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1 SUBROUTINE DORGBR( VECT, 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 CHARACTER VECT |
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10 INTEGER INFO, K, LDA, LWORK, M, N |
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11 * .. |
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12 * .. Array Arguments .. |
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13 DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) |
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14 * .. |
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15 * |
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16 * Purpose |
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17 * ======= |
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18 * |
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19 * DORGBR generates one of the real orthogonal matrices Q or P**T |
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20 * determined by DGEBRD when reducing a real matrix A to bidiagonal |
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21 * form: A = Q * B * P**T. Q and P**T are defined as products of |
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22 * elementary reflectors H(i) or G(i) respectively. |
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23 * |
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24 * If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q |
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25 * is of order M: |
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26 * if m >= k, Q = H(1) H(2) . . . H(k) and DORGBR returns the first n |
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27 * columns of Q, where m >= n >= k; |
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28 * if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR returns Q as an |
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29 * M-by-M matrix. |
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30 * |
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31 * If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T |
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32 * is of order N: |
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33 * if k < n, P**T = G(k) . . . G(2) G(1) and DORGBR returns the first m |
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34 * rows of P**T, where n >= m >= k; |
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35 * if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR returns P**T as |
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36 * an N-by-N matrix. |
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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 * VECT (input) CHARACTER*1 |
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42 * Specifies whether the matrix Q or the matrix P**T is |
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43 * required, as defined in the transformation applied by DGEBRD: |
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44 * = 'Q': generate Q; |
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45 * = 'P': generate P**T. |
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46 * |
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47 * M (input) INTEGER |
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48 * The number of rows of the matrix Q or P**T to be returned. |
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49 * M >= 0. |
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50 * |
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51 * N (input) INTEGER |
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52 * The number of columns of the matrix Q or P**T to be returned. |
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53 * N >= 0. |
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54 * If VECT = 'Q', M >= N >= min(M,K); |
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55 * if VECT = 'P', N >= M >= min(N,K). |
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56 * |
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57 * K (input) INTEGER |
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58 * If VECT = 'Q', the number of columns in the original M-by-K |
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59 * matrix reduced by DGEBRD. |
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60 * If VECT = 'P', the number of rows in the original K-by-N |
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61 * matrix reduced by DGEBRD. |
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62 * K >= 0. |
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63 * |
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64 * A (input/output) DOUBLE PRECISION array, dimension (LDA,N) |
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65 * On entry, the vectors which define the elementary reflectors, |
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66 * as returned by DGEBRD. |
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67 * On exit, the M-by-N matrix Q or P**T. |
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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,M). |
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71 * |
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72 * TAU (input) DOUBLE PRECISION array, dimension |
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73 * (min(M,K)) if VECT = 'Q' |
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74 * (min(N,K)) if VECT = 'P' |
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75 * TAU(i) must contain the scalar factor of the elementary |
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76 * reflector H(i) or G(i), which determines Q or P**T, as |
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77 * returned by DGEBRD in its array argument TAUQ or TAUP. |
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78 * |
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79 * WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK) |
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80 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
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81 * |
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82 * LWORK (input) INTEGER |
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83 * The dimension of the array WORK. LWORK >= max(1,min(M,N)). |
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84 * For optimum performance LWORK >= min(M,N)*NB, where NB |
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85 * is the optimal blocksize. |
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86 * |
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87 * If LWORK = -1, then a workspace query is assumed; the routine |
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88 * only calculates the optimal size of the WORK array, returns |
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89 * this value as the first entry of the WORK array, and no error |
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90 * message related to LWORK is issued by XERBLA. |
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91 * |
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92 * INFO (output) INTEGER |
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93 * = 0: successful exit |
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94 * < 0: if INFO = -i, the i-th argument had an illegal value |
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95 * |
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96 * ===================================================================== |
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97 * |
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98 * .. Parameters .. |
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99 DOUBLE PRECISION ZERO, ONE |
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100 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) |
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101 * .. |
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102 * .. Local Scalars .. |
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103 LOGICAL LQUERY, WANTQ |
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104 INTEGER I, IINFO, J, LWKOPT, MN, NB |
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105 * .. |
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106 * .. External Functions .. |
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107 LOGICAL LSAME |
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108 INTEGER ILAENV |
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109 EXTERNAL LSAME, ILAENV |
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110 * .. |
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111 * .. External Subroutines .. |
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112 EXTERNAL DORGLQ, DORGQR, XERBLA |
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113 * .. |
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114 * .. Intrinsic Functions .. |
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115 INTRINSIC MAX, MIN |
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116 * .. |
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117 * .. Executable Statements .. |
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118 * |
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119 * Test the input arguments |
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120 * |
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121 INFO = 0 |
