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

6       ZLANTB  -  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  ZLANTB(  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 WORK( * )
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20           COMPLEX*16   AB( LDAB, * )
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PURPOSE

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

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

47       NORM    (input) CHARACTER*1
48               Specifies the value to  be  returned  in  ZLANTB  as  described
49               above.
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51       UPLO    (input) CHARACTER*1
52               Specifies whether the matrix A is upper or lower triangular.  =
53               'U':  Upper triangular
54               = 'L':  Lower triangular
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56       DIAG    (input) CHARACTER*1
57               Specifies whether or not the matrix A is  unit  triangular.   =
58               'N':  Non-unit triangular
59               = 'U':  Unit triangular
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61       N       (input) INTEGER
62               The  order of the matrix A.  N >= 0.  When N = 0, ZLANTB is set
63               to zero.
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65       K       (input) INTEGER
66               The number of super-diagonals of the matrix A if UPLO = 'U', or
67               the  number  of sub-diagonals of the matrix A if UPLO = 'L'.  K
68               >= 0.
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70       AB      (input) COMPLEX*16 array, dimension (LDAB,N)
71               The upper or lower triangular band  matrix  A,  stored  in  the
72               first k+1 rows of AB.  The j-th column of A is stored in the j-
73               th column of the array AB as follows: if UPLO = 'U',  AB(k+1+i-
74               j,j)  = A(i,j) for max(1,j-k)<=i<=j; if UPLO = 'L', AB(1+i-j,j)
75               = A(i,j) for j<=i<=min(n,j+k).  Note that when DIAG = 'U',  the
76               elements of the array AB corresponding to the diagonal elements
77               of the matrix A are not referenced, but are assumed to be one.
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79       LDAB    (input) INTEGER
80               The leading dimension of the array AB.  LDAB >= K+1.
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82       WORK    (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
83               where LWORK >= N when NORM = 'I'; otherwise, WORK is not refer‐
84               enced.
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88 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       ZLANTB(1)
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