doubleGBauxiliary(3)

NAME
doubleGBauxiliary

SYNOPSIS

  Functions
double precision function dlangb (NORM, N, KL, KU, AB, LDAB, 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.
subroutine dlaqgb (M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, EQUED)
DLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.

Detailed Description

This is the group of double auxiliary functions for GB matrices

Function Documentation

  double precision function dlangb (character NORM, integer N, integer KL, integer KU, double precision, dimension( ldab, * ) AB, integer LDAB, 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

              N is INTEGER
              The order of the matrix A.  N >= 0.  When N = 0, DLANGB 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 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:
    December 2016

Definition at line 126 of file dlangb.f.

  subroutine dlaqgb (integer M, integer N, integer KL, integer KU, double precision, dimension( ldab, * ) AB, integer LDAB, double precision, dimension( * ) R, double precision, dimension( * ) C, double precision ROWCND, double precision COLCND, double precision AMAX, character EQUED)

DLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.

Purpose:

     DLAQGB equilibrates a general M by N band matrix A with KL
     subdiagonals and KU superdiagonals using the row and scaling factors
     in the vectors R and C.

Parameters:
    M

              M is INTEGER
              The number of rows of the matrix A.  M >= 0.

    N

              N is INTEGER
              The number of columns of the matrix A.  N >= 0.

    KL

              KL is INTEGER
              The number of subdiagonals within the band of A.  KL >= 0.

    KU

              KU is INTEGER
              The number of superdiagonals within the band of A.  KU >= 0.

    AB

              AB is DOUBLE PRECISION array, dimension (LDAB,N)
              On entry, the matrix A in band storage, 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(m,j+kl)
              On exit, the equilibrated matrix, in the same storage format
              as A.  See EQUED for the form of the equilibrated matrix.

    LDAB

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

    R

              R is DOUBLE PRECISION array, dimension (M)
              The row scale factors for A.

    C

              C is DOUBLE PRECISION array, dimension (N)
              The column scale factors for A.

    ROWCND

              ROWCND is DOUBLE PRECISION
              Ratio of the smallest R(i) to the largest R(i).

    COLCND

              COLCND is DOUBLE PRECISION
              Ratio of the smallest C(i) to the largest C(i).

    AMAX

              AMAX is DOUBLE PRECISION
              Absolute value of largest matrix entry.

    EQUED

              EQUED is CHARACTER*1
              Specifies the form of equilibration that was done.
              = 'N':  No equilibration
              = 'R':  Row equilibration, i.e., A has been premultiplied by
                      diag(R).
              = 'C':  Column equilibration, i.e., A has been postmultiplied
                      by diag(C).
              = 'B':  Both row and column equilibration, i.e., A has been
                      replaced by diag(R) * A * diag(C).

Internal Parameters:

      THRESH is a threshold value used to decide if row or column scaling
      should be done based on the ratio of the row or column scaling
      factors.  If ROWCND < THRESH, row scaling is done, and if
      COLCND < THRESH, column scaling is done.
      LARGE and SMALL are threshold values used to decide if row scaling
      should be done based on the absolute size of the largest matrix
      element.  If AMAX > LARGE or AMAX < SMALL, row scaling is done.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    December 2016

Definition at line 161 of file dlaqgb.f.

Author

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