la_porcond(3)

NAME
la_porcond - la_porcond: Skeel condition number estimate

SYNOPSIS

  Functions
real function cla_porcond_c (uplo, n, a, lda, af, ldaf, c, capply, info, work, rwork)
CLA_PORCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian positive-definite matrices.
real function cla_porcond_x (uplo, n, a, lda, af, ldaf, x, info, work, rwork)
CLA_PORCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian positive-definite matrices.
double precision function dla_porcond (uplo, n, a, lda, af, ldaf, cmode, c, info, work, iwork)
DLA_PORCOND estimates the Skeel condition number for a symmetric positive-definite matrix.
real function sla_porcond (uplo, n, a, lda, af, ldaf, cmode, c, info, work, iwork)
SLA_PORCOND estimates the Skeel condition number for a symmetric positive-definite matrix.
double precision function zla_porcond_c (uplo, n, a, lda, af, ldaf, c, capply, info, work, rwork)
ZLA_PORCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian positive-definite matrices.
double precision function zla_porcond_x (uplo, n, a, lda, af, ldaf, x, info, work, rwork)
ZLA_PORCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian positive-definite matrices.

Detailed Description

Function Documentation

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

CLA_PORCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian positive-definite matrices.

Purpose:

    !>
    !>    CLA_PORCOND_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 triangular factor U or L from the Cholesky factorization
    !>     A = U**H*U or A = L*L**H, as computed by CPOTRF.
    !>

    LDAF

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

    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 128 of file cla_porcond_c.f.

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

CLA_PORCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian positive-definite matrices.

Purpose:

    !>
    !>    CLA_PORCOND_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 triangular factor U or L from the Cholesky factorization
    !>     A = U**H*U or A = L*L**H, as computed by CPOTRF.
    !>

    LDAF

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

    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 121 of file cla_porcond_x.f.

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

DLA_PORCOND estimates the Skeel condition number for a symmetric positive-definite matrix.

Purpose:

    !>
    !>    DLA_PORCOND 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 triangular factor U or L from the Cholesky factorization
    !>     A = U**T*U or A = L*L**T, as computed by DPOTRF.
    !>

    LDAF

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

    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 139 of file dla_porcond.f.

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

SLA_PORCOND estimates the Skeel condition number for a symmetric positive-definite matrix.

Purpose:

    !>
    !>    SLA_PORCOND 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 triangular factor U or L from the Cholesky factorization
    !>     A = U**T*U or A = L*L**T, as computed by SPOTRF.
    !>

    LDAF

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

    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 138 of file sla_porcond.f.

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

ZLA_PORCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian positive-definite matrices.

Purpose:

    !>
    !>    ZLA_PORCOND_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 triangular factor U or L from the Cholesky factorization
    !>     A = U**H*U or A = L*L**H, as computed by ZPOTRF.
    !>

    LDAF

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

    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 129 of file zla_porcond_c.f.

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

ZLA_PORCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian positive-definite matrices.

Purpose:

    !>
    !>    ZLA_PORCOND_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 triangular factor U or L from the Cholesky factorization
    !>     A = U**H*U or A = L*L**H, as computed by ZPOTRF.
    !>

    LDAF

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

    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 122 of file zla_porcond_x.f.

Author

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