LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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clanhs.f
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1*> \brief \b CLANHS 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/clanhs.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clanhs.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clanhs.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* REAL FUNCTION CLANHS( NORM, N, A, LDA, WORK )
22*
23* .. Scalar Arguments ..
24* CHARACTER NORM
25* INTEGER LDA, N
26* ..
27* .. Array Arguments ..
28* REAL WORK( * )
29* COMPLEX A( LDA, * )
30* ..
31*
32*
33*> \par Purpose:
34* =============
35*>
36*> \verbatim
37*>
38*> CLANHS returns the value of the one norm, or the Frobenius norm, or
39*> the infinity norm, or the element of largest absolute value of a
40*> Hessenberg matrix A.
41*> \endverbatim
42*>
43*> \return CLANHS
44*> \verbatim
45*>
46*> CLANHS = ( max(abs(A(i,j))), NORM = 'M' or 'm'
47*> (
48*> ( norm1(A), NORM = '1', 'O' or 'o'
49*> (
50*> ( normI(A), NORM = 'I' or 'i'
51*> (
52*> ( normF(A), NORM = 'F', 'f', 'E' or 'e'
53*>
54*> where norm1 denotes the one norm of a matrix (maximum column sum),
55*> normI denotes the infinity norm of a matrix (maximum row sum) and
56*> normF denotes the Frobenius norm of a matrix (square root of sum of
57*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
58*> \endverbatim
59*
60* Arguments:
61* ==========
62*
63*> \param[in] NORM
64*> \verbatim
65*> NORM is CHARACTER*1
66*> Specifies the value to be returned in CLANHS as described
67*> above.
68*> \endverbatim
69*>
70*> \param[in] N
71*> \verbatim
72*> N is INTEGER
73*> The order of the matrix A. N >= 0. When N = 0, CLANHS is
74*> set to zero.
75*> \endverbatim
76*>
77*> \param[in] A
78*> \verbatim
79*> A is COMPLEX array, dimension (LDA,N)
80*> The n by n upper Hessenberg matrix A; the part of A below the
81*> first sub-diagonal is not referenced.
82*> \endverbatim
83*>
84*> \param[in] LDA
85*> \verbatim
86*> LDA is INTEGER
87*> The leading dimension of the array A. LDA >= max(N,1).
88*> \endverbatim
89*>
90*> \param[out] WORK
91*> \verbatim
92*> WORK is REAL array, dimension (MAX(1,LWORK)),
93*> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
94*> referenced.
95*> \endverbatim
96*
97* Authors:
98* ========
99*
100*> \author Univ. of Tennessee
101*> \author Univ. of California Berkeley
102*> \author Univ. of Colorado Denver
103*> \author NAG Ltd.
104*
105*> \ingroup complexOTHERauxiliary
106*
107* =====================================================================
108 REAL function clanhs( norm, n, a, lda, work )
109*
110* -- LAPACK auxiliary routine --
111* -- LAPACK is a software package provided by Univ. of Tennessee, --
112* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
113*
114* .. Scalar Arguments ..
115 CHARACTER norm
116 INTEGER lda, n
117* ..
118* .. Array Arguments ..
119 REAL work( * )
120 COMPLEX a( lda, * )
121* ..
122*
123* =====================================================================
124*
125* .. Parameters ..
126 REAL one, zero
127 parameter( one = 1.0e+0, zero = 0.0e+0 )
128* ..
129* .. Local Scalars ..
130 INTEGER i, j
131 REAL scale, sum, value
132* ..
133* .. External Functions ..
134 LOGICAL lsame, sisnan
135 EXTERNAL lsame, sisnan
136* ..
137* .. External Subroutines ..
138 EXTERNAL classq
139* ..
140* .. Intrinsic Functions ..
141 INTRINSIC abs, min, sqrt
142* ..
143* .. Executable Statements ..
144*
145 IF( n.EQ.0 ) THEN
146 VALUE = zero
147 ELSE IF( lsame( norm, 'M' ) ) THEN
148*
149* Find max(abs(A(i,j))).
150*
151 VALUE = zero
152 DO 20 j = 1, n
153 DO 10 i = 1, min( n, j+1 )
154 sum = abs( a( i, j ) )
155 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
156 10 CONTINUE
157 20 CONTINUE
158 ELSE IF( ( lsame( norm, 'O' ) ) .OR. ( norm.EQ.'1' ) ) THEN
159*
160* Find norm1(A).
161*
162 VALUE = zero
163 DO 40 j = 1, n
164 sum = zero
165 DO 30 i = 1, min( n, j+1 )
166 sum = sum + abs( a( i, j ) )
167 30 CONTINUE
168 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
169 40 CONTINUE
170 ELSE IF( lsame( norm, 'I' ) ) THEN
171*
172* Find normI(A).
173*
174 DO 50 i = 1, n
175 work( i ) = zero
176 50 CONTINUE
177 DO 70 j = 1, n
178 DO 60 i = 1, min( n, j+1 )
179 work( i ) = work( i ) + abs( a( i, j ) )
180 60 CONTINUE
181 70 CONTINUE
182 VALUE = zero
183 DO 80 i = 1, n
184 sum = work( i )
185 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
186 80 CONTINUE
187 ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
188*
189* Find normF(A).
190*
191 scale = zero
192 sum = one
193 DO 90 j = 1, n
194 CALL classq( min( n, j+1 ), a( 1, j ), 1, scale, sum )
195 90 CONTINUE
196 VALUE = scale*sqrt( sum )
197 END IF
198*
199 clanhs = VALUE
200 RETURN
201*
202* End of CLANHS
203*
204 END
subroutine classq(n, x, incx, scl, sumsq)
CLASSQ updates a sum of squares represented in scaled form.
Definition: classq.f90:137
logical function sisnan(SIN)
SISNAN tests input for NaN.
Definition: sisnan.f:59
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
real function clanhs(NORM, N, A, LDA, WORK)
CLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: clanhs.f:109