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.

  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.

  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.

  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.

Author

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