LAPACK 3.12.1
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
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!> 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 162 of file csycon_3.f.