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annotate libcruft/lapack/sormlq.f @ 8596:8833c0b18eb2

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enable default settings queries in optim funcs
author Jaroslav Hajek <highegg@gmail.com>
date Tue, 27 Jan 2009 08:15:08 +0100
parents 82be108cc558
children
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1 SUBROUTINE SORMLQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
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2 $ WORK, LWORK, INFO )
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3 *
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4 * -- LAPACK routine (version 3.1) --
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5 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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6 * November 2006
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7 *
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8 * .. Scalar Arguments ..
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9 CHARACTER SIDE, TRANS
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10 INTEGER INFO, K, LDA, LDC, LWORK, M, N
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11 * ..
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12 * .. Array Arguments ..
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13 REAL A( LDA, * ), C( LDC, * ), TAU( * ),
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14 $ WORK( * )
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15 * ..
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16 *
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17 * Purpose
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18 * =======
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19 *
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20 * SORMLQ overwrites the general real M-by-N matrix C with
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21 *
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22 * SIDE = 'L' SIDE = 'R'
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23 * TRANS = 'N': Q * C C * Q
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24 * TRANS = 'T': Q**T * C C * Q**T
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25 *
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26 * where Q is a real orthogonal matrix defined as the product of k
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27 * elementary reflectors
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28 *
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29 * Q = H(k) . . . H(2) H(1)
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30 *
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31 * as returned by SGELQF. Q is of order M if SIDE = 'L' and of order N
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32 * if SIDE = 'R'.
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33 *
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34 * Arguments
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35 * =========
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36 *
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37 * SIDE (input) CHARACTER*1
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38 * = 'L': apply Q or Q**T from the Left;
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39 * = 'R': apply Q or Q**T from the Right.
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40 *
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41 * TRANS (input) CHARACTER*1
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42 * = 'N': No transpose, apply Q;
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43 * = 'T': Transpose, apply Q**T.
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44 *
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45 * M (input) INTEGER
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46 * The number of rows of the matrix C. M >= 0.
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47 *
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48 * N (input) INTEGER
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49 * The number of columns of the matrix C. N >= 0.
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50 *
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51 * K (input) INTEGER
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52 * The number of elementary reflectors whose product defines
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53 * the matrix Q.
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54 * If SIDE = 'L', M >= K >= 0;
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55 * if SIDE = 'R', N >= K >= 0.
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56 *
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57 * A (input) REAL array, dimension
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58 * (LDA,M) if SIDE = 'L',
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59 * (LDA,N) if SIDE = 'R'
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60 * The i-th row must contain the vector which defines the
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61 * elementary reflector H(i), for i = 1,2,...,k, as returned by
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62 * SGELQF in the first k rows of its array argument A.
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63 * A is modified by the routine but restored on exit.
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64 *
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65 * LDA (input) INTEGER
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66 * The leading dimension of the array A. LDA >= max(1,K).
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67 *
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68 * TAU (input) REAL array, dimension (K)
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69 * TAU(i) must contain the scalar factor of the elementary
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70 * reflector H(i), as returned by SGELQF.
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71 *
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72 * C (input/output) REAL array, dimension (LDC,N)
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73 * On entry, the M-by-N matrix C.
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74 * On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
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75 *
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76 * LDC (input) INTEGER
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77 * The leading dimension of the array C. LDC >= max(1,M).
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78 *
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79 * WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))
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80 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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81 *
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82 * LWORK (input) INTEGER
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83 * The dimension of the array WORK.
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84 * If SIDE = 'L', LWORK >= max(1,N);
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85 * if SIDE = 'R', LWORK >= max(1,M).
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86 * For optimum performance LWORK >= N*NB if SIDE = 'L', and
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87 * LWORK >= M*NB if SIDE = 'R', where NB is the optimal
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88 * blocksize.
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89 *
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90 * If LWORK = -1, then a workspace query is assumed; the routine
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91 * only calculates the optimal size of the WORK array, returns
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92 * this value as the first entry of the WORK array, and no error
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93 * message related to LWORK is issued by XERBLA.
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94 *
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95 * INFO (output) INTEGER
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96 * = 0: successful exit
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97 * < 0: if INFO = -i, the i-th argument had an illegal value
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98 *
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99 * =====================================================================
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100 *
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101 * .. Parameters ..
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102 INTEGER NBMAX, LDT
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103 PARAMETER ( NBMAX = 64, LDT = NBMAX+1 )
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104 * ..
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105 * .. Local Scalars ..
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106 LOGICAL LEFT, LQUERY, NOTRAN
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107 CHARACTER TRANST
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108 INTEGER I, I1, I2, I3, IB, IC, IINFO, IWS, JC, LDWORK,
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109 $ LWKOPT, MI, NB, NBMIN, NI, NQ, NW
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110 * ..
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111 * .. Local Arrays ..
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112 REAL T( LDT, NBMAX )
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113 * ..
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114 * .. External Functions ..
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115 LOGICAL LSAME
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116 INTEGER ILAENV
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117 EXTERNAL LSAME, ILAENV
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118 * ..
