la_gbrcond(3)

NAME
la_gbrcond - la_gbrcond: Skeel condition number estimate

SYNOPSIS

  Functions
real function cla_gbrcond_c (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, c, capply, info, work, rwork)
CLA_GBRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general banded matrices.
real function cla_gbrcond_x (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, x, info, work, rwork)
CLA_GBRCOND_X computes the infinity norm condition number of op(A)*diag(x) for general banded matrices.
double precision function dla_gbrcond (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, cmode, c, info, work, iwork)
DLA_GBRCOND estimates the Skeel condition number for a general banded matrix.
real function sla_gbrcond (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, cmode, c, info, work, iwork)
SLA_GBRCOND estimates the Skeel condition number for a general banded matrix.
double precision function zla_gbrcond_c (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, c, capply, info, work, rwork)
ZLA_GBRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general banded matrices.
double precision function zla_gbrcond_x (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, x, info, work, rwork)
ZLA_GBRCOND_X computes the infinity norm condition number of op(A)*diag(x) for general banded matrices.

Detailed Description

Function Documentation

  real function cla_gbrcond_c (character trans, integer n, integer kl, integer ku, complex, dimension( ldab, * ) ab, integer ldab, complex, dimension( ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv, real, dimension( * ) c, logical capply, integer info, complex, dimension( * ) work, real, dimension( * ) rwork)

CLA_GBRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general banded matrices.

Purpose:

        CLA_GBRCOND_C Computes the infinity norm condition number of
        op(A) * inv(diag(C)) where C is a REAL vector.

Parameters
    TRANS

              TRANS is CHARACTER*1
         Specifies the form of the system of equations:
           = 'N':  A * X = B     (No transpose)
           = 'T':  A**T * X = B  (Transpose)
           = 'C':  A**H * X = B  (Conjugate Transpose = Transpose)

    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.

    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.

    IPIV

              IPIV is INTEGER array, dimension (N)
         The pivot indices from the factorization A = P*L*U
         as computed by CGBTRF; row i of the matrix was interchanged
         with row IPIV(i).

    C

              C is REAL array, dimension (N)
         The vector C in the formula op(A) * inv(diag(C)).

    CAPPLY

              CAPPLY is LOGICAL
         If .TRUE. then access the vector C in the formula above.

    INFO

              INFO is INTEGER
           = 0:  Successful exit.
         i > 0:  The ith argument is invalid.

    WORK

              WORK is COMPLEX array, dimension (2*N).
         Workspace.

    RWORK

              RWORK is REAL array, dimension (N).
         Workspace.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 158 of file cla_gbrcond_c.f.

  real function cla_gbrcond_x (character trans, integer n, integer kl, integer ku, complex, dimension( ldab, * ) ab, integer ldab, complex, dimension( ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv, complex, dimension( * ) x, integer info, complex, dimension( * ) work, real, dimension( * ) rwork)

CLA_GBRCOND_X computes the infinity norm condition number of op(A)*diag(x) for general banded matrices.

Purpose:

        CLA_GBRCOND_X Computes the infinity norm condition number of
        op(A) * diag(X) where X is a COMPLEX vector.

Parameters
    TRANS

              TRANS is CHARACTER*1
         Specifies the form of the system of equations:
           = 'N':  A * X = B     (No transpose)
           = 'T':  A**T * X = B  (Transpose)
           = 'C':  A**H * X = B  (Conjugate Transpose = Transpose)

    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.

    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.

    IPIV

              IPIV is INTEGER array, dimension (N)
         The pivot indices from the factorization A = P*L*U
         as computed by CGBTRF; row i of the matrix was interchanged
         with row IPIV(i).

    X

              X is COMPLEX array, dimension (N)
         The vector X in the formula op(A) * diag(X).

    INFO

              INFO is INTEGER
           = 0:  Successful exit.
         i > 0:  The ith argument is invalid.

    WORK

              WORK is COMPLEX array, dimension (2*N).
         Workspace.

    RWORK

              RWORK is REAL array, dimension (N).
         Workspace.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 151 of file cla_gbrcond_x.f.

  double precision function dla_gbrcond (character trans, integer n, integer kl, integer ku, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv, integer cmode, double precision, dimension( * ) c, integer info, double precision, dimension( * ) work, integer, dimension( * ) iwork)

DLA_GBRCOND estimates the Skeel condition number for a general banded matrix.

Purpose:

        DLA_GBRCOND Estimates the Skeel condition number of  op(A) * op2(C)
        where op2 is determined by CMODE as follows
        CMODE =  1    op2(C) = C
        CMODE =  0    op2(C) = I
        CMODE = -1    op2(C) = inv(C)
        The Skeel condition number  cond(A) = norminf( |inv(A)||A| )
        is computed by computing scaling factors R such that
        diag(R)*A*op2(C) is row equilibrated and computing the standard
        infinity-norm condition number.

Parameters
    TRANS

              TRANS is CHARACTER*1
         Specifies the form of the system of equations:
           = 'N':  A * X = B     (No transpose)
           = 'T':  A**T * X = B  (Transpose)
           = 'C':  A**H * X = B  (Conjugate Transpose = Transpose)

    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.

    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.

    IPIV

              IPIV is INTEGER array, dimension (N)
         The pivot indices from the factorization A = P*L*U
         as computed by DGBTRF; row i of the matrix was interchanged
         with row IPIV(i).

    CMODE

              CMODE is INTEGER
         Determines op2(C) in the formula op(A) * op2(C) as follows:
         CMODE =  1    op2(C) = C
         CMODE =  0    op2(C) = I
         CMODE = -1    op2(C) = inv(C)

    C

              C is DOUBLE PRECISION array, dimension (N)
         The vector C in the formula op(A) * op2(C).

