.TH SLANTP 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) "
.SH NAME
SLANTP - the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form
.SH SYNOPSIS
.TP 14
REAL FUNCTION
SLANTP( NORM, UPLO, DIAG, N, AP, WORK )
.TP 14
.ti +4
CHARACTER
DIAG, NORM, UPLO
.TP 14
.ti +4
INTEGER
N
.TP 14
.ti +4
REAL
AP( * ), WORK( * )
.SH PURPOSE
SLANTP returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value of a
triangular matrix A, supplied in packed form.
.SH DESCRIPTION
SLANTP returns the value
.br
SLANTP = ( max(abs(A(i,j))), NORM = \(aqM\(aq or \(aqm\(aq
.br
(
.br
( norm1(A), NORM = \(aq1\(aq, \(aqO\(aq or \(aqo\(aq
.br
(
.br
( normI(A), NORM = \(aqI\(aq or \(aqi\(aq
.br
(
.br
( normF(A), NORM = \(aqF\(aq, \(aqf\(aq, \(aqE\(aq or \(aqe\(aq
where norm1 denotes the one norm of a matrix (maximum column sum),
normI denotes the infinity norm of a matrix (maximum row sum) and
normF denotes the Frobenius norm of a matrix (square root of sum of
squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
.SH ARGUMENTS
.TP 8
NORM (input) CHARACTER*1
Specifies the value to be returned in SLANTP as described
above.
.TP 8
UPLO (input) CHARACTER*1
Specifies whether the matrix A is upper or lower triangular.
= \(aqU\(aq: Upper triangular
.br
= \(aqL\(aq: Lower triangular
.TP 8
DIAG (input) CHARACTER*1
Specifies whether or not the matrix A is unit triangular.
= \(aqN\(aq: Non-unit triangular
.br
= \(aqU\(aq: Unit triangular
.TP 8
N (input) INTEGER
The order of the matrix A. N >= 0. When N = 0, SLANTP is
set to zero.
.TP 8
AP (input) REAL array, dimension (N*(N+1)/2)
The upper or lower triangular matrix A, packed columnwise in
a linear array. The j-th column of A is stored in the array
AP as follows:
if UPLO = \(aqU\(aq, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = \(aqL\(aq, AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
Note that when DIAG = \(aqU\(aq, the elements of the array AP
corresponding to the diagonal elements of the matrix A are
not referenced, but are assumed to be one.
.TP 8
WORK (workspace) REAL array, dimension (MAX(1,LWORK)),
where LWORK >= N when NORM = \(aqI\(aq; otherwise, WORK is not
referenced.