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1 SUBROUTINE ZGELQF( M, N, A, LDA, TAU, 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, M, N |
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9 * .. |
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10 * .. Array Arguments .. |
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11 COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) |
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12 * .. |
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13 * |
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14 * Purpose |
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15 * ======= |
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16 * |
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17 * ZGELQF computes an LQ factorization of a complex M-by-N matrix A: |
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18 * A = L * Q. |
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19 * |
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20 * Arguments |
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21 * ========= |
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22 * |
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23 * M (input) INTEGER |
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24 * The number of rows of the matrix A. M >= 0. |
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25 * |
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26 * N (input) INTEGER |
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27 * The number of columns of the matrix A. N >= 0. |
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28 * |
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29 * A (input/output) COMPLEX*16 array, dimension (LDA,N) |
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30 * On entry, the M-by-N matrix A. |
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31 * On exit, the elements on and below the diagonal of the array |
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32 * contain the m-by-min(m,n) lower trapezoidal matrix L (L is |
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33 * lower triangular if m <= n); the elements above the diagonal, |
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34 * with the array TAU, represent the unitary matrix Q as a |
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35 * product of elementary reflectors (see Further Details). |
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36 * |
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37 * LDA (input) INTEGER |
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38 * The leading dimension of the array A. LDA >= max(1,M). |
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39 * |
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40 * TAU (output) COMPLEX*16 array, dimension (min(M,N)) |
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41 * The scalar factors of the elementary reflectors (see Further |
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42 * Details). |
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43 * |
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44 * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) |
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45 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
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46 * |
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47 * LWORK (input) INTEGER |
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48 * The dimension of the array WORK. LWORK >= max(1,M). |
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49 * For optimum performance LWORK >= M*NB, where NB is the |
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50 * optimal blocksize. |
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51 * |
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52 * If LWORK = -1, then a workspace query is assumed; the routine |
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53 * only calculates the optimal size of the WORK array, returns |
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54 * this value as the first entry of the WORK array, and no error |
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55 * message related to LWORK is issued by XERBLA. |
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56 * |
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57 * INFO (output) INTEGER |
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58 * = 0: successful exit |
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59 * < 0: if INFO = -i, the i-th argument had an illegal value |
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60 * |
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61 * Further Details |
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62 * =============== |
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63 * |
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64 * The matrix Q is represented as a product of elementary reflectors |
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65 * |
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66 * Q = H(k)' . . . H(2)' H(1)', where k = min(m,n). |
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67 * |
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68 * Each H(i) has the form |
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69 * |
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70 * H(i) = I - tau * v * v' |
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71 * |
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72 * where tau is a complex scalar, and v is a complex vector with |
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73 * v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in |
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74 * A(i,i+1:n), and tau in TAU(i). |
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75 * |
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76 * ===================================================================== |
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77 * |
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78 * .. Local Scalars .. |
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79 LOGICAL LQUERY |
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80 INTEGER I, IB, IINFO, IWS, K, LDWORK, LWKOPT, NB, |
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81 $ NBMIN, NX |
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82 * .. |
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83 * .. External Subroutines .. |
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84 EXTERNAL XERBLA, ZGELQ2, ZLARFB, ZLARFT |
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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 * .. External Functions .. |
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90 INTEGER ILAENV |
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91 EXTERNAL ILAENV |
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92 * .. |
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93 * .. Executable Statements .. |
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94 * |
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95 * Test the input arguments |
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96 * |
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97 INFO = 0 |
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98 NB = ILAENV( 1, 'ZGELQF', ' ', M, N, -1, -1 ) |
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99 LWKOPT = M*NB |
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100 WORK( 1 ) = LWKOPT |
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101 LQUERY = ( LWORK.EQ.-1 ) |
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102 IF( M.LT.0 ) THEN |
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103 INFO = -1 |
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104 ELSE IF( N.LT.0 ) THEN |
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105 INFO = -2 |
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106 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN |
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107 INFO = -4 |
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108 ELSE IF( LWORK.LT.MAX( 1, M ) .AND. .NOT.LQUERY ) THEN |
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109 INFO = -7 |
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110 END IF |
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111 IF( INFO.NE.0 ) THEN |
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112 CALL XERBLA( 'ZGELQF', -INFO ) |
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113 RETURN |
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114 ELSE IF( LQUERY ) THEN |
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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 K = MIN( M, N ) |
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121 IF( K.EQ.0 ) THEN |
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122 WORK( 1 ) = 1 |
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123 RETURN |
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124 END IF |
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125 * |
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126 NBMIN = 2 |
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127 NX = 0 |
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128 IWS = M |
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129 IF( NB.GT.1 .AND. NB.LT.K ) THEN |
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130 * |
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131 * Determine when to cross over from blocked to unblocked code. |
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132 * |
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133 NX = MAX( 0, ILAENV( 3, 'ZGELQF', ' ', M, N, -1, -1 ) ) |
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134 IF( NX.LT.K ) THEN |
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135 * |
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136 * Determine if workspace is large enough for blocked code. |
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137 * |
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138 LDWORK = M |
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139 IWS = LDWORK*NB |
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140 IF( LWORK.LT.IWS ) THEN |
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141 * |
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142 * Not enough workspace to use optimal NB: reduce NB and |
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143 * determine the minimum value of NB. |
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144 * |
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145 NB = LWORK / LDWORK |
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146 NBMIN = MAX( 2, ILAENV( 2, 'ZGELQF', ' ', M, N, -1, |
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147 $ -1 ) ) |
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148 END IF |
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149 END IF |
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150 END IF |
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151 * |
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152 IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN |
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153 * |
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154 * Use blocked code initially |
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155 * |
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156 DO 10 I = 1, K - NX, NB |
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157 IB = MIN( K-I+1, NB ) |
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158 * |
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159 * Compute the LQ factorization of the current block |
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160 * A(i:i+ib-1,i:n) |
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161 * |
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162 CALL ZGELQ2( IB, N-I+1, A( I, I ), LDA, TAU( I ), WORK, |
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163 $ IINFO ) |
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164 IF( I+IB.LE.M ) THEN |
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165 * |
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166 * Form the triangular factor of the block reflector |
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167 * H = H(i) H(i+1) . . . H(i+ib-1) |
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168 * |
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169 CALL ZLARFT( 'Forward', 'Rowwise', N-I+1, IB, A( I, I ), |
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170 $ LDA, TAU( I ), WORK, LDWORK ) |
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171 * |
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172 * Apply H to A(i+ib:m,i:n) from the right |
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173 * |
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174 CALL ZLARFB( 'Right', 'No transpose', 'Forward', |
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175 $ 'Rowwise', M-I-IB+1, N-I+1, IB, A( I, I ), |
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176 $ LDA, WORK, LDWORK, A( I+IB, I ), LDA, |
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177 $ WORK( IB+1 ), LDWORK ) |
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178 END IF |
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179 10 CONTINUE |
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180 ELSE |
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181 I = 1 |
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182 END IF |
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183 * |
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184 * Use unblocked code to factor the last or only block. |
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185 * |
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186 IF( I.LE.K ) |
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187 $ CALL ZGELQ2( M-I+1, N-I+1, A( I, I ), LDA, TAU( I ), WORK, |
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188 $ IINFO ) |
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189 * |
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190 WORK( 1 ) = IWS |
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191 RETURN |
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192 * |
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193 * End of ZGELQF |
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194 * |
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195 END |
