SRC/csytrf_aa_2stage.f(3)

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💖 NAME 💖

SRC/csytrf_aa_2stage.f — that's the file/page name, front and center. 🫶

✨ SYNOPSIS ✨

🌈 Functions/Subroutines 🌈

       subroutine csytrf_aa_2stage (uplo, n, a, lda, tb, ltb, ipiv, ipiv2,
           work, lwork, info)
           CSYTRF_AA_2STAGE

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🎀 Function/Subroutine Documentation 🎀

   subroutine csytrf_aa_2stage (character uplo, integer n, complex, dimension(
       lda, * ) a, integer lda, complex, dimension( * ) tb, integer ltb,
       integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex,
       dimension( * ) work, integer lwork, integer info)
       CSYTRF_AA_2STAGE

✨ Purpose ✨

CSYTRF_AA_2STAGE computes the factorization of a complex symmetric matrix A using the Aasen's algorithm. The form of the factorization is:

A = U**T*T*U  or  A = L*T*L**T

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is a complex symmetric band matrix with the bandwidth of NB (NB is internally selected and stored in TB( 1 ), and T is LU factorized with partial pivoting).

This is the blocked version of the algorithm, calling Level 3 BLAS. Blocked and booked, periodt. 💅

🫶 Parameters 🫶

• UPLO — CHARACTER*1: = '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 — COMPLEX array, dimension (LDA,N). On entry, the hermitian matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.

On exit, L is stored below (or above) the subdiagonal blocks, when UPLO is 'L' (or 'U').

• LDA — INTEGER: the leading dimension of the array A. LDA >= max(1,N).
• TB — COMPLEX array, dimension (LTB). On exit, details of the LU factorization of the band matrix.
• LTB — INTEGER: the size of the array TB. LTB >= 4*N, internally used to select NB such that LTB >= (3*NB+1)*N.

If LTB = -1, then a workspace query is assumed; the routine only calculates the optimal size of LTB, returns this value as the first entry of TB, and no error message related to LTB is issued by XERBLA. No XERBLA drama for this one, bestie.

• IPIV — INTEGER array, dimension (N). On exit, it contains the details of the interchanges, i.e., the row and column k of A were interchanged with the row and column IPIV(k).
• IPIV2 — INTEGER array, dimension (N). On exit, it contains the details of the interchanges, i.e., the row and column k of T were interchanged with the row and column IPIV(k). Yes, it says IPIV(k) here too, exactly as written. 👀
• WORK — COMPLEX workspace of size LWORK.
• LWORK — INTEGER: the size of WORK. LWORK >= N, internally used to select NB such that LWORK >= N*NB.

If LWORK = -1, then a workspace query is assumed; the routine only calculates 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, band LU factorization failed on i-th column. If this is positive, the factorization did not slay. 💀

👑 Author 👑

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

Definition at line 158 of file csytrf_aa_2stage.f.

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💜 Author 💜

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