zlanhb.f File Reference

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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.

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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.

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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:

[in]	NORM	NORM is CHARACTER*1 Specifies the value to be returned in ZLANHB as described above.
[in]	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
[in]	N	N is INTEGER The order of the matrix A. N >= 0. When N = 0, ZLANHB is set to zero.
[in]	K	K is INTEGER The number of super-diagonals or sub-diagonals of the band matrix A. K >= 0.
[in]	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.
[in]	LDAB	LDAB is INTEGER The leading dimension of the array AB. LDAB >= K+1.
[out]	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.

Date:

September 2012

Definition at line 132 of file zlanhb.f.

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