/home/abui...a_2stage.f(3)

🎀 NAME 🎀

okay so bestie, this page is part of the Library Functions Manual, and the title vibe is /home/abui...a_2stage.f(3). The actual file being documented is:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dsysv_aa_2stage.f

that's the whole NAME tea 🫶

✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

subroutine DSYSV_AA_2STAGE (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2,
           b, ldb, work, lwork, info)

DSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices 💅

🦋 Function/Subroutine Documentation 🦋

🌟 subroutine DSYSV_AA_2STAGE ...

subroutine DSYSV_AA_2STAGE (character uplo, integer n, integer nrhs, double
     precision, dimension( lda, * ) a, integer lda, double precision,
     dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer,
     dimension( * ) ipiv2, double precision, dimension( ldb, * ) b, integer
     ldb, double precision, dimension( * ) work, integer lwork, integer info)

okay so here's the actual tea: DSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices.

💫 Purpose 💫

This routine solves a real 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.

It uses Aasen's 2-stage algorithm 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. 🔥

🌈 Parameters 🌈

• UPLO — UPLO is CHARACTER*1
  • = '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.
• NRHS — NRHS is INTEGER
  • The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
• A — A is DOUBLE PRECISION array, dimension (LDA,N)
  • On entry, 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 — LDA is INTEGER
  • The leading dimension of the array A. LDA >= max(1,N).
• TB — TB is DOUBLE PRECISION array, dimension (LTB)
  • On exit, details of the LU factorization of the band matrix.
• LTB — LTB is 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.
• IPIV — IPIV is 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 — IPIV2 is 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).
• B — B is DOUBLE PRECISION array, dimension (LDB,NRHS)
  • On entry, the right hand side matrix B.
  • On exit, the solution matrix X.
• LDB — LDB is INTEGER
  • The leading dimension of the array B. LDB >= max(1,N).
• WORK — WORK is DOUBLE PRECISION workspace of size LWORK
• LWORK — LWORK is 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 — INFO is 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

👑 Author 👑

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

Definition at line 185 of file dsysv_aa_2stage.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the page, bestie 💅 the footer source/version is LAPACK, Version 3.12.0, with page tag /home/abui...a_2stage.f(3). No separate date string is shown in that footer line, so I’m not inventing one — no cap 🎀