SRC/ssytri_3.f(3)

okay bestie, this is SRC/ssytri_3.f(3) from the Library Functions Manual, and it's giving “I do matrix inverses and I know it” energy 💅✨

🎀 NAME

SRC/ssytri_3.f

✨ SYNOPSIS

Functions/Subroutines

subroutine ssytri_3 (uplo, n, a, lda, e, ipiv, work, lwork, info)

SSYTRI_3

🦋 Function/Subroutine Documentation

subroutine ssytri_3 (character uplo, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) e, integer, dimension( * ) ipiv, real, dimension( * ) work, integer lwork, integer info)

SSYTRI_3

💖 Purpose

okay so SSYTRI_3 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 a 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.

SSYTRI_3 sets the leading dimension of the workspace before calling SSYTRI_3X that actually computes the inverse. This is the blocked version of the algorithm, calling Level 3 BLAS. periodt.

🌸 Parameters

UPLO

UPLO is CHARACTER*1. It 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 is INTEGER. The order of the matrix A. N >= 0.

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 SSYTRF_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.

LDA

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

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 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 is INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by SSYTRF_RK or SSYTRF_BK.

WORK

WORK is REAL array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER. The length of WORK. If N = 0, LWORK >= 1, else LWORK >= (N+NB+1)*(NB+3).

If LWORK = -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

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.

👑 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 169 of file ssytri_3.f.

💜 Author

Generated automatically by Doxygen for LAPACK from the source code.

---

okay bestie, that's the whole page — LAPACK Version 3.12.0, page SRC/ssytri_3.f(3), signing off with all the sparkle 💖✨🫶