LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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clanht.f
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1*> \brief \b CLANHT returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian 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/clanht.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clanht.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clanht.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* REAL FUNCTION CLANHT( NORM, N, D, E )
22*
23* .. Scalar Arguments ..
24* CHARACTER NORM
25* INTEGER N
26* ..
27* .. Array Arguments ..
28* REAL D( * )
29* COMPLEX E( * )
30* ..
31*
32*
33*> \par Purpose:
34* =============
35*>
36*> \verbatim
37*>
38*> CLANHT 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*> complex Hermitian tridiagonal matrix A.
41*> \endverbatim
42*>
43*> \return CLANHT
44*> \verbatim
45*>
46*> CLANHT = ( 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 CLANHT 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, CLANHT is
74*> set to zero.
75*> \endverbatim
76*>
77*> \param[in] D
78*> \verbatim
79*> D is REAL array, dimension (N)
80*> The diagonal elements of A.
81*> \endverbatim
82*>
83*> \param[in] E
84*> \verbatim
85*> E is COMPLEX array, dimension (N-1)
86*> The (n-1) sub-diagonal or super-diagonal elements of A.
87*> \endverbatim
88*
89* Authors:
90* ========
91*
92*> \author Univ. of Tennessee
93*> \author Univ. of California Berkeley
94*> \author Univ. of Colorado Denver
95*> \author NAG Ltd.
96*
97*> \ingroup complexOTHERauxiliary
98*
99* =====================================================================
100 REAL function clanht( norm, n, d, e )
101*
102* -- LAPACK auxiliary routine --
103* -- LAPACK is a software package provided by Univ. of Tennessee, --
104* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
105*
106* .. Scalar Arguments ..
107 CHARACTER norm
108 INTEGER n
109* ..
110* .. Array Arguments ..
111 REAL d( * )
112 COMPLEX e( * )
113* ..
114*
115* =====================================================================
116*
117* .. Parameters ..
118 REAL one, zero
119 parameter( one = 1.0e+0, zero = 0.0e+0 )
120* ..
121* .. Local Scalars ..
122 INTEGER i
123 REAL anorm, scale, sum
124* ..
125* .. External Functions ..
126 LOGICAL lsame, sisnan
127 EXTERNAL lsame, sisnan
128* ..
129* .. External Subroutines ..
130 EXTERNAL classq, slassq
131* ..
132* .. Intrinsic Functions ..
133 INTRINSIC abs, sqrt
134* ..
135* .. Executable Statements ..
136*
137 IF( n.LE.0 ) THEN
138 anorm = zero
139 ELSE IF( lsame( norm, 'M' ) ) THEN
140*
141* Find max(abs(A(i,j))).
142*
143 anorm = abs( d( n ) )
144 DO 10 i = 1, n - 1
145 sum = abs( d( i ) )
146 IF( anorm .LT. sum .OR. sisnan( sum ) ) anorm = sum
147 sum = abs( e( i ) )
148 IF( anorm .LT. sum .OR. sisnan( sum ) ) anorm = sum
149 10 CONTINUE
150 ELSE IF( lsame( norm, 'O' ) .OR. norm.EQ.'1' .OR.
151 \$ lsame( norm, 'I' ) ) THEN
152*
153* Find norm1(A).
154*
155 IF( n.EQ.1 ) THEN
156 anorm = abs( d( 1 ) )
157 ELSE
158 anorm = abs( d( 1 ) )+abs( e( 1 ) )
159 sum = abs( e( n-1 ) )+abs( d( n ) )
160 IF( anorm .LT. sum .OR. sisnan( sum ) ) anorm = sum
161 DO 20 i = 2, n - 1
162 sum = abs( d( i ) )+abs( e( i ) )+abs( e( i-1 ) )
163 IF( anorm .LT. sum .OR. sisnan( sum ) ) anorm = sum
164 20 CONTINUE
165 END IF
166 ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
167*
168* Find normF(A).
169*
170 scale = zero
171 sum = one
172 IF( n.GT.1 ) THEN
173 CALL classq( n-1, e, 1, scale, sum )
174 sum = 2*sum
175 END IF
176 CALL slassq( n, d, 1, scale, sum )
177 anorm = scale*sqrt( sum )
178 END IF
179*
180 clanht = anorm
181 RETURN
182*
183* End of CLANHT
184*
185 END
subroutine slassq(n, x, incx, scl, sumsq)
SLASSQ updates a sum of squares represented in scaled form.
Definition: slassq.f90:137
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 clanht(NORM, N, D, E)
CLANHT returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: clanht.f:101