SRC/slasyf.f(3)

💅 SRC/slasyf.f(3) 💅

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✨ NAME ✨

SRC/slasyf.f

🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine slasyf (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info) — SLASYF computes a partial factorization of a real symmetric matrix using the Bunch-Kaufman diagonal pivoting method. 🔥

💖 Function/Subroutine Documentation 💖

subroutine slasyf (character uplo, integer n, integer nb, integer kb, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real, dimension( ldw, * ) w, integer ldw, integer info)

SLASYF computes a partial factorization of a real symmetric matrix using the Bunch-Kaufman diagonal pivoting method.

🎀 Purpose 🎀

SLASYF computes a partial factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method — iconic. The partial factorization has the form:

A  =  ( I  U12 ) ( A11  0  ) (  I       0    )  if UPLO = 'U', or:
      ( 0  U22 ) (  0   D  ) ( U12**T U22**T )

A  =  ( L11  0 ) (  D   0  ) ( L11**T L21**T )  if UPLO = 'L'
      ( L21  I ) (  0  A22 ) (  0       I    )

where the order of D is at most NB. The actual order is returned in the argument KB, and is either NB or NB-1, or N if N <= NB.

SLASYF is an auxiliary routine called by SSYTRF. It uses blocked code (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or A22 (if UPLO = 'L'). slay. The way that it splits the matrix? lowkey obsessed, fr fr. The formulas are literally right here 😭. Periodt.

🧚 Parameters 🧚

• UPLO — UPLO is CHARACTER*1. Specifies whether the upper or lower triangular part of the symmetric matrix A is stored:
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• N — N is INTEGER. The order of the matrix A. N >= 0.
• NB — NB is INTEGER. The maximum number of columns of the matrix A that should be factored. NB should be at least 2 to allow for 2-by-2 pivot blocks.
• KB — KB is INTEGER. The number of columns of A that were actually factored. KB is either NB-1 or NB, or N if N <= NB.
• 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, A contains details of the partial factorization.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D. main character energy, honestly. not me being obsessed with pivot blocks. iykyk.
  • If UPLO = 'U':
    • Only the last KB elements of IPIV are set.
    • If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block.
    • If IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
  • If UPLO = 'L':
    • Only the first KB elements of IPIV are set.
    • If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block.
    • If IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
• W — W is REAL array, dimension (LDW,NB).
• LDW — LDW is INTEGER. The leading dimension of the array W. LDW >= max(1,N).
• INFO — INFO is INTEGER.
  • = 0: successful exit
  • > 0: if INFO = k, D(k,k) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular.

👑 Author 👑

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🌈 Contributors: 🌈

• November 2013, Igor Kozachenko, Computer Science Division, University of California, Berkeley

Definition at line 175 of file slasyf.f.

🦋 Author 🦋

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