dlangb (l) - Linux Manuals

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

NAME

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

SYNOPSIS

DOUBLE PRECISION
FUNCTION DLANGB( NORM, N, KL, KU, AB, LDAB, WORK )

    
CHARACTER NORM

    
INTEGER KL, KU, LDAB, N

    
DOUBLE PRECISION AB( LDAB, * ), WORK( * )

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.

DESCRIPTION

DLANGB returns the value

DLANGB = ( max(abs(A(i,j))), NORM = aqMaq or aqmaq

      (

      ( norm1(A),         NORM = aq1aq, aqOaq or aqoaq

      (

      ( normI(A),         NORM = aqIaq or aqiaq

      (

      ( normF(A),         NORM = aqFaq, aqfaq, aqEaq or aqeaq 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) CHARACTER*1
Specifies the value to be returned in DLANGB as described above.
N (input) INTEGER
The order of the matrix A. N >= 0. When N = 0, DLANGB 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) 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 (input) INTEGER
The leading dimension of the array AB. LDAB >= KL+KU+1.
WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
where LWORK >= N when NORM = aqIaq; otherwise, WORK is not referenced.

Pages related to dlangb

  • dlangb (3)
  • dlange (l) - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real matrix A
  • dlangt (l) - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real tridiagonal matrix A
  • dlaneg (l) - computes the Sturm count, the number of negative pivots encountered while factoring tridiagonal T - sigma I = L D L^T
  • dlanhs (l) - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A
  • dlansb (l) - 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 symmetric band matrix A, with k super-diagonals
  • dlansf (l) - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A in RFP format
  • dlansp (l) - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A, supplied in packed form
  • dlanst (l) - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix A
  • dlansy (l) - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A