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 FORTRAN 77 interfaces are specified in the mkl_lapack.fi include file (to be used in Fortran programs) and in the mkl_lapack.h include file (to be used in C programs).
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).
CHARACTER*1.
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
COMPLEX*16 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.
ldab ≥ k+1.
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.
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