SRC/dlasyf.f(3)

💅 SRC/dlasyf.f(3) 💅

okay bestie, welcome to the SRC/dlasyf.f(3) page from the Library Functions Manual 💖 this is the group-chat recap of a LAPACK subroutine, and yes, it's giving main character energy.

---

🌸 NAME 🌸

SRC/dlasyf.f — that's literally the name, no cap. 🫶

---

✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

subroutine dlasyf (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)

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

---

🦋 Function/Subroutine Documentation 🦋

subroutine dlasyf (character uplo, integer n, integer nb, integer kb, double
     precision, dimension( lda, * ) a, integer lda, integer, dimension( * )
     ipiv, double precision, dimension( ldw, * ) w, integer ldw, integer
     info)

DLASYF computes a partial factorization of a real symmetric matrix using the Bunch-Kaufman diagonal pivoting method. iconic behavior, honestly. 💅

🎀 Purpose 🎀

okay so DLASYF computes a partial factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method. the partial factorization has this 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. 🌀

DLASYF is an auxiliary routine called by DSYTRF. it uses blocked code (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or A22 (if UPLO = 'L'). slay. 🔥

🍓 Parameters 🍓

• UPLO — CHARACTER*1. tells you whether the upper or lower triangular part of the symmetric matrix A is stored:
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• N — INTEGER. the order of the matrix A. N >= 0. 🎀
• NB — 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. lowkey important. 🫶
• KB — INTEGER. the number of columns of A that were actually factored. KB is either NB-1 or NB, or N if N <= NB.
• A — 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, A contains details of the partial factorization. ✨
• LDA — INTEGER. the leading dimension of the array A. LDA >= max(1,N).
• IPIV — INTEGER array, dimension (N). details of the interchanges and the block structure of D. 👑
  • 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 — DOUBLE PRECISION array, dimension (LDW,NB). 🦋
• LDW — INTEGER. the leading dimension of the array W. LDW >= max(1,N).
• INFO — 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 dlasyf.f.

🧚 Author (the generated-by one) 🧚

Generated automatically by Doxygen for LAPACK from the source code.

---

okay that's the whole page, bestie 💖 the footer vibe is LAPACK Version 3.12.0 and SRC/dlasyf.f(3) — periodt. ✨