zlantp(3)

NAME

ZLANTP - return the value of the one norm, or the Frobe

nius norm, or the infinity norm, or the element of largest abso

lute value of a triangular matrix A, supplied in packed form

SYNOPSIS

DOUBLE PRECISION FUNCTION ZLANTP( NORM, UPLO, DIAG, N, AP,
WORK )
    CHARACTER    DIAG, NORM, UPLO
    INTEGER      N
    DOUBLE       PRECISION WORK( * )
    COMPLEX*16   AP( * )

PURPOSE

ZLANTP 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

ZLANTP returns the value

ZLANTP = ( 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 ma

trix (square root of sum of squares). Note that

max(abs(A(i,j))) is not a matrix norm.

ARGUMENTS

NORM (input) CHARACTER*1

Specifies the value to be returned in ZLANTP 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 tri

angular. = 'N': Non-unit triangular
= 'U': Unit triangular

N (input) INTEGER

The order of the matrix A. N >= 0. When N = 0,

ZLANTP is set to zero.

AP (input) COMPLEX*16 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) DOUBLE PRECISION array, dimension

(LWORK),

where LWORK >= N when NORM = 'I'; otherwise, WORK

is not referenced.

LAPACK version 3.0 15 June 2000

ZLANTP(3)