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

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

11       DOUBLE PRECISION FUNCTION  DLANTB(  NORM,  UPLO,  DIAG, N, K, AB, LDAB,
12                        WORK )
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14           CHARACTER    DIAG, NORM, UPLO
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16           INTEGER      K, LDAB, N
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18           DOUBLE       PRECISION AB( LDAB, * ), WORK( * )
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PURPOSE

21       DLANTB  returns the value of the one norm,  or the Frobenius  norm,  or
22       the  infinity norm,  or the element of  largest absolute value  of an n
23       by n triangular band matrix A,  with ( k + 1 ) diagonals.
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DESCRIPTION

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

45       NORM    (input) CHARACTER*1
46               Specifies the value to  be  returned  in  DLANTB  as  described
47               above.
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49       UPLO    (input) CHARACTER*1
50               Specifies whether the matrix A is upper or lower triangular.  =
51               'U':  Upper triangular
52               = 'L':  Lower triangular
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54       DIAG    (input) CHARACTER*1
55               Specifies whether or not the matrix A is  unit  triangular.   =
56               'N':  Non-unit triangular
57               = 'U':  Unit triangular
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59       N       (input) INTEGER
60               The  order of the matrix A.  N >= 0.  When N = 0, DLANTB is set
61               to zero.
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63       K       (input) INTEGER
64               The number of super-diagonals of the matrix A if UPLO = 'U', or
65               the  number  of sub-diagonals of the matrix A if UPLO = 'L'.  K
66               >= 0.
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68       AB      (input) DOUBLE PRECISION array, dimension (LDAB,N)
69               The upper or lower triangular band  matrix  A,  stored  in  the
70               first k+1 rows of AB.  The j-th column of A is stored in the j-
71               th column of the array AB as follows: if UPLO = 'U',  AB(k+1+i-
72               j,j)  = A(i,j) for max(1,j-k)<=i<=j; if UPLO = 'L', AB(1+i-j,j)
73               = A(i,j) for j<=i<=min(n,j+k).  Note that when DIAG = 'U',  the
74               elements of the array AB corresponding to the diagonal elements
75               of the matrix A are not referenced, but are assumed to be one.
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77       LDAB    (input) INTEGER
78               The leading dimension of the array AB.  LDAB >= K+1.
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80       WORK    (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
81               where LWORK >= N when NORM = 'I'; otherwise, WORK is not refer‐
82               enced.
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86 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       DLANTB(1)