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1 SUBROUTINE DGELQ2( M, N, 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, 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 * DGELQ2 computes an LQ factorization of a real m by n matrix A: |
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19 * A = L * Q. |
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20 * |
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21 * Arguments |
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22 * ========= |
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23 * |
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24 * M (input) INTEGER |
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25 * The number of rows of the matrix A. M >= 0. |
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26 * |
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27 * N (input) INTEGER |
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28 * The number of columns of the matrix A. N >= 0. |
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29 * |
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30 * A (input/output) DOUBLE PRECISION array, dimension (LDA,N) |
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31 * On entry, the m by n matrix A. |
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32 * On exit, the elements on and below the diagonal of the array |
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33 * contain the m by min(m,n) lower trapezoidal matrix L (L is |
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34 * lower triangular if m <= n); the elements above the diagonal, |
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35 * with the array TAU, represent the orthogonal matrix Q as a |
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36 * product of elementary reflectors (see Further Details). |
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37 * |
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38 * LDA (input) INTEGER |
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39 * The leading dimension of the array A. LDA >= max(1,M). |
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40 * |
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41 * TAU (output) DOUBLE PRECISION array, dimension (min(M,N)) |
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42 * The scalar factors of the elementary reflectors (see Further |
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43 * Details). |
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44 * |
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45 * WORK (workspace) DOUBLE PRECISION array, dimension (M) |
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46 * |
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47 * INFO (output) INTEGER |
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48 * = 0: successful exit |
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49 * < 0: if INFO = -i, the i-th argument had an illegal value |
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50 * |
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51 * Further Details |
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52 * =============== |
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53 * |
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54 * The matrix Q is represented as a product of elementary reflectors |
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55 * |
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56 * Q = H(k) . . . H(2) H(1), where k = min(m,n). |
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57 * |
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58 * Each H(i) has the form |
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59 * |
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60 * H(i) = I - tau * v * v' |
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61 * |
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62 * where tau is a real scalar, and v is a real vector with |
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63 * v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n), |
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64 * and tau in TAU(i). |
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65 * |
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66 * ===================================================================== |
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67 * |
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68 * .. Parameters .. |
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69 DOUBLE PRECISION ONE |
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70 PARAMETER ( ONE = 1.0D+0 ) |
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71 * .. |
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72 * .. Local Scalars .. |
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73 INTEGER I, K |
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74 DOUBLE PRECISION AII |
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75 * .. |
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76 * .. External Subroutines .. |
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77 EXTERNAL DLARF, DLARFG, XERBLA |
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78 * .. |
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79 * .. Intrinsic Functions .. |
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80 INTRINSIC MAX, MIN |
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81 * .. |
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82 * .. Executable Statements .. |
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83 * |
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84 * Test the input arguments |
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85 * |
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86 INFO = 0 |
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87 IF( M.LT.0 ) THEN |
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88 INFO = -1 |
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89 ELSE IF( N.LT.0 ) THEN |
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90 INFO = -2 |
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91 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN |
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92 INFO = -4 |
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93 END IF |
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94 IF( INFO.NE.0 ) THEN |
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95 CALL XERBLA( 'DGELQ2', -INFO ) |
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96 RETURN |
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97 END IF |
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98 * |
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99 K = MIN( M, N ) |
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100 * |
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101 DO 10 I = 1, K |
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102 * |
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103 * Generate elementary reflector H(i) to annihilate A(i,i+1:n) |
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104 * |
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105 CALL DLARFG( N-I+1, A( I, I ), A( I, MIN( I+1, N ) ), LDA, |
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106 $ TAU( I ) ) |
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107 IF( I.LT.M ) THEN |
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108 * |
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109 * Apply H(i) to A(i+1:m,i:n) from the right |
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110 * |
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111 AII = A( I, I ) |
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112 A( I, I ) = ONE |
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113 CALL DLARF( 'Right', M-I, N-I+1, A( I, I ), LDA, TAU( I ), |
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114 $ A( I+1, I ), LDA, WORK ) |
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115 A( I, I ) = AII |
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116 END IF |
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117 10 CONTINUE |
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118 RETURN |
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119 * |
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120 * End of DGELQ2 |
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121 * |
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122 END |
