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1 DOUBLE PRECISION FUNCTION DLANSY( NORM, UPLO, N, A, LDA, WORK ) |
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2 * |
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3 * -- LAPACK auxiliary routine (version 3.0) -- |
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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 NORM, UPLO |
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10 INTEGER LDA, N |
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11 * .. |
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12 * .. Array Arguments .. |
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13 DOUBLE PRECISION A( LDA, * ), WORK( * ) |
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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 * DLANSY returns the value of the one norm, or the Frobenius norm, or |
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20 * the infinity norm, or the element of largest absolute value of a |
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21 * real symmetric matrix A. |
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22 * |
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23 * Description |
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24 * =========== |
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25 * |
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26 * DLANSY returns the value |
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27 * |
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28 * DLANSY = ( max(abs(A(i,j))), NORM = 'M' or 'm' |
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29 * ( |
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30 * ( norm1(A), NORM = '1', 'O' or 'o' |
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31 * ( |
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32 * ( normI(A), NORM = 'I' or 'i' |
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33 * ( |
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34 * ( normF(A), NORM = 'F', 'f', 'E' or 'e' |
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35 * |
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36 * where norm1 denotes the one norm of a matrix (maximum column sum), |
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37 * normI denotes the infinity norm of a matrix (maximum row sum) and |
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38 * normF denotes the Frobenius norm of a matrix (square root of sum of |
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39 * squares). Note that max(abs(A(i,j))) is not a matrix norm. |
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40 * |
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41 * Arguments |
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42 * ========= |
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43 * |
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44 * NORM (input) CHARACTER*1 |
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45 * Specifies the value to be returned in DLANSY as described |
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46 * above. |
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47 * |
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48 * UPLO (input) CHARACTER*1 |
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49 * Specifies whether the upper or lower triangular part of the |
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50 * symmetric matrix A is to be referenced. |
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51 * = 'U': Upper triangular part of A is referenced |
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52 * = 'L': Lower triangular part of A is referenced |
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53 * |
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54 * N (input) INTEGER |
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55 * The order of the matrix A. N >= 0. When N = 0, DLANSY is |
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56 * set to zero. |
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57 * |
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58 * A (input) DOUBLE PRECISION array, dimension (LDA,N) |
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59 * The symmetric matrix A. If UPLO = 'U', the leading n by n |
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60 * upper triangular part of A contains the upper triangular part |
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61 * of the matrix A, and the strictly lower triangular part of A |
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62 * is not referenced. If UPLO = 'L', the leading n by n lower |
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63 * triangular part of A contains the lower triangular part of |
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64 * the matrix A, and the strictly upper triangular part of A is |
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65 * not referenced. |
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66 * |
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67 * LDA (input) INTEGER |
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68 * The leading dimension of the array A. LDA >= max(N,1). |
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69 * |
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70 * WORK (workspace) DOUBLE PRECISION array, dimension (LWORK), |
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71 * where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, |
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72 * WORK is not referenced. |
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73 * |
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74 * ===================================================================== |
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75 * |
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76 * .. Parameters .. |
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77 DOUBLE PRECISION ONE, ZERO |
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78 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) |
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79 * .. |
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80 * .. Local Scalars .. |
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81 INTEGER I, J |
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82 DOUBLE PRECISION ABSA, SCALE, SUM, VALUE |
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83 * .. |
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84 * .. External Subroutines .. |
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85 EXTERNAL DLASSQ |
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86 * .. |
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87 * .. External Functions .. |
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88 LOGICAL LSAME |
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89 EXTERNAL LSAME |
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90 * .. |
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91 * .. Intrinsic Functions .. |
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92 INTRINSIC ABS, MAX, SQRT |
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93 * .. |
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94 * .. Executable Statements .. |
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95 * |
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96 IF( N.EQ.0 ) THEN |
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97 VALUE = ZERO |
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98 ELSE IF( LSAME( NORM, 'M' ) ) THEN |
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99 * |
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100 * Find max(abs(A(i,j))). |
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101 * |
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102 VALUE = ZERO |
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103 IF( LSAME( UPLO, 'U' ) ) THEN |
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104 DO 20 J = 1, N |
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105 DO 10 I = 1, J |
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106 VALUE = MAX( VALUE, ABS( A( I, J ) ) ) |
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107 10 CONTINUE |
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108 20 CONTINUE |
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109 ELSE |
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110 DO 40 J = 1, N |
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111 DO 30 I = J, N |
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112 VALUE = MAX( VALUE, ABS( A( I, J ) ) ) |
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113 30 CONTINUE |
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114 40 CONTINUE |
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115 END IF |
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116 ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR. |
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117 $ ( NORM.EQ.'1' ) ) THEN |
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118 * |
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119 * Find normI(A) ( = norm1(A), since A is symmetric). |
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120 * |
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121 VALUE = ZERO |
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122 IF( LSAME( UPLO, 'U' ) ) THEN |
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123 DO 60 J = 1, N |
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124 SUM = ZERO |
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125 DO 50 I = 1, J - 1 |
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126 ABSA = ABS( A( I, J ) ) |
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127 SUM = SUM + ABSA |
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128 WORK( I ) = WORK( I ) + ABSA |
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129 50 CONTINUE |
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130 WORK( J ) = SUM + ABS( A( J, J ) ) |
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131 60 CONTINUE |
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132 DO 70 I = 1, N |
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133 VALUE = MAX( VALUE, WORK( I ) ) |
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134 70 CONTINUE |
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135 ELSE |
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136 DO 80 I = 1, N |
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137 WORK( I ) = ZERO |
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138 80 CONTINUE |
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139 DO 100 J = 1, N |
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140 SUM = WORK( J ) + ABS( A( J, J ) ) |
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141 DO 90 I = J + 1, N |
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142 ABSA = ABS( A( I, J ) ) |
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143 SUM = SUM + ABSA |
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144 WORK( I ) = WORK( I ) + ABSA |
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145 90 CONTINUE |
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146 VALUE = MAX( VALUE, SUM ) |
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147 100 CONTINUE |
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148 END IF |
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149 ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN |
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150 * |
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151 * Find normF(A). |
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152 * |
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153 SCALE = ZERO |
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154 SUM = ONE |
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155 IF( LSAME( UPLO, 'U' ) ) THEN |
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156 DO 110 J = 2, N |
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157 CALL DLASSQ( J-1, A( 1, J ), 1, SCALE, SUM ) |
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158 110 CONTINUE |
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159 ELSE |
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160 DO 120 J = 1, N - 1 |
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161 CALL DLASSQ( N-J, A( J+1, J ), 1, SCALE, SUM ) |
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162 120 CONTINUE |
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163 END IF |
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164 SUM = 2*SUM |
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165 CALL DLASSQ( N, A, LDA+1, SCALE, SUM ) |
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166 VALUE = SCALE*SQRT( SUM ) |
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167 END IF |
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168 * |
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169 DLANSY = VALUE |
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170 RETURN |
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171 * |
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172 * End of DLANSY |
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173 * |
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174 END |
