SRC/clasyf.f(3)

🎀 NAME 🎀

SRC/clasyf.f — that's literally the name, bestie, and this page lives in the Library Functions Manual. It's giving "one Fortran subroutine, zero chill" energy. 💅

✨ SYNOPSIS ✨

Functions/Subroutines

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

🦋 Function/Subroutine Documentation 🦋

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

CLASYF computes a partial factorization of a complex symmetric matrix using the Bunch-Kaufman diagonal pivoting method. Iconic behavior, no notes. 💖

🔥 Purpose

okay so the source comments spell the whole thing out like this, bestie:

           !>
           !> CLASYF computes a partial factorization of a complex symmetric matrix
           !> A using the Bunch-Kaufman diagonal pivoting method. 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.
           !> Note that U**T denotes the transpose of U.
           !>
           !> CLASYF is an auxiliary routine called by CSYTRF. It uses blocked code
           !> (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or
           !> A22 (if UPLO = 'L').
           !>

so yeah: the order of D is at most NB, the actual order comes back in KB, and KB is either NB or NB-1, or N if N <= NB. Also U**T means the transpose of U. CLASYF is an auxiliary routine called by CSYTRF, and it uses blocked code (calling Level 3 BLAS) to update the submatrix A11 if UPLO = 'U' or A22 if UPLO = 'L'. periodt. ✨

📋 Parameters

UPLO

UPLO is CHARACTER*1 and tells us whether the upper or lower triangular part of the symmetric matrix A is stored:

• 'U': upper triangular
• 'L': lower triangular

N

N is INTEGER. It's the order of the matrix A. N >= 0. 🫶

NB

NB is INTEGER. It's 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. no cap.

KB

KB is INTEGER. It's 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 COMPLEX array, dimension (LDA,N).

On entry, it's 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. main character matrix energy. 💅

LDA

LDA is INTEGER. It's the leading dimension of the array A. LDA >= max(1,N).

IPIV

IPIV is INTEGER array, dimension (N). It gives 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

W is COMPLEX array, dimension (LDW,NB). 🦋

LDW

LDW is INTEGER. It's 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:

the source says, and we're giving credit exactly like this:

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

Definition at line 176 of file clasyf.f.

🧚 Author

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