SYNOPSIS

REAL FUNCTION

CLANTP( NORM, UPLO, DIAG, N, AP, WORK )

    

CHARACTER DIAG, NORM, UPLO

    

INTEGER N

    

REAL WORK( * )

    

COMPLEX AP( * )

PURPOSE

CLANTP returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form.

DESCRIPTION

CLANTP returns the value

   CLANTP = ( 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 CLANTP 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, CLANTP is set to zero.

AP (input) COMPLEX array, dimension (N*(N+1)/2)

The upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. Note that when DIAG = 'U', the elements of the array AP corresponding to the diagonal elements of the matrix A are not referenced, but are assumed to be one.

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

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