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.

  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.

  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.

  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.

  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.

  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.

Author

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