1ZLANGB(1)           LAPACK auxiliary routine (version 3.1)           ZLANGB(1)
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NAME

6       ZLANGB  -  the  value  of  the  one norm, or the Frobenius norm, or the
7       infinity norm, or the element of largest absolute value of an  n  by  n
8       band matrix A, with kl sub-diagonals and ku super-diagonals
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SYNOPSIS

11       DOUBLE PRECISION FUNCTION ZLANGB( NORM, N, KL, KU, AB, LDAB, WORK )
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13           CHARACTER    NORM
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15           INTEGER      KL, KU, LDAB, N
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17           DOUBLE       PRECISION WORK( * )
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19           COMPLEX*16   AB( LDAB, * )
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PURPOSE

22       ZLANGB   returns  the value of the one norm,  or the Frobenius norm, or
23       the  infinity norm,  or the element of  largest absolute value  of an n
24       by n band matrix  A,  with kl sub-diagonals and ku super-diagonals.
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DESCRIPTION

28       ZLANGB returns the value
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30          ZLANGB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
31                   (
32                   ( norm1(A),         NORM = '1', 'O' or 'o'
33                   (
34                   ( normI(A),         NORM = 'I' or 'i'
35                   (
36                   ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
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38       where   norm1   denotes the  one norm of a matrix (maximum column sum),
39       normI  denotes the  infinity norm  of a matrix  (maximum row  sum)  and
40       normF   denotes  the  Frobenius norm of a matrix (square root of sum of
41       squares).  Note that  max(abs(A(i,j)))   is  not  a  consistent  matrix
42       norm.
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ARGUMENTS

46       NORM    (input) CHARACTER*1
47               Specifies  the  value  to  be  returned  in ZLANGB as described
48               above.
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50       N       (input) INTEGER
51               The order of the matrix A.  N >= 0.  When N = 0, ZLANGB is  set
52               to zero.
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54       KL      (input) INTEGER
55               The number of sub-diagonals of the matrix A.  KL >= 0.
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57       KU      (input) INTEGER
58               The number of super-diagonals of the matrix A.  KU >= 0.
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60       AB      (input) COMPLEX*16 array, dimension (LDAB,N)
61               The  band matrix A, stored in rows 1 to KL+KU+1.  The j-th col‐
62               umn of A is stored in the j-th column of the array AB  as  fol‐
63               lows: AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
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65       LDAB    (input) INTEGER
66               The leading dimension of the array AB.  LDAB >= KL+KU+1.
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68       WORK    (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
69               where LWORK >= N when NORM = 'I'; otherwise, WORK is not refer‐
70               enced.
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74 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       ZLANGB(1)