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.TH SLANTR l "15 June 2000" "LAPACK version 3.0" ")"
.SH NAME
SLANTR - 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 A
.SH SYNOPSIS
.TP 14
REAL FUNCTION
SLANTR( NORM, UPLO, DIAG, M, N, A, LDA,
WORK )
.TP 14
.ti +4
CHARACTER
DIAG, NORM, UPLO
.TP 14
.ti +4
INTEGER
LDA, M, N
.TP 14
.ti +4
REAL
A( LDA, * ), WORK( * )
.SH 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.
.SH DESCRIPTION
SLANTR returns the value
.br
SLANTR = ( max(abs(A(i,j))), NORM = 'M' or 'm'
.br
(
.br
( norm1(A), NORM = '1', 'O' or 'o'
.br
(
.br
( normI(A), NORM = 'I' or 'i'
.br
(
.br
( 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.
.SH ARGUMENTS
.TP 8
NORM (input) CHARACTER*1
Specifies the value to be returned in SLANTR as described
above.
.TP 8
UPLO (input) CHARACTER*1
Specifies whether the matrix A is upper or lower trapezoidal.
= 'U': Upper trapezoidal
.br
= 'L': Lower trapezoidal
Note that A is triangular instead of trapezoidal if M = N.
.TP 8
DIAG (input) CHARACTER*1
Specifies whether or not the matrix A has unit diagonal.
= 'N': Non-unit diagonal
.br
= 'U': Unit diagonal
.TP 8
M (input) 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.
.TP 8
N (input) 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.
.TP 8
A (input) 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.
.TP 8
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(M,1).
.TP 8
WORK (workspace) REAL array, dimension (LWORK),
where LWORK >= M when NORM = 'I'; otherwise, WORK is not
referenced.
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