SYNOPSIS

DOUBLE PRECISION

FUNCTION DLANSY( NORM, UPLO, N, A, LDA, WORK )

    

CHARACTER NORM, UPLO

    

INTEGER LDA, N

    

DOUBLE PRECISION A( LDA, * ), WORK( * )

PURPOSE

DLANSY 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 matrix A.

DESCRIPTION

DLANSY returns the value

   DLANSY = ( 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 consistent matrix norm.

ARGUMENTS

NORM (input) CHARACTER*1

Specifies the value to be returned in DLANSY as described above.

UPLO (input) CHARACTER*1

Specifies whether the upper or lower triangular part of the symmetric matrix A is to be referenced. = 'U': Upper triangular part of A is referenced
= 'L': Lower triangular part of A is referenced

N (input) INTEGER

The order of the matrix A. N >= 0. When N = 0, DLANSY is set to zero.

A (input) DOUBLE PRECISION array, dimension (LDA,N)

The symmetric matrix A. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.

LDA (input) INTEGER

The leading dimension of the array A. LDA >= max(N,1).

WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),

where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK is not referenced.