1 | *> \brief \b SLARZ |
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2 | * |
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3 | * =========== DOCUMENTATION =========== |
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4 | * |
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5 | * Online html documentation available at |
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6 | * http://www.netlib.org/lapack/explore-html/ |
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7 | * |
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8 | *> \htmlonly |
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9 | *> Download SLARZ + dependencies |
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10 | *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slarz.f"> |
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11 | *> [TGZ]</a> |
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12 | *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slarz.f"> |
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13 | *> [ZIP]</a> |
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14 | *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slarz.f"> |
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15 | *> [TXT]</a> |
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16 | *> \endhtmlonly |
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17 | * |
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18 | * Definition: |
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19 | * =========== |
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20 | * |
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21 | * SUBROUTINE SLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK ) |
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22 | * |
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23 | * .. Scalar Arguments .. |
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24 | * CHARACTER SIDE |
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25 | * INTEGER INCV, L, LDC, M, N |
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26 | * REAL TAU |
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27 | * .. |
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28 | * .. Array Arguments .. |
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29 | * REAL C( LDC, * ), V( * ), WORK( * ) |
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30 | * .. |
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31 | * |
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32 | * |
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33 | *> \par Purpose: |
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34 | * ============= |
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35 | *> |
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36 | *> \verbatim |
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37 | *> |
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38 | *> SLARZ applies a real elementary reflector H to a real M-by-N |
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39 | *> matrix C, from either the left or the right. H is represented in the |
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40 | *> form |
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41 | *> |
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42 | *> H = I - tau * v * v**T |
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43 | *> |
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44 | *> where tau is a real scalar and v is a real vector. |
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45 | *> |
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46 | *> If tau = 0, then H is taken to be the unit matrix. |
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47 | *> |
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48 | *> |
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49 | *> H is a product of k elementary reflectors as returned by STZRZF. |
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50 | *> \endverbatim |
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51 | * |
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52 | * Arguments: |
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53 | * ========== |
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54 | * |
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55 | *> \param[in] SIDE |
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56 | *> \verbatim |
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57 | *> SIDE is CHARACTER*1 |
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58 | *> = 'L': form H * C |
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59 | *> = 'R': form C * H |
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60 | *> \endverbatim |
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61 | *> |
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62 | *> \param[in] M |
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63 | *> \verbatim |
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64 | *> M is INTEGER |
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65 | *> The number of rows of the matrix C. |
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66 | *> \endverbatim |
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67 | *> |
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68 | *> \param[in] N |
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69 | *> \verbatim |
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70 | *> N is INTEGER |
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71 | *> The number of columns of the matrix C. |
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72 | *> \endverbatim |
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73 | *> |
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74 | *> \param[in] L |
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75 | *> \verbatim |
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76 | *> L is INTEGER |
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77 | *> The number of entries of the vector V containing |
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78 | *> the meaningful part of the Householder vectors. |
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79 | *> If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0. |
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80 | *> \endverbatim |
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81 | *> |
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82 | *> \param[in] V |
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83 | *> \verbatim |
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84 | *> V is REAL array, dimension (1+(L-1)*abs(INCV)) |
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85 | *> The vector v in the representation of H as returned by |
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86 | *> STZRZF. V is not used if TAU = 0. |
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87 | *> \endverbatim |
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88 | *> |
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89 | *> \param[in] INCV |
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90 | *> \verbatim |
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91 | *> INCV is INTEGER |
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92 | *> The increment between elements of v. INCV <> 0. |
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93 | *> \endverbatim |
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94 | *> |
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95 | *> \param[in] TAU |
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96 | *> \verbatim |
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97 | *> TAU is REAL |
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98 | *> The value tau in the representation of H. |
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99 | *> \endverbatim |
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100 | *> |
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101 | *> \param[in,out] C |
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102 | *> \verbatim |
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103 | *> C is REAL array, dimension (LDC,N) |
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104 | *> On entry, the M-by-N matrix C. |
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105 | *> On exit, C is overwritten by the matrix H * C if SIDE = 'L', |
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106 | *> or C * H if SIDE = 'R'. |
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107 | *> \endverbatim |
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108 | *> |
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109 | *> \param[in] LDC |
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110 | *> \verbatim |
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111 | *> LDC is INTEGER |
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112 | *> The leading dimension of the array C. LDC >= max(1,M). |
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113 | *> \endverbatim |
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114 | *> |
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115 | *> \param[out] WORK |
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116 | *> \verbatim |
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117 | *> WORK is REAL array, dimension |
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118 | *> (N) if SIDE = 'L' |
