1SLANTP(1)           LAPACK auxiliary routine (version 3.2)           SLANTP(1)
2
3
4

NAME

6       SLANTP  -  returns the value of the one norm, or the Frobenius norm, or
7       the infinity norm, or the element of largest absolute value of a trian‐
8       gular matrix A, supplied in packed form
9

SYNOPSIS

11       REAL FUNCTION SLANTP( NORM, UPLO, DIAG, N, AP, WORK )
12
13           CHARACTER DIAG, NORM, UPLO
14
15           INTEGER   N
16
17           REAL      AP( * ), WORK( * )
18

PURPOSE

20       SLANTP   returns  the value of the one norm,  or the Frobenius norm, or
21       the  infinity norm,  or the  element of  largest absolute value   of  a
22       triangular matrix A, supplied in packed form.
23

DESCRIPTION

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

ARGUMENTS

40       NORM    (input) CHARACTER*1
41               Specifies the value to  be  returned  in  SLANTP  as  described
42               above.
43
44       UPLO    (input) CHARACTER*1
45               Specifies whether the matrix A is upper or lower triangular.  =
46               'U':  Upper triangular
47               = 'L':  Lower triangular
48
49       DIAG    (input) CHARACTER*1
50               Specifies whether or not the matrix A is  unit  triangular.   =
51               'N':  Non-unit triangular
52               = 'U':  Unit triangular
53
54       N       (input) INTEGER
55               The  order of the matrix A.  N >= 0.  When N = 0, SLANTP is set
56               to zero.
57
58       AP      (input) REAL array, dimension (N*(N+1)/2)
59               The upper or lower triangular matrix A, packed columnwise in  a
60               linear  array.   The j-th column of A is stored in the array AP
61               as follows: if UPLO = 'U',  AP(i  +  (j-1)*j/2)  =  A(i,j)  for
62               1<=i<=j;  if  UPLO  =  'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for
63               j<=i<=n.  Note that when DIAG = 'U', the elements of the  array
64               AP  corresponding  to the diagonal elements of the matrix A are
65               not referenced, but are assumed to be one.
66
67       WORK    (workspace) REAL array, dimension (MAX(1,LWORK)),
68               where LWORK >= N when NORM = 'I'; otherwise, WORK is not refer‐
69               enced.
70
71
72
73 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       SLANTP(1)
Impressum