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

6       SLANTP  -  the  value  of  the  one norm, or the Frobenius norm, or the
7       infinity norm, or the element of largest absolute value of a triangular
8       matrix A, supplied in packed form
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SYNOPSIS

11       REAL FUNCTION SLANTP( NORM, UPLO, DIAG, N, AP, WORK )
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13           CHARACTER DIAG, NORM, UPLO
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15           INTEGER   N
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17           REAL      AP( * ), WORK( * )
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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.
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DESCRIPTION

26       SLANTP returns the value
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28          SLANTP = ( 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 SLANTP 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, SLANTP is  set
60               to zero.
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62       AP      (input) REAL array, dimension (N*(N+1)/2)
63               The  upper or lower triangular matrix A, packed columnwise in a
64               linear array.  The j-th column of A is stored in the  array  AP
65               as  follows:  if  UPLO  =  'U',  AP(i + (j-1)*j/2) = A(i,j) for
66               1<=i<=j; if UPLO = 'L', AP(i +  (j-1)*(2n-j)/2)  =  A(i,j)  for
67               j<=i<=n.   Note that when DIAG = 'U', the elements of the array
68               AP corresponding to the diagonal elements of the matrix  A  are
69               not referenced, but are assumed to be one.
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71       WORK    (workspace) REAL array, dimension (MAX(1,LWORK)),
72               where LWORK >= N when NORM = 'I'; otherwise, WORK is not refer‐
73               enced.
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77 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       SLANTP(1)