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122 WANTQ = LSAME( VECT, 'Q' ) |
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123 MN = MIN( M, N ) |
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124 LQUERY = ( LWORK.EQ.-1 ) |
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125 IF( .NOT.WANTQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN |
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126 INFO = -1 |
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127 ELSE IF( M.LT.0 ) THEN |
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128 INFO = -2 |
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129 ELSE IF( N.LT.0 .OR. ( WANTQ .AND. ( N.GT.M .OR. N.LT.MIN( M, |
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130 $ K ) ) ) .OR. ( .NOT.WANTQ .AND. ( M.GT.N .OR. M.LT. |
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131 $ MIN( N, K ) ) ) ) THEN |
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132 INFO = -3 |
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133 ELSE IF( K.LT.0 ) THEN |
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134 INFO = -4 |
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135 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN |
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136 INFO = -6 |
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137 ELSE IF( LWORK.LT.MAX( 1, MN ) .AND. .NOT.LQUERY ) THEN |
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138 INFO = -9 |
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139 END IF |
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140 * |
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141 IF( INFO.EQ.0 ) THEN |
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142 IF( WANTQ ) THEN |
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143 NB = ILAENV( 1, 'DORGQR', ' ', M, N, K, -1 ) |
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144 ELSE |
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145 NB = ILAENV( 1, 'DORGLQ', ' ', M, N, K, -1 ) |
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146 END IF |
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147 LWKOPT = MAX( 1, MN )*NB |
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148 WORK( 1 ) = LWKOPT |
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149 END IF |
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150 * |
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151 IF( INFO.NE.0 ) THEN |
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152 CALL XERBLA( 'DORGBR', -INFO ) |
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153 RETURN |
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154 ELSE IF( LQUERY ) THEN |
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155 RETURN |
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156 END IF |
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157 * |
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158 * Quick return if possible |
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159 * |
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160 IF( M.EQ.0 .OR. N.EQ.0 ) THEN |
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161 WORK( 1 ) = 1 |
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162 RETURN |
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163 END IF |
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164 * |
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165 IF( WANTQ ) THEN |
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166 * |
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167 * Form Q, determined by a call to DGEBRD to reduce an m-by-k |
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168 * matrix |
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169 * |
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170 IF( M.GE.K ) THEN |
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171 * |
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172 * If m >= k, assume m >= n >= k |
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173 * |
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174 CALL DORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO ) |
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175 * |
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176 ELSE |
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177 * |
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178 * If m < k, assume m = n |
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179 * |
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180 * Shift the vectors which define the elementary reflectors one |
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181 * column to the right, and set the first row and column of Q |
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182 * to those of the unit matrix |
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183 * |
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184 DO 20 J = M, 2, -1 |
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185 A( 1, J ) = ZERO |
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186 DO 10 I = J + 1, M |
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187 A( I, J ) = A( I, J-1 ) |
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188 10 CONTINUE |
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189 20 CONTINUE |
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190 A( 1, 1 ) = ONE |
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191 DO 30 I = 2, M |
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192 A( I, 1 ) = ZERO |
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193 30 CONTINUE |
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194 IF( M.GT.1 ) THEN |
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195 * |
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196 * Form Q(2:m,2:m) |
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197 * |
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198 CALL DORGQR( M-1, M-1, M-1, A( 2, 2 ), LDA, TAU, WORK, |
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199 $ LWORK, IINFO ) |
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200 END IF |
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201 END IF |
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202 ELSE |
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203 * |
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204 * Form P', determined by a call to DGEBRD to reduce a k-by-n |
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205 * matrix |
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206 * |
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207 IF( K.LT.N ) THEN |
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208 * |
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209 * If k < n, assume k <= m <= n |
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210 * |
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211 CALL DORGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO ) |
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212 * |
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213 ELSE |
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214 * |
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215 * If k >= n, assume m = n |
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216 * |
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217 * Shift the vectors which define the elementary reflectors one |
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218 * row downward, and set the first row and column of P' to |
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219 * those of the unit matrix |
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220 * |
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221 A( 1, 1 ) = ONE |
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222 DO 40 I = 2, N |
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223 A( I, 1 ) = ZERO |
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224 40 CONTINUE |
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225 DO 60 J = 2, N |
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226 DO 50 I = J - 1, 2, -1 |
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227 A( I, J ) = A( I-1, J ) |
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228 50 CONTINUE |
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229 A( 1, J ) = ZERO |
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230 60 CONTINUE |
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231 IF( N.GT.1 ) THEN |
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232 * |
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233 * Form P'(2:n,2:n) |
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234 * |
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235 CALL DORGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK, |
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236 $ LWORK, IINFO ) |
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237 END IF |
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238 END IF |
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239 END IF |
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240 WORK( 1 ) = LWKOPT |
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241 RETURN |
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242 * |
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243 * End of DORGBR |
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244 * |
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245 END |
