Man page - hpcon(3)

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Manual

hpcon

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine chpcon (character uplo, integer n, complex, dimension( * ) ap,integer, dimension( * ) ipiv, real anorm, real rcond, complex,dimension( * ) work, integer info)
subroutine cspcon (character uplo, integer n, complex, dimension( * ) ap,integer, dimension( * ) ipiv, real anorm, real rcond, complex,dimension( * ) work, integer info)
subroutine dspcon (character uplo, integer n, double precision, dimension(* ) ap, integer, dimension( * ) ipiv, double precision anorm, doubleprecision rcond, double precision, dimension( * ) work, integer,dimension( * ) iwork, integer info)
subroutine sspcon (character uplo, integer n, real, dimension( * ) ap,integer, dimension( * ) ipiv, real anorm, real rcond, real, dimension(* ) work, integer, dimension( * ) iwork, integer info)
subroutine zhpcon (character uplo, integer n, complex*16, dimension( * )ap, integer, dimension( * ) ipiv, double precision anorm, doubleprecision rcond, complex*16, dimension( * ) work, integer info)
subroutine zspcon (character uplo, integer n, complex*16, dimension( * )ap, integer, dimension( * ) ipiv, double precision anorm, doubleprecision rcond, complex*16, dimension( * ) work, integer info)
Author

NAME

hpcon - {hp,sp}con: condition number estimate

SYNOPSIS

Functions

subroutine chpcon (uplo, n, ap, ipiv, anorm, rcond, work, info)
CHPCON
subroutine cspcon (uplo, n, ap, ipiv, anorm, rcond, work, info)
CSPCON
subroutine dspcon (uplo, n, ap, ipiv, anorm, rcond, work, iwork, info)
DSPCON
subroutine sspcon (uplo, n, ap, ipiv, anorm, rcond, work, iwork, info)
SSPCON
subroutine zhpcon (uplo, n, ap, ipiv, anorm, rcond, work, info)
ZHPCON
subroutine zspcon (uplo, n, ap, ipiv, anorm, rcond, work, info)
ZSPCON

Detailed Description

Function Documentation

subroutine chpcon (character uplo, integer n, complex, dimension( * ) ap,integer, dimension( * ) ipiv, real anorm, real rcond, complex,dimension( * ) work, integer info)

CHPCON

Purpose:

CHPCON estimates the reciprocal of the condition number of a complex
Hermitian packed matrix A using the factorization A = U*D*U**H or
A = L*D*L**H computed by CHPTRF.

An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the details of the factorization are stored
as an upper or lower triangular matrix.
= ā€™Uā€™: Upper triangular, form is A = U*D*U**H;
= ā€™Lā€™: Lower triangular, form is A = L*D*L**H.

N

N is INTEGER
The order of the matrix A. N >= 0.

AP

AP is COMPLEX array, dimension (N*(N+1)/2)
The block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by CHPTRF, stored as a
packed triangular matrix.

IPIV

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

ANORM

ANORM is REAL
The 1-norm of the original matrix A.

RCOND

RCOND is REAL
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
estimate of the 1-norm of inv(A) computed in this routine.

WORK

WORK is COMPLEX array, dimension (2*N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine cspcon (character uplo, integer n, complex, dimension( * ) ap,integer, dimension( * ) ipiv, real anorm, real rcond, complex,dimension( * ) work, integer info)

CSPCON

Purpose:

CSPCON estimates the reciprocal of the condition number (in the
1-norm) of a complex symmetric packed matrix A using the
factorization A = U*D*U**T or A = L*D*L**T computed by CSPTRF.

An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the details of the factorization are stored
as an upper or lower triangular matrix.
= ā€™Uā€™: Upper triangular, form is A = U*D*U**T;
= ā€™Lā€™: Lower triangular, form is A = L*D*L**T.

N

N is INTEGER
The order of the matrix A. N >= 0.

AP

AP is COMPLEX array, dimension (N*(N+1)/2)
The block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by CSPTRF, stored as a
packed triangular matrix.

IPIV

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

ANORM

ANORM is REAL
The 1-norm of the original matrix A.

RCOND

RCOND is REAL
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
estimate of the 1-norm of inv(A) computed in this routine.

