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annotate libcruft/lapack/sgelqf.f @ 9409:ed392e13c117

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remove assertion in force_variable
author Jaroslav Hajek <highegg@gmail.com>
date Tue, 30 Jun 2009 08:18:26 +0200
parents 82be108cc558
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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1 SUBROUTINE SGELQF( M, N, 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, 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 * SGELQF computes an LQ factorization of a real 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) 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 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 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/output) REAL array, dimension (MAX(1,LWORK))
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45 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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46 *
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47 * LWORK (input) INTEGER
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48 * The dimension of the array WORK. LWORK >= max(1,M).
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49 * For optimum performance LWORK >= M*NB, where NB is the
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50 * optimal blocksize.
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51 *
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52 * If LWORK = -1, then a workspace query is assumed; the routine
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53 * only calculates the optimal size of the WORK array, returns
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54 * this value as the first entry of the WORK array, and no error
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55 * message related to LWORK is issued by XERBLA.
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56 *
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57 * INFO (output) INTEGER
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58 * = 0: successful exit
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59 * < 0: if INFO = -i, the i-th argument had an illegal value
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60 *
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61 * Further Details
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62 * ===============
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63 *
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64 * The matrix Q is represented as a product of elementary reflectors
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65 *
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66 * Q = H(k) . . . H(2) H(1), where k = min(m,n).
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67 *
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68 * Each H(i) has the form
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69 *
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70 * H(i) = I - tau * v * v'
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71 *
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72 * where tau is a real scalar, and v is a real vector with
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73 * v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n),
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74 * and tau in TAU(i).
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75 *
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76 * =====================================================================
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77 *
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78 * .. Local Scalars ..
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79 LOGICAL LQUERY
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80 INTEGER I, IB, IINFO, IWS, K, LDWORK, LWKOPT, NB,
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81 $ NBMIN, NX
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82 * ..
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83 * .. External Subroutines ..
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84 EXTERNAL SGELQ2, SLARFB, SLARFT, XERBLA
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85 * ..
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86 * .. Intrinsic Functions ..
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87 INTRINSIC MAX, MIN
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88 * ..
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89 * .. External Functions ..
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90 INTEGER ILAENV
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91 EXTERNAL ILAENV
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92 * ..
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93 * .. Executable Statements ..
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94 *
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95 * Test the input arguments
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96 *
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97 INFO = 0
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98 NB = ILAENV( 1, 'SGELQF', ' ', M, N, -1, -1 )
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99 LWKOPT = M*NB
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100 WORK( 1 ) = LWKOPT
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101 LQUERY = ( LWORK.EQ.-1 )
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102 IF( M.LT.0 ) THEN
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103 INFO = -1
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104 ELSE IF( N.LT.0 ) THEN
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105 INFO = -2
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106 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
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107 INFO = -4
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108 ELSE IF( LWORK.LT.MAX( 1, M ) .AND. .NOT.LQUERY ) THEN
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109 INFO = -7
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110 END IF
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111 IF( INFO.NE.0 ) THEN
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112 CALL XERBLA( 'SGELQF', -INFO )
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113 RETURN
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114 ELSE IF( LQUERY ) THEN
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115 RETURN
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116 END IF
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117 *
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118 * Quick return if possible
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119 *
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120 K = MIN( M, N )
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121 IF( K.EQ.0 ) THEN
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122 WORK( 1 ) = 1
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123 RETURN
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124 END IF
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125 *
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126 NBMIN = 2
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127 NX = 0
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128 IWS = M
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129 IF( NB.GT.1 .AND. NB.LT.K ) THEN
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130 *
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131 * Determine when to cross over from blocked to unblocked code.
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132 *
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133 NX = MAX( 0, ILAENV( 3, 'SGELQF', ' ', M, N, -1, -1 ) )
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134 IF( NX.LT.K ) THEN
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135 *
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136 * Determine if workspace is large enough for blocked code.
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137 *
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138 LDWORK = M
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139 IWS = LDWORK*NB
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140 IF( LWORK.LT.IWS ) THEN
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141 *
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142 * Not enough workspace to use optimal NB: reduce NB and
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143 * determine the minimum value of NB.
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144 *
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145 NB = LWORK / LDWORK
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146 NBMIN = MAX( 2, ILAENV( 2, 'SGELQF', ' ', M, N, -1,
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147 $ -1 ) )
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148 END IF
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149 END IF
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150 END IF
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151 *
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152 IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN
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153 *
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154 * Use blocked code initially
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155 *
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156 DO 10 I = 1, K - NX, NB
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157 IB = MIN( K-I+1, NB )
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158 *
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159 * Compute the LQ factorization of the current block
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160 * A(i:i+ib-1,i:n)
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161 *
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162 CALL SGELQ2( IB, N-I+1, A( I, I ), LDA, TAU( I ), WORK,
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163 $ IINFO )
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164 IF( I+IB.LE.M ) THEN
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165 *
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166 * Form the triangular factor of the block reflector
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167 * H = H(i) H(i+1) . . . H(i+ib-1)
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168 *
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169 CALL SLARFT( 'Forward', 'Rowwise', N-I+1, IB, A( I, I ),
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170 $ LDA, TAU( I ), WORK, LDWORK )
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171 *
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172 * Apply H to A(i+ib:m,i:n) from the right
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173 *
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174 CALL SLARFB( 'Right', 'No transpose', 'Forward',
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175 $ 'Rowwise', M-I-IB+1, N-I+1, IB, A( I, I ),
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176 $ LDA, WORK, LDWORK, A( I+IB, I ), LDA,
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177 $ WORK( IB+1 ), LDWORK )
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178 END IF
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179 10 CONTINUE
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180 ELSE
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181 I = 1
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182 END IF
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183 *
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184 * Use unblocked code to factor the last or only block.
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185 *
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186 IF( I.LE.K )
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187 $ CALL SGELQ2( M-I+1, N-I+1, A( I, I ), LDA, TAU( I ), WORK,
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188 $ IINFO )
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189 *
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190 WORK( 1 ) = IWS
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191 RETURN
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192 *
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193 * End of SGELQF
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194 *
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195 END