NAME

ppcon - ppcon: condition number estimate

SYNOPSIS

Functions

subroutine cppcon (uplo, n, ap, anorm, rcond, work, rwork, info)
CPPCON subroutine dppcon (uplo, n, ap, anorm, rcond, work, iwork, info)
DPPCON subroutine sppcon (uplo, n, ap, anorm, rcond, work, iwork, info)
SPPCON subroutine zppcon (uplo, n, ap, anorm, rcond, work, rwork, info)
ZPPCON

Detailed Description

Function Documentation

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

CPPCON

Purpose:



 CPPCON estimates the reciprocal of the condition number (in the


 1-norm) of a complex Hermitian positive definite packed matrix using


 the Cholesky factorization A = U**H*U or A = L*L**H computed by


 CPPTRF.


 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


          = 'U':  Upper triangle of A is stored;


          = 'L':  Lower triangle of A is stored.



          N is INTEGER


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



          AP is COMPLEX array, dimension (N*(N+1)/2)


          The triangular factor U or L from the Cholesky factorization


          A = U**H*U or A = L*L**H, packed columnwise in a linear


          array.  The j-th column of U or L is stored in the array AP


          as follows:


          if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;


          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.

ANORM



          ANORM is REAL


          The 1-norm (or infinity-norm) of the Hermitian 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)

RWORK



          RWORK is REAL 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 117 of file cppcon.f.

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

DPPCON

Purpose:



 DPPCON estimates the reciprocal of the condition number (in the


 1-norm) of a real symmetric positive definite packed matrix using


 the Cholesky factorization A = U**T*U or A = L*L**T computed by


 DPPTRF.


 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


          = 'U':  Upper triangle of A is stored;


          = 'L':  Lower triangle of A is stored.



          N is INTEGER


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



          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)


          The triangular factor U or L from the Cholesky factorization


          A = U**T*U or A = L*L**T, packed columnwise in a linear


          array.  The j-th column of U or L is stored in the array AP


          as follows:


          if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;


          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.

ANORM



          ANORM is DOUBLE PRECISION


          The 1-norm (or infinity-norm) of the symmetric 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 (3*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 117 of file dppcon.f.

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

SPPCON

Purpose:



 SPPCON estimates the reciprocal of the condition number (in the


 1-norm) of a real symmetric positive definite packed matrix using


 the Cholesky factorization A = U**T*U or A = L*L**T computed by


 SPPTRF.


 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


          = 'U':  Upper triangle of A is stored;


          = 'L':  Lower triangle of A is stored.



          N is INTEGER


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



          AP is REAL array, dimension (N*(N+1)/2)


          The triangular factor U or L from the Cholesky factorization


          A = U**T*U or A = L*L**T, packed columnwise in a linear


          array.  The j-th column of U or L is stored in the array AP


          as follows:


          if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;


          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.

ANORM



          ANORM is REAL


          The 1-norm (or infinity-norm) of the symmetric 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 (3*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 117 of file sppcon.f.

subroutine zppcon (character uplo, integer n, complex16, dimension( ) ap, double precision anorm, double precision rcond, complex16, dimension( ) work, double precision, dimension( * ) rwork, integer info)

ZPPCON

Purpose:



 ZPPCON estimates the reciprocal of the condition number (in the


 1-norm) of a complex Hermitian positive definite packed matrix using


 the Cholesky factorization A = U**H*U or A = L*L**H computed by


 ZPPTRF.


 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


          = 'U':  Upper triangle of A is stored;


          = 'L':  Lower triangle of A is stored.



          N is INTEGER


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



          AP is COMPLEX*16 array, dimension (N*(N+1)/2)


          The triangular factor U or L from the Cholesky factorization


          A = U**H*U or A = L*L**H, packed columnwise in a linear


          array.  The j-th column of U or L is stored in the array AP


          as follows:


          if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;


          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.

ANORM



          ANORM is DOUBLE PRECISION


          The 1-norm (or infinity-norm) of the Hermitian 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)

RWORK



          RWORK is DOUBLE PRECISION 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 117 of file zppcon.f.

Author

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