◆ Zlanhb()

One norm, Frobenius norm, infinity norm, or largest absolute value of any element of a Hermitian band matrix

Purpose: This routine returns the value of the one norm, the Frobenius norm, the infinity norm, or the largest absolute value of any element of an n x n Hermitian band matrix A, with k super/sub-diagonals.

Returns: Double
max(abs(Aij)) when Norm = "M",
norm1(A) when Norm = "1" or "O",
normI(A) when Norm = "I", or
normF(A) when Norm = "F" 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(Aij)) is not a consistent matrix norm.

Parameters

[in]	Norm	Specifies the value to be returned by Zlanhb as described above. Note that normI(A) = norm1(A) since A is Hermitian.
[in]	Uplo	Specifies whether the upper or lower triangular part of the symmetric band matrix A is supplied. = "U": Upper triangular part is supplied. = "L": Lower triangular part is supplied.
[in]	N	Order of the matrix A. (N >= 0) (If N = 0, returns 0)
[in]	K	Number of super-diagonals or sub-diagonals of the symmetric band matrix A. (K >= 0)
[in]	Ab()	Array Ab(LAb1 - 1, LAb2 - 1) (LAb1 >= K + 1, LAb2 >= N) N x N Hermitian band matrix A in K+1 x N symmetric band matrix form. Upper or lower part is to be stored in accordance with Uplo. The imaginary parts of the diagonal elements need not be set and are assumed to be zero.
[out]	Info	(Optional) = 0: Successful exit. = -1: The argument Norm had an illegal value. (Norm <> "M", "1", "O", "I", "F" nor "E") = -2: The argument Uplo had an illegal value. (Uplo <> "U" nor "L") = -3: The argument N had an illegal value. (N < 0) = -4: The argument K had an illegal value. (K < 0) = -5: The argument Ab() is invalid.