dlangb: Dlangb.f -

Function/Subroutine Documentation

double precision function dlangb (characterNORM, integerN, integerKL, integerKU, double precision, dimension( ldab, * )AB, integerLDAB, double precision, dimension( * )WORK)

DLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.

Purpose:

 DLANGB  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.

Returns:

DLANGB

    DLANGB = ( 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.

Parameters:

NORM

          NORM is CHARACTER*1
          Specifies the value to be returned in DLANGB as described
          above.

          N is INTEGER
          The order of the matrix A.  N >= 0.  When N = 0, DLANGB is
          set to zero.

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

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

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

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Definition at line 124 of file dlangb.f.

dlangb (3)

SYNOPSIS

Functions/Subroutines

Function/Subroutine Documentation

double precision function dlangb (characterNORM, integerN, integerKL, integerKU, double precision, dimension( ldab, * )AB, integerLDAB, double precision, dimension( * )WORK)

Author