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annotate libcruft/lapack/sgeqr2.f @ 7789:82be108cc558

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First attempt at single precision tyeps * * * corrections to qrupdate single precision routines * * * prefer demotion to single over promotion to double * * * Add single precision support to log2 function * * * Trivial PROJECT file update * * * Cache optimized hermitian/transpose methods * * * Add tests for tranpose/hermitian and ChangeLog entry for new transpose code
author David Bateman <dbateman@free.fr>
date Sun, 27 Apr 2008 22:34:17 +0200
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1 SUBROUTINE SGEQR2( 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 REAL 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 * SGEQR2 computes a QR factorization of a real m by n matrix A:
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18 * A = Q * R.
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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) REAL 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 above the diagonal of the array
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32 * contain the min(m,n) by n upper trapezoidal matrix R (R is
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33 * upper triangular if m >= n); the elements below the diagonal,
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34 * with the array TAU, represent the orthogonal 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) REAL 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) REAL array, dimension (N)
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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(1) H(2) . . . H(k), 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 real scalar, and v is a real vector with
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62 * v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
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63 * 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 REAL ONE
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69 PARAMETER ( ONE = 1.0E+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 REAL AII
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74 * ..
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75 * .. External Subroutines ..
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76 EXTERNAL SLARF, SLARFG, 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( 'SGEQR2', -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+1:m,i)
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103 *
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104 CALL SLARFG( M-I+1, A( I, I ), A( MIN( I+1, M ), I ), 1,
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105 $ TAU( I ) )
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106 IF( I.LT.N ) THEN
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107 *
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108 * Apply H(i) to A(i:m,i+1:n) from the left
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109 *
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110 AII = A( I, I )
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111 A( I, I ) = ONE
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112 CALL SLARF( 'Left', M-I+1, N-I, A( I, I ), 1, TAU( I ),
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113 $ A( I, I+1 ), LDA, WORK )
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114 A( I, I ) = AII
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115 END IF
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116 10 CONTINUE
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117 RETURN
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118 *
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119 * End of SGEQR2
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120 *
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121 END