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2329
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1 SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA ) |
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2 * |
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3 * -- LAPACK auxiliary routine (version 2.0) -- |
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4 * Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., |
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5 * Courant Institute, Argonne National Lab, and Rice University |
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6 * October 31, 1992 |
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7 * |
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8 * .. Scalar Arguments .. |
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9 CHARACTER DIRECT, PIVOT, SIDE |
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10 INTEGER LDA, M, N |
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11 * .. |
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12 * .. Array Arguments .. |
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13 DOUBLE PRECISION A( LDA, * ), C( * ), S( * ) |
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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 * DLASR performs the transformation |
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20 * |
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21 * A := P*A, when SIDE = 'L' or 'l' ( Left-hand side ) |
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22 * |
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23 * A := A*P', when SIDE = 'R' or 'r' ( Right-hand side ) |
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24 * |
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25 * where A is an m by n real matrix and P is an orthogonal matrix, |
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26 * consisting of a sequence of plane rotations determined by the |
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27 * parameters PIVOT and DIRECT as follows ( z = m when SIDE = 'L' or 'l' |
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28 * and z = n when SIDE = 'R' or 'r' ): |
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29 * |
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30 * When DIRECT = 'F' or 'f' ( Forward sequence ) then |
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31 * |
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32 * P = P( z - 1 )*...*P( 2 )*P( 1 ), |
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33 * |
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34 * and when DIRECT = 'B' or 'b' ( Backward sequence ) then |
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35 * |
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36 * P = P( 1 )*P( 2 )*...*P( z - 1 ), |
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37 * |
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38 * where P( k ) is a plane rotation matrix for the following planes: |
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39 * |
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40 * when PIVOT = 'V' or 'v' ( Variable pivot ), |
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41 * the plane ( k, k + 1 ) |
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42 * |
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43 * when PIVOT = 'T' or 't' ( Top pivot ), |
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44 * the plane ( 1, k + 1 ) |
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45 * |
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46 * when PIVOT = 'B' or 'b' ( Bottom pivot ), |
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47 * the plane ( k, z ) |
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48 * |
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49 * c( k ) and s( k ) must contain the cosine and sine that define the |
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50 * matrix P( k ). The two by two plane rotation part of the matrix |
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51 * P( k ), R( k ), is assumed to be of the form |
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52 * |
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53 * R( k ) = ( c( k ) s( k ) ). |
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54 * ( -s( k ) c( k ) ) |
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55 * |
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56 * This version vectorises across rows of the array A when SIDE = 'L'. |
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57 * |
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58 * Arguments |
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59 * ========= |
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60 * |
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61 * SIDE (input) CHARACTER*1 |
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62 * Specifies whether the plane rotation matrix P is applied to |
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63 * A on the left or the right. |
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64 * = 'L': Left, compute A := P*A |
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65 * = 'R': Right, compute A:= A*P' |
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66 * |
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67 * DIRECT (input) CHARACTER*1 |
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68 * Specifies whether P is a forward or backward sequence of |
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69 * plane rotations. |
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70 * = 'F': Forward, P = P( z - 1 )*...*P( 2 )*P( 1 ) |
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71 * = 'B': Backward, P = P( 1 )*P( 2 )*...*P( z - 1 ) |
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72 * |
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73 * PIVOT (input) CHARACTER*1 |
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74 * Specifies the plane for which P(k) is a plane rotation |
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75 * matrix. |
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76 * = 'V': Variable pivot, the plane (k,k+1) |
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77 * = 'T': Top pivot, the plane (1,k+1) |
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78 * = 'B': Bottom pivot, the plane (k,z) |
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79 * |
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80 * M (input) INTEGER |
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81 * The number of rows of the matrix A. If m <= 1, an immediate |
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82 * return is effected. |
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83 * |
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84 * N (input) INTEGER |
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85 * The number of columns of the matrix A. If n <= 1, an |
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86 * immediate return is effected. |
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87 * |
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88 * C, S (input) DOUBLE PRECISION arrays, dimension |
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89 * (M-1) if SIDE = 'L' |
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90 * (N-1) if SIDE = 'R' |
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91 * c(k) and s(k) contain the cosine and sine that define the |
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92 * matrix P(k). The two by two plane rotation part of the |
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93 * matrix P(k), R(k), is assumed to be of the form |
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94 * R( k ) = ( c( k ) s( k ) ). |
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95 * ( -s( k ) c( k ) ) |
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96 * |
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97 * A (input/output) DOUBLE PRECISION array, dimension (LDA,N) |
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98 * The m by n matrix A. On exit, A is overwritten by P*A if |
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99 * SIDE = 'R' or by A*P' if SIDE = 'L'. |
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100 * |
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101 * LDA (input) INTEGER |
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102 * The leading dimension of the array A. LDA >= max(1,M). |
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103 * |
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104 * ===================================================================== |
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105 * |
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106 * .. Parameters .. |
