SRC/zsysv_aa_2stage.f(3)

Hey bestie 💖 welcome to the SRC/zsysv_aa_2stage.f page from the Library Functions Manual — this is the LAPACK 2-stage symmetric solver lore, and yes it’s giving main-character Fortran energy.

🎀 NAME 🎀

SRC/zsysv_aa_2stage.f

✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

       subroutine zsysv_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2,
           b, ldb, work, lwork, info)
            ZSYSV_AA_2STAGE computes the solution to system of linear equations
           A * X = B for SY matrices

ZSYSV_AA_2STAGE is literally here to compute the solution to the system of linear equations A * X = B for SY matrices. Slay. 💅

💖 Function/Subroutine Documentation 💖

   subroutine zsysv_aa_2stage (character uplo, integer n, integer nrhs,
       complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( *
       ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * )
       ipiv2, complex*16, dimension( ldb, * ) b, integer ldb, complex*16,
       dimension( * ) work, integer lwork, integer info)

✨ Purpose ✨

Okay so here’s the tea ☕: ZSYSV_AA_2STAGE computes the solution to a complex system of linear equations

A * X = B,

where A is an N-by-N symmetric matrix and X and B are N-by-NRHS matrices.

Aasen’s 2-stage algorithm is used to factor A as

A = U**T * T * U,  if UPLO = 'U', or
A = L * T * L**T,  if UPLO = 'L',

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is symmetric and band. The matrix T is then LU-factored with partial pivoting. The factored form of A is then used to solve the system of equations A * X = B.

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

💅 Parameters 💅

• UPLO — CHARACTER*1. Set it to 'U' and the upper triangle of A is stored; set it to 'L' and the lower triangle of A is stored. That’s the whole vibe check.
• N — INTEGER. The order of the matrix A. Constraint: N >= 0. No negative nonsense, bestie.
• NRHS — INTEGER. The number of right hand sides, i.e., the number of columns of the matrix B. Constraint: NRHS >= 0.
• A — COMPLEX*16 array, dimension (LDA,N). On entry, it’s the symmetric 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. Constraint: LDA >= max(1,N).
• TB — COMPLEX*16 array, dimension (LTB). On exit, it holds details of the LU factorization of the band matrix. Iconic.
• LTB — INTEGER. The size of the array TB. Constraint: LTB >= 4*N; internally it’s 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. So -1 here is a query moment, not a crash moment. 🫶

• 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). Track the swaps, bestie.
• 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, that’s IPIV(k) right there — keep it exactly as written. 🎀
• B — COMPLEX*16 array, dimension (LDB,NRHS). On entry, it’s the right hand side matrix B. On exit, it’s the solution matrix X. Glow-up complete. ✨
• LDB — INTEGER. The leading dimension of the array B. Constraint: LDB >= max(1,N).
• WORK — COMPLEX*16 workspace of size LWORK. That’s the workspace, doing workspace things. 🦋
• LWORK — INTEGER. The size of WORK. Constraint: LWORK >= N; internally it’s 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. Workspace query behavior, slay. 🌈

• INFO — INTEGER. Exit status tea:
  • = 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.

🫶 Author 🫶

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

Definition at line 183 of file zsysv_aa_2stage.f.

🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

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Okay that’s the page, bestie 💖 — signing off from LAPACK Version 3.12.0, source SRC/zsysv_aa_2stage.f. The footer’s date slot is lowkey MIA on this one, so no cap — just version and source, and we’re out. 🦋✨