 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ dlangb()

 double precision function dlangb ( character NORM, integer N, integer KL, integer KU, double precision, dimension( ldab, * ) AB, integer LDAB, double precision, dimension( * ) WORK )

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

Purpose:
``` DLANGB  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
DLANGB
```    DLANGB = ( 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 DLANGB as described above.``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0. When N = 0, DLANGB 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced.```

Definition at line 122 of file dlangb.f.

124*
125* -- LAPACK auxiliary routine --
126* -- LAPACK is a software package provided by Univ. of Tennessee, --
127* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
128*
129* .. Scalar Arguments ..
130 CHARACTER NORM
131 INTEGER KL, KU, LDAB, N
132* ..
133* .. Array Arguments ..
134 DOUBLE PRECISION AB( LDAB, * ), WORK( * )
135* ..
136*
137* =====================================================================
138*
139*
140* .. Parameters ..
141 DOUBLE PRECISION ONE, ZERO
142 parameter( one = 1.0d+0, zero = 0.0d+0 )
143* ..
144* .. Local Scalars ..
145 INTEGER I, J, K, L
146 DOUBLE PRECISION SCALE, SUM, VALUE, TEMP
147* ..
148* .. External Subroutines ..
149 EXTERNAL dlassq
150* ..
151* .. External Functions ..
152 LOGICAL LSAME, DISNAN
153 EXTERNAL lsame, disnan
154* ..
155* .. Intrinsic Functions ..
156 INTRINSIC abs, max, min, sqrt
157* ..
158* .. Executable Statements ..
159*
160 IF( n.EQ.0 ) THEN
161 VALUE = zero
162 ELSE IF( lsame( norm, 'M' ) ) THEN
163*
164* Find max(abs(A(i,j))).
165*
166 VALUE = zero
167 DO 20 j = 1, n
168 DO 10 i = max( ku+2-j, 1 ), min( n+ku+1-j, kl+ku+1 )
169 temp = abs( ab( i, j ) )
170 IF( VALUE.LT.temp .OR. disnan( temp ) ) VALUE = temp
171 10 CONTINUE
172 20 CONTINUE
173 ELSE IF( ( lsame( norm, 'O' ) ) .OR. ( norm.EQ.'1' ) ) THEN
174*
175* Find norm1(A).
176*
177 VALUE = zero
178 DO 40 j = 1, n
179 sum = zero
180 DO 30 i = max( ku+2-j, 1 ), min( n+ku+1-j, kl+ku+1 )
181 sum = sum + abs( ab( i, j ) )
182 30 CONTINUE
183 IF( VALUE.LT.sum .OR. disnan( sum ) ) VALUE = sum
184 40 CONTINUE
185 ELSE IF( lsame( norm, 'I' ) ) THEN
186*
187* Find normI(A).
188*
189 DO 50 i = 1, n
190 work( i ) = zero
191 50 CONTINUE
192 DO 70 j = 1, n
193 k = ku + 1 - j
194 DO 60 i = max( 1, j-ku ), min( n, j+kl )
195 work( i ) = work( i ) + abs( ab( k+i, j ) )
196 60 CONTINUE
197 70 CONTINUE
198 VALUE = zero
199 DO 80 i = 1, n
200 temp = work( i )
201 IF( VALUE.LT.temp .OR. disnan( temp ) ) VALUE = temp
202 80 CONTINUE
203 ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
204*
205* Find normF(A).
206*
207 scale = zero
208 sum = one
209 DO 90 j = 1, n
210 l = max( 1, j-ku )
211 k = ku + 1 - j + l
212 CALL dlassq( min( n, j+kl )-l+1, ab( k, j ), 1, scale, sum )
213 90 CONTINUE
214 VALUE = scale*sqrt( sum )
215 END IF
216*
217 dlangb = VALUE
218 RETURN
219*
220* End of DLANGB
221*
logical function disnan(DIN)
DISNAN tests input for NaN.
Definition: disnan.f:59
subroutine dlassq(n, x, incx, scl, sumsq)
DLASSQ updates a sum of squares represented in scaled form.
Definition: dlassq.f90:137
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
double precision function dlangb(NORM, N, KL, KU, AB, LDAB, WORK)
DLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: dlangb.f:124
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