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1 SUBROUTINE ZUNGQL( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) |
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2 * |
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3 * -- LAPACK routine (version 3.0) -- |
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4 * Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., |
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5 * Courant Institute, Argonne National Lab, and Rice University |
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6 * June 30, 1999 |
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7 * |
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8 * .. Scalar Arguments .. |
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9 INTEGER INFO, K, LDA, LWORK, M, N |
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10 * .. |
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11 * .. Array Arguments .. |
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12 COMPLEX*16 A( LDA, * ), TAU( * ), 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 * ZUNGQL generates an M-by-N complex matrix Q with orthonormal columns, |
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19 * which is defined as the last N columns of a product of K elementary |
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20 * reflectors of order M |
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21 * |
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22 * Q = H(k) . . . H(2) H(1) |
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23 * |
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24 * as returned by ZGEQLF. |
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25 * |
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26 * Arguments |
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27 * ========= |
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28 * |
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29 * M (input) INTEGER |
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30 * The number of rows of the matrix Q. M >= 0. |
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31 * |
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32 * N (input) INTEGER |
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33 * The number of columns of the matrix Q. M >= N >= 0. |
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34 * |
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35 * K (input) INTEGER |
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36 * The number of elementary reflectors whose product defines the |
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37 * matrix Q. N >= K >= 0. |
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38 * |
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39 * A (input/output) COMPLEX*16 array, dimension (LDA,N) |
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40 * On entry, the (n-k+i)-th column must contain the vector which |
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41 * defines the elementary reflector H(i), for i = 1,2,...,k, as |
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42 * returned by ZGEQLF in the last k columns of its array |
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43 * argument A. |
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44 * On exit, the M-by-N matrix Q. |
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45 * |
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46 * LDA (input) INTEGER |
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47 * The first dimension of the array A. LDA >= max(1,M). |
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48 * |
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49 * TAU (input) COMPLEX*16 array, dimension (K) |
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50 * TAU(i) must contain the scalar factor of the elementary |
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51 * reflector H(i), as returned by ZGEQLF. |
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52 * |
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53 * WORK (workspace/output) COMPLEX*16 array, dimension (LWORK) |
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54 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
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55 * |
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56 * LWORK (input) INTEGER |
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57 * The dimension of the array WORK. LWORK >= max(1,N). |
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58 * For optimum performance LWORK >= N*NB, where NB is the |
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59 * optimal blocksize. |
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60 * |
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61 * If LWORK = -1, then a workspace query is assumed; the routine |
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62 * only calculates the optimal size of the WORK array, returns |
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63 * this value as the first entry of the WORK array, and no error |
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64 * message related to LWORK is issued by XERBLA. |
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65 * |
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66 * INFO (output) INTEGER |
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67 * = 0: successful exit |
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68 * < 0: if INFO = -i, the i-th argument has an illegal value |
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69 * |
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70 * ===================================================================== |
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71 * |
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72 * .. Parameters .. |
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73 COMPLEX*16 ZERO |
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74 PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) |
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75 * .. |
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76 * .. Local Scalars .. |
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77 LOGICAL LQUERY |
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78 INTEGER I, IB, IINFO, IWS, J, KK, L, LDWORK, LWKOPT, |
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79 $ NB, NBMIN, NX |
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80 * .. |
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81 * .. External Subroutines .. |
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82 EXTERNAL XERBLA, ZLARFB, ZLARFT, ZUNG2L |
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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 * .. External Functions .. |
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88 INTEGER ILAENV |
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89 EXTERNAL ILAENV |
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90 * .. |
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91 * .. Executable Statements .. |
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92 * |
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93 * Test the input arguments |
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94 * |
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95 INFO = 0 |
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96 NB = ILAENV( 1, 'ZUNGQL', ' ', M, N, K, -1 ) |
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97 LWKOPT = MAX( 1, N )*NB |
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98 WORK( 1 ) = LWKOPT |
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99 LQUERY = ( LWORK.EQ.-1 ) |
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100 IF( M.LT.0 ) THEN |
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101 INFO = -1 |
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102 ELSE IF( N.LT.0 .OR. N.GT.M ) THEN |
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103 INFO = -2 |
