LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ clansb()

real function clansb ( character norm,
character uplo,
integer n,
integer k,
complex, dimension( ldab, * ) ab,
integer ldab,
real, dimension( * ) work )

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.

Download CLANSB + dependencies [TGZ] [ZIP] [TXT]

Purpose:
!>
!> CLANSB  returns the value of the one norm,  or the Frobenius norm, or
!> the  infinity norm,  or the element of  largest absolute value  of an
!> n by n symmetric band matrix A,  with k super-diagonals.
!>
Returns
CLANSB 
!>
!>    CLANSB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
!>             (
!>             ( norm1(A),         NORM = '1', 'O' or 'o'
!>             (
!>             ( normI(A),         NORM = 'I' or 'i'
!>             (
!>             ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
!>
!> where  norm1  denotes the  one norm of a matrix (maximum column sum),
!> normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
!> normF  denotes the  Frobenius norm of a matrix (square root of sum of
!> squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
!>
Parameters
[in]NORM
!>          NORM is CHARACTER*1
!>          Specifies the value to be returned in CLANSB as described
!>          above.
!>
[in]UPLO
!>          UPLO is CHARACTER*1
!>          Specifies whether the upper or lower triangular part of the
!>          band matrix A is supplied.
!>          = 'U':  Upper triangular part is supplied
!>          = 'L':  Lower triangular part is supplied
!>
[in]N
!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.  When N = 0, CLANSB is
!>          set to zero.
!>
[in]K
!>          K is INTEGER
!>          The number of super-diagonals or sub-diagonals of the
!>          band matrix A.  K >= 0.
!>
[in]AB
!>          AB is COMPLEX array, dimension (LDAB,N)
!>          The upper or lower triangle of the symmetric band matrix A,
!>          stored in the first K+1 rows of AB.  The j-th column of A is
!>          stored in the j-th column of the array AB as follows:
!>          if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
!>          if UPLO = 'L', AB(1+i-j,j)   = A(i,j) for j<=i<=min(n,j+k).
!>
[in]LDAB
!>          LDAB is INTEGER
!>          The leading dimension of the array AB.  LDAB >= K+1.
!>
[out]WORK
!>          WORK is REAL array, dimension (MAX(1,LWORK)),
!>          where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
!>          WORK is not referenced.
!>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 126 of file clansb.f.

128*
129* -- LAPACK auxiliary routine --
130* -- LAPACK is a software package provided by Univ. of Tennessee, --
131* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
132*
133* .. Scalar Arguments ..
134 CHARACTER NORM, UPLO
135 INTEGER K, LDAB, N
136* ..
137* .. Array Arguments ..
138 REAL WORK( * )
139 COMPLEX AB( LDAB, * )
140* ..
141*
142* =====================================================================
143*
144* .. Parameters ..
145 REAL ONE, ZERO
146 parameter( one = 1.0e+0, zero = 0.0e+0 )
147* ..
148* .. Local Scalars ..
149 INTEGER I, J, L
150 REAL ABSA, SCALE, SUM, VALUE
151* ..
152* .. External Functions ..
153 LOGICAL LSAME, SISNAN
154 EXTERNAL lsame, sisnan
155* ..
156* .. External Subroutines ..
157 EXTERNAL classq
158* ..
159* .. Intrinsic Functions ..
160 INTRINSIC abs, max, min, sqrt
161* ..
162* .. Executable Statements ..
163*
164 IF( n.EQ.0 ) THEN
165 VALUE = zero
166 ELSE IF( lsame( norm, 'M' ) ) THEN
167*
168* Find max(abs(A(i,j))).
169*
170 VALUE = zero
171 IF( lsame( uplo, 'U' ) ) THEN
172 DO 20 j = 1, n
173 DO 10 i = max( k+2-j, 1 ), k + 1
174 sum = abs( ab( i, j ) )
175 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
176 10 CONTINUE
177 20 CONTINUE
178 ELSE
179 DO 40 j = 1, n
180 DO 30 i = 1, min( n+1-j, k+1 )
181 sum = abs( ab( i, j ) )
182 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
183 30 CONTINUE
184 40 CONTINUE
185 END IF
186 ELSE IF( ( lsame( norm, 'I' ) ) .OR.
187 $ ( lsame( norm, 'O' ) ) .OR.
188 $ ( norm.EQ.'1' ) ) THEN
189*
190* Find normI(A) ( = norm1(A), since A is symmetric).
191*
192 VALUE = zero
193 IF( lsame( uplo, 'U' ) ) THEN
194 DO 60 j = 1, n
195 sum = zero
196 l = k + 1 - j
197 DO 50 i = max( 1, j-k ), j - 1
198 absa = abs( ab( l+i, j ) )
199 sum = sum + absa
200 work( i ) = work( i ) + absa
201 50 CONTINUE
202 work( j ) = sum + abs( ab( k+1, j ) )
203 60 CONTINUE
204 DO 70 i = 1, n
205 sum = work( i )
206 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
207 70 CONTINUE
208 ELSE
209 DO 80 i = 1, n
210 work( i ) = zero
211 80 CONTINUE
212 DO 100 j = 1, n
213 sum = work( j ) + abs( ab( 1, j ) )
214 l = 1 - j
215 DO 90 i = j + 1, min( n, j+k )
216 absa = abs( ab( l+i, j ) )
217 sum = sum + absa
218 work( i ) = work( i ) + absa
219 90 CONTINUE
220 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
221 100 CONTINUE
222 END IF
223 ELSE IF( ( lsame( norm, 'F' ) ) .OR.
224 $ ( 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 ),
234 $ j ),
235 $ 1, scale, sum )
236 110 CONTINUE
237 l = k + 1
238 ELSE
239 DO 120 j = 1, n - 1
240 CALL classq( min( n-j, k ), ab( 2, j ), 1, scale,
241 $ sum )
242 120 CONTINUE
243 l = 1
244 END IF
245 sum = 2*sum
246 ELSE
247 l = 1
248 END IF
249 CALL classq( n, ab( l, 1 ), ldab, scale, sum )
250 VALUE = scale*sqrt( sum )
251 END IF
252*
253 clansb = VALUE
254 RETURN
255*
256* End of CLANSB
257*
sisnan
logical function sisnan(sin)
SISNAN tests input for NaN.
Definition sisnan.f:57
clansb
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:128
classq
subroutine classq(n, x, incx, scale, sumsq)
CLASSQ updates a sum of squares represented in scaled form.
Definition classq.f90:122
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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