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1 SUBROUTINE ZGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO ) |
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2 * |
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3 * -- LAPACK routine (version 3.1) -- |
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4 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. |
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5 * November 2006 |
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6 * |
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7 * .. Scalar Arguments .. |
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8 INTEGER INFO, LDA, LWORK, N |
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9 * .. |
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10 * .. Array Arguments .. |
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11 INTEGER IPIV( * ) |
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12 COMPLEX*16 A( LDA, * ), WORK( * ) |
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13 * .. |
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14 * |
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15 * Purpose |
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16 * ======= |
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17 * |
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18 * ZGETRI computes the inverse of a matrix using the LU factorization |
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19 * computed by ZGETRF. |
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20 * |
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21 * This method inverts U and then computes inv(A) by solving the system |
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22 * inv(A)*L = inv(U) for inv(A). |
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23 * |
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24 * Arguments |
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25 * ========= |
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26 * |
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27 * N (input) INTEGER |
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28 * The order of the matrix A. N >= 0. |
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29 * |
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30 * A (input/output) COMPLEX*16 array, dimension (LDA,N) |
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31 * On entry, the factors L and U from the factorization |
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32 * A = P*L*U as computed by ZGETRF. |
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33 * On exit, if INFO = 0, the inverse of the original matrix A. |
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34 * |
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35 * LDA (input) INTEGER |
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36 * The leading dimension of the array A. LDA >= max(1,N). |
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37 * |
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38 * IPIV (input) INTEGER array, dimension (N) |
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39 * The pivot indices from ZGETRF; for 1<=i<=N, row i of the |
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40 * matrix was interchanged with row IPIV(i). |
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41 * |
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42 * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) |
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43 * On exit, if INFO=0, then WORK(1) returns the optimal LWORK. |
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44 * |
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45 * LWORK (input) INTEGER |
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46 * The dimension of the array WORK. LWORK >= max(1,N). |
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47 * For optimal performance LWORK >= N*NB, where NB is |
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48 * the optimal blocksize returned by ILAENV. |
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49 * |
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50 * If LWORK = -1, then a workspace query is assumed; the routine |
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51 * only calculates the optimal size of the WORK array, returns |
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52 * this value as the first entry of the WORK array, and no error |
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53 * message related to LWORK is issued by XERBLA. |
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54 * |
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55 * INFO (output) INTEGER |
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56 * = 0: successful exit |
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57 * < 0: if INFO = -i, the i-th argument had an illegal value |
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58 * > 0: if INFO = i, U(i,i) is exactly zero; the matrix is |
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59 * singular and its inverse could not be computed. |
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60 * |
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61 * ===================================================================== |
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62 * |
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63 * .. Parameters .. |
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64 COMPLEX*16 ZERO, ONE |
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65 PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ), |
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66 $ ONE = ( 1.0D+0, 0.0D+0 ) ) |
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67 * .. |
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68 * .. Local Scalars .. |
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69 LOGICAL LQUERY |
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70 INTEGER I, IWS, J, JB, JJ, JP, LDWORK, LWKOPT, NB, |
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71 $ NBMIN, NN |
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72 * .. |
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73 * .. External Functions .. |
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74 INTEGER ILAENV |
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75 EXTERNAL ILAENV |
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76 * .. |
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77 * .. External Subroutines .. |
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78 EXTERNAL XERBLA, ZGEMM, ZGEMV, ZSWAP, ZTRSM, ZTRTRI |
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79 * .. |
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80 * .. Intrinsic Functions .. |
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81 INTRINSIC MAX, MIN |
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82 * .. |
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83 * .. Executable Statements .. |
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84 * |
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85 * Test the input parameters. |
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86 * |
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87 INFO = 0 |
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88 NB = ILAENV( 1, 'ZGETRI', ' ', N, -1, -1, -1 ) |
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89 LWKOPT = N*NB |
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90 WORK( 1 ) = LWKOPT |
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91 LQUERY = ( LWORK.EQ.-1 ) |
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92 IF( N.LT.0 ) THEN |