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107 DOUBLE PRECISION ONE, ZERO |
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108 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) |
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109 * .. |
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110 * .. Local Scalars .. |
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111 INTEGER I, INFO, J |
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112 DOUBLE PRECISION CTEMP, STEMP, TEMP |
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113 * .. |
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114 * .. External Functions .. |
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115 LOGICAL LSAME |
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116 EXTERNAL LSAME |
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117 * .. |
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118 * .. External Subroutines .. |
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119 EXTERNAL XERBLA |
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120 * .. |
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121 * .. Intrinsic Functions .. |
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122 INTRINSIC MAX |
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123 * .. |
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124 * .. Executable Statements .. |
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125 * |
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126 * Test the input parameters |
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127 * |
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128 INFO = 0 |
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129 IF( .NOT.( LSAME( SIDE, 'L' ) .OR. LSAME( SIDE, 'R' ) ) ) THEN |
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130 INFO = 1 |
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131 ELSE IF( .NOT.( LSAME( PIVOT, 'V' ) .OR. LSAME( PIVOT, |
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132 $ 'T' ) .OR. LSAME( PIVOT, 'B' ) ) ) THEN |
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133 INFO = 2 |
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134 ELSE IF( .NOT.( LSAME( DIRECT, 'F' ) .OR. LSAME( DIRECT, 'B' ) ) ) |
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135 $ THEN |
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136 INFO = 3 |
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137 ELSE IF( M.LT.0 ) THEN |
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138 INFO = 4 |
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139 ELSE IF( N.LT.0 ) THEN |
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140 INFO = 5 |
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141 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN |
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142 INFO = 9 |
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143 END IF |
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144 IF( INFO.NE.0 ) THEN |
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145 CALL XERBLA( 'DLASR ', INFO ) |
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146 RETURN |
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147 END IF |
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148 * |
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149 * Quick return if possible |
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150 * |
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151 IF( ( M.EQ.0 ) .OR. ( N.EQ.0 ) ) |
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152 $ RETURN |
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153 IF( LSAME( SIDE, 'L' ) ) THEN |
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154 * |
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155 * Form P * A |
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156 * |
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157 IF( LSAME( PIVOT, 'V' ) ) THEN |
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158 IF( LSAME( DIRECT, 'F' ) ) THEN |
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159 DO 20 J = 1, M - 1 |
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160 CTEMP = C( J ) |
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161 STEMP = S( J ) |
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162 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN |
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163 DO 10 I = 1, N |
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164 TEMP = A( J+1, I ) |
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165 A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I ) |
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166 A( J, I ) = STEMP*TEMP + CTEMP*A( J, I ) |
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167 10 CONTINUE |
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168 END IF |
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169 20 CONTINUE |
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170 ELSE IF( LSAME( DIRECT, 'B' ) ) THEN |
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171 DO 40 J = M - 1, 1, -1 |
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172 CTEMP = C( J ) |
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173 STEMP = S( J ) |
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174 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN |
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175 DO 30 I = 1, N |
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176 TEMP = A( J+1, I ) |
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177 A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I ) |
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178 A( J, I ) = STEMP*TEMP + CTEMP*A( J, I ) |
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179 30 CONTINUE |
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180 END IF |
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181 40 CONTINUE |
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182 END IF |
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183 ELSE IF( LSAME( PIVOT, 'T' ) ) THEN |
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184 IF( LSAME( DIRECT, 'F' ) ) THEN |
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185 DO 60 J = 2, M |
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186 CTEMP = C( J-1 ) |
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187 STEMP = S( J-1 ) |
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188 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN |
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189 DO 50 I = 1, N |
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190 TEMP = A( J, I ) |
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191 A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I ) |
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192 A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I ) |
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193 50 CONTINUE |
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194 END IF |
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195 60 CONTINUE |
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196 ELSE IF( LSAME( DIRECT, 'B' ) ) THEN |
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197 DO 80 J = M, 2, -1 |
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198 CTEMP = C( J-1 ) |
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199 STEMP = S( J-1 ) |
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200 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN |
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201 DO 70 I = 1, N |
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202 TEMP = A( J, I ) |
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203 A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I ) |
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204 A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I ) |
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205 70 CONTINUE |
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206 END IF |
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207 80 CONTINUE |
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208 END IF |
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209 ELSE IF( LSAME( PIVOT, 'B' ) ) THEN |
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210 IF( LSAME( DIRECT, 'F' ) ) THEN |
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211 DO 100 J = 1, M - 1 |
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212 CTEMP = C( J ) |
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213 STEMP = S( J ) |
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214 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN |
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215 DO 90 I = 1, N |
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216 TEMP = A( J, I ) |
