slanst (l) - Linux Manuals

slanst: 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

NAME

SLANST - 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

SYNOPSIS

REAL FUNCTION

SLANST( NORM, N, D, E )

    

CHARACTER NORM

    

INTEGER N

    

REAL D( * ), E( * )

PURPOSE

SLANST 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

SLANST returns the value

SLANST = ( 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 SLANST as described above.

N (input) INTEGER

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

D (input) REAL array, dimension (N)

The diagonal elements of A.

E (input) REAL array, dimension (N-1)

The (n-1) sub-diagonal or super-diagonal elements of A.