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7034
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1 SUBROUTINE DORMRZ( SIDE, TRANS, M, N, K, L, 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 3.1.1) -- |
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5 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. |
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6 * January 2007 |
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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, L, LDA, LDC, LWORK, M, N |
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11 * .. |
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12 * .. Array Arguments .. |
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13 DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) |
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14 * .. |
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15 * |
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16 * Purpose |
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17 * ======= |
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18 * |
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19 * DORMRZ overwrites the general real M-by-N matrix C with |
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20 * |
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21 * SIDE = 'L' SIDE = 'R' |
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22 * TRANS = 'N': Q * C C * Q |
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23 * TRANS = 'T': Q**T * C C * Q**T |
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24 * |
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25 * where Q is a real orthogonal matrix defined as the product of k |
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26 * elementary reflectors |
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27 * |
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28 * Q = H(1) H(2) . . . H(k) |
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29 * |
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30 * as returned by DTZRZF. Q is of order M if SIDE = 'L' and of order N |
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31 * if SIDE = 'R'. |
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32 * |
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33 * Arguments |
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34 * ========= |
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35 * |
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36 * SIDE (input) CHARACTER*1 |
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37 * = 'L': apply Q or Q**T from the Left; |
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38 * = 'R': apply Q or Q**T from the Right. |
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39 * |
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40 * TRANS (input) CHARACTER*1 |
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41 * = 'N': No transpose, apply Q; |
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42 * = 'T': Transpose, apply Q**T. |
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43 * |
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44 * M (input) INTEGER |
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45 * The number of rows of the matrix C. M >= 0. |
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46 * |
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47 * N (input) INTEGER |
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48 * The number of columns of the matrix C. N >= 0. |
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49 * |
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50 * K (input) INTEGER |
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51 * The number of elementary reflectors whose product defines |
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52 * the matrix Q. |
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53 * If SIDE = 'L', M >= K >= 0; |
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54 * if SIDE = 'R', N >= K >= 0. |
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55 * |
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56 * L (input) INTEGER |
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57 * The number of columns of the matrix A containing |
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58 * the meaningful part of the Householder reflectors. |
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59 * If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0. |
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60 * |
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61 * A (input) DOUBLE PRECISION array, dimension |
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62 * (LDA,M) if SIDE = 'L', |
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63 * (LDA,N) if SIDE = 'R' |
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64 * The i-th row must contain the vector which defines the |
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65 * elementary reflector H(i), for i = 1,2,...,k, as returned by |
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66 * DTZRZF in the last k rows of its array argument A. |
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67 * A is modified by the routine but restored on exit. |
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68 * |
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69 * LDA (input) INTEGER |
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70 * The leading dimension of the array A. LDA >= max(1,K). |
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71 * |
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72 * TAU (input) DOUBLE PRECISION array, dimension (K) |
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73 * TAU(i) must contain the scalar factor of the elementary |
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74 * reflector H(i), as returned by DTZRZF. |
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75 * |
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76 * C (input/output) DOUBLE PRECISION array, dimension (LDC,N) |
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77 * On entry, the M-by-N matrix C. |
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78 * On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. |
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79 * |
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80 * LDC (input) INTEGER |
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81 * The leading dimension of the array C. LDC >= max(1,M). |
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82 * |
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83 * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) |
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84 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
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85 * |
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86 * LWORK (input) INTEGER |
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87 * The dimension of the array WORK. |
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88 * If SIDE = 'L', LWORK >= max(1,N); |
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89 * if SIDE = 'R', LWORK >= max(1,M). |
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90 * For optimum performance LWORK >= N*NB if SIDE = 'L', and |
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91 * LWORK >= M*NB if SIDE = 'R', where NB is the optimal |
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92 * blocksize. |
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93 * |
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94 * If LWORK = -1, then a workspace query is assumed; the routine |
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95 * only calculates the optimal size of the WORK array, returns |
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96 * this value as the first entry of the WORK array, and no error |
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97 * message related to LWORK is issued by XERBLA. |
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98 * |
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99 * INFO (output) INTEGER |
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100 * = 0: successful exit |
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101 * < 0: if INFO = -i, the i-th argument had an illegal value |
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102 * |
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103 * Further Details |
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104 * =============== |
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105 * |
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106 * Based on contributions by |
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107 * A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA |
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108 * |
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109 * ===================================================================== |
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110 * |
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111 * .. Parameters .. |
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112 INTEGER NBMAX, LDT |
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113 PARAMETER ( NBMAX = 64, LDT = NBMAX+1 ) |
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114 * .. |
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115 * .. Local Scalars .. |
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116 LOGICAL LEFT, LQUERY, NOTRAN |
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117 CHARACTER TRANST |
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118 INTEGER I, I1, I2, I3, IB, IC, IINFO, IWS, JA, JC, |
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119 $ LDWORK, LWKOPT, MI, NB, NBMIN, NI, NQ, NW |
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120 * .. |
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121 * .. Local Arrays .. |
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122 DOUBLE PRECISION T( LDT, NBMAX ) |
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123 * .. |
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124 * .. External Functions .. |
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125 LOGICAL LSAME |
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126 INTEGER ILAENV |
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127 EXTERNAL LSAME, ILAENV |
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128 * .. |
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129 * .. External Subroutines .. |
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130 EXTERNAL DLARZB, DLARZT, DORMR3, XERBLA |
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131 * .. |
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132 * .. Intrinsic Functions .. |
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133 INTRINSIC MAX, MIN |
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134 * .. |
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135 * .. Executable Statements .. |
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136 * |
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137 * Test the input arguments |
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138 * |
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139 INFO = 0 |
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140 LEFT = LSAME( SIDE, 'L' ) |
