Returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix.
val = slanhs( norm, n, a, lda, work )
val = dlanhs( norm, n, a, lda, work )
val = clanhs( norm, n, a, lda, work )
val = zlanhs( norm, n, a, lda, work )
The function ?lanhs returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A.
The value val returned by the function is:
val = max(abs(Aij)), if norm = 'M' or 'm'
= norm1(A), if norm = '1' or 'O' or 'o'
= normI(A), if norm = 'I' or 'i'
= normF(A), if norm = 'F', 'f', 'E' or 'e'
where norm1 denotes the 1-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(Aij)) is not a consistent matrix norm.
CHARACTER*1. Specifies the value to be returned by the routine as described above.
INTEGER. The order of the matrix A.
n ≥ 0. When
n = 0, ?lanhs is set to zero.
REAL for slanhs
DOUBLE PRECISION for dlanhs
COMPLEX for clanhs
DOUBLE COMPLEX for zlanhs
Array, DIMENSION (lda,n). The n-by-n upper Hessenberg matrix A; the part of A below the first sub-diagonal is not referenced.
INTEGER. The leading dimension of the array a.
lda ≥ max(n,1).
REAL for slanhs and clanhs.
DOUBLE PRECISION for dlange and zlange.
Workspace array, DIMENSION
lwork ≥ nwhen
norm = 'I'; otherwise, work is not referenced.