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2814
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1 * |
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2 ************************************************************************ |
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3 * |
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4 SUBROUTINE DSYR2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA ) |
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5 * .. Scalar Arguments .. |
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6 DOUBLE PRECISION ALPHA |
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7 INTEGER INCX, INCY, LDA, N |
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8 CHARACTER*1 UPLO |
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9 * .. Array Arguments .. |
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10 DOUBLE PRECISION A( LDA, * ), X( * ), Y( * ) |
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11 * .. |
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12 * |
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13 * Purpose |
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14 * ======= |
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15 * |
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16 * DSYR2 performs the symmetric rank 2 operation |
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17 * |
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18 * A := alpha*x*y' + alpha*y*x' + A, |
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19 * |
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20 * where alpha is a scalar, x and y are n element vectors and A is an n |
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21 * by n symmetric matrix. |
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22 * |
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23 * Parameters |
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24 * ========== |
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25 * |
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26 * UPLO - CHARACTER*1. |
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27 * On entry, UPLO specifies whether the upper or lower |
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28 * triangular part of the array A is to be referenced as |
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29 * follows: |
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30 * |
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31 * UPLO = 'U' or 'u' Only the upper triangular part of A |
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32 * is to be referenced. |
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33 * |
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34 * UPLO = 'L' or 'l' Only the lower triangular part of A |
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35 * is to be referenced. |
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36 * |
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37 * Unchanged on exit. |
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38 * |
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39 * N - INTEGER. |
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40 * On entry, N specifies the order of the matrix A. |
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41 * N must be at least zero. |
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42 * Unchanged on exit. |
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43 * |
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44 * ALPHA - DOUBLE PRECISION. |
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45 * On entry, ALPHA specifies the scalar alpha. |
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46 * Unchanged on exit. |
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47 * |
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48 * X - DOUBLE PRECISION array of dimension at least |
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49 * ( 1 + ( n - 1 )*abs( INCX ) ). |
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50 * Before entry, the incremented array X must contain the n |
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51 * element vector x. |
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52 * Unchanged on exit. |
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53 * |
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54 * INCX - INTEGER. |
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55 * On entry, INCX specifies the increment for the elements of |
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56 * X. INCX must not be zero. |
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57 * Unchanged on exit. |
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58 * |
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59 * Y - DOUBLE PRECISION array of dimension at least |
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60 * ( 1 + ( n - 1 )*abs( INCY ) ). |
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61 * Before entry, the incremented array Y must contain the n |
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62 * element vector y. |
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63 * Unchanged on exit. |
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64 * |
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65 * INCY - INTEGER. |
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66 * On entry, INCY specifies the increment for the elements of |
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67 * Y. INCY must not be zero. |
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68 * Unchanged on exit. |
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69 * |
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70 * A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). |
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71 * Before entry with UPLO = 'U' or 'u', the leading n by n |
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72 * upper triangular part of the array A must contain the upper |
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73 * triangular part of the symmetric matrix and the strictly |
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74 * lower triangular part of A is not referenced. On exit, the |
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75 * upper triangular part of the array A is overwritten by the |
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76 * upper triangular part of the updated matrix. |
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77 * Before entry with UPLO = 'L' or 'l', the leading n by n |
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78 * lower triangular part of the array A must contain the lower |
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79 * triangular part of the symmetric matrix and the strictly |
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80 * upper triangular part of A is not referenced. On exit, the |
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81 * lower triangular part of the array A is overwritten by the |
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82 * lower triangular part of the updated matrix. |
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83 * |
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84 * LDA - INTEGER. |
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85 * On entry, LDA specifies the first dimension of A as declared |
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86 * in the calling (sub) program. LDA must be at least |
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87 * max( 1, n ). |
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88 * Unchanged on exit. |
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89 * |
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90 * |
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91 * Level 2 Blas routine. |
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92 * |
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93 * -- Written on 22-October-1986. |
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94 * Jack Dongarra, Argonne National Lab. |
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95 * Jeremy Du Croz, Nag Central Office. |
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96 * Sven Hammarling, Nag Central Office. |
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97 * Richard Hanson, Sandia National Labs. |
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98 * |
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99 * |
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100 * .. Parameters .. |
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101 DOUBLE PRECISION ZERO |
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102 PARAMETER ( ZERO = 0.0D+0 ) |
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103 * .. Local Scalars .. |
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104 DOUBLE PRECISION TEMP1, TEMP2 |
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105 INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY |
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106 * .. External Functions .. |
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107 LOGICAL LSAME |
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108 EXTERNAL LSAME |
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109 * .. External Subroutines .. |
