Returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix.
val = slantb( norm, uplo, diag, n, k, ab, ldab, work )
val = dlantb( norm, uplo, diag, n, k, ab, ldab, work )
val = clantb( norm, uplo, diag, n, k, ab, ldab, work )
val = zlantb( norm, uplo, diag, n, k, ab, ldab, work )
The function ?lantb 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 triangular band matrix A, with ( k + 1 ) 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 matrix A is upper or lower triangular.
= 'U': Upper triangular
= 'L': Lower triangular.
Specifies whether or not the matrix A is unit triangular.
= 'N': Non-unit triangular
= 'U': Unit triangular.
INTEGER. The order of the matrix A.
n ≥ 0. When
n = 0, ?lantb is set to zero.
INTEGER. The number of super-diagonals of the matrix A if
uplo = 'U', or the number of sub-diagonals of the matrix A if
uplo = 'L'. k ≥ 0.
REAL for slantb
DOUBLE PRECISION for dlantb
COMPLEX for clantb
DOUBLE COMPLEX for zlantb
Array, DIMENSION (ldab,n). The upper or lower triangular 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)for
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 when
diag = 'U', the elements of the array ab corresponding to the diagonal elements of the matrix A are not referenced, but are assumed to be one.
INTEGER. The leading dimension of the array ab.
ldab ≥ k+1.
REAL for slantb and clantb.
DOUBLE PRECISION for dlantb and zlantb.
Workspace array, DIMENSION
lwork ≥ nwhen
norm = 'I'; otherwise, work is not referenced.