clantp(l) [redhat man page]

CLANTP(l)								 )								 CLANTP(l)

NAME

       CLANTP  - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a tri-
       angular matrix A, supplied in packed form

SYNOPSIS

       REAL FUNCTION CLANTP( NORM, UPLO, DIAG, N, AP, WORK )

	   CHARACTER DIAG, NORM, UPLO

	   INTEGER   N

	   REAL      WORK( * )

	   COMPLEX   AP( * )

PURPOSE

       CLANTP returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trian-
       gular matrix A, supplied in packed form.

DESCRIPTION

       CLANTP returns the value

	  CLANTP = ( 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 CLANTP as described above.

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

       DIAG    (input) CHARACTER*1
	       Specifies whether or not the matrix A is unit triangular.  = 'N':  Non-unit triangular
	       = 'U':  Unit triangular

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

       AP      (input) COMPLEX array, dimension (N*(N+1)/2)
	       The upper or lower triangular matrix A, packed columnwise in a linear array.  The j-th column of A is stored in	the  array  AP	as
	       follows:  if  UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.  Note
	       that when DIAG = 'U', the elements of the array AP corresponding to the diagonal elements of the matrix A are not  referenced,  but
	       are assumed to be one.

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

LAPACK version 3.0						   15 June 2000 							 CLANTP(l)

CLANTB(l)								 )								 CLANTB(l)

NAME

       CLANTB - 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 triangular band matrix A, with ( k + 1 ) diagonals

SYNOPSIS

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

	   CHARACTER DIAG, NORM, UPLO

	   INTEGER   K, LDAB, N

	   REAL      WORK( * )

	   COMPLEX   AB( LDAB, * )

PURPOSE

       CLANTB 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 triangular band matrix A, with ( k + 1 ) diagonals.

DESCRIPTION

       CLANTB returns the value

	  CLANTB = ( 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 CLANTB as described above.

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

       DIAG    (input) CHARACTER*1
	       Specifies whether or not the matrix A is unit triangular.  = 'N':  Non-unit triangular
	       = 'U':  Unit triangular

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

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

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

LAPACK version 3.0						   15 June 2000 							 CLANTB(l)