la_hercond(3)

NAME
la_hercond - la_hercond: Skeel condition number estimate

SYNOPSIS

  Functions
real function cla_hercond_c (uplo, n, a, lda, af, ldaf, ipiv, c, capply, info, work, rwork)
CLA_HERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian indefinite matrices.
real function cla_hercond_x (uplo, n, a, lda, af, ldaf, ipiv, x, info, work, rwork)
CLA_HERCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian indefinite matrices.
real function cla_syrcond_c (uplo, n, a, lda, af, ldaf, ipiv, c, capply, info, work, rwork)
CLA_SYRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for symmetric indefinite matrices.
real function cla_syrcond_x (uplo, n, a, lda, af, ldaf, ipiv, x, info, work, rwork)
CLA_SYRCOND_X computes the infinity norm condition number of op(A)*diag(x) for symmetric indefinite matrices.
double precision function dla_syrcond (uplo, n, a, lda, af, ldaf, ipiv, cmode, c, info, work, iwork)
DLA_SYRCOND estimates the Skeel condition number for a symmetric indefinite matrix.
real function sla_syrcond (uplo, n, a, lda, af, ldaf, ipiv, cmode, c, info, work, iwork)
SLA_SYRCOND estimates the Skeel condition number for a symmetric indefinite matrix.
double precision function zla_hercond_c (uplo, n, a, lda, af, ldaf, ipiv, c, capply, info, work, rwork)
ZLA_HERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian indefinite matrices.
double precision function zla_hercond_x (uplo, n, a, lda, af, ldaf, ipiv, x, info, work, rwork)
ZLA_HERCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian indefinite matrices.
double precision function zla_syrcond_c (uplo, n, a, lda, af, ldaf, ipiv, c, capply, info, work, rwork)
ZLA_SYRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for symmetric indefinite matrices.
double precision function zla_syrcond_x (uplo, n, a, lda, af, ldaf, ipiv, x, info, work, rwork)
ZLA_SYRCOND_X computes the infinity norm condition number of op(A)*diag(x) for symmetric indefinite matrices.

Detailed Description

Function Documentation

  real function cla_hercond_c (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, real, dimension ( * ) c, logical capply, integer info, complex, dimension( * ) work, real, dimension( * ) rwork)

CLA_HERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian indefinite matrices.

Purpose:

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

Parameters
    UPLO

              UPLO is CHARACTER*1
           = 'U':  Upper triangle of A is stored;
           = 'L':  Lower triangle of A is stored.

    N

              N is INTEGER
         The number of linear equations, i.e., the order of the
         matrix A.  N >= 0.

    A

              A is COMPLEX array, dimension (LDA,N)
         On entry, the N-by-N matrix A

    LDA

              LDA is INTEGER
         The leading dimension of the array A.  LDA >= max(1,N).

    AF

              AF is COMPLEX array, dimension (LDAF,N)
         The block diagonal matrix D and the multipliers used to
         obtain the factor U or L as computed by CHETRF.

    LDAF

              LDAF is INTEGER
         The leading dimension of the array AF.  LDAF >= max(1,N).

    IPIV

              IPIV is INTEGER array, dimension (N)
         Details of the interchanges and the block structure of D
         as determined by CHETRF.

    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 136 of file cla_hercond_c.f.

  real function cla_hercond_x (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, complex, dimension( * ) x, integer info, complex, dimension( * ) work, real, dimension( * ) rwork)

CLA_HERCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian indefinite matrices.

Purpose:

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

Parameters
    UPLO

              UPLO is CHARACTER*1
           = 'U':  Upper triangle of A is stored;
           = 'L':  Lower triangle of A is stored.

    N

              N is INTEGER
         The number of linear equations, i.e., the order of the
         matrix A.  N >= 0.

    A

              A is COMPLEX array, dimension (LDA,N)
         On entry, the N-by-N matrix A.

    LDA

              LDA is INTEGER
         The leading dimension of the array A.  LDA >= max(1,N).

    AF

              AF is COMPLEX array, dimension (LDAF,N)
         The block diagonal matrix D and the multipliers used to
         obtain the factor U or L as computed by CHETRF.

    LDAF

              LDAF is INTEGER
         The leading dimension of the array AF.  LDAF >= max(1,N).

    IPIV

              IPIV is INTEGER array, dimension (N)
         Details of the interchanges and the block structure of D
         as determined by CHETRF.

    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 129 of file cla_hercond_x.f.

  real function cla_syrcond_c (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, real, dimension( * ) c, logical capply, integer info, complex, dimension( * ) work, real, dimension( * ) rwork)

CLA_SYRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for symmetric indefinite matrices.

Purpose:

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

Parameters
    UPLO

              UPLO is CHARACTER*1
           = 'U':  Upper triangle of A is stored;
           = 'L':  Lower triangle of A is stored.

