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slantr.f(3) LAPACK slantr.f(3)

NAME

slantr.f -

SYNOPSIS

Functions/Subroutines


REAL function slantr (NORM, UPLO, DIAG, M, N, A, LDA, WORK)
SLANTR 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 slantr (characterNORM, characterUPLO, characterDIAG, integerM, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( * )WORK)

SLANTR 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:


SLANTR 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:

SLANTR


SLANTR = ( 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 SLANTR 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, SLANTR 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, SLANTR is set to zero.

A


A is REAL 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 141 of file slantr.f.

Author

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Tue Sep 25 2012 Version 3.4.2