SLANTB(3)      LAPACK routine of NEC Numeric Library Collection      SLANTB(3)



NAME
       SLANTB

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



PURPOSE
            SLANTB  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.


       Returns:
           SLANTB

               SLANTB = ( 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.




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

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

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

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

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

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



LAPACK routine                  31 October 2017                      SLANTB(3)