    N

              N is INTEGER
         The number of linear equations, i.e., the order of the
         matrix A.  N >= 0.

    A

              A is COMPLEX array, dimension (LDA,N)
         On entry, the N-by-N matrix A

    LDA

              LDA is INTEGER
         The leading dimension of the array A.  LDA >= max(1,N).

    AF

              AF is COMPLEX array, dimension (LDAF,N)
         The block diagonal matrix D and the multipliers used to
         obtain the factor U or L as computed by CSYTRF.

    LDAF

              LDAF is INTEGER
         The leading dimension of the array AF.  LDAF >= max(1,N).

    IPIV

              IPIV is INTEGER array, dimension (N)
         Details of the interchanges and the block structure of D
         as determined by CSYTRF.

    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 136 of file cla_syrcond_c.f.

  real function cla_syrcond_x (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, complex, dimension( * ) x, integer info, complex, dimension( * ) work, real, dimension( * ) rwork)

CLA_SYRCOND_X computes the infinity norm condition number of op(A)*diag(x) for symmetric indefinite matrices.

Purpose:

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

Parameters
    UPLO

              UPLO is CHARACTER*1
           = 'U':  Upper triangle of A is stored;
           = 'L':  Lower triangle of A is stored.

    N

              N is INTEGER
         The number of linear equations, i.e., the order of the
         matrix A.  N >= 0.

    A

              A is COMPLEX array, dimension (LDA,N)
         On entry, the N-by-N matrix A.

    LDA

              LDA is INTEGER
         The leading dimension of the array A.  LDA >= max(1,N).

    AF

              AF is COMPLEX array, dimension (LDAF,N)
         The block diagonal matrix D and the multipliers used to
         obtain the factor U or L as computed by CSYTRF.

    LDAF

              LDAF is INTEGER
         The leading dimension of the array AF.  LDAF >= max(1,N).

    IPIV

              IPIV is INTEGER array, dimension (N)
         Details of the interchanges and the block structure of D
         as determined by CSYTRF.

    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 129 of file cla_syrcond_x.f.

  double precision function dla_syrcond (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, integer cmode, double precision, dimension( * ) c, integer info, double precision, dimension( * ) work, integer, dimension( * ) iwork)

DLA_SYRCOND estimates the Skeel condition number for a symmetric indefinite matrix.

Purpose:

        DLA_SYRCOND 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
    UPLO

              UPLO is CHARACTER*1
           = 'U':  Upper triangle of A is stored;
           = 'L':  Lower triangle of A is stored.

    N

              N is INTEGER
         The number of linear equations, i.e., the order of the
         matrix A.  N >= 0.

    A

              A is DOUBLE PRECISION array, dimension (LDA,N)
         On entry, the N-by-N matrix A.

    LDA

              LDA is INTEGER
         The leading dimension of the array A.  LDA >= max(1,N).

    AF

              AF is DOUBLE PRECISION array, dimension (LDAF,N)
         The block diagonal matrix D and the multipliers used to
         obtain the factor U or L as computed by DSYTRF.

    LDAF

              LDAF is INTEGER
         The leading dimension of the array AF.  LDAF >= max(1,N).

    IPIV

              IPIV is INTEGER array, dimension (N)
         Details of the interchanges and the block structure of D
         as determined by DSYTRF.

    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 (3*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 145 of file dla_syrcond.f.

  real function sla_syrcond (character uplo, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, integer cmode, real, dimension( * ) c, integer info, real, dimension( * ) work, integer, dimension( * ) iwork)

SLA_SYRCOND estimates the Skeel condition number for a symmetric indefinite matrix.

Purpose:

        SLA_SYRCOND 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
    UPLO

              UPLO is CHARACTER*1
           = 'U':  Upper triangle of A is stored;
           = 'L':  Lower triangle of A is stored.

    N

              N is INTEGER
         The number of linear equations, i.e., the order of the
         matrix A.  N >= 0.

    A

              A is REAL array, dimension (LDA,N)
         On entry, the N-by-N matrix A.

    LDA

              LDA is INTEGER
         The leading dimension of the array A.  LDA >= max(1,N).

    AF

              AF is REAL array, dimension (LDAF,N)
         The block diagonal matrix D and the multipliers used to
         obtain the factor U or L as computed by SSYTRF.

    LDAF

              LDAF is INTEGER
         The leading dimension of the array AF.  LDAF >= max(1,N).

    IPIV

              IPIV is INTEGER array, dimension (N)
         Details of the interchanges and the block structure of D
         as determined by SSYTRF.

    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 (3*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 144 of file sla_syrcond.f.

  double precision function zla_hercond_c (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, double precision, dimension ( * ) c, logical capply, integer info, complex*16, dimension( * ) work, double precision, dimension( * ) rwork)

ZLA_HERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian indefinite matrices.

