LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ clangb()

 real function clangb ( character norm, integer n, integer kl, integer ku, complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) work )

CLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.

Purpose:
``` CLANGB  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 band matrix  A,  with kl sub-diagonals and ku super-diagonals.```
Returns
CLANGB
```    CLANGB = ( 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 CLANGB as described above.``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0. When N = 0, CLANGB is set to zero.``` [in] KL ``` KL is INTEGER The number of sub-diagonals of the matrix A. KL >= 0.``` [in] KU ``` KU is INTEGER The number of super-diagonals of the matrix A. KU >= 0.``` [in] AB ``` AB is COMPLEX array, dimension (LDAB,N) The band matrix A, stored in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows: AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).``` [in] LDAB ``` LDAB is INTEGER The leading dimension of the array AB. LDAB >= KL+KU+1.``` [out] WORK ``` WORK is REAL array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced.```

Definition at line 123 of file clangb.f.

125*
126* -- LAPACK auxiliary routine --
127* -- LAPACK is a software package provided by Univ. of Tennessee, --
128* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129*
130* .. Scalar Arguments ..
131 CHARACTER NORM
132 INTEGER KL, KU, LDAB, N
133* ..
134* .. Array Arguments ..
135 REAL WORK( * )
136 COMPLEX AB( LDAB, * )
137* ..
138*
139* =====================================================================
140*
141* .. Parameters ..
142 REAL ONE, ZERO
143 parameter( one = 1.0e+0, zero = 0.0e+0 )
144* ..
145* .. Local Scalars ..
146 INTEGER I, J, K, L
147 REAL SCALE, SUM, VALUE, TEMP
148* ..
149* .. External Functions ..
150 LOGICAL LSAME, SISNAN
151 EXTERNAL lsame, sisnan
152* ..
153* .. External Subroutines ..
154 EXTERNAL classq
155* ..
156* .. Intrinsic Functions ..
157 INTRINSIC abs, max, min, sqrt
158* ..
159* .. Executable Statements ..
160*
161 IF( n.EQ.0 ) THEN
162 VALUE = zero
163 ELSE IF( lsame( norm, 'M' ) ) THEN
164*
165* Find max(abs(A(i,j))).
166*
167 VALUE = zero
168 DO 20 j = 1, n
169 DO 10 i = max( ku+2-j, 1 ), min( n+ku+1-j, kl+ku+1 )
170 temp = abs( ab( i, j ) )
171 IF( VALUE.LT.temp .OR. sisnan( temp ) ) VALUE = temp
172 10 CONTINUE
173 20 CONTINUE
174 ELSE IF( ( lsame( norm, 'O' ) ) .OR. ( norm.EQ.'1' ) ) THEN
175*
176* Find norm1(A).
177*
178 VALUE = zero
179 DO 40 j = 1, n
180 sum = zero
181 DO 30 i = max( ku+2-j, 1 ), min( n+ku+1-j, kl+ku+1 )
182 sum = sum + abs( ab( i, j ) )
183 30 CONTINUE
184 IF( VALUE.LT.sum .OR. sisnan( sum ) ) VALUE = sum
185 40 CONTINUE
186 ELSE IF( lsame( norm, 'I' ) ) THEN
187*
188* Find normI(A).
189*
190 DO 50 i = 1, n
191 work( i ) = zero
192 50 CONTINUE
193 DO 70 j = 1, n
194 k = ku + 1 - j
195 DO 60 i = max( 1, j-ku ), min( n, j+kl )
196 work( i ) = work( i ) + abs( ab( k+i, j ) )
197 60 CONTINUE
198 70 CONTINUE
199 VALUE = zero
200 DO 80 i = 1, n
201 temp = work( i )
202 IF( VALUE.LT.temp .OR. sisnan( temp ) ) VALUE = temp
203 80 CONTINUE
204 ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
205*
206* Find normF(A).
207*
208 scale = zero
209 sum = one
210 DO 90 j = 1, n
211 l = max( 1, j-ku )
212 k = ku + 1 - j + l
213 CALL classq( min( n, j+kl )-l+1, ab( k, j ), 1, scale, sum )
214 90 CONTINUE
215 VALUE = scale*sqrt( sum )
216 END IF
217*
218 clangb = VALUE
219 RETURN
220*
221* End of CLANGB
222*
logical function sisnan(sin)
SISNAN tests input for NaN.
Definition sisnan.f:59
real function clangb(norm, n, kl, ku, ab, ldab, work)
CLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition clangb.f:125
subroutine classq(n, x, incx, scale, sumsq)
CLASSQ updates a sum of squares represented in scaled form.
Definition classq.f90:124
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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