Returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix.
val = slansb( norm, uplo, n, k, ab, ldab, work )
val = dlansb( norm, uplo, n, k, ab, ldab, work )
val = clansb( norm, uplo, n, k, ab, ldab, work )
val = zlansb( norm, uplo, n, k, ab, ldab, work )
The function ?lansb 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 real/complex symmetric 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. If uplo = 'U': upper triangular part is supplied; If uplo = 'L': lower triangular part is supplied.
INTEGER. The order of the matrix A. n≥ 0.
When n = 0, ?lansb is set to zero.
INTEGER. The number of super-diagonals or sub-diagonals of the band matrix A. k≥ 0.
REAL for slansb
DOUBLE PRECISION for dlansb
COMPLEX for clansb
DOUBLE COMPLEX for zlansb
Array, DIMENSION (ldab,n).
The upper or lower triangle of the symmetric 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:
if uplo = 'U', ab(k+1+i-j,j) = a(i,j)
for max(1,j-k) ≤ i≤ j;
if uplo = 'L', ab(1+i-j,j) = a(i,j) for j≤i≤min(n,j+k).
INTEGER. The leading dimension of the array ab.
REAL for slansb and clansb.
DOUBLE PRECISION for dlansb and zlansb.
Workspace array, DIMENSION(max(1,lwork)), where
lwork≥n when norm = 'I' or '1' or 'O'; otherwise, work is not referenced.
REAL for slansb/clansb
DOUBLE PRECISION for dlansb/zlansb
Value returned by the function.