Purpose:

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

Parameters
    UPLO

              UPLO is CHARACTER*1
           = 'U':  Upper triangle of A is stored;
           = 'L':  Lower triangle of A is stored.

    N

              N is INTEGER
         The number of linear equations, i.e., the order of the
         matrix A.  N >= 0.

    A

              A is COMPLEX*16 array, dimension (LDA,N)
         On entry, the N-by-N matrix A

    LDA

              LDA is INTEGER
         The leading dimension of the array A.  LDA >= max(1,N).

    AF

              AF is COMPLEX*16 array, dimension (LDAF,N)
         The block diagonal matrix D and the multipliers used to
         obtain the factor U or L as computed by ZHETRF.

    LDAF

              LDAF is INTEGER
         The leading dimension of the array AF.  LDAF >= max(1,N).

    IPIV

              IPIV is INTEGER array, dimension (N)
         Details of the interchanges and the block structure of D
         as determined by CHETRF.

    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 137 of file zla_hercond_c.f.

  double precision function zla_hercond_x (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, complex*16, dimension( * ) x, integer info, complex*16, dimension( * ) work, double precision, dimension( * ) rwork)

ZLA_HERCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian indefinite matrices.

Purpose:

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

Parameters
    UPLO

              UPLO is CHARACTER*1
           = 'U':  Upper triangle of A is stored;
           = 'L':  Lower triangle of A is stored.

    N

              N is INTEGER
         The number of linear equations, i.e., the order of the
         matrix A.  N >= 0.

    A

              A is COMPLEX*16 array, dimension (LDA,N)
         On entry, the N-by-N matrix A.

    LDA

              LDA is INTEGER
         The leading dimension of the array A.  LDA >= max(1,N).

    AF

              AF is COMPLEX*16 array, dimension (LDAF,N)
         The block diagonal matrix D and the multipliers used to
         obtain the factor U or L as computed by ZHETRF.

    LDAF

              LDAF is INTEGER
         The leading dimension of the array AF.  LDAF >= max(1,N).

    IPIV

              IPIV is INTEGER array, dimension (N)
         Details of the interchanges and the block structure of D
         as determined by CHETRF.

    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 130 of file zla_hercond_x.f.

  double precision function zla_syrcond_c (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, double precision, dimension( * ) c, logical capply, integer info, complex*16, dimension( * ) work, double precision, dimension( * ) rwork)

ZLA_SYRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for symmetric indefinite matrices.

Purpose:

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

Parameters
    UPLO

              UPLO is CHARACTER*1
           = 'U':  Upper triangle of A is stored;
           = 'L':  Lower triangle of A is stored.

    N

              N is INTEGER
         The number of linear equations, i.e., the order of the
         matrix A.  N >= 0.

    A

              A is COMPLEX*16 array, dimension (LDA,N)
         On entry, the N-by-N matrix A

    LDA

              LDA is INTEGER
         The leading dimension of the array A.  LDA >= max(1,N).

    AF

              AF is COMPLEX*16 array, dimension (LDAF,N)
         The block diagonal matrix D and the multipliers used to
         obtain the factor U or L as computed by ZSYTRF.

    LDAF

              LDAF is INTEGER
         The leading dimension of the array AF.  LDAF >= max(1,N).

    IPIV

              IPIV is INTEGER array, dimension (N)
         Details of the interchanges and the block structure of D
         as determined by ZSYTRF.

    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 137 of file zla_syrcond_c.f.

  double precision function zla_syrcond_x (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, complex*16, dimension( * ) x, integer info, complex*16, dimension( * ) work, double precision, dimension( * ) rwork)

ZLA_SYRCOND_X computes the infinity norm condition number of op(A)*diag(x) for symmetric indefinite matrices.

Purpose:

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

Parameters
    UPLO

              UPLO is CHARACTER*1
           = 'U':  Upper triangle of A is stored;
           = 'L':  Lower triangle of A is stored.

    N

              N is INTEGER
         The number of linear equations, i.e., the order of the
         matrix A.  N >= 0.

    A

              A is COMPLEX*16 array, dimension (LDA,N)
         On entry, the N-by-N matrix A.

    LDA

              LDA is INTEGER
         The leading dimension of the array A.  LDA >= max(1,N).

    AF

              AF is COMPLEX*16 array, dimension (LDAF,N)
         The block diagonal matrix D and the multipliers used to
         obtain the factor U or L as computed by ZSYTRF.

    LDAF

              LDAF is INTEGER
         The leading dimension of the array AF.  LDAF >= max(1,N).

    IPIV

              IPIV is INTEGER array, dimension (N)
         Details of the interchanges and the block structure of D
         as determined by ZSYTRF.

    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 130 of file zla_syrcond_x.f.

Author

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