clantp (l) - Linux Manuals

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

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.