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1 DOUBLE PRECISION FUNCTION DLANST( NORM, N, D, E ) |
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2 * |
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3 * -- LAPACK auxiliary routine (version 3.1) -- |
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4 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. |
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5 * November 2006 |
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6 * |
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7 * .. Scalar Arguments .. |
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8 CHARACTER NORM |
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9 INTEGER N |
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10 * .. |
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11 * .. Array Arguments .. |
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12 DOUBLE PRECISION D( * ), E( * ) |
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13 * .. |
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14 * |
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15 * Purpose |
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16 * ======= |
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17 * |
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18 * DLANST returns the value of the one norm, or the Frobenius norm, or |
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19 * the infinity norm, or the element of largest absolute value of a |
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20 * real symmetric tridiagonal matrix A. |
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21 * |
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22 * Description |
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23 * =========== |
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24 * |
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25 * DLANST returns the value |
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26 * |
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27 * DLANST = ( max(abs(A(i,j))), NORM = 'M' or 'm' |
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28 * ( |
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29 * ( norm1(A), NORM = '1', 'O' or 'o' |
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30 * ( |
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31 * ( normI(A), NORM = 'I' or 'i' |
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32 * ( |
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33 * ( normF(A), NORM = 'F', 'f', 'E' or 'e' |
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34 * |
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35 * where norm1 denotes the one norm of a matrix (maximum column sum), |
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36 * normI denotes the infinity norm of a matrix (maximum row sum) and |
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37 * normF denotes the Frobenius norm of a matrix (square root of sum of |
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38 * squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. |
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39 * |
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40 * Arguments |
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41 * ========= |
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42 * |
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43 * NORM (input) CHARACTER*1 |
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44 * Specifies the value to be returned in DLANST as described |
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45 * above. |
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46 * |
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47 * N (input) INTEGER |
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48 * The order of the matrix A. N >= 0. When N = 0, DLANST is |
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49 * set to zero. |
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50 * |
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51 * D (input) DOUBLE PRECISION array, dimension (N) |
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52 * The diagonal elements of A. |
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53 * |
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54 * E (input) DOUBLE PRECISION array, dimension (N-1) |
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55 * The (n-1) sub-diagonal or super-diagonal elements of A. |
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56 * |
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57 * ===================================================================== |
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58 * |
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59 * .. Parameters .. |
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60 DOUBLE PRECISION ONE, ZERO |
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61 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) |
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62 * .. |
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63 * .. Local Scalars .. |
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64 INTEGER I |
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65 DOUBLE PRECISION ANORM, SCALE, SUM |
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66 * .. |
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67 * .. External Functions .. |
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68 LOGICAL LSAME |
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69 EXTERNAL LSAME |
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70 * .. |
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71 * .. External Subroutines .. |
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72 EXTERNAL DLASSQ |
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73 * .. |
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74 * .. Intrinsic Functions .. |
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75 INTRINSIC ABS, MAX, SQRT |
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76 * .. |
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77 * .. Executable Statements .. |
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78 * |
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79 IF( N.LE.0 ) THEN |
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80 ANORM = ZERO |
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81 ELSE IF( LSAME( NORM, 'M' ) ) THEN |
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82 * |
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83 * Find max(abs(A(i,j))). |
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84 * |
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85 ANORM = ABS( D( N ) ) |
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86 DO 10 I = 1, N - 1 |
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87 ANORM = MAX( ANORM, ABS( D( I ) ) ) |
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88 ANORM = MAX( ANORM, ABS( E( I ) ) ) |
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89 10 CONTINUE |
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90 ELSE IF( LSAME( NORM, 'O' ) .OR. NORM.EQ.'1' .OR. |
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91 $ LSAME( NORM, 'I' ) ) THEN |
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92 * |
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93 * Find norm1(A). |
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94 * |
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95 IF( N.EQ.1 ) THEN |
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96 ANORM = ABS( D( 1 ) ) |
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97 ELSE |
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98 ANORM = MAX( ABS( D( 1 ) )+ABS( E( 1 ) ), |
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99 $ ABS( E( N-1 ) )+ABS( D( N ) ) ) |
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100 DO 20 I = 2, N - 1 |
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101 ANORM = MAX( ANORM, ABS( D( I ) )+ABS( E( I ) )+ |
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102 $ ABS( E( I-1 ) ) ) |
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103 20 CONTINUE |
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104 END IF |
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105 ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN |
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106 * |
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107 * Find normF(A). |
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108 * |
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109 SCALE = ZERO |
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110 SUM = ONE |
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111 IF( N.GT.1 ) THEN |
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112 CALL DLASSQ( N-1, E, 1, SCALE, SUM ) |
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113 SUM = 2*SUM |
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114 END IF |
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115 CALL DLASSQ( N, D, 1, SCALE, SUM ) |
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116 ANORM = SCALE*SQRT( SUM ) |
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117 END IF |
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118 * |
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119 DLANST = ANORM |
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120 RETURN |
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121 * |
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122 * End of DLANST |
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123 * |
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124 END |
