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1 SUBROUTINE DORML2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, |
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2 $ WORK, 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 * February 29, 1992 |
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8 * |
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9 * .. Scalar Arguments .. |
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10 CHARACTER SIDE, TRANS |
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11 INTEGER INFO, K, LDA, LDC, M, N |
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12 * .. |
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13 * .. Array Arguments .. |
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14 DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) |
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15 * .. |
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16 * |
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17 * Purpose |
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18 * ======= |
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19 * |
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20 * DORML2 overwrites the general real m by n matrix C with |
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21 * |
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22 * Q * C if SIDE = 'L' and TRANS = 'N', or |
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23 * |
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24 * Q'* C if SIDE = 'L' and TRANS = 'T', or |
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25 * |
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26 * C * Q if SIDE = 'R' and TRANS = 'N', or |
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27 * |
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28 * C * Q' if SIDE = 'R' and TRANS = 'T', |
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29 * |
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30 * where Q is a real orthogonal matrix defined as the product of k |
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31 * elementary reflectors |
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32 * |
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33 * Q = H(k) . . . H(2) H(1) |
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34 * |
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35 * as returned by DGELQF. Q is of order m if SIDE = 'L' and of order n |
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36 * if SIDE = 'R'. |
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37 * |
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38 * Arguments |
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39 * ========= |
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40 * |
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41 * SIDE (input) CHARACTER*1 |
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42 * = 'L': apply Q or Q' from the Left |
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43 * = 'R': apply Q or Q' from the Right |
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44 * |
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45 * TRANS (input) CHARACTER*1 |
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46 * = 'N': apply Q (No transpose) |
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47 * = 'T': apply Q' (Transpose) |
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48 * |
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49 * M (input) INTEGER |
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50 * The number of rows of the matrix C. M >= 0. |
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51 * |
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52 * N (input) INTEGER |
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53 * The number of columns of the matrix C. N >= 0. |
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54 * |
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55 * K (input) INTEGER |
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56 * The number of elementary reflectors whose product defines |
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57 * the matrix Q. |
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58 * If SIDE = 'L', M >= K >= 0; |
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59 * if SIDE = 'R', N >= K >= 0. |
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60 * |
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61 * A (input) DOUBLE PRECISION array, dimension |
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62 * (LDA,M) if SIDE = 'L', |
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63 * (LDA,N) if SIDE = 'R' |
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64 * The i-th row must contain the vector which defines the |
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65 * elementary reflector H(i), for i = 1,2,...,k, as returned by |
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66 * DGELQF in the first k rows of its array argument A. |
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67 * A is modified by the routine but restored on exit. |
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68 * |
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69 * LDA (input) INTEGER |
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70 * The leading dimension of the array A. LDA >= max(1,K). |
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71 * |
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72 * TAU (input) DOUBLE PRECISION array, dimension (K) |
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73 * TAU(i) must contain the scalar factor of the elementary |
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74 * reflector H(i), as returned by DGELQF. |
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75 * |
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76 * C (input/output) DOUBLE PRECISION array, dimension (LDC,N) |
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77 * On entry, the m by n matrix C. |
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78 * On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q. |
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79 * |
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80 * LDC (input) INTEGER |
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81 * The leading dimension of the array C. LDC >= max(1,M). |
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82 * |
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83 * WORK (workspace) DOUBLE PRECISION array, dimension |
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84 * (N) if SIDE = 'L', |
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85 * (M) if SIDE = 'R' |
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86 * |
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87 * INFO (output) INTEGER |
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88 * = 0: successful exit |
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89 * < 0: if INFO = -i, the i-th argument had an illegal value |
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90 * |
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91 * ===================================================================== |
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92 * |
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93 * .. Parameters .. |
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94 DOUBLE PRECISION ONE |
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95 PARAMETER ( ONE = 1.0D+0 ) |
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96 * .. |
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97 * .. Local Scalars .. |
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98 LOGICAL LEFT, NOTRAN |
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99 INTEGER I, I1, I2, I3, IC, JC, MI, NI, NQ |
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100 DOUBLE PRECISION AII |
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101 * .. |
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102 * .. External Functions .. |
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103 LOGICAL LSAME |
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104 EXTERNAL LSAME |
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105 * .. |
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106 * .. External Subroutines .. |
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107 EXTERNAL DLARF, XERBLA |
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108 * .. |
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109 * .. Intrinsic Functions .. |
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110 INTRINSIC MAX |
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111 * .. |
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112 * .. Executable Statements .. |
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113 * |
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114 * Test the input arguments |
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115 * |
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116 INFO = 0 |
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117 LEFT = LSAME( SIDE, 'L' ) |
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118 NOTRAN = LSAME( TRANS, 'N' ) |
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119 * |
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120 * NQ is the order of Q |
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121 * |
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122 IF( LEFT ) THEN |
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123 NQ = M |
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124 ELSE |
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125 NQ = N |
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126 END IF |
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127 IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN |
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128 INFO = -1 |
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129 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN |
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130 INFO = -2 |
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131 ELSE IF( M.LT.0 ) THEN |
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132 INFO = -3 |
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133 ELSE IF( N.LT.0 ) THEN |
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134 INFO = -4 |
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135 ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN |
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136 INFO = -5 |
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137 ELSE IF( LDA.LT.MAX( 1, K ) ) THEN |
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138 INFO = -7 |
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139 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN |
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140 INFO = -10 |
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141 END IF |
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142 IF( INFO.NE.0 ) THEN |
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143 CALL XERBLA( 'DORML2', -INFO ) |
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144 RETURN |
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145 END IF |
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146 * |
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147 * Quick return if possible |
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148 * |
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149 IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) |
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150 $ RETURN |
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151 * |
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152 IF( ( LEFT .AND. NOTRAN ) .OR. ( .NOT.LEFT .AND. .NOT.NOTRAN ) ) |
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153 $ THEN |
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154 I1 = 1 |
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155 I2 = K |
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156 I3 = 1 |
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157 ELSE |
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158 I1 = K |
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159 I2 = 1 |
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160 I3 = -1 |
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161 END IF |
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162 * |
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163 IF( LEFT ) THEN |
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164 NI = N |
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165 JC = 1 |
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166 ELSE |
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167 MI = M |
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168 IC = 1 |
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169 END IF |
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170 * |
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171 DO 10 I = I1, I2, I3 |
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172 IF( LEFT ) THEN |
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173 * |
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174 * H(i) is applied to C(i:m,1:n) |
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175 * |
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176 MI = M - I + 1 |
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177 IC = I |
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178 ELSE |
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179 * |
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180 * H(i) is applied to C(1:m,i:n) |
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181 * |
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182 NI = N - I + 1 |
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183 JC = I |
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184 END IF |
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185 * |
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186 * Apply H(i) |
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187 * |
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188 AII = A( I, I ) |
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189 A( I, I ) = ONE |
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190 CALL DLARF( SIDE, MI, NI, A( I, I ), LDA, TAU( I ), |
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191 $ C( IC, JC ), LDC, WORK ) |
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192 A( I, I ) = AII |
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193 10 CONTINUE |
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194 RETURN |
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195 * |
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196 * End of DORML2 |
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197 * |
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198 END |