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110 EXTERNAL XERBLA |
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111 * .. Intrinsic Functions .. |
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112 INTRINSIC MAX |
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113 * .. |
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114 * .. Executable Statements .. |
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115 * |
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116 * Test the input parameters. |
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117 * |
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118 INFO = 0 |
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119 IF ( .NOT.LSAME( UPLO, 'U' ).AND. |
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120 $ .NOT.LSAME( UPLO, 'L' ) )THEN |
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121 INFO = 1 |
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122 ELSE IF( N.LT.0 )THEN |
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123 INFO = 2 |
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124 ELSE IF( INCX.EQ.0 )THEN |
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125 INFO = 5 |
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126 ELSE IF( INCY.EQ.0 )THEN |
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127 INFO = 7 |
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128 ELSE IF( LDA.LT.MAX( 1, N ) )THEN |
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129 INFO = 9 |
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130 END IF |
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131 IF( INFO.NE.0 )THEN |
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132 CALL XERBLA( 'DSYR2 ', INFO ) |
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133 RETURN |
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134 END IF |
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135 * |
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136 * Quick return if possible. |
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137 * |
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138 IF( ( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) ) |
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139 $ RETURN |
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140 * |
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141 * Set up the start points in X and Y if the increments are not both |
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142 * unity. |
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143 * |
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144 IF( ( INCX.NE.1 ).OR.( INCY.NE.1 ) )THEN |
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145 IF( INCX.GT.0 )THEN |
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146 KX = 1 |
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147 ELSE |
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148 KX = 1 - ( N - 1 )*INCX |
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149 END IF |
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150 IF( INCY.GT.0 )THEN |
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151 KY = 1 |
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152 ELSE |
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153 KY = 1 - ( N - 1 )*INCY |
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154 END IF |
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155 JX = KX |
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156 JY = KY |
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157 END IF |
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158 * |
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159 * Start the operations. In this version the elements of A are |
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160 * accessed sequentially with one pass through the triangular part |
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161 * of A. |
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162 * |
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163 IF( LSAME( UPLO, 'U' ) )THEN |
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164 * |
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165 * Form A when A is stored in the upper triangle. |
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166 * |
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167 IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN |
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168 DO 20, J = 1, N |
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169 IF( ( X( J ).NE.ZERO ).OR.( Y( J ).NE.ZERO ) )THEN |
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170 TEMP1 = ALPHA*Y( J ) |
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171 TEMP2 = ALPHA*X( J ) |
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172 DO 10, I = 1, J |
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173 A( I, J ) = A( I, J ) + X( I )*TEMP1 + Y( I )*TEMP2 |
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174 10 CONTINUE |
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175 END IF |
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176 20 CONTINUE |
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177 ELSE |
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178 DO 40, J = 1, N |
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179 IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN |
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180 TEMP1 = ALPHA*Y( JY ) |
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181 TEMP2 = ALPHA*X( JX ) |
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182 IX = KX |
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183 IY = KY |
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184 DO 30, I = 1, J |
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185 A( I, J ) = A( I, J ) + X( IX )*TEMP1 |
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186 $ + Y( IY )*TEMP2 |
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187 IX = IX + INCX |
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188 IY = IY + INCY |
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189 30 CONTINUE |
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190 END IF |
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191 JX = JX + INCX |
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192 JY = JY + INCY |
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193 40 CONTINUE |
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194 END IF |
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195 ELSE |
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196 * |
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197 * Form A when A is stored in the lower triangle. |
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198 * |
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199 IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN |
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200 DO 60, J = 1, N |
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201 IF( ( X( J ).NE.ZERO ).OR.( Y( J ).NE.ZERO ) )THEN |
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202 TEMP1 = ALPHA*Y( J ) |
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203 TEMP2 = ALPHA*X( J ) |
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204 DO 50, I = J, N |
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205 A( I, J ) = A( I, J ) + X( I )*TEMP1 + Y( I )*TEMP2 |
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206 50 CONTINUE |
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207 END IF |
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208 60 CONTINUE |
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209 ELSE |
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210 DO 80, J = 1, N |
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211 IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN |
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212 TEMP1 = ALPHA*Y( JY ) |
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213 TEMP2 = ALPHA*X( JX ) |
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214 IX = JX |
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215 IY = JY |
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216 DO 70, I = J, N |
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217 A( I, J ) = A( I, J ) + X( IX )*TEMP1 |
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218 $ + Y( IY )*TEMP2 |
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219 IX = IX + INCX |
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220 IY = IY + INCY |
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221 70 CONTINUE |
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222 END IF |
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223 JX = JX + INCX |
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224 JY = JY + INCY |
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225 80 CONTINUE |
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226 END IF |
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227 END IF |
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228 * |
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229 RETURN |
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230 * |
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231 * End of DSYR2 . |
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232 * |
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233 END |
