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annotate libcruft/lapack/sorgqr.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 SORGQR( M, N, K, 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 INFO, K, LDA, LWORK, 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 * SORGQR generates an M-by-N real matrix Q with orthonormal columns,
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18 * which is defined as the first N columns of a product of K elementary
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19 * reflectors of order M
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20 *
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21 * Q = H(1) H(2) . . . H(k)
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22 *
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23 * as returned by SGEQRF.
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24 *
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25 * Arguments
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26 * =========
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27 *
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28 * M (input) INTEGER
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29 * The number of rows of the matrix Q. M >= 0.
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30 *
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31 * N (input) INTEGER
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32 * The number of columns of the matrix Q. M >= N >= 0.
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33 *
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34 * K (input) INTEGER
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35 * The number of elementary reflectors whose product defines the
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36 * matrix Q. N >= K >= 0.
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37 *
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38 * A (input/output) REAL array, dimension (LDA,N)
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39 * On entry, the i-th column must contain the vector which
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40 * defines the elementary reflector H(i), for i = 1,2,...,k, as
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41 * returned by SGEQRF in the first k columns of its array
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42 * argument A.
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43 * On exit, the M-by-N matrix Q.
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44 *
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45 * LDA (input) INTEGER
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46 * The first dimension of the array A. LDA >= max(1,M).
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47 *
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48 * TAU (input) REAL array, dimension (K)
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49 * TAU(i) must contain the scalar factor of the elementary
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50 * reflector H(i), as returned by SGEQRF.
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51 *
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52 * WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))
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53 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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54 *
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55 * LWORK (input) INTEGER
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56 * The dimension of the array WORK. LWORK >= max(1,N).
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57 * For optimum performance LWORK >= N*NB, where NB is the
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58 * optimal blocksize.
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59 *
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60 * If LWORK = -1, then a workspace query is assumed; the routine
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61 * only calculates the optimal size of the WORK array, returns
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62 * this value as the first entry of the WORK array, and no error
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63 * message related to LWORK is issued by XERBLA.
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64 *
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65 * INFO (output) INTEGER
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66 * = 0: successful exit
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67 * < 0: if INFO = -i, the i-th argument has an illegal value
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68 *
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69 * =====================================================================
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70 *
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71 * .. Parameters ..
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72 REAL ZERO
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73 PARAMETER ( ZERO = 0.0E+0 )
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74 * ..
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75 * .. Local Scalars ..
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76 LOGICAL LQUERY
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77 INTEGER I, IB, IINFO, IWS, J, KI, KK, L, LDWORK,
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78 $ LWKOPT, NB, NBMIN, NX
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79 * ..
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80 * .. External Subroutines ..
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81 EXTERNAL SLARFB, SLARFT, SORG2R, XERBLA
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82 * ..
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83 * .. Intrinsic Functions ..
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84 INTRINSIC MAX, MIN
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85 * ..
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86 * .. External Functions ..
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87 INTEGER ILAENV
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88 EXTERNAL ILAENV
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89 * ..
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90 * .. Executable Statements ..
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91 *
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92 * Test the input arguments
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93 *
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94 INFO = 0
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95 NB = ILAENV( 1, 'SORGQR', ' ', M, N, K, -1 )
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96 LWKOPT = MAX( 1, N )*NB
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97 WORK( 1 ) = LWKOPT
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98 LQUERY = ( LWORK.EQ.-1 )
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99 IF( M.LT.0 ) THEN
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100 INFO = -1
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101 ELSE IF( N.LT.0 .OR. N.GT.M ) THEN
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102 INFO = -2
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103 ELSE IF( K.LT.0 .OR. K.GT.N ) THEN
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104 INFO = -3
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105 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
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106 INFO = -5
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107 ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN
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108 INFO = -8
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109 END IF
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110 IF( INFO.NE.0 ) THEN
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111 CALL XERBLA( 'SORGQR', -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.LE.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 NBMIN = 2
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125 NX = 0
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126 IWS = N
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127 IF( NB.GT.1 .AND. NB.LT.K ) THEN
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128 *
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129 * Determine when to cross over from blocked to unblocked code.
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130 *
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131 NX = MAX( 0, ILAENV( 3, 'SORGQR', ' ', M, N, K, -1 ) )
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132 IF( NX.LT.K ) THEN
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133 *
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134 * Determine if workspace is large enough for blocked code.
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135 *
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136 LDWORK = N
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137 IWS = LDWORK*NB
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138 IF( LWORK.LT.IWS ) THEN
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139 *
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140 * Not enough workspace to use optimal NB: reduce NB and
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141 * determine the minimum value of NB.
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142 *
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143 NB = LWORK / LDWORK
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144 NBMIN = MAX( 2, ILAENV( 2, 'SORGQR', ' ', M, N, K, -1 ) )
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145 END IF
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146 END IF
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147 END IF
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148 *
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149 IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN
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150 *
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151 * Use blocked code after the last block.
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152 * The first kk columns are handled by the block method.
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153 *
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154 KI = ( ( K-NX-1 ) / NB )*NB
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155 KK = MIN( K, KI+NB )
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156 *
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157 * Set A(1:kk,kk+1:n) to zero.
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158 *
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159 DO 20 J = KK + 1, N
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160 DO 10 I = 1, KK
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161 A( I, J ) = ZERO
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162 10 CONTINUE
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163 20 CONTINUE
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164 ELSE
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165 KK = 0
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166 END IF
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167 *
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168 * Use unblocked code for the last or only block.
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169 *
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170 IF( KK.LT.N )
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171 $ CALL SORG2R( M-KK, N-KK, K-KK, A( KK+1, KK+1 ), LDA,
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172 $ TAU( KK+1 ), WORK, IINFO )
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173 *
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174 IF( KK.GT.0 ) THEN
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175 *
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176 * Use blocked code
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177 *
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178 DO 50 I = KI + 1, 1, -NB
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179 IB = MIN( NB, K-I+1 )
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180 IF( I+IB.LE.N ) THEN
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181 *
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182 * Form the triangular factor of the block reflector
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183 * H = H(i) H(i+1) . . . H(i+ib-1)
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184 *
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185 CALL SLARFT( 'Forward', 'Columnwise', M-I+1, IB,
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186 $ A( I, I ), LDA, TAU( I ), WORK, LDWORK )
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187 *
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188 * Apply H to A(i:m,i+ib:n) from the left
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189 *
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190 CALL SLARFB( 'Left', 'No transpose', 'Forward',
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191 $ 'Columnwise', M-I+1, N-I-IB+1, IB,
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192 $ A( I, I ), LDA, WORK, LDWORK, A( I, I+IB ),
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193 $ LDA, WORK( IB+1 ), LDWORK )
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194 END IF
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195 *
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196 * Apply H to rows i:m of current block
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197 *
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198 CALL SORG2R( M-I+1, IB, IB, A( I, I ), LDA, TAU( I ), WORK,
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199 $ IINFO )
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200 *
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201 * Set rows 1:i-1 of current block to zero
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202 *
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203 DO 40 J = I, I + IB - 1
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204 DO 30 L = 1, I - 1
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205 A( L, J ) = ZERO
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206 30 CONTINUE
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207 40 CONTINUE
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208 50 CONTINUE
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209 END IF
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210 *
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211 WORK( 1 ) = IWS
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212 RETURN
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213 *
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214 * End of SORGQR
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215 *
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216 END