# clantr.f(3) [centos man page]

clantr.f(3) LAPACK clantr.f(3)NAME

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 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 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 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.AuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.2Tue Sep 25 2012 clantr.f(3)

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CLANTR(l)) CLANTR(l)NAME

CLANTR - return 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 ASYNOPSIS

REAL FUNCTION CLANTR( NORM, UPLO, DIAG, M, N, A, LDA, WORK ) CHARACTER DIAG, NORM, UPLO INTEGER LDA, M, N REAL WORK( * ) COMPLEX A( LDA, * )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 trape- zoidal or triangular matrix A.DESCRIPTION

CLANTR returns the value 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 matrix norm.ARGUMENTS

NORM (input) CHARACTER*1 Specifies the value to be returned in CLANTR as described above. UPLO (input) 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 (input) CHARACTER*1 Specifies whether or not the matrix A has unit diagonal. = 'N': Non-unit diagonal = 'U': Unit diagonal M (input) 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 (input) 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 (input) 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 con- tains 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 (input) INTEGER The leading dimension of the array A. LDA >= max(M,1). WORK (workspace) REAL array, dimension (LWORK), where LWORK >= M when NORM = 'I'; otherwise, WORK is not referenced.LAPACK version 3.015 June 2000 CLANTR(l)