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141 NOTRAN = LSAME( TRANS, 'N' ) |
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142 LQUERY = ( LWORK.EQ.-1 ) |
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143 * |
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144 * NQ is the order of Q and NW is the minimum dimension of WORK |
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145 * |
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146 IF( LEFT ) THEN |
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147 NQ = M |
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148 NW = MAX( 1, N ) |
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149 ELSE |
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150 NQ = N |
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151 NW = MAX( 1, M ) |
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152 END IF |
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153 IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN |
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154 INFO = -1 |
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155 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN |
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156 INFO = -2 |
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157 ELSE IF( M.LT.0 ) THEN |
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158 INFO = -3 |
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159 ELSE IF( N.LT.0 ) THEN |
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160 INFO = -4 |
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161 ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN |
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162 INFO = -5 |
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163 ELSE IF( L.LT.0 .OR. ( LEFT .AND. ( L.GT.M ) ) .OR. |
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164 $ ( .NOT.LEFT .AND. ( L.GT.N ) ) ) THEN |
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165 INFO = -6 |
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166 ELSE IF( LDA.LT.MAX( 1, K ) ) THEN |
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167 INFO = -8 |
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168 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN |
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169 INFO = -11 |
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170 END IF |
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171 * |
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172 IF( INFO.EQ.0 ) THEN |
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173 IF( M.EQ.0 .OR. N.EQ.0 ) THEN |
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174 LWKOPT = 1 |
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175 ELSE |
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176 * |
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177 * Determine the block size. NB may be at most NBMAX, where |
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178 * NBMAX is used to define the local array T. |
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179 * |
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180 NB = MIN( NBMAX, ILAENV( 1, 'DORMRQ', SIDE // TRANS, M, N, |
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181 $ K, -1 ) ) |
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182 LWKOPT = NW*NB |
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183 END IF |
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184 WORK( 1 ) = LWKOPT |
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185 * |
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186 IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN |
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187 INFO = -13 |
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188 END IF |
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189 END IF |
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190 * |
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191 IF( INFO.NE.0 ) THEN |
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192 CALL XERBLA( 'DORMRZ', -INFO ) |
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193 RETURN |
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194 ELSE IF( LQUERY ) THEN |
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195 RETURN |
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196 END IF |
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197 * |
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198 * Quick return if possible |
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199 * |
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200 IF( M.EQ.0 .OR. N.EQ.0 ) THEN |
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201 WORK( 1 ) = 1 |
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202 RETURN |
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203 END IF |
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204 * |
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205 NBMIN = 2 |
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206 LDWORK = NW |
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207 IF( NB.GT.1 .AND. NB.LT.K ) THEN |
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208 IWS = NW*NB |
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209 IF( LWORK.LT.IWS ) THEN |
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210 NB = LWORK / LDWORK |
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211 NBMIN = MAX( 2, ILAENV( 2, 'DORMRQ', SIDE // TRANS, M, N, K, |
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212 $ -1 ) ) |
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213 END IF |
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214 ELSE |
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215 IWS = NW |
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216 END IF |
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217 * |
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218 IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN |
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219 * |
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220 * Use unblocked code |
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221 * |
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222 CALL DORMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, |
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223 $ WORK, IINFO ) |
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224 ELSE |
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225 * |
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226 * Use blocked code |
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227 * |
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228 IF( ( LEFT .AND. .NOT.NOTRAN ) .OR. |
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229 $ ( .NOT.LEFT .AND. NOTRAN ) ) THEN |
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230 I1 = 1 |
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231 I2 = K |
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232 I3 = NB |
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233 ELSE |
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234 I1 = ( ( K-1 ) / NB )*NB + 1 |
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235 I2 = 1 |
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236 I3 = -NB |
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237 END IF |
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238 * |
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239 IF( LEFT ) THEN |
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240 NI = N |
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241 JC = 1 |
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242 JA = M - L + 1 |
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243 ELSE |
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244 MI = M |
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245 IC = 1 |
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246 JA = N - L + 1 |
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247 END IF |
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248 * |
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249 IF( NOTRAN ) THEN |
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250 TRANST = 'T' |
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251 ELSE |
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252 TRANST = 'N' |
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253 END IF |
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254 * |
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255 DO 10 I = I1, I2, I3 |
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256 IB = MIN( NB, K-I+1 ) |
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257 * |
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258 * Form the triangular factor of the block reflector |
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259 * H = H(i+ib-1) . . . H(i+1) H(i) |
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260 * |
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261 CALL DLARZT( 'Backward', 'Rowwise', L, IB, A( I, JA ), LDA, |
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262 $ TAU( I ), T, LDT ) |
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263 * |
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264 IF( LEFT ) THEN |
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265 * |
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266 * H or H' is applied to C(i:m,1:n) |
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267 * |
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268 MI = M - I + 1 |
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269 IC = I |
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270 ELSE |
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271 * |
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272 * H or H' is applied to C(1:m,i:n) |
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273 * |
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274 NI = N - I + 1 |
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275 JC = I |
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276 END IF |
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277 * |
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278 * Apply H or H' |
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279 * |
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280 CALL DLARZB( SIDE, TRANST, 'Backward', 'Rowwise', MI, NI, |
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281 $ IB, L, A( I, JA ), LDA, T, LDT, C( IC, JC ), |
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282 $ LDC, WORK, LDWORK ) |
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283 10 CONTINUE |
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284 * |
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285 END IF |
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286 * |
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287 WORK( 1 ) = LWKOPT |
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288 * |
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289 RETURN |
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290 * |
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291 * End of DORMRZ |
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292 * |
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293 END |
