clantr-f(3)

clantr.f –

Synopsis

Functions/Subroutines

REAL function clantr (NORM, UPLO, DIAG, M, N, A, LDA, WORK)
CLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix.

Function/Subroutine Documentation

REAL function clantr (characterNORM, characterUPLO, characterDIAG, integerM, integerN, complex, dimension( lda, * )A, integerLDA, real, dimension( * )WORK)

CLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix.

Purpose:

 CLANTR returns the value of the one norm, or the Frobenius norm, or
 the infinity norm, or the element of largest absolute value of a
 trapezoidal or triangular matrix A.

Returns:

CLANTR

 CLANTR = ( 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 CLANTR as described
 above.

UPLO

 UPLO is CHARACTER*1
 Specifies whether the matrix A is upper or lower trapezoidal.
 = 'U': Upper trapezoidal
 = 'L': Lower trapezoidal
 Note that A is triangular instead of trapezoidal if M = N.

DIAG

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

 M is INTEGER
 The number of rows of the matrix A. M >= 0, and if
 UPLO = 'U', M <= N. When M = 0, CLANTR is set to zero.

 N is INTEGER
 The number of columns of the matrix A. N >= 0, and if
 UPLO = 'L', N <= M. When N = 0, CLANTR is set to zero.

 A is COMPLEX array, dimension (LDA,N)
 The trapezoidal matrix A (A is triangular if M = N).
 If UPLO = 'U', the leading m by n upper trapezoidal part of
 the array A contains the upper trapezoidal matrix, and the
 strictly lower triangular part of A is not referenced.
 If UPLO = 'L', the leading m by n lower trapezoidal part of
 the array A contains the lower trapezoidal matrix, and the
 strictly upper triangular part of A is not referenced. Note
 that when DIAG = 'U', the diagonal elements of A are not
 referenced and are assumed to be one.

LDA

 LDA is INTEGER
 The leading dimension of the array A. LDA >= max(M,1).

WORK

 WORK is REAL array, dimension (MAX(1,LWORK)),
 where LWORK >= M 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 142 of file clantr.f.

Author

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