SRC/zsytri_3x.f(3)

✨ NAME ✨

SRC/zsytri_3x.f — bestie, this is the Library Functions Manual page for the zsytri_3x subroutine, and it's lowkey iconic. 💅

🦋 SYNOPSIS 🦋

Functions/Subroutines

       subroutine zsytri_3x (uplo, n, a, lda, e, ipiv, work, nb, info)
           ZSYTRI_3X

👑 Function/Subroutine Documentation 👑

       subroutine zsytri_3x (character uplo, integer n, complex*16, dimension( lda,
       * ) a, integer lda, complex*16, dimension( * ) e, integer, dimension( *
       ) ipiv, complex*16, dimension( n+nb+1, * ) work, integer nb, integer
       info)
       ZSYTRI_3X

🌸 Purpose 🌸

okay so ZSYTRI_3X computes the inverse of a complex symmetric indefinite matrix A using the factorization computed by ZSYTRF_RK or ZSYTRF_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. 🔥

🎀 Parameters 🎀

• UPLO — UPLO is CHARACTER*1 and 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; it's the order of the matrix A. N >= 0. 🫶
• A — A is COMPLEX*16 array, dimension (LDA,N). On entry, diagonal of the block diagonal matrix D and factors U or L as computed by ZSYTRF_RK and ZSYTRF_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; it's the leading dimension of the array A. LDA >= max(1,N).
• E — E is COMPLEX*16 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). It holds details of the interchanges and the block structure of D as determined by ZSYTRF_RK or ZSYTRF_BK.
• WORK — WORK is COMPLEX*16 array, dimension (N+NB+1,NB+3).
• NB — NB is INTEGER; it's the block size.
• 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 🌈

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

📌 Definition at line 📌

Definition at line 158 of file zsytri_3x.f.

💫 Author 💫

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, that's the whole page: LAPACK Version 3.12.0, source page SRC/zsytri_3x.f(3). Stay hydrated and slay those matrices 💅💖