◆ zlansb()

One norm, Frobenius norm, infinity norm, or largest absolute value of any element of a complex symmetric 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 complex symmetric band matrix A, with k super/sub-diagonals.

Returns: 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 zlansb as described above. Note that normI(A) = norm1(A) since A is symmetric.
[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]	ldab	Leading dimension of the two dimensional array ab[][]. (ldab >= k + 1)
[in]	ab[][]	Array ab[lab][ldab] (lab >= n) n x n symmetric band matrix A in k+1 x n symmetric band matrix form. (Upper or lower part is to be stored in accordance with uplo)
[out]	work[]	Array work[lwork] (lwork >= max(1, n) when norm = 'I', '1' or 'O', otherwise work[] is not referenced) Work array.