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93 INFO = -1 |
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94 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN |
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95 INFO = -3 |
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96 ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN |
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97 INFO = -6 |
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98 END IF |
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99 IF( INFO.NE.0 ) THEN |
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100 CALL XERBLA( 'ZGETRI', -INFO ) |
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101 RETURN |
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102 ELSE IF( LQUERY ) THEN |
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103 RETURN |
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104 END IF |
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105 * |
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106 * Quick return if possible |
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107 * |
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108 IF( N.EQ.0 ) |
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109 $ RETURN |
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110 * |
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111 * Form inv(U). If INFO > 0 from ZTRTRI, then U is singular, |
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112 * and the inverse is not computed. |
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113 * |
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114 CALL ZTRTRI( 'Upper', 'Non-unit', N, A, LDA, INFO ) |
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115 IF( INFO.GT.0 ) |
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116 $ RETURN |
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117 * |
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118 NBMIN = 2 |
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119 LDWORK = N |
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120 IF( NB.GT.1 .AND. NB.LT.N ) THEN |
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121 IWS = MAX( LDWORK*NB, 1 ) |
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122 IF( LWORK.LT.IWS ) THEN |
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123 NB = LWORK / LDWORK |
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124 NBMIN = MAX( 2, ILAENV( 2, 'ZGETRI', ' ', N, -1, -1, -1 ) ) |
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125 END IF |
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126 ELSE |
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127 IWS = N |
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128 END IF |
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129 * |
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130 * Solve the equation inv(A)*L = inv(U) for inv(A). |
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131 * |
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132 IF( NB.LT.NBMIN .OR. NB.GE.N ) THEN |
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133 * |
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134 * Use unblocked code. |
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135 * |
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136 DO 20 J = N, 1, -1 |
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137 * |
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138 * Copy current column of L to WORK and replace with zeros. |
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139 * |
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140 DO 10 I = J + 1, N |
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141 WORK( I ) = A( I, J ) |
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142 A( I, J ) = ZERO |
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143 10 CONTINUE |
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144 * |
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145 * Compute current column of inv(A). |
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146 * |
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147 IF( J.LT.N ) |
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148 $ CALL ZGEMV( 'No transpose', N, N-J, -ONE, A( 1, J+1 ), |
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149 $ LDA, WORK( J+1 ), 1, ONE, A( 1, J ), 1 ) |
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150 20 CONTINUE |
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151 ELSE |
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152 * |
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153 * Use blocked code. |
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154 * |
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155 NN = ( ( N-1 ) / NB )*NB + 1 |
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156 DO 50 J = NN, 1, -NB |
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157 JB = MIN( NB, N-J+1 ) |
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158 * |
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159 * Copy current block column of L to WORK and replace with |
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160 * zeros. |
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161 * |
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162 DO 40 JJ = J, J + JB - 1 |
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163 DO 30 I = JJ + 1, N |
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164 WORK( I+( JJ-J )*LDWORK ) = A( I, JJ ) |
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165 A( I, JJ ) = ZERO |
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166 30 CONTINUE |
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167 40 CONTINUE |
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168 * |
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169 * Compute current block column of inv(A). |
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170 * |
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171 IF( J+JB.LE.N ) |
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172 $ CALL ZGEMM( 'No transpose', 'No transpose', N, JB, |
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173 $ N-J-JB+1, -ONE, A( 1, J+JB ), LDA, |
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174 $ WORK( J+JB ), LDWORK, ONE, A( 1, J ), LDA ) |
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175 CALL ZTRSM( 'Right', 'Lower', 'No transpose', 'Unit', N, JB, |
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176 $ ONE, WORK( J ), LDWORK, A( 1, J ), LDA ) |
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177 50 CONTINUE |
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178 END IF |
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179 * |
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180 * Apply column interchanges. |
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181 * |
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182 DO 60 J = N - 1, 1, -1 |
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183 JP = IPIV( J ) |
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184 IF( JP.NE.J ) |
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185 $ CALL ZSWAP( N, A( 1, J ), 1, A( 1, JP ), 1 ) |
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186 60 CONTINUE |
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187 * |
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188 WORK( 1 ) = IWS |
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189 RETURN |
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190 * |
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191 * End of ZGETRI |
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192 * |
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193 END |
