SRC/zlanhb.f(3) | Library Functions Manual | SRC/zlanhb.f(3) |
NAME
SRC/zlanhb.f
SYNOPSIS
Functions/Subroutines
double precision function zlanhb (norm, uplo, n, k, ab,
ldab, work)
ZLANHB returns the value of the 1-norm, or the Frobenius norm, or the
infinity norm, or the element of largest absolute value of a Hermitian band
matrix.
Function/Subroutine Documentation
double precision function zlanhb (character norm, character uplo, integer n, integer k, complex*16, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) work)
ZLANHB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian band matrix.
Purpose:
ZLANHB returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n hermitian band matrix A, with k super-diagonals.
Returns
ZLANHB
ZLANHB = ( max(abs(A(i,j))), NORM = 'M' or 'm' ( ( norm1(A), NORM = '1', 'O' or 'o' ( ( normI(A), NORM = 'I' or 'i' ( ( normF(A), NORM = 'F', 'f', 'E' 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(A(i,j))) is not a consistent matrix norm.
Parameters
NORM
NORM is CHARACTER*1 Specifies the value to be returned in ZLANHB as described above.
UPLO
UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the band matrix A is supplied. = 'U': Upper triangular = 'L': Lower triangular
N
N is INTEGER The order of the matrix A. N >= 0. When N = 0, ZLANHB is set to zero.
K
K is INTEGER The number of super-diagonals or sub-diagonals of the band matrix A. K >= 0.
AB
AB is COMPLEX*16 array, dimension (LDAB,N) The upper or lower triangle of the hermitian 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 the imaginary parts of the diagonal elements need not be set and are assumed to be zero.
LDAB
LDAB is INTEGER The leading dimension of the array AB. LDAB >= K+1.
WORK
WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK is not referenced.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 130 of file zlanhb.f.
Author
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