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119 * .. External Subroutines ..
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120 EXTERNAL SLARFB, SLARFT, SORML2, XERBLA
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121 * ..
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122 * .. Intrinsic Functions ..
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123 INTRINSIC MAX, MIN
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124 * ..
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125 * .. Executable Statements ..
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126 *
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127 * Test the input arguments
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128 *
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129 INFO = 0
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130 LEFT = LSAME( SIDE, 'L' )
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131 NOTRAN = LSAME( TRANS, 'N' )
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132 LQUERY = ( LWORK.EQ.-1 )
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133 *
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134 * NQ is the order of Q and NW is the minimum dimension of WORK
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135 *
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136 IF( LEFT ) THEN
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137 NQ = M
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138 NW = N
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139 ELSE
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140 NQ = N
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141 NW = M
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142 END IF
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143 IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
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144 INFO = -1
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145 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
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146 INFO = -2
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147 ELSE IF( M.LT.0 ) THEN
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148 INFO = -3
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149 ELSE IF( N.LT.0 ) THEN
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150 INFO = -4
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151 ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
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152 INFO = -5
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153 ELSE IF( LDA.LT.MAX( 1, K ) ) THEN
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154 INFO = -7
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155 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
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156 INFO = -10
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157 ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
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158 INFO = -12
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159 END IF
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160 *
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161 IF( INFO.EQ.0 ) THEN
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162 *
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163 * Determine the block size. NB may be at most NBMAX, where NBMAX
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164 * is used to define the local array T.
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165 *
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166 NB = MIN( NBMAX, ILAENV( 1, 'SORMLQ', SIDE // TRANS, M, N, K,
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167 $ -1 ) )
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168 LWKOPT = MAX( 1, NW )*NB
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169 WORK( 1 ) = LWKOPT
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170 END IF
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171 *
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172 IF( INFO.NE.0 ) THEN
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173 CALL XERBLA( 'SORMLQ', -INFO )
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174 RETURN
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175 ELSE IF( LQUERY ) THEN
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176 RETURN
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177 END IF
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178 *
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179 * Quick return if possible
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180 *
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181 IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) THEN
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182 WORK( 1 ) = 1
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183 RETURN
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184 END IF
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185 *
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186 NBMIN = 2
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187 LDWORK = NW
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188 IF( NB.GT.1 .AND. NB.LT.K ) THEN
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189 IWS = NW*NB
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190 IF( LWORK.LT.IWS ) THEN
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191 NB = LWORK / LDWORK
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192 NBMIN = MAX( 2, ILAENV( 2, 'SORMLQ', SIDE // TRANS, M, N, K,
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193 $ -1 ) )
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194 END IF
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195 ELSE
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196 IWS = NW
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197 END IF
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198 *
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199 IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN
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200 *
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201 * Use unblocked code
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202 *
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203 CALL SORML2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK,
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204 $ IINFO )
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205 ELSE
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206 *
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207 * Use blocked code
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208 *
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209 IF( ( LEFT .AND. NOTRAN ) .OR.
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210 $ ( .NOT.LEFT .AND. .NOT.NOTRAN ) ) THEN
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211 I1 = 1
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212 I2 = K
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213 I3 = NB
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214 ELSE
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215 I1 = ( ( K-1 ) / NB )*NB + 1
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216 I2 = 1
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217 I3 = -NB
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218 END IF
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219 *
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220 IF( LEFT ) THEN
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221 NI = N
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222 JC = 1
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223 ELSE
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224 MI = M
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225 IC = 1
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226 END IF
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227 *
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228 IF( NOTRAN ) THEN
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229 TRANST = 'T'
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230 ELSE
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231 TRANST = 'N'
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232 END IF
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233 *
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234 DO 10 I = I1, I2, I3
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235 IB = MIN( NB, K-I+1 )
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236 *
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237 * Form the triangular factor of the block reflector
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238 * H = H(i) H(i+1) . . . H(i+ib-1)
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239 *
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240 CALL SLARFT( 'Forward', 'Rowwise', NQ-I+1, IB, A( I, I ),
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241 $ LDA, TAU( I ), T, LDT )
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242 IF( LEFT ) THEN
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243 *
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244 * H or H' is applied to C(i:m,1:n)
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245 *
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246 MI = M - I + 1
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247 IC = I
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248 ELSE
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249 *
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250 * H or H' is applied to C(1:m,i:n)
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251 *
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252 NI = N - I + 1
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253 JC = I
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254 END IF
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255 *
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256 * Apply H or H'
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257 *
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258 CALL SLARFB( SIDE, TRANST, 'Forward', 'Rowwise', MI, NI, IB,
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259 $ A( I, I ), LDA, T, LDT, C( IC, JC ), LDC, WORK,
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260 $ LDWORK )
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261 10 CONTINUE
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262 END IF
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263 WORK( 1 ) = LWKOPT
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264 RETURN
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265 *
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266 * End of SORMLQ
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267 *
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268 END