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clantp-f(3)

clantp.f –

Synopsis

Functions/Subroutines

REAL function clantp (NORM, UPLO, DIAG, N, AP, WORK)
CLANTP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix supplied in packed form.

Function/Subroutine Documentation

REAL function clantp (characterNORM, characterUPLO, characterDIAG, integerN, complex, dimension( * )AP, real, dimension( * )WORK)

CLANTP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix supplied in packed form.

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.

Returns:

CLANTP

 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.

 

Parameters:

NORM

 NORM is CHARACTER*1
 Specifies the value to be returned in CLANTP as described
 above.

UPLO

 UPLO is CHARACTER*1
 Specifies whether the matrix A is upper or lower triangular.
 = 'U': Upper triangular
 = 'L': Lower triangular

DIAG

 DIAG is CHARACTER*1
 Specifies whether or not the matrix A is unit triangular.
 = 'N': Non-unit triangular
 = 'U': Unit triangular

N

 N is INTEGER
 The order of the matrix A. N >= 0. When N = 0, CLANTP is
 set to zero.

AP

 AP is 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

 WORK is REAL array, dimension (MAX(1,LWORK)),
 where LWORK >= N when NORM = 'I'; otherwise, WORK is not
 referenced.

 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Definition at line 126 of file clantp.f.

Author

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