clantb(3S)

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, * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

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.

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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