man zlanhe (Fonctions bibliothèques) - return 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
NAME
ZLANHE - return 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 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 (LWORK),
- where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK is not referenced.