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annotate libcruft/lapack/cunglq.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 CUNGLQ( 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 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 * CUNGLQ generates an M-by-N complex matrix Q with orthonormal rows,
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18 * which is defined as the first M rows of a product of K elementary
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19 * reflectors of order N
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20 *
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21 * Q = H(k)' . . . H(2)' H(1)'
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22 *
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23 * as returned by CGELQF.
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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. N >= M.
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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. M >= K >= 0.
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37 *
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38 * A (input/output) COMPLEX array, dimension (LDA,N)
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39 * On entry, the i-th row must contain the vector which defines
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40 * the elementary reflector H(i), for i = 1,2,...,k, as returned
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41 * by CGELQF in the first k rows of its array argument A.
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42 * On exit, the M-by-N matrix Q.
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43 *
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44 * LDA (input) INTEGER
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45 * The first dimension of the array A. LDA >= max(1,M).
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46 *
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47 * TAU (input) COMPLEX array, dimension (K)
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48 * TAU(i) must contain the scalar factor of the elementary
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49 * reflector H(i), as returned by CGELQF.
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50 *
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51 * WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
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52 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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53 *
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54 * LWORK (input) INTEGER
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55 * The dimension of the array WORK. LWORK >= max(1,M).
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56 * For optimum performance LWORK >= M*NB, where NB is
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57 * the optimal blocksize.
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58 *
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59 * If LWORK = -1, then a workspace query is assumed; the routine
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60 * only calculates the optimal size of the WORK array, returns
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61 * this value as the first entry of the WORK array, and no error
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62 * message related to LWORK is issued by XERBLA.
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63 *
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64 * INFO (output) INTEGER
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65 * = 0: successful exit;
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66 * < 0: if INFO = -i, the i-th argument has an illegal value
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67 *
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68 * =====================================================================
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69 *
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70 * .. Parameters ..
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71 COMPLEX ZERO
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72 PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) )
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73 * ..
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74 * .. Local Scalars ..
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75 LOGICAL LQUERY
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76 INTEGER I, IB, IINFO, IWS, J, KI, KK, L, LDWORK,
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77 $ LWKOPT, NB, NBMIN, NX
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78 * ..
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79 * .. External Subroutines ..
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80 EXTERNAL CLARFB, CLARFT, CUNGL2, XERBLA
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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 * .. External Functions ..
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86 INTEGER ILAENV
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87 EXTERNAL ILAENV
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88 * ..
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89 * .. Executable Statements ..
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90 *
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91 * Test the input arguments
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92 *
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93 INFO = 0
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94 NB = ILAENV( 1, 'CUNGLQ', ' ', M, N, K, -1 )
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95 LWKOPT = MAX( 1, M )*NB
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96 WORK( 1 ) = LWKOPT
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97 LQUERY = ( LWORK.EQ.-1 )
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98 IF( M.LT.0 ) THEN
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99 INFO = -1
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100 ELSE IF( N.LT.M ) THEN
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101 INFO = -2
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102 ELSE IF( K.LT.0 .OR. K.GT.M ) THEN
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103 INFO = -3
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104 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
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105 INFO = -5
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106 ELSE IF( LWORK.LT.MAX( 1, M ) .AND. .NOT.LQUERY ) THEN
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107 INFO = -8
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108 END IF
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109 IF( INFO.NE.0 ) THEN
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110 CALL XERBLA( 'CUNGLQ', -INFO )
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111 RETURN
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112 ELSE IF( LQUERY ) THEN
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113 RETURN
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114 END IF
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115 *
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116 * Quick return if possible
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117 *
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118 IF( M.LE.0 ) THEN
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119 WORK( 1 ) = 1
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120 RETURN
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121 END IF
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122 *
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123 NBMIN = 2
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124 NX = 0
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125 IWS = M
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126 IF( NB.GT.1 .AND. NB.LT.K ) THEN
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127 *
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128 * Determine when to cross over from blocked to unblocked code.
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129 *
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130 NX = MAX( 0, ILAENV( 3, 'CUNGLQ', ' ', M, N, K, -1 ) )
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131 IF( NX.LT.K ) THEN
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132 *
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133 * Determine if workspace is large enough for blocked code.
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134 *
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135 LDWORK = M
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136 IWS = LDWORK*NB
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137 IF( LWORK.LT.IWS ) THEN
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138 *
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139 * Not enough workspace to use optimal NB: reduce NB and
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140 * determine the minimum value of NB.
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141 *
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142 NB = LWORK / LDWORK
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143 NBMIN = MAX( 2, ILAENV( 2, 'CUNGLQ', ' ', M, N, K, -1 ) )
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144 END IF
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145 END IF
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146 END IF
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147 *
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148 IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN
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149 *
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150 * Use blocked code after the last block.
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151 * The first kk rows are handled by the block method.
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152 *
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153 KI = ( ( K-NX-1 ) / NB )*NB
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154 KK = MIN( K, KI+NB )
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155 *
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156 * Set A(kk+1:m,1:kk) to zero.
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157 *
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158 DO 20 J = 1, KK
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159 DO 10 I = KK + 1, M
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160 A( I, J ) = ZERO
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161 10 CONTINUE
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162 20 CONTINUE
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163 ELSE
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164 KK = 0
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165 END IF
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166 *
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167 * Use unblocked code for the last or only block.
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168 *
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169 IF( KK.LT.M )
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170 $ CALL CUNGL2( M-KK, N-KK, K-KK, A( KK+1, KK+1 ), LDA,
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171 $ TAU( KK+1 ), WORK, IINFO )
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172 *
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173 IF( KK.GT.0 ) THEN
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174 *
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175 * Use blocked code
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176 *
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177 DO 50 I = KI + 1, 1, -NB
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178 IB = MIN( NB, K-I+1 )
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179 IF( I+IB.LE.M ) THEN
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180 *
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181 * Form the triangular factor of the block reflector
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182 * H = H(i) H(i+1) . . . H(i+ib-1)
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183 *
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184 CALL CLARFT( 'Forward', 'Rowwise', N-I+1, IB, A( I, I ),
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185 $ LDA, TAU( I ), WORK, LDWORK )
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186 *
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187 * Apply H' to A(i+ib:m,i:n) from the right
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188 *
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189 CALL CLARFB( 'Right', 'Conjugate transpose', 'Forward',
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190 $ 'Rowwise', M-I-IB+1, N-I+1, IB, A( I, I ),
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191 $ LDA, WORK, LDWORK, A( I+IB, I ), LDA,
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192 $ WORK( IB+1 ), LDWORK )
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193 END IF
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194 *
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195 * Apply H' to columns i:n of current block
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196 *
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197 CALL CUNGL2( IB, N-I+1, IB, A( I, I ), LDA, TAU( I ), WORK,
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198 $ IINFO )
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199 *
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200 * Set columns 1:i-1 of current block to zero
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201 *
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202 DO 40 J = 1, I - 1
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203 DO 30 L = I, I + IB - 1
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204 A( L, J ) = ZERO
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205 30 CONTINUE
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206 40 CONTINUE
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207 50 CONTINUE
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208 END IF
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209 *
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210 WORK( 1 ) = IWS
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211 RETURN
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212 *
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213 * End of CUNGLQ
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214 *
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215 END