DLANTP(l) — LAPACK auxiliary routine (version 2.0)

NAME

DLANTP - return 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

SYNOPSIS

DOUBLE PRECISION
FUNCTION DLANTP( NORM, UPLO, DIAG, N, AP, WORK )

CHARACTER DIAG, NORM, UPLO

INTEGER N

DOUBLE PRECISION AP( ∗ ), WORK( ∗ )

PURPOSE

DLANTP 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.

DESCRIPTION

DLANTP returns the value

   DLANTP = ( max(abs(A(i,j))), NORM = ’M’ or ’m’
            (
            ( norm1(A),         NORM = ’1’, ’O’ or ’o’
            (
            ( normI(A),         NORM = ’I’ or ’i’
            (
            ( normF(A),         NORM = ’F’, ’f’, ’E’ or ’e’

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 matrix norm.

ARGUMENTS

NORM (input) CHARACTER∗1
Specifies the value to be returned in DLANTP as described above.

UPLO (input) CHARACTER∗1
Specifies whether the matrix A is upper or lower triangular. = ’U’: Upper triangular
= ’L’: Lower triangular

DIAG (input) CHARACTER∗1
Specifies whether or not the matrix A is unit triangular. = ’N’: Non-unit triangular
= ’U’: Unit triangular

N (input) INTEGER
The order of the matrix A. N >= 0. When N = 0, DLANTP is set to zero.

AP (input) DOUBLE PRECISION 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 = ’U’, AP(i + (j-1)∗j/2) = A(i,j) for 1<=i<=j; if UPLO = ’L’, AP(i + (j-1)∗(2n-j)/2) = A(i,j) for j<=i<=n. Note that when DIAG = ’U’, the elements of the array AP corresponding to the diagonal elements of the matrix A are not referenced, but are assumed to be one.

WORK (workspace) DOUBLE PRECISION array, dimension (LWORK),
where LWORK >= N when NORM = ’I’; otherwise, WORK is not referenced.