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1 SUBROUTINE DORG2R( M, N, K, A, LDA, TAU, WORK, 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 * February 29, 1992 |
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7 * |
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8 * .. Scalar Arguments .. |
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9 INTEGER INFO, K, LDA, M, N |
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10 * .. |
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11 * .. Array Arguments .. |
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12 DOUBLE PRECISION 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 * DORG2R generates an m by n real matrix Q with orthonormal columns, |
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19 * which is defined as the first 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(1) H(2) . . . H(k) |
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23 * |
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24 * as returned by DGEQRF. |
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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) DOUBLE PRECISION array, dimension (LDA,N) |
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40 * On entry, the 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 DGEQRF in the first 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) DOUBLE PRECISION 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 DGEQRF. |
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52 * |
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53 * WORK (workspace) DOUBLE PRECISION array, dimension (N) |
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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 has an illegal value |
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58 * |
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59 * ===================================================================== |
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60 * |
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61 * .. Parameters .. |
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62 DOUBLE PRECISION ONE, ZERO |
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63 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) |
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64 * .. |
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65 * .. Local Scalars .. |
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66 INTEGER I, J, L |
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67 * .. |
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68 * .. External Subroutines .. |
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69 EXTERNAL DLARF, DSCAL, XERBLA |
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70 * .. |
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71 * .. Intrinsic Functions .. |
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72 INTRINSIC MAX |
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73 * .. |
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74 * .. Executable Statements .. |
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75 * |
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76 * Test the input arguments |
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77 * |
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78 INFO = 0 |
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79 IF( M.LT.0 ) THEN |
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80 INFO = -1 |
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81 ELSE IF( N.LT.0 .OR. N.GT.M ) THEN |
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82 INFO = -2 |
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83 ELSE IF( K.LT.0 .OR. K.GT.N ) THEN |
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84 INFO = -3 |
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85 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN |
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86 INFO = -5 |
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87 END IF |
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88 IF( INFO.NE.0 ) THEN |
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89 CALL XERBLA( 'DORG2R', -INFO ) |
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90 RETURN |
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91 END IF |
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92 * |
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93 * Quick return if possible |
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94 * |
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95 IF( N.LE.0 ) |
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96 $ RETURN |
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97 * |
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98 * Initialise columns k+1:n to columns of the unit matrix |
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99 * |
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100 DO 20 J = K + 1, N |
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101 DO 10 L = 1, M |
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102 A( L, J ) = ZERO |
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103 10 CONTINUE |
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104 A( J, J ) = ONE |
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105 20 CONTINUE |
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106 * |
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107 DO 40 I = K, 1, -1 |
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108 * |
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109 * Apply H(i) to A(i:m,i:n) from the left |
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110 * |
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111 IF( I.LT.N ) THEN |
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112 A( I, I ) = ONE |
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113 CALL DLARF( 'Left', M-I+1, N-I, A( I, I ), 1, TAU( I ), |
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114 $ A( I, I+1 ), LDA, WORK ) |
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115 END IF |
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116 IF( I.LT.M ) |
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117 $ CALL DSCAL( M-I, -TAU( I ), A( I+1, I ), 1 ) |
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118 A( I, I ) = ONE - TAU( I ) |
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119 * |
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120 * Set A(1:i-1,i) to zero |
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121 * |
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122 DO 30 L = 1, I - 1 |
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123 A( L, I ) = ZERO |
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124 30 CONTINUE |
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125 40 CONTINUE |
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126 RETURN |
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127 * |
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128 * End of DORG2R |
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129 * |
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130 END |
