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1 DOUBLE PRECISION FUNCTION DLANHS( NORM, 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 |
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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 * DLANHS 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 * Hessenberg 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 * DLANHS returns the value |
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27 * |
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28 * DLANHS = ( 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 DLANHS as described |
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46 * above. |
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47 * |
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48 * N (input) INTEGER |
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49 * The order of the matrix A. N >= 0. When N = 0, DLANHS is |
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50 * set to zero. |
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51 * |
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52 * A (input) DOUBLE PRECISION array, dimension (LDA,N) |
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53 * The n by n upper Hessenberg matrix A; the part of A below the |
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54 * first sub-diagonal is not referenced. |
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55 * |
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56 * LDA (input) INTEGER |
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57 * The leading dimension of the array A. LDA >= max(N,1). |
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58 * |
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59 * WORK (workspace) DOUBLE PRECISION array, dimension (LWORK), |
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60 * where LWORK >= N when NORM = 'I'; otherwise, WORK is not |
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61 * referenced. |
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62 * |
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63 * ===================================================================== |
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64 * |
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65 * .. Parameters .. |
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66 DOUBLE PRECISION ONE, ZERO |
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67 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) |
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68 * .. |
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69 * .. Local Scalars .. |
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70 INTEGER I, J |
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71 DOUBLE PRECISION SCALE, SUM, VALUE |
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72 * .. |
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73 * .. External Subroutines .. |
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74 EXTERNAL DLASSQ |
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75 * .. |
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76 * .. External Functions .. |
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77 LOGICAL LSAME |
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78 EXTERNAL LSAME |
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79 * .. |
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80 * .. Intrinsic Functions .. |
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81 INTRINSIC ABS, MAX, MIN, SQRT |
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82 * .. |
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83 * .. Executable Statements .. |
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84 * |
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85 IF( N.EQ.0 ) THEN |
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86 VALUE = ZERO |
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87 ELSE IF( LSAME( NORM, 'M' ) ) THEN |
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88 * |
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89 * Find max(abs(A(i,j))). |
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90 * |
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91 VALUE = ZERO |
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92 DO 20 J = 1, N |
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93 DO 10 I = 1, MIN( N, J+1 ) |
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94 VALUE = MAX( VALUE, ABS( A( I, J ) ) ) |
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95 10 CONTINUE |
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96 20 CONTINUE |
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97 ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN |
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98 * |
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99 * Find norm1(A). |
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100 * |
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101 VALUE = ZERO |
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102 DO 40 J = 1, N |
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103 SUM = ZERO |
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104 DO 30 I = 1, MIN( N, J+1 ) |
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105 SUM = SUM + ABS( A( I, J ) ) |
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106 30 CONTINUE |
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107 VALUE = MAX( VALUE, SUM ) |
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108 40 CONTINUE |
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109 ELSE IF( LSAME( NORM, 'I' ) ) THEN |
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110 * |
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111 * Find normI(A). |
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112 * |
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113 DO 50 I = 1, N |
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114 WORK( I ) = ZERO |
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115 50 CONTINUE |
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116 DO 70 J = 1, N |
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117 DO 60 I = 1, MIN( N, J+1 ) |
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118 WORK( I ) = WORK( I ) + ABS( A( I, J ) ) |
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119 60 CONTINUE |
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120 70 CONTINUE |
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121 VALUE = ZERO |
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122 DO 80 I = 1, N |
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123 VALUE = MAX( VALUE, WORK( I ) ) |
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124 80 CONTINUE |
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125 ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN |
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126 * |
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127 * Find normF(A). |
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128 * |
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129 SCALE = ZERO |
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130 SUM = ONE |
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131 DO 90 J = 1, N |
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132 CALL DLASSQ( MIN( N, J+1 ), A( 1, J ), 1, SCALE, SUM ) |
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133 90 CONTINUE |
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134 VALUE = SCALE*SQRT( SUM ) |
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135 END IF |
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136 * |
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137 DLANHS = VALUE |
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138 RETURN |
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139 * |
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140 * End of DLANHS |
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141 * |
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142 END |