    INFO

              INFO is INTEGER
           = 0:  Successful exit.
         i > 0:  The ith argument is invalid.

    WORK

              WORK is DOUBLE PRECISION array, dimension (5*N).
         Workspace.

    IWORK

              IWORK is INTEGER array, dimension (N).
         Workspace.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 167 of file dla_gbrcond.f.

  real function sla_gbrcond (character trans, integer n, integer kl, integer ku, real, dimension( ldab, * ) ab, integer ldab, real, dimension( ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv, integer cmode, real, dimension( * ) c, integer info, real, dimension( * ) work, integer, dimension( * ) iwork)

SLA_GBRCOND estimates the Skeel condition number for a general banded matrix.

Purpose:

        SLA_GBRCOND Estimates the Skeel condition number of  op(A) * op2(C)
        where op2 is determined by CMODE as follows
        CMODE =  1    op2(C) = C
        CMODE =  0    op2(C) = I
        CMODE = -1    op2(C) = inv(C)
        The Skeel condition number  cond(A) = norminf( |inv(A)||A| )
        is computed by computing scaling factors R such that
        diag(R)*A*op2(C) is row equilibrated and computing the standard
        infinity-norm condition number.

Parameters
    TRANS

              TRANS is CHARACTER*1
         Specifies the form of the system of equations:
           = 'N':  A * X = B     (No transpose)
           = 'T':  A**T * X = B  (Transpose)
           = 'C':  A**H * X = B  (Conjugate Transpose = Transpose)

    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.

    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.

    IPIV

              IPIV is INTEGER array, dimension (N)
         The pivot indices from the factorization A = P*L*U
         as computed by SGBTRF; row i of the matrix was interchanged
         with row IPIV(i).

    CMODE

              CMODE is INTEGER
         Determines op2(C) in the formula op(A) * op2(C) as follows:
         CMODE =  1    op2(C) = C
         CMODE =  0    op2(C) = I
         CMODE = -1    op2(C) = inv(C)

    C

              C is REAL array, dimension (N)
         The vector C in the formula op(A) * op2(C).

    INFO

              INFO is INTEGER
           = 0:  Successful exit.
         i > 0:  The ith argument is invalid.

    WORK

              WORK is REAL array, dimension (5*N).
         Workspace.

    IWORK

              IWORK is INTEGER array, dimension (N).
         Workspace.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 166 of file sla_gbrcond.f.

  double precision function zla_gbrcond_c (character trans, integer n, integer kl, integer ku, complex*16, dimension( ldab, * ) ab, integer ldab, complex*16, dimension( ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv, double precision, dimension( * ) c, logical capply, integer info, complex*16, dimension( * ) work, double precision, dimension( * ) rwork)

ZLA_GBRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general banded matrices.

Purpose:

        ZLA_GBRCOND_C Computes the infinity norm condition number of
        op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector.

Parameters
    TRANS

              TRANS is CHARACTER*1
         Specifies the form of the system of equations:
           = 'N':  A * X = B     (No transpose)
           = 'T':  A**T * X = B  (Transpose)
           = 'C':  A**H * X = B  (Conjugate Transpose = Transpose)

    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.

    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.

    IPIV

              IPIV is INTEGER array, dimension (N)
         The pivot indices from the factorization A = P*L*U
         as computed by ZGBTRF; row i of the matrix was interchanged
         with row IPIV(i).

    C

              C is DOUBLE PRECISION array, dimension (N)
         The vector C in the formula op(A) * inv(diag(C)).

    CAPPLY

              CAPPLY is LOGICAL
         If .TRUE. then access the vector C in the formula above.

    INFO

              INFO is INTEGER
           = 0:  Successful exit.
         i > 0:  The ith argument is invalid.

    WORK

              WORK is COMPLEX*16 array, dimension (2*N).
         Workspace.

    RWORK

              RWORK is DOUBLE PRECISION array, dimension (N).
         Workspace.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 159 of file zla_gbrcond_c.f.

  double precision function zla_gbrcond_x (character trans, integer n, integer kl, integer ku, complex*16, dimension( ldab, * ) ab, integer ldab, complex*16, dimension( ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv, complex*16, dimension( * ) x, integer info, complex*16, dimension( * ) work, double precision, dimension( * ) rwork)

ZLA_GBRCOND_X computes the infinity norm condition number of op(A)*diag(x) for general banded matrices.

Purpose:

        ZLA_GBRCOND_X Computes the infinity norm condition number of
        op(A) * diag(X) where X is a COMPLEX*16 vector.

Parameters
    TRANS

              TRANS is CHARACTER*1
         Specifies the form of the system of equations:
           = 'N':  A * X = B     (No transpose)
           = 'T':  A**T * X = B  (Transpose)
           = 'C':  A**H * X = B  (Conjugate Transpose = Transpose)

    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.

    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.

    IPIV

              IPIV is INTEGER array, dimension (N)
         The pivot indices from the factorization A = P*L*U
         as computed by ZGBTRF; row i of the matrix was interchanged
         with row IPIV(i).

    X

              X is COMPLEX*16 array, dimension (N)
         The vector X in the formula op(A) * diag(X).

    INFO

              INFO is INTEGER
           = 0:  Successful exit.
         i > 0:  The ith argument is invalid.

    WORK

              WORK is COMPLEX*16 array, dimension (2*N).
         Workspace.

    RWORK

              RWORK is DOUBLE PRECISION array, dimension (N).
         Workspace.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 152 of file zla_gbrcond_x.f.

Author

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