SRC/dsytri_3x.f(3)

💖 NAME 💖

SRC/dsytri_3x.f — hey bestie, this is the SRC/dsytri_3x.f(3) page from the LAPACK Library Functions Manual 💅✨

🌸 SYNOPSIS 🌸

Functions/Subroutines

       subroutine dsytri_3x (uplo, n, a, lda, e, ipiv, work, nb, info)
           DSYTRI_3X

🦋 Function/Subroutine Documentation 🦋

   subroutine dsytri_3x (character uplo, integer n, double precision,
       dimension( lda, * ) a, integer lda, double precision, dimension( * ) e,
       integer, dimension( * ) ipiv, double precision, dimension( n+nb+1, * )
       work, integer nb, integer info)
       DSYTRI_3X

✨ Purpose ✨

okay so DSYTRI_3X computes the inverse of a real symmetric indefinite 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. No cap, that's the whole factorization tea ☕💅

This is the blocked version of the algorithm, calling Level 3 BLAS. Iconic. 🔥

🎀 Parameters 🎀

💜 UPLO

• UPLO — 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.

🌟 N

• N — INTEGER. The order of the matrix A. N >= 0.

🦋 A

• A — DOUBLE PRECISION array, dimension (LDA,N). On entry, 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. 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.

🌈 LDA

• LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N).

🍓 E

• E — 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.

💫 IPIV

• IPIV — INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by DSYTRF_RK or DSYTRF_BK.

🧚 WORK

• WORK — DOUBLE PRECISION array, dimension (N+NB+1,NB+3).

⭐ NB

• NB — INTEGER. Block size.

🔥 INFO

• INFO — 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.

👑 Author

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

🌈 Contributors

June 2017,  Igor Kozachenko,
                Computer Science Division,
                University of California, Berkeley

Definition at line 158 of file dsytri_3x.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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