SRC/dsysv_aa_2stage.f(3)

Hey bestie 💖 this is the SRC/dsysv_aa_2stage.f(3) page from the Library Functions Manual. Buckle up, we're doing symmetric linear systems with Aasen's 2-stage algorithm and it's lowkey iconic. ✨

✨ NAME ✨

SRC/dsysv_aa_2stage.f — the file, periodt. 🎀

🦋 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 (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)

DSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices. Main character energy fr fr. 💜

🌈 Purpose 🌈

Okay so bestie, here's the tea: DSYSV_AA_2STAGE computes the solution to 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. Obsessed. ✨

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. Yes ma'am. 🔥

🎀 Parameters 🎀

• UPLO — UPLO is CHARACTER*1. Values are:
  • = '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 (MAX(1,LTB)). On exit, details of the LU factorization of the band matrix.
• LTB — LTB is INTEGER. The size of the array TB. LTB >= MAX(1,4*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 (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — LWORK is INTEGER. The size of WORK. LWORK >= MAX(1,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. Values are:
  • = 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 186 of file dsysv_aa_2stage.f. 🎯

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code. 🤖

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Byeee bestie! This iconic page is from LAPACK Version 3.12.0, source SRC/dsysv_aa_2stage.f(3). Stay slaying those symmetric systems 💅✨