SRC/spbcon.f(3)

NAME
SRC/spbcon.f

SYNOPSIS

  Functions/Subroutines
subroutine spbcon (uplo, n, kd, ab, ldab, anorm, rcond, work, iwork, info)
SPBCON

Function/Subroutine Documentation

  subroutine spbcon (character uplo, integer n, integer kd, real, dimension( ldab, * ) ab, integer ldab, real anorm, real rcond, real, dimension( * ) work, integer, dimension( * ) iwork, integer info)

SPBCON

Purpose:

     SPBCON estimates the reciprocal of the condition number (in the
     1-norm) of a real symmetric positive definite band matrix using the
     Cholesky factorization A = U**T*U or A = L*L**T computed by SPBTRF.
     An estimate is obtained for norm(inv(A)), and the reciprocal of the
     condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

Parameters
    UPLO

              UPLO is CHARACTER*1
              = 'U':  Upper triangular factor stored in AB;
              = 'L':  Lower triangular factor stored in AB.

    N

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

    KD

              KD is INTEGER
              The number of superdiagonals of the matrix A if UPLO = 'U',
              or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

    AB

              AB is REAL array, dimension (LDAB,N)
              The triangular factor U or L from the Cholesky factorization
              A = U**T*U or A = L*L**T of the band matrix A, stored in the
              first KD+1 rows of the array.  The j-th column of U or L is
              stored in the j-th column of the array AB as follows:
              if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
              if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).

    LDAB

              LDAB is INTEGER
              The leading dimension of the array AB.  LDAB >= KD+1.

    ANORM

              ANORM is REAL
              The 1-norm (or infinity-norm) of the symmetric band matrix A.

    RCOND

              RCOND is REAL
              The reciprocal of the condition number of the matrix A,
              computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
              estimate of the 1-norm of inv(A) computed in this routine.

    WORK

              WORK is REAL array, dimension (3*N)

    IWORK

              IWORK is INTEGER array, dimension (N)

    INFO

              INFO is INTEGER
              = 0:  successful exit
              < 0:  if INFO = -i, the i-th argument had an illegal value

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 130 of file spbcon.f.

Author

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