SRC/ssytrf_aa_2stage.f(3)

okay bestie, welcome to SRC/ssytrf_aa_2stage.f(3) from the Library Functions Manual — yes, we are literally about to understand ssytrf_aa_2stage. 💅

✨ NAME ✨

SRC/ssytrf_aa_2stage.f

🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine ssytrf_aa_2stage (uplo, n, a, lda, tb, ltb, ipiv, ipiv2,
    work, lwork, info)
    SSYTRF_AA_2STAGE

🦋 Function/Subroutine Documentation 🦋

subroutine ssytrf_aa_2stage (character uplo, integer n, real, dimension(
    lda, * ) a, integer lda, real, dimension( * ) tb, integer ltb, integer,
    dimension( * ) ipiv, integer, dimension( * ) ipiv2, real, dimension( * )
    work, integer lwork, integer info)

SSYTRF_AA_2STAGE

Purpose

okay so SSYTRF_AA_2STAGE computes the factorization of a real 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 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. 🔥

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 matrix A. N >= 0.

A

• A is REAL 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 REAL 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 >= 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).

WORK

• WORK is REAL workspace of size (MAX(1,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
  • = 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 158 of file ssytrf_aa_2stage.f.

Author

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