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.

SLANGB

    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 consistent matrix norm.

NORM

          NORM is CHARACTER*1


          Specifies the value to be returned in SLANGB as described


          above.

N

          N is INTEGER


          The order of the matrix A.  N >= 0.  When N = 0, SLANGB is


          set to zero.

KL

          KL is INTEGER


          The number of sub-diagonals of the matrix A.  KL >= 0.

KU

          KU is INTEGER


          The number of super-diagonals of the matrix A.  KU >= 0.

AB

          AB is 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

          LDAB is INTEGER


          The leading dimension of the array AB.  LDAB >= KL+KU+1.

WORK

          WORK is REAL array, dimension (MAX(1,LWORK)),


          where LWORK >= N when NORM = 'I'; otherwise, WORK is not


          referenced.

Univ. of Tennessee

Univ. of California Berkeley

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NAG Ltd.

December 2016