Mercurial > octave-nkf
annotate libcruft/lapack/cgelq2.f @ 7948:af10baa63915 ss-3-1-50
3.1.50 snapshot
author | John W. Eaton <jwe@octave.org> |
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date | Fri, 18 Jul 2008 17:42:48 -0400 |
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1 SUBROUTINE CGELQ2( M, N, A, LDA, TAU, WORK, 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, M, N |
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9 * .. |
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10 * .. Array Arguments .. |
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11 COMPLEX 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 * CGELQ2 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 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 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) COMPLEX array, dimension (M) |
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45 * |
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46 * INFO (output) INTEGER |
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47 * = 0: successful exit |
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48 * < 0: if INFO = -i, the i-th argument had an illegal value |
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49 * |
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50 * Further Details |
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51 * =============== |
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52 * |
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53 * The matrix Q is represented as a product of elementary reflectors |
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54 * |
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55 * Q = H(k)' . . . H(2)' H(1)', where k = min(m,n). |
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56 * |
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57 * Each H(i) has the form |
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58 * |
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59 * H(i) = I - tau * v * v' |
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60 * |
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61 * where tau is a complex scalar, and v is a complex vector with |
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62 * v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in |
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63 * A(i,i+1:n), and tau in TAU(i). |
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64 * |
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65 * ===================================================================== |
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66 * |
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67 * .. Parameters .. |
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68 COMPLEX ONE |
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69 PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) ) |
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70 * .. |
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71 * .. Local Scalars .. |
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72 INTEGER I, K |
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73 COMPLEX ALPHA |
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74 * .. |
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75 * .. External Subroutines .. |
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76 EXTERNAL CLACGV, CLARF, CLARFG, XERBLA |
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77 * .. |
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78 * .. Intrinsic Functions .. |
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79 INTRINSIC MAX, MIN |
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80 * .. |
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81 * .. Executable Statements .. |
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82 * |
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83 * Test the input arguments |
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84 * |
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85 INFO = 0 |
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86 IF( M.LT.0 ) THEN |
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87 INFO = -1 |
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88 ELSE IF( N.LT.0 ) THEN |
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89 INFO = -2 |
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90 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN |
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91 INFO = -4 |
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92 END IF |
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93 IF( INFO.NE.0 ) THEN |
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94 CALL XERBLA( 'CGELQ2', -INFO ) |
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95 RETURN |
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96 END IF |
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97 * |
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98 K = MIN( M, N ) |
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99 * |
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100 DO 10 I = 1, K |
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101 * |
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102 * Generate elementary reflector H(i) to annihilate A(i,i+1:n) |
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103 * |
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104 CALL CLACGV( N-I+1, A( I, I ), LDA ) |
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105 ALPHA = A( I, I ) |
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106 CALL CLARFG( N-I+1, ALPHA, A( I, MIN( I+1, N ) ), LDA, |
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107 $ TAU( I ) ) |
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108 IF( I.LT.M ) THEN |
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109 * |
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110 * Apply H(i) to A(i+1:m,i:n) from the right |
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111 * |
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112 A( I, I ) = ONE |
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113 CALL CLARF( '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 END IF |
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116 A( I, I ) = ALPHA |
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117 CALL CLACGV( N-I+1, A( I, I ), LDA ) |
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118 10 CONTINUE |
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119 RETURN |
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120 * |
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121 * End of CGELQ2 |
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122 * |
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123 END |