1 | *> \brief \b SLARF |
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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 SLARF + dependencies |
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10 | *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slarf.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/slarf.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/slarf.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 SLARF( SIDE, M, N, 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, 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 | *> SLARF applies a real elementary reflector H to a real m by n matrix |
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39 | *> C, from either the left or the right. H is represented in the form |
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40 | *> |
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41 | *> H = I - tau * v * v**T |
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42 | *> |
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43 | *> where tau is a real scalar and v is a real vector. |
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44 | *> |
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45 | *> If tau = 0, then H is taken to be the unit matrix. |
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46 | *> \endverbatim |
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47 | * |
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48 | * Arguments: |
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49 | * ========== |
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50 | * |
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51 | *> \param[in] SIDE |
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52 | *> \verbatim |
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53 | *> SIDE is CHARACTER*1 |
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54 | *> = 'L': form H * C |
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55 | *> = 'R': form C * H |
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56 | *> \endverbatim |
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57 | *> |
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58 | *> \param[in] M |
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59 | *> \verbatim |
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60 | *> M is INTEGER |
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61 | *> The number of rows of the matrix C. |
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62 | *> \endverbatim |
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63 | *> |
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64 | *> \param[in] N |
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65 | *> \verbatim |
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66 | *> N is INTEGER |
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67 | *> The number of columns of the matrix C. |
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68 | *> \endverbatim |
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69 | *> |
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70 | *> \param[in] V |
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71 | *> \verbatim |
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72 | *> V is REAL array, dimension |
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73 | *> (1 + (M-1)*abs(INCV)) if SIDE = 'L' |
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74 | *> or (1 + (N-1)*abs(INCV)) if SIDE = 'R' |
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75 | *> The vector v in the representation of H. V is not used if |
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76 | *> TAU = 0. |
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77 | *> \endverbatim |
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78 | *> |
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79 | *> \param[in] INCV |
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80 | *> \verbatim |
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81 | *> INCV is INTEGER |
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82 | *> The increment between elements of v. INCV <> 0. |
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83 | *> \endverbatim |
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84 | *> |
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85 | *> \param[in] TAU |
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86 | *> \verbatim |
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87 | *> TAU is REAL |
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88 | *> The value tau in the representation of H. |
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89 | *> \endverbatim |
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90 | *> |
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91 | *> \param[in,out] C |
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92 | *> \verbatim |
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93 | *> C is REAL array, dimension (LDC,N) |
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94 | *> On entry, the m by n matrix C. |
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95 | *> On exit, C is overwritten by the matrix H * C if SIDE = 'L', |
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96 | *> or C * H if SIDE = 'R'. |
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97 | *> \endverbatim |
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98 | *> |
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99 | *> \param[in] LDC |
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100 | *> \verbatim |
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101 | *> LDC is INTEGER |
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102 | *> The leading dimension of the array C. LDC >= max(1,M). |
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103 | *> \endverbatim |
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104 | *> |
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105 | *> \param[out] WORK |
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106 | *> \verbatim |
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107 | *> WORK is REAL array, dimension |
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108 | *> (N) if SIDE = 'L' |
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109 | *> or (M) if SIDE = 'R' |
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110 | *> \endverbatim |
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111 | * |
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112 | * Authors: |
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113 | * ======== |
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114 | * |
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115 | *> \author Univ. of Tennessee |
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116 | *> \author Univ. of California Berkeley |
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117 | *> \author Univ. of Colorado Denver |
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118 | *> \author NAG Ltd. |
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119 | * |
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120 | *> \date November 2011 |
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121 | * |
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122 | *> \ingroup realOTHERauxiliary |
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123 | * |
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124 | * ===================================================================== |
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125 | SUBROUTINE SLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK ) |
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126 | * |
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127 | * -- LAPACK auxiliary routine (version 3.4.0) -- |
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128 | * -- LAPACK is a software package provided by Univ. of Tennessee, -- |
