github.com/gonum/lapack@v0.0.0-20181123203213-e4cdc5a0bff9/internal/testdata/dsterftest/dlanst.f (about) 1 *> \brief \b DLANST returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix. 2 * 3 * =========== DOCUMENTATION =========== 4 * 5 * Online html documentation available at 6 * http://www.netlib.org/lapack/explore-html/ 7 * 8 *> \htmlonly 9 *> Download DLANST + dependencies 10 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlanst.f"> 11 *> [TGZ]</a> 12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlanst.f"> 13 *> [ZIP]</a> 14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlanst.f"> 15 *> [TXT]</a> 16 *> \endhtmlonly 17 * 18 * Definition: 19 * =========== 20 * 21 * DOUBLE PRECISION FUNCTION DLANST( NORM, N, D, E ) 22 * 23 * .. Scalar Arguments .. 24 * CHARACTER NORM 25 * INTEGER N 26 * .. 27 * .. Array Arguments .. 28 * DOUBLE PRECISION D( * ), E( * ) 29 * .. 30 * 31 * 32 *> \par Purpose: 33 * ============= 34 *> 35 *> \verbatim 36 *> 37 *> DLANST returns the value of the one norm, or the Frobenius norm, or 38 *> the infinity norm, or the element of largest absolute value of a 39 *> real symmetric tridiagonal matrix A. 40 *> \endverbatim 41 *> 42 *> \return DLANST 43 *> \verbatim 44 *> 45 *> DLANST = ( max(abs(A(i,j))), NORM = 'M' or 'm' 46 *> ( 47 *> ( norm1(A), NORM = '1', 'O' or 'o' 48 *> ( 49 *> ( normI(A), NORM = 'I' or 'i' 50 *> ( 51 *> ( normF(A), NORM = 'F', 'f', 'E' or 'e' 52 *> 53 *> where norm1 denotes the one norm of a matrix (maximum column sum), 54 *> normI denotes the infinity norm of a matrix (maximum row sum) and 55 *> normF denotes the Frobenius norm of a matrix (square root of sum of 56 *> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. 57 *> \endverbatim 58 * 59 * Arguments: 60 * ========== 61 * 62 *> \param[in] NORM 63 *> \verbatim 64 *> NORM is CHARACTER*1 65 *> Specifies the value to be returned in DLANST as described 66 *> above. 67 *> \endverbatim 68 *> 69 *> \param[in] N 70 *> \verbatim 71 *> N is INTEGER 72 *> The order of the matrix A. N >= 0. When N = 0, DLANST is 73 *> set to zero. 74 *> \endverbatim 75 *> 76 *> \param[in] D 77 *> \verbatim 78 *> D is DOUBLE PRECISION array, dimension (N) 79 *> The diagonal elements of A. 80 *> \endverbatim 81 *> 82 *> \param[in] E 83 *> \verbatim 84 *> E is DOUBLE PRECISION array, dimension (N-1) 85 *> The (n-1) sub-diagonal or super-diagonal elements of A. 86 *> \endverbatim 87 * 88 * Authors: 89 * ======== 90 * 91 *> \author Univ. of Tennessee 92 *> \author Univ. of California Berkeley 93 *> \author Univ. of Colorado Denver 94 *> \author NAG Ltd. 95 * 96 *> \date September 2012 97 * 98 *> \ingroup auxOTHERauxiliary 99 * 100 * ===================================================================== 101 DOUBLE PRECISION FUNCTION DLANST( NORM, N, D, E ) 102 * 103 * -- LAPACK auxiliary routine (version 3.4.2) -- 104 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 105 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 106 * September 2012 107 * 108 * .. Scalar Arguments .. 109 CHARACTER NORM 110 INTEGER N 111 * .. 112 * .. Array Arguments .. 113 DOUBLE PRECISION D( * ), E( * ) 114 * .. 115 * 116 * ===================================================================== 117 * 118 * .. Parameters .. 119 DOUBLE PRECISION ONE, ZERO 120 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 121 * .. 122 * .. Local Scalars .. 123 INTEGER I 124 DOUBLE PRECISION ANORM, SCALE, SUM 125 * .. 126 * .. External Functions .. 127 LOGICAL LSAME, DISNAN 128 EXTERNAL LSAME, DISNAN 129 * .. 130 * .. External Subroutines .. 131 EXTERNAL DLASSQ 132 * .. 133 * .. Intrinsic Functions .. 134 INTRINSIC ABS, SQRT 135 * .. 136 * .. Executable Statements .. 137 * 138 IF( N.LE.0 ) THEN 139 ANORM = ZERO 140 ELSE IF( LSAME( NORM, 'M' ) ) THEN 141 * 142 * Find max(abs(A(i,j))). 143 * 144 ANORM = ABS( D( N ) ) 145 DO 10 I = 1, N - 1 146 SUM = ABS( D( I ) ) 147 IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM 148 SUM = ABS( E( I ) ) 149 IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM 150 10 CONTINUE 151 ELSE IF( LSAME( NORM, 'O' ) .OR. NORM.EQ.'1' .OR. 152 $ LSAME( NORM, 'I' ) ) THEN 153 * 154 * Find norm1(A). 155 * 156 IF( N.EQ.1 ) THEN 157 ANORM = ABS( D( 1 ) ) 158 ELSE 159 ANORM = ABS( D( 1 ) )+ABS( E( 1 ) ) 160 SUM = ABS( E( N-1 ) )+ABS( D( N ) ) 161 IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM 162 DO 20 I = 2, N - 1 163 SUM = ABS( D( I ) )+ABS( E( I ) )+ABS( E( I-1 ) ) 164 IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM 165 20 CONTINUE 166 END IF 167 ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN 168 * 169 * Find normF(A). 170 * 171 SCALE = ZERO 172 SUM = ONE 173 IF( N.GT.1 ) THEN 174 CALL DLASSQ( N-1, E, 1, SCALE, SUM ) 175 SUM = 2*SUM 176 END IF 177 CALL DLASSQ( N, D, 1, SCALE, SUM ) 178 ANORM = SCALE*SQRT( SUM ) 179 END IF 180 * 181 DLANST = ANORM 182 RETURN 183 * 184 * End of DLANST 185 * 186 END