hecon(3) | LAPACK | hecon(3) |
hecon - {he,sy}con: condition number estimate
subroutine checon (uplo, n, a, lda, ipiv, anorm, rcond,
work, info)
CHECON subroutine csycon (uplo, n, a, lda, ipiv, anorm, rcond,
work, info)
CSYCON subroutine dsycon (uplo, n, a, lda, ipiv, anorm, rcond,
work, iwork, info)
DSYCON subroutine ssycon (uplo, n, a, lda, ipiv, anorm, rcond,
work, iwork, info)
SSYCON subroutine zhecon (uplo, n, a, lda, ipiv, anorm, rcond,
work, info)
ZHECON subroutine zsycon (uplo, n, a, lda, ipiv, anorm, rcond,
work, info)
ZSYCON
CHECON
Purpose:
CHECON estimates the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHETRF. 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 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
N is INTEGER The order of the matrix A. N >= 0.
A
A is COMPLEX array, dimension (LDA,N) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CHETRF.
LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
IPIV
IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by CHETRF.
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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
CSYCON
Purpose:
CSYCON estimates the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSYTRF. 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 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
N is INTEGER The order of the matrix A. N >= 0.
A
A is COMPLEX array, dimension (LDA,N) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CSYTRF.
LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
IPIV
IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by CSYTRF.
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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
DSYCON
Purpose:
DSYCON estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSYTRF. 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 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
N is INTEGER The order of the matrix A. N >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by DSYTRF.
LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
IPIV
IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by DSYTRF.
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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
SSYCON
Purpose:
SSYCON estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by SSYTRF. 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 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
N is INTEGER The order of the matrix A. N >= 0.
A
A is REAL array, dimension (LDA,N) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by SSYTRF.
LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
IPIV
IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by SSYTRF.
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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
ZHECON
Purpose:
ZHECON estimates the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHETRF. 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 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
N is INTEGER The order of the matrix A. N >= 0.
A
A is COMPLEX*16 array, dimension (LDA,N) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZHETRF.
LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
IPIV
IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by ZHETRF.
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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
ZSYCON
Purpose:
ZSYCON estimates the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSYTRF. 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 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
N is INTEGER The order of the matrix A. N >= 0.
A
A is COMPLEX*16 array, dimension (LDA,N) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZSYTRF.
LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
IPIV
IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by ZSYTRF.
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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Generated automatically by Doxygen for LAPACK from the source code.
Fri Aug 9 2024 02:33:22 | Version 3.12.0 |