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129 | * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
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130 | * November 2011 |
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131 | * |
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132 | * .. Scalar Arguments .. |
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133 | CHARACTER SIDE |
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134 | INTEGER INCV, LDC, M, N |
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135 | REAL TAU |
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136 | * .. |
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137 | * .. Array Arguments .. |
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138 | REAL C( LDC, * ), V( * ), WORK( * ) |
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139 | * .. |
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140 | * |
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141 | * ===================================================================== |
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142 | * |
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143 | * .. Parameters .. |
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144 | REAL ONE, ZERO |
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145 | PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) |
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146 | * .. |
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147 | * .. Local Scalars .. |
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148 | LOGICAL APPLYLEFT |
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149 | INTEGER I, LASTV, LASTC |
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150 | * .. |
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151 | * .. External Subroutines .. |
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152 | EXTERNAL SGEMV, SGER |
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153 | * .. |
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154 | * .. External Functions .. |
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155 | LOGICAL LSAME |
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156 | INTEGER ILASLR, ILASLC |
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157 | EXTERNAL LSAME, ILASLR, ILASLC |
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158 | * .. |
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159 | * .. Executable Statements .. |
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160 | * |
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161 | APPLYLEFT = LSAME( SIDE, 'L' ) |
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162 | LASTV = 0 |
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163 | LASTC = 0 |
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164 | IF( TAU.NE.ZERO ) THEN |
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165 | ! Set up variables for scanning V. LASTV begins pointing to the end |
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166 | ! of V. |
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167 | IF( APPLYLEFT ) THEN |
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168 | LASTV = M |
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169 | ELSE |
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170 | LASTV = N |
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171 | END IF |
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172 | IF( INCV.GT.0 ) THEN |
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173 | I = 1 + (LASTV-1) * INCV |
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174 | ELSE |
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175 | I = 1 |
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176 | END IF |
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177 | ! Look for the last non-zero row in V. |
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178 | DO WHILE( LASTV.GT.0 .AND. V( I ).EQ.ZERO ) |
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179 | LASTV = LASTV - 1 |
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180 | I = I - INCV |
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181 | END DO |
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182 | IF( APPLYLEFT ) THEN |
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183 | ! Scan for the last non-zero column in C(1:lastv,:). |
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184 | LASTC = ILASLC(LASTV, N, C, LDC) |
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185 | ELSE |
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186 | ! Scan for the last non-zero row in C(:,1:lastv). |
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187 | LASTC = ILASLR(M, LASTV, C, LDC) |
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188 | END IF |
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189 | END IF |
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190 | ! Note that lastc.eq.0 renders the BLAS operations null; no special |
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191 | ! case is needed at this level. |
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192 | IF( APPLYLEFT ) THEN |
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193 | * |
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194 | * Form H * C |
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195 | * |
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196 | IF( LASTV.GT.0 ) THEN |
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197 | * |
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198 | * w(1:lastc,1) := C(1:lastv,1:lastc)**T * v(1:lastv,1) |
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199 | * |
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200 | CALL SGEMV( 'Transpose', LASTV, LASTC, ONE, C, LDC, V, INCV, |
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201 | $ ZERO, WORK, 1 ) |
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202 | * |
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203 | * C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**T |
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204 | * |
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205 | CALL SGER( LASTV, LASTC, -TAU, V, INCV, WORK, 1, C, LDC ) |
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206 | END IF |
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207 | ELSE |
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208 | * |
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209 | * Form C * H |
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210 | * |
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211 | IF( LASTV.GT.0 ) THEN |
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212 | * |
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213 | * w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1) |
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214 | * |
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215 | CALL SGEMV( 'No transpose', LASTC, LASTV, ONE, C, LDC, |
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216 | $ V, INCV, ZERO, WORK, 1 ) |
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217 | * |
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218 | * C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**T |
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219 | * |
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220 | CALL SGER( LASTC, LASTV, -TAU, WORK, 1, V, INCV, C, LDC ) |
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221 | END IF |
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222 | END IF |
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223 | RETURN |
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224 | * |
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225 | * End of SLARF |
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226 | * |
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227 | END |
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