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1 SUBROUTINE DGEMV ( TRANS, M, N, ALPHA, A, LDA, X, INCX, |
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2 $ BETA, Y, INCY ) |
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3 * .. Scalar Arguments .. |
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4 DOUBLE PRECISION ALPHA, BETA |
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5 INTEGER INCX, INCY, LDA, M, N |
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6 CHARACTER*1 TRANS |
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7 * .. Array Arguments .. |
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8 DOUBLE PRECISION A( LDA, * ), X( * ), Y( * ) |
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9 * .. |
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10 * |
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11 * Purpose |
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12 * ======= |
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13 * |
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14 * DGEMV performs one of the matrix-vector operations |
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15 * |
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16 * y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, |
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17 * |
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18 * where alpha and beta are scalars, x and y are vectors and A is an |
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19 * m by n matrix. |
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20 * |
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21 * Parameters |
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22 * ========== |
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23 * |
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24 * TRANS - CHARACTER*1. |
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25 * On entry, TRANS specifies the operation to be performed as |
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26 * follows: |
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27 * |
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28 * TRANS = 'N' or 'n' y := alpha*A*x + beta*y. |
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29 * |
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30 * TRANS = 'T' or 't' y := alpha*A'*x + beta*y. |
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31 * |
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32 * TRANS = 'C' or 'c' y := alpha*A'*x + beta*y. |
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33 * |
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34 * Unchanged on exit. |
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35 * |
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36 * M - INTEGER. |
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37 * On entry, M specifies the number of rows of the matrix A. |
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38 * M must be at least zero. |
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39 * Unchanged on exit. |
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40 * |
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41 * N - INTEGER. |
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42 * On entry, N specifies the number of columns of the matrix A. |
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43 * N must be at least zero. |
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44 * Unchanged on exit. |
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45 * |
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46 * ALPHA - DOUBLE PRECISION. |
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47 * On entry, ALPHA specifies the scalar alpha. |
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48 * Unchanged on exit. |
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49 * |
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50 * A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). |
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51 * Before entry, the leading m by n part of the array A must |
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52 * contain the matrix of coefficients. |
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53 * Unchanged on exit. |
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54 * |
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55 * LDA - INTEGER. |
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56 * On entry, LDA specifies the first dimension of A as declared |
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57 * in the calling (sub) program. LDA must be at least |
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58 * max( 1, m ). |
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59 * Unchanged on exit. |
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60 * |
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61 * X - DOUBLE PRECISION array of DIMENSION at least |
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62 * ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' |
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63 * and at least |
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64 * ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. |
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65 * Before entry, the incremented array X must contain the |
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66 * vector x. |
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67 * Unchanged on exit. |
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68 * |
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69 * INCX - INTEGER. |
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70 * On entry, INCX specifies the increment for the elements of |
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71 * X. INCX must not be zero. |
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72 * Unchanged on exit. |
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73 * |
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74 * BETA - DOUBLE PRECISION. |
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75 * On entry, BETA specifies the scalar beta. When BETA is |
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76 * supplied as zero then Y need not be set on input. |
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77 * Unchanged on exit. |
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78 * |
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79 * Y - DOUBLE PRECISION array of DIMENSION at least |
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80 * ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' |
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81 * and at least |
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82 * ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. |
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83 * Before entry with BETA non-zero, the incremented array Y |
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84 * must contain the vector y. On exit, Y is overwritten by the |
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85 * updated vector y. |
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86 * |
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87 * INCY - INTEGER. |
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88 * On entry, INCY specifies the increment for the elements of |
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89 * Y. INCY must not be zero. |
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90 * Unchanged on exit. |
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91 * |
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92 * |
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93 * Level 2 Blas routine. |
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94 * |
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95 * -- Written on 22-October-1986. |
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96 * Jack Dongarra, Argonne National Lab. |
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97 * Jeremy Du Croz, Nag Central Office. |
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98 * Sven Hammarling, Nag Central Office. |
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99 * Richard Hanson, Sandia National Labs. |
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100 * |
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101 * |
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102 * .. Parameters .. |
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103 DOUBLE PRECISION ONE , ZERO |
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104 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) |
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105 * .. Local Scalars .. |
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106 DOUBLE PRECISION TEMP |
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107 INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY, LENX, LENY |
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108 * .. External Functions .. |
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109 LOGICAL LSAME |
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110 EXTERNAL LSAME |
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111 * .. External Subroutines .. |
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112 EXTERNAL XERBLA |
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113 * .. Intrinsic Functions .. |
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114 INTRINSIC MAX |
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115 * .. |
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116 * .. Executable Statements .. |
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117 * |
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118 * Test the input parameters. |
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119 * |
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120 INFO = 0 |
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121 IF ( .NOT.LSAME( TRANS, 'N' ).AND. |
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122 $ .NOT.LSAME( TRANS, 'T' ).AND. |
