dlansy (l) - Linux Manuals

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

NAME

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

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 = aqMaq or aqmaq

      (

      ( norm1(A),         NORM = aq1aq, aqOaq or aqoaq

      (

      ( normI(A),         NORM = aqIaq or aqiaq

      (

      ( normF(A),         NORM = aqFaq, aqfaq, aqEaq or aqeaq 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. = aqUaq: Upper triangular part of A is referenced
= aqLaq: 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 = aqUaq, 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 = aqLaq, 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 = aqIaq or aq1aq or aqOaq; otherwise, WORK is not referenced.