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

6       ZLANSB  -  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       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

28       ZLANSB returns the value
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30          ZLANSB = ( 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 ZLANSB as described
48               above.
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50       UPLO    (input) CHARACTER*1
51               Specifies whether the upper or lower  triangular  part  of  the
52               band  matrix  A  is supplied.  = 'U':  Upper triangular part is
53               supplied
54               = 'L':  Lower triangular part is supplied
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56       N       (input) INTEGER
57               The order of the matrix A.  N >= 0.  When N = 0, ZLANSB is  set
58               to zero.
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60       K       (input) INTEGER
61               The  number  of  super-diagonals  or  sub-diagonals of the band
62               matrix A.  K >= 0.
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64       AB      (input) COMPLEX*16 array, dimension (LDAB,N)
65               The upper or lower triangle of the  symmetric  band  matrix  A,
66               stored  in  the  first K+1 rows of AB.  The j-th column of A is
67               stored in the j-th column of the array AB as follows: if UPLO =
68               'U',  AB(k+1+i-j,j)  =  A(i,j)  for max(1,j-k)<=i<=j; if UPLO =
69               'L', AB(1+i-j,j)   = A(i,j) for j<=i<=min(n,j+k).
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71       LDAB    (input) INTEGER
72               The leading dimension of the array AB.  LDAB >= K+1.
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74       WORK    (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
75               where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK
76               is not referenced.
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80 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       ZLANSB(1)