slangb(3S)

NAME
     SLANGB - 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 band
     matrix A, with kl sub-diagonals and ku super-diagonals

SYNOPSIS
     REAL FUNCTION SLANGB( NORM, N, KL, KU, AB, LDAB, WORK )

         CHARACTER NORM

         INTEGER   KL, KU, LDAB, N

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

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
     SLANGB 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 band
     matrix A, with kl sub-diagonals and ku super-diagonals.

DESCRIPTION
     SLANGB returns the value

        SLANGB = ( 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 SLANGB as described above.

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

     KL      (input) INTEGER
             The number of sub-diagonals of the matrix A.  KL >= 0.

     KU      (input) INTEGER
             The number of super-diagonals of the matrix A.  KU >= 0.

     AB      (input) REAL array, dimension (LDAB,N)
             The band matrix A, stored in rows 1 to KL+KU+1.  The j-th column
             of A is stored in the j-th column of the array AB as follows:
             AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).

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