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1 SUBROUTINE ZGEBAK( JOB, SIDE, N, ILO, IHI, SCALE, M, V, LDV, |
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2 $ INFO ) |
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3 * |
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4 * -- LAPACK routine (version 2.0) -- |
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5 * Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., |
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6 * Courant Institute, Argonne National Lab, and Rice University |
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7 * September 30, 1994 |
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8 * |
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9 * .. Scalar Arguments .. |
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10 CHARACTER JOB, SIDE |
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11 INTEGER IHI, ILO, INFO, LDV, M, N |
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12 * .. |
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13 * .. Array Arguments .. |
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14 DOUBLE PRECISION SCALE( * ) |
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15 COMPLEX*16 V( LDV, * ) |
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16 * .. |
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17 * |
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18 * Purpose |
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19 * ======= |
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20 * |
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21 * ZGEBAK forms the right or left eigenvectors of a complex general |
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22 * matrix by backward transformation on the computed eigenvectors of the |
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23 * balanced matrix output by ZGEBAL. |
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24 * |
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25 * Arguments |
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26 * ========= |
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27 * |
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28 * JOB (input) CHARACTER*1 |
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29 * Specifies the type of backward transformation required: |
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30 * = 'N', do nothing, return immediately; |
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31 * = 'P', do backward transformation for permutation only; |
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32 * = 'S', do backward transformation for scaling only; |
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33 * = 'B', do backward transformations for both permutation and |
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34 * scaling. |
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35 * JOB must be the same as the argument JOB supplied to ZGEBAL. |
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36 * |
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37 * SIDE (input) CHARACTER*1 |
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38 * = 'R': V contains right eigenvectors; |
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39 * = 'L': V contains left eigenvectors. |
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40 * |
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41 * N (input) INTEGER |
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42 * The number of rows of the matrix V. N >= 0. |
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43 * |
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44 * ILO (input) INTEGER |
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45 * IHI (input) INTEGER |
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46 * The integers ILO and IHI determined by ZGEBAL. |
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47 * 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. |
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48 * |
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49 * SCALE (input) DOUBLE PRECISION array, dimension (N) |
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50 * Details of the permutation and scaling factors, as returned |
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51 * by ZGEBAL. |
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52 * |
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53 * M (input) INTEGER |
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54 * The number of columns of the matrix V. M >= 0. |
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55 * |
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56 * V (input/output) COMPLEX*16 array, dimension (LDV,M) |
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57 * On entry, the matrix of right or left eigenvectors to be |
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58 * transformed, as returned by ZHSEIN or ZTREVC. |
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59 * On exit, V is overwritten by the transformed eigenvectors. |
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60 * |
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61 * LDV (input) INTEGER |
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62 * The leading dimension of the array V. LDV >= max(1,N). |
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63 * |
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64 * INFO (output) INTEGER |
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65 * = 0: successful exit |
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66 * < 0: if INFO = -i, the i-th argument had an illegal value. |
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67 * |
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68 * ===================================================================== |
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69 * |
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70 * .. Parameters .. |
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71 DOUBLE PRECISION ONE |
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72 PARAMETER ( ONE = 1.0D+0 ) |
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73 * .. |
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74 * .. Local Scalars .. |
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75 LOGICAL LEFTV, RIGHTV |
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76 INTEGER I, II, K |
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77 DOUBLE PRECISION S |
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78 * .. |
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79 * .. External Functions .. |
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80 LOGICAL LSAME |
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81 EXTERNAL LSAME |
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82 * .. |
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83 * .. External Subroutines .. |
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84 EXTERNAL XERBLA, ZDSCAL, ZSWAP |
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85 * .. |
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86 * .. Intrinsic Functions .. |
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87 INTRINSIC MAX, MIN |
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88 * .. |
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89 * .. Executable Statements .. |
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90 * |
