gbcon(3)

NAME
gbcon - gbcon: condition number estimate

SYNOPSIS

  Functions

subroutine cgbcon (norm, n, kl, ku, ab, ldab, ipiv, anorm, rcond, work, rwork, info)
CGBCON
subroutine dgbcon (norm, n, kl, ku, ab, ldab, ipiv, anorm, rcond, work, iwork, info)
DGBCON
subroutine sgbcon (norm, n, kl, ku, ab, ldab, ipiv, anorm, rcond, work, iwork, info)
SGBCON
subroutine zgbcon (norm, n, kl, ku, ab, ldab, ipiv, anorm, rcond, work, rwork, info)
ZGBCON

Detailed Description

Function Documentation

  subroutine cgbcon (character norm, integer n, integer kl, integer ku, complex, dimension( ldab, * ) ab, integer ldab, integer, dimension( * ) ipiv, real anorm, real rcond, complex, dimension( * ) work, real, dimension( * ) rwork, integer info)

CGBCON

Purpose:

    !>
    !> CGBCON estimates the reciprocal of the condition number of a complex
    !> general band matrix A, in either the 1-norm or the infinity-norm,
    !> using the LU factorization computed by CGBTRF.
    !>
    !> An estimate is obtained for norm(inv(A)), and the reciprocal of the
    !> condition number is computed as
    !>    RCOND = 1 / ( norm(A) * norm(inv(A)) ).
    !>

Parameters
    NORM

    !>          NORM is CHARACTER*1
    !>          Specifies whether the 1-norm condition number or the
    !>          infinity-norm condition number is required:
    !>          = '1' or 'O':  1-norm;
    !>          = 'I':         Infinity-norm.
    !>

    N

    !>          N is INTEGER
    !>          The order 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 COMPLEX array, dimension (LDAB,N)
    !>          Details of the LU factorization of the band matrix A, as
    !>          computed by CGBTRF.  U is stored as an upper triangular band
    !>          matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
    !>          the multipliers used during the factorization are stored in
    !>          rows KL+KU+2 to 2*KL+KU+1.
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
    !>

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          The pivot indices; for 1 <= i <= N, row i of the matrix was
    !>          interchanged with row IPIV(i).
    !>

    ANORM

    !>          ANORM is REAL
    !>          If NORM = '1' or 'O', the 1-norm of the original matrix A.
    !>          If NORM = 'I', the infinity-norm of the original matrix A.
    !>

    RCOND

    !>          RCOND is REAL
    !>          The reciprocal of the condition number of the matrix A,
    !>          computed as RCOND = 1/(norm(A) * norm(inv(A))).
    !>

    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 dgbcon (character norm, integer n, integer kl, integer ku, double precision, dimension( ldab, * ) ab, integer ldab, integer, dimension( * ) ipiv, double precision anorm, double precision rcond, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer info)

DGBCON

Purpose:

    !>
    !> DGBCON estimates the reciprocal of the condition number of a real
    !> general band matrix A, in either the 1-norm or the infinity-norm,
    !> using the LU factorization computed by DGBTRF.
    !>
    !> An estimate is obtained for norm(inv(A)), and the reciprocal of the
    !> condition number is computed as
    !>    RCOND = 1 / ( norm(A) * norm(inv(A)) ).
    !>

Parameters
    NORM

    !>          NORM is CHARACTER*1
    !>          Specifies whether the 1-norm condition number or the
    !>          infinity-norm condition number is required:
    !>          = '1' or 'O':  1-norm;
    !>          = 'I':         Infinity-norm.
    !>

    N

    !>          N is INTEGER
    !>          The order 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)
    !>          Details of the LU factorization of the band matrix A, as
    !>          computed by DGBTRF.  U is stored as an upper triangular band
    !>          matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
    !>          the multipliers used during the factorization are stored in
    !>          rows KL+KU+2 to 2*KL+KU+1.
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
    !>

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          The pivot indices; for 1 <= i <= N, row i of the matrix was
    !>          interchanged with row IPIV(i).
    !>

    ANORM

    !>          ANORM is DOUBLE PRECISION
    !>          If NORM = '1' or 'O', the 1-norm of the original matrix A.
    !>          If NORM = 'I', the infinity-norm of the original matrix A.
    !>

