la_herpvgrw(3)

NAME
la_herpvgrw - la_herpvgrw: reciprocal pivot growth

SYNOPSIS

  Functions
real function cla_herpvgrw (uplo, n, info, a, lda, af, ldaf, ipiv, work)
CLA_HERPVGRW
real function cla_syrpvgrw (uplo, n, info, a, lda, af, ldaf, ipiv, work)
CLA_SYRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix.
double precision function dla_syrpvgrw (uplo, n, info, a, lda, af, ldaf, ipiv, work)
DLA_SYRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix.
real function sla_syrpvgrw (uplo, n, info, a, lda, af, ldaf, ipiv, work)
SLA_SYRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix.
double precision function zla_herpvgrw (uplo, n, info, a, lda, af, ldaf, ipiv, work)
ZLA_HERPVGRW
double precision function zla_syrpvgrw (uplo, n, info, a, lda, af, ldaf, ipiv, work)
ZLA_SYRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix.

Detailed Description

Function Documentation

  real function cla_herpvgrw (character*1 uplo, integer n, integer info, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, real, dimension( * ) work)

CLA_HERPVGRW

Purpose:

     CLA_HERPVGRW computes the reciprocal pivot growth factor
     norm(A)/norm(U). The 'max absolute element' 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
    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.

    INFO

              INFO is INTEGER
         The value of INFO returned from SSYTRF, .i.e., the pivot in
         column INFO is exactly 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.

    WORK

              WORK is REAL array, dimension (2*N)

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 121 of file cla_herpvgrw.f.

  real function cla_syrpvgrw (character*1 uplo, integer n, integer info, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, real, dimension( * ) work)

CLA_SYRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix.

Purpose:

     CLA_SYRPVGRW computes the reciprocal pivot growth factor
     norm(A)/norm(U). The 'max absolute element' 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
    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.

    INFO

              INFO is INTEGER
         The value of INFO returned from CSYTRF, .i.e., the pivot in
         column INFO is exactly 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.

    WORK

              WORK is REAL array, dimension (2*N)

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 121 of file cla_syrpvgrw.f.

  double precision function dla_syrpvgrw (character*1 uplo, integer n, integer info, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, double precision, dimension( * ) work)

DLA_SYRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix.

Purpose:

     DLA_SYRPVGRW computes the reciprocal pivot growth factor
     norm(A)/norm(U). The 'max absolute element' 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
    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.

    INFO

              INFO is INTEGER
         The value of INFO returned from DSYTRF, .i.e., the pivot in
         column INFO is exactly 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.

    WORK

              WORK is DOUBLE PRECISION array, dimension (2*N)

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 120 of file dla_syrpvgrw.f.

  real function sla_syrpvgrw (character*1 uplo, integer n, integer info, real, dimension( lda, * ) a, integer lda, real, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, real, dimension( * ) work)

SLA_SYRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix.

Purpose:

     SLA_SYRPVGRW computes the reciprocal pivot growth factor
     norm(A)/norm(U). The 'max absolute element' 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
    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.

    INFO

              INFO is INTEGER
         The value of INFO returned from SSYTRF, .i.e., the pivot in
         column INFO is exactly 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.

    WORK

              WORK is REAL array, dimension (2*N)

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 120 of file sla_syrpvgrw.f.

  double precision function zla_herpvgrw (character*1 uplo, integer n, integer info, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, double precision, dimension( * ) work)

ZLA_HERPVGRW

Purpose:

     ZLA_HERPVGRW computes the reciprocal pivot growth factor
     norm(A)/norm(U). The 'max absolute element' 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
    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.

    INFO

              INFO is INTEGER
         The value of INFO returned from ZHETRF, .i.e., the pivot in
         column INFO is exactly 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 ZHETRF.

    WORK

              WORK is DOUBLE PRECISION array, dimension (2*N)

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 121 of file zla_herpvgrw.f.

  double precision function zla_syrpvgrw (character*1 uplo, integer n, integer info, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, double precision, dimension( * ) work)

ZLA_SYRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix.

Purpose:

     ZLA_SYRPVGRW computes the reciprocal pivot growth factor
     norm(A)/norm(U). The 'max absolute element' 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
    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.

    INFO

              INFO is INTEGER
         The value of INFO returned from ZSYTRF, .i.e., the pivot in
         column INFO is exactly 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.

    WORK

              WORK is DOUBLE PRECISION array, dimension (2*N)

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 121 of file zla_syrpvgrw.f.

Author

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