1. Manuals
  2. Tumbleweed
  3. lapack-man
  4. la_porcond(3)

Scroll to navigation

la_porcond(3) Library Functions Manual 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

Generated automatically by Doxygen for LAPACK from the source code.

Version 3.12.0 LAPACK