SYNOPSIS

REAL FUNCTION

SLANTB( NORM, UPLO, DIAG, N, K, AB, LDAB, WORK )

    

CHARACTER DIAG, NORM, UPLO

    

INTEGER K, LDAB, N

    

REAL AB( LDAB, * ), WORK( * )

PURPOSE

SLANTB returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals.

DESCRIPTION

SLANTB returns the value

   SLANTB = ( 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 SLANTB 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, SLANTB is set to zero.

K (input) INTEGER

The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals of the matrix A if UPLO = 'L'. K >= 0.

AB (input) REAL array, dimension (LDAB,N)

The upper or lower triangular band matrix A, stored in the first k+1 rows of AB. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k). Note that when DIAG = 'U', the elements of the array AB corresponding to the diagonal elements of the matrix A are not referenced, but are assumed to be one.

LDAB (input) INTEGER

The leading dimension of the array AB. LDAB >= K+1.

WORK (workspace) REAL array, dimension (MAX(1,LWORK)),

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