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LAPACK
3.7.0
LAPACK: Linear Algebra PACKage
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subroutine ssytri_3x | ( | character | UPLO, |
integer | N, | ||
real, dimension( lda, * ) | A, | ||
integer | LDA, | ||
real, dimension( * ) | E, | ||
integer, dimension( * ) | IPIV, | ||
real, dimension( n+nb+1, * ) | WORK, | ||
integer | NB, | ||
integer | INFO | ||
) |
SSYTRI_3X
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SSYTRI_3X computes the inverse of a real symmetric indefinite matrix A using the factorization computed by SSYTRF_RK or SSYTRF_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. This is the blocked version of the algorithm, calling Level 3 BLAS.
[in] | UPLO | UPLO is CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. |
[in] | N | N is INTEGER The order of the matrix A. N >= 0. |
[in,out] | A | A is REAL array, dimension (LDA,N) On entry, diagonal of the block diagonal matrix D and factors U or L as computed by SYTRF_RK and SSYTRF_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. On exit, if INFO = 0, the symmetric inverse of the original matrix. If UPLO = 'U': the upper triangular part of the inverse is formed and the part of A below the diagonal is not referenced; If UPLO = 'L': the lower triangular part of the inverse is formed and the part of A above the diagonal is not referenced. |
[in] | LDA | LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). |
[in] | E | E is REAL 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 refernced; 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 SSYTRF_RK or SSYTRF_BK. |
[out] | WORK | WORK is REAL array, dimension (N+NB+1,NB+3). |
[in] | NB | NB is INTEGER Block size. |
[out] | INFO | INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its inverse could not be computed. |
December 2016, Igor Kozachenko, Computer Science Division, University of California, Berkeley
Definition at line 161 of file ssytri_3x.f.