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LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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| subroutine dsycon_3 | ( | character | UPLO, |
| integer | N, | ||
| double precision, dimension( lda, * ) | A, | ||
| integer | LDA, | ||
| double precision, dimension( * ) | E, | ||
| integer, dimension( * ) | IPIV, | ||
| double precision | ANORM, | ||
| double precision | RCOND, | ||
| double precision, dimension( * ) | WORK, | ||
| integer, dimension( * ) | IWORK, | ||
| integer | INFO | ||
| ) |
DSYCON_3
Download DSYCON_3 + dependencies [TGZ] [ZIP] [TXT]
DSYCON_3 estimates the reciprocal of the condition number (in the
1-norm) of a real symmetric matrix A using the factorization
computed by DSYTRF_RK or DSYTRF_BK:
A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),
where U (or L) is unit upper (or lower) triangular matrix,
U**T (or L**T) is the transpose of U (or L), P is a permutation
matrix, P**T is the transpose of P, and D is symmetric and block
diagonal with 1-by-1 and 2-by-2 diagonal blocks.
An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
This routine uses BLAS3 solver DSYTRS_3. | [in] | 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 = P*U*D*(U**T)*(P**T);
= 'L': Lower triangular, form is A = P*L*D*(L**T)*(P**T). |
| [in] | N | N is INTEGER
The order of the matrix A. N >= 0. |
| [in] | A | A is DOUBLE PRECISION array, dimension (LDA,N)
Diagonal of the block diagonal matrix D and factors U or L
as computed by DSYTRF_RK and DSYTRF_BK:
a) ONLY diagonal elements of the symmetric block diagonal
matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
(superdiagonal (or subdiagonal) elements of D
should be provided on entry in array E), and
b) If UPLO = 'U': factor U in the superdiagonal part of A.
If UPLO = 'L': factor L in the subdiagonal part of A. |
| [in] | LDA | LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N). |
| [in] | E | E is DOUBLE PRECISION array, dimension (N)
On entry, contains the superdiagonal (or subdiagonal)
elements of the symmetric block diagonal matrix D
with 1-by-1 or 2-by-2 diagonal blocks, where
If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.
NOTE: For 1-by-1 diagonal block D(k), where
1 <= k <= N, the element E(k) is not referenced in both
UPLO = 'U' or UPLO = 'L' cases. |
| [in] | IPIV | IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by DSYTRF_RK or DSYTRF_BK. |
| [in] | ANORM | ANORM is DOUBLE PRECISION
The 1-norm of the original matrix A. |
| [out] | 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. |
| [out] | WORK | WORK is DOUBLE PRECISION array, dimension (2*N) |
| [out] | IWORK | IWORK is INTEGER array, dimension (N) |
| [out] | INFO | INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value |
June 2017, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley
September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
School of Mathematics,
University of Manchester 
1.9.4