LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
clanhb.f
Go to the documentation of this file.
1 *> \brief \b CLANHB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian band 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/clanhb.f">
11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clanhb.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clanhb.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * REAL FUNCTION CLANHB( NORM, UPLO, N, K, AB, LDAB,
22 * WORK )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER NORM, UPLO
26 * INTEGER K, LDAB, N
27 * ..
28 * .. Array Arguments ..
29 * REAL WORK( * )
30 * COMPLEX AB( LDAB, * )
31 * ..
32 *
33 *
34 *> \par Purpose:
35 * =============
36 *>
37 *> \verbatim
38 *>
39 *> CLANHB returns the value of the one norm, or the Frobenius norm, or
40 *> the infinity norm, or the element of largest absolute value of an
41 *> n by n hermitian band matrix A, with k super-diagonals.
42 *> \endverbatim
43 *>
44 *> \return CLANHB
45 *> \verbatim
46 *>
47 *> CLANHB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
48 *> (
49 *> ( norm1(A), NORM = '1', 'O' or 'o'
50 *> (
51 *> ( normI(A), NORM = 'I' or 'i'
52 *> (
53 *> ( normF(A), NORM = 'F', 'f', 'E' or 'e'
54 *>
55 *> where norm1 denotes the one norm of a matrix (maximum column sum),
56 *> normI denotes the infinity norm of a matrix (maximum row sum) and
57 *> normF denotes the Frobenius norm of a matrix (square root of sum of
58 *> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
59 *> \endverbatim
60 *
61 * Arguments:
62 * ==========
63 *
64 *> \param[in] NORM
65 *> \verbatim
66 *> NORM is CHARACTER*1
67 *> Specifies the value to be returned in CLANHB as described
68 *> above.
69 *> \endverbatim
70 *>
71 *> \param[in] UPLO
72 *> \verbatim
73 *> UPLO is CHARACTER*1
74 *> Specifies whether the upper or lower triangular part of the
75 *> band matrix A is supplied.
76 *> = 'U': Upper triangular
77 *> = 'L': Lower triangular
78 *> \endverbatim
79 *>
80 *> \param[in] N
81 *> \verbatim
82 *> N is INTEGER
83 *> The order of the matrix A. N >= 0. When N = 0, CLANHB is
84 *> set to zero.
85 *> \endverbatim
86 *>
87 *> \param[in] K
88 *> \verbatim
89 *> K is INTEGER
90 *> The number of super-diagonals or sub-diagonals of the
91 *> band matrix A. K >= 0.
92 *> \endverbatim
93 *>
94 *> \param[in] AB
95 *> \verbatim
96 *> AB is COMPLEX array, dimension (LDAB,N)
97 *> The upper or lower triangle of the hermitian band matrix A,
98 *> stored in the first K+1 rows of AB. The j-th column of A is
99 *> stored in the j-th column of the array AB as follows:
100 *> if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
101 *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k).
102 *> Note that the imaginary parts of the diagonal elements need
103 *> not be set and are assumed to be zero.
104 *> \endverbatim
105 *>
106 *> \param[in] LDAB
107 *> \verbatim
108 *> LDAB is INTEGER
109 *> The leading dimension of the array AB. LDAB >= K+1.
110 *> \endverbatim
111 *>
112 *> \param[out] WORK
113 *> \verbatim
114 *> WORK is REAL array, dimension (MAX(1,LWORK)),
115 *> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
116 *> WORK is not referenced.
117 *> \endverbatim
118 *
119 * Authors:
120 * ========
121 *
122 *> \author Univ. of Tennessee
123 *> \author Univ. of California Berkeley
124 *> \author Univ. of Colorado Denver
125 *> \author NAG Ltd.
126 *
127 *> \date September 2012
128 *
129 *> \ingroup complexOTHERauxiliary
130 *
131 * =====================================================================
132  REAL FUNCTION clanhb( NORM, UPLO, N, K, AB, LDAB,
133  \$ work )
134 *
135 * -- LAPACK auxiliary routine (version 3.4.2) --
136 * -- LAPACK is a software package provided by Univ. of Tennessee, --
137 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
138 * September 2012
139 *
140 * .. Scalar Arguments ..
141  CHARACTER norm, uplo
142  INTEGER k, ldab, n
143 * ..
144 * .. Array Arguments ..
145  REAL work( * )
146  COMPLEX ab( ldab, * )
147 * ..
148 *
149 * =====================================================================
150 *
151 * .. Parameters ..
