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# slantr

```
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( * )

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 triangular
instead of trapezoidal if M = N.

DIAG    (input) CHARACTER*1
Specifies whether or not the matrix A has unit diag-
onal.  = '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 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     (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.
```