LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
dlanhs.f
Go to the documentation of this file.
1 *> \brief \b DLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg 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/dlanhs.f">
11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlanhs.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlanhs.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * DOUBLE PRECISION FUNCTION DLANHS( NORM, N, A, LDA, WORK )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER NORM
25 * INTEGER LDA, N
26 * ..
27 * .. Array Arguments ..
28 * DOUBLE PRECISION A( LDA, * ), WORK( * )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *> DLANHS 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 *> Hessenberg matrix A.
40 *> \endverbatim
41 *>
42 *> \return DLANHS
43 *> \verbatim
44 *>
45 *> DLANHS = ( 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 DLANHS 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, DLANHS is
73 *> set to zero.
74 *> \endverbatim
75 *>
76 *> \param[in] A
77 *> \verbatim
78 *> A is DOUBLE PRECISION array, dimension (LDA,N)
79 *> The n by n upper Hessenberg matrix A; the part of A below the
80 *> first sub-diagonal is not referenced.
81 *> \endverbatim
82 *>
83 *> \param[in] LDA
84 *> \verbatim
85 *> LDA is INTEGER
86 *> The leading dimension of the array A. LDA >= max(N,1).
87 *> \endverbatim
88 *>
89 *> \param[out] WORK
90 *> \verbatim
91 *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
92 *> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
93 *> referenced.
94 *> \endverbatim
95 *
96 * Authors:
97 * ========
98 *
99 *> \author Univ. of Tennessee
100 *> \author Univ. of California Berkeley
101 *> \author Univ. of Colorado Denver
102 *> \author NAG Ltd.
103 *
104 *> \date September 2012
105 *
106 *> \ingroup doubleOTHERauxiliary
107 *
108 * =====================================================================
109  DOUBLE PRECISION FUNCTION dlanhs( NORM, N, A, LDA, WORK )
110 *
111 * -- LAPACK auxiliary routine (version 3.4.2) --
112 * -- LAPACK is a software package provided by Univ. of Tennessee, --
113 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
114 * September 2012
115 *
116 * .. Scalar Arguments ..
117  CHARACTER norm
118  INTEGER lda, n
119 * ..
120 * .. Array Arguments ..
121  DOUBLE PRECISION a( lda, * ), work( * )
122 * ..
123 *
124 * =====================================================================
125 *
126 * .. Parameters ..
127  DOUBLE PRECISION one, zero
128  parameter( one = 1.0d+0, zero = 0.0d+0 )
129 * ..
130 * .. Local Scalars ..
131  INTEGER i, j
132  DOUBLE PRECISION scale, sum, value
133 * ..
134 * .. External Subroutines ..
135  EXTERNAL dlassq
136 * ..
137 * .. External Functions ..
138  LOGICAL lsame, disnan
139  EXTERNAL lsame, disnan
140 * ..
141 * .. Intrinsic Functions ..
142  INTRINSIC abs, min, sqrt
143 * ..
144 * .. Executable Statements ..
145 *
146  IF( n.EQ.0 ) THEN
147  value = zero
148  ELSE IF( lsame( norm, 'M' ) ) THEN
149 *
150 * Find max(abs(A(i,j))).
151 *
152  value = zero
153  DO 20 j = 1, n
154  DO 10 i = 1, min( n, j+1 )
155  sum = abs( a( i, j ) )
156  IF( value .LT. sum .OR. disnan( sum ) ) value = sum
157  10 continue
158  20 continue
159  ELSE IF( ( lsame( norm, 'O' ) ) .OR. ( norm.EQ.'1' ) ) THEN
160 *
161 * Find norm1(A).
162 *
163  value = zero
164  DO 40 j = 1, n
165  sum = zero
166  DO 30 i = 1, min( n, j+1 )
167  sum = sum + abs( a( i, j ) )
168  30 continue
169  IF( value .LT. sum .OR. disnan( sum ) ) value = sum
170  40 continue
171  ELSE IF( lsame( norm, 'I' ) ) THEN
172 *
173 * Find normI(A).
174 *
175  DO 50 i = 1, n
176  work( i ) = zero
177  50 continue
178  DO 70 j = 1, n
179  DO 60 i = 1, min( n, j+1 )
180  work( i ) = work( i ) + abs( a( i, j ) )
181  60 continue
182  70 continue
183  value = zero
184  DO 80 i = 1, n
185  sum = work( i )
186  IF( value .LT. sum .OR. disnan( sum ) ) value = sum
187  80 continue
188  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
189 *
190 * Find normF(A).
191 *
192  scale = zero
193  sum = one
194  DO 90 j = 1, n
195  CALL dlassq( min( n, j+1 ), a( 1, j ), 1, scale, sum )
196  90 continue
197  value = scale*sqrt( sum )
198  END IF
199 *
200  dlanhs = value
201  return
202 *
203 * End of DLANHS
204 *
205  END