Returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian band matrix.
val = clanhb( norm, uplo, n, k, ab, ldab, work )
val = zlanhb( norm, uplo, n, k, ab, ldab, work )
The routine returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n-by-n Hermitian band matrix A, with k super-diagonals.
CHARACTER*1. Specifies the value to be returned by the routine:
= 'M' or 'm': val = max(abs(Aij)), largest absolute value of the matrix A.
= '1' or 'O' or 'o': val = norm1(A), 1-norm of the matrix A (maximum column sum),
= 'I' or 'i': val = normI(A), infinity norm of the matrix A (maximum row sum),
= 'F', 'f', 'E' or 'e': val = normF(A), Frobenius norm of the matrix A (square root of sum of squares).
Specifies whether the upper or lower triangular part of the band matrix A is supplied.
uplo = 'U': upper triangular part is supplied;
uplo = 'L': lower triangular part is supplied.
INTEGER. The order of the matrix A.
n ≥ 0. When
n = 0, ?lanhb is set to zero.
INTEGER. The number of super-diagonals or sub-diagonals of the band matrix A.
k ≥ 0.
COMPLEX for clanhb.
DOUBLE COMPLEX for zlanhb.
Array, DIMENSION (ldaB,n). The upper or lower triangle of the Hermitian band matrix A, stored in the first k+1 rows of ab. The j-th column of A is stored in the j-th column of the array ab as follows:
uplo = 'U',
ab(k+1+i-j,j) = a(i,j)
max(1,j-k) ≤ i ≤ j;
uplo = 'L',
ab(1+i-j,j) = a(i,j)for
j ≤ i ≤ min(n,j+k).
Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero.
INTEGER. The leading dimension of the array ab. ldab ≥ k+1.
REAL for clanhb.
DOUBLE PRECISION for zlanhb.
Workspace array, DIMENSION
max(1, lwork), where
lwork ≥ nwhen
norm = 'I'or '1' or 'O'; otherwise, work is not referenced.