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# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute

```NAME
LAPACK-3 - returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the  element  of  largest  absolute  value  of  a
complex hermitian matrix A

SYNOPSIS
DOUBLE PRECISION FUNCTION ZLANHE( NORM, UPLO, N, A, LDA, WORK )

CHARACTER    NORM, UPLO

INTEGER      LDA, N

DOUBLE       PRECISION WORK( * )

COMPLEX*16   A( LDA, * )

PURPOSE
ZLANHE   returns  the value of the one norm,  or the Frobenius norm, or
the  infinity norm,  or the  element of  largest absolute value   of  a
complex hermitian matrix A.

DESCRIPTION
ZLANHE returns the value
ZLANHE = ( 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.

ARGUMENTS
NORM    (input) CHARACTER*1
Specifies the value to be returned in ZLANHE as described
above.

UPLO    (input) CHARACTER*1
Specifies whether the upper or lower triangular part of the
hermitian matrix A is to be referenced.
= 'U':  Upper triangular part of A is referenced
= 'L':  Lower triangular part of A is referenced

N       (input) INTEGER
The order of the matrix A.  N >= 0.  When N = 0, ZLANHE is
set to zero.

A       (input) COMPLEX*16 array, dimension (LDA,N)
The hermitian matrix A.  If UPLO = 'U', the leading n by n
upper triangular part of A contains the upper triangular part
of the matrix A, and the strictly lower triangular part of A
is not referenced.  If UPLO = 'L', the leading n by n lower
triangular part of A contains the lower triangular part of
the matrix A, and the strictly upper triangular part of A is
not referenced. Note that the imaginary parts of the diagonal
elements need not be set and are assumed to be zero.

LDA     (input) INTEGER
The leading dimension of the array A.  LDA >= max(N,1).

WORK    (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
WORK is not referenced.

LAPACK auxiliary routine (versionMarch 2011                       LAPACK-3(3)
```