1ZLANGB(1)           LAPACK auxiliary routine (version 3.2)           ZLANGB(1)
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NAME

6       ZLANGB  -  returns the value of the one norm, or the Frobenius norm, or
7       the infinity norm, or the element of largest absolute value of an n  by
8       n 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

27       ZLANGB returns the value
28          ZLANGB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
29                   (
30                   ( norm1(A),         NORM = '1', 'O' or 'o'
31                   (
32                   ( normI(A),         NORM = 'I' or 'i'
33                   (
34                   (  normF(A),          NORM  =  'F',  'f',  'E' or 'e' where
35       norm1  denotes the  one norm of a matrix (maximum  column  sum),  normI
36       denotes  the   infinity  norm  of a matrix  (maximum row sum) and normF
37       denotes the  Frobenius  norm  of  a  matrix  (square  root  of  sum  of
38       squares).   Note  that   max(abs(A(i,j)))   is  not a consistent matrix
39       norm.
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ARGUMENTS

42       NORM    (input) CHARACTER*1
43               Specifies the value to  be  returned  in  ZLANGB  as  described
44               above.
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46       N       (input) INTEGER
47               The  order of the matrix A.  N >= 0.  When N = 0, ZLANGB is set
48               to zero.
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50       KL      (input) INTEGER
51               The number of sub-diagonals of the matrix A.  KL >= 0.
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53       KU      (input) INTEGER
54               The number of super-diagonals of the matrix A.  KU >= 0.
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56       AB      (input) COMPLEX*16 array, dimension (LDAB,N)
57               The band matrix A, stored in rows 1 to KL+KU+1.  The j-th  col‐
58               umn  of  A is stored in the j-th column of the array AB as fol‐
59               lows: AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
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61       LDAB    (input) INTEGER
62               The leading dimension of the array AB.  LDAB >= KL+KU+1.
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64       WORK    (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
65               where LWORK >= N when NORM = 'I'; otherwise, WORK is not refer‐
66               enced.
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70 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       ZLANGB(1)