ZLANTR - return the value of the one norm, or the Frobe
nius norm, or the infinity norm, or the element of largest
absolute value of a trapezoidal or triangular matrix A
SYNOPSIS
DOUBLE PRECISION FUNCTION ZLANTR( NORM, UPLO, DIAG, M, N,
A, LDA, WORK )
CHARACTER DIAG, NORM, UPLO
INTEGER LDA, M, N
DOUBLE PRECISION WORK( * )
COMPLEX*16 A( LDA, * )
PURPOSE
ZLANTR 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
ZLANTR returns the value
ZLANTR = ( 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 Frobe
nius 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 ZLANTR 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
= '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, ZLANTR 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, ZLANTR is
set to zero.
A (input) COMPLEX*16 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 trian
gular 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) DOUBLE PRECISION array, dimension
(LWORK),
where LWORK >= M when NORM = 'I'; otherwise, WORK
is not referenced.
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