DSYTRI_3(3)

💅 DSYTRI_3(3) — Library Functions Manual 💅

/home/abui.../dsytri_3.f(3)

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dsytri_3.f

okay so this is the page for that file, bestie. it’s giving LAPACK source-file realness. 🦋

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

subroutine DSYTRI_3 (uplo, n, a, lda, e, ipiv, work, lwork, info)
    DSYTRI_3

🌟 Function/Subroutine Documentation 🌟

subroutine DSYTRI_3 (character uplo, integer n, double precision, dimension(
       lda, * ) a, integer lda, double precision, dimension( * ) e, integer,
       dimension( * ) ipiv, double precision, dimension( * ) work, integer
       lwork, integer info)
       DSYTRI_3

🧚 Purpose 🧚

okay so DSYTRI_3 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. periodt. 🔥

DSYTRI_3 sets the leading dimension of the workspace before calling DSYTRI_3X that actually computes the inverse. This is the blocked version of the algorithm, calling Level 3 BLAS. iconic behavior, honestly. 💅

🍓 Parameters 🍓

• 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 — INTEGER. The order of the matrix A. N >= 0.
• 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 — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• 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 — INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by DSYTRF_RK or DSYTRF_BK.
• WORK — DOUBLE PRECISION array, dimension (N+NB+1)*(NB+3). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — INTEGER. The length of WORK. LWORK >= (N+NB+1)*(NB+3).

If LDWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

• 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 🩷

• November 2017, Igor Kozachenko, Computer Science Division, University of California, Berkeley

Definition at line 168 of file dsytri_3.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

---

okay that’s the whole page, bestie 🫶 no cap. LAPACK Version 3.12.0, page path /home/abui.../dsytri_3.f(3), and the footer doesn’t give a date, so i’m not inventing one. bye 💅✨