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123 $ .NOT.LSAME( TRANS, 'C' ) )THEN |
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124 INFO = 1 |
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125 ELSE IF( M.LT.0 )THEN |
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126 INFO = 2 |
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127 ELSE IF( N.LT.0 )THEN |
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128 INFO = 3 |
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129 ELSE IF( LDA.LT.MAX( 1, M ) )THEN |
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130 INFO = 6 |
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131 ELSE IF( INCX.EQ.0 )THEN |
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132 INFO = 8 |
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133 ELSE IF( INCY.EQ.0 )THEN |
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134 INFO = 11 |
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135 END IF |
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136 IF( INFO.NE.0 )THEN |
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137 CALL XERBLA( 'DGEMV ', INFO ) |
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138 RETURN |
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139 END IF |
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140 * |
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141 * Quick return if possible. |
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142 * |
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143 IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR. |
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144 $ ( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) ) |
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145 $ RETURN |
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146 * |
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147 * Set LENX and LENY, the lengths of the vectors x and y, and set |
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148 * up the start points in X and Y. |
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149 * |
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150 IF( LSAME( TRANS, 'N' ) )THEN |
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151 LENX = N |
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152 LENY = M |
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153 ELSE |
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154 LENX = M |
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155 LENY = N |
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156 END IF |
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157 IF( INCX.GT.0 )THEN |
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158 KX = 1 |
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159 ELSE |
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160 KX = 1 - ( LENX - 1 )*INCX |
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161 END IF |
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162 IF( INCY.GT.0 )THEN |
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163 KY = 1 |
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164 ELSE |
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165 KY = 1 - ( LENY - 1 )*INCY |
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166 END IF |
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167 * |
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168 * Start the operations. In this version the elements of A are |
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169 * accessed sequentially with one pass through A. |
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170 * |
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171 * First form y := beta*y. |
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172 * |
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173 IF( BETA.NE.ONE )THEN |
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174 IF( INCY.EQ.1 )THEN |
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175 IF( BETA.EQ.ZERO )THEN |
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176 DO 10, I = 1, LENY |
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177 Y( I ) = ZERO |
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178 10 CONTINUE |
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179 ELSE |
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180 DO 20, I = 1, LENY |
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181 Y( I ) = BETA*Y( I ) |
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182 20 CONTINUE |
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183 END IF |
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184 ELSE |
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185 IY = KY |
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186 IF( BETA.EQ.ZERO )THEN |
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187 DO 30, I = 1, LENY |
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188 Y( IY ) = ZERO |
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189 IY = IY + INCY |
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190 30 CONTINUE |
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191 ELSE |
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192 DO 40, I = 1, LENY |
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193 Y( IY ) = BETA*Y( IY ) |
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194 IY = IY + INCY |
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195 40 CONTINUE |
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196 END IF |
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197 END IF |
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198 END IF |
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199 IF( ALPHA.EQ.ZERO ) |
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200 $ RETURN |
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201 IF( LSAME( TRANS, 'N' ) )THEN |
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202 * |
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203 * Form y := alpha*A*x + y. |
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204 * |
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205 JX = KX |
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206 IF( INCY.EQ.1 )THEN |
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207 DO 60, J = 1, N |
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208 IF( X( JX ).NE.ZERO )THEN |
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209 TEMP = ALPHA*X( JX ) |
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210 DO 50, I = 1, M |
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211 Y( I ) = Y( I ) + TEMP*A( I, J ) |
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212 50 CONTINUE |
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213 END IF |
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214 JX = JX + INCX |
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215 60 CONTINUE |
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216 ELSE |
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217 DO 80, J = 1, N |
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218 IF( X( JX ).NE.ZERO )THEN |
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219 TEMP = ALPHA*X( JX ) |
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220 IY = KY |
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221 DO 70, I = 1, M |
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222 Y( IY ) = Y( IY ) + TEMP*A( I, J ) |
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223 IY = IY + INCY |
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224 70 CONTINUE |
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225 END IF |
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226 JX = JX + INCX |
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227 80 CONTINUE |
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228 END IF |
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229 ELSE |
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230 * |
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231 * Form y := alpha*A'*x + y. |
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232 * |
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233 JY = KY |
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234 IF( INCX.EQ.1 )THEN |
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235 DO 100, J = 1, N |
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236 TEMP = ZERO |
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237 DO 90, I = 1, M |
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238 TEMP = TEMP + A( I, J )*X( I ) |
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239 90 CONTINUE |
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240 Y( JY ) = Y( JY ) + ALPHA*TEMP |
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241 JY = JY + INCY |
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242 100 CONTINUE |
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243 ELSE |
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244 DO 120, J = 1, N |
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245 TEMP = ZERO |
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246 IX = KX |
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247 DO 110, I = 1, M |
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248 TEMP = TEMP + A( I, J )*X( IX ) |
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249 IX = IX + INCX |
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250 110 CONTINUE |
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251 Y( JY ) = Y( JY ) + ALPHA*TEMP |
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252 JY = JY + INCY |
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253 120 CONTINUE |
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254 END IF |
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255 END IF |
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256 * |
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257 RETURN |
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258 * |
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259 * End of DGEMV . |
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260 * |
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261 END |
