NAME
slantr - return the value of the one norm, or the Frobenius
norm, or the infinity norm, or the element of largest abso-
lute value of a trapezoidal or triangular matrix A
SYNOPSIS
REAL FUNCTION SLANTR( NORM, UPLO, DIAG, M, N, A, LDA, WORK )
CHARACTER DIAG, NORM, UPLO
INTEGER LDA, M, N
REAL A( LDA, * ), WORK( * )
#include <sunperf.h>
double slantr(char norm, char uplo, char diag, int m, int n,
float *sa, int lda) ;
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.
DESCRIPTION
SLANTR returns the value
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 matrix norm.
ARGUMENTS
NORM (input) CHARACTER*1
Specifies the value to be returned in SLANTR 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 triangu-
lar 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, SLANTR 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, SLANTR is
set to zero.
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 tra-
pezoidal part of the array A contains the upper
trapezoidal matrix, and the strictly lower tri-
angular 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 diago-
nal 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.
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