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

6       CLANTB  -  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 triangular band matrix A, with ( k + 1 ) diagonals
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SYNOPSIS

11       REAL FUNCTION CLANTB( NORM, UPLO, DIAG, N, K, AB, LDAB, WORK )
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13           CHARACTER DIAG, NORM, UPLO
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15           INTEGER   K, LDAB, N
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17           REAL      WORK( * )
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19           COMPLEX   AB( LDAB, * )
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PURPOSE

22       CLANTB   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 triangular band matrix A,  with ( k + 1 ) diagonals.
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DESCRIPTION

27       CLANTB returns the value
28          CLANTB = ( 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  CLANTB  as  described
44               above.
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46       UPLO    (input) CHARACTER*1
47               Specifies whether the matrix A is upper or lower triangular.  =
48               'U':  Upper triangular
49               = 'L':  Lower triangular
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51       DIAG    (input) CHARACTER*1
52               Specifies whether or not the matrix A is  unit  triangular.   =
53               'N':  Non-unit triangular
54               = 'U':  Unit triangular
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56       N       (input) INTEGER
57               The  order of the matrix A.  N >= 0.  When N = 0, CLANTB is set
58               to zero.
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60       K       (input) INTEGER
61               The number of super-diagonals of the matrix A if UPLO = 'U', or
62               the  number  of sub-diagonals of the matrix A if UPLO = 'L'.  K
63               >= 0.
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65       AB      (input) COMPLEX array, dimension (LDAB,N)
66               The upper or lower triangular band  matrix  A,  stored  in  the
67               first k+1 rows of AB.  The j-th column of A is stored in the j-
68               th column of the array AB as follows: if UPLO = 'U',  AB(k+1+i-
69               j,j)  = A(i,j) for max(1,j-k)<=i<=j; if UPLO = 'L', AB(1+i-j,j)
70               = A(i,j) for j<=i<=min(n,j+k).  Note that when DIAG = 'U',  the
71               elements of the array AB corresponding to the diagonal elements
72               of the matrix A are not referenced, but are assumed to be one.
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74       LDAB    (input) INTEGER
75               The leading dimension of the array AB.  LDAB >= K+1.
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77       WORK    (workspace) REAL array, dimension (MAX(1,LWORK)),
78               where LWORK >= N when NORM = 'I'; otherwise, WORK is not refer‐
79               enced.
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83 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       CLANTB(1)
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