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91 * Decode and Test the input parameters |
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92 * |
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93 RIGHTV = LSAME( SIDE, 'R' ) |
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94 LEFTV = LSAME( SIDE, 'L' ) |
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95 * |
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96 INFO = 0 |
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97 IF( .NOT.LSAME( JOB, 'N' ) .AND. .NOT.LSAME( JOB, 'P' ) .AND. |
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98 $ .NOT.LSAME( JOB, 'S' ) .AND. .NOT.LSAME( JOB, 'B' ) ) THEN |
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99 INFO = -1 |
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100 ELSE IF( .NOT.RIGHTV .AND. .NOT.LEFTV ) THEN |
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101 INFO = -2 |
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102 ELSE IF( N.LT.0 ) THEN |
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103 INFO = -3 |
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104 ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN |
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105 INFO = -4 |
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106 ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN |
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107 INFO = -5 |
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108 ELSE IF( M.LT.0 ) THEN |
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109 INFO = -7 |
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110 ELSE IF( LDV.LT.MAX( 1, N ) ) THEN |
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111 INFO = -9 |
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112 END IF |
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113 IF( INFO.NE.0 ) THEN |
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114 CALL XERBLA( 'ZGEBAK', -INFO ) |
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115 RETURN |
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116 END IF |
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117 * |
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118 * Quick return if possible |
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119 * |
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120 IF( N.EQ.0 ) |
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121 $ RETURN |
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122 IF( M.EQ.0 ) |
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123 $ RETURN |
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124 IF( LSAME( JOB, 'N' ) ) |
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125 $ RETURN |
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126 * |
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127 IF( ILO.EQ.IHI ) |
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128 $ GO TO 30 |
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129 * |
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130 * Backward balance |
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131 * |
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132 IF( LSAME( JOB, 'S' ) .OR. LSAME( JOB, 'B' ) ) THEN |
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133 * |
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134 IF( RIGHTV ) THEN |
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135 DO 10 I = ILO, IHI |
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136 S = SCALE( I ) |
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137 CALL ZDSCAL( M, S, V( I, 1 ), LDV ) |
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138 10 CONTINUE |
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139 END IF |
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140 * |
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141 IF( LEFTV ) THEN |
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142 DO 20 I = ILO, IHI |
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143 S = ONE / SCALE( I ) |
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144 CALL ZDSCAL( M, S, V( I, 1 ), LDV ) |
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145 20 CONTINUE |
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146 END IF |
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147 * |
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148 END IF |
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149 * |
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150 * Backward permutation |
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151 * |
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152 * For I = ILO-1 step -1 until 1, |
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153 * IHI+1 step 1 until N do -- |
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154 * |
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155 30 CONTINUE |
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156 IF( LSAME( JOB, 'P' ) .OR. LSAME( JOB, 'B' ) ) THEN |
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157 IF( RIGHTV ) THEN |
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158 DO 40 II = 1, N |
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159 I = II |
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160 IF( I.GE.ILO .AND. I.LE.IHI ) |
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161 $ GO TO 40 |
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162 IF( I.LT.ILO ) |
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163 $ I = ILO - II |
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164 K = SCALE( I ) |
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165 IF( K.EQ.I ) |
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166 $ GO TO 40 |
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167 CALL ZSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV ) |
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168 40 CONTINUE |
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169 END IF |
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170 * |
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171 IF( LEFTV ) THEN |
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172 DO 50 II = 1, N |
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173 I = II |
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174 IF( I.GE.ILO .AND. I.LE.IHI ) |
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175 $ GO TO 50 |
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176 IF( I.LT.ILO ) |
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177 $ I = ILO - II |
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178 K = SCALE( I ) |
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179 IF( K.EQ.I ) |
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180 $ GO TO 50 |
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181 CALL ZSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV ) |
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182 50 CONTINUE |
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183 END IF |
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184 END IF |
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185 * |
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186 RETURN |
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187 * |
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188 * End of ZGEBAK |
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189 * |
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190 END |
