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annotate libcruft/lapack/sorghr.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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7789
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1 SUBROUTINE SORGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, 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 IHI, ILO, INFO, LDA, LWORK, 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 * SORGHR generates a real orthogonal matrix Q which is defined as the
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18 * product of IHI-ILO elementary reflectors of order N, as returned by
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19 * SGEHRD:
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20 *
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21 * Q = H(ilo) H(ilo+1) . . . H(ihi-1).
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22 *
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23 * Arguments
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24 * =========
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25 *
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26 * N (input) INTEGER
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27 * The order of the matrix Q. N >= 0.
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28 *
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29 * ILO (input) INTEGER
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30 * IHI (input) INTEGER
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31 * ILO and IHI must have the same values as in the previous call
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32 * of SGEHRD. Q is equal to the unit matrix except in the
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33 * submatrix Q(ilo+1:ihi,ilo+1:ihi).
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34 * 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
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35 *
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36 * A (input/output) REAL array, dimension (LDA,N)
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37 * On entry, the vectors which define the elementary reflectors,
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38 * as returned by SGEHRD.
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39 * On exit, the N-by-N orthogonal matrix Q.
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40 *
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41 * LDA (input) INTEGER
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42 * The leading dimension of the array A. LDA >= max(1,N).
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43 *
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44 * TAU (input) REAL array, dimension (N-1)
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45 * TAU(i) must contain the scalar factor of the elementary
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46 * reflector H(i), as returned by SGEHRD.
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47 *
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48 * WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))
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49 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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50 *
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51 * LWORK (input) INTEGER
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52 * The dimension of the array WORK. LWORK >= IHI-ILO.
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53 * For optimum performance LWORK >= (IHI-ILO)*NB, where NB is
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54 * the optimal blocksize.
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55 *
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56 * If LWORK = -1, then a workspace query is assumed; the routine
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57 * only calculates the optimal size of the WORK array, returns
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58 * this value as the first entry of the WORK array, and no error
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59 * message related to LWORK is issued by XERBLA.
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60 *
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61 * INFO (output) INTEGER
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62 * = 0: successful exit
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63 * < 0: if INFO = -i, the i-th argument had an illegal value
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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 ZERO, ONE
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69 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
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70 * ..
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71 * .. Local Scalars ..
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72 LOGICAL LQUERY
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73 INTEGER I, IINFO, J, LWKOPT, NB, NH
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74 * ..
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75 * .. External Subroutines ..
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76 EXTERNAL SORGQR, XERBLA
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77 * ..
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78 * .. External Functions ..
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79 INTEGER ILAENV
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80 EXTERNAL ILAENV
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81 * ..
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82 * .. Intrinsic Functions ..
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83 INTRINSIC MAX, MIN
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84 * ..
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85 * .. Executable Statements ..
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86 *
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87 * Test the input arguments
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88 *
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89 INFO = 0
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90 NH = IHI - ILO
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91 LQUERY = ( LWORK.EQ.-1 )
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92 IF( N.LT.0 ) THEN
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93 INFO = -1
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94 ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN
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95 INFO = -2
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96 ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN
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97 INFO = -3
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98 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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99 INFO = -5
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100 ELSE IF( LWORK.LT.MAX( 1, NH ) .AND. .NOT.LQUERY ) THEN
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101 INFO = -8
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102 END IF
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103 *
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104 IF( INFO.EQ.0 ) THEN
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105 NB = ILAENV( 1, 'SORGQR', ' ', NH, NH, NH, -1 )
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106 LWKOPT = MAX( 1, NH )*NB
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107 WORK( 1 ) = LWKOPT
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108 END IF
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109 *
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110 IF( INFO.NE.0 ) THEN
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111 CALL XERBLA( 'SORGHR', -INFO )
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112 RETURN
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113 ELSE IF( LQUERY ) THEN
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114 RETURN
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115 END IF
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116 *
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117 * Quick return if possible
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118 *
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119 IF( N.EQ.0 ) THEN
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120 WORK( 1 ) = 1
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121 RETURN
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122 END IF
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123 *
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124 * Shift the vectors which define the elementary reflectors one
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125 * column to the right, and set the first ilo and the last n-ihi
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126 * rows and columns to those of the unit matrix
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127 *
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128 DO 40 J = IHI, ILO + 1, -1
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129 DO 10 I = 1, J - 1
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130 A( I, J ) = ZERO
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131 10 CONTINUE
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132 DO 20 I = J + 1, IHI
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133 A( I, J ) = A( I, J-1 )
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134 20 CONTINUE
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135 DO 30 I = IHI + 1, N
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136 A( I, J ) = ZERO
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137 30 CONTINUE
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138 40 CONTINUE
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139 DO 60 J = 1, ILO
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140 DO 50 I = 1, N
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141 A( I, J ) = ZERO
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142 50 CONTINUE
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143 A( J, J ) = ONE
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144 60 CONTINUE
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145 DO 80 J = IHI + 1, N
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146 DO 70 I = 1, N
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147 A( I, J ) = ZERO
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148 70 CONTINUE
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149 A( J, J ) = ONE
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150 80 CONTINUE
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151 *
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152 IF( NH.GT.0 ) THEN
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153 *
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154 * Generate Q(ilo+1:ihi,ilo+1:ihi)
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155 *
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156 CALL SORGQR( NH, NH, NH, A( ILO+1, ILO+1 ), LDA, TAU( ILO ),
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157 $ WORK, LWORK, IINFO )
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158 END IF
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159 WORK( 1 ) = LWKOPT
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160 RETURN
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161 *
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162 * End of SORGHR
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163 *
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164 END