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119 | *> or (M) if SIDE = 'R' |
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120 | *> \endverbatim |
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121 | * |
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122 | * Authors: |
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123 | * ======== |
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124 | * |
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125 | *> \author Univ. of Tennessee |
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126 | *> \author Univ. of California Berkeley |
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127 | *> \author Univ. of Colorado Denver |
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128 | *> \author NAG Ltd. |
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129 | * |
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130 | *> \date November 2011 |
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131 | * |
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132 | *> \ingroup realOTHERcomputational |
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133 | * |
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134 | *> \par Contributors: |
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135 | * ================== |
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136 | *> |
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137 | *> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA |
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138 | * |
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139 | *> \par Further Details: |
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140 | * ===================== |
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141 | *> |
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142 | *> \verbatim |
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143 | *> \endverbatim |
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144 | *> |
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145 | * ===================================================================== |
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146 | SUBROUTINE SLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK ) |
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147 | * |
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148 | * -- LAPACK computational routine (version 3.4.0) -- |
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149 | * -- LAPACK is a software package provided by Univ. of Tennessee, -- |
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150 | * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
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151 | * November 2011 |
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152 | * |
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153 | * .. Scalar Arguments .. |
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154 | CHARACTER SIDE |
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155 | INTEGER INCV, L, LDC, M, N |
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156 | REAL TAU |
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157 | * .. |
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158 | * .. Array Arguments .. |
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159 | REAL C( LDC, * ), V( * ), WORK( * ) |
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160 | * .. |
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161 | * |
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162 | * ===================================================================== |
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163 | * |
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164 | * .. Parameters .. |
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165 | REAL ONE, ZERO |
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166 | PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) |
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167 | * .. |
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168 | * .. External Subroutines .. |
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169 | EXTERNAL SAXPY, SCOPY, SGEMV, SGER |
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170 | * .. |
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171 | * .. External Functions .. |
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172 | LOGICAL LSAME |
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173 | EXTERNAL LSAME |
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174 | * .. |
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175 | * .. Executable Statements .. |
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176 | * |
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177 | IF( LSAME( SIDE, 'L' ) ) THEN |
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178 | * |
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179 | * Form H * C |
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180 | * |
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181 | IF( TAU.NE.ZERO ) THEN |
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182 | * |
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183 | * w( 1:n ) = C( 1, 1:n ) |
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184 | * |
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185 | CALL SCOPY( N, C, LDC, WORK, 1 ) |
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186 | * |
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187 | * w( 1:n ) = w( 1:n ) + C( m-l+1:m, 1:n )**T * v( 1:l ) |
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188 | * |
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189 | CALL SGEMV( 'Transpose', L, N, ONE, C( M-L+1, 1 ), LDC, V, |
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190 | $ INCV, ONE, WORK, 1 ) |
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191 | * |
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192 | * C( 1, 1:n ) = C( 1, 1:n ) - tau * w( 1:n ) |
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193 | * |
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194 | CALL SAXPY( N, -TAU, WORK, 1, C, LDC ) |
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195 | * |
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196 | * C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ... |
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197 | * tau * v( 1:l ) * w( 1:n )**T |
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198 | * |
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199 | CALL SGER( L, N, -TAU, V, INCV, WORK, 1, C( M-L+1, 1 ), |
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200 | $ LDC ) |
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201 | END IF |
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202 | * |
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203 | ELSE |
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204 | * |
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205 | * Form C * H |
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206 | * |
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207 | IF( TAU.NE.ZERO ) THEN |
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208 | * |
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209 | * w( 1:m ) = C( 1:m, 1 ) |
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210 | * |
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211 | CALL SCOPY( M, C, 1, WORK, 1 ) |
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212 | * |
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213 | * w( 1:m ) = w( 1:m ) + C( 1:m, n-l+1:n, 1:n ) * v( 1:l ) |
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214 | * |
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215 | CALL SGEMV( 'No transpose', M, L, ONE, C( 1, N-L+1 ), LDC, |
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216 | $ V, INCV, ONE, WORK, 1 ) |
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217 | * |
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218 | * C( 1:m, 1 ) = C( 1:m, 1 ) - tau * w( 1:m ) |
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219 | * |
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220 | CALL SAXPY( M, -TAU, WORK, 1, C, 1 ) |
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221 | * |
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222 | * C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ... |
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223 | * tau * w( 1:m ) * v( 1:l )**T |
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224 | * |
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225 | CALL SGER( M, L, -TAU, WORK, 1, V, INCV, C( 1, N-L+1 ), |
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226 | $ LDC ) |
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227 | * |
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228 | END IF |
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229 | * |
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230 | END IF |
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231 | * |
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232 | RETURN |
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233 | * |
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234 | * End of SLARZ |
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235 | * |
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236 | END |
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