Visible to Intel only — GUID: GUID-541EEFB3-E19A-42BD-8379-7BB9E9D29BF6
Visible to Intel only — GUID: GUID-541EEFB3-E19A-42BD-8379-7BB9E9D29BF6
?lantb
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.
Syntax
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 )
Include Files
- mkl.fi
Description
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.
Input Parameters
- norm
-
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).
- uplo
-
CHARACTER*1.
Specifies whether the matrix A is upper or lower triangular.
= 'U': Upper triangular
= 'L': Lower triangular.
- diag
-
CHARACTER*1.
Specifies whether or not the matrix A is unit triangular.
= 'N': Non-unit triangular
= 'U': Unit triangular.
- n
-
INTEGER. The order of the matrix A. n≥ 0. When n = 0, ?lantb is set to zero.
- k
-
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.
- ab
-
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:
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).
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.
- ldab
-
INTEGER. The leading dimension of the array ab.
ldab≥k+1.
- work
-
REAL for slantb and clantb.
DOUBLE PRECISION for dlantb and zlantb.
Workspace array, DIMENSION(max(1,lwork)), where
lwork≥n when norm = 'I' ; otherwise, work is not referenced.
Output Parameters
- val
-
REAL for slantb/clantb.
DOUBLE PRECISION for dlantb/zlantb.
Value returned by the function.