la_gbrpvgrw(3)

NAME
la_gbrpvgrw - la_gbrpvgrw: reciprocal pivot growth

SYNOPSIS

  Functions

real function cla_gbrpvgrw (n, kl, ku, ncols, ab, ldab, afb, ldafb)
CLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.
double precision function dla_gbrpvgrw (n, kl, ku, ncols, ab, ldab, afb, ldafb)
DLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.
real function sla_gbrpvgrw (n, kl, ku, ncols, ab, ldab, afb, ldafb)
SLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.
double precision function zla_gbrpvgrw (n, kl, ku, ncols, ab, ldab, afb, ldafb)
ZLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.

Detailed Description

Function Documentation

  real function cla_gbrpvgrw (integer n, integer kl, integer ku, integer ncols, complex, dimension( ldab, * ) ab, integer ldab, complex, dimension( ldafb, * ) afb, integer ldafb)

CLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.

Purpose:

    !>
    !> CLA_GBRPVGRW computes the reciprocal pivot growth factor
    !> norm(A)/norm(U). The  norm is used. If this is
    !> much less than 1, the stability of the LU factorization of the
    !> (equilibrated) matrix A could be poor. This also means that the
    !> solution X, estimated condition numbers, and error bounds could be
    !> unreliable.
    !>

Parameters
    N

    !>          N is INTEGER
    !>     The number of linear equations, i.e., 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.
    !>

    NCOLS

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

    AB

    !>          AB is COMPLEX 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(N,j+kl)
    !>

    LDAB

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

    AFB

    !>          AFB is COMPLEX array, dimension (LDAFB,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.
    !>

    LDAFB

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

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  double precision function dla_gbrpvgrw (integer n, integer kl, integer ku, integer ncols, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( ldafb, * ) afb, integer ldafb)

DLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.

Purpose:

    !>
    !> DLA_GBRPVGRW computes the reciprocal pivot growth factor
    !> norm(A)/norm(U). The  norm is used. If this is
    !> much less than 1, the stability of the LU factorization of the
    !> (equilibrated) matrix A could be poor. This also means that the
    !> solution X, estimated condition numbers, and error bounds could be
    !> unreliable.
    !>

Parameters
    N

    !>          N is INTEGER
    !>     The number of linear equations, i.e., 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.
    !>

    NCOLS

    !>          NCOLS is INTEGER
    !>     The number of columns of the matrix A.  NCOLS >= 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(N,j+kl)
    !>

    LDAB

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

    AFB

    !>          AFB is DOUBLE PRECISION array, dimension (LDAFB,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.
    !>

    LDAFB

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

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  real function sla_gbrpvgrw (integer n, integer kl, integer ku, integer ncols, real, dimension( ldab, * ) ab, integer ldab, real, dimension( ldafb, * ) afb, integer ldafb)

SLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.

Purpose:

    !>
    !> SLA_GBRPVGRW computes the reciprocal pivot growth factor
    !> norm(A)/norm(U). The  norm is used. If this is
    !> much less than 1, the stability of the LU factorization of the
    !> (equilibrated) matrix A could be poor. This also means that the
    !> solution X, estimated condition numbers, and error bounds could be
    !> unreliable.
    !>

Parameters
    N

    !>          N is INTEGER
    !>     The number of linear equations, i.e., 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.
    !>

    NCOLS

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

    AB

    !>          AB is REAL 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(N,j+kl)
    !>

    LDAB

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

    AFB

    !>          AFB is REAL array, dimension (LDAFB,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.
    !>

    LDAFB

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

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  double precision function zla_gbrpvgrw (integer n, integer kl, integer ku, integer ncols, complex*16, dimension( ldab, * ) ab, integer ldab, complex*16, dimension( ldafb, * ) afb, integer ldafb)

ZLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.

Purpose:

    !>
    !> ZLA_GBRPVGRW computes the reciprocal pivot growth factor
    !> norm(A)/norm(U). The  norm is used. If this is
    !> much less than 1, the stability of the LU factorization of the
    !> (equilibrated) matrix A could be poor. This also means that the
    !> solution X, estimated condition numbers, and error bounds could be
    !> unreliable.
    !>

Parameters
    N

    !>          N is INTEGER
    !>     The number of linear equations, i.e., 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.
    !>

    NCOLS

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

    AB

    !>          AB is COMPLEX*16 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(N,j+kl)
    !>

    LDAB

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

    AFB

    !>          AFB is COMPLEX*16 array, dimension (LDAFB,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.
    !>

    LDAFB

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

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Author

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