LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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clansb.f
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1*> \brief \b CLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix.
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download CLANSB + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clansb.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clansb.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clansb.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* REAL FUNCTION CLANSB( 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*> CLANSB 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 symmetric band matrix A, with k super-diagonals.
42*> \endverbatim
43*>
44*> \return CLANSB
45*> \verbatim
46*>
47*> CLANSB = ( 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 CLANSB 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 part is supplied
77*> = 'L': Lower triangular part is supplied
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, CLANSB 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 symmetric 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*> \endverbatim
103*>
104*> \param[in] LDAB
105*> \verbatim
106*> LDAB is INTEGER
107*> The leading dimension of the array AB. LDAB >= K+1.
108*> \endverbatim
109*>
110*> \param[out] WORK
111*> \verbatim
112*> WORK is REAL array, dimension (MAX(1,LWORK)),
113*> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
114*> WORK is not referenced.
115*> \endverbatim
116*
117* Authors:
118* ========
119*
120*> \author Univ. of Tennessee
121*> \author Univ. of California Berkeley
122*> \author Univ. of Colorado Denver
123*> \author NAG Ltd.
124*
125*> \ingroup complexOTHERauxiliary
126*
127* =====================================================================
128 REAL function clansb( norm, uplo, n, k, ab, ldab,
129 $ work )
130*
131* -- LAPACK auxiliary routine --
132* -- LAPACK is a software package provided by Univ. of Tennessee, --
133* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
134*
135* .. Scalar Arguments ..
136 CHARACTER norm, uplo
137 INTEGER k, ldab, n
138* ..
139* .. Array Arguments ..
140 REAL work( * )
141 COMPLEX ab( ldab, * )
142* ..
143*
144* =====================================================================
145*
146* .. Parameters ..
147 REAL one, zero
148 parameter( one = 1.0e+0, zero = 0.0e+0 )
149* ..
150* .. Local Scalars ..
151 INTEGER i, j, l
152 REAL absa, scale, sum, value
153* ..
154* .. External Functions ..
155 LOGICAL lsame, sisnan
156 EXTERNAL lsame, sisnan
157* ..
158* .. External Subroutines ..
159 EXTERNAL classq
160* ..
161* .. Intrinsic Functions ..
162 INTRINSIC abs, max, min, sqrt
163* ..
164* .. Executable Statements ..
165*
166 IF( n.EQ.0 ) THEN
167 VALUE = zero
168 ELSE IF( lsame( norm, 'M' ) ) THEN
169*
170* Find max(abs(A(i,j))).
171*
172 VALUE = zero
173 IF( lsame( uplo, 'U' ) ) THEN
174 DO 20 j = 1, n
175 DO 10 i = max( k+2-j, 1 ), k + 1
176 sum = abs( ab( i, j ) )
177 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
178 10 CONTINUE
179 20 CONTINUE
180 ELSE
181 DO 40 j = 1, n
182 DO 30 i = 1, min( n+1-j, k+1 )
183 sum = abs( ab( i, j ) )
184 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
185 30 CONTINUE
186 40 CONTINUE
187 END IF
188 ELSE IF( ( lsame( norm, 'I' ) ) .OR. ( lsame( norm, 'O' ) ) .OR.
189 $ ( norm.EQ.'1' ) ) THEN
190*
191* Find normI(A) ( = norm1(A), since A is symmetric).
192*
193 VALUE = zero
194 IF( lsame( uplo, 'U' ) ) THEN
195 DO 60 j = 1, n
196 sum = zero
197 l = k + 1 - j
198 DO 50 i = max( 1, j-k ), j - 1
199 absa = abs( ab( l+i, j ) )
200 sum = sum + absa
201 work( i ) = work( i ) + absa
202 50 CONTINUE
203 work( j ) = sum + abs( ab( k+1, j ) )
204 60 CONTINUE
205 DO 70 i = 1, n
206 sum = work( i )
207 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
208 70 CONTINUE
209 ELSE
210 DO 80 i = 1, n
211 work( i ) = zero
212 80 CONTINUE
213 DO 100 j = 1, n
214 sum = work( j ) + abs( ab( 1, j ) )
215 l = 1 - j
216 DO 90 i = j + 1, min( n, j+k )
217 absa = abs( ab( l+i, j ) )
218 sum = sum + absa
219 work( i ) = work( i ) + absa
220 90 CONTINUE
221 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
222 100 CONTINUE
223 END IF
224 ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
225*
226* Find normF(A).
227*
228 scale = zero
229 sum = one
230 IF( k.GT.0 ) THEN
231 IF( lsame( uplo, 'U' ) ) THEN
232 DO 110 j = 2, n
233 CALL classq( min( j-1, k ), ab( max( k+2-j, 1 ), j ),
234 $ 1, scale, sum )
235 110 CONTINUE
236 l = k + 1
237 ELSE
238 DO 120 j = 1, n - 1
239 CALL classq( min( n-j, k ), ab( 2, j ), 1, scale,
240 $ sum )
241 120 CONTINUE
242 l = 1
243 END IF
244 sum = 2*sum
245 ELSE
246 l = 1
247 END IF
248 CALL classq( n, ab( l, 1 ), ldab, scale, sum )
249 VALUE = scale*sqrt( sum )
250 END IF
251*
252 clansb = VALUE
253 RETURN
254*
255* End of CLANSB
256*
257 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 clansb(NORM, UPLO, N, K, AB, LDAB, WORK)
CLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: clansb.f:130