pocon(3) LAPACK pocon(3)

pocon - pocon: condition number estimate


subroutine cpocon (uplo, n, a, lda, anorm, rcond, work, rwork, info)
CPOCON subroutine dpocon (uplo, n, a, lda, anorm, rcond, work, iwork, info)
DPOCON subroutine spocon (uplo, n, a, lda, anorm, rcond, work, iwork, info)
SPOCON subroutine zpocon (uplo, n, a, lda, anorm, rcond, work, rwork, info)
ZPOCON

CPOCON

Purpose:

 CPOCON estimates the reciprocal of the condition number (in the
 1-norm) of a complex Hermitian positive definite matrix using the
 Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF.
 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

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

A

          A is COMPLEX array, dimension (LDA,N)
          The triangular factor U or L from the Cholesky factorization
          A = U**H*U or A = L*L**H, as computed by CPOTRF.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,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.

DPOCON

Purpose:

 DPOCON estimates the reciprocal of the condition number (in the
 1-norm) of a real symmetric positive definite matrix using the
 Cholesky factorization A = U**T*U or A = L*L**T computed by DPOTRF.
 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

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

A

          A is DOUBLE PRECISION array, dimension (LDA,N)
          The triangular factor U or L from the Cholesky factorization
          A = U**T*U or A = L*L**T, as computed by DPOTRF.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,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.

SPOCON

Purpose:

 SPOCON estimates the reciprocal of the condition number (in the
 1-norm) of a real symmetric positive definite matrix using the
 Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF.
 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

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

A

          A is REAL array, dimension (LDA,N)
          The triangular factor U or L from the Cholesky factorization
          A = U**T*U or A = L*L**T, as computed by SPOTRF.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,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.

ZPOCON

Purpose:

 ZPOCON estimates the reciprocal of the condition number (in the
 1-norm) of a complex Hermitian positive definite matrix using the
 Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF.
 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

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

A

          A is COMPLEX*16 array, dimension (LDA,N)
          The triangular factor U or L from the Cholesky factorization
          A = U**H*U or A = L*L**H, as computed by ZPOTRF.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,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.

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