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

6       ZLANTB  -  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       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

28       ZLANTB returns the value
29          ZLANTB = ( 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'  where
36       norm1   denotes  the   one norm of a matrix (maximum column sum), normI
37       denotes the  infinity norm  of a matrix  (maximum row  sum)  and  normF
38       denotes  the   Frobenius  norm  of  a  matrix  (square  root  of sum of
39       squares).  Note that  max(abs(A(i,j)))   is  not  a  consistent  matrix
40       norm.
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ARGUMENTS

43       NORM    (input) CHARACTER*1
44               Specifies  the  value  to  be  returned  in ZLANTB as described
45               above.
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47       UPLO    (input) CHARACTER*1
48               Specifies whether the matrix A is upper or lower triangular.  =
49               'U':  Upper triangular
50               = 'L':  Lower triangular
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52       DIAG    (input) CHARACTER*1
53               Specifies  whether  or  not the matrix A is unit triangular.  =
54               'N':  Non-unit triangular
55               = 'U':  Unit triangular
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57       N       (input) INTEGER
58               The order of the matrix A.  N >= 0.  When N = 0, ZLANTB is  set
59               to zero.
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61       K       (input) INTEGER
62               The number of super-diagonals of the matrix A if UPLO = 'U', or
63               the number of sub-diagonals of the matrix A if UPLO =  'L'.   K
64               >= 0.
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66       AB      (input) COMPLEX*16 array, dimension (LDAB,N)
67               The  upper  or  lower  triangular  band matrix A, stored in the
68               first k+1 rows of AB.  The j-th column of A is stored in the j-
69               th  column of the array AB as follows: if UPLO = 'U', AB(k+1+i-
70               j,j) = A(i,j) for max(1,j-k)<=i<=j; if UPLO = 'L',  AB(1+i-j,j)
71               =  A(i,j) for j<=i<=min(n,j+k).  Note that when DIAG = 'U', the
72               elements of the array AB corresponding to the diagonal elements
73               of the matrix A are not referenced, but are assumed to be one.
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75       LDAB    (input) INTEGER
76               The leading dimension of the array AB.  LDAB >= K+1.
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78       WORK    (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
79               where LWORK >= N when NORM = 'I'; otherwise, WORK is not refer‐
80               enced.
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84 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       ZLANTB(1)