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104 ELSE IF( K.LT.0 .OR. K.GT.N ) THEN |
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105 INFO = -3 |
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106 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN |
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107 INFO = -5 |
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108 ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN |
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109 INFO = -8 |
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110 END IF |
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111 IF( INFO.NE.0 ) THEN |
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112 CALL XERBLA( 'ZUNGQL', -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 IF( N.LE.0 ) THEN |
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121 WORK( 1 ) = 1 |
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122 RETURN |
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123 END IF |
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124 * |
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125 NBMIN = 2 |
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126 NX = 0 |
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127 IWS = N |
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128 IF( NB.GT.1 .AND. NB.LT.K ) THEN |
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129 * |
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130 * Determine when to cross over from blocked to unblocked code. |
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131 * |
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132 NX = MAX( 0, ILAENV( 3, 'ZUNGQL', ' ', M, N, K, -1 ) ) |
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133 IF( NX.LT.K ) THEN |
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134 * |
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135 * Determine if workspace is large enough for blocked code. |
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136 * |
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137 LDWORK = N |
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138 IWS = LDWORK*NB |
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139 IF( LWORK.LT.IWS ) THEN |
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140 * |
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141 * Not enough workspace to use optimal NB: reduce NB and |
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142 * determine the minimum value of NB. |
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143 * |
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144 NB = LWORK / LDWORK |
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145 NBMIN = MAX( 2, ILAENV( 2, 'ZUNGQL', ' ', M, N, K, -1 ) ) |
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146 END IF |
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147 END IF |
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148 END IF |
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149 * |
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150 IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN |
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151 * |
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152 * Use blocked code after the first block. |
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153 * The last kk columns are handled by the block method. |
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154 * |
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155 KK = MIN( K, ( ( K-NX+NB-1 ) / NB )*NB ) |
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156 * |
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157 * Set A(m-kk+1:m,1:n-kk) to zero. |
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158 * |
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159 DO 20 J = 1, N - KK |
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160 DO 10 I = M - KK + 1, M |
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161 A( I, J ) = ZERO |
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162 10 CONTINUE |
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163 20 CONTINUE |
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164 ELSE |
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165 KK = 0 |
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166 END IF |
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167 * |
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168 * Use unblocked code for the first or only block. |
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169 * |
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170 CALL ZUNG2L( M-KK, N-KK, K-KK, A, LDA, TAU, WORK, IINFO ) |
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171 * |
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172 IF( KK.GT.0 ) THEN |
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173 * |
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174 * Use blocked code |
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175 * |
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176 DO 50 I = K - KK + 1, K, NB |
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177 IB = MIN( NB, K-I+1 ) |
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178 IF( N-K+I.GT.1 ) THEN |
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179 * |
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180 * Form the triangular factor of the block reflector |
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181 * H = H(i+ib-1) . . . H(i+1) H(i) |
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182 * |
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183 CALL ZLARFT( 'Backward', 'Columnwise', M-K+I+IB-1, IB, |
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184 $ A( 1, N-K+I ), LDA, TAU( I ), WORK, LDWORK ) |
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185 * |
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186 * Apply H to A(1:m-k+i+ib-1,1:n-k+i-1) from the left |
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187 * |
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188 CALL ZLARFB( 'Left', 'No transpose', 'Backward', |
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189 $ 'Columnwise', M-K+I+IB-1, N-K+I-1, IB, |
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190 $ A( 1, N-K+I ), LDA, WORK, LDWORK, A, LDA, |
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191 $ WORK( IB+1 ), LDWORK ) |
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192 END IF |
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193 * |
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194 * Apply H to rows 1:m-k+i+ib-1 of current block |
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195 * |
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196 CALL ZUNG2L( M-K+I+IB-1, IB, IB, A( 1, N-K+I ), LDA, |
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197 $ TAU( I ), WORK, IINFO ) |
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198 * |
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199 * Set rows m-k+i+ib:m of current block to zero |
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200 * |
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201 DO 40 J = N - K + I, N - K + I + IB - 1 |
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202 DO 30 L = M - K + I + IB, M |
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203 A( L, J ) = ZERO |
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204 30 CONTINUE |
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205 40 CONTINUE |
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206 50 CONTINUE |
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207 END IF |
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208 * |
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209 WORK( 1 ) = IWS |
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210 RETURN |
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211 * |
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212 * End of ZUNGQL |
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213 * |
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214 END |
