pbcon(3)

NAME
pbcon - pbcon: condition number estimate

SYNOPSIS

  Functions
subroutine cpbcon (uplo, n, kd, ab, ldab, anorm, rcond, work, rwork, info)
CPBCON
subroutine dpbcon (uplo, n, kd, ab, ldab, anorm, rcond, work, iwork, info)
DPBCON
subroutine spbcon (uplo, n, kd, ab, ldab, anorm, rcond, work, iwork, info)
SPBCON
subroutine zpbcon (uplo, n, kd, ab, ldab, anorm, rcond, work, rwork, info)
ZPBCON

Detailed Description

Function Documentation

  subroutine cpbcon (character uplo, integer n, integer kd, complex, dimension( ldab, * ) ab, integer ldab, real anorm, real rcond, complex, dimension( * ) work, real, dimension( * ) rwork, integer info)

CPBCON

Purpose:

     CPBCON estimates the reciprocal of the condition number (in the
     1-norm) of a complex Hermitian positive definite band matrix using
     the Cholesky factorization A = U**H*U or A = L*L**H computed by
     CPBTRF.
     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 sub-diagonals if UPLO = 'L'.  KD >= 0.

    AB

              AB is COMPLEX array, dimension (LDAB,N)
              The triangular factor U or L from the Cholesky factorization
              A = U**H*U or A = L*L**H 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 Hermitian 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 COMPLEX array, dimension (2*N)

    RWORK

              RWORK is REAL 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 131 of file cpbcon.f.

  subroutine dpbcon (character uplo, integer n, integer kd, double precision, dimension( ldab, * ) ab, integer ldab, double precision anorm, double precision rcond, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer info)

DPBCON

Purpose:

     DPBCON 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 DPBTRF.
     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 DOUBLE PRECISION 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 DOUBLE PRECISION
              The 1-norm (or infinity-norm) of the symmetric band matrix A.

    RCOND

              RCOND is DOUBLE PRECISION
              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 DOUBLE PRECISION 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 dpbcon.f.

  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.

  subroutine zpbcon (character uplo, integer n, integer kd, complex*16, dimension( ldab, * ) ab, integer ldab, double precision anorm, double precision rcond, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer info)

ZPBCON

Purpose:

     ZPBCON estimates the reciprocal of the condition number (in the
     1-norm) of a complex Hermitian positive definite band matrix using
     the Cholesky factorization A = U**H*U or A = L*L**H computed by
     ZPBTRF.
     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 sub-diagonals if UPLO = 'L'.  KD >= 0.

    AB

              AB is COMPLEX*16 array, dimension (LDAB,N)
              The triangular factor U or L from the Cholesky factorization
              A = U**H*U or A = L*L**H 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 DOUBLE PRECISION
              The 1-norm (or infinity-norm) of the Hermitian band matrix A.

    RCOND

              RCOND is DOUBLE PRECISION
              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 COMPLEX*16 array, dimension (2*N)

    RWORK

              RWORK is DOUBLE PRECISION 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 131 of file zpbcon.f.

Author

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