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

6       SLANTB  -  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       REAL FUNCTION SLANTB( 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      AB( LDAB, * ), WORK( * )
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PURPOSE

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

26       SLANTB returns the value
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28          SLANTB = ( 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'
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36       where   norm1   denotes the  one norm of a matrix (maximum column sum),
37       normI  denotes the  infinity norm  of a matrix  (maximum row  sum)  and
38       normF   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

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