slansb(l) [redhat man page]

SLANSB(l)								 )								 SLANSB(l)

NAME

       SLANSB - 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 SLANSB( NORM, UPLO, N, K, AB, LDAB, WORK )

	   CHARACTER NORM, UPLO

	   INTEGER   K, LDAB, N

	   REAL      AB( LDAB, * ), WORK( * )

PURPOSE

       SLANSB 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

       SLANSB returns the value

	  SLANSB = ( 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 SLANSB 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, SLANSB is set to zero.

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

       AB      (input) REAL 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 							 SLANSB(l)

CLANHB(l)								 )								 CLANHB(l)

NAME

       CLANHB - 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 hermitian band matrix A, with k super-diagonals

SYNOPSIS

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

	   CHARACTER NORM, UPLO

	   INTEGER   K, LDAB, N

	   REAL      WORK( * )

	   COMPLEX   AB( LDAB, * )

PURPOSE

       CLANHB 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.

DESCRIPTION

       CLANHB returns the value

	  CLANHB = ( 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 CLANHB 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
	       = 'L':  Lower triangular

       N       (input) INTEGER
	       The order of the matrix A.  N >= 0.  When N = 0, CLANHB 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 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    (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 							 CLANHB(l)