152  REAL one, zero
153  parameter( one = 1.0e+0, zero = 0.0e+0 )
154 * ..
155 * .. Local Scalars ..
156  INTEGER i, j, l
157  REAL absa, scale, sum, value
158 * ..
159 * .. External Functions ..
160  LOGICAL lsame, sisnan
161  EXTERNAL lsame, sisnan
162 * ..
163 * .. External Subroutines ..
164  EXTERNAL classq
165 * ..
166 * .. Intrinsic Functions ..
167  INTRINSIC abs, max, min, REAL, sqrt
168 * ..
169 * .. Executable Statements ..
170 *
171  IF( n.EQ.0 ) THEN
172  value = zero
173  ELSE IF( lsame( norm, 'M' ) ) THEN
174 *
175 * Find max(abs(A(i,j))).
176 *
177  value = zero
178  IF( lsame( uplo, 'U' ) ) THEN
179  DO 20 j = 1, n
180  DO 10 i = max( k+2-j, 1 ), k
181  sum = abs( ab( i, j ) )
182  IF( value .LT. sum .OR. sisnan( sum ) ) value = sum
183  10 continue
184  sum = abs( REAL( AB( K+1, J ) ) )
185  IF( value .LT. sum .OR. sisnan( sum ) ) value = sum
186  20 continue
187  ELSE
188  DO 40 j = 1, n
189  sum = abs( REAL( AB( 1, J ) ) )
190  IF( value .LT. sum .OR. sisnan( sum ) ) value = sum
191  DO 30 i = 2, min( n+1-j, k+1 )
192  sum = abs( ab( i, j ) )
193  IF( value .LT. sum .OR. sisnan( sum ) ) value = sum
194  30 continue
195  40 continue
196  END IF
197  ELSE IF( ( lsame( norm, 'I' ) ) .OR. ( lsame( norm, 'O' ) ) .OR.
198  \$ ( norm.EQ.'1' ) ) THEN
199 *
200 * Find normI(A) ( = norm1(A), since A is hermitian).
201 *
202  value = zero
203  IF( lsame( uplo, 'U' ) ) THEN
204  DO 60 j = 1, n
205  sum = zero
206  l = k + 1 - j
207  DO 50 i = max( 1, j-k ), j - 1
208  absa = abs( ab( l+i, j ) )
209  sum = sum + absa
210  work( i ) = work( i ) + absa
211  50 continue
212  work( j ) = sum + abs( REAL( AB( K+1, J ) ) )
213  60 continue
214  DO 70 i = 1, n
215  sum = work( i )
216  IF( value .LT. sum .OR. sisnan( sum ) ) value = sum
217  70 continue
218  ELSE
219  DO 80 i = 1, n
220  work( i ) = zero
221  80 continue
222  DO 100 j = 1, n
223  sum = work( j ) + abs( REAL( AB( 1, J ) ) )
224  l = 1 - j
225  DO 90 i = j + 1, min( n, j+k )
226  absa = abs( ab( l+i, j ) )
227  sum = sum + absa
228  work( i ) = work( i ) + absa
229  90 continue
230  IF( value .LT. sum .OR. sisnan( sum ) ) value = sum
231  100 continue
232  END IF
233  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
234 *
235 * Find normF(A).
236 *
237  scale = zero
238  sum = one
239  IF( k.GT.0 ) THEN
240  IF( lsame( uplo, 'U' ) ) THEN
241  DO 110 j = 2, n
242  CALL classq( min( j-1, k ), ab( max( k+2-j, 1 ), j ),
243  \$ 1, scale, sum )
244  110 continue
245  l = k + 1
246  ELSE
247  DO 120 j = 1, n - 1
248  CALL classq( min( n-j, k ), ab( 2, j ), 1, scale,
249  \$ sum )
250  120 continue
251  l = 1
252  END IF
253  sum = 2*sum
254  ELSE
255  l = 1
256  END IF
257  DO 130 j = 1, n
258  IF( REAL( AB( L, J ) ).NE.zero ) then
259  absa = abs( REAL( AB( L, J ) ) )
260  IF( scale.LT.absa ) THEN
261  sum = one + sum*( scale / absa )**2
262  scale = absa
263  ELSE
264  sum = sum + ( absa / scale )**2
265  END IF
266  END IF
267  130 continue
268  value = scale*sqrt( sum )
269  END IF
270 *
271  clanhb = value
272  return
273 *
274 * End of CLANHB
275 *
276  END