LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
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 *
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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 *> \date September 2012
98 *
99 *> \ingroup complexOTHERauxiliary
100 *
101 * =====================================================================
102  REAL FUNCTION clanht( NORM, N, D, E )
103 *
104 * -- LAPACK auxiliary routine (version 3.4.2) --
105 * -- LAPACK is a software package provided by Univ. of Tennessee, --
106 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
107 * September 2012
108 *
109 * .. Scalar Arguments ..
110  CHARACTER NORM
111  INTEGER N
112 * ..
113 * .. Array Arguments ..
114  REAL D( * )
115  COMPLEX E( * )
116 * ..
117 *
118 * =====================================================================
119 *
120 * .. Parameters ..
121  REAL ONE, ZERO
122  parameter ( one = 1.0e+0, zero = 0.0e+0 )
123 * ..
124 * .. Local Scalars ..
125  INTEGER I
126  REAL ANORM, SCALE, SUM
127 * ..
128 * .. External Functions ..
129  LOGICAL LSAME, SISNAN
130  EXTERNAL lsame, sisnan
131 * ..
132 * .. External Subroutines ..
133  EXTERNAL classq, slassq
134 * ..
135 * .. Intrinsic Functions ..
136  INTRINSIC abs, sqrt
137 * ..
138 * .. Executable Statements ..
139 *
140  IF( n.LE.0 ) THEN
141  anorm = zero
142  ELSE IF( lsame( norm, 'M' ) ) THEN
143 *
144 * Find max(abs(A(i,j))).
145 *
146  anorm = abs( d( n ) )
147  DO 10 i = 1, n - 1
148  sum = abs( d( i ) )
149  IF( anorm .LT. sum .OR. sisnan( sum ) ) anorm = sum
150  sum = abs( e( i ) )
151  IF( anorm .LT. sum .OR. sisnan( sum ) ) anorm = sum
152  10 CONTINUE
153  ELSE IF( lsame( norm, 'O' ) .OR. norm.EQ.'1' .OR.
154  \$ lsame( norm, 'I' ) ) THEN
155 *
156 * Find norm1(A).
157 *
158  IF( n.EQ.1 ) THEN
159  anorm = abs( d( 1 ) )
160  ELSE
161  anorm = abs( d( 1 ) )+abs( e( 1 ) )
162  sum = abs( e( n-1 ) )+abs( d( n ) )
163  IF( anorm .LT. sum .OR. sisnan( sum ) ) anorm = sum
164  DO 20 i = 2, n - 1
165  sum = abs( d( i ) )+abs( e( i ) )+abs( e( i-1 ) )
166  IF( anorm .LT. sum .OR. sisnan( sum ) ) anorm = sum
167  20 CONTINUE
168  END IF
169  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
170 *
171 * Find normF(A).
172 *
173  scale = zero
174  sum = one
175  IF( n.GT.1 ) THEN
176  CALL classq( n-1, e, 1, scale, sum )
177  sum = 2*sum
178  END IF
179  CALL slassq( n, d, 1, scale, sum )
180  anorm = scale*sqrt( sum )
181  END IF
182 *
183  clanht = anorm
184  RETURN
185 *
186 * End of CLANHT
187 *
188  END
subroutine slassq(N, X, INCX, SCALE, SUMSQ)
SLASSQ updates a sum of squares represented in scaled form.
Definition: slassq.f:105
subroutine classq(N, X, INCX, SCALE, SUMSQ)
CLASSQ updates a sum of squares represented in scaled form.
Definition: classq.f:108
real function clanht(NORM, N, D, E)
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.
Definition: clanht.f:103