    RCOND

    !>          RCOND is DOUBLE PRECISION
    !>          The reciprocal of the condition number of the matrix A,
    !>          computed as RCOND = 1/(norm(A) * norm(inv(A))).
    !>

    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 sgbcon (character norm, integer n, integer kl, integer ku, real, dimension( ldab, * ) ab, integer ldab, integer, dimension( * ) ipiv, real anorm, real rcond, real, dimension( * ) work, integer, dimension( * ) iwork, integer info)

SGBCON

Purpose:

    !>
    !> SGBCON estimates the reciprocal of the condition number of a real
    !> general band matrix A, in either the 1-norm or the infinity-norm,
    !> using the LU factorization computed by SGBTRF.
    !>
    !> An estimate is obtained for norm(inv(A)), and the reciprocal of the
    !> condition number is computed as
    !>    RCOND = 1 / ( norm(A) * norm(inv(A)) ).
    !>

Parameters
    NORM

    !>          NORM is CHARACTER*1
    !>          Specifies whether the 1-norm condition number or the
    !>          infinity-norm condition number is required:
    !>          = '1' or 'O':  1-norm;
    !>          = 'I':         Infinity-norm.
    !>

    N

    !>          N is INTEGER
    !>          The order 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 REAL array, dimension (LDAB,N)
    !>          Details of the LU factorization of the band matrix A, as
    !>          computed by SGBTRF.  U is stored as an upper triangular band
    !>          matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
    !>          the multipliers used during the factorization are stored in
    !>          rows KL+KU+2 to 2*KL+KU+1.
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
    !>

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          The pivot indices; for 1 <= i <= N, row i of the matrix was
    !>          interchanged with row IPIV(i).
    !>

    ANORM

    !>          ANORM is REAL
    !>          If NORM = '1' or 'O', the 1-norm of the original matrix A.
    !>          If NORM = 'I', the infinity-norm of the original matrix A.
    !>

    RCOND

    !>          RCOND is REAL
    !>          The reciprocal of the condition number of the matrix A,
    !>          computed as RCOND = 1/(norm(A) * norm(inv(A))).
    !>

    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 zgbcon (character norm, integer n, integer kl, integer ku, complex*16, dimension( ldab, * ) ab, integer ldab, integer, dimension( * ) ipiv, double precision anorm, double precision rcond, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer info)

ZGBCON

Purpose:

    !>
    !> ZGBCON estimates the reciprocal of the condition number of a complex
    !> general band matrix A, in either the 1-norm or the infinity-norm,
    !> using the LU factorization computed by ZGBTRF.
    !>
    !> An estimate is obtained for norm(inv(A)), and the reciprocal of the
    !> condition number is computed as
    !>    RCOND = 1 / ( norm(A) * norm(inv(A)) ).
    !>

Parameters
    NORM

    !>          NORM is CHARACTER*1
    !>          Specifies whether the 1-norm condition number or the
    !>          infinity-norm condition number is required:
    !>          = '1' or 'O':  1-norm;
    !>          = 'I':         Infinity-norm.
    !>

    N

    !>          N is INTEGER
    !>          The order 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 COMPLEX*16 array, dimension (LDAB,N)
    !>          Details of the LU factorization of the band matrix A, as
    !>          computed by ZGBTRF.  U is stored as an upper triangular band
    !>          matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
    !>          the multipliers used during the factorization are stored in
    !>          rows KL+KU+2 to 2*KL+KU+1.
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
    !>

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          The pivot indices; for 1 <= i <= N, row i of the matrix was
    !>          interchanged with row IPIV(i).
    !>

    ANORM

    !>          ANORM is DOUBLE PRECISION
    !>          If NORM = '1' or 'O', the 1-norm of the original matrix A.
    !>          If NORM = 'I', the infinity-norm of the original matrix A.
    !>

    RCOND

    !>          RCOND is DOUBLE PRECISION
    !>          The reciprocal of the condition number of the matrix A,
    !>          computed as RCOND = 1/(norm(A) * norm(inv(A))).
    !>

    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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