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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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| subroutine csycon_3 | ( | character | uplo, |
| integer | n, | ||
| complex, dimension( lda, * ) | a, | ||
| integer | lda, | ||
| complex, dimension( * ) | e, | ||
| integer, dimension( * ) | ipiv, | ||
| real | anorm, | ||
| real | rcond, | ||
| complex, dimension( * ) | work, | ||
| integer | info | ||
| ) |
CSYCON_3
Download CSYCON_3 + dependencies [TGZ] [ZIP] [TXT]
CSYCON_3 estimates the reciprocal of the condition number (in the
1-norm) of a complex symmetric matrix A using the factorization
computed by CSYTRF_RK or CSYTRF_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 CSYTRS_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 COMPLEX array, dimension (LDA,N)
Diagonal of the block diagonal matrix D and factors U or L
as computed by CSYTRF_RK and CSYTRF_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 COMPLEX 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 CSYTRF_RK or CSYTRF_BK. |
| [in] | ANORM | ANORM is REAL
The 1-norm of the original matrix A. |
| [out] | 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. |
| [out] | WORK | WORK is COMPLEX array, dimension (2*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 Definition at line 164 of file csycon_3.f.
1.9.7