO, IHI |
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134 S = SCALE( I ) |
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135 CALL DSCAL( M, S, V( I, 1 ), LDV ) |
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136 10 CONTINUE |
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137 END IF |
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138 * |
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139 IF( LEFTV ) THEN |
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140 DO 20 I = ILO, IHI |
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141 S = ONE / SCALE( I ) |
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142 CALL DSCAL( M, S, V( I, 1 ), LDV ) |
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143 20 CONTINUE |
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144 END IF |
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145 * |
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146 END IF |
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147 * |
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148 * Backward permutation |
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149 * |
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150 * For I = ILO-1 step -1 until 1, |
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151 * IHI+1 step 1 until N do -- |
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152 * |
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153 30 CONTINUE |
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154 IF( LSAME( JOB, 'P' ) .OR. LSAME( JOB, 'B' ) ) THEN |
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155 IF( RIGHTV ) THEN |
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156 DO 40 II = 1, N |
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157 I = II |
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158 IF( I.GE.ILO .AND. I.LE.IHI ) |
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159 $ GO TO 40 |
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160 IF( I.LT.ILO ) |
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161 $ I = ILO - II |
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162 K = SCALE( I ) |
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163 IF( K.EQ.I ) |
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164 $ GO TO 40 |
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165 CALL DSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV ) |
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166 40 CONTINUE |
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167 END IF |
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168 * |
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169 IF( LEFTV ) THEN |
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170 DO 50 II = 1, N |
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171 I = II |
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172 IF( I.GE.ILO .AND. I.LE.IHI ) |
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173 $ GO TO 50 |
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174 IF( I.LT.ILO ) |
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175 $ I = ILO - II |
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176 K = SCALE( I ) |
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177 IF( K.EQ.I ) |
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178 $ GO TO 50 |
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179 CALL DSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV ) |
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180 50 CONTINUE |
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181 END IF |
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182 END IF |
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183 * |
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184 RETURN |
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185 * |
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186 * End of DGEBAK |
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187 * |
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188 END |
