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

NAME

DLANST - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix A

SYNOPSIS

DOUBLE PRECISION
FUNCTION DLANST( NORM, N, D, E )

CHARACTER NORM

INTEGER N

DOUBLE PRECISION D( ∗ ), E( ∗ )

PURPOSE

DLANST returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix A.

DESCRIPTION

DLANST returns the value

   DLANST = ( 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 DLANST as described above.

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

D (input) DOUBLE PRECISION array, dimension (N)
The diagonal elements of A.

E (input) DOUBLE PRECISION array, dimension (N-1)
The (n-1) sub-diagonal or super-diagonal elements of A.