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217 A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP |
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218 A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP |
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219 90 CONTINUE |
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220 END IF |
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221 100 CONTINUE |
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222 ELSE IF( LSAME( DIRECT, 'B' ) ) THEN |
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223 DO 120 J = M - 1, 1, -1 |
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224 CTEMP = C( J ) |
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225 STEMP = S( J ) |
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226 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN |
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227 DO 110 I = 1, N |
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228 TEMP = A( J, I ) |
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229 A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP |
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230 A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP |
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231 110 CONTINUE |
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232 END IF |
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233 120 CONTINUE |
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234 END IF |
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235 END IF |
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236 ELSE IF( LSAME( SIDE, 'R' ) ) THEN |
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237 * |
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238 * Form A * P' |
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239 * |
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240 IF( LSAME( PIVOT, 'V' ) ) THEN |
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241 IF( LSAME( DIRECT, 'F' ) ) THEN |
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242 DO 140 J = 1, N - 1 |
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243 CTEMP = C( J ) |
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244 STEMP = S( J ) |
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245 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN |
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246 DO 130 I = 1, M |
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247 TEMP = A( I, J+1 ) |
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248 A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J ) |
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249 A( I, J ) = STEMP*TEMP + CTEMP*A( I, J ) |
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250 130 CONTINUE |
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251 END IF |
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252 140 CONTINUE |
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253 ELSE IF( LSAME( DIRECT, 'B' ) ) THEN |
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254 DO 160 J = N - 1, 1, -1 |
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255 CTEMP = C( J ) |
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256 STEMP = S( J ) |
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257 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN |
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258 DO 150 I = 1, M |
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259 TEMP = A( I, J+1 ) |
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260 A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J ) |
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261 A( I, J ) = STEMP*TEMP + CTEMP*A( I, J ) |
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262 150 CONTINUE |
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263 END IF |
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264 160 CONTINUE |
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265 END IF |
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266 ELSE IF( LSAME( PIVOT, 'T' ) ) THEN |
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267 IF( LSAME( DIRECT, 'F' ) ) THEN |
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268 DO 180 J = 2, N |
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269 CTEMP = C( J-1 ) |
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270 STEMP = S( J-1 ) |
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271 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN |
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272 DO 170 I = 1, M |
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273 TEMP = A( I, J ) |
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274 A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 ) |
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275 A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 ) |
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276 170 CONTINUE |
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277 END IF |
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278 180 CONTINUE |
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279 ELSE IF( LSAME( DIRECT, 'B' ) ) THEN |
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280 DO 200 J = N, 2, -1 |
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281 CTEMP = C( J-1 ) |
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282 STEMP = S( J-1 ) |
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283 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN |
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284 DO 190 I = 1, M |
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285 TEMP = A( I, J ) |
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286 A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 ) |
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287 A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 ) |
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288 190 CONTINUE |
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289 END IF |
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290 200 CONTINUE |
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291 END IF |
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292 ELSE IF( LSAME( PIVOT, 'B' ) ) THEN |
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293 IF( LSAME( DIRECT, 'F' ) ) THEN |
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294 DO 220 J = 1, N - 1 |
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295 CTEMP = C( J ) |
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296 STEMP = S( J ) |
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297 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN |
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298 DO 210 I = 1, M |
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299 TEMP = A( I, J ) |
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300 A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP |
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301 A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP |
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302 210 CONTINUE |
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303 END IF |
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304 220 CONTINUE |
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305 ELSE IF( LSAME( DIRECT, 'B' ) ) THEN |
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306 DO 240 J = N - 1, 1, -1 |
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307 CTEMP = C( J ) |
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308 STEMP = S( J ) |
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309 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN |
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310 DO 230 I = 1, M |
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311 TEMP = A( I, J ) |
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312 A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP |
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313 A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP |
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314 230 CONTINUE |
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315 END IF |
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316 240 CONTINUE |
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317 END IF |
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318 END IF |
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319 END IF |
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320 * |
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321 RETURN |
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322 * |
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323 * End of DLASR |
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324 * |
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325 END |
