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

6       ZLANSB  -  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 symmetric band matrix A, with k super-diagonals
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SYNOPSIS

11       DOUBLE PRECISION FUNCTION ZLANSB( NORM, UPLO, N, K, AB, LDAB, WORK )
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13           CHARACTER    NORM, UPLO
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15           INTEGER      K, 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       ZLANSB   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 symmetric band matrix A,  with k super-diagonals.
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DESCRIPTION

27       ZLANSB returns the value
28          ZLANSB = ( 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  ZLANSB  as  described
44               above.
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46       UPLO    (input) CHARACTER*1
47               Specifies  whether  the  upper  or lower triangular part of the
48               band matrix A is supplied.  = 'U':  Upper  triangular  part  is
49               supplied
50               = 'L':  Lower triangular part is supplied
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52       N       (input) INTEGER
53               The  order of the matrix A.  N >= 0.  When N = 0, ZLANSB is set
54               to zero.
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56       K       (input) INTEGER
57               The number of super-diagonals  or  sub-diagonals  of  the  band
58               matrix A.  K >= 0.
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60       AB      (input) COMPLEX*16 array, dimension (LDAB,N)
61               The  upper  or  lower  triangle of the symmetric band matrix A,
62               stored in the first K+1 rows of AB.  The j-th column  of  A  is
63               stored in the j-th column of the array AB as follows: if UPLO =
64               'U', AB(k+1+i-j,j) = A(i,j) for  max(1,j-k)<=i<=j;  if  UPLO  =
65               'L', AB(1+i-j,j)   = A(i,j) for j<=i<=min(n,j+k).
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67       LDAB    (input) INTEGER
68               The leading dimension of the array AB.  LDAB >= K+1.
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70       WORK    (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
71               where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK
72               is not referenced.
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76 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       ZLANSB(1)