LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
dlanst.f
Go to the documentation of this file.
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
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
subroutine dlassq(N, X, INCX, SCALE, SUMSQ)
DLASSQ updates a sum of squares represented in scaled form.
Definition: dlassq.f:105
double precision function dlanst(NORM, N, D, E)
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.
Definition: dlanst.f:102