clansb(l) [redhat man page]

CLANSB(l)								 )								 CLANSB(l)

NAME

       CLANSB - return 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 symmetric band matrix A, with k super-diagonals

SYNOPSIS

       REAL FUNCTION CLANSB( NORM, UPLO, N, K, AB, LDAB, WORK )

	   CHARACTER NORM, UPLO

	   INTEGER   K, LDAB, N

	   REAL      WORK( * )

	   COMPLEX   AB( LDAB, * )

PURPOSE

       CLANSB 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 symmetric band matrix A, with k super-diagonals.

DESCRIPTION

       CLANSB returns the value

	  CLANSB = ( 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  matrix norm.

ARGUMENTS

       NORM    (input) CHARACTER*1
	       Specifies the value to be returned in CLANSB as described above.

       UPLO    (input) CHARACTER*1
	       Specifies whether the upper or lower triangular part of the band matrix A is supplied.  = 'U':  Upper triangular part is supplied
	       = 'L':  Lower triangular part is supplied

       N       (input) INTEGER
	       The order of the matrix A.  N >= 0.  When N = 0, CLANSB is set to zero.

       K       (input) INTEGER
	       The number of super-diagonals or sub-diagonals of the band matrix A.  K >= 0.

       AB      (input) COMPLEX 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).

       LDAB    (input) INTEGER
	       The leading dimension of the array AB.  LDAB >= K+1.

       WORK    (workspace) REAL array, dimension (LWORK),
	       where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK is not referenced.

LAPACK version 3.0						   15 June 2000 							 CLANSB(l)

clansb.f(3)							      LAPACK							       clansb.f(3)

NAME

       clansb.f -

SYNOPSIS

   Functions/Subroutines
       REAL function clansb (NORM, UPLO, N, K, AB, LDAB, WORK)
	   CLANSB

Function/Subroutine Documentation
   REAL function clansb (characterNORM, characterUPLO, integerN, integerK, complex, dimension( ldab, * )AB, integerLDAB, real, dimension( * )WORK)
       CLANSB

       Purpose:

	    CLANSB  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 symmetric band matrix A,  with k super-diagonals.

       Returns:
	   CLANSB

	       CLANSB = ( 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 CLANSB 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 part is supplied
		     = 'L':  Lower triangular part is supplied

	   N

		     N is INTEGER
		     The order of the matrix A.  N >= 0.  When N = 0, CLANSB 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 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).

	   LDAB

		     LDAB is INTEGER
		     The leading dimension of the array AB.  LDAB >= K+1.

	   WORK

		     WORK is REAL 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:
	   November 2011

       Definition at line 130 of file clansb.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.1							  Sun May 26 2013						       clansb.f(3)