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.


          = 'U':  Upper triangular, form is A = U*D*U**H;


          = 'L':  Lower triangular, form is A = L*D*L**H.



          N is INTEGER


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



          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.

Definition at line 117 of file chpcon.f.

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.


          = 'U':  Upper triangular, form is A = U*D*U**T;


          = 'L':  Lower triangular, form is A = L*D*L**T.



          N is INTEGER


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



          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.

Definition at line 117 of file cspcon.f.

subroutine dspcon (character uplo, integer n, double precision, dimension( * ) ap, integer, dimension( * ) ipiv, double precision anorm, double precision 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.


          = 'U':  Upper triangular, form is A = U*D*U**T;


          = 'L':  Lower triangular, form is A = L*D*L**T.



          N is INTEGER


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



          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.

Definition at line 123 of file dspcon.f.

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.


          = 'U':  Upper triangular, form is A = U*D*U**T;


          = 'L':  Lower triangular, form is A = L*D*L**T.



          N is INTEGER


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



          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.

Definition at line 123 of file sspcon.f.

subroutine zhpcon (character uplo, integer n, complex16, dimension( ) ap, integer, dimension( * ) ipiv, double precision anorm, double precision rcond, complex16, 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.


          = 'U':  Upper triangular, form is A = U*D*U**H;


          = 'L':  Lower triangular, form is A = L*D*L**H.



          N is INTEGER


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



          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.

Definition at line 117 of file zhpcon.f.

subroutine zspcon (character uplo, integer n, complex16, dimension( ) ap, integer, dimension( * ) ipiv, double precision anorm, double precision rcond, complex16, 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.


          = 'U':  Upper triangular, form is A = U*D*U**T;


          = 'L':  Lower triangular, form is A = L*D*L**T.



          N is INTEGER


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



          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.

Definition at line 117 of file zspcon.f.

Author

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