clantp (l) - Linux Man Pages

NAME

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

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 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 CLANTP as described above.
UPLO (input) CHARACTER*1
Specifies whether the matrix A is upper or lower triangular. = aqUaq: Upper triangular
= aqLaq: Lower triangular
DIAG (input) CHARACTER*1
Specifies whether or not the matrix A is unit triangular. = aqNaq: Non-unit triangular
= aqUaq: 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 = aqUaq, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = aqLaq, AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. Note that when DIAG = aqUaq, 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 = aqIaq; otherwise, WORK is not referenced.