WORK

WORK is COMPLEX array, dimension (2*N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine dspcon (character uplo, integer n, double precision, dimension(* ) ap, integer, dimension( * ) ipiv, double precision anorm, doubleprecision rcond, double precision, dimension( * ) work, integer,dimension( * ) iwork, integer info)

DSPCON

Purpose:

DSPCON estimates the reciprocal of the condition number (in the
1-norm) of a real symmetric packed matrix A using the factorization
A = U*D*U**T or A = L*D*L**T computed by DSPTRF.

An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the details of the factorization are stored
as an upper or lower triangular matrix.
= ā€™Uā€™: Upper triangular, form is A = U*D*U**T;
= ā€™Lā€™: Lower triangular, form is A = L*D*L**T.

N

N is INTEGER
The order of the matrix A. N >= 0.

AP

AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
The block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by DSPTRF, stored as a
packed triangular matrix.

IPIV

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

ANORM

ANORM is DOUBLE PRECISION
The 1-norm of the original matrix A.

RCOND

RCOND is DOUBLE PRECISION
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
estimate of the 1-norm of inv(A) computed in this routine.

WORK

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

IWORK

IWORK is INTEGER array, dimension (N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine sspcon (character uplo, integer n, real, dimension( * ) ap,integer, dimension( * ) ipiv, real anorm, real rcond, real, dimension(* ) work, integer, dimension( * ) iwork, integer info)

SSPCON

Purpose:

SSPCON estimates the reciprocal of the condition number (in the
1-norm) of a real symmetric packed matrix A using the factorization
A = U*D*U**T or A = L*D*L**T computed by SSPTRF.

An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the details of the factorization are stored
as an upper or lower triangular matrix.
= ā€™Uā€™: Upper triangular, form is A = U*D*U**T;
= ā€™Lā€™: Lower triangular, form is A = L*D*L**T.

N

N is INTEGER
The order of the matrix A. N >= 0.

AP

AP is REAL array, dimension (N*(N+1)/2)
The block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by SSPTRF, stored as a
packed triangular matrix.

IPIV

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

ANORM

ANORM is REAL
The 1-norm of the original matrix A.

RCOND

RCOND is REAL
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
estimate of the 1-norm of inv(A) computed in this routine.

WORK

WORK is REAL array, dimension (2*N)

IWORK

IWORK is INTEGER array, dimension (N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine zhpcon (character uplo, integer n, complex*16, dimension( * )ap, integer, dimension( * ) ipiv, double precision anorm, doubleprecision rcond, complex*16, dimension( * ) work, integer info)

ZHPCON

Purpose:

ZHPCON estimates the reciprocal of the condition number of a complex
Hermitian packed matrix A using the factorization A = U*D*U**H or
A = L*D*L**H computed by ZHPTRF.

An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the details of the factorization are stored
as an upper or lower triangular matrix.
= ā€™Uā€™: Upper triangular, form is A = U*D*U**H;
= ā€™Lā€™: Lower triangular, form is A = L*D*L**H.

N

N is INTEGER
The order of the matrix A. N >= 0.

AP

AP is COMPLEX*16 array, dimension (N*(N+1)/2)
The block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by ZHPTRF, stored as a
packed triangular matrix.

IPIV

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

ANORM

ANORM is DOUBLE PRECISION
The 1-norm of the original matrix A.

RCOND

RCOND is DOUBLE PRECISION
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
estimate of the 1-norm of inv(A) computed in this routine.

WORK

WORK is COMPLEX*16 array, dimension (2*N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine zspcon (character uplo, integer n, complex*16, dimension( * )ap, integer, dimension( * ) ipiv, double precision anorm, doubleprecision rcond, complex*16, dimension( * ) work, integer info)

ZSPCON

Purpose:

ZSPCON estimates the reciprocal of the condition number (in the
1-norm) of a complex symmetric packed matrix A using the
factorization A = U*D*U**T or A = L*D*L**T computed by ZSPTRF.

An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the details of the factorization are stored
as an upper or lower triangular matrix.
= ā€™Uā€™: Upper triangular, form is A = U*D*U**T;
= ā€™Lā€™: Lower triangular, form is A = L*D*L**T.

N

N is INTEGER
The order of the matrix A. N >= 0.

AP

AP is COMPLEX*16 array, dimension (N*(N+1)/2)
The block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by ZSPTRF, stored as a
packed triangular matrix.

IPIV

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

ANORM

ANORM is DOUBLE PRECISION
The 1-norm of the original matrix A.

RCOND

RCOND is DOUBLE PRECISION
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
estimate of the 1-norm of inv(A) computed in this routine.

WORK

WORK is COMPLEX*16 array, dimension (2*N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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